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Sample records for two-matrix hypergeometric function

  1. HYPERDIRE. HYPERgeometric functions DIfferential REduction. MATEMATICA based packages for differential reduction of generalized hypergeometric functions. FD and FS Horn-type hypergeometric functions of three variables

    International Nuclear Information System (INIS)

    Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Moch, Sven-Olaf; Hamburg Univ.

    2013-12-01

    HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions F D of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions F S of three variables. Both functions are related with one-loop Feynman diagrams.

  2. HYPERDIRE. HYPERgeometric functions DIfferential REduction. MATEMATICA based packages for differential reduction of generalized hypergeometric functions. F{sub D} and F{sub S} Horn-type hypergeometric functions of three variables

    Energy Technology Data Exchange (ETDEWEB)

    Bytev, Vladimir V. [Joint Inst. for Nuclear Research, Dubna (Russian Federation); Kalmykov, Mikhail Yu. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Moch, Sven-Olaf [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2013-12-15

    HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions F{sub D} of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions F{sub S} of three variables. Both functions are related with one-loop Feynman diagrams.

  3. HYPERDIRE. HYPERgeometric functions DIfferential REduction. MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFp-1, F1, F2, F3, F4

    International Nuclear Information System (INIS)

    Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

    2013-05-01

    HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions p+1 F p , and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F 1 , F 2 , F 3 , F 4 of two variables.

  4. Conformal field theory and functions of hypergeometric type

    International Nuclear Information System (INIS)

    Isachenkov, Mikhail

    2016-03-01

    Conformal field theory provides a universal description of various phenomena in natural sciences. Its development, swift and successful, belongs to the major highlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeometric functions always assumed a slower pace throughout the centuries of its existence. Functional identities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesis investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point functions of the 2d strange metal CFT, three-point functions of primaries of the non-rational Toda CFT and kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of these problems. Several new methods inspired by extensions of classical results on hypergeometric functions, are presented.

  5. Conformal field theory and functions of hypergeometric type

    Energy Technology Data Exchange (ETDEWEB)

    Isachenkov, Mikhail

    2016-03-15

    Conformal field theory provides a universal description of various phenomena in natural sciences. Its development, swift and successful, belongs to the major highlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeometric functions always assumed a slower pace throughout the centuries of its existence. Functional identities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesis investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point functions of the 2d strange metal CFT, three-point functions of primaries of the non-rational Toda CFT and kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of these problems. Several new methods inspired by extensions of classical results on hypergeometric functions, are presented.

  6. Elliptic hypergeometric functions associated with root systems

    OpenAIRE

    Rosengren, Hjalmar; Warnaar, S. Ole

    2017-01-01

    We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integeral and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson).

  7. Elliptic hypergeometric functions and the representation theory

    International Nuclear Information System (INIS)

    Spiridonov, V.P.

    2011-01-01

    Full text: (author)Elliptic hypergeometric functions were discovered around ten years ago. They represent the top level known generalization of the Euler beta integral and Euler-Gauss 2 F 1 hypergeometric function. In general form they are defined by contour integrals involving elliptic gamma functions. We outline the structure of the simplest examples of such functions and discuss their relations to the representation theory of the classical Lie groups and their various deformations. In one of the constructions elliptic hypergeometric integrals describe purely group-theoretical objects having the physical meaning of superconformal indices of four-dimensional supersymmetric gauge field theories

  8. Hypergeometric Functions with Integral Parameter Differences

    DEFF Research Database (Denmark)

    Karlsson, Per W.

    1971-01-01

    For a generalized hypergeometric function pFq(z) with positive integral differences between certain numerator and denominator parameters, a formula expressing the pFq(z) as a finite sum of lower-order functions is proved. From this formula, Minton's two summation theorems for p = q + 1, z = 1...

  9. HYPERDIRE. HYPERgeometric functions DIfferential REduction. MATHEMATICA based packages for differential reduction of generalized hypergeometric functions {sub p}F{sub p-1}, F{sub 1}, F{sub 2}, F{sub 3}, F{sub 4}

    Energy Technology Data Exchange (ETDEWEB)

    Bytev, Vladimir V.; Kalmykov, Mikhail Yu. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Institute for Nuclear Research, Dubna (Russian Federation); Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2013-05-15

    HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions {sub p+1}F{sub p}, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F{sub 1}, F{sub 2}, F{sub 3}, F{sub 4} of two variables.

  10. Finding new relationships between hypergeometric functions by evaluating Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A. [Santa Barbara Univ., CA (United States). Kavli Inst. for Theoretical Physics; Tarasov, Oleg V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2011-08-15

    Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F{sub 1}. From the comparison of this expression with a previously known one, a new relation between the Appell functions F{sub 1} and F{sub 4} is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F{sub 1} function with particular arguments to the hypergeometric function {sub 3}F{sub 2} is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F{sub 1} functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F{sub 1} function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F{sub 1} function and the Gaussian hypergeometric function {sub 2}F{sub 1} whose argument is the ratio of polynomials of degree six is presented. (orig.)

  11. Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators

    NARCIS (Netherlands)

    Koornwinder, T.H.

    2015-01-01

    For each of the eight n-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential

  12. Generalized hypergeometric coherent states

    International Nuclear Information System (INIS)

    Appl, Thomas; Schiller, Diethard H

    2004-01-01

    We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disc and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces as well as generalized hypergeometric Husimi distributions and corresponding phase distributions

  13. RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

    Science.gov (United States)

    Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

  14. CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions

    CERN Document Server

    Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions

    2007-01-01

    This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.

  15. On Approximation of Hyper-geometric Function Values of a Special Class

    Directory of Open Access Journals (Sweden)

    P. L. Ivankov

    2017-01-01

    Full Text Available Investigations of arithmetic properties of the hyper-geometric function values make it possible to single out two trends, namely, Siegel’s method and methods based on the effective construction of a linear approximating form. There are also methods combining both approaches mentioned.  The Siegel’s method allows obtaining the most general results concerning the abovementioned problems. In many cases it was used to establish the algebraic independence of the values of corresponding functions. Although the effective methods do not allow obtaining propositions of such generality they have nevertheless some advantages. Among these advantages one can distinguish at least two: a higher precision of the quantitative results obtained by effective methods and a possibility to study the hyper-geometric functions with irrational parameters.In this paper we apply the effective construction to estimate a measure of the linear independence of the hyper-geometric function values over the imaginary quadratic field. The functions themselves were chosen by a special way so that it could be possible to demonstrate a new approach to the effective construction of a linear approximating form. This approach makes it possible also to extend the well-known effective construction methods of the linear approximating forms for poly-logarithms to the functions of more general type.To obtain the arithmetic result we had to establish a linear independence of the functions under consideration over the field of rational functions. It is apparently impossible to apply directly known theorems containing sufficient (and in some cases needful and sufficient conditions for the system of functions appearing in the theorems mentioned. For this reason, a special technique has been developed to solve this problem.The paper presents the obtained arithmetic results concerning the values of integral functions, but, with appropriate alterations, the theorems proved can be adapted to

  16. Multivariable hypergeometric functions for ion-atom collisions

    Energy Technology Data Exchange (ETDEWEB)

    Gasaneo, G.; Colavecchia, F.D.; Garibotti, C.R

    1999-06-03

    In this work we present a correlated wave function for a three-body continuum Coulomb problem. This state is described by the two-variables PHI{sub 2} hypergeometric function. We examine the properties of this function and their differences with previous uncorrelated models. The PHI{sub 2} wave function can be considered as a final state of ion-atom ionizing collisions, giving rise to both undistorted (Born-PHI{sub 2}) and distorted (EIS-PHI{sub 2}) models. We obtain double differential cross sections with the Born-PHI{sub 2} theory for proton-helium collisions in the intermediate to high energy regime. They exhibit all the main features of the electronic emission process and agree with the experimental data.

  17. Hypergeometric series recurrence relations and some new orthogonal functions

    International Nuclear Information System (INIS)

    Wilson, J.A.

    1978-01-01

    A set of hypergeometric orthogonal polynomials, a set of biorthogonal rational functions generalizing them, and some new three-term relations for hypergeometric series containing properties of these functions are exhibited. The orthogonal polynomials depend on four free parameters, and their orthogonality relations include as special or limiting cases the orthogonalities for the classical polynomials, the Hahn and dual Hahn polynomials, Pollaczek's polynomials orthogonal on an infinite interval, and the 6-j symbols of angular momentum in quantum mechanics. Their properties include a second-order difference equation and a Rodrigues-type formula involving a divided difference operator

  18. GKZ Hypergeometric Structures

    NARCIS (Netherlands)

    Stienstra, J.

    2007-01-01

    This text is based on lectures by the author in the Summer School Algebraic Geometry and Hypergeometric Functions in Istanbul in June 2005. It gives a review of some of the basic aspects of the theory of hypergeometric structures of Gelfand, Kapranov and Zelevinsky, including Differential

  19. HYPERDIRE HYPERgeometric functions DIfferential REduction. Mathematica-based packages for the differential reduction of generalized hypergeometric functions. Lauricella function FC of three variables

    International Nuclear Information System (INIS)

    Bytev, Vladimir V.; Kniehl, Bernd A.

    2016-12-01

    We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function F C of three variables.

  20. Rigidity of monodromies for Appell's hypergeometric functions

    Directory of Open Access Journals (Sweden)

    Yoshishige Haraoka

    2015-01-01

    Full Text Available For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeometric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.

  1. HYPERDIRE HYPERgeometric functions DIfferential REduction. Mathematica-based packages for the differential reduction of generalized hypergeometric functions. Lauricella function F{sub C} of three variables

    Energy Technology Data Exchange (ETDEWEB)

    Bytev, Vladimir V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Institute for Nuclear Research, Dubna (Russian Federation); Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2016-12-15

    We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function F{sub C} of three variables.

  2. Large parameter cases of the Gauss hypergeometric function

    NARCIS (Netherlands)

    N.M. Temme (Nico)

    2002-01-01

    textabstractWe consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters {it a, b, c} are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.), which results are already available and

  3. Special values of the hypergeometric series

    CERN Document Server

    Ebisu, Akihito

    2017-01-01

    In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series F(a,b;c;x) and shows that values of F(a,b;c;x) at some points x can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of F(a,b;c;x) that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values.

  4. Differential reduction of generalized hypergeometric functions from Feynman diagrams. One-variable case

    Energy Technology Data Exchange (ETDEWEB)

    Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

    2010-03-15

    The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed. (orig.)

  5. Matrix transformation relation for the radial integrals of lepton scattering processes

    International Nuclear Information System (INIS)

    Sud, K.K.; Soto Vargas, C.W.; Sharma, D.K.

    1988-01-01

    The radial integrals of many physical problems involving products of initial- and final-state wave functions and the Coulomb interaction are expressible in terms of special cases of generalized hypergeometric functions. In the present work, the generalized hypergeometric functions become elements of a gamma vector which, by means of a partial differential equation and a matrix transformation relation, can be used in calculating the gamma vector in physical regions where the hypergeometric functions are nonconvergent or very slowly converging. Our matrix transformation relation contains the special cases of Gauss' hypergeometric functions 2 F 1 , Appell's hypergeometric functions F 2 , and Lauricella's functions L F transformation relations. The use of contiguous relations along with the transformation relations presented in this paper will facilitate the calculation of physical processes involving such radial integrals

  6. One loop integration with hypergeometric series by using recursion relations

    International Nuclear Information System (INIS)

    Watanabe, Norihisa; Kaneko, Toshiaki

    2014-01-01

    General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with ''LoopTools'' for the case of two- and three-point functions as examples

  7. Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

    Science.gov (United States)

    Bentalha, Zine el abidine

    2018-06-01

    Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

  8. SOME PROPERTIES OF HORN TYPE SECOND ORDER DOUBLE HYPERGEOMETRIC SERIES

    Directory of Open Access Journals (Sweden)

    Anvar Hasanov

    2018-04-01

    Full Text Available Horn [1931, Hypergeometrische Funktionen zweier Veranderlichen, Math. Ann.,105(1, 381-407], (corrections in Borngasser [1933, Uber hypergeometrische funkionen zweier Veranderlichen, Dissertation, Darmstadt], defined and investigated ten second order hypergeometric series of two variables. In the course of further investigation of Horn’s series, we noticed the existence of hypergeometric double series H*2 analogous to Horn’s double series H*2. The principal object of this paper is to present a natural further step toward the mathematical properties and presentations concerning the analogous hypergeometric double series H*2 Indeed, motivated by the important role of the Horn’s functions in several diverse fields of physics and the contributions toward the unification and generalization of the hyper-geometric functions, we establish a system of partial differential equations, integral representations, expansions, analytic continuation, transformation formulas and generating relations. Also, we discuss the links for the various results, which are presented in this paper, with known results.

  9. Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution

    DEFF Research Database (Denmark)

    Fog, Agner

    2008-01-01

    Two different probability distributions are both known in the literature as "the" noncentral hypergeometric distribution. Wallenius' noncentral hypergeometric distribution can be described by an urn model without replacement with bias. Fisher's noncentral hypergeometric distribution...... is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...... distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems....

  10. Auto-focusing accelerating hyper-geometric laser beams

    International Nuclear Information System (INIS)

    Kovalev, A A; Kotlyar, V V; Porfirev, A P

    2016-01-01

    We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory. (paper)

  11. Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation

    International Nuclear Information System (INIS)

    Sanders, Sören; Holthaus, Martin

    2017-01-01

    We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose–Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions. (paper)

  12. Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation

    Science.gov (United States)

    Sanders, Sören; Holthaus, Martin

    2017-11-01

    We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.

  13. Some results associated with a generalized basic hypergeometric function

    Directory of Open Access Journals (Sweden)

    Rajeev K. Gupta

    2009-05-01

    Full Text Available In this paper, we define a q-extension of the new generalized hypergeometric function given by Saxena et al. in [13], and have investigated the properties of the above new function such as q-differentiation and q-integral representation. The results presented are of general character and the results given earlier by Saxena and Kalla in [14], Virchenko, Kalla and Al-Zamel in [15], Al-Musallam and Kalla in [2, 3], Kobayashi in [7, 8], Saxena et al. in [13], Kumbhat et al. in [11] follow as special cases.

  14. Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces

    International Nuclear Information System (INIS)

    Neretin, Yu A

    2001-01-01

    The index hypergeometric transform (also called the Olevskii transform or the Jacobi transform) generalizes the spherical transform in L 2 on rank 1 symmetric spaces (that is, real, complex, and quaternionic Lobachevskii spaces). The aim of this paper is to obtain properties of the index hypergeometric transform imitating the analysis of Berezin kernels on rank 1 symmetric spaces. The problem of the explicit construction of a unitary operator identifying L 2 and a Berezin space is also discussed. This problem reduces to an integral expression (the Λ-function), which apparently cannot be expressed in a finite form in terms of standard special functions. (Only for certain special values of the parameter can this expression be reduced to the so-called Volterra type special functions.) Properties of this expression are investigated. For some series of symmetric spaces of large rank the above operator of unitary equivalence can be expressed in terms of the determinant of a matrix of Λ-functions

  15. From the hypergeometric differential equation to a non-linear Schrödinger one

    International Nuclear Information System (INIS)

    Plastino, A.; Rocca, M.C.

    2015-01-01

    We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre–Rego-Monteiro–Tsallis one. - Highlights: • We show that the q-exponential is a hypergeometric function. • It thus obeys the hypergeometric differential equation (HDE). • We show that the HDE can be cast as a non-linear Schrödinger equation. • This is different from the Nobre, Rego-Monteiro, Tsallis one.

  16. Multivariable hypergeometric solutions for three charged particles

    Energy Technology Data Exchange (ETDEWEB)

    Gasaneo, G.; Colavecchia, F.D.; Garibotti, C.R. [Comision Nacional de Energia Atomica, San Carlos de Bariloche (Argentina). Centro Atomico Bariloche]|[Consejo Nacional de Investigaciones Cientificas y Tecnicas, San Carlos de Bariloche (Argentina); Miraglia, J.E.; Macri, P. [IAFE, Consejo de Investigaciones Cientificas y Tecnicas, Buenos Aires (Argentina)

    1997-04-28

    We present a new wavefunction which describes the ion-atom problem above the ionization threshold. This is an approximate solution of the Schrodinger equation for the three-body Coulomb problem that can be expressed in terms of a confluent hypergeometric function of two variables. The proposed wavefunction includes correlation among the motions of the three particles and verifies the correct Coulombic asymptotic behaviours. (author).

  17. The star-triangle relation, lens partition function, and hypergeometric sum/integrals

    Energy Technology Data Exchange (ETDEWEB)

    Gahramanov, Ilmar [Max Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Radiation Problems ANAS,B. Vahabzade 9, AZ1143 Baku (Azerbaijan); Department of Mathematics, Khazar University,Mehseti St. 41, AZ1096 Baku (Azerbaijan); Kels, Andrew P. [Institute of Physics, University of Tokyo,Komaba, Tokyo 153-8902 (Japan)

    2017-02-08

    The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S{sub b}{sup 3}/ℤ{sub r}) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.

  18. The star-triangle relation, lens partition function, and hypergeometric sum/integrals

    International Nuclear Information System (INIS)

    Gahramanov, Ilmar; Kels, Andrew P.

    2017-01-01

    The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S b 3 /ℤ r ) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.

  19. Basic hypergeometric functions and covariant spaces for even-dimensional representations of Uq[osp(1/2)

    International Nuclear Information System (INIS)

    Aizawa, N; Chakrabarti, R; Mohammed, S S Naina; Segar, J

    2007-01-01

    Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and is observed that they may be expressed in terms of the Q-Hahn polynomials. We next investigate representations of the quantum supergroup OSp q (1/2) which are not well defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even-dimensional representations of the quantum supergroup OSp q (1/2)

  20. Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

    Directory of Open Access Journals (Sweden)

    Junesang Choi

    2014-01-01

    Full Text Available A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving the Fp(α,β(·. In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functions Fp(α,β,m(·. Some interesting special cases of our main results are also considered.

  1. Composite fields, generalized hypergeometric functions and the U(1)Y symmetry in the AdS/CFT correspondence

    International Nuclear Information System (INIS)

    Hoffmann, L.; Leonhardt, T.; Mesref, L.; Ruehl, W.

    2001-01-01

    We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of U(1) Y symmetry for four-point functions

  2. Composite fields, generalized hypergeometric functions and the U(1)Y symmetry in the AdS/CFT correspondence

    Science.gov (United States)

    Hoffmann, L.; Leonhardt, T.; Mesref, L.; Rühl, W.

    2001-09-01

    We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of U(1)Y symmetry for four-point functions.

  3. Numerically satisfactory solutions of hypergeometric recursions

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2007-01-01

    textabstractEach family of Gauss hypergeometric functions $$ f_n={}_2F_1(a+\\varepsilon_1n, b+\\varepsilon_2n ;c+\\varepsilon_3n; z),\\quad n\\in {\\mathbb Z}\\,, $$ for fixed $\\varepsilon_j=0,\\pm1$ (not all $\\varepsilon_j$ equal to zero) satisfies a second order linear difference equation of the

  4. Classification of hypergeometric identities for pi and other logarithms of algebraic numbers.

    Science.gov (United States)

    Chudnovsky, D V; Chudnovsky, G V

    1998-03-17

    This paper provides transcendental and algebraic framework for the classification of identities expressing pi and other logarithms of algebraic numbers as rapidly convergent generalized hypergeometric series in rational parameters. Algebraic and arithmetic relations between values of p+1Fp hypergeometric functions and their values are analyzed. The existing identities are explained, and new exhaustive classes of new ones are presented.

  5. The Lambert-W step-potential – an exactly solvable confluent hypergeometric potential

    Energy Technology Data Exchange (ETDEWEB)

    Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, 0203 Ashtarak (Armenia); Armenian State Pedagogical University, 0010 Yerevan (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)

    2016-02-15

    We present an asymmetric step–barrier potential for which the one-dimensional stationary Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert W-function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection at transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or variable variation regions, the reflection coefficient is smaller because of the lesser steepness of the potential on the particle incidence side. Presenting the derivation of the Lambert potential we show that this is a four-parametric sub-potential of a more general five-parametric one also solvable in terms of the confluent hypergeometric functions. The latter potential, however, is a conditionally integrable one. Finally, we show that there exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function. - Highlights: • We introduce an asymmetric step-barrier potential for which the 1D Schrödinger equation is exactly solved in terms of confluent hypergeometric functions. • The potential is given in terms of the Lambert-function, which is an implicitly elementary function also known as the product logarithm. • This is a four-parametric specification of a more general five-parametric potential also solvable in terms of the confluent hypergeometric functions. • There exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function.

  6. Correlation functions of two-matrix models

    International Nuclear Information System (INIS)

    Bonora, L.; Xiong, C.S.

    1993-11-01

    We show how to calculate correlation functions of two matrix models without any approximation technique (except for genus expansion). In particular we do not use any continuum limit technique. This allows us to find many solutions which are invisible to the latter technique. To reach our goal we make full use of the integrable hierarchies and their reductions which were shown in previous papers to naturally appear in multi-matrix models. The second ingredient we use, even though to a lesser extent, are the W-constraints. In fact an explicit solution of the relevant hierarchy, satisfying the W-constraints (string equation), underlies the explicit calculation of the correlation functions. The correlation functions we compute lend themselves to a possible interpretation in terms of topological field theories. (orig.)

  7. Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters

    Energy Technology Data Exchange (ETDEWEB)

    Kalmykov, M.Yu.; Kniehl, B.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2008-07-15

    We prove the following theorems: 1) The Laurent expansions in {epsilon} of the Gauss hypergeometric functions {sub 2}F{sub 1}(I{sub 1}+a{epsilon},I{sub 2}+b{epsilon};I{sub 3}+(p)/(q)+c{epsilon};z), {sub 2}F{sub 1}(I{sub 1}+(p)/(q)+a{epsilon},I{sub 2}+(p/q)+b{epsilon};I{sub 3}+(p)/(q)+c{epsilon};z) and {sub 2}F{sub 1}(I{sub 1}+(p)/(q)+ a{epsilon},I{sub 2}+b{epsilon};I{sub 3}+(p)/(q)+c{epsilon};z), where I{sub 1},I{sub 2},I{sub 3},p,q are arbitrary integers, a,b,c are arbitrary numbers and {epsilon} is an infinitesimal parameter, are expressible in terms of multiple polylogarithms of q-roots of unity with coefficients that are ratios of polynomials; 2) The Laurent expansion of the Gauss hypergeometric function {sub 2}F{sub 1}(I{sub 1}+(p)/(q)+a{epsilon},I{sub 2}+b{epsilon};I{sub 3}+c{epsilon};z) is expressible in terms of multiple polylogarithms of q-roots of unity times powers of logarithm with coefficients that are ratios of polynomials; 3) The multiple inverse rational sums {sigma}{sup {infinity}}{sub j=1}({gamma}(j))/({gamma}(1+j-(p)/(q))) (z{sup j})/(j{sup c}) S{sub a{sub 1}}(j-1).. S{sub a{sub p}}(j-1) and the multiple rational sums {sigma}{sup {infinity}}{sub j=1} ({gamma}(j+(p)/(q)))/({gamma}(1+j)) (z{sup j})/(j{sup c}) S{sub a{sub 1}}(j-1).. S{sub a{sub p}}(j-1), where S{sub a}(j)={sigma}{sup j}{sub k=1}(1)/(k{sup a}) is a harmonic series and c is an arbitrary integer, are expressible in terms of multiple polylogarithms; 4) The generalized hypergeometric functions {sub p}F{sub p.1}((vector)A+(vector)a{epsilon};(vector)B+(vector)b{epsilon},(p)/(q)+B{sub p-1};z) and {sub p}F{sub p-1}((vector)A+(vector)a{epsilon},(p)/(q)+A{sub p};(vector)B+(vector)b{epsilon};z) are expressible in terms of multiple polylogarithms with coefficients that are ratios of polynomials. (orig.)

  8. Numerically satisfactory solutions of hypergeometric recursions

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2006-01-01

    textabstractEach family of Gauss hypergeometric functions $f_n = 2F_1(a+epsilon 1n,b+epsilon 2n;c+epsilon 3n;z), nin Z$, for fixed epsilon_j = 0,pm 1$ (not all epsilon j equal to zero) satisfies a second order linear difference equation of the form $A_n f_{n-1} + B_n f_n + C_n f_{n+1} = 0$. Because

  9. Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

    Directory of Open Access Journals (Sweden)

    Resat Yilmazer

    2016-02-01

    Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

  10. Development of sample size allocation program using hypergeometric distribution

    International Nuclear Information System (INIS)

    Kim, Hyun Tae; Kwack, Eun Ho; Park, Wan Soo; Min, Kyung Soo; Park, Chan Sik

    1996-01-01

    The objective of this research is the development of sample allocation program using hypergeometric distribution with objected-oriented method. When IAEA(International Atomic Energy Agency) performs inspection, it simply applies a standard binomial distribution which describes sampling with replacement instead of a hypergeometric distribution which describes sampling without replacement in sample allocation to up to three verification methods. The objective of the IAEA inspection is the timely detection of diversion of significant quantities of nuclear material, therefore game theory is applied to its sampling plan. It is necessary to use hypergeometric distribution directly or approximate distribution to secure statistical accuracy. Improved binomial approximation developed by Mr. J. L. Jaech and correctly applied binomial approximation are more closer to hypergeometric distribution in sample size calculation than the simply applied binomial approximation of the IAEA. Object-oriented programs of 1. sample approximate-allocation with correctly applied standard binomial approximation, 2. sample approximate-allocation with improved binomial approximation, and 3. sample approximate-allocation with hypergeometric distribution were developed with Visual C ++ and corresponding programs were developed with EXCEL(using Visual Basic for Application). 8 tabs., 15 refs. (Author)

  11. Complex curve of the two-matrix model and its tau-function

    International Nuclear Information System (INIS)

    Kazakov, Vladimir A; Marshakov, Andrei

    2003-01-01

    We study the Hermitian and normal two-matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex curve, different from the hyperelliptic curve of the one-matrix model. The matrix model quantities are expressed through the periods of meromorphic generating differential on this curve and the partition function of the multiple support solution, as a function of filling numbers and coefficients of the matrix potential, is shown to be a quasiclassical tau-function. The relation to N = 1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multi-matrix models with tree-like interactions is considered

  12. Some Instructional Issues in Hypergeometric Distribution

    Directory of Open Access Journals (Sweden)

    Anwar H. Joarder

    2012-07-01

    Full Text Available 800x600 Normal 0 false false false EN-US X-NONE X-NONE A brief introduction to sampling without replacement is presented. We represent the probability of a sample outcome in sampling without replacement from a finite population by three equivalent forms involving permutation and combination. Then it is used to calculate the probability of any number of successes in a given sample. The resulting forms are equivalent to the well known mass function of the hypergeometric distribution. Vandermonde’s identity readily justifies different forms of the mass function. One of the new form of the mass function embodies binomial coefficient showing much resemblance to that of binomial distribution. It also yields some interesting identities. Some other related issues are discussed.

  13. Observations on the summability of confluent hypergeometric functions and on semiclassical quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Silverstone, H.J.; Nakai, S.; Harris, J.G.

    1985-09-01

    Asymptotic expansions for Airy functions and more generally confluent hypergeometric functions, which are of fundamental importance in semiclassical quantum mechanics, are summable. The Stokes lines of the expansions are cuts of the Borel sums of the power series occurring in the expansions. At a Stokes line on which the function is continuous, the asymptotic expansions change discontinuously, but their composite sums do not: a fact that greatly clarifies the role of the Stokes line. On a Stokes line itself, it is still possible to evaluate the asymptotic expansion by Borel summation via analytic continuation, and as a consequence complex expansions may have real sums, and vice versa. This observation has important implications for the significance and use of asymptotic expansions recently derived for the resonances of the LoSurdo-Stark effect and for the energy eigenvalues of H/sub 2/ /sup +/. For both of these problems the physical values of the expansion parameters, the electric field strength and the reciprocal of the internuclear distance, lie on Stokes lines.

  14. The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach

    International Nuclear Information System (INIS)

    Qureshi, M I; Rafat, M; Azad, S Ismail

    2010-01-01

    The motion of a simple pendulum of arbitrary amplitude is usually treated by approximate methods. By using generalized hypergeometric functions, it is however possible to solve the problem exactly. In this paper, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. A new and exact expression for the time of swinging of a simple pendulum from the vertical position to an arbitrary angular position θ is given by equation (3.10). The time period of such a pendulum is also exactly expressible in terms of hypergeometric functions. The exact expressions thus obtained are used to plot the graphs that compare the exact time period T(θ 0 ) with the time period T(0) (based on simple harmonic approximation). We also compare the relative difference between T(0) and T(θ 0 ) found from the exact equation of motion with the usual perturbation theory estimate. The treatment is intended for graduate students, who have acquired some familiarity with the hypergeometric functions. This approach may also be profitably used by specialists who encounter during their investigations nonlinear differential equations similar in form to the pendulum equation. Such nonlinear differential equations could arise in diverse fields, such as acoustic vibrations, oscillations in small molecules, turbulence and electronic filters, among others.

  15. The O(αs3) massive operator matrix elements of O(nf) for the structure function F2(x,Q2) and transversity

    International Nuclear Information System (INIS)

    Ablinger, J.; Bluemlein, J.; Klein, S.; Schneider, C.; Wissbrock, F.

    2011-01-01

    The contributions ∝n f to the O(α s 3 ) massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit Q 2 >>m 2 are computed for the structure function F 2 (x,Q 2 ) and transversity for general values of the Mellin variable N. Here, for two matrix elements, A qq,Q PS (N) and A qg,Q (N), the complete result is obtained. A first independent computation of the contributions to the 3-loop anomalous dimensions γ qg (N), γ qq PS (N), and γ qq NS,(TR) (N) is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.

  16. Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement

    International Nuclear Information System (INIS)

    van Diejen, J.F.

    1997-01-01

    Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl. (orig.)

  17. Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model

    International Nuclear Information System (INIS)

    Sanders, Sören; Holthaus, Martin

    2017-01-01

    We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems. (paper)

  18. Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose-Hubbard model

    Science.gov (United States)

    Sanders, Sören; Holthaus, Martin

    2017-10-01

    We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

  19. Green function of the model two-centre quantum-mechanical problem

    International Nuclear Information System (INIS)

    Khoma, M.V.; Lazur, V.Yu.

    2002-01-01

    The expansions of a Green function for the Simmons molecular potential (SMP) in terms of spheroidal function are built. The solutions of degenerate hypergeometric equation are used as basis function system while expanding regular and irregular model spheroidal functions into series. Rather simple three-terms recurrence relations are obtained for the coefficients of these expansions. Much attentions is given to different asymptotic representation as well as Sturmian expansions of the Green function of the two-centre SMP wave functions. In all cases considered the Green function is reduced to the form similar to the Hostler's representation of the Coulomb Green function

  20. Two-loop massive operator matrix elements for unpolarized heavy flavor production to O({epsilon})

    Energy Technology Data Exchange (ETDEWEB)

    Bierenbaum, I.; Bluemlein, J.; Klein, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

    2008-02-15

    We calculate the O({alpha}{sup 2}{sub s}) massive operator matrix elements for the twist-2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q{sup 2}>>m{sup 2}, up to the O({epsilon}) contributions. These terms contribute through the renormalization of the O({alpha}{sup 3}{sub s}) heavy flavor Wilson coefficients of the structure function F{sub 2}(x,Q{sup 2}). The calculation has been performed using light-cone expansion techniques without using the integration-by-parts method. We represent the individual Feynman diagrams by generalized hypergeometric structures, the {epsilon}-expansion of which leads to infinite sums depending on the Mellin variable N. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the Sigma package. (orig.)

  1. Some Connections between the Spherical and Parabolic Bases on the Cone Expressed in terms of the Macdonald Function

    OpenAIRE

    Shilin, I. A.; Choi, Junesang

    2014-01-01

    Computing the matrix elements of the linear operator, which transforms the spherical basis of $SO(3,1)$ -representation space into the hyperbolic basis, very recently, Shilin and Choi (2013) presented an integral formula involving the product of two Legendre functions of the first kind expressed in terms of ${ }_{4}{F}_{3}$ -hypergeometric function and, using the general Mehler-Fock transform, another integral formula for the Legendre function of the first kind. In the sequel, we investigate ...

  2. Distinguishing between Binomial, Hypergeometric and Negative Binomial Distributions

    Science.gov (United States)

    Wroughton, Jacqueline; Cole, Tarah

    2013-01-01

    Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre- and post-tests that were designed to assess the…

  3. Vortex beam characterization in terms of Hypergeometric- Gaussian modes

    CSIR Research Space (South Africa)

    Sephton, Bereneice C

    2016-10-01

    Full Text Available in Optics: The 100th OSA Annual Meeting and Exhibit/Laser Science XXXII , 17-21 October 2016, Rochester Riverside Convention Center, Rochester, New York United States Vortex beam characterization in terms of Hypergeometric- Gaussian modes Sephton...

  4. Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions

    International Nuclear Information System (INIS)

    Spiridonov, V.P.; Vartanov, G.S.

    2012-03-01

    Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from SL(3, Z)-modular transformation properties of the kernels of dual indices.

  5. Coupling coefficients for tensor product representations of quantum SU(2)

    International Nuclear Information System (INIS)

    Groenevelt, Wolter

    2014-01-01

    We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions

  6. Coupling coefficients for tensor product representations of quantum SU(2)

    Science.gov (United States)

    Groenevelt, Wolter

    2014-10-01

    We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.

  7. Two- and three-point functions in the D=1 matrix model

    International Nuclear Information System (INIS)

    Ben-Menahem, S.

    1991-01-01

    The critical behavior of the genus-zero two-point function in the D=1 matrix model is carefully analyzed for arbitrary embedding-space momentum. Kostov's result is recovered for momenta below a certain value P 0 (which is 1/√α' in the continuum language), with a non-universal form factor which is expressed simply in terms of the critical fermion trajectory. For momenta above P 0 , the Kostov scaling term is found to be subdominant. We then extend the large-N WKB treatment to calculate the genus-zero three-point function, and elucidate its critical behavior when all momenta are below P 0 . The resulting universal scaling behavior, as well as the non-universal form factor for the three-point function, are related to the two-point functions of the individual external momenta, through the factorization familiar from continuum conformal field theories. (orig.)

  8. An asymptotic formula of the divergent bilateral basic hypergeometric series

    OpenAIRE

    Morita, Takeshi

    2012-01-01

    We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\\psi_0 (a;-;q,\\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\\to 1-0$ of our asymptotic formula.

  9. Some New Formulas for the Generalized Hypergeometric Series

    Directory of Open Access Journals (Sweden)

    Sumi P. Krishnan

    Full Text Available The aim of this research paper is to provide some new formulas for the generalized hypergeometric series. The results are derived with the help of the extensions of Euler's and Kummer's classical transformations. As special cases, we have recovered several results due to Sharma. The results established in this paper are simple, interesting, easily obtainable and may be useful.

  10. Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions

    Energy Technology Data Exchange (ETDEWEB)

    Spiridonov, V.P. [Joint Institute for Nuclear Research, Dubna (Russian Federation); Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2012-05-15

    Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from SL(3, Z)-modular transformation properties of the kernels of dual indices.

  11. Factorization method for difference equations of hypergeometric type on nonuniform lattices

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez-Nodarse, R. [Departamento de Analisis Matematico, Universidad de Sevilla, Sevilla (Spain); Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain); Costas-Santos, R.S. [Departamento de Analisis Matematico, Universidad de Sevilla, Sevilla (Spain)

    2001-07-13

    We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given. (author)

  12. Singular value correlation functions for products of Wishart random matrices

    International Nuclear Information System (INIS)

    Akemann, Gernot; Kieburg, Mario; Wei, Lu

    2013-01-01

    We consider the product of M quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalizes the classical Wishart–Laguerre Gaussian unitary ensemble with M = 1. In this paper, we first compute the joint probability distribution for the singular values of the product matrix when the matrix size N and the number M are fixed but arbitrary. This leads to a determinantal point process which can be realized in two different ways. First, it can be written as a one-matrix singular value model with a non-standard Jacobian, or second, for M ⩾ 2, as a two-matrix singular value model with a set of auxiliary singular values and a weight proportional to the Meijer G-function. For both formulations, we determine all singular value correlation functions in terms of the kernels of biorthogonal polynomials which we explicitly construct. They are given in terms of the hypergeometric and Meijer G-functions, generalizing the Laguerre polynomials for M = 1. Our investigation was motivated from applications in telecommunication of multi-layered scattering multiple-input and multiple-output channels. We present the ergodic mutual information for finite-N for such a channel model with M − 1 layers of scatterers as an example. (paper)

  13. Evaluation of integrals involving powers of (1-x2) and two associated Legendre functions or Gegenbauer polynomials

    International Nuclear Information System (INIS)

    Rashid, M.A.

    1984-08-01

    Integrals involving powers of (1-x 2 ) and two associated Legendre functions or two Gegenbauer polynomials are evaluated as finite sums which can be expressed in terms of terminating hypergeometric function 4 F 3 . The integrals which are evaluated are ∫sub(-1)sup(1)[Psub(l)sup(m)(x)Psub(k)sup(n)(x)]/[(1-x 2 )sup(p+1)]dx and ∫sub(-1)sup(1)Csub(l)sup(α)(x)Csub(k)sup(β)(x)[(1-x 2 )sup[(α+β-3)/2-p

  14. The O({alpha}{sup 3}{sub s}n{sub f}T{sup 2}{sub F}C{sub A,F}) contributions to the gluonic massive operator matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes; Hasselhuhn, Alexander [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [Technische Hochschule Aachen (Germany). Inst. fuer Theoretische Physik E; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

    2012-05-15

    The O({alpha}{sub s}{sup 3}n{sub f}T{sub F}{sup 2}C{sub A,F}) terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable N. These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of N is provided.

  15. Solutions of the two-level problem in terms of biconfluent Heun functions

    Energy Technology Data Exchange (ETDEWEB)

    Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak (Armenia)]. E-mail: artur@ec.sci.am; Suominen, Kalle-Antti [Helsinki Institute of Physics, Helsinki (Finland); Department of Applied Physics, University of Turku, Turku (Finland)

    2001-08-17

    Five four-parametric classes of quantum mechanical two-level models permitting solutions in terms of the biconfluent Heun function are derived. Three of these classes are generalizations of the well known classes of Landau-Zener, Nikitin and Crothers. It is shown that two other classes describe super- and sublinear and essentially nonlinear level crossings, as well as processes with three crossing points. In particular, these classes include two-level models where the field amplitude is constant and the detuning varies as {delta}{sub 0}t+{delta}{sub 2}t{sup 3} or {approx}t{sup 1/3}. For the essentially nonlinear cubic-crossing model, {delta}{sub t}{approx}{delta}{sub 2}t{sup 3}, the general solution of the two-level problem is shown to be expressed as series of confluent hypergeometric functions. (author)

  16. Two-matrix models and c =1 string theory

    International Nuclear Information System (INIS)

    Bonora, L.; Xiong Chuansheng

    1994-05-01

    We show that the most general two-matrix model with bilinear coupling underlies c = 1 string theory. More precisely we prove that W 1+∞ constraints, a subset of the correlation functions and the integrable hierarchy characterizing such two-matrix model, correspond exactly to the W 1+∞ constraints, to the discrete tachyon correlation functions and the integrable hierarchy of the c = 1 string theory. (orig.)

