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Sample records for riemann function

  1. Exploring the Riemann zeta function 190 years from Riemann's birth

    CERN Document Server

    Nikeghbali, Ashkan; Rassias, Michael

    2017-01-01

    This book is concerned with the Riemann Zeta Function, its generalizations, and various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis and Probability Theory. Eminent experts in the field illustrate both old and new results towards the solution of long-standing problems and include key historical remarks. Offering a unified, self-contained treatment of broad and deep areas of research, this book will be an excellent tool for researchers and graduate students working in Mathematics, Mathematical Physics, Engineering and Cryptography.

  2. Functionals of finite Riemann surfaces

    CERN Document Server

    Schiffer, Menahem

    1954-01-01

    This advanced monograph on finite Riemann surfaces, based on the authors' 1949-50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of ""a plethora of ideas, each interesting in its own right,"" noting that ""the patient reader will be richly rewarded."" Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theo

  3. Lectures on the Riemann zeta function

    CERN Document Server

    Iwaniec, H

    2014-01-01

    The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. Th...

  4. Meromorphic functions and cohomology on a Riemann surface

    International Nuclear Information System (INIS)

    Gomez-Mont, X.

    1989-01-01

    The objective of this set of notes is to introduce a series of concepts of Complex Analytic Geometry on a Riemann Surface. We motivate the introduction of cohomology groups through the analysis of meromorphic functions. We finish by showing that the set of infinitesimal deformations of a Riemann surface (the tangent space to Teichmueller space) may be computed as a Cohomology group. (author). 6 refs

  5. The sewing technique and correlation functions on arbitrary Riemann surfaces

    International Nuclear Information System