  17. A scan statistic for binary outcome based on hypergeometric probability model, with an application to detecting spatial clusters of Japanese encephalitis.

    Science.gov (United States)

    Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong

    2013-01-01

    As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.

  18. The O({alpha}{sub s}{sup 3}n{sub f}T{sub F}{sup 2}C{sub A,F}) contributions to the gluonic massive operator matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes, E-mail: johannes.bluemlein@desy.de [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Hasselhuhn, Alexander [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Klein, Sebastian [Institute for Theoretical Physics E, RWTH Aachen University, D-52056 Aachen (Germany); Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstrasse 69, A-4040 Linz (Austria)

    2013-01-11

    The O({alpha}{sub s}{sup 3}n{sub f}T{sub F}{sup 2}C{sub A,F}) terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable N using a new summation technique. These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of N is provided.

  19. Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials

    Directory of Open Access Journals (Sweden)

    Ernest G. Kalnins

    2013-10-01

    Full Text Available We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2 and so(3. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

  20. Time-dependent reduced density matrix functional theory applied to laser-driven, correlated two-electron dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

    2013-07-01

    Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.

  1. Spectral transformation chains and some new biorthogonal rational functions

    International Nuclear Information System (INIS)

    Spiridonov, V.

    2000-01-01

    A discrete-time chain, associated with the generalized eigenvalue problem for two Jacobi matrices, is derived. Various discrete and continuous symmetries of this integrable equation are revealed. A class of its rational, elementary and elliptic function solutions, appearing from a similarity reduction, are constructed. The latter lead to large families of biorthogonal rational functions based upon the very-well-posed balanced hypergeometric series of three types: the standard hypergeometric series 9 F 8 , basic series 10 φ 9 and its elliptic analogue 10 E 9 . For an important subclass of the elliptic biorthogonal rational functions the weight function and normalization constants are determined explicitly. (orig.)

  2. Quantum communication through a spin chain with interaction determined by a Jacobi matrix

    International Nuclear Information System (INIS)

    Chakrabarti, R; Van der Jeugt, J

    2010-01-01

    We obtain the time-dependent correlation function describing the evolution of a single spin excitation state in a linear spin chain with isotropic nearest-neighbour XY coupling, where the Hamiltonian is related to the Jacobi matrix of a set of orthogonal polynomials. For the Krawtchouk polynomial case, an arbitrary element of the correlation function is expressed in a simple closed form. Its asymptotic limit corresponds to the Jacobi matrix of the Charlier polynomial, and may be understood as a unitary evolution resulting from a Heisenberg group element. Correlation functions for Hamiltonians corresponding to Jacobi matrices for the Hahn, dual Hahn and Racah polynomials are also studied. For the Hahn polynomials we obtain the general correlation function, some of its special cases and the limit related to the Meixner polynomials, where the su(1, 1) algebra describes the underlying symmetry. For the cases of dual Hahn and Racah polynomials, the general expressions of the correlation functions contain summations which are not of hypergeometric type. Simplifications, however, occur in special cases.

  3. Iterated elliptic and hypergeometric integrals for Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Radu, C.S.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Van Hoeij, M.; Imamoglu, E. [Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics; Raab, C.G. [Linz Univ. (Austria). Inst. for Algebra

    2017-05-15

    We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as {sub 2}F{sub 1} Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ{sub i} functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η{sup κ}(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

  4. Iterated elliptic and hypergeometric integrals for Feynman diagrams

    International Nuclear Information System (INIS)

    Ablinger, J.; Radu, C.S.; Schneider, C.; Bluemlein, J.; Freitas, A. de; Van Hoeij, M.; Imamoglu, E.; Raab, C.G.

    2017-05-01

    We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as _2F_1 Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ_i functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η"κ(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

  5. Special functions and the theory of group representations

    CERN Document Server

    Vilenkin, N Ja

    1968-01-01

    A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group SU(2), and the hypergeometric function and representations of the group SL(2,R), as well as many other classes of special functions.

  6. Spectral function from Reduced Density Matrix Functional Theory

    Science.gov (United States)

    Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

    2015-03-01

    In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

  7. Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution

    Science.gov (United States)

    Samohyl, Robert Wayne

    2017-10-01

    This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The

  8. On application of the S-matrix two-point function to nuclear data evaluation

    International Nuclear Information System (INIS)

    Igarasi, S.

    1992-01-01

    Statistical model calculation using S-matrix two-point function (STF) was tried. The results were compared with those calculated with the Hauser-Feshbach formula (HF) with and without resonance level-width fluctuation corrections (WFC). The STF gave almost the same cross sections as calculated using Moldauer's degrees of freedom for the χ 2 -distributions (MCD). The effect of the WFC to the final states in continuum was also studied using the HF with WFC of the MCD and of Porter-Thomas distribution (PTD). The HF with the MCD is recommended for practical calculation of the cross sections. (orig.)

  9. A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system

    Science.gov (United States)

    Chen, Kewei; Zhan, Hongbin

    2018-06-01

    The reactive solute transport in a single fracture bounded by upper and lower matrixes is a classical problem that captures the dominant factors affecting transport behavior beyond pore scale. A parallel fracture-matrix system which considers the interaction among multiple paralleled fractures is an extension to a single fracture-matrix system. The existing analytical or semi-analytical solution for solute transport in a parallel fracture-matrix simplifies the problem to various degrees, such as neglecting the transverse dispersion in the fracture and/or the longitudinal diffusion in the matrix. The difficulty of solving the full two-dimensional (2-D) problem lies in the calculation of the mass exchange between the fracture and matrix. In this study, we propose an innovative Green's function approach to address the 2-D reactive solute transport in a parallel fracture-matrix system. The flux at the interface is calculated numerically. It is found that the transverse dispersion in the fracture can be safely neglected due to the small scale of fracture aperture. However, neglecting the longitudinal matrix diffusion would overestimate the concentration profile near the solute entrance face and underestimate the concentration profile at the far side. The error caused by neglecting the longitudinal matrix diffusion decreases with increasing Peclet number. The longitudinal matrix diffusion does not have obvious influence on the concentration profile in long-term. The developed model is applied to a non-aqueous-phase-liquid (DNAPL) contamination field case in New Haven Arkose of Connecticut in USA to estimate the Trichloroethylene (TCE) behavior over 40 years. The ratio of TCE mass stored in the matrix and the injected TCE mass increases above 90% in less than 10 years.

  10. Sampling Methods for Wallenius' and Fisher's Noncentral Hypergeometric Distributions

    DEFF Research Database (Denmark)

    Fog, Agner

    2008-01-01

    the mode, ratio-of-uniforms rejection method, and rejection by sampling in the tau domain. Methods for the multivariate distributions include: simulation of urn experiments, conditional method, Gibbs sampling, and Metropolis-Hastings sampling. These methods are useful for Monte Carlo simulation of models...... of biased sampling and models of evolution and for calculating moments and quantiles of the distributions.......Several methods for generating variates with univariate and multivariate Wallenius' and Fisher's noncentral hypergeometric distributions are developed. Methods for the univariate distributions include: simulation of urn experiments, inversion by binary search, inversion by chop-down search from...

  11. A Matrix Splitting Method for Composite Function Minimization

    KAUST Repository

    Yuan, Ganzhao

    2016-12-07

    Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Incorporating a new Gaussian elimination procedure, the matrix splitting method achieves state-of-the-art performance. For convex problems, we establish the global convergence, convergence rate, and iteration complexity of MSM, while for non-convex problems, we prove its global convergence. Finally, we validate the performance of our matrix splitting method on two particular applications: nonnegative matrix factorization and cardinality regularized sparse coding. Extensive experiments show that our method outperforms existing composite function minimization techniques in term of both efficiency and efficacy.

  12. A Matrix Splitting Method for Composite Function Minimization

    KAUST Repository

    Yuan, Ganzhao; Zheng, Wei-Shi; Ghanem, Bernard

    2016-01-01

    Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Incorporating a new Gaussian elimination procedure, the matrix splitting method achieves state-of-the-art performance. For convex problems, we establish the global convergence, convergence rate, and iteration complexity of MSM, while for non-convex problems, we prove its global convergence. Finally, we validate the performance of our matrix splitting method on two particular applications: nonnegative matrix factorization and cardinality regularized sparse coding. Extensive experiments show that our method outperforms existing composite function minimization techniques in term of both efficiency and efficacy.

  13. A J matrix engine for density functional theory calculations

    International Nuclear Information System (INIS)

    White, C.A.; Head-Gordon, M.

    1996-01-01

    We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics

  14. The Candida albicans Biofilm Matrix: Composition, Structure and Function.

    Science.gov (United States)

    Pierce, Christopher G; Vila, Taissa; Romo, Jesus A; Montelongo-Jauregui, Daniel; Wall, Gina; Ramasubramanian, Anand; Lopez-Ribot, Jose L

    2017-03-01

    A majority of infections caused by Candida albicans -the most frequent fungal pathogen-are associated with biofilm formation. A salient feature of C. albicans biofilms is the presence of the biofilm matrix. This matrix is composed of exopolymeric materials secreted by sessile cells within the biofilm, in which all classes of macromolecules are represented, and provides protection against environmental challenges. In this review, we summarize the knowledge accumulated during the last two decades on the composition, structure, and function of the C. albicans biofilm matrix. Knowledge of the matrix components, its structure, and function will help pave the way to novel strategies to combat C. albicans biofilm infections.

  15. An Outlyingness Matrix for Multivariate Functional Data Classification

    KAUST Repository

    Dai, Wenlin

    2017-08-25

    The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by extending directional outlyingness, an effective measure of the shape variation of curves that combines the direction of outlyingness with conventional statistical depth. We propose two classifiers based on directional outlyingness and the outlyingness matrix, respectively. Our classifiers provide better performance compared with existing depth-based classifiers when applied on both univariate and multivariate functional data from simulation studies. We also test our methods on two data problems: speech recognition and gesture classification, and obtain results that are consistent with the findings from the simulated data.

  16. Special functions & their applications

    CERN Document Server

    Lebedev, N N

    1972-01-01

    Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

  17. Z4-symmetric factorized S-matrix in two space-time dimensions

    International Nuclear Information System (INIS)

    Zamolodchikov, A.B.

    1979-01-01

    The factorized S-matrix with internal symmetry Z 4 is constructed in two space-time dimensions. The two-particle amplitudes are obtained by means of solving the factorization, unitarity and analyticity equations. The solution of factorization equations can be expressed in terms of elliptic functions. The S-matrix cotains the resonance poles naturally. The simple formal relation between the general factorized S-matrices and the Baxter-type lattice transfer matrices is found. In the sense of this relation the Z 4 -symmetric S-matrix corresponds to the Baxter transfer matrix itself. (orig.)

  18. Alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter

    Directory of Open Access Journals (Sweden)

    Mika Tanda

    2015-01-01

    Full Text Available We compute alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter and discuss the singularity structures of the Borel transforms of the WKB solution expressed in terms of its alien derivatives.

  19. The problem of the universal density functional and the density matrix functional theory

    International Nuclear Information System (INIS)

    Bobrov, V. B.; Trigger, S. A.

    2013-01-01

    The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.

  20. Fractional Fourier transform for confluent hypergeometric beams

    International Nuclear Information System (INIS)

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-01-01

    Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

  1. Functional equation for the Mordell-Tornheim multiple zeta-function

    OpenAIRE

    Okamoto, Takuya; Onozuka, Tomokazu

    2016-01-01

    We show a relation between the Mordell-Tornheim multiple zeta-function and the confluent hypergeometric function, and using it, we give the functional equation for the Mordell-Tornheim multiple zeta-function. In the double case, the functional equation includes the known functional equation for the Euler-Zagier double zeta-function.

  2. Matrix string partition function

    CERN Document Server

    Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre

    1998-01-01

    We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.

  3. Group theoretical basis of some identities for the generalized hypergeometric series

    International Nuclear Information System (INIS)

    Beyer, W.A.; Louck, J.D.; Stein, P.R.

    1987-01-01

    It is shown that Thomae's identity between two 3 F 2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group S 5 is an invariance group of this series. A similar result is proved for the terminating Saalschuetzian 4 F 3 series, where S 6 is shown to be the invariance group of this series (or S 5 if one parameter is eliminated by using the Saalschuetz condition). Here Bailey's identity is realized as a permutation of appropriately defined parameters. Finally, the set of three-term relations between 3 F 2 series of unit argument discovered by Thomae [J. Thomae, J. Reine Angew. Math. 87, 26 (1879)] and systematized by Whipple [F. J. Whipple, Proc. London Math. Soc. 23, 104 (1925)] is shown to be transformed into itself under the action of the group S 6 x Λ, where Λ is a two-element group. The 12 left cosets of S 6 x Λ with respect to the invariance group S 5 are the structural elements underlying the three-term relations. The symbol manipulator macsyma was used to obtain preliminary results

  4. Inequalities for the Modified k-Bessel Function

    Directory of Open Access Journals (Sweden)

    Saiful Rahman Mondal

    2017-07-01

    Full Text Available The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.

  5. Appell functions and the scalar one-loop three-point integrals in Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Cabral-Rosetti, L G [Departamento de Posgrado, Centro Interdisciplinario de Investigacion y Docencia en Educacion Tecnica (CIIDET), Av. Universidad 282 Pte., Col. Centro, A. Postal 752, C.P. 76000, Santiago de Queretaro, Qro. (Mexico); Sanchis-Lozano, M A [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, 46100 Burjassot, Valencia (Spain)

    2006-05-15

    The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.

  6. Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

    Science.gov (United States)

    Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

    2017-03-01

    Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

  7. The general expression for the transition amplitude of two-photon ionization of atomic hydrogen

    Energy Technology Data Exchange (ETDEWEB)

    Karule, E [Institute of Atomic Physics and Spectroscopy, University of Latvia, Raina Boulevard 19, Riga, LV-1586 (Latvia); Moine, B [Universite Paris Sud, 91405 Orsay Cedex (France)

    2003-05-28

    Two-photon ionization of atomic hydrogen with an excess photon is revisited. The non-relativistic dipole approximation and Coulomb Green function (CGF) formalism are applied. Using the CGF Sturmian expansion straightforwardly, one gets the radial transition amplitude in the form of an infinite sum over Gauss hypergeometric functions which are polynomials. It is convergent if all intermediate states are in the discrete spectrum. In the case of two-photon ionization with an excess photon, when photoionization is also possible, intermediate states are in the continuum. We performed the explicit summation over intermediate states and got a simple general expression for the radial transition amplitude in the form of a finite sum over Appell hypergeometric functions, which are not polynomials. An Appell function may be expressed as an infinite sum over Gauss functions. In the case of ionization by an excess photon, Gauss functions are transformed to give a convergent radial transition amplitude for the whole region. The generalized cross sections for two-photon above-threshold ionization of atomic hydrogen in the ground state and excited states calculated by us agree very well with results of previous calculations. Generalized cross sections for two-photon ionization of positronium in the ground state are obtained by scaling those for atomic hydrogen.

  8. Reduced density matrix functional theory via a wave function based approach

    Energy Technology Data Exchange (ETDEWEB)

    Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)

    2016-07-01

    We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

  9. Factorisations for partition functions of random Hermitian matrix models

    International Nuclear Information System (INIS)

    Jackson, D.M.; Visentin, T.I.

    1996-01-01

    The partition function Z N , for Hermitian-complex matrix models can be expressed as an explicit integral over R N , where N is a positive integer. Such an integral also occurs in connection with random surfaces and models of two dimensional quantum gravity. We show that Z N can be expressed as the product of two partition functions, evaluated at translated arguments, for another model, giving an explicit connection between the two models. We also give an alternative computation of the partition function for the φ 4 -model.The approach is an algebraic one and holds for the functions regarded as formal power series in the appropriate ring. (orig.)

  10. Massively parallel sparse matrix function calculations with NTPoly

    Science.gov (United States)

    Dawson, William; Nakajima, Takahito

    2018-04-01

    We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

  11. Dirac Coulomb Green's function and its application to relativistic Rayleigh scattering

    International Nuclear Information System (INIS)

    Wong, M.K.F.; Yeh, E.H.Y.

    1985-01-01

    The Dirac Coulomb Green's function is obtained in both coordinate and momentum space. The Green's function in coordinate space is obtained by the eigenfunction expansion method in terms of the wave functions obtained by Wong and Yeh. The result is simpler than those obtained previously by other authors, in that the radial part for each component contains one term only instead of four terms. Our Green's function reduces to the Schroedinger Green's function upon some simple conditions, chiefly by neglecting the spin and replacing lambda by l. The Green's function in momentum space is obtained as the Fourier transform of the coordinate space Green's function, and is expressed in terms of basically three types of functions: (1) F/sub A/ (α; β 1 β 2 β 3 ; γ 1 γ 2 γ 3 ; z 1 z 2 z 3 ), (2) the hypergeometric function, and (3) spherical harmonics. The matrix element for Rayleigh scattering, or elastic Compton scattering, from relativistically bound electrons is then obtained in analytically closed form. The matrix element is written basically in terms of the coordinate space Dirac Coulomb Green's function. The technique used in the evaluation of the matrix element is based on the calculation of the momentum space Dirac Coulomb Green's function. Finally the relativistic result is compared with the nonrelativistic result

  12. Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez-Nodarse, R [Departamento de Analisis Matematico, Universidad de Sevilla, Apdo. 1160, E-41080 Sevilla (Spain); Atakishiyev, N M [Instituto de Matematicas, UNAM, Apartado Postal 273-3, CP 62210 Cuernavaca, Morelos, Mexico (Germany); Costas-Santos, R S [Departamento de Matematicas, EPS, Universidad Carlos III de Madrid, Ave. Universidad 30, E-28911, Leganes, Madrid (Spain)

    2005-01-07

    We argue that one can factorize the difference equation of hypergeometric type on non-uniform lattices in the general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues, this directly leads to the dynamical symmetry algebra su{sub q}(1, 1), whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the q-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.

  13. Differential analysis of matrix convex functions II

    DEFF Research Database (Denmark)

    Hansen, Frank; Tomiyama, Jun

    2009-01-01

    We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided...

  14. An Outlyingness Matrix for Multivariate Functional Data Classification

    KAUST Repository

    Dai, Wenlin; Genton, Marc G.

    2017-01-01

    outlyingness with conventional statistical depth. We propose two classifiers based on directional outlyingness and the outlyingness matrix, respectively. Our classifiers provide better performance compared with existing depth-based classifiers when applied on both univariate and multivariate functional data from simulation studies. We also test our methods on two data problems: speech recognition and gesture classification, and obtain results that are consistent with the findings from the simulated data.

  15. Full spectrum of the two-photon and the two-mode quantum Rabi models

    International Nuclear Information System (INIS)

    Dossa, Anselme F.; Avossevou, Gabriel Y. H.

    2014-01-01

    This paper is concerned with the rigorous analytical determination of the spectrum of the two-photon and the two-mode quantum Rabi models. To reach this goal, we exploit the hidden symmetries in these models by means of the unitary and similarity transformations in addition to the Bargmann-Fock space description. In each case, the purely quantum mechanical problem of the Rabi model studied is reduced to solutions for differential equations. This eventually gives a third-order differential equation for each of these models, which is reduced to a second-order differential equation by additional transformations. The analytical expressions of the wave functions describing the energy levels are obtained in terms of the confluent hypergeometric functions

  16. W-infinity ward identities and correlation functions in the c = 1 matrix model

    International Nuclear Information System (INIS)

    Das, S.R.; Dhar, A.; Mandal, G.; Wadia, S.R.

    1992-01-01

    In this paper, the authors explore consequences of W-infinity symmetry in the fermionic field theory of the c = 1 matrix model. The authors derive exact Ward identities relating correlation functions of the bilocal operator. These identities can be expressed as equations satisfied by the effective action of a three-dimensional theory and contain non-perturbative information about the model. The authors use thee identities to calculate the two-point function of the bilocal operator in the double scaling limit. The authors extract the operator whose two-point correlator has a single pole at an (imaginary) integer value of the energy. The authors then rewrite the W-infinity charges in terms of operators in the matrix model and use this to derive constraints satisfied by the partition function of the matrix model with a general time dependent potential

  17. Symmetries of some hypergeometric series: Implications for 3j- and 6j-coefficients

    International Nuclear Information System (INIS)

    Louck, J.D.; Beyer, W.A.; Biedenharn, L.C.; Stein, P.R.

    1986-10-01

    The occurrence of generalized hypergeometric series as factors, in the Wigner-Clebsch-Gordan (3j) and Racah (6j) coefficients is well known. The recently discovered S 5 symmetry of the Saalscheutzian 4 F 3 series may be used to extend the symmetries of the 6j-coefficients to the much larger group generated by S 5 and the group of Regge symmetries. (A similar extension may be carried out for the 3j-coefficients). The required extension of the domain of definition of the 6j-coefficients and the properties of its symmetry group is developed here. 7 refs

  18. Reduction of Double Clausenian Hypergeometric Functions

    DEFF Research Database (Denmark)

    Karlsson, Per W.

    1996-01-01

    The reduction formulas under consideration are those for which the conditions upon the variables are other than 'fixed values'. Known results are discussed, and some new formulas are derived by series manipulations from various known summation and transformation theorems. The ten functions in thi...

  19. Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

    Science.gov (United States)

    Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

    2018-01-01

    Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

  20. A two-matrix alternative

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2013-01-01

    Roč. 26, 15 December (2013), s. 836-841 ISSN 1537-9582 Institutional support: RVO:67985807 Keywords : two-matrix alternative * solution * algorithm Subject RIV: BA - General Mathematics Impact factor: 0.514, year: 2013 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol26_pp836-841.pdf

  1. Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

    Science.gov (United States)

    Abdelaziz, Y.; Maillard, J.-M.

    2017-05-01

    We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same {}_2F1 hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus {}_2F1 hypergeometric function example. We then focus on identities relating the same {}_2F1 hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to {}_3F2 , hypergeometric functions, and show that one just reduces to the previous {}_2F1 cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a _2F1 hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or {}_2F1 hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to

  2. Closed form for two-photon free-free transition matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Karule, Erna E-mail: karule@latnet.lv

    2000-08-01

    Two-photon free-free transitions happen in the multiphoton ionization with more than one excess photon and in Bremsstrahlung. Up to now, the configuration space free-free transition amplitudes have not been written in closed form. We propose a modified Coulomb Green's function (CGF) Sturm ian expansion which allows one to obtain expressions for two-photon radial transition matrix elements in the closed form which are easy to continue analytically to calculate free-free transitions in H.

  3. Two-point correlation function for Dirichlet L-functions

    Science.gov (United States)

    Bogomolny, E.; Keating, J. P.

    2013-03-01

    The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

  4. Two-point correlation function for Dirichlet L-functions

    International Nuclear Information System (INIS)

    Bogomolny, E; Keating, J P

    2013-01-01

    The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy–Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question. (paper)

  5. Enhanced Matrix Power Function for Cryptographic Primitive Construction

    Directory of Open Access Journals (Sweden)

    Eligijus Sakalauskas

    2018-02-01

    Full Text Available A new enhanced matrix power function (MPF is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left–right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1 the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2 the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ problem which can be reckoned as hard; (3 the estimation of the effectiveness of direct MPF value computation; and (4 the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF, since the effective (polynomial-time inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources.

  6. Evaluation of integrals with hypergeometric and logarithmic functions

    Directory of Open Access Journals (Sweden)

    Sofo Anthony

    2018-02-01

    Full Text Available We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package.

  7. The finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain

    Science.gov (United States)

    Göhmann, Frank; Hasenclever, Nils P.; Seel, Alexander

    2005-10-01

    We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length m. On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.

  8. Airspace Operations Demo Functional Requirements Matrix

    Science.gov (United States)

    2005-01-01

    The Flight IPT assessed the reasonableness of demonstrating each of the Access 5 Step 1 functional requirements. The functional requirements listed in this matrix are from the September 2005 release of the Access 5 Functional Requirements Document. The demonstration mission considered was a notional Western US mission (WUS). The conclusion of the assessment is that 90% of the Access 5 Step 1 functional requirements can be demonstrated using the notional Western US mission.

  9. The two-mass contribution to the three-loop pure singlet operator matrix element

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de; Schoenwald, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2017-11-15

    We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function F{sub 2}(x,Q{sup 2}) at O(α{sup 3}{sub s}) as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.

  10. String beta function equations from c=1 matrix model

    CERN Document Server

    Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R

    1995-01-01

    We derive the \\sigma-model tachyon \\beta-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c=1 matrix model. The tachyon \\beta-function equation is satisfied by a \\underbar{nonlocal} and \\underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c=1 matrix model. We also comment on the realization of the W-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c=1 matrix model.

  11. Fractional Vector Calculus and Fractional Special Function

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2010-01-01

    Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

  12. Off-shell two-particle scattering amplitude in the P-matrix approach

    International Nuclear Information System (INIS)

    Babenko, V.A.; Petrov, N.M.

    1988-01-01

    A generalization of the P-matrix approach which makes it possible to describe the interaction of two particles off the energy shell is proposed. Explicit separation in the wave function of a part corresponding to free motion yields a compact expression for the off-shell scattering amplitude and gives directly a method for separable expansion of the amplitude

  13. Sparse Matrix for ECG Identification with Two-Lead Features

    Directory of Open Access Journals (Sweden)

    Kuo-Kun Tseng

    2015-01-01

    Full Text Available Electrocardiograph (ECG human identification has the potential to improve biometric security. However, improvements in ECG identification and feature extraction are required. Previous work has focused on single lead ECG signals. Our work proposes a new algorithm for human identification by mapping two-lead ECG signals onto a two-dimensional matrix then employing a sparse matrix method to process the matrix. And that is the first application of sparse matrix techniques for ECG identification. Moreover, the results of our experiments demonstrate the benefits of our approach over existing methods.

  14. The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions

    KAUST Repository

    Huang, Jianhua Z.

    2009-12-01

    Two-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value decomposition (SVD) of the data matrix. We focus on a penalization approach and solve the nontrivial problem of constructing proper two-way penalties from oneway regression penalties. We introduce conditional cross-validated smoothing parameter selection whereby left-singular vectors are cross- validated conditional on right-singular vectors, and vice versa. The concept can be realized as part of an alternating optimization algorithm. In addition to the penalization approach, we briefly consider two-way regularization with basis expansion. The proposed methods are illustrated with one simulated and two real data examples. Supplemental materials available online show that several "natural" approaches to penalized SVDs are flawed and explain why so. © 2009 American Statistical Association.

  15. A New Method of Creating Technology/Function Matrix for Systematic Innovation without Expert

    Directory of Open Access Journals (Sweden)

    Tien-Yuan Cheng

    2012-02-01

    Full Text Available The technology/function matrix is comprised by specific technologies and functions, and through the technology/function matrix we can known what the technologies with functions have opportunities for innovation of product or technology. However, the technology/function matrix is very difficult to create, because the patents need to be read, analyzed and categorized into the technology/function matrix always more than hundreds or thousands. In this research, I propose a method to create a technology/function matrix just need to execute patent search without reading and analyzing patents. Through the proposed method anyone can create a technology/function matrix in a short time without experts’ help even if there are thousands of thousands of patents need to be read and analyzed.

  16. Algunas integrales impropias con límites de integración infinitos que involucran a la generalización τ de la función hipergeométrica de Gauss Some improper integrals with integration infinity limit involving generalizad hypergeometric function 2R1(a, b; c; τ ; z

    Directory of Open Access Journals (Sweden)

    Jaime Castillo Pérez

    2007-06-01

    Full Text Available En 1991 M. Dotsenko presentó una generalización de la función hipergeométrica de Gauss denotada por 2Rτ1 (z, estableciendo además tanto su representación en serie como también su representación integral. Es importante notar que en 1999 Nina Virchenko y luego, en el 2003, Leda Galué consideraron esta función, introduciendo un conjunto de fórmulas de recurrencia y de diferenciación las cuales permiten simplificar algunos cálculos complicados. Kalla y colaboradores estudiaron esta función y presentaron una nueva forma unificada de la función Gamma, luego en el 2006, Castillo y colaboradores presentaron algunas representaciones simples para ésta función. En este trabajo se establecen algunas integrales impropias con límites de integración infinitos que involucran a la generalización τ de la función hipergeométrica de Gauss 2R1(a, b; c; τ ; z.In 1991 M. Dotsenko presented a generalization of Gauss’ hypergeometric function refered as 2Rτ1(z, and established its representation in series and integral. It is important to remark that in 1999 Nina Virchenko and, later in 2003, Leda Galu´e considered this function by introducing a set of recurrence and differentiation formulas; they permit simplify some complicated calculus. Kalla et al estudied this function and they presented a new unified form of the gamma function. Later in 2006, Castillo et al present some simple representation for this function. Along this paper work some improper integrals with integration infinity limit involving generalized hypergeometric function2R1(a, b; c; τ ; z are displayed.

  17. Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

    Science.gov (United States)

    Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus

    2017-10-01

    We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

  18. Interpolation of rational matrix functions

    CERN Document Server

    Ball, Joseph A; Rodman, Leiba

    1990-01-01

    This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...

  19. Time-dependent occupation numbers in reduced-density-matrix-functional theory: Application to an interacting Landau-Zener model

    International Nuclear Information System (INIS)

    Requist, Ryan; Pankratov, Oleg

    2011-01-01

    We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.

  20. Function Projective Synchronization of Two Identical New Hyperchaotic Systems

    International Nuclear Information System (INIS)

    Li Xin; Chen Yong

    2007-01-01

    A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.

  1. Generalized Mittag-Leffler Function and Its Properties

    Directory of Open Access Journals (Sweden)

    Banu Yılmaz Yaşar

    2014-12-01

    Full Text Available Recently, Srivastava, Çetinkaya and Kıymaz defined the generalized Pochhammer symbol and obtained some relations. In this paper, we define the generalized Mittag-Leffler function via the generalized Pochhammer symbol and present some recurrence relation, derivative properties, integral representation. Moreover, we obtain a relation between Wright hypergeometric function and the generalized Mittag-Leffler function.

  2. Reduced density matrix embedding. General formalism and inter-domain correlation functional.

    Science.gov (United States)

    Pernal, Katarzyna

    2016-08-03

    An embedding method for a one-electron reduced density matrix (1-RDM) is proposed. It is based on partitioning of 1-RDM into domains and describing each domain in the effective potential of the other ones. To assure N-representability of the total 1-RDM N-representability and strong-orthogonality conditions are imposed on the domains. The total energy is given as a sum of single-domain energies and domain-domain electron interaction contributions. Higher than two-body inter-domain interaction terms are neglected. The two-body correlation terms are approximated by deriving inter-domain correlation from couplings of density fluctuations of two domains at a time. Unlike in most density embedding methods kinetic energy is treated exactly and it is not required that densities pertaining to the domains are only weakly overlapping. We propose to treat each domain by a corrected perfect-pairing functional. On a few examples it is shown that the embedding reduced density matrix functional method (ERDMF) yields excellent results for molecules that are well described by a single Lewis structure even if strong static intra-domain or dynamic inter-domain correlation effects must be accounted for.

  3. Some exact Bradlow vortex solutions

    Energy Technology Data Exchange (ETDEWEB)

    Gudnason, Sven Bjarke [Institute of Modern Physics, Chinese Academy of Sciences,Lanzhou 730000 (China); Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)

    2017-05-08

    We consider the Bradlow equation for vortices which was recently found by Manton and find a two-parameter class of analytic solutions in closed form on nontrivial geometries with non-constant curvature. The general solution to our class of metrics is given by a hypergeometric function and the area of the vortex domain by the Gaussian hypergeometric function.

  4. Recovery of the Dirac system from the rectangular Weyl matrix function

    International Nuclear Information System (INIS)

    Fritzsche, B; Kirstein, B; Roitberg, I Ya; Sakhnovich, A L

    2012-01-01

    Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are studied for such Weyl functions, and some results are new even for the square Weyl functions. High-energy asymptotics of Weyl functions and Borg–Marchenko-type uniqueness results are derived too. (paper)

  5. Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

    International Nuclear Information System (INIS)

    Dzhamay, Anton

    2009-01-01

    We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

  6. Universality of correlation functions in random matrix models of QCD

    International Nuclear Information System (INIS)

    Jackson, A.D.; Sener, M.K.; Verbaarschot, J.J.M.

    1997-01-01

    We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a schematic temperature dependence. We calculate the correlation functions analytically using the technique of Itzykson-Zuber integrals for arbitrary complex supermatrices. An alternative exact calculation for arbitrary matrix size is given for the special case of zero temperature, and we reproduce the well-known Laguerre kernel. At finite temperature, the microscopic limit of the correlation functions are calculated in the saddle-point approximation. The main result of this paper is that the microscopic universality of correlation functions is maintained even though unitary invariance is broken by the addition of a deterministic matrix to the ensemble. (orig.)

  7. Decay of autoionizing states in time-dependent density functional and reduced density matrix functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

    2013-07-01

    Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

  8. Conformal four point functions and the operator product expansion

    International Nuclear Information System (INIS)

    Dolan, F.A.; Osborn, H.

    2001-01-01

    Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z,x which are simply related to u,v. The operator product expansion analysis is applied to the explicit expressions for the four point function found for free scalar, fermion and vector field theories in four dimensions. The results for four point functions obtained by using the AdS/CFT correspondence are also analysed in terms of functions related to those appearing in the operator product discussion

  9. The chiral Gaussian two-matrix ensemble of real asymmetric matrices

    International Nuclear Information System (INIS)

    Akemann, G; Phillips, M J; Sommers, H-J

    2010-01-01

    We solve a family of Gaussian two-matrix models with rectangular N x (N + ν) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter μ. Our model can be thought of as the chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class. It has the property that its eigenvalues are either real, purely imaginary or come in complex conjugate eigenvalue pairs. The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions. All n-point density correlation functions are expressed for finite N in terms of a Pfaffian form. This contains a kernel involving Laguerre polynomials in the complex plane as a building block which was previously computed by the authors. This kernel can be expressed in terms of the kernel for complex non-Hermitian matrices, generalizing the known relation among ensembles of Hermitian random matrices. Compact expressions are given for the density at finite N as an example, as well as its microscopic large-N limits at the origin for fixed ν at strong and weak non-Hermiticity.

  10. Differential analysis of matrix convex functions

    DEFF Research Database (Denmark)

    Hansen, Frank; Tomiyama, Jun

    2007-01-01

    We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for ma...

  11. Specialisation of extracellular matrix for function in tendons and ligaments

    Science.gov (United States)

    Birch, Helen L.; Thorpe, Chavaunne T.; Rumian, Adam P.

    2013-01-01

    Summary Tendons and ligaments are similar structures in terms of their composition, organisation and mechanical properties. The distinction between them stems from their anatomical location; tendons form a link between muscle and bone while ligaments link bones to bones. A range of overlapping functions can be assigned to tendon and ligaments and each structure has specific mechanical properties which appear to be suited for particular in vivo function. The extracellular matrix in tendon and ligament varies in accordance with function, providing appropriate mechanical properties. The most useful framework in which to consider extracellular matrix differences therefore is that of function rather than anatomical location. In this review we discuss what is known about the relationship between functional requirements, structural properties from molecular to gross level, cellular gene expression and matrix turnover. The relevance of this information is considered by reviewing clinical aspects of tendon and ligament repair and reconstructive procedures. PMID:23885341

  12. Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    2010-01-01

    textabstractExpansions in terms of Bessel functions are considered of the Kummer function ${}_1F_1(a;c,z)$ (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic

  13. Clebsch-Gordan and Racah coefficients of SUpq(2)

    International Nuclear Information System (INIS)

    Kachurik, I.I.

    1993-01-01

    Explicit expressions for the Clebsch-Gordan coefficients and for the Racah coefficients of the two-parametric quantum algebra SU pq (2) are derived. They are given as finite sums and as terminating basic hypergeometric functions 3 φ 2 and 4 φ 3 . It is indicated how other expressions for these coefficients can be derived with the help of basic hypergeometric functions. (author). 11 refs

  14. Two-body density matrix for closed s-d shell nuclei

    International Nuclear Information System (INIS)

    Dimitrova, S.S.; Kadrev, D.N.; Antonov, A.N.; Stoitsov, M.V.

    2000-01-01

    The two-body density matrix for 4 He, 16 O and 40 Ca within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated. (orig.)

  15. A two-loop test of M(atrix) theory

    International Nuclear Information System (INIS)

    Becker, K.

    1997-01-01

    We consider the scattering of two Dirichlet zero-branes in M(atrix) theory. Using the formulation of M(atrix) theory in terms of ten-dimensional super Yang-Mills theory dimensionally reduced to (0+1) dimensions, we obtain the effective (velocity-dependent) potential describing these particles. At one loop we obtain the well-known result for the leading order of the effective potential V eff ∝v 4 /r 7 , where v and r are the relative velocity and distance between the two zero-branes, respectively. A calculation of the effective potential at two loops shows that no renormalizations of the v 4 term of the effective potential occur at this order. (orig.)

  16. One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings

    Directory of Open Access Journals (Sweden)

    Tsunehide Kuroki

    2017-06-01

    Full Text Available In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond–Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.

  17. One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings

    Energy Technology Data Exchange (ETDEWEB)

    Kuroki, Tsunehide, E-mail: kuroki@dg.kagawa-nct.ac.jp [General Eduction, National Institute of Technology, Kagawa College, 551 Kohda, Takuma-cho, Mitoyo, Kagawa 769-1192 (Japan); Sugino, Fumihiko, E-mail: fusugino@gmail.com [Okayama Institute for Quantum Physics, Furugyocho 1-7-36, Naka-ku, Okayama 703-8278 (Japan)

    2017-06-15

    In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond–Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.

  18. One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings

    International Nuclear Information System (INIS)

    Kuroki, Tsunehide; Sugino, Fumihiko

    2017-01-01

    In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond–Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.

  19. Special functions for scientists and engineers

    CERN Document Server

    Bell, William Wallace

    1968-01-01

    Clear and comprehensive, this text provides undergraduates with a straightforward guide to special functions. It is equally suitable as a reference volume for professionals, and readers need no higher level of mathematical knowledge beyond elementary calculus. Topics include the solution of second-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; Gegenbauer and Jacobi polynomials; and hypergeometric and other special functions. Three appendices offer convenient t

  20. Matrix intensification alters avian functional group composition in adjacent rainforest fragments.

    Directory of Open Access Journals (Sweden)

    Justus P Deikumah

    Full Text Available Conversion of farmland land-use matrices to surface mining is an increasing threat to the habitat quality of forest remnants and their constituent biota, with consequences for ecosystem functionality. We evaluated the effects of matrix type on bird community composition and the abundance and evenness within avian functional groups in south-west Ghana. We hypothesized that surface mining near remnants may result in a shift in functional composition of avifaunal communities, potentially disrupting ecological processes within tropical forest ecosystems. Matrix intensification and proximity to the remnant edge strongly influenced the abundance of members of several functional guilds. Obligate frugivores, strict terrestrial insectivores, lower and upper strata birds, and insect gleaners were most negatively affected by adjacent mining matrices, suggesting certain ecosystem processes such as seed dispersal may be disrupted by landscape change in this region. Evenness of these functional guilds was also lower in remnants adjacent to surface mining, regardless of the distance from remnant edge, with the exception of strict terrestrial insectivores. These shifts suggest matrix intensification can influence avian functional group composition and related ecosystem-level processes in adjacent forest remnants. The management of matrix habitat quality near and within mine concessions is important for improving efforts to preserveavian biodiversity in landscapes undergoing intensification such as through increased surface mining.

  1. Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

    International Nuclear Information System (INIS)

    Itagaki, Masafumi; Sahashi, Naoki.

    1997-01-01

    The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

  2. Matrix Transfer Function Design for Flexible Structures: An Application

    Science.gov (United States)

    Brennan, T. J.; Compito, A. V.; Doran, A. L.; Gustafson, C. L.; Wong, C. L.

    1985-01-01

    The application of matrix transfer function design techniques to the problem of disturbance rejection on a flexible space structure is demonstrated. The design approach is based on parameterizing a class of stabilizing compensators for the plant and formulating the design specifications as a constrained minimization problem in terms of these parameters. The solution yields a matrix transfer function representation of the compensator. A state space realization of the compensator is constructed to investigate performance and stability on the nominal and perturbed models. The application is made to the ACOSSA (Active Control of Space Structures) optical structure.

  3. Matrix method for two-dimensional waveguide mode solution

    Science.gov (United States)

    Sun, Baoguang; Cai, Congzhong; Venkatesh, Balajee Seshasayee

    2018-05-01

    In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a 'folded' plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.

  4. A real-space stochastic density matrix approach for density functional electronic structure.

    Science.gov (United States)

    Beck, Thomas L

    2015-12-21

    The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

  5. A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

    Science.gov (United States)

    Tenney, D. R.

    1974-01-01

    The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

  6. Families of Meromorphic Multivalent Functions Associated with the Dziok-Raina Operator

    Directory of Open Access Journals (Sweden)

    G. Murugusundaramoorthy

    2013-07-01

    Full Text Available Making use a linear operator, which is defined here by means of the Hadamard product (or convolution, involving the Wright’s generalized hypergeometric function , we introduce two novel subclassesP p(q,s,α1;A,B,λ andP+p(q,s,α1;A,B,λ of meromorphically multivalent functions oforder λ(0 ≤ λ < p in the punctured disc U∗. In this paper we investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions . We also derive many interesting results for the Hadamard products of functions belonging to the classP+p(q,s,α1;A,B,λ.

  7. Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

    Science.gov (United States)

    Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri

    2015-09-08

    We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

  8. Exact 2-point function in Hermitian matrix model

    International Nuclear Information System (INIS)

    Morozov, A.; Shakirov, Sh.

    2009-01-01

    J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.

  9. Marichev-Saigo-Maeda fractional integration operators of the Bassel functions

    Directory of Open Access Journals (Sweden)

    Sunil D. Purohit

    2012-05-01

    Full Text Available In this paper, we apply generalized operators of fractional integration involving Appell’s function F_3 (. due to Marichev-Saigo-Maeda, to the Bessel function of first kind. The results are expressed in terms of generalized Wright function and hypergeometric functions _pF_q . Special cases involving this function are mentioned. Results given recently by Kilbas and Sebastian follow as special cases of the theorems establish here.

  10. Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

    International Nuclear Information System (INIS)

    Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin

    2014-01-01

    This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)

  11. Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses

    Directory of Open Access Journals (Sweden)

    J. Ablinger

    2017-08-01

    Full Text Available Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=mc2/mb2∼1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.

  12. Extracellular matrix hydrogels from decellularized tissues: Structure and function.

    Science.gov (United States)

    Saldin, Lindsey T; Cramer, Madeline C; Velankar, Sachin S; White, Lisa J; Badylak, Stephen F

    2017-02-01

    Extracellular matrix (ECM) bioscaffolds prepared from decellularized tissues have been used to facilitate constructive and functional tissue remodeling in a variety of clinical applications. The discovery that these ECM materials could be solubilized and subsequently manipulated to form hydrogels expanded their potential in vitro and in vivo utility; i.e. as culture substrates comparable to collagen or Matrigel, and as injectable materials that fill irregularly-shaped defects. The mechanisms by which ECM hydrogels direct cell behavior and influence remodeling outcomes are only partially understood, but likely include structural and biological signals retained from the native source tissue. The present review describes the utility, formation, and physical and biological characterization of ECM hydrogels. Two examples of clinical application are presented to demonstrate in vivo utility of ECM hydrogels in different organ systems. Finally, new research directions and clinical translation of ECM hydrogels are discussed. More than 70 papers have been published on extracellular matrix (ECM) hydrogels created from source tissue in almost every organ system. The present manuscript represents a review of ECM hydrogels and attempts to identify structure-function relationships that influence the tissue remodeling outcomes and gaps in the understanding thereof. There is a Phase 1 clinical trial now in progress for an ECM hydrogel. Copyright © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

  13. New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

    Science.gov (United States)

    Abd-Elhameed, W. M.

    2017-07-01

    In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

  14. Scattering of long folded strings and mixed correlators in the two-matrix model

    International Nuclear Information System (INIS)

    Bourgine, J.-E.; Hosomichi, K.; Kostov, I.; Matsuo, Y.

    2008-01-01

    We study the interactions of Maldacena's long folded strings in two-dimensional string theory. We find the amplitude for a state containing two long folded strings to come and go back to infinity. We calculate this amplitude both in the worldsheet theory and in the dual matrix model, the matrix quantum mechanics. The matrix model description allows to evaluate the amplitudes involving any number of long strings, which are given by the mixed trace correlators in an effective two-matrix model

  15. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-01

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  16. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-21

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  17. Some Families of the Incomplete H-Functions and the Incomplete \\overline H -Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications

    Science.gov (United States)

    Srivastava, H. M.; Saxena, R. K.; Parmar, R. K.

    2018-01-01

    Our present investigation is inspired by the recent interesting extensions (by Srivastava et al. [35]) of a pair of the Mellin-Barnes type contour integral representations of their incomplete generalized hypergeometric functions p γ q and p Γ q by means of the incomplete gamma functions γ( s, x) and Γ( s, x). Here, in this sequel, we introduce a family of the relatively more general incomplete H-functions γ p,q m,n ( z) and Γ p,q m,n ( z) as well as their such special cases as the incomplete Fox-Wright generalized hypergeometric functions p Ψ q (γ) [ z] and p Ψ q (Γ) [ z]. The main object of this paper is to study and investigate several interesting properties of these incomplete H-functions, including (for example) decomposition and reduction formulas, derivative formulas, various integral transforms, computational representations, and so on. We apply some substantially general Riemann-Liouville and Weyl type fractional integral operators to each of these incomplete H-functions. We indicate the easilyderivable extensions of the results presented here that hold for the corresponding incomplete \\overline H -functions as well. Potential applications of many of these incomplete special functions involving (for example) probability theory are also indicated.

  18. Duality of two-point functions for confined non-relativistic quark-antiquark systems

    International Nuclear Information System (INIS)

    Fishbane, P.M.; Gasiorowicz, S.G.; Kaus, P.

    1985-01-01

    An analog to the scattering matrix describes the spectrum and high-energy behavior of confined systems. We show that for non-relativistic systems this S-matrix is identical to a two-point function which transparently describes the bound states for all angular momenta. Confined systems can thus be described in a dual fashion. This result makes it possible to study the modification of linear trajectories (originating in a long-range confining potential) due to short range forces which are unknown except for the way in which they modify the asymptotic behavior of the two point function. A type of effective range expansion is one way to calculate the energy shifts. 9 refs

  19. Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); IHES, Bures-sur-Yvette (France)

    2017-05-15

    Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m{sup 2}{sub c}/m{sup 2}{sub b}∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A{sup (3)}{sub gq}. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A{sub gg}. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.

  20. Extended Riemann-Liouville type fractional derivative operator with applications

    Directory of Open Access Journals (Sweden)

    Agarwal P.

    2017-12-01

    Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.

  1. Wiener-Hopf factorization of piecewise meromorphic matrix-valued functions

    International Nuclear Information System (INIS)

    Adukov, Victor M

    2009-01-01

    Let D + be a multiply connected domain bounded by a contour Γ, let D - be the complement of D + union Γ in C-bar=C union {∞}, and a(t) be a continuous invertible matrix-valued function on Γ which can be meromorphically extended into the open disconnected set D - (as a piecewise meromorphic matrix-valued function). An explicit solution of the Wiener-Hopf factorization problem for a(t) is obtained and the partial factorization indices of a(t) are calculated. Here an explicit solution of a factorization problem is meant in the sense of reducing it to the investigation of finitely many systems of linear algebraic equations with matrices expressed in closed form, that is, in quadratures. Bibliography: 15 titles.

  2. Nuclear matrix and structural and functional compartmentalization of the eucaryotic cell nucleus.

    Science.gov (United States)

    Razin, S V; Borunova, V V; Iarovaia, O V; Vassetzky, Y S

    2014-07-01

    Becoming popular at the end of the 20th century, the concept of the nuclear matrix implies the existence of a nuclear skeleton that organizes functional elements in the cell nucleus. This review presents a critical analysis of the results obtained in the study of nuclear matrix in the light of current views on the organization of the cell nucleus. Numerous studies of nuclear matrix have failed to provide evidence of the existence of such a structure. Moreover, the existence of a filamentous structure that supports the nuclear compartmentalization appears to be unnecessary, since this function is performed by the folded genome itself.

  3. Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter.

    Science.gov (United States)

    Yi, Sun; Nelson, Patrick W; Ulsoy, A Galip

    2007-04-01

    In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.

  4. Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions

    OpenAIRE

    Yaşar, Banu Yılmaz; Özarslan, Mehmet Ali

    2016-01-01

    In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\\i}ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions. Applied Mathematics and Computation, 2014, 226 : 484-491] is defined. Several potentially useful properties of the unified family such as generating function, integral representation, Laplace transform and Mellin tran...

  5. The Einstein action for algebras of matrix valued functions - Toy models

    International Nuclear Information System (INIS)

    Hajac, P.M.

    1995-10-01

    Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for M 4 (R). It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made. (author). 14 refs

  6. One-point functions in AdS/dCFT from matrix product states

    International Nuclear Information System (INIS)

    Buhl-Mortensen, Isak; Leeuw, Marius de; Kristjansen, Charlotte; Zarembo, Konstantin

    2016-01-01

    One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k=2 result times a k-dependent pre-factor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k=2 and k=3 respectively. We furthermore find evidence that the matrix product states for k=2 and k=3 are related via a ratio of Baxter’s Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.

  7. Supersymmetry in random matrix theory

    International Nuclear Information System (INIS)

    Kieburg, Mario

    2010-01-01

    I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)

  8. Supersymmetry in random matrix theory

    Energy Technology Data Exchange (ETDEWEB)

    Kieburg, Mario

    2010-05-04

    I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)

  9. The structure and function of the pericellular matrix of articular cartilage.

    Science.gov (United States)

    Wilusz, Rebecca E; Sanchez-Adams, Johannah; Guilak, Farshid

    2014-10-01

    Chondrocytes in articular cartilage are surrounded by a narrow pericellular matrix (PCM) that is both biochemically and biomechanically distinct from the extracellular matrix (ECM) of the tissue. While the PCM was first observed nearly a century ago, its role is still under investigation. In support of early hypotheses regarding its function, increasing evidence indicates that the PCM serves as a transducer of biochemical and biomechanical signals to the chondrocyte. Work over the past two decades has established that the PCM in adult tissue is defined biochemically by several molecular components, including type VI collagen and perlecan. On the other hand, the biomechanical properties of this structure have only recently been measured. Techniques such as micropipette aspiration, in situ imaging, computational modeling, and atomic force microscopy have determined that the PCM exhibits distinct mechanical properties as compared to the ECM, and that these properties are influenced by specific PCM components as well as disease state. Importantly, the unique relationships among the mechanical properties of the chondrocyte, PCM, and ECM in different zones of cartilage suggest that this region significantly influences the stress-strain environment of the chondrocyte. In this review, we discuss recent advances in the measurement of PCM mechanical properties and structure that further increase our understanding of PCM function. Taken together, these studies suggest that the PCM plays a critical role in controlling the mechanical environment and mechanobiology of cells in cartilage and other cartilaginous tissues, such as the meniscus or intervertebral disc. Copyright © 2014 International Society of Matrix Biology. Published by Elsevier B.V. All rights reserved.

  10. Patchwork structure-function analysis of the Sendai virus matrix protein.

    Science.gov (United States)

    Mottet-Osman, Geneviève; Miazza, Vincent; Vidalain, Pierre-Olivier; Roux, Laurent

    2014-09-01

    Paramyxoviruses contain a bi-lipidic envelope decorated by two transmembrane glycoproteins and carpeted on the inner surface with a layer of matrix proteins (M), thought to bridge the glycoproteins with the viral nucleocapsids. To characterize M structure-function features, a set of M domains were mutated or deleted. The genes encoding these modified M were incorporated into recombinant Sendai viruses and expressed as supplemental proteins. Using a method of integrated suppression complementation system (ISCS), the functions of these M mutants were analyzed in the context of the infection. Cellular membrane association, localization at the cell periphery, nucleocapsid binding, cellular protein interactions and promotion of viral particle formation were characterized in relation with the mutations. At the end, lack of nucleocapsid binding go together with lack of cell surface localization and both features definitely correlate with loss of M global function estimated by viral particle production. Copyright © 2014 Elsevier Inc. All rights reserved.

  11. Three-level models solvable in terms of the Clausen function

    International Nuclear Information System (INIS)

    Ishkhanyan, Artur; Suominen, Kalle-Antti

    2003-01-01

    The problem of analytical integrability of the three-level problem by reduction of the time-dependent Schroedinger equations to the third-order linear differential equation satisfied by the generalized hypergeometric functions 3 F 2 is considered. A total of 12 infinite classes of models solvable in terms of these functions is found, most of which are new and others are generalizations of the previously known families

  12. Genus one super-Green function revisited and superstring amplitudes with non-maximal supersymmetry

    International Nuclear Information System (INIS)

    Itoyama, H.; Yano, Kohei

    2016-01-01

    We reexamine genus one super-Green functions with general boundary conditions twisted by (α,β) for (σ,τ) directions in the eigenmode expansion and derive expressions as infinite series of hypergeometric functions. Using these, we compute one-loop superstring amplitudes with non-maximal supersymmetry, taking the example of massless vector emissions of open string type I Z 2 orbifold

  13. The Einstein action for algebras of matrix valued functions - Toy models

    Energy Technology Data Exchange (ETDEWEB)

    Hajac, P M

    1995-10-01

    Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for M{sub 4}(R). It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made. (author). 14 refs.

  14. Comment on "Nonuniqueness of algebraic first-order density-matrix functionals"

    Science.gov (United States)

    Gritsenko, O. V.

    2018-02-01

    Wang and Knowles (WK) [Phys. Rev. A 92, 012520 (2015), 10.1103/PhysRevA.92.012520] have given a counterexample to the conventional in reduced density-matrix functional theory representation of the second-order reduced density matrix (2RDM) Γi j ,k l in the basis of the natural orbitals as a function Γi j ,k l(n ) of the orbital occupation numbers (ONs) ni. The observed nonuniqueness of Γi j ,k l for prototype systems of different symmetry has been interpreted as the inherent inability of ON functions to reproduce the 2RDM, due to the insufficient information contained in the 1RDM spectrum. In this Comment, it is argued that, rather than totally invalidating Γi j ,k l(n ) , the WK example exposes its symmetry dependence which, as well as the previously established analogous dependence in density functional theory, is demonstrated with a general formulation based on the Levy constrained search.

  15. Degenerate T coefficients and their relation to Wigner's 3j symbols and the D function

    International Nuclear Information System (INIS)

    Kuznetsov, G.I.; Smorodinskij, Ya.A.

    1977-01-01

    On basis of various representations of the T coefficients and using limiting procedures, var//uios degenerate cases are studied for these coefficients and their relation This enables one to find relations between the hypergeometric function 4 F 3 (....1) and the functions 3 F 2 (...1) and 2 F 1 (...1/2)

  16. Computing wave functions in multichannel collisions with non-local potentials using the R-matrix method

    Science.gov (United States)

    Bonitati, Joey; Slimmer, Ben; Li, Weichuan; Potel, Gregory; Nunes, Filomena

    2017-09-01

    The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique combined with the Gauss quadrature for the Lagrange-mesh method to efficiently solve for the wave functions of projectile nuclei in low energy collisions (1-100 MeV) involving an arbitrary number of channels. We include the local Woods-Saxon potential, the non-local potential of Perey and Buck, a Coulomb potential, and a coupling potential to computationally solve for the wave function of two nuclei at short distances. Object oriented programming is used to increase modularity, and parallel programming techniques are introduced to reduce computation time. We conclude that the R-matrix method is an effective method to predict the wave functions of nuclei in scattering problems involving both multiple channels and non-local potentials. Michigan State University iCER ACRES REU.

  17. Generalized fractional integration of the \\overline{H}-function

    Directory of Open Access Journals (Sweden)

    Praveen Agarwal

    2012-11-01

    Full Text Available A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera. In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials inSaigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.

  18. A matrix model for WZW

    International Nuclear Information System (INIS)

    Dorey, Nick; Tong, David; Turner, Carl

    2016-01-01

    We study a U(N) gauged matrix quantum mechanics which, in the large N limit, is closely related to the chiral WZW conformal field theory. This manifests itself in two ways. First, we construct the left-moving Kac-Moody algebra from matrix degrees of freedom. Secondly, we compute the partition function of the matrix model in terms of Schur and Kostka polynomials and show that, in the large N limit, it coincides with the partition function of the WZW model. This same matrix model was recently shown to describe non-Abelian quantum Hall states and the relationship to the WZW model can be understood in this framework.

  19. Luigi Gatteschi's work on asymptotics of special functions and their zeros

    Science.gov (United States)

    Gautschi, Walter; Giordano, Carla

    2008-12-01

    A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

  20. Extended Krylov subspaces approximations of matrix functions. Application to computational electromagnetics

    Energy Technology Data Exchange (ETDEWEB)

    Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)

    1996-12-31

    There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.

  1. Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems

    International Nuclear Information System (INIS)

    Meer, R. van; Gritsenko, O. V.; Baerends, E. J.

    2014-01-01

    Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ω α and oscillator strengths f α for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ω α (R) curves along the bond dissociation coordinate R for the molecules LiH, Li 2 , and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate

  2. Impact of matrix stiffness on fibroblast function

    Energy Technology Data Exchange (ETDEWEB)

    El-Mohri, Hichem; Wu, Yang; Mohanty, Swetaparna; Ghosh, Gargi, E-mail: gargi@umich.edu

    2017-05-01

    Chronic non-healing wounds, caused by impaired production of growth factors and reduced vascularization, represent a significant burden to patients, health care professionals, and health care system. While several wound dressing biomaterials have been developed, the impact of the mechanical properties of the dressings on the residing cells and consequently on the healing of the wounds is largely overlooked. The primary focus of this study is to explore whether manipulation of the substrate mechanics can regulate the function of fibroblasts, particularly in the context of their angiogenic activity. A photocrosslinkable hydrogel platform with orthogonal control over gel modulus and cell adhesive sites was developed to explore the quantitative relationship between ECM compliance and fibroblast function. Increase in matrix stiffness resulted in enhanced fibroblast proliferation and stress fiber formation. However, the angiogenic activity of fibroblasts was found to be optimum when the cells were seeded on compliant matrices. Thus, the observations suggest that the stiffness of the wound dressing material may play an important role in the progression of wound healing. - Highlights: • Proliferation and stress fiber formation of fibroblasts increase with increasing matrix mechanics. • Cell area correlates with the growth of fibroblasts. • Angiogenic activity of fibroblasts optimum when cells seeded on compliant gels.

  3. Analytic result for the one-loop scalar pentagon integral with massless propagators

    International Nuclear Information System (INIS)

    Kniehl, Bernd A.; Tarasov, Oleg V.

    2010-01-01

    The method of dimensional recurrences proposed by one of the authors (O. V.Tarasov, 1996) is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F 3 and the Gauss hypergeometric function 2 F 1 , both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions 2 F 1 . For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions 2 F 1 are presented in d=2-2ε, 4-2ε, and 6-2ε dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2ε dimensions is given in terms of the Appell function F 3 and the Gauss hypergeometric function 2 F 1 . (orig.)

  4. Analytic result for the one-loop scalar pentagon integral with massless propagators

    International Nuclear Information System (INIS)

    Kniehl, Bernd A.; Tarasov, Oleg V.

    2010-01-01

    The method of dimensional recurrences proposed by Tarasov (1996, 2000) is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F 3 and the Gauss hypergeometric function 2 F 1 , both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions 2 F 1 . For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions 2 F 1 are presented in d=2-2ε, 4-2ε, and 6-2ε dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2ε dimensions is given in terms of the Appell function F 3 and the Gauss hypergeometric function 2 F 1 .

  5. Three-level models solvable in terms of the Clausen function

    Energy Technology Data Exchange (ETDEWEB)

    Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak-2, 378410 (Armenia); Suominen, Kalle-Antti [Helsinki Institute of Physics, PL 64, FIN-00014 Helsingin yliopisto (Finland)

    2003-07-04

    The problem of analytical integrability of the three-level problem by reduction of the time-dependent Schroedinger equations to the third-order linear differential equation satisfied by the generalized hypergeometric functions {sub 3}F{sub 2} is considered. A total of 12 infinite classes of models solvable in terms of these functions is found, most of which are new and others are generalizations of the previously known families.

  6. Two Distinct Isoforms of Matrix Metalloproteinase-2 Are Associated with Human Delayed Kidney Graft Function.

    Directory of Open Access Journals (Sweden)

    Shaynah Wanga

    Full Text Available Delayed graft function (DGF is a frequent complication of renal transplantation, particularly in the setting of transplantation of kidneys derived from deceased donors and expanded-criteria donors. DGF results from tubular epithelial cell injury and has immediate and long term consequences. These include requirement for post-transplantation dialysis, increased incidence of acute rejection, and poorer long-term outcomes. DGF represents one of the clearest clinical examples of renal acute ischemia/reperfusion injury. Experimental studies have demonstrated that ischemia/reperfusion injury induces the synthesis of the full length secreted isoform of matrix metalloproteinase-2 (FL-MMP-2, as well as an intracellular N-terminal truncated MMP-2 isoform (NTT-MMP-2 that initiates an innate immune response. We hypothesized that the two MMP-2 isoforms mediate tubular epithelial cell injury in DGF. Archival renal biopsy sections from 10 protocol biopsy controls and 41 cases with a clinical diagnosis of DGF were analyzed for the extent of tubular injury, expression of the FL-MMP-2 and NTT-MMP-2 isoforms by immunohistochemistry (IHC, in situ hybridization, and qPCR to determine isoform abundance. Differences in transcript abundance were related to tubular injury score. Markers of MMP-2-mediated injury included TUNEL staining and assessment of peritubular capillary density. There was a clear relationship between tubular epithelial cell expression of both FL-MMP-2 and NTT-MMP-2 IHC with the extent of tubular injury. The MMP-2 isoforms were detected in the same tubular segments and were present at sites of tubular injury. qPCR demonstrated highly significant increases in both the FL-MMP-2 and NTT-MMP-2 transcripts. Statistical analysis revealed highly significant associations between FL-MMP-2 and NTT-MMP-2 transcript abundance and the extent of tubular injury, with NTT-MMP-2 having the strongest association. We conclude that two distinct MMP-2 isoforms are

  7. An application of hypergeometric functions to a problem in function theory

    Directory of Open Access Journals (Sweden)

    Daniel S. Moak

    1984-01-01

    Full Text Available In some recent work in univalent function theory, Aharonov, Friedland, and Brannan studied the series (1+xtα(1−tβ=∑n=0∞An(α,β(xtn. Brannan posed the problem of determining S={(α,β:|An(α,β(eiθ|0,   β>0,   n=1,2,3,…}. Brannan showed that if β≥α≥0, and α+β≥2, then (α,β∈S. He also proved that (α,1∈S for α≥1. Brannan showed that for 0|A2k(α,1(1| for k any integer. In this paper, we show that (α,β∈S for α≥1 and β≥1.

  8. Relative Contribution of Matrix Structure, Patch Resources and Management to the Local Densities of Two Large Blue Butterfly Species.

    Science.gov (United States)

    Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal

    2016-01-01

    The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.

  9. Relative Contribution of Matrix Structure, Patch Resources and Management to the Local Densities of Two Large Blue Butterfly Species

    Science.gov (United States)

    Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal

    2016-01-01

    The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942

  10. Closed-Form Representations of the Density Function and Integer Moments of the Sample Correlation Coefficient

    Directory of Open Access Journals (Sweden)

    Serge B. Provost

    2015-07-01

    Full Text Available This paper provides a simplified representation of the exact density function of R, the sample correlation coefficient. The odd and even moments of R are also obtained in closed forms. Being expressed in terms of generalized hypergeometric functions, the resulting representations are readily computable. Some numerical examples corroborate the validity of the results derived herein.

  11. On functional determinants of matrix differential operators with multiple zero modes

    NARCIS (Netherlands)

    Falco, G.M.; Fedorenko, Andrey A; Gruzberg, Ilya A

    2017-01-01

    We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of $r\\times r$ matrix second order differential

  12. Statistical Analysis of the Figure of Merit of a Two-Level Thermoelectric System: A Random Matrix Approach

    KAUST Repository

    Abbout, Adel; Ouerdane, Henni; Goupil, Christophe

    2016-01-01

    Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.

  13. Statistical Analysis of the Figure of Merit of a Two-Level Thermoelectric System: A Random Matrix Approach

    KAUST Repository

    Abbout, Adel

    2016-08-05

    Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.

  14. Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator

    Directory of Open Access Journals (Sweden)

    Kunle Adegoke

    2016-01-01

    Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.

  15. Analytic continuation of massless two-loop four-point functions

    International Nuclear Information System (INIS)

    Gehrmann, T.; Remiddi, E.

    2002-01-01

    We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like 1→3 decay to Minkowskian regions relevant to all 1→3 and 2→2 reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron-positron annihilation. (author)

  16. Analysis of the half-projected Hartree--Fock function: density matrix, natural orbitals, and configuration interaction equivalence

    International Nuclear Information System (INIS)

    Smeyers, Y.G.; Delgado-Barrio, G.

    1976-01-01

    The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized

  17. Endothelial cell-derived matrix promotes the metabolic functional maturation of hepatocyte via integrin-Src signalling.

    Science.gov (United States)

    Guo, Xinyue; Li, Weihong; Ma, Minghui; Lu, Xin; Zhang, Haiyan

    2017-11-01

    The extracellular matrix (ECM) microenvironment is involved in the regulation of hepatocyte phenotype and function. Recently, the cell-derived extracellular matrix has been proposed to represent the bioactive and biocompatible materials of the native ECM. Here, we show that the endothelial cell-derived matrix (EC matrix) promotes the metabolic maturation of human adipose stem cell-derived hepatocyte-like cells (hASC-HLCs) through the activation of the transcription factor forkhead box protein A2 (FOXA2) and the nuclear receptors hepatocyte nuclear factor 4 alpha (HNF4α) and pregnane X receptor (PXR). Reducing the fibronectin content in the EC matrix or silencing the expression of α5 integrin in the hASC-HLCs inhibited the effect of the EC matrix on Src phosphorylation and hepatocyte maturation. The inhibition of Src phosphorylation using the inhibitor PP2 or silencing the expression of Src in hASC-HLCs also attenuated the up-regulation of the metabolic function of hASC-HLCs in a nuclear receptor-dependent manner. These data elucidate integrin-Src signalling linking the extrinsic EC matrix signals and metabolic functional maturation of hepatocyte. This study provides a model for studying the interaction between hepatocytes and non-parenchymal cell-derived matrix. © 2017 The Authors. Journal of Cellular and Molecular Medicine published by John Wiley & Sons Ltd and Foundation for Cellular and Molecular Medicine.

  18. The universal R-matrix and its associated quantum algebra as functionals of the classical r-matrix: the sl2 case

    International Nuclear Information System (INIS)

    Freidel, L.; Maillet, J.M.

    1992-09-01

    Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra U h (sl 2 ) and its universal quantum R-matrix are explicitly constructed as functionals of the associated classical r-matrix. In this framework, the quantum algebra U h (sl 2 ) is naturally imbedded in the universal enveloping algebra of the sl 2 current algebra. (author) 13 refs

  19. Generating matrix elements of the hamiltonian of the algebraic version of resonating group method on intrinsic wave functions with various oscillator lengths

    International Nuclear Information System (INIS)

    Badalov, S.A.; Filippov, G.F.

    1986-01-01

    The receipts to calculate the generating matrix elements of the algebraic version of resonating group method (RGM) are given for two- and three-cluster nucleon systems, the center of mass motion being separeted exactly. For the Hamiltonian with Gaussian nucleon-nucleon potential dependence the generating matrix elements of the RGM algebraic version can be written down explictly if matrix elements of the corresponding system on wave functions of the Brink cluster model are known

  20. Three-loop SM beta-functions for matrix Yukawa couplings

    Directory of Open Access Journals (Sweden)

    A.V. Bednyakov

    2014-10-01

    Full Text Available We present the extension of our previous results for three-loop Yukawa coupling beta-functions to the case of complex Yukawa matrices describing the flavour structure of the SM. The calculation is carried out in the context of unbroken phase of the SM with the help of the MINCER program in a general linear gauge and cross-checked by means of MATAD/BAMBA codes. In addition, ambiguities in Yukawa matrix beta-functions are studied.

  1. Analytic result for the one-loop scalar pentagon integral with massless propagators

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A.; Tarasov, Oleg V. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

    2010-01-15

    The method of dimensional recurrences proposed by one of the authors (O. V.Tarasov, 1996) is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F{sub 3} and the Gauss hypergeometric function {sub 2}F{sub 1}, both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions {sub 2}F{sub 1}. For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions {sub 2}F{sub 1} are presented in d=2-2{epsilon}, 4-2{epsilon}, and 6-2{epsilon} dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2{epsilon} dimensions is given in terms of the Appell function F{sub 3} and the Gauss hypergeometric function {sub 2}F{sub 1}. (orig.)

  2. Reduced density-matrix functional theory: Correlation and spectroscopy.

    Science.gov (United States)

    Di Sabatino, S; Berger, J A; Reining, L; Romaniello, P

    2015-07-14

    In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

  3. The theory of contractions of 2D 2nd order quantum superintegrable systems and its relation to the Askey scheme for hypergeometric orthogonal polynomials

    International Nuclear Information System (INIS)

    Miller, Willard Jr

    2014-01-01

    We describe a contraction theory for 2nd order superintegrable systems, showing that all such systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. Analogously, all of the quadratic symmetry algebras of these systems can be obtained by a sequence of contractions starting from S9. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.This relates the scheme directly to explicitly solvable quantum mechanical systems. Amazingly, all of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2, C). The present paper concentrates on describing this intimate link between Lie algebra and superintegrable system contractions, with the detailed calculations presented elsewhere. Joint work with E. Kalnins, S. Post, E. Subag and R. Heinonen.

  4. Matrix thermalization

    International Nuclear Information System (INIS)

    Craps, Ben; Evnin, Oleg; Nguyen, Kévin

    2017-01-01

    Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

  5. Matrix thermalization

    Science.gov (United States)

    Craps, Ben; Evnin, Oleg; Nguyen, Kévin

    2017-02-01

    Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

  6. Matrix thermalization

    Energy Technology Data Exchange (ETDEWEB)

    Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University, Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Nguyen, Kévin [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)

    2017-02-08

    Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

  7. Values of the polygamma functions at rational arguments

    International Nuclear Information System (INIS)

    Choi, Junesang; Cvijovic, Djurdje

    2007-01-01

    Gauss in 1812, in his celebrated memoir on the hypergeometric series, presented a remarkable formula for the psi (or digamma) function, ψ(z), at rational arguments z, which can be expressed in terms of elementary functions. Davis in 1935 extended Gauss's result to the polygamma functions ψ (n) (z) (n element of N) by using a known series representation of ψ (n) (z) in an elementary yet technical way. Koelbig in 1996, in his CERN technical report, also gave two extensions to ψ (n) (z) by using the series definition of polylogarithm function and the above-known series representation. Here we aim at deriving general formulae expressing ψ (n) (z) (n element of N 0 ) as rational arguments in terms of other functions, which will be obtained in two ways. In addition, several special cases are also considered and, as a by-product of our main results, we derive, in a simple and unified manner, all formulae given by Gauss, Davis and Koelbig. Finally, it should be noted that all our results, in view of the relationship between ψ (n) (z) and the Hurwitz zeta function, ζ(s, a), could be rewritten in the representation of ζ(s, a)

  8. A bispectral q-hypergeometric basis for a class of quantum integrable models

    Science.gov (United States)

    Baseilhac, Pascal; Martin, Xavier

    2018-01-01

    For the class of quantum integrable models generated from the q-Onsager algebra, a basis of bispectral multivariable q-orthogonal polynomials is exhibited. In the first part, it is shown that the multivariable Askey-Wilson polynomials with N variables and N + 3 parameters introduced by Gasper and Rahman [Dev. Math. 13, 209 (2005)] generate a family of infinite dimensional modules for the q-Onsager algebra, whose fundamental generators are realized in terms of the multivariable q-difference and difference operators proposed by Iliev [Trans. Am. Math. Soc. 363, 1577 (2011)]. Raising and lowering operators extending those of Sahi [SIGMA 3, 002 (2007)] are also constructed. In the second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the N variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In the third part, eigenfunctions of the q-Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie's relations. In the fourth part, the analysis is extended to the special case q = 1. This framework provides a q-hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions (q ≠ 1).

  9. Structure and function of the interphotoreceptor matrix surrounding retinal photoreceptor cells.

    Science.gov (United States)

    Ishikawa, Makoto; Sawada, Yu; Yoshitomi, Takeshi

    2015-04-01

    The interphotoreceptor matrix (IPM) is a highly organized structure with interconnected domains surrounding cone and rod photoreceptor cells and extends throughout the subretinal space. Based on known roles of the extracellular matrix in other tissues, the IPM is thought to have several prominent functions including serving as a receptor for growth factors, regulating retinoid transport, participating in cytoskeletal organization in surrounding cells, and regulation of oxygen and nutrient transport. In addition, a number of studies suggest that the IPM also may play a significant role in the etiology of retinal degenerative disorders. In this review, we describe the present knowledge concerning the structure and function of the IPM under physiological and pathological conditions. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

  10. Analytic structure and power series expansion of the Jost function for the two-dimensional problem

    International Nuclear Information System (INIS)

    Rakityansky, S A; Elander, N

    2012-01-01

    For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. (paper)

  11. Random Correlation Matrix and De-Noising

    OpenAIRE

    Ken-ichi Mitsui; Yoshio Tabata

    2006-01-01

    In Finance, the modeling of a correlation matrix is one of the important problems. In particular, the correlation matrix obtained from market data has the noise. Here we apply the de-noising processing based on the wavelet analysis to the noisy correlation matrix, which is generated by a parametric function with random parameters. First of all, we show that two properties, i.e. symmetry and ones of all diagonal elements, of the correlation matrix preserve via the de-noising processing and the...

  12. The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications

    Directory of Open Access Journals (Sweden)

    Yirong Yao

    2013-01-01

    Full Text Available We solve optimization problems on the ranks and inertias of the quadratic Hermitian matrix function subject to a consistent system of matrix equations and . As applications, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities , and in the Löwner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.

  13. Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies

    DEFF Research Database (Denmark)

    Morningstar, Colin; Bulava, John; Singha, Bijit

    2017-01-01

    An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating...

  14. 1/2-BPS correlators as c = 1 S-matrix

    International Nuclear Information System (INIS)

    Jevicki, Antal; Yoneya, Tamiaki

    2007-01-01

    We argue from two complementary viewpoints of Holography that the 2-point correlation functions of 1/2-BPS multi-trace operators in the large-N (planar) limit are nothing but the (Wick-rotated) S-matrix elements of c = 1 matrix model. On the bulk side, we consider an Euclideanized version of the so-called bubbling geometries and show that the corresponding droplets reach the conformal boundary. Then the scattering matrix of fluctuations of the droplets gives directly the two-point correlators through the GKPW prescription. On the Yang-Mills side, we show that the two-point correlators of holomorphic and anti-holomorphic operators are essentially equivalent with the transformation functions between asymptotic in- and out-states of c = 1 matrix model. Extension to non-planar case is also discussed

  15. Off-energy-shell variations of two-nucleon transition matrix and three-nucleon problem

    International Nuclear Information System (INIS)

    Stingl, M.; Sauer, P.U.

    1975-01-01

    For a schematic three-nucleon problem, approximate analytic expressions are derived for the functional derivatives of measurable three-particle quantities with respect to off-shell variations of the triplet-s two-nucleon transition matrix. Those quantities include neutron-deuteron scattering lengths, trinucleon binding energies, and the 3 He charge form-factor minimum; correlations between off-shell changes in the latter two are discussed. An indication is given how results of this kind may be to decide whether or not a given set of discrepancies between calculated and experimental three-nucleon observables can be reconciled in terms of off-shell variations of a nonretarded hermitean two-nucleon interaction. The treatment is not restricted to special classes of phase-shift equivalent potentials or phase-shift preserving transformations but instead makes use of a systematic parameterization of off-shell variations in terms of symmetric rational approximants of increasing order

  16. On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions

    Directory of Open Access Journals (Sweden)

    Dumitru Baleanu

    2014-01-01

    Full Text Available A remarkably large number of fractional integral formulas involving the number of special functions, have been investigated by many authors. Very recently, Agarwal (National Academy Science Letters gave some integral transform and fractional integral formulas involving the Fpα,β·. In this sequel, here, we aim to establish some image formulas by applying generalized operators of the fractional integration involving Appell’s function F3(· due to Marichev-Saigo-Maeda. Some interesting special cases of our main results are also considered.

  17. Fabrication of Functionalized MOFs Incorporated Mixed Matrix Hollow Fiber Membrane for Gas Separation

    Directory of Open Access Journals (Sweden)

    Haitao Zhu

    2017-01-01

    Full Text Available The metal-organic framework (MOFs of MIL-53 was functionalized by aminosilane grafting and then incorporated into Ultem®1000 polymer matrix to fabricate mixed matrix hollow fiber membrane (MMHFM with high separation performance. SEM, XRD, and TGA were performed to characterize the functionalized MIL-53 and prepared MMHFM. The filler particles were embedded in membrane successfully and dispersed well in the polymer matrix. The incorporation of MOFs endowed MMHFM better thermal stability. Moreover, effects of solvent ratio in spinning dope, spinning condition, and testing temperature on gas separation performance of MMHFM were investigated. By optimizing dope composition, air gap distance, and bore fluid composition, MMHFM containing functionalized MIL-53 achieved excellent gas permeance and CO2/N2 selectivity. The CO2 permeance increased from 12.2 GPU for pure Ultem HFM to 30.9 GPU and the ideal CO2/N2 selectivity was enhanced from 25.4 to 34.7 simultaneously. Additionally, gas permeance increased but the selectivity decreased with the temperature increase, which followed the solution-diffusion based transport mechanism.

  18. Global unitary fixing and matrix-valued correlations in matrix models

    International Nuclear Information System (INIS)

    Adler, Stephen L.; Horwitz, Lawrence P.

    2003-01-01

    We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev-Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev-Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions

  19. On the structure and functions of gelatinase B/matrix metalloproteinase-9 in neuroinflammation.

    Science.gov (United States)

    Vandooren, Jennifer; Van Damme, Jo; Opdenakker, Ghislain

    2014-01-01

    The blood-brain barrier (BBB) is a specific structure that is composed of two basement membranes (BMs) and that contributes to the control of neuroinflammation. As long as the BBB is intact, extravasated leukocytes may accumulate between two BMs, generating vascular cuffs. Specific matrix metalloproteinases, MMP-2 and MMP-9, have been shown to cleave BBB beta-dystroglycan and to disintegrate thereby the parenchymal BM, resulting in encephalomyelitis. This knowledge has been added to the molecular basis of the REGA model to understand the pathogenesis of multiple sclerosis, and it gives further ground for the use of MMP inhibitors for the treatment of acute neuroinflammation. MMP-9 is associated with central nervous system inflammation and occurs in various forms: monomers and multimers. None of the various neurological and neuropathologic functions of MMP-9 have been associated with either molecular structure or molecular form, and therefore, in-depth structure-function studies are needed before medical intervention with MMP-9-specific inhibitors is initiated.

  20. Matrix metalloproteinase sensing via porous silicon microcavity devices functionalized with human antibodies

    Energy Technology Data Exchange (ETDEWEB)

    Martin, Marta; Gergely, Csilla [GES-UMR 5650, CNRS, Universite Montpellier 2, Pl. Eugene Bataillon 34095, Montpellier Cedex 5 (France); Taleb Bendiab, Chakib; Massif, Laurent; Cuisinier, Frederic [EA4203, Faculte d' Odontologie, Universite Montpellier 1, Montpellier Cedex 5 (France); Palestino, Gabriela [Facultad de Ciencias Quimicas, Universidad Autonoma de San Luis Potosi, Av. Salvador Nava 6, 78000 San Luis Potosi (Mexico); Agarwal, Vivechana [CIICAP, Universidad Autonoma del Estado de Morelos, Av. Universidad 1001, Col Chamilpa, Cuernavaca, Mor. (Mexico)

    2011-06-15

    Porous silicon microcavity (PSiMc) structures were used as support material for specific sensing of matrix metalloproteinases (MMPs). For lower concentrations of MMP-8, the structures were tested with two types of functionalization methods. Silanization of the oxidized porous silicon structures, followed by glutaraldehyde chemistry was found to give very inconsistent results. The use of biotinilated bovine serum albumin linked to the naked PSiMc was found to be an alternative method to attach the anti MMP-8 human antibody, previously modified with streptavidin, which was further used to sense MMP-8 (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  1. Hermite-Hadamard Type Integral Inequalities for Functions Whose Second-Order Mixed Derivatives Are Coordinated (s,m-P-Convex

    Directory of Open Access Journals (Sweden)

    Yu-Mei Bai

    2018-01-01

    Full Text Available We establish some new Hermite-Hadamard type integral inequalities for functions whose second-order mixed derivatives are coordinated (s,m-P-convex. An expression form of Hermite-Hadamard type integral inequalities via the beta function and the hypergeometric function is also presented. Our results provide a significant complement to the work of Wu et al. involving the Hermite-Hadamard type inequalities for coordinated (s,m-P-convex functions in an earlier article.

  2. Mimicking the extracellular matrix with functionalized, metal-assembled collagen peptide scaffolds.

    Science.gov (United States)

    Hernandez-Gordillo, Victor; Chmielewski, Jean

    2014-08-01

    Natural and synthetic three-dimensional (3-D) scaffolds that mimic the microenvironment of the extracellular matrix (ECM), with growth factor storage/release and the display of cell adhesion signals, offer numerous advantages for regenerative medicine and in vitro morphogenesis and oncogenesis modeling. Here we report the design of collagen mimetic peptides (CMPs) that assemble into a highly crosslinked 3-D matrix in response to metal ion stimuli, that may be functionalized with His-tagged cargoes, such as green fluorescent protein (GFP-His8) and human epidermal growth factor (hEGF-His6). The bound hEGF-His6 was found to gradually release from the matrix in vitro and induce cell proliferation in the EGF-dependent cell line MCF10A. The additional incorporation of a cell adhesion sequence (RGDS) at the N-terminus of the CMP creates an environment that facilitated the organization of matrix-encapsulated MCF10A cells into spheroid structures, thus mimicking the ECM environment. Copyright © 2014 Elsevier Ltd. All rights reserved.

  3. 3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS

    International Nuclear Information System (INIS)

    Hasselhuhn, Alexander

    2013-11-01

    In the present thesis several new contributions are made to achieve this goal. Different gauge-invariant subsets of graphs, i.e. whole color factors, are calculated, in order to break the ground for the systematic evaluation of new topologies and to develop corresponding computer algebra codes and computational algorithms to render a part of these problems. Furthermore, also some new results are obtained on the 2-loop level. The work focuses on the heavy quark corrections in the asymptotic region Q 2 >> m 2 , where the heavy flavor Wilson coefficients factorize into the light flavor Wilson coefficients and massive operator matrix elements. New contributions are obtained for the complete O(α s 3 n f T F 2 ) corrections to the operator matrix elements A gq,Q and A gg,Q . The computation of the Feynman integrals is performed using representations in generalized hypergeometric functions and finite sums. These sums are performed using modern symbolic summation methods implemented in the packages Sigma, Evaluate Multi Sums, and Sum Production. The results are renormalized and checked against Mellin moments. Furthermore, also the 2-loop corrections to the polarized massive OMEs ΔA gq,Q and ΔA gg,Q are calculated. Since the calculations are performed in dimensional regularization and Levi-Civita tensors are present in the diagrams, the OMEs are subject to a finite renormalization. New methods are developed to calculate genuine 3-loop topologies of ladder- and V-type, taking into account the number of heavy quark lines involved. The calculation methods involves mapping the Feynman parameterized representations onto multi-sums and using properties of Appell functions and other generalizations of hypergeometric functions. Two integrals are presented, for which the solution with summation methods remains yet an open problem. At three loops, for the first time also graphs with two distinct massive lines occur. A new method is presented for the calculation of such diagrams

  4. Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules.

    Science.gov (United States)

    Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M

    2016-10-11

    We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

  5. Knowledge Enrichment Analysis for Human Tissue- Specific Genes Uncover New Biological Insights

    Directory of Open Access Journals (Sweden)

    Gong Xiu-Jun

    2012-06-01

    Full Text Available The expression and regulation of genes in different tissues are fundamental questions to be answered in biology. Knowledge enrichment analysis for tissue specific (TS and housekeeping (HK genes may help identify their roles in biological process or diseases and gain new biological insights.In this paper, we performed the knowledge enrichment analysis for 17,343 genes in 84 human tissues using Gene Set Enrichment Analysis (GSEA and Hypergeometric Analysis (HA against three biological ontologies: Gene Ontology (GO, KEGG pathways and Disease Ontology (DO respectively.The analyses results demonstrated that the functions of most gene groups are consistent with their tissue origins. Meanwhile three interesting new associations for HK genes and the skeletal muscle tissuegenes are found. Firstly, Hypergeometric analysis against KEGG database for HK genes disclosed that three disease terms (Parkinson’s disease, Huntington’s disease, Alzheimer’s disease are intensively enriched.Secondly, Hypergeometric analysis against the KEGG database for Skeletal Muscle tissue genes shows that two cardiac diseases of “Hypertrophic cardiomyopathy (HCM” and “Arrhythmogenic right ventricular cardiomyopathy (ARVC” are heavily enriched, which are also considered as no relationship with skeletal functions.Thirdly, “Prostate cancer” is intensively enriched in Hypergeometric analysis against the disease ontology (DO for the Skeletal Muscle tissue genes, which is a much unexpected phenomenon.

  6. The dimer interface of the membrane type 1 matrix metalloproteinase hemopexin domain: crystal structure and biological functions.

    Science.gov (United States)

    Tochowicz, Anna; Goettig, Peter; Evans, Richard; Visse, Robert; Shitomi, Yasuyuki; Palmisano, Ralf; Ito, Noriko; Richter, Klaus; Maskos, Klaus; Franke, Daniel; Svergun, Dmitri; Nagase, Hideaki; Bode, Wolfram; Itoh, Yoshifumi

    2011-03-04

    Homodimerization is an essential step for membrane type 1 matrix metalloproteinase (MT1-MMP) to activate proMMP-2 and to degrade collagen on the cell surface. To uncover the molecular basis of the hemopexin (Hpx) domain-driven dimerization of MT1-MMP, a crystal structure of the Hpx domain was solved at 1.7 Å resolution. Two interactions were identified as potential biological dimer interfaces in the crystal structure, and mutagenesis studies revealed that the biological dimer possesses a symmetrical interaction where blades II and III of molecule A interact with blades III and II of molecule B. The mutations of amino acids involved in the interaction weakened the dimer interaction of Hpx domains in solution, and incorporation of these mutations into the full-length enzyme significantly inhibited dimer-dependent functions on the cell surface, including proMMP-2 activation, collagen degradation, and invasion into the three-dimensional collagen matrix, whereas dimer-independent functions, including gelatin film degradation and two-dimensional cell migration, were not affected. These results shed light on the structural basis of MT1-MMP dimerization that is crucial to promote cellular invasion.

  7. A Gordeyev integral for electrostatic waves in a magnetized plasma with a kappa velocity distribution

    International Nuclear Information System (INIS)

    Mace, R.L.

    2003-01-01

    A Gordeyev-type integral for the investigation of electrostatic waves in magnetized plasma having a kappa or generalized Lorentzian velocity distribution is derived. The integral readily reduces, in the unmagnetized and parallel propagation limits, to simple expressions involving the Z κ function. For propagation perpendicular to the magnetic field, it is shown that the Gordeyev integral can be written in closed form as a sum of two generalized hypergeometric functions, which permits easy analysis of the dispersion relation for electrostatic waves. Employing the same analytical techniques used for the kappa distribution, it is further shown that the well-known Gordeyev integral for a Maxwellian distribution can be written very concisely as a generalized hypergeometric function in the limit of perpendicular propagation. This expression, in addition to its mathematical conciseness, has other advantages over the traditional sum over modified Bessel functions form. Examples of the utility of these generalized hypergeometric series, especially how they simplify analyses of electrostatic waves propagating perpendicular to the magnetic field, are given. The new expression for the Gordeyev integral for perpendicular propagation is solved numerically to obtain the dispersion relations for the electrostatic Bernstein modes in a plasma with a kappa distribution

  8. Reduced density matrix functional theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Baldsiefen, Tim

    2012-10-15

    Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to

  9. Reduced density matrix functional theory at finite temperature

    International Nuclear Information System (INIS)

    Baldsiefen, Tim

    2012-10-01

    Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct

  10. Neutron-deuteron scattering calculations with W-matrix representation of the two-body input

    International Nuclear Information System (INIS)

    Bartnik, E.A.; Haberzettl, H.; Januschke, T.; Kerwath, U.; Sandhas, W.

    1987-05-01

    Employing the W-matrix representation of the partial-wave T matrix introduced by Bartnik, Haberzettl, and Sandhas, we show for the example of the Malfliet-Tjon potentials I and III that the single-term separable part of the W-matrix representation, when used as input in three-nucleon neutron-deuteron scattering calculations, is fully capable of reproducing the exact results obtained by Kloet and Tjon. This approximate two-body input not only satisfies the two-body off-shell unitarity relation but, moreover, it also contains a parameter which may be used in optimizing the three-body data. We present numerical evidence that there exists a variational (minimum) principle for the determination of the three-body binding energy which allows one to choose this parameter also in the absence of an exact reference calculation. Our results for neutron-deuteron scattering show that it is precisely this choice of the parameter which provides optimal scattering data. We conclude that the W-matrix approach, despite its simplicity, is a remarkably efficient tool for high-quality three-nucleon calculations. (orig.)

  11. Solution to urn models of pairwise interaction with application to social, physical, and biological sciences

    Science.gov (United States)

    Pickering, William; Lim, Chjan

    2017-07-01

    We investigate a family of urn models that correspond to one-dimensional random walks with quadratic transition probabilities that have highly diverse applications. Well-known instances of these two-urn models are the Ehrenfest model of molecular diffusion, the voter model of social influence, and the Moran model of population genetics. We also provide a generating function method for diagonalizing the corresponding transition matrix that is valid if and only if the underlying mean density satisfies a linear differential equation and express the eigenvector components as terms of ordinary hypergeometric functions. The nature of the models lead to a natural extension to interaction between agents in a general network topology. We analyze the dynamics on uncorrelated heterogeneous degree sequence networks and relate the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms.

  12. Spectral correlation functions of the sum of two independent complex Wishart matrices with unequal covariances

    International Nuclear Information System (INIS)

    Akemann, Gernot; Checinski, Tomasz; Kieburg, Mario

    2016-01-01

    We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random matrices. Typically ensembles with correlations among the matrix elements are much more difficult to solve. Using a combination of supersymmetry, superbosonisation and bi-orthogonal functions we are able to determine all spectral k -point density correlation functions of H for arbitrary matrix size N . In the half-degenerate case, when one of the covariance matrices is proportional to the identity, the recent results by Kumar for the joint eigenvalue distribution of H serve as our starting point. In this case the ensemble has a bi-orthogonal structure and we explicitly determine its kernel, providing its exact solution for finite N . The kernel follows from computing the expectation value of a single characteristic polynomial. In the general non-degenerate case the generating function for the k -point resolvent is determined from a supersymmetric evaluation of the expectation value of k ratios of characteristic polynomials. Numerical simulations illustrate our findings for the spectral density at finite N and we also give indications how to do the asymptotic large- N analysis. (paper)

  13. Effects of matrix characteristics and interpatch distance on functional connectivity in fragmented temperate rainforests.

    Science.gov (United States)

    Magrach, Ainhoa; Larrinaga, Asier R; Santamaría, Luis

    2012-04-01

    The connectivity of remnant patches of habitat may affect the persistence of species in fragmented landscapes. We evaluated the effects of the structural connectivity of forest patches (i.e., distance between patches) and matrix class (land-cover type) on the functional connectivity of 3 bird species (the White-crested Elaenia [Elaenia albiceps], the Green-backed Firecrown Hummingbird [Sephanoides sephaniodes], and the Austral Thrush [Turdus falklandii]). We measured functional connectivity as the rate at which each species crossed from one patch to another. We also evaluated whether greater functional connectivity translated into greater ecological connectivity (dispersal of fruit and pollen) by comparing among forest patches fruit set of a plant pollinated by hummingbirds and abundance of seedlings and adults of 2 plants with bird- and wind-dispersed seeds. Interpatch distance was strongly associated with functional connectivity, but its effect was not independent of matrix class. For one of the bird-dispersed plants, greater functional connectivity for White-crested Elaenias and Austral Thrushes (both frugivores) was associated with higher densities of this plant. The lack of a similar association for the wind-dispersed species suggests this effect is linked to the dispersal vector. The abundance of the hummingbird-pollinated species was not related to the presence of hummingbirds. Interpatch distance and matrix class affect animal movement in fragmented landscapes and may have a cascading effect on the distribution of some animal-dispersed species. On the basis of our results, we believe effort should be invested in optimizing patch configuration and modifying the matrix so as to mitigate the effects of patch isolation in fragmented landscapes. ©2012 Society for Conservation Biology.

  14. Sequential optimization of matrix chain multiplication relative to different cost functions

    KAUST Repository

    Chikalov, Igor; Hussain, Shahid; Moshkov, Mikhail

    2011-01-01

    In this paper, we present a methodology to optimize matrix chain multiplication sequentially relative to different cost functions such as total number of scalar multiplications, communication overhead in a multiprocessor environment, etc. For n matrices our optimization procedure requires O(n 3) arithmetic operations per one cost function. This work is done in the framework of a dynamic programming extension that allows sequential optimization relative to different criteria. © 2011 Springer-Verlag Berlin Heidelberg.

  15. The functional matrix hypothesis revisited. 3. The genomic thesis.

    Science.gov (United States)

    Moss, M L

    1997-09-01

    Although the initial versions of the functional matrix hypothesis (FMH) theoretically posited the ontogenetic primacy of "function," it is only in recent years that advances in the morphogenetic, engineering, and computer sciences provided an integrated experimental and numerical data base that permitted recent significant revisions of the FMH--revisions that strongly support the primary role of function in craniofacial growth and development. Acknowledging that the currently dominant scientific paradigm suggests that genomic, instead of epigenetic (functional) factors, regulate (cause, control) such growth, an analysis of this continuing controversy was deemed useful. Accordingly the method of dialectical analysis, is employed, stating a thesis, an antithesis, and a resolving synthesis based primarily on an extensive review of the pertinent current literature. This article extensively reviews the genomic hypothesis and offers a critique intended to remove some of the unintentional conceptual obscurantism that has recently come to surround it.

  16. Functionalized carbon nanotubes mixed matrix membranes of polymers of intrinsic microporosity for gas separation.

    Science.gov (United States)

    Khan, Muntazim Munir; Filiz, Volkan; Bengtson, Gisela; Shishatskiy, Sergey; Rahman, Mushfequr; Abetz, Volker

    2012-09-06

    The present work reports on the gas transport behavior of mixed matrix membranes (MMM) which were prepared from multi-walled carbon nanotubes (MWCNTs) and dispersed within polymers of intrinsic microporosity (PIM-1) matrix. The MWCNTs were chemically functionalized with poly(ethylene glycol) (PEG) for a better dispersion in the polymer matrix. MMM-incorporating functionalized MWCNTs (f-MWCNTs) were fabricated by dip-coating method using microporous polyacrylonitrile membrane as a support and were characterized for gas separation performance. Gas permeation measurements show that MMM incorporated with pristine or functionalized MWCNTs exhibited improved gas separation performance compared to pure PIM-1. The f-MWCNTs MMM show better performance in terms of permeance and selectivity in comparison to pristine MWCNTs. The gas permeances of the derived MMM are increased to approximately 50% without sacrificing the selectivity at 2 wt.% of f-MWCNTs' loading. The PEG groups on the MWCNTs have strong interaction with CO2 which increases the solubility of polar gas and limit the solubility of nonpolar gas, which is advantageous for CO2/N2 selectivity. The addition of f-MWCNTs inside the polymer matrix also improved the long-term gas transport stability of MMM in comparison with PIM-1. The high permeance, selectivity, and long term stability of the fabricated MMM suggest that the reported approach can be utilized in practical gas separation technology.

  17. Higher-order automatic differentiation of mathematical functions

    Science.gov (United States)

    Charpentier, Isabelle; Dal Cappello, Claude

    2015-04-01

    Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

  18. Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States

    Directory of Open Access Journals (Sweden)

    Paul B. Slater

    2015-01-01

    Full Text Available Previously, a formula, incorporating a 5F4 hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments ρPTnρk/ρk of 4×4 density-matrices (ρ and their partial transposes (|ρPT|, was applied with k=0 to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,… are found—via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2, (standard two-qubit (α=1, and two-quater[nionic]bit (α=2 cases. We deduce rather simple companion (rebit, qubit, quaterbit, … formulas that successfully reproduce the rational values assumed for general  k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.

  19. In vitro model to study the effects of matrix stiffening on Ca2+ handling and myofilament function in isolated adult rat cardiomyocytes.

    Science.gov (United States)

    van Deel, Elza D; Najafi, Aref; Fontoura, Dulce; Valent, Erik; Goebel, Max; Kardux, Kim; Falcão-Pires, Inês; van der Velden, Jolanda

    2017-07-15

    This paper describes a novel model that allows exploration of matrix-induced cardiomyocyte adaptations independent of the passive effect of matrix rigidity on cardiomyocyte function. Detachment of adult cardiomyocytes from the matrix enables the study of matrix effects on cell shortening, Ca 2+ handling and myofilament function. Cell shortening and Ca 2+ handling are altered in cardiomyocytes cultured for 24 h on a stiff matrix. Matrix stiffness-impaired cardiomyocyte contractility is reversed upon normalization of extracellular stiffness. Matrix stiffness-induced reduction in unloaded shortening is more pronounced in cardiomyocytes isolated from obese ZSF1 rats with heart failure with preserved ejection fraction compared to lean ZSF1 rats. Extracellular matrix (ECM) stiffening is a key element of cardiac disease. Increased rigidity of the ECM passively inhibits cardiac contraction, but if and how matrix stiffening also actively alters cardiomyocyte contractility is incompletely understood. In vitro models designed to study cardiomyocyte-matrix interaction lack the possibility to separate passive inhibition by a stiff matrix from active matrix-induced alterations of cardiomyocyte properties. Here we introduce a novel experimental model that allows exploration of cardiomyocyte functional alterations in response to matrix stiffening. Adult rat cardiomyocytes were cultured for 24 h on matrices of tuneable stiffness representing the healthy and the diseased heart and detached from their matrix before functional measurements. We demonstrate that matrix stiffening, independent of passive inhibition, reduces cell shortening and Ca 2+ handling but does not alter myofilament-generated force. Additionally, detachment of adult cultured cardiomyocytes allowed the transfer of cells from one matrix to another. This revealed that stiffness-induced cardiomyocyte changes are reversed when matrix stiffness is normalized. These matrix stiffness-induced changes in cardiomyocyte

  20. Extended biorthogonal matrix polynomials

    Directory of Open Access Journals (Sweden)

    Ayman Shehata

    2017-01-01

    Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.

  1. Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model

    International Nuclear Information System (INIS)

    Szabo, Richard J; Tierz, Miguel

    2010-01-01

    We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on S 2 . We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak-coupling phase. We study the strong-coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first-order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on S 3 , and hence to q-deformed Yang-Mills theory on S 2 . In particular, the ground-state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply laced gauge groups.

  2. Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface

    Energy Technology Data Exchange (ETDEWEB)

    Buecking, N

    2007-11-05

    In this work a new theoretical formalism is introduced in order to simulate the phononinduced relaxation of a non-equilibrium distribution to equilibrium at a semiconductor surface numerically. The non-equilibrium distribution is effected by an optical excitation. The approach in this thesis is to link two conventional, but approved methods to a new, more global description: while semiconductor surfaces can be investigated accurately by density-functional theory, the dynamical processes in semiconductor heterostructures are successfully described by density matrix theory. In this work, the parameters for density-matrix theory are determined from the results of density-functional calculations. This work is organized in two parts. In Part I, the general fundamentals of the theory are elaborated, covering the fundamentals of canonical quantizations as well as the theory of density-functional and density-matrix theory in 2{sup nd} order Born approximation. While the formalism of density functional theory for structure investigation has been established for a long time and many different codes exist, the requirements for density matrix formalism concerning the geometry and the number of implemented bands exceed the usual possibilities of the existing code in this field. A special attention is therefore attributed to the development of extensions to existing formulations of this theory, where geometrical and fundamental symmetries of the structure and the equations are used. In Part II, the newly developed formalism is applied to a silicon (001)surface in a 2 x 1 reconstruction. As first step, density-functional calculations using the LDA functional are completed, from which the Kohn-Sham-wave functions and eigenvalues are used to calculate interaction matrix elements for the electron-phonon-coupling an the optical excitation. These matrix elements are determined for the optical transitions from valence to conduction bands and for electron-phonon processes inside the

  3. Two genetic loci produce distinct carbohydrate-rich structural components of the Pseudomonas aeruginosa biofilm matrix.

    Science.gov (United States)

    Friedman, Lisa; Kolter, Roberto

    2004-07-01

    Pseudomonas aeruginosa forms biofilms, which are cellular aggregates encased in an extracellular matrix. Molecular genetics studies of three common autoaggregative phenotypes, namely wrinkled colonies, pellicles, and solid-surface-associated biofilms, led to the identification of two loci, pel and psl, that are involved in the production of carbohydrate-rich components of the biofilm matrix. The pel gene cluster is involved in the production of a glucose-rich matrix material in P. aeruginosa strain PA14 (L. Friedman and R. Kolter, Mol. Microbiol. 51:675-690, 2004). Here we investigate the role of the pel gene cluster in P. aeruginosa strain ZK2870 and identify a second genetic locus, termed psl, involved in the production of a mannose-rich matrix material. The 11 predicted protein products of the psl genes are homologous to proteins involved in carbohydrate processing. P. aeruginosa is thus able to produce two distinct carbohydrate-rich matrix materials. Either carbohydrate-rich matrix component appears to be sufficient for mature biofilm formation, and at least one of them is required for mature biofilm formation in P. aeruginosa strains PA14 and ZK2870. Copyright 2004 American Society for Microbiology

  4. Data Hiding Based on a Two-Layer Turtle Shell Matrix

    Directory of Open Access Journals (Sweden)

    Xiao-Zhu Xie

    2018-02-01

    Full Text Available Data hiding is a technology that embeds data into a cover carrier in an imperceptible way while still allowing the hidden data to be extracted accurately from the stego-carrier, which is one important branch of computer science and has drawn attention of scholars in the last decade. Turtle shell-based (TSB schemes have become popular in recent years due to their higher embedding capacity (EC and better visual quality of the stego-image than most of the none magic matrices based (MMB schemes. This paper proposes a two-layer turtle shell matrix-based (TTSMB scheme for data hiding, in which an extra attribute presented by a 4-ary digit is assigned to each element of the turtle shell matrix with symmetrical distribution. Therefore, compared with the original TSB scheme, two more bits are embedded into each pixel pair to obtain a higher EC up to 2.5 bits per pixel (bpp. The experimental results reveal that under the condition of the same visual quality, the EC of the proposed scheme outperforms state-of-the-art data hiding schemes.

  5. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

    Science.gov (United States)

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

  6. Effective functionalization of carbon nanotubes for bisphenol F epoxy matrix composites

    Directory of Open Access Journals (Sweden)

    Zhe Wang

    2012-08-01

    Full Text Available A brand-new type of multifunctional nanocomposites with high DC conductivity and enhanced mechanical strength was fabricated. Ionic liquid functionalized Carbon Nanotubes (CNTs-IL were embedded into epoxy matrix with covalent bonding by the attached epoxy groups. The highest DC conductivity was 8.38 x 10-3 S.m-1 with 1.0 wt. (% loading of CNTs-IL and the tensile strength was increased by 36.4% only at a 0.5 wt. (% concentration. A mixing solvent was used to disperse CNTs-IL in the epoxy monomer. The dispersion and distribution of CNTs-IL in the polymer matrix were measured by utilizing both optical microscopy and scanning electron microscopy, respectively.

  7. Microlocal study of S-matrix singularity structure

    International Nuclear Information System (INIS)

    Kawai, Takahiro; Kyoto Univ.; Stapp, H.P.

    1975-01-01

    Support is adduced for two related conjectures of simplicity of the analytic structure of the S-matrix and related function; namely, Sato's conjecture that the S-matrix is a solution of a maximally over-determined system of pseudo-differential equations, and our conjecture that the singularity spectrum of any bubble diagram function has the conormal structure with respect to a canonical decomposition of the solutions of the relevant Landau equations. This latter conjecture eliminates the open sets of allowed singularities that existing procedures permit. (orig.) [de

  8. Mitochondrial function in engineered cardiac tissues is regulated by extracellular matrix elasticity and tissue alignment.

    Science.gov (United States)

    Lyra-Leite, Davi M; Andres, Allen M; Petersen, Andrew P; Ariyasinghe, Nethika R; Cho, Nathan; Lee, Jezell A; Gottlieb, Roberta A; McCain, Megan L

    2017-10-01

    Mitochondria in cardiac myocytes are critical for generating ATP to meet the high metabolic demands associated with sarcomere shortening. Distinct remodeling of mitochondrial structure and function occur in cardiac myocytes in both developmental and pathological settings. However, the factors that underlie these changes are poorly understood. Because remodeling of tissue architecture and extracellular matrix (ECM) elasticity are also hallmarks of ventricular development and disease, we hypothesize that these environmental factors regulate mitochondrial function in cardiac myocytes. To test this, we developed a new procedure to transfer tunable polydimethylsiloxane disks microcontact-printed with fibronectin into cell culture microplates. We cultured Sprague-Dawley neonatal rat ventricular myocytes within the wells, which consistently formed tissues following the printed fibronectin, and measured oxygen consumption rate using a Seahorse extracellular flux analyzer. Our data indicate that parameters associated with baseline metabolism are predominantly regulated by ECM elasticity, whereas the ability of tissues to adapt to metabolic stress is regulated by both ECM elasticity and tissue alignment. Furthermore, bioenergetic health index, which reflects both the positive and negative aspects of oxygen consumption, was highest in aligned tissues on the most rigid substrate, suggesting that overall mitochondrial function is regulated by both ECM elasticity and tissue alignment. Our results demonstrate that mitochondrial function is regulated by both ECM elasticity and myofibril architecture in cardiac myocytes. This provides novel insight into how extracellular cues impact mitochondrial function in the context of cardiac development and disease. NEW & NOTEWORTHY A new methodology has been developed to measure O 2 consumption rates in engineered cardiac tissues with independent control over tissue alignment and matrix elasticity. This led to the findings that matrix

  9. Targeting a single function of the multifunctional matrix metalloprotease MT1-MMP

    DEFF Research Database (Denmark)

    Ingvarsen, Signe; Porse, Astrid; Erpicum, Charlotte

    2013-01-01

    and pathological events, has been complicated by the lack of specific inhibitors and the fact that some of the potent MMPs are multifunctional enzymes. These factors have also hampered the setup of therapeutic strategies targeting MMP activity. A tempting target is the membrane-associated MT1-MMP, which has well......-documented importance in matrix degradation but which takes part in more than one pathway in this regard. In this report, we describe the selective targeting of a single function of this enzyme by means of a specific monoclonal antibody against MT1-MMP, raised in an MT1-MMP knock-out mouse. The antibody blocks...... matrix in vitro, as well as in lymphatic vessel sprouting assayed ex vivo. This is the first example of the complete inactivation of a single function of a multifunctional MMP and the use of this strategy to pursue its role....

  10. Analytic and numeric Green's functions for a two-dimensional electron gas in an orthogonal magnetic field

    International Nuclear Information System (INIS)

    Cresti, Alessandro; Grosso, Giuseppe; Parravicini, Giuseppe Pastori

    2006-01-01

    We have derived closed analytic expressions for the Green's function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green's functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green's function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of the Green's function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green's function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems

  11. Orbital functionals in density-matrix- and current-density-functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Helbig, N

    2006-05-15

    Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized

  12. Two-Dimensional Space-Time Analysis and Matrix Represen-Tation on the Principle of the Capacitive Displacement Transducer

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Z Y [College of Metrological Technology and Engineering, China Jiliang University, Hangzhou (China); Luo, J X [Zhejiang Radio Factory, Zhejiang (China)

    2006-10-15

    In order to provide a design method of the capacitive displacement transducer and to improve its measuring performance it is desperately needed to offer a refined mathematic model of the transducer of mulitiphase drive and phase-modulated. On the basis of fully considering its characteristic of digital signals, first it is found that their actual waveforms and space-time characteristics could be tersely represented by matrixes [u{sub ij}], [c{sub j}] and [v{sub i}], and corresponding matrix elements u{sub ij}, c{sub j} and v{sub i} through deeply analyzing space-time and quantum characteristics of their mulitiphase driving signals U{sub i}(t), capacitive coupling signals C{sub j}(x) and output signal V(t). and space-time transform function possessed by U(x,t) itself. Then the basic expression of the relations of the transducer is derived, which is expressed by matrixes, thereby the characteristics of space-time transform and phase modulation are brought to light. The demodulation process and demodulated waveforms and its characteristics in the transducer are also expressed by demodulated matrixes [b{sub ij}]. Finally, the reason for the principle and periodic error produced in the transducer is revealed by sampling matrix [s{sub ij}]. Thus the full process of the produce of driving signals, modulation, demodulation and space-time transform that happen in the transducer, also waveforms and characteristics of various signals in the process are concisely expressed by two-dimensional space-time matrixes. Experimental results indicate that the use of the mathematical model enables its resolving power to reach 1 {mu}m, and the mathematical model proposed is an all-things-considered model to express processes that happen in the transducer.

  13. Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

    Science.gov (United States)

    Córdova, Clay; Heidenreich, Ben; Popolitov, Alexandr; Shakirov, Shamil

    2018-02-01

    We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarithmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.

  14. Perturbation theory corrections to the two-particle reduced density matrix variational method.

    Science.gov (United States)

    Juhasz, Tamas; Mazziotti, David A

    2004-07-15

    In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.

  15. Robust Improvement in Estimation of a Covariance Matrix in an Elliptically Contoured Distribution Respect to Quadratic Loss Function

    Directory of Open Access Journals (Sweden)

    Z. Khodadadi

    2008-03-01

    Full Text Available Let S be matrix of residual sum of square in linear model Y = Aβ + e where matrix e is distributed as elliptically contoured with unknown scale matrix Σ. In present work, we consider the problem of estimating Σ with respect to squared loss function, L(Σˆ , Σ = tr(ΣΣˆ −1 −I 2 . It is shown that improvement of the estimators were obtained by James, Stein [7], Dey and Srivasan [1] under the normality assumption remains robust under an elliptically contoured distribution respect to squared loss function

  16. Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

    Science.gov (United States)

    Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

    2018-04-01

    We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

  17. Chudnovsky-Ramanujan Type Formulae for the Legendre Family

    OpenAIRE

    Chen, Imin; Glebov, Gleb

    2017-01-01

    We apply the method established in our previous work to derive a Chudnovsky-Ramanujan type formula for the Legendre family of elliptic curves. As a result, we prove two identities for $1/\\pi$ in terms of hypergeometric functions.

  18. Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

    International Nuclear Information System (INIS)

    Chen Changyuan; Sun Dongsheng; Lu Falin

    2007-01-01

    Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

  19. Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions

    Directory of Open Access Journals (Sweden)

    Marina Popolizio

    2018-01-01

    Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.

  20. Program package for calculating matrix elements of two-cluster structures in nuclei

    International Nuclear Information System (INIS)

    Krivec, R.; Mihailovic, M.V.; Kernforschungszentrum Karlsruhe G.m.b.H.

    1982-01-01

    Matrix elements of operators between Slater determinants of two-cluster structures must be expanded into partial waves for the purpose of angular momentum projection. The expansion coefficients contain integrals over the spherical angles theta and phi. (orig.)

  1. Structure-function correlations in glaucoma using matrix and standard automated perimetry versus time-domain and spectral-domain OCT devices.

    Science.gov (United States)

    Pinto, Luciano Moreira; Costa, Elaine Fiod; Melo, Luiz Alberto S; Gross, Paula Blasco; Sato, Eduardo Toshio; Almeida, Andrea Pereira; Maia, Andre; Paranhos, Augusto

    2014-04-10

    We examined the structure-function relationship between two perimetric tests, the frequency doubling technology (FDT) matrix and standard automated perimetry (SAP), and two optical coherence tomography (OCT) devices (time-domain and spectral-domain). This cross-sectional study included 97 eyes from 29 healthy individuals, and 68 individuals with early, moderate, or advanced primary open-angle glaucoma. The correlations between overall and sectorial parameters of retinal nerve fiber layer thickness (RNFL) measured with Stratus and Spectralis OCT, and the visual field sensitivity obtained with FDT matrix and SAP were assessed. The relationship also was evaluated using a previously described linear model. The correlation coefficients for the threshold sensitivity measured with SAP and Stratus OCT ranged from 0.44 to 0.79, and those for Spectralis OCT ranged from 0.30 to 0.75. Regarding FDT matrix, the correlation ranged from 0.40 to 0.79 with Stratus OCT and from 0.39 to 0.79 with Spectralis OCT. Stronger correlations were found in the overall measurements and the arcuate sectors for both visual fields and OCT devices. A linear relationship was observed between FDT matrix sensitivity and the OCT devices. The previously described linear model fit the data from SAP and the OCT devices well, particularly in the inferotemporal sector. The FDT matrix and SAP visual sensitivities were related strongly to the RNFL thickness measured with the Stratus and Spectralis OCT devices, particularly in the overall and arcuate sectors. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

  2. Interdisciplinary matrix in economics: two applications to the transition from socialism to capitalism.

    Science.gov (United States)

    Jakimowicz, Aleksander

    2009-10-01

    The 7-fold interdisciplinary matrix is introduced. This integrated methodological point of view is original, although it is based on ideas of others in various ways. The name for this new approach draws on the Kuhnian notion of a disciplinary matrix. There are four components of the Kuhnian matrix on which the existence of scientific communities hinges: symbolic generalizations, models, values, and exemplars. In this context the term "paradigm" should refer to exemplars. The interdisciplinary matrix is composed of seven elements: cybernetics, catastrophe theory, fractal geometry, deterministic chaos, artificial intelligence, theory of complexity, and humanistic values. Scientific developments have recently brought substantial changes in the structure of scientific communities. Transferability of ideas and thoughts contributed to the creation of scientific communities, which unite representatives of various professions. When researching into certain phenomena we no longer need to develop theories for them from scratch, as we can draw on the achievements in other disciplines. Two examples of the employment of the interdisciplinary matrix in macroeconomics are elaborated here: the investment cycle model in socialist economy, and the model of economic transformation based on chaotic hysteresis.

  3. Full four-dimensional and reciprocal Mueller matrix bidirectional reflectance distribution function of sintered polytetrafluoroethylene.

    Science.gov (United States)

    Germer, Thomas A

    2017-11-20

    We measured the Mueller matrix bidirectional reflectance distribution function (BRDF) of a sintered polytetrafluoroethylene (PTFE) sample over the scattering hemisphere for six incident angles (0°-75° in 15° steps) and for four wavelengths (351 nm, 532 nm, 633 nm, and 1064 nm). The data for each wavelength were fit to a phenomenological description for the Mueller matrix BRDF, which is an extension of the bidirectional surface scattering modes developed by Koenderink and van Doorn [J. Opt. Soc. Am. A.15, 2903 (1998)JOAOD60740-323210.1364/JOSAA.15.002903] for unpolarized BRDF. This description is designed to be complete, to obey the appropriate reciprocity conditions, and to provide a full description of the Mueller matrix BRDF as a function of incident and scattering directions for each wavelength. The description was further extended by linearizing the surface scattering mode coefficients with wavelength. This data set and its parameterization provides a comprehensive on-demand description of the reflectance properties for this commonly used diffuse reflectance reference material over a wide range of wavelengths.

  4. Estimating the two-particle K-matrix for multiple partial waves and decay channels from finite-volume energies

    Directory of Open Access Journals (Sweden)

    Colin Morningstar

    2017-11-01

    Full Text Available An implementation of estimating the two-to-two K-matrix from finite-volume energies based on the Lüscher formalism and involving a Hermitian matrix known as the “box matrix” is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the K-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to S=2 and orbital angular momenta up to L=6 are obtained for total momenta in several directions. First tests involving ρ-meson decay to two pions include the L=3 and L=5 partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.

  5. Hadron matrix elements of quark operators in the relativistic quark model

    Energy Technology Data Exchange (ETDEWEB)

    Bando, Masako; Toya, Mihoko [Kyoto Univ. (Japan). Dept. of Physics; Sugimoto, Hiroshi

    1979-07-01

    General formulae for evaluating matrix elements of two- and four-quark operators sandwiched by one-hadron states are presented on the basis of the relativistic quark model. Observed hadronic quantities are expressed in terms of those matrix elements of two- and four-quark operators. One observes various type of relativistic expression for the matrix elements which in the non-relativistic case reduce to simple expression of the so-called ''the wave function at the origin /sup +/psi(0)/sup +/''.

  6. Inhomogeneity induced and appropriately parameterized semilocal exchange and correlation energy functionals in two-dimensions

    Science.gov (United States)

    Patra, Abhilash; Jana, Subrata; Samal, Prasanjit

    2018-04-01

    The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate techniques to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In addition to the exchange functionals, a suitable correlation functional is also constructed by working upon the local correlation functional developed for 2D homogeneous electron gas. The non-local effects are induced into the correlation functional by a parametric form of one of the newly constructed exchange energy functionals. The proposed functionals are applied to the parabolic quantum dots with a varying number of confined electrons and the confinement strength. The results obtained with the aforementioned functionals are quite satisfactory, which indicates why these are suitable for two-dimensional quantum systems.

  7. Strong correlation in acene sheets from the active-space variational two-electron reduced density matrix method: effects of symmetry and size.

    Science.gov (United States)

    Pelzer, Kenley; Greenman, Loren; Gidofalvi, Gergely; Mazziotti, David A

    2011-06-09

    Polyaromatic hydrocarbons (PAHs) are a class of organic molecules with importance in several branches of science, including medicine, combustion chemistry, and materials science. The delocalized π-orbital systems in PAHs require highly accurate electronic structure methods to capture strong electron correlation. Treating correlation in PAHs has been challenging because (i) traditional wave function methods for strong correlation have not been applicable since they scale exponentially in the number of strongly correlated orbitals, and (ii) alternative methods such as the density-matrix renormalization group and variational two-electron reduced density matrix (2-RDM) methods have not been applied beyond linear acene chains. In this paper we extend the earlier results from active-space variational 2-RDM theory [Gidofalvi, G.; Mazziotti, D. A. J. Chem. Phys. 2008, 129, 134108] to the more general two-dimensional arrangement of rings--acene sheets--to study the relationship between geometry and electron correlation in PAHs. The acene-sheet calculations, if performed with conventional wave function methods, would require wave function expansions with as many as 1.5 × 10(17) configuration state functions. To measure electron correlation, we employ several RDM-based metrics: (i) natural-orbital occupation numbers, (ii) the 1-RDM von Neumann entropy, (iii) the correlation energy per carbon atom, and (iv) the squared Frobenius norm of the cumulant 2-RDM. The results confirm a trend of increasing polyradical character with increasing molecular size previously observed in linear PAHs and reveal a corresponding trend in two-dimensional (arch-shaped) PAHs. Furthermore, in PAHs of similar size they show significant variations in correlation with geometry. PAHs with the strictly linear geometry (chains) exhibit more electron correlation than PAHs with nonlinear geometries (sheets).

  8. Membrane-type-3 matrix metalloproteinase (MT3-MMP functions as a matrix composition-dependent effector of melanoma cell invasion.

    Directory of Open Access Journals (Sweden)

    Olga Tatti

    Full Text Available In primary human melanoma, the membrane-type matrix metalloproteinase, MT3-MMP, is overexpressed in the most aggressive nodular-type tumors. Unlike MT1-MMP and MT2-MMP, which promote cell invasion through basement membranes and collagen type I-rich tissues, the function of MT3-MMP in tumor progression remains unclear. Here, we demonstrate that MT3-MMP inhibits MT1-MMP-driven melanoma cell invasion in three-dimensional collagen, while yielding an altered, yet MT1-MMP-dependent, form of expansive growth behavior that phenocopies the formation of nodular cell colonies. In melanoma cell lines originating from advanced primary or metastatic lesions, endogenous MT3-MMP expression was associated with limited collagen-invasive potential. In the cell lines with highest MT3-MMP expression relative to MT1-MMP, collagen-invasive activity was increased following stable MT3-MMP gene silencing. Consistently, MT3-MMP overexpression in cells derived from less advanced superficially spreading melanoma lesions, or in the MT3-MMP knockdown cells, reduced MT1-MMP-dependent collagen invasion. Rather than altering MT1-MMP transcription, MT3-MMP interacted with MT1-MMP in membrane complexes and reduced its cell surface expression. By contrast, as a potent fibrinolytic enzyme, MT3-MMP induced efficient invasion of the cells in fibrin, a provisional matrix component frequently found at tumor-host tissue interfaces and perivascular spaces of melanoma. Since MT3-MMP was significantly upregulated in biopsies of human melanoma metastases, these results identify MT3-MMP as a matrix-dependent modifier of the invasive tumor cell functions during melanoma progression.

  9. A random matrix model for elliptic curve L-functions of finite conductor

    International Nuclear Information System (INIS)

    Dueñez, E; Huynh, D K; Keating, J P; Snaith, N C; Miller, S J

    2012-01-01

    We propose a random-matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of the critical zeros of these L-functions away from the centre of the critical strip was observed numerically by Miller (2006 Exp. Math. 15 257–79); such behaviour deviates qualitatively from the conjectural limiting distribution of the zeros (for large conductors this distribution is expected to approach the one-level density of eigenvalues of orthogonal matrices after appropriate rescaling). Our purpose here is to provide a random-matrix model for Miller’s surprising discovery. We consider the family of even quadratic twists of a given elliptic curve. The main ingredient in our model is a calculation of the eigenvalue distribution of random orthogonal matrices whose characteristic polynomials are larger than some given value at the symmetry point in the spectra. We call this sub-ensemble of SO(2N) the excised orthogonal ensemble. The sieving-off of matrices with small values of the characteristic polynomial is akin to the discretization of the central values of L-functions implied by the formulae of Waldspurger and Kohnen–Zagier. The cut-off scale appropriate to modelling elliptic curve L-functions is exponentially small relative to the matrix size N. The one-level density of the excised ensemble can be expressed in terms of that of the well-known Jacobi ensemble, enabling the former to be explicitly calculated. It exhibits an exponentially small (on the scale of the mean spacing) hard gap determined by the cut-off value, followed by soft repulsion on a much larger scale. Neither of these features is present in the one-level density of SO(2N). When N → ∞ we recover the limiting orthogonal behaviour. Our results agree qualitatively with Miller’s discrepancy. Choosing the cut-off appropriately gives a model in good quantitative agreement with the number-theoretical data. (paper)

  10. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-14

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  11. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

    Science.gov (United States)

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-01

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  12. Analytical solutions to orthotropic variable thickness disk problems

    Directory of Open Access Journals (Sweden)

    Ahmet N. ERASLAN

    2016-02-01

    Full Text Available An analytical model is developed to estimate the mechanical response of nonisothermal, orthotropic, variable thickness disks under a variety of boundary conditions. Combining basic mechanical equations of disk geometry with the equations of orthotropic material, the elastic equation of the disk is obtained. This equation is transformed into a standard hypergeometric differential equation by means of a suitable transformation. An analytical solution is then obtained in terms of hypergeometric functions. The boundary conditions used to complete the solutions simulate rotating annular disks with two free surfaces, stationary annular disks with pressurized inner and free outer surfaces, and free inner and pressurized outer surfaces. The results of the solutions to each of these cases are presented in graphical forms. It is observed that, for the three cases investigated the elastic orthotropy parameter turns out to be an important parameter affecting the elastic behaviorKeywords: Orthotropic disk, Variable thickness, Thermoelasticity, Hypergeometric equation

  13. Symmetries of integrable hierarchies and matrix model constraints

    International Nuclear Information System (INIS)

    Vos, K. de

    1992-01-01

    The orbit construction associates a soliton hierarchy to every level-one vertex realization of a simply laced affine Kac-Moody algebra g. We show that the τ-function of such a hierarchy has the (truncated) Virasoro algebra as an algebra of infinitesimal symmetry transformations. To prove this we use an appropriate bilinear form of these hierarchies together with the coset construction of conformal field theory. For A 1 (1) the orbit construction gives either the Toda or the KdV hierarchy. These both occur in the one-matrix model of two-dimensional quantum gravity, before and after the double scaling limit respectively. The truncated Virasoro symmetry algebra is exactly the algebra of constraints of the one-matrix model. The partition function of the one-matrix model is therefore an invariant τ-function. We also consider the case of A 1 (1) with l>1. Surprisingly, the symmetry algebra in that case is not simply a truncated Casimir algebra. It appears that again only the Virasoro symmetry survives. We speculate on the relation with multi-matrix models. (orig.)

  14. A Three-Phase Dual-Input Matrix Converter for Grid Integration of Two AC Type Energy Resources

    DEFF Research Database (Denmark)

    Liu, Xiong; Wang, Peng; Chiang Loh, Poh

    2013-01-01

    This paper proposes a novel dual-input matrix converter (DIMC) to integrate two three-phase ac type energy resources to a power grid. The proposed matrix converter is developed based on the traditional indirect matrix converter under reverse power flow operation mode, but with its six......-to-output voltage boost capability since power flows from the converter’s voltage source side to its current source side. Commanded currents can be extracted from the two input sources to the grid. The proposed control and modulation schemes guarantee sinusoidal input and output waveforms as well as unity input......-switch voltage source converter replaced by a nine-switch configuration. With the additional three switches, the proposed DIMC can provide six in put terminals, which make it possible to integrate two independent ac sources into a single grid-tied power electronics interface. The proposed converter has input...

  15. SIMULATIONS OF WIDE-FIELD WEAK-LENSING SURVEYS. II. COVARIANCE MATRIX OF REAL-SPACE CORRELATION FUNCTIONS

    International Nuclear Information System (INIS)

    Sato, Masanori; Matsubara, Takahiko; Takada, Masahiro; Hamana, Takashi

    2011-01-01

    Using 1000 ray-tracing simulations for a Λ-dominated cold dark model in Sato et al., we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in previous measurements. The shear correlation function of a particular separation angle is affected by Fourier modes over a wide range of multipoles, even beyond a survey area, which complicates the analysis of the covariance matrix. To overcome such obstacles we first construct Gaussian shear simulations from the 1000 realizations and then use the Gaussian simulations to disentangle the Gaussian covariance contribution to the covariance matrix we measured from the original simulations. We found that an analytical formula of Gaussian covariance overestimates the covariance amplitudes due to an effect of the finite survey area. Furthermore, the clean separation of the Gaussian covariance allows us to examine the non-Gaussian covariance contributions as a function of separation angles and source redshifts. For upcoming surveys with typical source redshifts of z s = 0.6 and 1.0, the non-Gaussian contribution to the diagonal covariance components at 1 arcmin scales is greater than the Gaussian contribution by a factor of 20 and 10, respectively. Predictions based on the halo model qualitatively well reproduce the simulation results, however show a sizable disagreement in the covariance amplitudes. By combining these simulation results we develop a fitting formula to the covariance matrix for a survey with arbitrary area coverage, taking into account effects of the finiteness of survey area on the Gaussian covariance.

  16. Two-loop operator matrix elements for massive fermionic local twist-2 operators in QED

    International Nuclear Information System (INIS)

    Bluemlein, J.; Freitas, A. de; Universidad Simon Bolivar, Caracas; Neerven, W.L. van

    2011-11-01

    We describe the calculation of the two--loop massive operator matrix elements with massive external fermions in QED. We investigate the factorization of the O(α 2 ) initial state corrections to e + e - annihilation into a virtual boson for large cms energies s >>m 2 e into massive operator matrix elements and the massless Wilson coefficients of the Drell-Yan process adapting the color coefficients to the case of QED, as proposed by F. A. Berends et. al. (Nucl. Phys. B 297 (1988)429). Our calculations show explicitly that the representation proposed there works at one-loop order and up to terms linear in ln (s/m 2 e ) at two-loop order. However, the two-loop constant part contains a few structural terms, which have not been obtained in previous direct calculations. (orig.)

  17. Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity

    International Nuclear Information System (INIS)

    Akemann, G.

    2002-01-01

    The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex matrices, we can prove that all k-point correlation functions including an arbitrary number of Dirac mass terms are universal close to the origin. To this aim we establish the universality of the asymptotics of orthogonal polynomials in the complex plane. The universality of the correlation functions then follows from that of the kernel of orthogonal polynomials and a mapping of massive to massless correlators

  18. Structure of the two-neutrino double-β decay matrix elements within perturbation theory

    Science.gov (United States)

    Štefánik, Dušan; Šimkovic, Fedor; Faessler, Amand

    2015-06-01

    The two-neutrino double-β Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-β decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-β decay matrix elements on the like-nucleon pairing, particle-particle T =0 and T =1 , and particle-hole proton-neutron interactions is obtained. It is found that double-β decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-β decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further, energy-weighted Fermi and Gamow-Teller sum rules connecting Δ Z =2 nuclei are discussed. It is proposed that these sum rules can be used to study the residual interactions of the nuclear Hamiltonian, which are relevant for charge-changing nuclear transitions.

  19. Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

    International Nuclear Information System (INIS)

    Bluemlein, Johannes; Phan, Khiem Hong; Vietnam National Univ., Ho Chi Minh City; Riemann, Tord; Silesia Univ., Chorzow

    2017-11-01

    Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension d in terms of (generalized) hypergeometric functions 2 F 1 and F 1 . Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at d=4+2n, n non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

  20. Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Phan, Khiem Hong [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Vietnam National Univ., Ho Chi Minh City (Viet Nam). Univ. of Science; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Silesia Univ., Chorzow (Poland). Inst. of Physics

    2017-11-15

    Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension d in terms of (generalized) hypergeometric functions {sub 2}F{sub 1} and F{sub 1}. Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at d=4+2n, n non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

  1. Tree-level gluon amplitudes on the celestial sphere

    Science.gov (United States)

    Schreiber, Anders Ø.; Volovich, Anastasia; Zlotnikov, Michael

    2018-06-01

    Pasterski, Shao and Strominger have recently proposed that massless scattering amplitudes can be mapped to correlators on the celestial sphere at infinity via a Mellin transform. We apply this prescription to arbitrary n-point tree-level gluon amplitudes. The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian Gr (4 , n), while generic non-MHV amplitudes are given by more complicated Gelfand A-hypergeometric functions.

  2. Studies of P-matrix formalism on the basis of the potential description of two-particle interaction

    International Nuclear Information System (INIS)

    Babenko, V.A.; Petrov, N.M.

    1991-01-01

    A study is made of mathematical and physical aspects of the P-matrix approach within the framework of the potential description of two particle interaction when the dynamics is based on the nonrelativistic Schroedinger equation. A dispersion formula for the P-matrix is derived correctly, different ways of its expansion by means of which it is possible to develop different methods of an approximate description of the quantities characterizing the two-particle interaction are suggested. 15 refs. (author)

  3. Matrix regulators in neural stem cell functions.

    Science.gov (United States)

    Wade, Anna; McKinney, Andrew; Phillips, Joanna J

    2014-08-01

    Neural stem/progenitor cells (NSPCs) reside within a complex and dynamic extracellular microenvironment, or niche. This niche regulates fundamental aspects of their behavior during normal neural development and repair. Precise yet dynamic regulation of NSPC self-renewal, migration, and differentiation is critical and must persist over the life of an organism. In this review, we summarize some of the major components of the NSPC niche and provide examples of how cues from the extracellular matrix regulate NSPC behaviors. We use proteoglycans to illustrate the many diverse roles of the niche in providing temporal and spatial regulation of cellular behavior. The NSPC niche is comprised of multiple components that include; soluble ligands, such as growth factors, morphogens, chemokines, and neurotransmitters, the extracellular matrix, and cellular components. As illustrated by proteoglycans, a major component of the extracellular matrix, the NSPC, niche provides temporal and spatial regulation of NSPC behaviors. The factors that control NSPC behavior are vital to understand as we attempt to modulate normal neural development and repair. Furthermore, an improved understanding of how these factors regulate cell proliferation, migration, and differentiation, crucial for malignancy, may reveal novel anti-tumor strategies. This article is part of a Special Issue entitled Matrix-mediated cell behaviour and properties. Copyright © 2014 Elsevier B.V. All rights reserved.

  4. Exactly solvable birth and death processes

    International Nuclear Information System (INIS)

    Sasaki, Ryu

    2009-01-01

    Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.

  5. Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

    International Nuclear Information System (INIS)

    Ablinger, J.; Schneider, C.; Manteuffel, A. von

    2015-09-01

    Three loop ladder and V-topology diagrams contributing to the massive operator matrix element A Qg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

  6. Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

    Science.gov (United States)

    Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

    2016-05-01

    Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

  7. Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

    Science.gov (United States)

    Zulfatman; Marzuki, Mohammad; Alif Mardiyah, Nur

    2017-04-01

    Two-link flexible manipulator is a manipulator robot which at least one of its arms is made of lightweight material and not rigid. Flexible robot manipulator has some advantages over the rigid robot manipulator, such as lighter, requires less power and costs, and to result greater payload. However, suitable control algorithm to maintain the two-link flexible robot manipulator in accurate positioning is very challenging. In this study, sliding mode control (SMC) was employed as robust control algorithm due to its insensitivity on the system parameter variations and the presence of disturbances when the system states are sliding on a sliding surface. SMC algorithm was combined with linear matrix inequality (LMI), which aims to reduce the effects of chattering coming from the oscillation of the state during sliding on the sliding surface. Stability of the control algorithm is guaranteed by Lyapunov function candidate. Based on simulation works, SMC based LMI resulted in better performance improvements despite the disturbances with significant chattering reduction. This was evident from the decline of the sum of squared tracking error (SSTE) and the sum of squared of control input (SSCI) indexes respectively 25.4% and 19.4%.

  8. The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de; Schoenwald, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Goedicke, A. [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany). Inst. fuer Theoretische Teilchenphysik; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC)

    2017-12-15

    We report on our latest results in the calculation of the two-mass contributions to 3-loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inelastic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and A{sub gq,Q} OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME A{sub gg,Q} are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two-mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.

  9. 3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS

    Energy Technology Data Exchange (ETDEWEB)

    Hasselhuhn, Alexander

    2013-11-15

    In the present thesis several new contributions are made to achieve this goal. Different gauge-invariant subsets of graphs, i.e. whole color factors, are calculated, in order to break the ground for the systematic evaluation of new topologies and to develop corresponding computer algebra codes and computational algorithms to render a part of these problems. Furthermore, also some new results are obtained on the 2-loop level. The work focuses on the heavy quark corrections in the asymptotic region Q{sup 2} >> m{sup 2}, where the heavy flavor Wilson coefficients factorize into the light flavor Wilson coefficients and massive operator matrix elements. New contributions are obtained for the complete O({alpha}{sub s}{sup 3}n{sub f}T{sub F}{sup 2}) corrections to the operator matrix elements A{sub gq,Q} and A{sub gg,Q}. The computation of the Feynman integrals is performed using representations in generalized hypergeometric functions and finite sums. These sums are performed using modern symbolic summation methods implemented in the packages Sigma, Evaluate Multi Sums, and Sum Production. The results are renormalized and checked against Mellin moments. Furthermore, also the 2-loop corrections to the polarized massive OMEs {Delta}A{sub gq,Q} and {Delta}A{sub gg,Q} are calculated. Since the calculations are performed in dimensional regularization and Levi-Civita tensors are present in the diagrams, the OMEs are subject to a finite renormalization. New methods are developed to calculate genuine 3-loop topologies of ladder- and V-type, taking into account the number of heavy quark lines involved. The calculation methods involves mapping the Feynman parameterized representations onto multi-sums and using properties of Appell functions and other generalizations of hypergeometric functions. Two integrals are presented, for which the solution with summation methods remains yet an open problem. At three loops, for the first time also graphs with two distinct massive lines occur

  10. Effect of S-1 combined with oxaliplatin on serum tumor markers, matrix metalloproteinase and immune function in elderly patients with gastric cancer

    Directory of Open Access Journals (Sweden)

    Yong-Feng Shan

    2017-10-01

    Full Text Available Objective: To investigate the effect of Compound Tegafur and Oteracil Potassium Sustained Capsules (S-1 combined with oxaliplatin chemotherapy on serum tumor marker matrix metalloproteinase and immune function in elderly patients with gastric cancer. Methods: According to the random data table, 80 cases of elderly patients with gastric cancer were divided into control group and observation group (n=40, patients in the control group were treated with oxaliplatin combined with Capecitabine Tablets, and the observation group patients were treated with S-1 combined with oxaliplatin, all treated for 6 cycles, before and after treatment, levels of serum tumor markers, matrix metalloproteinase and immune function were compared between the two groups. Results: Before treatment, there was no significant difference in the levels of CEA, CA125, CA19-9, MMP-2, MMP-9, CD3 + , CD4 + , CD8 + and CD4 + /CD8 + between the two groups; After treatment, the levels of CEA, CA125, CA19-9, MMP-2, MMP-9 and CD8 + in the two groups were significantly lower than those in the same group before treatment, and the levels of the observation group[(7.79±2.78 ng/ mL, (22.56±7.31 U/mL, (13.48±3.05 U/mL, (57.84±8.93 ng/mL, (199.14±67.39 ng/ mL and (26.21±4.18%] were significantly lower than those in the control group; Compared with the group before treatment, the levels of CD3 + , CD4 + and CD4 + /CD8 + in the two groups were significantly increased, and the observation group [(66.89±5.84%, (41.63±5.24% and (1.37±0.29] was significantly higher than the control group. Conclusion: S-1 combined with oxaliplatin chemotherapy can effectively reduce serum tumor markers and matrix metalloproteinase levels, improve immune function, has an important clinical value.

  11. Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

    KAUST Repository

    Bisetti, Fabrizio

    2012-06-01

    Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.

  12. T -matrix approach to quark-gluon plasma

    Science.gov (United States)

    Liu, Shuai Y. F.; Rapp, Ralf

    2018-03-01

    A self-consistent thermodynamic T -matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static T -matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding T -matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism, including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy, and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly coupled solution, which features color potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near Tc, and a strongly coupled solution with a strong color potential (much larger than the free energy), resulting in broad nonquasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching Tc.

  13. A conditionally exactly solvable generalization of the inverse square root potential

    Energy Technology Data Exchange (ETDEWEB)

    Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, Ashtarak 0203 (Armenia); Armenian State Pedagogical University, Yerevan 0010 (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)

    2016-11-25

    We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. - Highlights: • We present a conditionally exactly solvable singular potential for 1D Schrödinger equation. • Each of the two fundamental solutions is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. • The exact equation for the energy spectrum is written using two Hermite functions that do not reduce to polynomials.

  14. Functional role of EMMPRIN in the formation and mineralisation of dental matrix in mouse molars.

    Science.gov (United States)

    Xie, Ming; Xing, Guofang; Hou, Liwen; Bao, Jing; Chen, Yuqing; Jiao, Ting; Zhang, Fuqiang

    2015-02-01

    Our previous research has shown that the extracellular matrix metalloproteinase inducer (EMMPRIN) is expressed during and may function in the early development of tooth germs. In the present study, we observed the specific expression of EMMPRIN in ameloblasts and odontoblasts during the middle and late stages of tooth germ development using immunohistochemistry. Furthermore, to extend our understanding of the function of EMMPRIN in odontogenesis, we used an anti-EMMPRIN function-blocking antibody to remove EMMPRIN activity in tooth germ culture in vitro. Both the formation and mineralisation of dental hard tissues were suppressed in the tooth germ culture after the abrogation of EMMPRIN. Meanwhile, significant reductions in VEGF, MMP-9, ALPL, ameloblastin, amelogenin and enamelin expression were observed in antibody-treated tooth germ explants compared to control and normal serum-treated explants. The current results illustrate that EMMPRIN may play a critical role in the processing and maturation of the dental matrix.

  15. A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

    Science.gov (United States)

    Ishkhanyan, Tigran A.; Krainov, Vladimir P.; Ishkhanyan, Artur M.

    2018-05-01

    We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term x-1/2 with arbitrary strength and a repulsive centrifugal barrier core x-2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

  16. Right ventricular function after repair of tetralogy of Fallot: a comparison between bovine pericardium and porcine small intestinal extracellular matrix.

    Science.gov (United States)

    Naik, Ronak; Johnson, Jason; Kumar, T K S; Philip, Ranjit; Boston, Umar; Knott-Craig, Christopher J

    2017-05-29

    The porcine small intestinal extracellular matrix reportedly has the potential to differentiate into viable myocardial cells. When used in tetralogy of Fallot repair, it may improve right ventricular function. We evaluated right ventricular function after repair of tetralogy of Fallot with extracellular matrix versus bovine pericardium. Subjects with non-transannular repair of tetralogy of Fallot with at least 1 year of follow-up were selected. The extracellular matrix and bovine pericardium groups were compared. We used three-dimensional right ventricular ejection fraction, right ventricle global longitudinal strain, and tricuspid annular plane systolic excursion to assess right ventricular function. The extracellular matrix group had 11 patients, whereas the bovine pericardium group had 10 patients. No differences between the groups were found regarding sex ratio, age at surgery, and cardiopulmonary bypass time. The follow-up period was 28±12.6 months in the extracellular matrix group and 50.05±17.6 months in the bovine pericardium group (p=0.001). The mean three-dimensional right ventricular ejection fraction (55.7±5.0% versus 55.3±5.2%, p=0.73), right ventricular global longitudinal strain (-18.5±3.0% versus -18.0±2.2%, p=0.44), and tricuspid annular plane systolic excursions (1.59±0.16 versus 1.59±0.2, p=0.93) were similar in the extracellular matrix group and in the bovine pericardium group, respectively. Right ventricular global longitudinal strain in healthy children is reported at -29±3% in literature. In a small cohort of the patients undergoing non-transannular repair of tetralogy of Fallot, there was no significant difference in right ventricular function between groups having extracellular matrix versus bovine pericardium patches followed-up for more than 1 year. Lower right ventricular longitudinal strain noted in both the groups compared to healthy children.

  17. Revised Line Profile Function for Hydrogenic Species

    Directory of Open Access Journals (Sweden)

    Sapar A.

    2012-09-01

    Full Text Available Analytical series expansions for the hydrogenic spectral line profile functions are derived starting from the three single expressions, obtained by integrating twice the convolution of the Holtsmark, Lorentz and Doppler line profile functions. We get well converging series expansions for the line wings and centers by reducing the number of arguments in the profile function by one, introducing the module of the Holtsmark and Lorentz profiles as a new argument. In the intermediate part of the line, the parabolic cylinder functions expressed via the confluent hypergeometric series, are used. The multi-component Stark splitting of the hydrogenic spectral lines and the modeled stochastic electron transitions in the electric field of the adjacent ions generate wide Doppler plateaux at the line centers, with the characteristic widths estimated from the fit to the characteristic width of the Holtsmark profile. This additional Doppler broadening of the line profile function removes the central dip typical to the Holtsmark profile.

  18. On- and off-resonance radiation-atom-coupling matrix elements involving extended atomic wave functions

    Science.gov (United States)

    Komninos, Yannis; Mercouris, Theodoros; Nicolaides, Cleanthes A.

    2014-01-01

    In continuation of our earlier works, we present results concerning the computation of matrix elements of the multipolar Hamiltonian (MPH) between extended wave functions that are obtained numerically. The choice of the MPH is discussed in connection with the broader issue of the form of radiation-atom (or -molecule) interaction that is appropriate for the systematic solution of various problems of matter-radiation interaction. We derive analytic formulas, in terms of the sine-integral function and spherical Bessel functions of various orders, for the cumulative radial integrals that were obtained and calculated by Komninos, Mercouris, and Nicolaides [Phys. Rev. A 71, 023410 (2005), 10.1103/PhysRevA.71.023410]. This development allows the much faster and more accurate computation of such matrix elements, a fact that enhances the efficiency with which the time-dependent Schrödinger equation is solved nonperturbatively, in the framework of the state-specific expansion approach. The formulas are applicable to the general case where a pair of orbitals with angular parts |ℓ1,m1> and |ℓ2,m2> are coupled radiatively. As a test case, we calculate the matrix elements of the electric field and of the paramagnetic operators for on- and off-resonance transitions, between hydrogenic circular states of high angular momentum, whose quantum numbers are chosen so as to satisfy electric dipole and electric quadrupole selection rules. Because of the nature of their wave function (they are nodeless and the large centrifugal barrier keeps their overwhelming part at large distances from the nucleus), the validity of the electric dipole approximation in various applications where the off-resonance couplings must be considered becomes precarious. For example, for the transition from the circular state with n = 20 to that with n = 21, for which ≈400 a.u., the dipole approximation starts to fail already at XUV wavelengths (λ <125nm).

  19. Neutrino Mass Matrix Textures: A Data-driven Approach

    CERN Document Server

    Bertuzzo, E; Machado, P A N

    2013-01-01

    We analyze the neutrino mass matrix entries and their correlations in a probabilistic fashion, constructing probability distribution functions using the latest results from neutrino oscillation fits. Two cases are considered: the standard three neutrino scenario as well as the inclusion of a new sterile neutrino that potentially explains the reactor and gallium anomalies. We discuss the current limits and future perspectives on the mass matrix elements that can be useful for model building.

  20. Matrix quantum mechanics on S1/Z2

    Directory of Open Access Journals (Sweden)

    P. Betzios

    2018-03-01

    Full Text Available We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

  1. Matrix quantum mechanics on S1 /Z2

    Science.gov (United States)

    Betzios, P.; Gürsoy, U.; Papadoulaki, O.

    2018-03-01

    We study Matrix Quantum Mechanics on the Euclidean time orbifold S1 /Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

  2. Analogies between random matrix ensembles and the one-component plasma in two-dimensions

    Directory of Open Access Journals (Sweden)

    Peter J. Forrester

    2016-03-01

    Full Text Available The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We address this theme in a systematic fashion, identifying the plasma system for the Ginibre ensemble of non-Hermitian Gaussian random matrices G, the spherical ensemble of the product of an inverse Ginibre matrix and a Ginibre matrix G1−1G2, and the ensemble formed by truncating unitary matrices, as well as for products of such matrices. We do this when each has either real, complex or real quaternion elements. One consequence of this analogy is that the leading form of the eigenvalue density follows as a corollary. Another is that the eigenvalue correlations must obey sum rules known to characterise the plasma system, and this leads us to an exhibit of an integral identity satisfied by the two-particle correlation for real quaternion matrices in the neighbourhood of the real axis. Further random matrix ensembles investigated from this viewpoint are self dual non-Hermitian matrices, in which a previous study has related to the one-component plasma system in a disk at inverse temperature β=4, and the ensemble formed by the single row and column of quaternion elements from a member of the circular symplectic ensemble.

  3. New solutions of Heun's general equation

    International Nuclear Information System (INIS)

    Ishkhanyan, Artur; Suominen, Kalle-Antti

    2003-01-01

    We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

  4. Matrix metalloproteinases and left ventricular function and structure in spinal cord injured subjects.

    Science.gov (United States)

    Schreiber, Roberto; Paim, Layde R; de Rossi, Guilherme; Matos-Souza, José R; Costa E Silva, Anselmo de A; Souza, Cristiane M; Borges, Mariane; Azevedo, Eliza R; Alonso, Karina C; Gorla, José I; Cliquet, Alberto; Nadruz, Wilson

    2014-11-01

    Subjects with spinal cord injury (SCI) exhibit impaired left ventricular (LV) diastolic function, which has been reported to be attenuated by regular physical activity. This study investigated the relationship between circulating matrix metalloproteinases (MMPs) and tissue inhibitors of MMPs (TIMPs) and echocardiographic parameters in SCI subjects and the role of physical activity in this regard. Forty-two men with SCI [19 sedentary (S-SCI) and 23 physically-active (PA-SCI)] were evaluated by clinical, anthropometric, laboratory, and echocardiographic analysis. Plasmatic pro-MMP-2, MMP-2, MMP-8, pro-MMP-9, MMP-9, TIMP-1 and TIMP-2 levels were determined by enzyme-linked immunosorbent assay and zymography. PA-SCI subjects presented lower pro-MMP-2 and pro-MMP-2/TIMP-2 levels and improved markers of LV diastolic function (lower E/Em and higher Em and E/A values) than S-SCI ones. Bivariate analysis showed that pro-MMP-2 correlated inversely with Em and directly with E/Em, while MMP-9 correlated directly with LV mass index and LV end-diastolic diameter in the whole sample. Following multiple regression analysis, pro-MMP-2, but not physical activity, remained associated with Em, while MMP-9 was associated with LV mass index in the whole sample. These findings suggest differing roles for MMPs in LV structure and function regulation and an interaction among pro-MMP-2, diastolic function and physical activity in SCI subjects. Copyright © 2014 Elsevier B.V. All rights reserved.

  5. Comparison of two matrix data structures for advanced CSM testbed applications

    Science.gov (United States)

    Regelbrugge, M. E.; Brogan, F. A.; Nour-Omid, B.; Rankin, C. C.; Wright, M. A.

    1989-01-01

    The first section describes data storage schemes presently used by the Computational Structural Mechanics (CSM) testbed sparse matrix facilities and similar skyline (profile) matrix facilities. The second section contains a discussion of certain features required for the implementation of particular advanced CSM algorithms, and how these features might be incorporated into the data storage schemes described previously. The third section presents recommendations, based on the discussions of the prior sections, for directing future CSM testbed development to provide necessary matrix facilities for advanced algorithm implementation and use. The objective is to lend insight into the matrix structures discussed and to help explain the process of evaluating alternative matrix data structures and utilities for subsequent use in the CSM testbed.

  6. MATLAB matrix algebra

    CERN Document Server

    Pérez López, César

    2014-01-01

    MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and ...

  7. Matrix theory selected topics and useful results

    CERN Document Server

    Mehta, Madan Lal

    1989-01-01

    Matrices and operations on matrices ; determinants ; elementary operations on matrices (continued) ; eigenvalues and eigenvectors, diagonalization of normal matrices ; functions of a matrix ; positive definiteness, various polar forms of a matrix ; special matrices ; matrices with quaternion elements ; inequalities ; generalised inverse of a matrix ; domain of values of a matrix, location and dispersion of eigenvalues ; symmetric functions ; integration over matrix variables ; permanents of doubly stochastic matrices ; infinite matrices ; Alexander matrices, knot polynomials, torsion numbers.

  8. Novel insights into the function and dynamics of extracellular matrix in liver fibrosis

    DEFF Research Database (Denmark)

    Karsdal, Morten A; Manon-Jensen, Tina; Genovese, Federica

    2015-01-01

    Emerging evidence suggests that altered components and posttranslational modifications of proteins in the extracellular matrix (ECM) may both initiate and drive disease progression. The ECM is a complex grid consisting of multiple proteins, most of which play a vital role in containing......) explore key structural and functional components of the ECM as exemplified by monogenetic disorders leading to severe pathologies, 2) discuss selected pathological posttranslational modifications of ECM proteins resulting in altered functional (signaling) properties from the original structural proteins......, and 3) discuss how these findings support the novel concept that an increasing number of components of the ECM harbor signaling functions that can modulate fibrotic liver disease. The ECM entails functions in addition to anchoring cells and modulating their migratory behavior. Key ECM components...

  9. Evaluation of the multi-sums for large scale problems

    International Nuclear Information System (INIS)

    Bluemlein, J.; Hasselhuhn, A.; Schneider, C.

    2012-02-01

    A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter ε can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)

  10. Evaluation of the multi-sums for large scale problems

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, J.; Hasselhuhn, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

    2012-02-15

    A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter {epsilon} can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)

  11. Matrix stiffness-modulated proliferation and secretory function of the airway smooth muscle cells.

    Science.gov (United States)

    Shkumatov, Artem; Thompson, Michael; Choi, Kyoung M; Sicard, Delphine; Baek, Kwanghyun; Kim, Dong Hyun; Tschumperlin, Daniel J; Prakash, Y S; Kong, Hyunjoon

    2015-06-01

    Multiple pulmonary conditions are characterized by an abnormal misbalance between various tissue components, for example, an increase in the fibrous connective tissue and loss/increase in extracellular matrix proteins (ECM). Such tissue remodeling may adversely impact physiological function of airway smooth muscle cells (ASMCs) responsible for contraction of airways and release of a variety of bioactive molecules. However, few efforts have been made to understand the potentially significant impact of tissue remodeling on ASMCs. Therefore, this study reports how ASMCs respond to a change in mechanical stiffness of a matrix, to which ASMCs adhere because mechanical stiffness of the remodeled airways is often different from the physiological stiffness. Accordingly, using atomic force microscopy (AFM) measurements, we found that the elastic modulus of the mouse bronchus has an arithmetic mean of 23.1 ± 14 kPa (SD) (median 18.6 kPa). By culturing ASMCs on collagen-conjugated polyacrylamide hydrogels with controlled elastic moduli, we found that gels designed to be softer than average airway tissue significantly increased cellular secretion of vascular endothelial growth factor (VEGF). Conversely, gels stiffer than average airways stimulated cell proliferation, while reducing VEGF secretion and agonist-induced calcium responses of ASMCs. These dependencies of cellular activities on elastic modulus of the gel were correlated with changes in the expression of integrin-β1 and integrin-linked kinase (ILK). Overall, the results of this study demonstrate that changes in matrix mechanics alter cell proliferation, calcium signaling, and proangiogenic functions in ASMCs. Copyright © 2015 the American Physiological Society.

  12. Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

    Science.gov (United States)

    Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

    2018-03-01

    In this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d - 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models.

  13. Single-particle density matrix and superfluidity in the two-dimensional Bose Coulomb fluid

    International Nuclear Information System (INIS)

    Minguzzi, A.; Tosi, M.P.; Davoudi, B.

    2002-01-01

    A study by Magro and Ceperley [Phys. Rev. Lett. 73, 826 (1994)] has shown that the ground state of the two-dimensional fluid of charged bosons with logarithmic interactions is not Bose condensed, but exhibits algebraic off-diagonal order in the single-particle density matrix ρ(r). We use a hydrodynamic Hamiltonian expressed in terms of density and phase operators, in combination with an f-sum rule on the superfluid fraction, to reproduce these results and to extend the evaluation of the density matrix to finite temperature T. This approach allows us to treat the liquid as a superfluid in the absence of a condensate. The algebraic decay of the one-body density matrix is due to correlations between phase fluctuations, and we find that the exponent in the power law is determined by the superfluid density n s (T). We also find that the plasmon gap in the single-particle energy spectrum at long wavelengths decreases with increasing T and closes at the critical temperature for the onset of superfluidity

  14. Matrix metalloproteinase-12 (MMP-12) in osteoclasts

    DEFF Research Database (Denmark)

    Hou, Peng; Troen, Tine; Ovejero, Maria C

    2004-01-01

    Osteoclasts require matrix metalloproteinase (MMP) activity and cathepsin K to resorb bone, but the critical MMP has not been identified. Osteoclasts express MMP-9 and MMP-14, which do not appear limiting for resorption, and the expression of additional MMPs is not clear. MMP-12, also called...... bone show MMP-12 expression in osteoclasts in calvariae and long bones. We also demonstrate that recombinant MMP-12 cleaves the putative functional domains of osteopontin and bone sialoprotein, two bone matrix proteins that strongly influence osteoclast activities, such as attachment, spreading...

  15. Function of Matrix IGF-1 in Coupling Bone Resorption and Formation

    Science.gov (United States)

    Crane, Janet L.; Cao, Xu

    2013-01-01

    Balancing bone resorption and formation is the quintessential component for the prevention of osteoporosis. Signals that determine the recruitment, replication, differentiation, function, and apoptosis of osteoblasts and osteoclasts direct bone remodeling and determine whether bone tissue is gained, lost, or balanced. Therefore understanding the signaling pathways involved in the coupling process will help develop further targets for osteoporosis therapy, by blocking bone resorption or enhancing bone formation in a space and time dependent manner. Insulin-like growth factor type 1 (IGF-1) has long been known to play a role in bone strength. It is one of the most abundant substances in the bone matrix, circulates systemically and is secreted locally, and has a direct relationship with bone mineral density. Recent data has helped further our understanding of the direct role of IGF-1 signaling in coupling bone remodeling which will be discussed in this review. The bone marrow microenvironment plays a critical role in the fate of MSCs and HSCs and thus how IGF-1 interacts with other factors in the microenvironment are equally important. While previous clinical trials with IGF-1 administration have been unsuccessful at enhancing bone formation, advances in basic science studies have provided insight into further mechanisms that should be considered for future trials. Additional basic science studies dissecting the regulation and the function of matrix IGF-1 in modeling and remodeling will continue to provide further insight for future directions for anabolic therapies for osteoporosis. PMID:24068256

  16. Function of matrix IGF-1 in coupling bone resorption and formation.

    Science.gov (United States)

    Crane, Janet L; Cao, Xu

    2014-02-01

    Balancing bone resorption and formation is the quintessential component for the prevention of osteoporosis. Signals that determine the recruitment, replication, differentiation, function, and apoptosis of osteoblasts and osteoclasts direct bone remodeling and determine whether bone tissue is gained, lost, or balanced. Therefore, understanding the signaling pathways involved in the coupling process will help develop further targets for osteoporosis therapy, by blocking bone resorption or enhancing bone formation in a space- and time-dependent manner. Insulin-like growth factor type 1 (IGF-1) has long been known to play a role in bone strength. It is one of the most abundant substances in the bone matrix, circulates systemically and is secreted locally, and has a direct relationship with bone mineral density. Recent data has helped further our understanding of the direct role of IGF-1 signaling in coupling bone remodeling which will be discussed in this review. The bone marrow microenvironment plays a critical role in the fate of mesenchymal stem cells and hematopoietic stem cells and thus how IGF-1 interacts with other factors in the microenvironment are equally important. While previous clinical trials with IGF-1 administration have been unsuccessful at enhancing bone formation, advances in basic science studies have provided insight into further mechanisms that should be considered for future trials. Additional basic science studies dissecting the regulation and the function of matrix IGF-1 in modeling and remodeling will continue to provide further insight for future directions for anabolic therapies for osteoporosis.

  17. Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security

    Directory of Open Access Journals (Sweden)

    Eligijus Sakalauskas

    2017-01-01

    Full Text Available The improved version of the author’s previously declared asymmetric cipher protocol based on matrix power function (MPF is presented. Proposed modification avoids discrete logarithm attack (DLA which could be applied to the previously declared protocol. This attack allows us to transform the initial system of MPF equations to so-called matrix multivariate quadratic (MMQ system of equations, which is a system representing a subclass of multivariate quadratic (MQ systems of equations. We are making a conjecture that avoidance of DLA in protocol, presented here, should increase its security, since an attempt to solve the initial system of MPF equations would appear to be no less complex than solving the system of MMQ equations. No algorithms are known to solve such a system of equations. Security parameters and their secure values are defined. Security analysis against chosen plaintext attack (CPA and chosen ciphertext attack (CCA is presented. Measures taken to prevent DLA attack increase the security of this protocol with respect to the previously declated protocol.

  18. Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion

    Directory of Open Access Journals (Sweden)

    Qiuyu Wang

    2016-06-01

    Full Text Available In this paper, we  propose a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point. This algorithm preserves the computational simplicity of classical proximal gradient algorithm where a singular value decomposition in proximal operator is involved. Global convergence is followed directly in the literature. Numerical results are reported to show the efficiency of the algorithm.

  19. Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

    Science.gov (United States)

    Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

    2018-05-01

    Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure

  20. Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism ( S-quantization)

    Science.gov (United States)

    Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.

    2017-10-01

    Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate

  1. Integrins and extracellular matrix in mechanotransduction

    Directory of Open Access Journals (Sweden)

    Ramage L

    2011-12-01

    Full Text Available Lindsay RamageQueen’s Medical Research Institute, University of Edinburgh, Edinburgh, UKAbstract: Integrins are a family of cell surface receptors which mediate cell–matrix and cell–cell adhesions. Among other functions they provide an important mechanical link between the cells external and intracellular environments while the adhesions that they form also have critical roles in cellular signal-transduction. Cell–matrix contacts occur at zones in the cell surface where adhesion receptors cluster and when activated the receptors bind to ligands in the extracellular matrix. The extracellular matrix surrounds the cells of tissues and forms the structural support of tissue which is particularly important in connective tissues. Cells attach to the extracellular matrix through specific cell-surface receptors and molecules including integrins and transmembrane proteoglycans. Integrins work alongside other proteins such as cadherins, immunoglobulin superfamily cell adhesion molecules, selectins, and syndecans to mediate cell–cell and cell–matrix interactions and communication. Activation of adhesion receptors triggers the formation of matrix contacts in which bound matrix components, adhesion receptors, and associated intracellular cytoskeletal and signaling molecules form large functional, localized multiprotein complexes. Cell–matrix contacts are important in a variety of different cell and tissue properties including embryonic development, inflammatory responses, wound healing, and adult tissue homeostasis. This review summarizes the roles and functions of integrins and extracellular matrix proteins in mechanotransduction.Keywords: ligand binding, α subunit, ß subunit, focal adhesion, cell differentiation, mechanical loading, cell–matrix interaction

  2. Quasi-particle energy spectra in local reduced density matrix functional theory.

    Science.gov (United States)

    Lathiotakis, Nektarios N; Helbig, Nicole; Rubio, Angel; Gidopoulos, Nikitas I

    2014-10-28

    Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A 90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C20 isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solids.

  3. Self-consistent embedding of density-matrix renormalization group wavefunctions in a density functional environment.

    Science.gov (United States)

    Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus

    2015-01-28

    We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.

  4. Solution of Differential Equations with Polynomial Coefficients with the Aid of an Analytic Continuation of Laplace Transform

    Directory of Open Access Journals (Sweden)

    Tohru Morita

    2016-03-01

    Full Text Available In a series of papers, we discussed the solution of Laplace’s differential equation (DE by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC of Riemann–Liouville fractional derivative (fD and the distribution theory in the space D′R or the AC of Laplace transform. We now obtain the solutions of the hypergeometric DE, which are expressed by the hypergeometric functions, with the aid of the AC of Riemann–Liouville fD, and the distribution theory in the space D′r,R, which is introduced in this paper, or by the term-by-term inverse Laplace transform of AC of Laplace transform of the solution expressed by a series.

  5. Residual, restarting and Richardson iteration for the matrix exponential

    NARCIS (Netherlands)

    Bochev, Mikhail A.; Grimm, Volker; Hochbruck, Marlis

    2013-01-01

    A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential of a given matrix times a given vector has to be computed.

  6. Residual, restarting and Richardson iteration for the matrix exponential

    NARCIS (Netherlands)

    Bochev, Mikhail A.

    2010-01-01

    A well-known problem in computing some matrix functions iteratively is a lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Assume, the matrix exponential of a given matrix times a given vector has to be computed. We

  7. Non-Hermitian Extensions of Wishart Random Matrix Ensembles

    International Nuclear Information System (INIS)

    Akemann, G.

    2011-01-01

    We briefly review the solution of three ensembles of non-Hermitian random matrices generalizing the Wishart-Laguerre (also called chiral) ensembles. These generalizations are realized as Gaussian two-matrix models, where the complex eigenvalues of the product of the two independent rectangular matrices are sought, with the matrix elements of both matrices being either real, complex or quaternion real. We also present the more general case depending on a non-Hermiticity parameter, that allows us to interpolate between the corresponding three Hermitian Wishart ensembles with real eigenvalues and the maximally non-Hermitian case. All three symmetry classes are explicitly solved for finite matrix size N x M for all complex eigenvalue correlations functions (and real or mixed correlations for real matrix elements). These are given in terms of the corresponding kernels built from orthogonal or skew-orthogonal Laguerre polynomials in the complex plane. We then present the corresponding three Bessel kernels in the complex plane in the microscopic large-N scaling limit at the origin, both at weak and strong non-Hermiticity with M - N ≥ 0 fixed. (author)

  8. The matrix elements of the potential energy operator between the Sp(2,R) basis generating functions. Near-magic nuclei

    International Nuclear Information System (INIS)

    Filippov, G.F.; Ovcharenko, V.I.; Teryoshin, Yu.V.

    1980-01-01

    For near-magnetic nuclei, the matrix elements of the central exchange nucleon-nucleon interaction potential energy operator between the generating functions of the total basis of the Sn are obtained. The basis states are highest weigt vectorsp(2,R) irreducible representatio of the SO(3) irredicible representation and in addition, have a definite O(A-1) symmetry. The Sp(2,R) basis generating matrix elements simplify essentially the problem of calculating the spectrum of collective excitations of the atomic nucleus over an intrinsic function of definite O(A-1) symmetry

  9. On spin and matrix models in the complex plane

    International Nuclear Information System (INIS)

    Damgaard, P.H.; Heller, U.M.

    1993-01-01

    We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of two-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-N partition function zeros in the complex plane. (orig.)

  10. Classification of matrix-product ground states corresponding to one-dimensional chains of two-state sites of nearest neighbor interactions

    International Nuclear Information System (INIS)

    Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad; Aghamohammadi, Amir

    2011-01-01

    A complete classification is given for one-dimensional chains with nearest-neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.

  11. Biological function evaluation and effects of laser micro-pore burn-denatured acellular dermal matrix.

    Science.gov (United States)

    Zhang, Youlai; Zeng, Yuanlin; Xin, Guohua; Zou, Lijin; Ding, Yuewei; Duyin, Jiang

    2018-03-01

    In the field of burns repairs, many problems exist in the shortage of donor skin, the expense of allograft or xenograft skin, temporary substitution and unsatisfactory extremity function after wound healing. Previous studies showed that burn-denatured skin could return to normal dermis formation and function. This study investigates the application of laser micro-pore burn-denatured acellular dermis matrix (DADM) from an escharotomy in the repair of burn wounds and evaluates the biological properties and wound repair effects of DADM in implantation experiments in Kunming mice. Specific-pathogen-free (SPF) Kunming mice were used in this study. A deep II° burn wound was created on the dorsum of the mice by an electric heated water bath. The full-thickness wound tissue was harvested. The necrotic tissue and subcutaneous tissue were removed. The denatured dermis was preserved and treated with 0.25% trypsin, 0.5% Triton X-100. The DADM was drilled by laser micro-pore. The biological properties and grafting effects of laser micro-pore burn-DADM were evaluated by morphology, cytokine expression levels and subcutaneous implantation experiments in Kunming mice. We found statistical significance (Ppore burn-DADM (experimental group) compared to the control group (no laser micro-pore burn-DADM). Cytokine expression level was different in the dermal matrixes harvested at various time points after burn (24h, 48h, 72h and infected wound group). Comparing the dermal matrix from 24h burn tissue to infected wound tissue, the expression level of IL-6, MMP-24, VE-cadherin and VEGF were decreased. We found no inflammatory cells infiltration in the dermal matrix were observed in both experimental and control groups (24h burn group), while the obviously vascular infiltration and fiber fusion were observed in the experimental group after subcutaneous implantation experiments. There was better bio-performance, low immunogenicity and better dermal incorporation after treated by laser

  12. Reactive fillers based on SWCNTs functionalized with matrix-based moieties for the production of epoxy composites with superior and tunable properties

    International Nuclear Information System (INIS)

    González-Domínguez, Jose M; Ansón-Casaos, A; Martínez, M Teresa; Martínez-Rubí, Yadienka; Simard, Benoit; Díez-Pascual, Ana M; Gómez-Fatou, Marian

    2012-01-01

    Composite materials based on epoxy matrix and single-walled carbon nanotubes (SWCNTs) are able to exhibit outstanding improvements in physical properties when using a tailored covalent functionalization with matrix-based moieties containing terminal amines or epoxide rings. The proper choice of grafted moiety and integration protocol makes it feasible to tune the composite physical properties. At 0.5 wt% SWCNT loading, these composites exhibit up to 65% improvement in storage modulus, 91% improvement in tensile strength, and 65% improvement in toughness. A 15 °C increase in the glass transition temperature relative to the parent matrix was also achieved. This suggests that a highly improved interfacial bonding between matrix and filler, coupled to improved dispersion, are achieved. The degradation temperatures show an upshift in the range of 40–60 °C, which indicates superior thermal performance. Electrical conductivity ranges from ∼10 −13 to ∼10 −3 S cm −1 , which also shows the possibility of tuning the insulating or conductive behaviour of the composites. The chemical affinity of the functionalization moieties with the matrix and the unchanged molecular structure at the SWCNT/matrix interface are responsible for such improvements. (paper)

  13. Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

    KAUST Repository

    Bisetti, Fabrizio

    2012-01-01

    with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix

  14. New solutions of Heun's general equation

    Energy Technology Data Exchange (ETDEWEB)

    Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak (Armenia); Suominen, Kalle-Antti [Helsinki Institute of Physics, PL 64, Helsinki (Finland)

    2003-02-07

    We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

  15. Love waves in functionally graded piezoelectric materials by stiffness matrix method.

    Science.gov (United States)

    Ben Salah, Issam; Wali, Yassine; Ben Ghozlen, Mohamed Hédi

    2011-04-01

    A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO(2), the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour. Copyright © 2010 Elsevier B.V. All rights reserved.

  16. Hyperfine electron-nuclear interactions in the frame of the Density Functional and of the Density Matrix Methods

    International Nuclear Information System (INIS)

    Pavlov, R.L.; Pavlov, L.I.; Raychev, P.P.; Garistov, V.P.; Dimitrova-Ivanovich, M.

    2002-01-01

    The matrix elements and expectation values of the hyperfine interaction operators are presented in a form suitable for numerical implementation in density matrix methods. The electron-nuclear spin-spin (dipolar and contact) interactions are considered, as well as the interaction between nuclear spin and electron-orbital motions. These interactions from the effective Breit-Pauli Hamiltonian determine the hyperfine structure in ESR spectra and contribute to chemical shifts in NMR. Applying the Wigner-Eckart theorem in the irreducible tensor-operator technique and the spin-space separation scheme, the matrix elements and expectation values of these relativistic corrections are expressed in analytical form. The final results are presented as products, or sums of products, of factors determined by the spin and (or) angular momentum symmetry and a spatial part determined by the action of the symmetrized tensor-operators on the normalized matrix or function of the spin or charge distribution.

  17. Nuclear matrix - structure, function and pathogenesis.

    Science.gov (United States)

    Wasąg, Piotr; Lenartowski, Robert

    2016-12-20

    The nuclear matrix (NM), or nuclear skeleton, is the non-chromatin, ribonucleoproteinaceous framework that is resistant to high ionic strength buffers, nonionic detergents, and nucleolytic enzymes. The NM fulfills a structural role in eukaryotic cells and is responsible for maintaining the shape of the nucleus and the spatial organization of chromatin. Moreover, the NM participates in several cellular processes, such as DNA replication/repair, gene expression, RNA transport, cell signaling and differentiation, cell cycle regulation, apoptosis and carcinogenesis. Short nucleotide sequences called scaffold/matrix attachment regions (S/MAR) anchor the chromatin loops to the NM proteins (NMP). The NMP composition is dynamic and depends on the cell type and differentiation stage or metabolic activity. Alterations in the NMP composition affect anchoring of the S/MARs and thus alter gene expression. This review aims to systematize information about the skeletal structure of the nucleus, with particular emphasis on the organization of the NM and its role in selected cellular processes. We also discuss several diseases that are caused by aberrant NM structure or dysfunction of individual NM elements.

  18. Matrix regularization of 4-manifolds

    OpenAIRE

    Trzetrzelewski, M.

    2012-01-01

    We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...

  19. Matrix-assisted peptide synthesis on nanoparticles.

    Science.gov (United States)

    Khandadash, Raz; Machtey, Victoria; Weiss, Aryeh; Byk, Gerardo

    2014-09-01

    We report a new method for multistep peptide synthesis on polymeric nanoparticles of differing sizes. Polymeric nanoparticles were functionalized via their temporary embedment into a magnetic inorganic matrix that allows multistep peptide synthesis. The matrix is removed at the end of the process for obtaining nanoparticles functionalized with peptides. The matrix-assisted synthesis on nanoparticles was proved by generating various biologically relevant peptides. Copyright © 2014 European Peptide Society and John Wiley & Sons, Ltd.

  20. Elastic modulus of Al-Si/SiC metal matrix composites as a function of volume fraction

    Energy Technology Data Exchange (ETDEWEB)

    Santhosh Kumar, S; Rajasekharan, T [Powder Metallurgy Group, Defence Metallurgical Research Laboratory, Kanchanbagh PO, Hyderabad-500 058 (India); Seshu Bai, V [School of Physics, University of Hyderabad, Central University PO, Hyderabad-500 046 (India); Rajkumar, K V; Sharma, G K; Jayakumar, T, E-mail: dearsanthosh@gmail.co [Non-Destructive Evaluation Division, Indira Gandhi Center for Atomic Research, Kalpakkam, Chennai-603 102 (India)

    2009-09-07

    Aluminum alloy matrix composites have emerged as candidate materials for electronic packaging applications in the field of aerospace semiconductor electronics. Composites prepared by the pressureless infiltration technique with high volume fractions in the range 0.41-0.70 were studied using ultrasonic velocity measurements. For different volume fractions of SiC, the longitudinal velocity and shear velocity were found to be in the range of 7600-9300 m s{sup -1} and 4400-5500 m s{sup -1}, respectively. The elastic moduli of the composites were determined from ultrasonic velocities and were analysed as a function of the volume fraction of the reinforcement. The observed variation is discussed in the context of existing theoretical models for the effective elastic moduli of two-phase systems.

  1. Extremely compact formulas for the Fourier transform of a product of two-centre Slater-type orbitals

    International Nuclear Information System (INIS)

    Vukovic, T; Dmitrovic, S

    2010-01-01

    A compact formula for the Fourier transform of a product of Slater-type orbitals on different centres is derived. The integral is reduced to a finite one-dimensional integration over non-oscillatory hypergeometric functions of type 1 F 2 (x;y;z). The formula is valid for all quantum numbers and does not involve the reduced Bessel functions that are usually used to evaluate these integrals. Reduced formulas are calculated for some special directions in the reciprocal space. Also, some useful identities for the Fourier transforms of a product of Slater-type orbitals with correlated sets of parameters are obtained. In order to illustrate simple and efficient use of the presented results, we have applied them to graphene.

  2. Multichannel quantum defect and reduced R-matrix

    International Nuclear Information System (INIS)

    Hategan, C.; Ionescu, R.A.; Cutoiu, D.; Gugiu, M.

    2002-01-01

    The collision of an electron with the atomic electronic core or the scattering of a nucleon on the atomic nucleus, usually, result into multiparticle excitations producing a resonance of a compound system, followed by its decay in reaction channels. Both in the electron-atom collisions and in nucleon-nucleus reactions, these multichannel resonances are described by poles of all R-Matrix elements. The resonances originating in single particle states, either in electron-atom collision or in nucleon-nucleus scattering, are approached in quite different descriptions. For example, the single-particle resonance in nuclear scattering is described, in R-Matrix Theory, by a perturbative method due to Bloch. The original single-nucleon state overlaps the actual states of the nucleus, resulting into a micro-giant description of the single particle resonance. The spectroscopic aspects of the single particle state, mixed with actual nuclear states, are subject of nucleon (or single particle) Strength Function. The electron, involving single particle Rydberg state in an atomic collision, 'avoids' its wave function mixing with that of inner multielectron core, because it is spatially far-away located from that core. This process is usually described by the Multichannel Quantum Defect Theory (MQDT). In the electron-atom scattering rather the effect of inner multielectron core on Rydberg electrons is studied by means of a global parameter, historically called 'Quantum Defect'. Both these types of resonances have in common the preserving of the single-particle wave function in a complex system with multiparticle excitations. In this work one approaches description of single-particle (electron or nucleon) resonance in a multichannel system. The single particle multichannel resonances are not longer described by a R-Matrix pole (specific for resonances originating in multiparticle excitations) but rather by a natural method for incorporating a single particle state in R-Matrix Theory

  3. Densis. Densimetric representation of two-dimensional matrices

    International Nuclear Information System (INIS)

    Los Arcos Merino, J.M.

    1978-01-01

    Densis is a Fortran V program which allows off-line control of a Calcomp digital plotter, to represent a two-dimensional matrix of numerical elements in the form of a variable shading intensity map in two colours. Each matrix element is associated to a square of a grid which is traced over by lines whose number is a function of the element value according to a selected scale. Program features, subroutine structure and running instructions, are described. Some typical results, for gamma-gamma coincidence experimental data and a sampled two-dimensional function, are indicated. (author)

  4. Effect of nano size 3% wt TaC particles dispersion in two different metallic matrix composites

    International Nuclear Information System (INIS)

    Gomes, U.U.; Oliveira, L.A.; Souza, C.P.; Menezes, R.C.; Furukava, M.; Torres, Y.

    2009-01-01

    This work studies the characteristics of two different metallic matrixes composites, ferritic and austenitic steels, reinforced with 3% wt nano size tantalum carbide by powder metallurgy. The starting powders were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The effects of the nano sized carbide dispersion on the matrix microstructures and its consequences on the mechanical properties were identified. The preliminary results showed that the sintering were influenced by morphology and the distribution of carbide and the alloys. (author)

  5. Large-N limit of the two-Hermitian-matrix model by the hidden BRST method

    International Nuclear Information System (INIS)

    Alfaro, J.

    1993-01-01

    This paper discusses the large-N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden Becchi-Rouet-Stora-Tyutin method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large N

  6. Mesoporous tungsten titanate as matrix for matrix-assisted laser desorption/ionization time-of-flight mass spectrometry analysis of biomolecules

    International Nuclear Information System (INIS)

    Shan Zhe; Han Lu; Yuan Minjia; Deng Chunhui; Zhao Dongyuan; Tu Bo; Yang Pengyuan

    2007-01-01

    In this paper, mesoporous tungsten titanate (WTiO) with different nano-pore structures was utilized as matrix for the analysis of short peptides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS). Effect of characteristic features of mesoporous matrices on laser desorption/ionization process was investigated. Experiments showed that the ordered two-dimensional and three-dimensional mesoporous matrices were superior in performance to the non-ordered WTiO matrix. The dramatic enhancement of signal sensitivity by the ordered mesoporous matrices can be reasonably attributed to the ordered structure, which facilitated the understanding on structure-function relationship in mesoporous cavity for laser desorption process of adsorbed biomolecules. With the ordered mesoporous matrix, the short peptides are successfully detected. The presence of trace alkali metal salt effectively increased the analyte ion yields and the MALDI-TOFMS using the inorganic mesoporous matrices displayed a high salt tolerance. The developed technique also showed a satisfactory performance in peptide-mapping and amino-acid sequencing analysis

  7. Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (I)-Formalism

    Institute of Scientific and Technical Information of China (English)

    DAI Lian-Rong; PAN Feng

    2001-01-01

    The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the Un representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.

  8. Matrix elements of intraband transitions in quantum dot intermediate band solar cells: the influence of quantum dot presence on the extended-state electron wave-functions

    International Nuclear Information System (INIS)

    Nozawa, Tomohiro; Arakawa, Yasuhiko

    2014-01-01

    The intraband transitions which are essential for quantum dot intermediate band solar cells (QD IBSCs) are theoretically investigated by estimating the matrix elements from a ground bound state, which is often regarded as an intermediate band (IB), to conduction band (CB) states for a structure with a quantum dot (QD) embedded in a matrix (a QD/matrix structure). We have found that the QD pushes away the electron envelope functions (probability densities) from the QD region in almost all quantum states above the matrix CB minimum. As a result, the matrix elements of the intraband transitions in the QD/matrix structure are largely reduced, compared to those calculated assuming the envelope functions of free electrons (i.e., plane-wave envelope functions) in a matrix structure as the final states of the intraband transitions. The result indicates the strong influence of the QD itself on the intraband transitions from the IB to the CB states in QD IBSC devices. This work will help in better understanding the problem of the intraband transitions and give new insight, that is, engineering of quantum states is indispensable for the realization of QD IBSCs with high solar energy conversion efficiencies. (paper)

  9. The role of singular values of measured frequency response function matrix in modal damping estimation (Part I: Theory)

    OpenAIRE

    Pápai, Ferenc; Szűcs, István

    2015-01-01

    The singular value decomposition of the measured frequency response function matrix, as a very effective tool of experimental modal analysis is used over the last twenty-five years. The complex mode indication function has become a common numerical tool in processing experimental data. There are many references on the development of complex mode indication function including the enhanced mode indication function and its use together with the enhanced frequency response function to form spatia...

  10. The role of singular values of measured frequency response function matrix in modal damping estimation (Part II: Investigations)

    OpenAIRE

    Pápai, Ferenc; Szűcs, István

    2015-01-01

    The singular value decomposition of the measured frequency response function matrix, as a very effective tool of experimental modal analysis is used over the last twenty-five years. The complex mode indication function has become a common numerical tool in processing experimental data. There are many references on the development of complex mode indication function including the enhanced mode indication function and its use together with the enhanced frequency response function to form spatia...

  11. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  12. R-matrix study of ionization in barium via two-photon interfering routes

    International Nuclear Information System (INIS)

    Aymar, M.; Luc-Koenig, E.; Lecomte, J. M.; Millet, M.; Lyras, A.

    2000-01-01

    A quantitative analysis of part of the experimental data reported by Wang, Chen and Elliott [1,3] who studied in barium coherent control through two-color resonant interfering paths is reported. Dynamics of the two-color photoionization process, described as an adiabatic process in the rotating wave approximation, is governed by the coherent excitation of the 6s6p and 6s7p 1 P 1 intermediate states. Interference effects are found to play a minor role. The required atomic parameters are obtained from a theoretical approach based on a combination of jj-coupled eigenchannel R-matrix and Multichannel Quantum Defect Theory

  13. Quantitative evaluation of the matrix effect in bioanalytical methods based on LC-MS: A comparison of two approaches.

    Science.gov (United States)

    Rudzki, Piotr J; Gniazdowska, Elżbieta; Buś-Kwaśnik, Katarzyna

    2018-06-05

    Liquid chromatography coupled to mass spectrometry (LC-MS) is a powerful tool for studying pharmacokinetics and toxicokinetics. Reliable bioanalysis requires the characterization of the matrix effect, i.e. influence of the endogenous or exogenous compounds on the analyte signal intensity. We have compared two methods for the quantitation of matrix effect. The CVs(%) of internal standard normalized matrix factors recommended by the European Medicines Agency were evaluated against internal standard normalized relative matrix effects derived from Matuszewski et al. (2003). Both methods use post-extraction spiked samples, but matrix factors require also neat solutions. We have tested both approaches using analytes of diverse chemical structures. The study did not reveal relevant differences in the results obtained with both calculation methods. After normalization with the internal standard, the CV(%) of the matrix factor was on average 0.5% higher than the corresponding relative matrix effect. The method adopted by the European Medicines Agency seems to be slightly more conservative in the analyzed datasets. Nine analytes of different structures enabled a general overview of the problem, still, further studies are encouraged to confirm our observations. Copyright © 2018 Elsevier B.V. All rights reserved.

  14. Non-relativistic quantum mechanics

    CERN Document Server

    Puri, Ravinder R

    2017-01-01

    This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...

  15. Comparative analyses identified species-specific functional roles in oral microbial genomes

    Science.gov (United States)

    Chen, Tsute; Gajare, Prasad; Olsen, Ingar; Dewhirst, Floyd E.

    2017-01-01

    ABSTRACT The advent of next generation sequencing is producing more genomic sequences for various strains of many human oral microbial species and allows for insightful functional comparisons at both intra- and inter-species levels. This study performed in-silico functional comparisons for currently available genomic sequences of major species associated with periodontitis including Aggregatibacter actinomycetemcomitans (AA), Porphyromonas gingivalis (PG), Treponema denticola (TD), and Tannerella forsythia (TF), as well as several cariogenic and commensal streptococcal species. Complete or draft sequences were annotated with the RAST to infer structured functional subsystems for each genome. The subsystems profiles were clustered to groups of functions with similar patterns. Functional enrichment and depletion were evaluated based on hypergeometric distribution to identify subsystems that are unique or missing between two groups of genomes. Unique or missing metabolic pathways and biological functions were identified in different species. For example, components involved in flagellar motility were found only in the motile species TD, as expected, with few exceptions scattered in several streptococcal species, likely associated with chemotaxis. Transposable elements were only found in the two Bacteroidales species PG and TF, and half of the AA genomes. Genes involved in CRISPR were prevalent in most oral species. Furthermore, prophage related subsystems were also commonly found in most species except for PG and Streptococcus mutans, in which very few genomes contain prophage components. Comparisons between pathogenic (P) and nonpathogenic (NP) genomes also identified genes potentially important for virulence. Two such comparisons were performed between AA (P) and several A. aphrophilus (NP) strains, and between S. mutans + S. sobrinus (P) and other oral streptococcal species (NP). This comparative genomics approach can be readily used to identify functions unique to

  16. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.

    Science.gov (United States)

    Hoy, Erik P; Mazziotti, David A

    2015-08-14

    Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

  17. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure

    Energy Technology Data Exchange (ETDEWEB)

    Hoy, Erik P.; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

    2015-08-14

    Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

  18. Schwarzian conditions for linear differential operators with selected differential Galois groups

    International Nuclear Information System (INIS)

    Abdelaziz, Y; Maillard, J-M

    2017-01-01

    We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi–Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings. (paper)

  19. Schwarzian conditions for linear differential operators with selected differential Galois groups

    Science.gov (United States)

    Abdelaziz, Y.; Maillard, J.-M.

    2017-11-01

    We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi-Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings.

  20. Designing a two-rank acceptance sampling plan for quality inspection of geospatial data products

    Science.gov (United States)

    Tong, Xiaohua; Wang, Zhenhua; Xie, Huan; Liang, Dan; Jiang, Zuoqin; Li, Jinchao; Li, Jun

    2011-10-01

    To address the disadvantages of classical sampling plans designed for traditional industrial products, we originally propose a two-rank acceptance sampling plan (TRASP) for the inspection of geospatial data outputs based on the acceptance quality level (AQL). The first rank sampling plan is to inspect the lot consisting of map sheets, and the second is to inspect the lot consisting of features in an individual map sheet. The TRASP design is formulated as an optimization problem with respect to sample size and acceptance number, which covers two lot size cases. The first case is for a small lot size with nonconformities being modeled by a hypergeometric distribution function, and the second is for a larger lot size with nonconformities being modeled by a Poisson distribution function. The proposed TRASP is illustrated through two empirical case studies. Our analysis demonstrates that: (1) the proposed TRASP provides a general approach for quality inspection of geospatial data outputs consisting of non-uniform items and (2) the proposed acceptance sampling plan based on TRASP performs better than other classical sampling plans. It overcomes the drawbacks of percent sampling, i.e., "strictness for large lot size, toleration for small lot size," and those of a national standard used specifically for industrial outputs, i.e., "lots with different sizes corresponding to the same sampling plan."

  1. Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

    Science.gov (United States)

    Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco

    2018-05-01

    In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.

  2. Extracellular matrix components supporting human islet function in alginate-based immunoprotective microcapsules for treatment of diabetes

    NARCIS (Netherlands)

    Llacua Carrasco, Luis; de Haan, Bart J; Smink, Sandra A; de Vos, Paul

    In the pancreas, extracellular matrix (ECM) components play an import role in providing mechanical and physiological support, and also contribute to the function of islets. These ECM-connections are damaged during islet-isolation from the pancreas and are not fully recovered after encapsulation and

  3. Rigorous derivation of the mean-field green functions of the two-band Hubbard model of superconductivity

    International Nuclear Information System (INIS)

    Adam, G.; Adam, S.

    2007-01-01

    The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T c superconductivity in cuprates rests on the Hubbard operator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean-field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, the use of spectral representations allows the identification and elimination of exponentially small quantities. This procedure secures the reduction of the correlation order to the GMFA-GF expressions

  4. Alginate as immobilization matrix and stabilizing agent in a two-phase liquid system: application in lipase-catalysed reactions.

    Science.gov (United States)

    Hertzberg, S; Kvittingen, L; Anthonsen, T; Skjåk-Braek, G

    1992-01-01

    Alginate was evaluated as an immobilization matrix for enzyme-catalyzed reactions in organic solvents. In contrast to most hydrogels, calcium alginate was found to be stable in a range of organic solvents and to retain the enzyme inside the gel matrix. In hydrophobic solvents, the alginate gel (greater than 95% water) thus provided a stable, two-phase liquid system. The lipase from Candida cylindracea, after immobilization in alginate beads, catalysed esterification and transesterification in n-hexane under both batch and continuous-flow conditions. The operational stability of the lipase was markedly enhanced by alginate entrapment. In the esterification of butanoic acid with n-butanol, better results were obtained in the typical hydrophilic calcium alginate beads than in less hydrophilic matrices. The effects of substrate concentration, matrix area, and polarity of the substrate alcohols and of the organic solvent on the esterification activity were examined. The transesterification of octyl 2-bromopropanoate with ethanol was less efficient than that of ethyl 2-bromopropanoate with octanol. By using the hydrophilic alginate gel as an immobilization matrix in combination with a mobile hydrophobic phase, a two-phase liquid system was achieved with definite advantages for a continuous, enzyme-catalysed process.

  5. Transfer matrices and excitations with matrix product states

    International Nuclear Information System (INIS)

    Zauner, V; Rams, M M; Verstraete, F; Draxler, D; Vanderstraeten, L; Degroote, M; Haegeman, J; Stojevic, V; Schuch, N

    2015-01-01

    We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM’s eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson’s numerical renormalization group along the virtual (imaginary time) dimension of the system. (paper)

  6. Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave

    DEFF Research Database (Denmark)

    Frisvad, Jeppe Revall

    2018-01-01

    of the complex hypergeometric function 2F1 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far......In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation......-field scattering components, that is, the phase function. I include recurrence formulae for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity...

  7. Two types of mineral-related matrix vesicles in the bone mineralization of zebrafish

    International Nuclear Information System (INIS)

    Yang, L; Zhang, Y; Cui, F Z

    2007-01-01

    Two types of mineral-related matrix vesicle, multivesicular body (MVB) and monovesicle, were detected in the skeletal bone of zebrafish. Transmission electron microscopy and energy dispersive spectroscopy (EDS) analyses of the vesicular inclusions reveal that both types of vesicles contain calcium and phosphorus, suggesting that these vesicles may be involved in mineral ion delivery for the bone mineralization of zebrafish. However, their size and substructure are quite different. Monovesicles, whose diameter ranges from 100 nm to 550 nm, are similar to the previously reported normal matrix vesicles, while MVBs have a larger size of 700-1000 nm in nominal diameter and possess a substructure that is composed of smaller vesicles with their average size around 100 nm. The presence of mineral-related MVBs, which is first identified in zebrafish bone, indicates that the mineralization-associated transportation process of mineral ions is more complicated than is ordinarily imagined

  8. Extracellular matrix structure.

    Science.gov (United States)

    Theocharis, Achilleas D; Skandalis, Spyros S; Gialeli, Chrysostomi; Karamanos, Nikos K

    2016-02-01

    Extracellular matrix (ECM) is a non-cellular three-dimensional macromolecular network composed of collagens, proteoglycans/glycosaminoglycans, elastin, fibronectin, laminins, and several other glycoproteins. Matrix components bind each other as well as cell adhesion receptors forming a complex network into which cells reside in all tissues and organs. Cell surface receptors transduce signals into cells from ECM, which regulate diverse cellular functions, such as survival, growth, migration, and differentiation, and are vital for maintaining normal homeostasis. ECM is a highly dynamic structural network that continuously undergoes remodeling mediated by several matrix-degrading enzymes during normal and pathological conditions. Deregulation of ECM composition and structure is associated with the development and progression of several pathologic conditions. This article emphasizes in the complex ECM structure as to provide a better understanding of its dynamic structural and functional multipotency. Where relevant, the implication of the various families of ECM macromolecules in health and disease is also presented. Copyright © 2015 Elsevier B.V. All rights reserved.

  9. Measurement of the presampled two-dimensional modulation transfer function of digital imaging systems

    International Nuclear Information System (INIS)

    Fetterly, Kenneth A.; Hangiandreou, Nicholas J.; Schueler, Beth A.; Ritenour, E. Russell

    2002-01-01

    The purpose of this work was to develop methods to measure the presampled two-dimensional modulation transfer function (2D MTF) of digital imaging systems. A custom x-ray 'point source' phantom was created by machining 256 holes with diameter 0.107 mm through a 0.5-mm-thick copper plate. The phantom was imaged several times, resulting in many images of individual x-ray 'spots'. The center of each spot (with respect to the pixel matrix) was determined to subpixel accuracy by fitting each spot to a 2D Gaussian function. The subpixel spot center locations were used to create a 5x oversampled system point spread function (PSF), which characterizes the optical and electrical properties of the system and is independent of the pixel sampling of the original image. The modulus of the Fourier transform of the PSF was calculated. Next, the Fourier function was normalized to the zero frequency value. Finally, the Fourier transform function was divided by the first-order Bessel function that defined the frequency content of the holes, resulting in the presampled 2D MTF. The presampled 2D MTF of a 0.1 mm pixel pitch computed radiography system and 0.2 mm pixel pitch flat panel digital imaging system that utilized a cesium iodide scintillator was measured. Comparison of the axial components of the 2D MTF to one-dimensional MTF measurements acquired using an edge device method demonstrated that the two methods produced consistent results

  10. Matrix comparison, Part 2

    DEFF Research Database (Denmark)

    Schneider, Jesper Wiborg; Borlund, Pia

    2007-01-01

    The present two-part article introduces matrix comparison as a formal means for evaluation purposes in informetric studies such as cocitation analysis. In the first part, the motivation behind introducing matrix comparison to informetric studies, as well as two important issues influencing such c...

  11. Tensor products of Uq′sl-caret(2)-modules and the big q2-Jacobi function transform

    International Nuclear Information System (INIS)

    Gade, R. M.

    2013-01-01

    Four tensor products of evaluation modules of the quantum affine algebra U q ′ sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {τ (r,t) } r,t∈Z ≥0 and {τ (r,t) } r,t∈Z ≥0 involving big q 2 -Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplest sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q 2 -Jacobi function transform pair. An integral decomposition is obtained for the sum τ (r,t) . A partial description of the relation between the decompositions of the tensor products with respect to U q sl(2) or with respect to its complement in U q ′ sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U q ′ sl-caret(2)-submodules is discussed.

  12. How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

    Science.gov (United States)

    Klees, R.; Slobbe, D. C.; Farahani, H. H.

    2018-03-01

    The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

  13. Loop equations and topological recursion for the arbitrary-$\\beta$ two-matrix model

    CERN Document Server

    Bergère, Michel; Marchal, Olivier; Prats-Ferrer, Aleix

    2012-01-01

    We write the loop equations for the $\\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.

  14. Closed-Form Expressions for the Matrix Exponential

    Directory of Open Access Journals (Sweden)

    F. De Zela

    2014-04-01

    Full Text Available We discuss a method to obtain closed-form expressions of f(A, where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. We show the advantages of the method in comparison with standard approaches, especially when dealing with the exponential of low-dimensional matrices. In contrast to other approaches that require, e.g., solving differential equations, the present method only requires the construction of the inverse of the Vandermonde matrix. We show the advantages of the method by applying it to different cases, mostly restricting the calculational effort to the handling of two-by-two matrices.

  15. Water exchange and pressure transfer between conduits and matrix and their influence on hydrodynamics of two karst aquifers with sinking streams

    Science.gov (United States)

    Bailly-Comte, Vincent; Martin, Jonathan B.; Jourde, Hervé; Screaton, Elizabeth J.; Pistre, Séverin; Langston, Abigail

    2010-05-01

    SummaryKarst aquifers are heterogeneous media where conduits usually drain water from lower permeability volumes (matrix and fractures). For more than a century, various approaches have used flood recession curves, which integrate all hydrodynamic processes in a karst aquifer, to infer physical properties of the movement and storage of groundwater. These investigations typically only consider flow to the conduits and thus have lacked quantitative observations of how pressure transfer and water exchange between matrix and conduit during flooding could influence recession curves. We present analyses of simultaneous discharge and water level time series of two distinctly different karst systems, one with low porosity and permeability matrix rocks in southern France, and one with high porosity and permeability matrix rocks in north-central Florida (USA). We apply simple mathematical models of flood recession using time series representations of recharge, storage, and discharge processes in the karst aquifer. We show that karst spring hydrographs can be interpreted according to pressure transfer between two distinct components of the aquifer, conduit and matrix porosity, which induce two distinct responses at the spring. Water exchange between conduits and matrix porosity successively control the flow regime at the spring. This exchange is governed by hydraulic head differences between conduits and matrix, head gradients within conduits, and the contrast of permeability between conduits and matrix. These observations have consequences for physical interpretations of recession curves and modeling of karst spring flows, particularly for the relative magnitudes of base flow and quick flow from karst springs. Finally, these results suggest that similar analyses of recession curves can be applied to karst aquifers with distinct physical characteristics utilizing well and spring hydrograph data, but information must be known about the hydrodynamics and physical properties of

  16. Human 2'-phosphodiesterase localizes to the mitochondrial matrix with a putative function in mitochondrial RNA turnover

    DEFF Research Database (Denmark)

    Poulsen, Jesper Buchhave; Andersen, Kasper Røjkjær; Kjær, Karina Hansen

    2011-01-01

    . Interestingly, 2′-PDE shares both functionally and structurally characteristics with the CCR4-type exonuclease–endonuclease–phosphatase family of deadenylases. Here we show that 2′-PDE locates to the mitochondrial matrix of human cells, and comprise an active 3′–5′ exoribonuclease exhibiting a preference...

  17. Structural, biochemical, cellular, and functional changes in skeletal muscle extracellular matrix with aging

    DEFF Research Database (Denmark)

    Kragstrup, T W; Kjaer, M; Mackey, A L

    2011-01-01

    The extracellular matrix (ECM) of skeletal muscle is critical for force transmission and for the passive elastic response of skeletal muscle. Structural, biochemical, cellular, and functional changes in skeletal muscle ECM contribute to the deterioration in muscle mechanical properties with aging....... Structural changes include an increase in the collagen concentration, a change in the elastic fiber system, and an increase in fat infiltration of skeletal muscle. Biochemical changes include a decreased turnover of collagen with potential accumulation of enzymatically mediated collagen cross...

  18. Matrix metalloproteinases in the brain and blood–brain barrier: Versatile breakers and makers

    Science.gov (United States)

    Rempe, Ralf G; Hartz, Anika MS

    2016-01-01

    Matrix metalloproteinases are versatile endopeptidases with many different functions in the body in health and disease. In the brain, matrix metalloproteinases are critical for tissue formation, neuronal network remodeling, and blood–brain barrier integrity. Many reviews have been published on matrix metalloproteinases before, most of which focus on the two best studied matrix metalloproteinases, the gelatinases MMP-2 and MMP-9, and their role in one or two diseases. In this review, we provide a broad overview of the role various matrix metalloproteinases play in brain disorders. We summarize and review current knowledge and understanding of matrix metalloproteinases in the brain and at the blood–brain barrier in neuroinflammation, multiple sclerosis, cerebral aneurysms, stroke, epilepsy, Alzheimer’s disease, Parkinson’s disease, and brain cancer. We discuss the detrimental effects matrix metalloproteinases can have in these conditions, contributing to blood–brain barrier leakage, neuroinflammation, neurotoxicity, demyelination, tumor angiogenesis, and cancer metastasis. We also discuss the beneficial role matrix metalloproteinases can play in neuroprotection and anti-inflammation. Finally, we address matrix metalloproteinases as potential therapeutic targets. Together, in this comprehensive review, we summarize current understanding and knowledge of matrix metalloproteinases in the brain and at the blood–brain barrier in brain disorders. PMID:27323783

  19. Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

    Science.gov (United States)

    Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Xu, Richard Yi Da; Luo, Xiangfeng

    2018-05-01

    Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

  20. Parallelism in matrix computations

    CERN Document Server

    Gallopoulos, Efstratios; Sameh, Ahmed H

    2016-01-01

    This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...

  1. Nucleon matrix elements using the variational method in lattice QCD

    International Nuclear Information System (INIS)

    Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ., SA

    2016-06-01

    The extraction of hadron matrix elements in lattice QCD using the standard two- and threepoint correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current g_A, the scalar current g_S and the quark momentum fraction left angle x right angle of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.

  2. BCS wave function, matrix product states, and the Ising conformal field theory

    Science.gov (United States)

    Montes, Sebastián; Rodríguez-Laguna, Javier; Sierra, Germán

    2017-11-01

    We present a characterization of the many-body lattice wave functions obtained from the conformal blocks (CBs) of the Ising conformal field theory (CFT). The formalism is interpreted as a matrix product state using continuous ancillary degrees of freedom. We provide analytic and numerical evidence that the resulting states can be written as BCS states. We give a complete proof that the translationally invariant 1D configurations have a BCS form and we find suitable parent Hamiltonians. In particular, we prove that the ground state of the finite-size critical Ising transverse field (ITF) Hamiltonian can be obtained with this construction. Finally, we study 2D configurations using an operator product expansion (OPE) approximation. We associate these states to the weak pairing phase of the p +i p superconductor via the scaling of the pairing function and the entanglement spectrum.

  3. Matrix Metalloproteinase Enzyme Family

    Directory of Open Access Journals (Sweden)

    Ozlem Goruroglu Ozturk

    2013-04-01

    Full Text Available Matrix metalloproteinases play an important role in many biological processes such as embriogenesis, tissue remodeling, wound healing, and angiogenesis, and in some pathological conditions such as atherosclerosis, arthritis and cancer. Currently, 24 genes have been identified in humans that encode different groups of matrix metalloproteinase enzymes. This review discuss the members of the matrix metalloproteinase family and their substrate specificity, structure, function and the regulation of their enzyme activity by tissue inhibitors. [Archives Medical Review Journal 2013; 22(2.000: 209-220

  4. Adaptive generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling and different dimensions

    International Nuclear Information System (INIS)

    Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin

    2013-01-01

    This paper investigates generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling, non-identical topological structures and different dimensions. Based on Lyapunov stability theory, generalized function matrix projective lag synchronization criteria are derived by using the adaptive control method. In addition, the three-dimensional fractional-order chaotic system and the four-dimensional integer-order hyperchaotic system as the nodes of the drive and the response networks, respectively, are analyzed in detail, and numerical simulation results are presented to illustrate the effectiveness of the theoretical results. (paper)

  5. Enhanced selectivity in mixed matrix membranes for CO2 capture through efficient dispersion of amine-functionalized MOF nanoparticles

    Science.gov (United States)

    Ghalei, Behnam; Sakurai, Kento; Kinoshita, Yosuke; Wakimoto, Kazuki; Isfahani, Ali Pournaghshband; Song, Qilei; Doitomi, Kazuki; Furukawa, Shuhei; Hirao, Hajime; Kusuda, Hiromu; Kitagawa, Susumu; Sivaniah, Easan

    2017-07-01

    Mixed matrix membranes (MMMs) for gas separation applications have enhanced selectivity when compared with the pure polymer matrix, but are commonly reported with low intrinsic permeability, which has major cost implications for implementation of membrane technologies in large-scale carbon capture projects. High-permeability polymers rarely generate sufficient selectivity for energy-efficient CO2 capture. Here we report substantial selectivity enhancements within high-permeability polymers as a result of the efficient dispersion of amine-functionalized, nanosized metal-organic framework (MOF) additives. The enhancement effects under optimal mixing conditions occur with minimal loss in overall permeability. Nanosizing of the MOF enhances its dispersion within the polymer matrix to minimize non-selective microvoid formation around the particles. Amination of such MOFs increases their interaction with thepolymer matrix, resulting in a measured rigidification and enhanced selectivity of the overall composite. The optimal MOF MMM performance was verified in three different polymer systems, and also over pressure and temperature ranges suitable for carbon capture.

  6. Partially separable t matrix

    International Nuclear Information System (INIS)

    Sasakawa, T.; Okuno, H.; Ishikawa, S.; Sawada, T.

    1982-01-01

    The off-shell t matrix is expressed as a sum of one nonseparable and one separable terms so that it is useful for applications to more-than-two body problems. All poles are involved in this one separable term. Both the nonseparable and the separable terms of the kernel G 0 t are regular at the origin. The nonseparable term of this kernel vanishes at large distances, while the separable term behaves asymptotically as the spherical Hankel function. These properties make our expression free from defects inherent in the Jost or the K-matrix expressions, and many applications are anticipated. As the application, a compact expression of the many-level formula is presented. Also the application is suggested to the breakup threebody problem based on the Faddeev equation. It is demonstrated that the breakup amplitude is expressed in a simple and physically interesting form and we can calculate it in coordinate space

  7. q-Virasoro constraints in matrix models

    Energy Technology Data Exchange (ETDEWEB)

    Nedelin, Anton [Dipartimento di Fisica, Università di Milano-Bicocca and INFN, sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano (Italy); Department of Physics and Astronomy, Uppsala university,Box 516, SE-75120 Uppsala (Sweden); Zabzine, Maxim [Department of Physics and Astronomy, Uppsala university,Box 516, SE-75120 Uppsala (Sweden)

    2017-03-20

    The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new families of matrix models and we have very limited knowledge about these matrix models. We concentrate on elliptic generalization of hermitian matrix model which corresponds to calculation of partition function on S{sup 3}×S{sup 1} for vector multiplet. We derive the q-Virasoro constraints for this matrix model. We also observe some interesting algebraic properties of the q-Virasoro algebra.

  8. Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

    International Nuclear Information System (INIS)

    Gebremariam, B.; Bogner, S.K.; Duguet, T.

    2011-01-01

    The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in (arXiv:0910.4979) by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N 2 LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.

  9. Comparison of matrix methods for elastic wave scattering problems

    International Nuclear Information System (INIS)

    Tsao, S.J.; Varadan, V.K.; Varadan, V.V.

    1983-01-01

    This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error

  10. Wigner Function:from Ensemble Average of Density Operator to Its One Matrix Element in Entangled Pure States

    Institute of Scientific and Technical Information of China (English)

    FAN Hong-Yi

    2002-01-01

    We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.

  11. Matrix model calculations beyond the spherical limit

    International Nuclear Information System (INIS)

    Ambjoern, J.; Chekhov, L.; Kristjansen, C.F.; Makeenko, Yu.

    1993-01-01

    We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prove that the hermitian and the complex matrix model are equivalent in the double scaling limit and that in this limit they are both equivalent to the Kontsevich model. We discuss how our results away from the double scaling limit are related to the structure of moduli space. (orig.)

  12. Involvement of extracellular matrix constituents in breast cancer

    Energy Technology Data Exchange (ETDEWEB)

    Lochter, Andre; Bissell, Mina J

    1995-06-01

    It has recently been established that the extracellular matrix is required for normal functional differentiation of mammary epithelia not only in culture, but also in vivo. The mechanisms by which extracellular matrix affects differentiation, as well as the nature of extracellular matrix constituents which have major impacts on mammary gland function, have only now begun to be dissected. The intricate variety of extracellular matrix-mediated events and the remarkable degree of plasticity of extracellular matrix structure and composition at virtually all times during ontogeny, make such studies difficult. Similarly, during carcinogenesis, the extracellular matrix undergoes gross alterations, the consequences of which are not yet precisely understood. Nevertheless, an increasing amount of data suggests that the extracellular matrix and extracellular matrix-receptors might participate in the control of most, if not all, of the successive stages of breast tumors, from appearance to progression and metastasis.

  13. Matrix Metalloproteinases as Regulators of Vein Structure and Function: Implications in Chronic Venous Disease.

    Science.gov (United States)

    MacColl, Elisabeth; Khalil, Raouf A

    2015-12-01

    Lower-extremity veins have efficient wall structure and function and competent valves that permit upward movement of deoxygenated blood toward the heart against hydrostatic venous pressure. Matrix metalloproteinases (MMPs) play an important role in maintaining vein wall structure and function. MMPs are zinc-binding endopeptidases secreted as inactive pro-MMPs by fibroblasts, vascular smooth muscle (VSM), and leukocytes. Pro-MMPs are activated by various activators including other MMPs and proteinases. MMPs cause degradation of extracellular matrix (ECM) proteins such as collagen and elastin, and could have additional effects on the endothelium, as well as VSM cell migration, proliferation, Ca(2+) signaling, and contraction. Increased lower-extremity hydrostatic venous pressure is thought to induce hypoxia-inducible factors and other MMP inducers/activators such as extracellular matrix metalloproteinase inducer, prostanoids, chymase, and hormones, leading to increased MMP expression/activity, ECM degradation, VSM relaxation, and venous dilation. Leukocyte infiltration and inflammation of the vein wall cause further increases in MMPs, vein wall dilation, valve degradation, and different clinical stages of chronic venous disease (CVD), including varicose veins (VVs). VVs are characterized by ECM imbalance, incompetent valves, venous reflux, wall dilation, and tortuosity. VVs often show increased MMP levels, but may show no change or decreased levels, depending on the VV region (atrophic regions with little ECM versus hypertrophic regions with abundant ECM) and MMP form (inactive pro-MMP versus active MMP). Management of VVs includes compression stockings, venotonics, and surgical obliteration or removal. Because these approaches do not treat the causes of VVs, alternative methods are being developed. In addition to endogenous tissue inhibitors of MMPs, synthetic MMP inhibitors have been developed, and their effects in the treatment of VVs need to be examined

  14. Structural and functional polymer-matrix composites for electromagnetic applications

    Science.gov (United States)

    Wu, Junhua

    This dissertation addresses the science and technology of functional and structural polymer-matrix composite materials for electromagnetic applications, which include electromagnetic interference (EMI) shielding and low observability (Stealth). The structural composites are continuous carbon fiber epoxy-matrix composites, which are widely used for airframes. The functional composites are composites with discontinuous fillers and in both bulk and coating forms. Through composite structure variation, attractive electromagnetic properties have been achieved. With no degradation of the tensile strength or modulus, the shielding effectiveness of the structural composites has been improved by enhancing multiple reflections through light activation of the carbon fiber. The multiple reflections loss of the electromagnetic wave increases from 1.1 to 10.2 dB at 1.0 GHz due to the activation. Such a large effect of multiple reflections has not been previously reported in any material. The observability of these composites has been lowered by decreasing the electrical conductivity (and hence decreasing the reflection loss) through carbon fiber coating. The incorporation of mumetal, a magnetic alloy particulate filler (28-40 mum size), in a latex paint has been found to be effective for enhancing the shielding only if the electrical resistivity of the resulting composite coating is below 10 O.cm, as rendered by a conductive particulate filler, such as nickel flake (14-20 mum size). This effectiveness (39 dB at 1.0 GHz) is attributed to the absorption of the electromagnetic wave by the mumetal and the nickel flake, with the high conductivity rendered by the presence of the nickel flake resulting in a relatively high reflection loss of 15.5 dB. Without the nickel flake, the mumetal gives only 3 dB of shielding and 1.5 dB of reflection loss at 1.0 GHz. Nickel powder (0.3-0.5 mum size) has been found to be an effective filler for improving the shielding of polyethersulfone (PES

  15. The massless two-loop two-point function

    International Nuclear Information System (INIS)

    Bierenbaum, I.; Weinzierl, S.

    2003-01-01

    We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter ε. As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals. (orig.)

  16. Unbiased minimum variance estimator of a matrix exponential function. Application to Boltzmann/Bateman coupled equations solving

    International Nuclear Information System (INIS)

    Dumonteil, E.; Diop, C. M.

    2009-01-01

    This paper derives an unbiased minimum variance estimator (UMVE) of a matrix exponential function of a normal wean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. The last section will present numerical results on a simple example. (authors)

  17. Conservation and Divergence in the Candida Species Biofilm Matrix Mannan-Glucan Complex Structure, Function, and Genetic Control.

    Science.gov (United States)

    Dominguez, Eddie; Zarnowski, Robert; Sanchez, Hiram; Covelli, Antonio S; Westler, William M; Azadi, Parastoo; Nett, Jeniel; Mitchell, Aaron P; Andes, David R

    2018-04-03

    Candida biofilms resist the effects of available antifungal therapies. Prior studies with Candida albicans biofilms show that an extracellular matrix mannan-glucan complex (MGCx) contributes to antifungal sequestration, leading to drug resistance. Here we implement biochemical, pharmacological, and genetic approaches to explore a similar mechanism of resistance for the three most common clinically encountered non- albicans Candida species (NAC). Our findings reveal that each Candida species biofilm synthesizes a mannan-glucan complex and that the antifungal-protective function of this complex is conserved. Structural similarities extended primarily to the polysaccharide backbone (α-1,6-mannan and β-1,6-glucan). Surprisingly, biochemical analysis uncovered stark differences in the branching side chains of the MGCx among the species. Consistent with the structural analysis, similarities in the genetic control of MGCx production for each Candida species also appeared limited to the synthesis of the polysaccharide backbone. Each species appears to employ a unique subset of modification enzymes for MGCx synthesis, likely accounting for the observed side chain diversity. Our results argue for the conservation of matrix function among Candida spp. While biogenesis is preserved at the level of the mannan-glucan complex backbone, divergence emerges for construction of branching side chains. Thus, the MGCx backbone represents an ideal drug target for effective pan- Candida species biofilm therapy. IMPORTANCE Candida species, the most common fungal pathogens, frequently grow as a biofilm. These adherent communities tolerate extremely high concentrations of antifungal agents, due in large part, to a protective extracellular matrix. The present studies define the structural, functional, and genetic similarities and differences in the biofilm matrix from the four most common Candida species. Each species synthesizes an extracellular mannan-glucan complex (MGCx) which

  18. Characterizing full matrix constants of piezoelectric single crystals with strong anisotropy using two samples

    Science.gov (United States)

    Tang, Liguo; Zhang, Yang; Cao, Wenwu

    2016-10-01

    Although the self-consistency of the full matrix material constants of a piezoelectric sample obtained by the resonant ultrasonic spectroscopy technique can be guaranteed because all constants come from the same sample, it is a great challenge to determine the constants of a piezoelectric sample with strong anisotropy because it might not be possible to identify enough resonance modes from the resonance spectrum. To overcome this difficulty, we developed a strategy to use two samples of similar geometries to increase the number of easy identifiable modes. Unlike the IEEE resonance methods, sample-to-sample variation here is negligible because the two samples have almost the same dimensions, cut from the same specimen and poled under the same conditions. Using this method, we have measured the full matrix constants of a [011]c poled 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 single crystal, which has 17 independent constants. The self-consistency of the obtained results is checked by comparing the calculated elastic stiffness constants c33 D , c44 D , and c55 D with those directly measured ones using the ultrasonic pulse-echo method.

  19. Ramiprilate inhibits functional matrix metalloproteinase activity in Crohn's disease fistulas

    DEFF Research Database (Denmark)

    Efsen, Eva; Saermark, Torben; Hansen, Alastair

    2011-01-01

    Increased expression of matrix metalloproteinase (MMP)-2, -3 and -9 has been demonstrated in Crohn's disease fistulas, but it is unknown whether these enzymes are biologically active and represent a therapeutic target. Therefore, we investigated the proteolytic activity of MMPs in fistula tissue...... from six controls were also included. Total functional MMP activity was measured by a high-pressure liquid chromatography (HPLC)-based, fluorogenic MMP-substrate cleavage assay, and the specific activity of MMP-2, -3 and -9 by the MMP Biotrak Activity Assay. The MMP inhibitors comprised ethylene......-9.83) compared with non-Crohn's fistulas, [0.32 ng/ml, range 0-2.66, (p MMP-9 activity [0.64 ng/ml, range 0-5.66 and 0.17 ng/ml, range 0-1.1, respectively (p MMP activity level by 42% and suppressed the specific MMP-3...

  20. Engineering a collagen matrix that replicates the biological properties of native extracellular matrix.

    Science.gov (United States)

    Nam, Kwangwoo; Sakai, Yuuki; Funamoto, Seiichi; Kimura, Tsuyoshi; Kishida, Akio

    2011-01-01

    In this study, we aimed to replicate the function of native tissues that can be used in tissue engineering and regenerative medicine. The key to such replication is the preparation of an artificial collagen matrix that possesses a structure resembling that of the extracellular matrix. We, therefore, prepared a collagen matrix by fibrillogenesis in a NaCl/Na(2)HPO(4) aqueous solution using a dialysis cassette and investigated its biological behavior in vitro and in vivo. The in vitro cell adhesion and proliferation did not show any significant differences. The degradation rate in the living body could be controlled according to the preparation condition, where the collagen matrix with high water content (F-collagen matrix, >98%) showed fast degradation and collagen matrix with lower water content (T-collagen matrix, >80%) showed no degradation for 8 weeks. The degradation did not affect the inflammatory response at all and relatively faster wound healing response was observed. Comparing this result with that of collagen gel and decellularized cornea, it can be concluded that the structural factor is very important and no cell abnormal behavior would be observed for quaternary structured collagen matrix.

  1. A two-dimensional matrix correction for off-axis portal dose prediction errors

    International Nuclear Information System (INIS)

    Bailey, Daniel W.; Kumaraswamy, Lalith; Bakhtiari, Mohammad; Podgorsak, Matthew B.

    2013-01-01

    Purpose: This study presents a follow-up to a modified calibration procedure for portal dosimetry published by Bailey et al. [“An effective correction algorithm for off-axis portal dosimetry errors,” Med. Phys. 36, 4089–4094 (2009)]. A commercial portal dose prediction system exhibits disagreement of up to 15% (calibrated units) between measured and predicted images as off-axis distance increases. The previous modified calibration procedure accounts for these off-axis effects in most regions of the detecting surface, but is limited by the simplistic assumption of radial symmetry. Methods: We find that a two-dimensional (2D) matrix correction, applied to each calibrated image, accounts for off-axis prediction errors in all regions of the detecting surface, including those still problematic after the radial correction is performed. The correction matrix is calculated by quantitative comparison of predicted and measured images that span the entire detecting surface. The correction matrix was verified for dose-linearity, and its effectiveness was verified on a number of test fields. The 2D correction was employed to retrospectively examine 22 off-axis, asymmetric electronic-compensation breast fields, five intensity-modulated brain fields (moderate-high modulation) manipulated for far off-axis delivery, and 29 intensity-modulated clinical fields of varying complexity in the central portion of the detecting surface. Results: Employing the matrix correction to the off-axis test fields and clinical fields, predicted vs measured portal dose agreement improves by up to 15%, producing up to 10% better agreement than the radial correction in some areas of the detecting surface. Gamma evaluation analyses (3 mm, 3% global, 10% dose threshold) of predicted vs measured portal dose images demonstrate pass rate improvement of up to 75% with the matrix correction, producing pass rates that are up to 30% higher than those resulting from the radial correction technique alone. As

  2. Simple and practical approach for computing the ray Hessian matrix in geometrical optics.

    Science.gov (United States)

    Lin, Psang Dain

    2018-02-01

    A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.

  3. Oxidation modifies the structure and function of the extracellular matrix generated by human coronary artery endothelial cells.

    Science.gov (United States)

    Chuang, Christine Y; Degendorfer, Georg; Hammer, Astrid; Whitelock, John M; Malle, Ernst; Davies, Michael J

    2014-04-15

    ECM (extracellular matrix) materials, such as laminin, perlecan, type IV collagen and fibronectin, play a key role in determining the structure of the arterial wall and the properties of cells that interact with the ECM. The aim of the present study was to investigate the effect of peroxynitrous acid, an oxidant generated by activated macrophages, on the structure and function of the ECM laid down by HCAECs (human coronary artery endothelial cells) in vitro and in vivo. We show that exposure of HCAEC-derived native matrix components to peroxynitrous acid (but not decomposed oxidant) at concentrations >1 μM results in a loss of antibody recognition of perlecan, collagen IV, and cell-binding sites on laminin and fibronectin. Loss of recognition was accompanied by decreased HCAEC adhesion. Real-time PCR showed up-regulation of inflammation-associated genes, including MMP7 (matrix metalloproteinase 7) and MMP13, as well as down-regulation of the laminin α2 chain, in HCAECs cultured on peroxynitrous acid-treated matrix compared with native matrix. Immunohistochemical studies provided evidence of co-localization of laminin with 3-nitrotyrosine, a biomarker of peroxynitrous acid damage, in type II-III/IV human atherosclerotic lesions, consistent with matrix damage occurring during disease development in vivo. The results of the present study suggest a mechanism through which peroxynitrous acid modifies endothelial cell-derived native ECM proteins of the arterial basement membrane in atherosclerotic lesions. These changes to ECM and particularly perlecan and laminin may be important in inducing cellular dysfunction and contribute to atherogenesis.

  4. EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations

    International Nuclear Information System (INIS)

    Garbow, Burton S.; Cline, A.K.; Meyering, J.

    1993-01-01

    1 - Description of problem or function: EISPACK3 is a collection of 75 FORTRAN subroutines, both single- and double-precision, that compute the eigenvalues and eigenvectors of nine classes of matrices. The package can determine the Eigen-system of complex general, complex Hermitian, real general, real symmetric, real symmetric band, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices. In addition, there are two routines which use the singular value decomposition to solve certain least squares problem. The individual subroutines are - Identification/Description: BAKVEC: Back transform vectors of matrix formed by FIGI; BALANC: Balance a real general matrix; BALBAK: Back transform vectors of matrix formed by BALANC; BANDR: Reduce sym. band matrix to sym. tridiag. matrix; BANDV: Find some vectors of sym. band matrix; BISECT: Find some values of sym. tridiag. matrix; BQR: Find some values of sym. band matrix; CBABK2: Back transform vectors of matrix formed by CBAL; CBAL: Balance a complex general matrix; CDIV: Perform division of two complex quantities; CG: Driver subroutine for a complex general matrix; CH: Driver subroutine for a complex Hermitian matrix; CINVIT: Find some vectors of complex Hess. matrix; COMBAK: Back transform vectors of matrix formed by COMHES; COMHES: Reduce complex matrix to complex Hess. (elementary); COMLR: Find all values of complex Hess. matrix (LR); COMLR2: Find all values/vectors of cmplx Hess. matrix (LR); CCMQR: Find all values of complex Hessenberg matrix (QR); COMQR2: Find all values/vectors of cmplx Hess. matrix (QR); CORTB: Back transform vectors of matrix formed by CORTH; CORTH: Reduce complex matrix to complex Hess. (unitary); CSROOT: Find square root of complex quantity; ELMBAK: Back transform vectors of matrix formed by ELMHES; ELMHES: Reduce real matrix to real Hess. (elementary); ELTRAN: Accumulate transformations from ELMHES (for HQR2); EPSLON: Estimate unit roundoff

  5. Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix

    International Nuclear Information System (INIS)

    Hernandez, E.; Mondragon, A.; Jauregui, A.

    2002-01-01

    An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions ol complex wave number. In this bi orthonormal basis, any operator f (H r (l) which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan block of rank two. The occurrence of a double pole in the Green's function, as well as the non-exponential time evolution of the Gamow-Jordan generalized eigenfunctions are associated to the Jordan block in the complex energy representation. (Author)

  6. Matrix regularization of embedded 4-manifolds

    International Nuclear Information System (INIS)

    Trzetrzelewski, Maciej

    2012-01-01

    We consider products of two 2-manifolds such as S 2 ×S 2 , embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N 2 ×N 2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S 3 also possible).

  7. Factors associated with continuance commitment to FAA matrix teams.

    Science.gov (United States)

    1993-11-01

    Several organizations within the FAA employ matrix teams to achieve cross-functional coordination. Matrix team members typically represent different organizational functions required for project accomplishment (e.g., research and development, enginee...

  8. Correlated density matrix theory of spatially inhomogeneous Bose fluids

    International Nuclear Information System (INIS)

    Gernoth, K.A.; Clark, J.W.; Ristig, M.L.

    1994-06-01

    In this paper, the variational Hartree-Jastrow theory of the ground state of spatially inhomogeneous Bose systems is extended to finite temperatures. The theory presented here is a generalization also in the sense that it extends the correlated density matrix approach, formulated previously for uniform Bose fluids, to systems with nonuniform density profiles. The method provides a framework in which the effects of thermal excitations on the spatial structure of a Bose fluid, as represented by the density profile and the two-body distribution functions, may be discussed on the basis on an ab initio microscopic description of the system. Thermal excitations make their appearance through self-consistently determined one-body and two-body potentials which enter the nonlinear, coupled Euler-Lagrange equations for the one-body density and for the pair distribution function. Since back-flow correlations are neglected, the excitations are described by a Feynman eigenvalue equation, suitably generalized to nonzero temperatures. The only external quantities entering the correlated density matrix theory elaborated here are the bare two-body interaction potential and, in actual applications, the boundary conditions to be imposed on the one-body density. 30 refs

  9. Links between matrix bulk density, macropore characteristics and hydraulic behavior of soils

    DEFF Research Database (Denmark)

    Katuwal, Sheela; Møldrup, Per; Lamandé, Mathieu

    2013-01-01

    characteristics on soil hydraulic functions has rarely been studied. With the objective of studying the links between these parameters we quantified macropore characteristics of intact soil columns (19 cm diameter x 20 cm high) from two agricultural field sites (Silstrup and Faardrup) in Denmark using coarse...... resolution X-ray CT and linked them with laboratory measurements of air permeability and leaching experiment. In addition to macropore characteristics, we also quantified the CT-number of the matrix as a measure of the bulk density of the matrix, i.e., excluding macropores in the soil. Soils from the two...

  10. POLLA-NESC, Resonance Parameter R-Matrix to S-Matrix Conversion by Reich-Moore Method

    International Nuclear Information System (INIS)

    Saussure, G. de; Perez, R.B.

    1975-01-01

    1 - Description of problem or function: The program transforms a set of r-matrix nuclear resonance parameters into a set of equivalent s-matrix (or Kapur-Peierls) resonance parameters. 2 - Method of solution: The program utilizes the multilevel formalism of Reich and Moore and avoids diagonalization of the level matrix. The parameters are obtained by a direct partial fraction expansion of the Reich-Moore expression of the collision matrix. This approach appears simpler and faster when the number of fission channels is known and small. The method is particularly useful when a large number of levels must be considered because it does not require diagonalization of a large level matrix. 3 - Restrictions on the complexity of the problem: By DIMENSION statements, the program is limited to maxima of 100 levels and 5 channels

  11. Fisher matrix forecast on cosmological parameters from the dark energy survey 2-point angular correlation function

    Energy Technology Data Exchange (ETDEWEB)

    Sobreira, F.; Rosenfeld, R. [Universidade Estadual Paulista Julio de Mesquita Filho (IFT/UNESP), Sao Paulo, SP (Brazil). Inst. Fisica Teorica; Simoni, F. de; Costa, L.A.N. da; Gaia, M.A.G.; Ramos, B.; Ogando, R.; Makler, M. [Laboratorio Interinstitucional de e-Astronomia (LIneA), Rio de Janeiro, RJ (Brazil)

    2011-07-01

    Full text: We study the cosmological constraints expected for the upcoming project Dark Energy Survey (DES) with the full functional form of the 2-point angular correlation function. The angular correlation function model applied in this work includes the effects of linear redshift-space distortion, photometric redshift errors (assumed to be Gaussian) and non-linearities prevenient from gravitational infall. The Fisher information matrix is constructed with the full covariance matrix, which takes the correlation between nearby redshift shells in a proper manner. The survey was sliced into 20 redshift shells in the range 0:4 {<=} z {<=} 1:40 with a variable angular scale in order to search only the scale around the signal from the baryon acoustic oscillation, therefore well within the validity of the non-linear model employed. We found that under those assumptions and with a flat {Lambda}CDM WMAP7 fiducial model, the DES will be able to constrain the dark energy equation of state parameter w with a precision of {approx} 20% and the cold dark matter with {approx} 11% when marginalizing over the other 25 parameters (bias is treated as a free parameter for each shell). When applying WMAP7 priors on {Omega}{sub baryon}, {Omega} c{sub dm}, n{sub s}, and HST priors on the Hubble parameter, w is constrained with {approx} 9% precision. This shows that the full shape of the angular correlation function with DES data will be a powerful probe to constrain cosmological parameters. (author)

  12. M(atrix) theory: matrix quantum mechanics as a fundamental theory

    International Nuclear Information System (INIS)

    Taylor, Washington

    2001-01-01

    This article reviews the matrix model of M theory. M theory is an 11-dimensional quantum theory of gravity that is believed to underlie all superstring theories. M theory is currently the most plausible candidate for a theory of fundamental physics which reconciles gravity and quantum field theory in a realistic fashion. Evidence for M theory is still only circumstantial -- no complete background-independent formulation of the theory exists as yet. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, it has appeared in a different guise as the discrete light-cone quantization of M theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory that reduces to a supersymmetric theory of gravity at low energies. Although its fundamental degrees of freedom are essentially pointlike, higher-dimensional fluctuating objects (branes) arise through the non-Abelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed

  13. Integrative systems and synthetic biology of cell-matrix adhesion sites.

    Science.gov (United States)

    Zamir, Eli

    2016-09-02

    The complexity of cell-matrix adhesion convolves its roles in the development and functioning of multicellular organisms and their evolutionary tinkering. Cell-matrix adhesion is mediated by sites along the plasma membrane that anchor the actin cytoskeleton to the matrix via a large number of proteins, collectively called the integrin adhesome. Fundamental challenges for understanding how cell-matrix adhesion sites assemble and function arise from their multi-functionality, rapid dynamics, large number of components and molecular diversity. Systems biology faces these challenges in its strive to understand how the integrin adhesome gives rise to functional adhesion sites. Synthetic biology enables engineering intracellular modules and circuits with properties of interest. In this review I discuss some of the fundamental questions in systems biology of cell-matrix adhesion and how synthetic biology can help addressing them.

  14. The structure of solutions of the matrix linear unilateral polynomial equation with two variables

    Directory of Open Access Journals (Sweden)

    N. S. Dzhaliuk

    2017-07-01

    Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

  15. Complex matrix model duality

    International Nuclear Information System (INIS)

    Brown, T.W.

    2010-11-01

    The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)

  16. Complex matrix model duality

    Energy Technology Data Exchange (ETDEWEB)

    Brown, T.W.

    2010-11-15

    The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)

  17. Constructing HVS-Based Optimal Substitution Matrix Using Enhanced Differential Evolution

    Directory of Open Access Journals (Sweden)

    Shu-Fen Tu

    2013-01-01

    Full Text Available Least significant bit (LSB substitution is a method of information hiding. The secret message is embedded into the last k bits of a cover-image in order to evade the notice of hackers. The security and stego-image quality are two main limitations of the LSB substitution method. Therefore, some researchers have proposed an LSB substitution matrix to address these two issues. Finding the optimal LSB substitution matrix can be conceptualized as a problem of combinatorial optimization. In this paper, we adopt a different heuristic method based on other researchers’ method, called enhanced differential evolution (EDE, to construct an optimal LSB substitution matrix. Differing from other researchers, we adopt an HVS-based measurement as a fitness function and embed the secret by modifying the pixel to a closest value rather than simply substituting the LSBs. Our scheme extracts the secret by modular operations as simple LSB substitution does. The experimental results show that the proposed embedding algorithm indeed improves imperceptibility of stego-images substantially.

  18. Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder

    Science.gov (United States)

    Wang, Rong; Wang, Li; Yang, Yong; Li, Jiajia; Wu, Ying; Lin, Pan

    2016-11-01

    Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6 -7 % of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.

  19. Extracellular Matrix-Mediated Maturation of Human Pluripotent Stem Cell-Derived Cardiac Monolayer Structure and Electrophysiological Function.

    Science.gov (United States)

    Herron, Todd J; Rocha, Andre Monteiro Da; Campbell, Katherine F; Ponce-Balbuena, Daniela; Willis, B Cicero; Guerrero-Serna, Guadalupe; Liu, Qinghua; Klos, Matt; Musa, Hassan; Zarzoso, Manuel; Bizy, Alexandra; Furness, Jamie; Anumonwo, Justus; Mironov, Sergey; Jalife, José

    2016-04-01

    Human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) monolayers generated to date display an immature embryonic-like functional and structural phenotype that limits their utility for research and cardiac regeneration. In particular, the electrophysiological function of hPSC-CM monolayers and bioengineered constructs used to date are characterized by slow electric impulse propagation velocity and immature action potential profiles. Here, we have identified an optimal extracellular matrix for significant electrophysiological and structural maturation of hPSC-CM monolayers. hPSC-CM plated in the optimal extracellular matrix combination have impulse propagation velocities ≈2× faster than previously reported (43.6±7.0 cm/s; n=9) and have mature cardiomyocyte action potential profiles, including hyperpolarized diastolic potential and rapid action potential upstroke velocity (146.5±17.7 V/s; n=5 monolayers). In addition, the optimal extracellular matrix promoted hypertrophic growth of cardiomyocytes and the expression of key mature sarcolemmal (SCN5A, Kir2.1, and connexin43) and myofilament markers (cardiac troponin I). The maturation process reported here relies on activation of integrin signaling pathways: neutralization of β1 integrin receptors via blocking antibodies and pharmacological blockade of focal adhesion kinase activation prevented structural maturation. Maturation of human stem cell-derived cardiomyocyte monolayers is achieved in a 1-week period by plating cardiomyocytes on PDMS (polydimethylsiloxane) coverslips rather than on conventional 2-dimensional cell culture formats, such as glass coverslips or plastic dishes. Activation of integrin signaling and focal adhesion kinase is essential for significant maturation of human cardiac monolayers. © 2016 American Heart Association, Inc.

  20. Unitarity or asymptotic completeness equations and analytic structure of the S matrix and Green functions

    International Nuclear Information System (INIS)

    Iagolnitzer, D.

    1983-11-01

    Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense

  1. Extracellular matrix component signaling in cancer

    DEFF Research Database (Denmark)

    Multhaupt, Hinke A. B.; Leitinger, Birgit; Gullberg, Donald

    2016-01-01

    Cell responses to the extracellular matrix depend on specific signaling events. These are important from early development, through differentiation and tissue homeostasis, immune surveillance, and disease pathogenesis. Signaling not only regulates cell adhesion cytoskeletal organization and motil...... as well as matrix constitution and protein crosslinking. Here we summarize roles of the three major matrix receptor types, with emphasis on how they function in tumor progression. [on SciFinder(R)]...

  2. HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS

    Directory of Open Access Journals (Sweden)

    Jiameng Wu

    2018-01-01

    Full Text Available The infinite depth free surface Green function (GF and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method.

  3. Relationship between plasma matrix metalloproteinase levels, pulmonary function, bronchodilator response, and emphysema severity.

    Science.gov (United States)

    Koo, Hyeon-Kyoung; Hong, Yoonki; Lim, Myoung Nam; Yim, Jae-Joon; Kim, Woo Jin

    2016-01-01

    Chronic obstructive pulmonary disease (COPD) is characterized by chronic inflammation in the airway and lung. A protease-antiprotease imbalance has been suggested as a possible pathogenic mechanism for COPD. We evaluated the relationship between matrix metalloproteinase (MMP) levels and COPD severity. Plasma levels of MMP-1, MMP-8, MMP-9, and MMP-12 were measured in 57 COPD patients and 36 normal controls. The relationship between MMP levels and lung function, emphysema index, bronchial wall thickness, pulmonary artery pressure, and quality of life was examined using general linear regression analyses. There were significant associations of MMP-1 with bronchodilator reversibility and of MMP-8 and MMP-9 with lung function. Also, MMP-1, MMP-8, and MMP-9 levels were correlated with the emphysema index, independent of lung function. However, MMP-12 was not associated with lung function or emphysema severity. Associations between MMP levels and bronchial wall thickness, pulmonary artery pressure, and quality of life were not statistically significant. Plasma levels of MMP-1, MMP-8, and MMP-9 are associated with COPD severity and can be used as a biomarker to better understand the characteristics of COPD patients.

  4. Reformulation of the Hermitean 1-matrix model as an effective field theory

    Energy Technology Data Exchange (ETDEWEB)

    Klitz, Alexander

    2009-07-15

    The formal Hermitean 1-matrix model is shown to be equivalent to an effective field theory. The correlation functions and the free energy of the matrix model correspond directly to the correlation functions and the free energy of the effective field theory. The loop equation of the field theory coupling constants is stated. Despite its length, this loop equation is simpler than the loop equations in the matrix model formalism itself since it does not contain operator inversions in any sense, but consists instead only of derivative operators and simple projection operators. Therefore the solution of the loop equation could be given for an arbitrary number of cuts up to the fifth order in the topological expansion explicitly. Two different methods of obtaining the contributions to the free energy of the higher orders are given, one depending on an operator H and one not depending on it. (orig.)

  5. Graphene-Reinforced Metal and Polymer Matrix Composites

    Science.gov (United States)

    Kasar, Ashish K.; Xiong, Guoping; Menezes, Pradeep L.

    2018-06-01

    Composites have tremendous applicability due to their excellent capabilities. The performance of composites mainly depends on the reinforcing material applied. Graphene is successful as an efficient reinforcing material due to its versatile as well as superior properties. Even at very low content, graphene can dramatically improve the properties of polymer and metal matrix composites. This article reviews the fabrication followed by mechanical and tribological properties of metal and polymer matrix composites filled with different kinds of graphene, including single-layer, multilayer, and functionalized graphene. Results reported to date in literature indicate that functionalized graphene or graphene oxide-polymer composites are promising materials offering significantly improved strength and frictional properties. A similar trend of improved properties has been observed in case of graphene-metal matrix composites. However, achieving higher graphene loading with uniform dispersion in metal matrix composites remains a challenge. Although graphene-reinforced composites face some challenges, such as understanding the graphene-matrix interaction or fabrication techniques, graphene-reinforced polymer and metal matrix composites have great potential for application in various fields due to their outstanding properties.

  6. Structure and function of ameloblastin as an extracellular matrix protein: adhesion, calcium binding, and CD63 interaction in human and mouse.

    Science.gov (United States)

    Zhang, Xu; Diekwisch, Thomas G H; Luan, Xianghong

    2011-12-01

    The functional significance of extracellular matrix proteins in the life of vertebrates is underscored by a high level of sequence variability in tandem with a substantial degree of conservation in terms of cell-cell and cell-matrix adhesion interactions. Many extracellular matrix proteins feature multiple adhesion domains for successful attachment to substrates, such as integrin, CD63, and heparin. Here we have used homology and ab initio modeling algorithms to compare mouse ameloblastin (mAMBN) and human ameloblastin (hABMN) isoforms and to analyze their potential for cell adhesion and interaction with other matrix molecules as well as calcium binding. Sequence comparison between mAMBN and hAMBN revealed a 26-amino-acid deletion in mAMBN, corresponding to a helix-loop-helix frameshift. The human AMBN domain (174Q-201G), homologous to the mAMBN 157E-178I helix-loop-helix region, formed a helix-loop motif with an extended loop, suggesting a higher degree of flexibility of hAMBN compared with mAMBN, as confirmed by molecular dynamics simulation. Heparin-binding domains, CD63-interaction domains, and calcium-binding sites in both hAMBN and mAMBN support the concept of AMBN as an extracellular matrix protein. The high level of conservation between AMBN functional domains related to adhesion and differentiation was remarkable when compared with only 61% amino acid sequence homology. © 2011 Eur J Oral Sci.

  7. Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz

    Science.gov (United States)

    Vanicat, Matthieu

    2018-04-01

    We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.

  8. Efficiency criterion for teleportation via channel matrix, measurement matrix and collapsed matrix

    Directory of Open Access Journals (Sweden)

    Xin-Wei Zha

    Full Text Available In this paper, three kinds of coefficient matrixes (channel matrix, measurement matrix, collapsed matrix associated with the pure state for teleportation are presented, the general relation among channel matrix, measurement matrix and collapsed matrix is obtained. In addition, a criterion for judging whether a state can be teleported successfully is given, depending on the relation between the number of parameter of an unknown state and the rank of the collapsed matrix. Keywords: Channel matrix, Measurement matrix, Collapsed matrix, Teleportation

  9. Multi-threaded Sparse Matrix-Matrix Multiplication for Many-Core and GPU Architectures.

    Energy Technology Data Exchange (ETDEWEB)

    Deveci, Mehmet [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Trott, Christian Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2017-12-01

    Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scienti c computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.

  10. Universal correlators for multi-arc complex matrix models

    International Nuclear Information System (INIS)

    Akemann, G.

    1997-01-01

    The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the Hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and Hermitian model. (orig.)

  11. Deformed type 0A matrix model and super-Liouville theory for fermionic black holes

    International Nuclear Information System (INIS)

    Ahn, Changrim; Kim, Chanju; Park, Jaemo; Suyama, Takao; Yamamoto, Masayoshi

    2006-01-01

    We consider a c-circumflex = 1 model in the fermionic black hole background. For this purpose we consider a model which contains both the N 1 and the N = 2 super-Liouville interactions. We propose that this model is dual to a recently proposed type 0A matrix quantum mechanics model with vortex deformations. We support our conjecture by showing that non-perturbative corrections to the free energy computed by both the matrix model and the super-Liouville theories agree exactly by treating the N = 2 interaction as a small perturbation. We also show that a two-point function on sphere calculated from the deformed type 0A matrix model is consistent with that of the N = 2 super-Liouville theory when the N = 1 interaction becomes small. This duality between the matrix model and super-Liouville theories leads to a conjecture for arbitrary n-point correlation functions of the N = 1 super-Liouville theory on the sphere

  12. Transition matrices and orbitals from reduced density matrix theory

    Energy Technology Data Exchange (ETDEWEB)

    Etienne, Thibaud [Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur (Belgium)

    2015-06-28

    In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.

  13. Regular perturbation theory for two-electron atoms

    International Nuclear Information System (INIS)

    Feranchuk, I.D.; Triguk, V.V.

    2011-01-01

    Regular perturbation theory (RPT) for the ground and excited states of two-electron atoms or ions is developed. It is shown for the first time that summation of the matrix elements from the electron-electron interaction operator over all intermediate states can be calculated in a closed form by means of the two-particle Coulomb Green's function constructed in the Letter. It is shown that the second order approximation of RPT includes the main part of the correlation energy both for the ground and excited states. This approach can be also useful for description of two-electron atoms in external fields. -- Highlights: → We develop regular perturbation theory for the two-electron atoms or ions. → We calculate the sum of the matrix elements over all intermediate states. → We construct the two-particle Coulomb Green's function.

  14. A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments

    Directory of Open Access Journals (Sweden)

    Ayşe Betül Koç

    2014-01-01

    Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.

  15. SU(3) techniques for angular momentum projected matrix elements in multi-cluster problems

    International Nuclear Information System (INIS)

    Hecht, K.T.; Zahn, W.

    1978-01-01

    In the theory of integral transforms for the evaluation of the resonating group kernels needed for cluster model calculations, the evaluation of matrix elements in an angular momentum coupled basis has proved to be difficult for cluster problems involving more than two fragments. For multi-cluster wave functions SU(3) coupling and recoupling techniques can furnish a tool for the practical evaluation matrix elements in an angular momentum coupled basis if the several relative motion harmonic oscillator functions in Bargmann space have simple SU(3) coupling properties. The method is illustrated by a three-cluster problem, such as 12 C = α + α + α, involving three 1 S clusters. 2 references

  16. Hydrogel-Embedded Model Photocatalytic System Investigated by Raman and IR Spectroscopy Assisted by Density Functional Theory Calculations and Two-Dimensional Correlation Analysis.

    Science.gov (United States)

    Geitner, Robert; Götz, Stefan; Stach, Robert; Siegmann, Michael; Krebs, Patrick; Zechel, Stefan; Schreyer, Kristin; Winter, Andreas; Hager, Martin D; Schubert, Ulrich S; Gräfe, Stefanie; Dietzek, Benjamin; Mizaikoff, Boris; Schmitt, Michael; Popp, Jürgen

    2018-03-15

    The presented study reports the synthesis and the vibrational spectroscopic characterization of different matrix-embedded model photocatalysts. The goal of the study is to investigate the interaction of a polymer matrix with photosensitizing dyes and metal complexes for potential future photocatalytic applications. The synthesis focuses on a new rhodamine B derivate and a Pt(II) terpyridine complex, which both contain a polymerizable methacrylate moiety and an acid labile acylhydrazone group. The methacrylate moieties are afterward utilized to synthesize functional model hydrogels mainly consisting of poly(ethylene glycol) methacrylate units. The pH-dependent and temperature-dependent behavior of the hydrogels is investigated by means of Raman and IR spectroscopy assisted by density functional theory calculations and two-dimensional correlation spectroscopy. The spectroscopic results reveal that the Pt(II) terpyridine complex can be released from the polymer matrix by cleaving the C═N bond in an acid environment. The same behavior could not be observed in the case of the rhodamine B dye although it features a comparable C═N bond. The temperature-dependent study shows that the water evaporation has a significant influence neither on the molecular structure of the hydrogel nor on the model photocatalytic moieties.

  17. The nuclear reaction matrix

    International Nuclear Information System (INIS)

    Krenciglowa, E.M.; Kung, C.L.; Kuo, T.T.S.; Osnes, E.; and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794)

    1976-01-01

    Different definitions of the reaction matrix G appropriate to the calculation of nuclear structure are reviewed and discussed. Qualitative physical arguments are presented in support of a two-step calculation of the G-matrix for finite nuclei. In the first step the high-energy excitations are included using orthogonalized plane-wave intermediate states, and in the second step the low-energy excitations are added in, using harmonic oscillator intermediate states. Accurate calculations of G-matrix elements for nuclear structure calculations in the Aapprox. =18 region are performed following this procedure and treating the Pauli exclusion operator Q 2 /sub p/ by the method of Tsai and Kuo. The treatment of Q 2 /sub p/, the effect of the intermediate-state spectrum and the energy dependence of the reaction matrix are investigated in detail. The present matrix elements are compared with various matrix elements given in the literature. In particular, close agreement is obtained with the matrix elements calculated by Kuo and Brown using approximate methods

  18. Five- and six-electron harmonium atoms: Highly accurate electronic properties and their application to benchmarking of approximate 1-matrix functionals

    Science.gov (United States)

    Cioslowski, Jerzy; Strasburger, Krzysztof

    2018-04-01

    Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.

  19. Chimeric cellulase matrix for investigating intramolecular synergism between non-hydrolytic disruptive functions of carbohydrate-binding modules and catalytic hydrolysis.

    Science.gov (United States)

    Wang, Yuguo; Tang, Rentao; Tao, Jin; Wang, Xiaonan; Zheng, Baisong; Feng, Yan

    2012-08-24

    The conversion of renewable cellulosic biomass is of considerable interest for the production of biofuels and materials. The bottleneck in the efficient conversion is the compactness and resistance of crystalline cellulose. Carbohydrate-binding modules (CBMs), which disrupt crystalline cellulose via non-hydrolytic mechanisms, are expected to overcome this bottleneck. However, the lack of convenient methods for quantitative analysis of the disruptive functions of CBMs have hindered systematic studies and molecular modifications. Here we established a practical and systematic platform for quantifying and comparing the non-hydrolytic disruptive activities of CBMs via the synergism of CBMs and a catalytic module within designed chimeric cellulase molecules. Bioinformatics and computational biology were also used to provide a deeper understanding. A convenient vector was constructed to serve as a cellulase matrix into which heterologous CBM sequences can be easily inserted. The resulting chimeric cellulases were suitable for studying disruptive functions, and their activities quantitatively reflected the disruptive functions of CBMs on crystalline cellulose. In addition, this cellulase matrix can be used to construct novel chimeric cellulases with high hydrolytic activities toward crystalline cellulose.

  20. Chimeric Cellulase Matrix for Investigating Intramolecular Synergism between Non-hydrolytic Disruptive Functions of Carbohydrate-binding Modules and Catalytic Hydrolysis*

    Science.gov (United States)

    Wang, Yuguo; Tang, Rentao; Tao, Jin; Wang, Xiaonan; Zheng, Baisong; Feng, Yan

    2012-01-01

    The conversion of renewable cellulosic biomass is of considerable interest for the production of biofuels and materials. The bottleneck in the efficient conversion is the compactness and resistance of crystalline cellulose. Carbohydrate-binding modules (CBMs), which disrupt crystalline cellulose via non-hydrolytic mechanisms, are expected to overcome this bottleneck. However, the lack of convenient methods for quantitative analysis of the disruptive functions of CBMs have hindered systematic studies and molecular modifications. Here we established a practical and systematic platform for quantifying and comparing the non-hydrolytic disruptive activities of CBMs via the synergism of CBMs and a catalytic module within designed chimeric cellulase molecules. Bioinformatics and computational biology were also used to provide a deeper understanding. A convenient vector was constructed to serve as a cellulase matrix into which heterologous CBM sequences can be easily inserted. The resulting chimeric cellulases were suitable for studying disruptive functions, and their activities quantitatively reflected the disruptive functions of CBMs on crystalline cellulose. In addition, this cellulase matrix can be used to construct novel chimeric cellulases with high hydrolytic activities toward crystalline cellulose. PMID:22778256

  1. Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

    Science.gov (United States)

    Pan, Guangming; Wang, Shaochen; Zhou, Wang

    2017-10-01

    In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.

  2. Regularization of quantum gravity in the matrix model approach

    International Nuclear Information System (INIS)

    Ueda, Haruhiko

    1991-02-01

    We study divergence problem of the partition function in the matrix model approach for two-dimensional quantum gravity. We propose a new model V(φ) = 1/2Trφ 2 + g 4 /NTrφ 4 + g'/N 4 Tr(φ 4 ) 2 and show that in the sphere case it has no divergence problem and the critical exponent is of pure gravity. (author)

  3. Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search

    Science.gov (United States)

    Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong

    2009-11-01

    The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.

  4. An additive matrix preconditioning method with application for domain decomposition and two-level matrix partitionings

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe

    2010-01-01

    Roč. 5910, - (2010), s. 76-83 ISSN 0302-9743. [International Conference on Large-Scale Scientific Computations, LSSC 2009 /7./. Sozopol, 04.06.2009-08.06.2009] R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z30860518 Keywords : additive matrix * condition number * domain decomposition Subject RIV: BA - General Mathematics www.springerlink.com

  5. The new cooling tower principle Matrix-Multiflow; Das neue Kuehlturmprinzip Matrix-Multiflow

    Energy Technology Data Exchange (ETDEWEB)

    Juran, H. [Technisches Pressebuero, Koenigswinter (Germany); Plocki, O. [Marley Kuehlturm GmbH, Duesseldorf (Germany)

    1995-11-01

    All cooling tower construction built so far can be assigned fluidically to the cross-flow or counterflow principle. The new Matrix-Multiflow System, which was developed in cell-construction with ducted aeration for large cooling capacities of the industry and energy economy, corresponds basically to none of the two principles, even if constructively it represents a modified cross-flow tower with cross-flow film internals. In the following the development, function, construction, defined properties and application demand of this patented cooling tower principle is described. It takes over adn extends the typical advantages of the cross-flow principle and minimizes the disadvantages with regard to the counterflow principle. (orig.) [Deutsch] Alle bisher gebauten Kuehlturmausfuehrungen lassen sich stroemungstechnisch dem Kreuz- oder Gegenstromprinzip zuordnen. Das neue Matrix-Multiflow-System, das in Zellenbauweise mit Zwangsbelueftung fuer grosse Kuehlleistungen der Industrie und Energiewirtschaft entwickelt wurde, entspricht im Grunde keinem der beiden Prinzipien, auch wenn es konstruktiv einen modifizierten Kreuzstromturm mit Kreuzstromfilmeinbauten darstellt. Nachfolgend werden Entwicklung, Funktion, Ausfuehrung, markante Eigenschaften und Anwendungsbedarf dieses patentierten Kuehlturmprinzips beschrieben. Es uebernimmt oder erweitert die typischen Vorteile des Kreuzstromprinzips und minimiert die Nachteile gegenueber dem Gegenstromprinzip weitgehend. (orig.)

  6. Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

    Energy Technology Data Exchange (ETDEWEB)

    Deveci, Mehmet [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Trott, Christian Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2018-01-01

    Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.

  7. Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

    Science.gov (United States)

    Ma, Q.; Boulet, C.; Tipping, R. H.

    2014-01-01

    The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

  8. Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

    International Nuclear Information System (INIS)

    Feng Yi-Fu; Zhang Qing-Ling; Feng De-Zhi

    2012-01-01

    The global stability problem of Takagi—Sugeno (T—S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated. Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism. Firstly, using both Finsler's lemma and an improved homogeneous matrix polynomial technique, and applying an affine parameter-dependent Lyapunov—Krasovskii functional, we obtain the convergent LMI-based stability criteria. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique. Secondly, to further reduce the conservatism, a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs, which is suitable to the homogeneous matrix polynomials setting. Finally, two illustrative examples are given to show the efficiency of the proposed approaches

  9. Gamow state vectors as functionals over subspaces of the nuclear space

    International Nuclear Information System (INIS)

    Bohm, A.

    1979-12-01

    Exponentially decaying Gamow state vectors are obtained from S-matrix poles in the lower half of the second sheet, and are defined as functionals over a subspace of the nuclear space, PHI. Exponentially growing Gamow state vectors are obtained from S-matrix poles in the upper half of the second sheet, and are defined as functionals over another subspace of PHI. On functionals over these two subspaces the dynamical group of time development splits into two semigroups

  10. Benchmark Two-Good Utility Functions

    NARCIS (Netherlands)

    de Jaegher, K.

    Benchmark two-good utility functions involving a good with zero income elasticity and unit income elasticity are well known. This paper derives utility functions for the additional benchmark cases where one good has zero cross-price elasticity, unit own-price elasticity, and zero own price

  11. Standard Errors for Matrix Correlations.

    Science.gov (United States)

    Ogasawara, Haruhiko

    1999-01-01

    Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)

  12. New angular quadrature sets: effect on the conditioning number of the LTSN two dimensional transport matrix

    International Nuclear Information System (INIS)

    Hauser, Eliete Biasotto; Romero, Debora Angrizano

    2009-01-01

    The main objective of this work is to utilize a new angular quadrature sets based on Legendre and Chebyshev polynomials, and to analyse their effects on the number of LTS N matrix conditioning for the problem of discrete coordinates of neutron transport with two dimension cartesian geometry with isotropic scattering, and an energy group, in non multiplicative homogenous domains

  13. Spectral inverse problem for q-deformed harmonic oscillator

    Indian Academy of Sciences (India)

    - out direct ... concepts, exact knowledge of the spectrum is not enough for the reconstruction of ..... As the superpotential is related to the ground-state wave function, we demand ..... q-hypergeometric function multiplied by some weight factor.

  14. LABAN-PEL: a two-dimensional, multigroup diffusion, high-order response matrix code

    International Nuclear Information System (INIS)

    Mueller, E.Z.

    1991-06-01

    The capabilities of LABAN-PEL is described. LABAN-PEL is a modified version of the two-dimensional, high-order response matrix code, LABAN, written by Lindahl. The new version extends the capabilities of the original code with regard to the treatment of neutron migration by including an option to utilize full group-to-group diffusion coefficient matrices. In addition, the code has been converted from single to double precision and the necessary routines added to activate its multigroup capability. The coding has also been converted to standard FORTRAN-77 to enhance the portability of the code. Details regarding the input data requirements and calculational options of LABAN-PEL are provided. 13 refs

  15. Two-loop massive fermionic operator matrix elements and intial state QED corrections to e{sup +}e{sup -}{yields}{gamma}{sup *}/Z{sup *}

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Universidad Simon Bolivar, Caracas (Venezuela). Dept. de Fisica; Neerven, W. van [Leiden Univ. (Netherlands). Lorentz Institute

    2008-12-15

    We describe the calculation of the two-loop massive operator matrix elements for massive external fermions. These matrix elements are needed for the calculation of the O({alpha}{sup 2}) initial state radiative corrections to e{sup +}e{sup -} annihilation into a neutral virtual gauge boson, based on the renormalization group technique. (orig.)

  16. Recovery of the matrix operators in the similarity and congruency transformations: Applications in polarimetry

    International Nuclear Information System (INIS)

    November, L.J.

    1993-01-01

    Formulas are presented for the recovery of the matrix operators in arbitrary-order similarity and congruency transformations. Two independent input and output matrix pairs exactly determine the similarity-transformation matrix operator, while three independent Hermitian-matrix pairs are required for the congruency-transformation operator. The congruency transformation is the natural form for the quantum observables of a multiple-element wave function, e.g., for polarized-light transfer: the recovery of the Jones matrix for a nondepolarizing device is demonstrated, given any three linearly independent partially polarized input Stokes states. The recovery formula gives a good solution even with large added noise in the test matrices. Combined with numerical least-squares methods, the formula can give an optimized solution for measures of observation error. A more general operator, which includes the effect of isotropic depolarization, is defined, and its recovery is demonstrated also. The recovery formulas have a three-dimensional geometric interpretation in the second-order case, e.g., in the Poincare sphere. It is pointed out that the geometric property is a purely mathematical property of quantum observables that arises without referring to spatial characteristics for the underlying wave function. 36 refs., 9 figs

  17. Effective Kratzer and Coulomb potentials as limit cases of a multiparameter exponential-type potential

    Energy Technology Data Exchange (ETDEWEB)

    García-Ravelo, J., E-mail: g.ravelo@hotmail.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, México D.F., 07738 (Mexico); Menéndez, A.; García-Martínez, J. [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, México D.F., 07738 (Mexico); Schulze-Halberg, A. [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, IN 46408 (United States)

    2014-06-13

    We show that the effective Kratzer and Coulomb potentials can be obtained by taking particular limits of a multiparameter exponential potential that was studied recently. Moreover, we demonstrate that the bound state solutions of the exponential potential reduce correctly to their well-known counterparts associated with the Kratzer and Coulomb potentials. As a byproduct, we obtain a new limit relation for the hypergeometric function. - Highlights: • Kratzer and Coulomb potentials are limit cases of an exponential-type potential. • From exact s-waves, approximate solutions for l-waves are obtained. • l-waves of the potential tend to the solutions of the Kratzer and Coulomb potentials. • A non-evident identity between hypergeometric functions is demonstrated.

  18. Effective Kratzer and Coulomb potentials as limit cases of a multiparameter exponential-type potential

    International Nuclear Information System (INIS)

    García-Ravelo, J.; Menéndez, A.; García-Martínez, J.; Schulze-Halberg, A.

    2014-01-01

    We show that the effective Kratzer and Coulomb potentials can be obtained by taking particular limits of a multiparameter exponential potential that was studied recently. Moreover, we demonstrate that the bound state solutions of the exponential potential reduce correctly to their well-known counterparts associated with the Kratzer and Coulomb potentials. As a byproduct, we obtain a new limit relation for the hypergeometric function. - Highlights: • Kratzer and Coulomb potentials are limit cases of an exponential-type potential. • From exact s-waves, approximate solutions for l-waves are obtained. • l-waves of the potential tend to the solutions of the Kratzer and Coulomb potentials. • A non-evident identity between hypergeometric functions is demonstrated

  19. Project-matrix models of marketing organization

    Directory of Open Access Journals (Sweden)

    Gutić Dragutin

    2009-01-01

    Full Text Available Unlike theory and practice of corporation organization, in marketing organization numerous forms and contents at its disposal are not reached until this day. It can be well estimated that marketing organization today in most of our companies and in almost all its parts, noticeably gets behind corporation organization. Marketing managers have always been occupied by basic, narrow marketing activities as: sales growth, market analysis, market growth and market share, marketing research, introduction of new products, modification of products, promotion, distribution etc. They rarely found it necessary to focus a bit more to different aspects of marketing management, for example: marketing planning and marketing control, marketing organization and leading. This paper deals with aspects of project - matrix marketing organization management. Two-dimensional and more-dimensional models are presented. Among two-dimensional, these models are analyzed: Market management/products management model; Products management/management of product lifecycle phases on market model; Customers management/marketing functions management model; Demand management/marketing functions management model; Market positions management/marketing functions management model. .

  20. ADAM12 induces actin cytoskeleton and extracellular matrix reorganization during early adipocyte differentiation by regulating beta1 integrin function

    DEFF Research Database (Denmark)

    Kawaguchi, Nobuko; Sundberg, Christina; Kveiborg, Marie

    2003-01-01

    -100 from cells overexpressing ADAM12 than from control cells. Collectively, these results show that surface expression of ADAM12 impairs the function of beta1 integrins and, consequently, alters the organization of the actin cytoskeleton and extracellular matrix. These events may be necessary...

  1. Parallel R-matrix computation

    International Nuclear Information System (INIS)

    Heggarty, J.W.

    1999-06-01

    For almost thirty years, sequential R-matrix computation has been used by atomic physics research groups, from around the world, to model collision phenomena involving the scattering of electrons or positrons with atomic or molecular targets. As considerable progress has been made in the understanding of fundamental scattering processes, new data, obtained from more complex calculations, is of current interest to experimentalists. Performing such calculations, however, places considerable demands on the computational resources to be provided by the target machine, in terms of both processor speed and memory requirement. Indeed, in some instances the computational requirements are so great that the proposed R-matrix calculations are intractable, even when utilising contemporary classic supercomputers. Historically, increases in the computational requirements of R-matrix computation were accommodated by porting the problem codes to a more powerful classic supercomputer. Although this approach has been successful in the past, it is no longer considered to be a satisfactory solution due to the limitations of current (and future) Von Neumann machines. As a consequence, there has been considerable interest in the high performance multicomputers, that have emerged over the last decade which appear to offer the computational resources required by contemporary R-matrix research. Unfortunately, developing codes for these machines is not as simple a task as it was to develop codes for successive classic supercomputers. The difficulty arises from the considerable differences in the computing models that exist between the two types of machine and results in the programming of multicomputers to be widely acknowledged as a difficult, time consuming and error-prone task. Nevertheless, unless parallel R-matrix computation is realised, important theoretical and experimental atomic physics research will continue to be hindered. This thesis describes work that was undertaken in

  2. Hartree--Fock density matrix equation

    International Nuclear Information System (INIS)

    Cohen, L.; Frishberg, C.

    1976-01-01

    An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does

  3. Information matrix estimation procedures for cognitive diagnostic models.

    Science.gov (United States)

    Liu, Yanlou; Xin, Tao; Andersson, Björn; Tian, Wei

    2018-03-06

    Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance. © 2018 The British Psychological Society.

  4. Efficient diagonalization of the sparse matrices produced within the framework of the UK R-matrix molecular codes

    Science.gov (United States)

    Galiatsatos, P. G.; Tennyson, J.

    2012-11-01

    The most time consuming step within the framework of the UK R-matrix molecular codes is that of the diagonalization of the inner region Hamiltonian matrix (IRHM). Here we present the method that we follow to speed up this step. We use shared memory machines (SMM), distributed memory machines (DMM), the OpenMP directive based parallel language, the MPI function based parallel language, the sparse matrix diagonalizers ARPACK and PARPACK, a variation for real symmetric matrices of the official coordinate sparse matrix format and finally a parallel sparse matrix-vector product (PSMV). The efficient application of the previous techniques rely on two important facts: the sparsity of the matrix is large enough (more than 98%) and in order to get back converged results we need a small only part of the matrix spectrum.

  5. Timelike single-logarithm-resummed splitting functions

    Energy Technology Data Exchange (ETDEWEB)

    Albino, S.; Bolzoni, P.; Kniehl, B.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kotikov, A.V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

    2011-08-15

    We calculate the single logarithmic contributions to the quark singlet and gluon matrix of timelike splitting functions at all orders in the modified minimal-subtraction (MS) scheme. We fix two of the degrees of freedom of this matrix from the analogous results in the massive-gluon regularization scheme by using the relation between that scheme and the MS scheme. We determine this scheme transformation from the double logarithmic contributions to the timelike splitting functions and the coefficient functions of inclusive particle production in e{sup +}e{sup -} annihilation now available in both schemes. The remaining two degrees of freedom are fixed by reasonable physical assumptions. The results agree with the fixed-order results at next-to-next-to-leading order in the literature. (orig.)

  6. Dynamic Matrix Rank

    DEFF Research Database (Denmark)

    Frandsen, Gudmund Skovbjerg; Frandsen, Peter Frands

    2009-01-01

    We consider maintaining information about the rank of a matrix under changes of the entries. For n×n matrices, we show an upper bound of O(n1.575) arithmetic operations and a lower bound of Ω(n) arithmetic operations per element change. The upper bound is valid when changing up to O(n0.575) entries...... in a single column of the matrix. We also give an algorithm that maintains the rank using O(n2) arithmetic operations per rank one update. These bounds appear to be the first nontrivial bounds for the problem. The upper bounds are valid for arbitrary fields, whereas the lower bound is valid for algebraically...... closed fields. The upper bound for element updates uses fast rectangular matrix multiplication, and the lower bound involves further development of an earlier technique for proving lower bounds for dynamic computation of rational functions....

  7. The response-matrix based AFEN method for the hexagonal geometry

    International Nuclear Information System (INIS)

    Noh, Jae Man; Kim, Keung Koo; Zee, Sung Quun; Joo, Hyung Kook; Cho, Byng Oh; Jeong, Hyung Guk; Cho, Jin Young

    1998-03-01

    The analytic function expansion nodal (AFEN) method, developed to overcome the limitations caused by the transverse integration, has been successfully to predict the neutron behavior in the hexagonal core as well as rectangular core. In the hexagonal node, the transverse leakage resulted from the transverse integration has some singular terms such as delta-function and step-functions near the node center line. In most nodal methods using the transverse integration, the accuracy of nodal method is degraded because the transverse leakage is approximated as a smooth function across the node center line by ignoring singular terms. However, the AFEN method in which there is no transverse leakage term in deriving nodal coupling equations keeps good accuracy for hexagonal node. In this study, the AFEN method which shows excellent accuracy in the hexagonal core analyses is reformulated as a response matrix form. This form of the AFEN method can be implemented easily to nodal codes based on the response matrix method. Therefore, the Coarse Mesh Rebalance (CMR) acceleration technique which is one of main advantages of the response matrix method can be utilized for the AFEN method. The response matrix based AFEN method has been successfully implemented into the MASTER code and its accuracy and computational efficiency were examined by analyzing the two- and three- dimensional benchmark problem of VVER-440. Based on the results, it can be concluded that the newly formulated AFEN method predicts accurately the assembly powers (within 0.2% average error) as well as the effective multiplication factor (within 0.2% average error) as well as the effective multiplication factor (within 20 pcm error). In addition, the CMR acceleration technique is quite efficient in reducing the computation time of the AFEN method by 8 to 10 times. (author). 22 refs., 1 tab., 4 figs

  8. Characterization of Epoxy Functionalized Graphite Nanoparticles and the Physical Properties of Epoxy Matrix Nanocomposites

    Science.gov (United States)

    Miller, Sandi G.; Bauer, Jonathan L.; Maryanski, Michael J.; Heimann, Paula J.; Barlow, Jeremy P.; Gosau, Jan-Michael; Allred, Ronald E.

    2010-01-01

    This work presents a novel approach to the functionalization of graphite nanoparticles. The technique provides a mechanism for covalent bonding between the filler and matrix, with minimal disruption to the sp2 hybridization of the pristine graphene sheet. Functionalization proceeded by covalently bonding an epoxy monomer to the surface of expanded graphite, via a coupling agent, such that the epoxy concentration was measured as approximately 4 wt.%. The impact of dispersing this material into an epoxy resin was evaluated with respect to the mechanical properties and electrical conductivity of the graphite-epoxy nanocomposite. At a loading as low as 0.5 wt.%, the electrical conductivity was increased by five orders of magnitude relative to the base resin. The material yield strength was increased by 30% and Young s modulus by 50%. These results were realized without compromise to the resin toughness.

  9. Minimal solution for inconsistent singular fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    M. Nikuie

    2013-10-01

    Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

  10. Radiation and penetration matrix elements for magnetic quadrupole transitions between Nilsson states in odd nuclei

    International Nuclear Information System (INIS)

    Feresin, A.P.; Guseva, I.S.

    1984-01-01

    Single-particle matrix elements for magnetic quadrupole gamma radiation in odd deformed nuclei, calculated with the aid of Nilsson-potential wave functions, are presented. Also given are the internal conversion penetration matrix elements, calculated in the same manner. The penetration matrix elements are needed to estimate the nuclear penetration parameter, which determines the deviation of experimental internal conversion coefficients from their standard values given in tables. Matrix elements are given for transitions between all pairs of Nilsson single-particle states with ΔN = 1 and ΔK = 0, 1, and 2 for the nuclear shells with 4< or =N< or =7 and for the two deformation values epsilon = 0.2 and 0.3

  11. Modeling and Simulation of Matrix Converter

    DEFF Research Database (Denmark)

    Liu, Fu-rong; Klumpner, Christian; Blaabjerg, Frede

    2005-01-01

    This paper discusses the modeling and simulation of matrix converter. Two models of matrix converter are presented: one is based on indirect space vector modulation and the other is based on power balance equation. The basis of these two models is• given and the process on modeling is introduced...

  12. Development of a Java Package for Matrix Programming

    OpenAIRE

    Lim, Ngee-Peng; Ling, Maurice HT; Lim, Shawn YC; Choi, Ji-Hee; Teo, Henry BK

    2003-01-01

    We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object class. Class matrix defines a matrix as a two-dimensional array of float types, and contains the following mathematical methods: transpose, adjoint, determinant, inverse, minor and cofactor. Class matrix_operations contains the following mathematical method...

  13. Integration of concepts: cardiac extracellular matrix remodeling after myocardial infarction

    NARCIS (Netherlands)

    Cleutjens, Jack P. M.; Creemers, Esther E. J. M.

    2002-01-01

    The cardiac extracellular matrix consists of a three-dimensional structural network of interstitial collagens to which other matrix components are attached. The main physiological functions of this network are to retain tissue integrity and cardiac pump function. Collagen deposition is controlled

  14. Matrix of response functions for xenon gamma-ray detector

    International Nuclear Information System (INIS)

    Shustov, A.E.; Vlasik, K.F.; Grachev, V.M.; Dmitrenko, V.V.; Novikov, A.S.; P'ya, S.N.; Ulin, S.E.; Uteshev, Z.M.; Chernysheva, I.V.

    2014-01-01

    An approach of creation of response matrix using simulation GEANT4 gamma-ray Monte-Carlo method has been described for gamma-ray spectrometer based on high pressure xenon impulse ionization chamber with a shielding grid [ru

  15. Structure constants in the N=1 super-Liouville field theory

    International Nuclear Information System (INIS)

    Poghossian, R.H.

    1997-01-01

    The symmetry algebra of N=1 super-Liouville field theory in two dimensions is the infinite-dimensional N=1 superconformal algebra, which allows one to prove that correlation functions containing degenerated fields obey some partial linear differential equations. In the special case of four-point function, including a primary field degenerated at the first level, these differential equations can be solved via hypergeometric functions. Taking into account mutual locality properties of fields and investigating s- and t-channel singularities we obtain some functional relations for three-point correlation functions. Solving this functional equations we obtain three-point functions in both Neveu-Schwarz and Ramond sectors. (orig.)

  16. Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations

    NARCIS (Netherlands)

    Jarlebring, E.; Hochstenbach, M.E.

    2009-01-01

    Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called

  17. Non-negative Matrix Factorization for Binary Data

    DEFF Research Database (Denmark)

    Larsen, Jacob Søgaard; Clemmensen, Line Katrine Harder

    We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though...... this is in theory not appropriate for binary data, and thus we propose a novel Non-negative Matrix Factorization based on the logistic link function. Furthermore we generalize the method to handle missing data. The formulation of the method is compared to a previously proposed method (Tome et al., 2015). We compare...... the performance of the Logistic Non-negative Matrix Factorization to Least Squares Non-negative Matrix Factorization and Kullback-Leibler (KL) Non-negative Matrix Factorization on sets of binary data: a synthetic dataset, a set of student comments on their professors collected in a binary term-document matrix...

  18. Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

    Science.gov (United States)

    Chen, Zhenhua; Chen, Xun; Wu, Wei

    2013-04-01

    In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.

  19. Quantum Crystallography: Density Matrix-Density Functional Theory and the X-Ray Diffraction Experiment

    Science.gov (United States)

    Soirat, Arnaud J. A.

    Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine

  20. Hankel Matrix Correlation Function-Based Subspace Identification Method for UAV Servo System

    Directory of Open Access Journals (Sweden)

    Minghong She

    2018-01-01

    Full Text Available For the identification problem of closed-loop subspace model, we propose a zero space projection method based on the estimation of correlation function to fill the block Hankel matrix of identification model by combining the linear algebra with geometry. By using the same projection of related data in time offset set and LQ decomposition, the multiplication operation of projection is achieved and dynamics estimation of the unknown equipment system model is obtained. Consequently, we have solved the problem of biased estimation caused when the open-loop subspace identification algorithm is applied to the closed-loop identification. A simulation example is given to show the effectiveness of the proposed approach. In final, the practicability of the identification algorithm is verified by hardware test of UAV servo system in real environment.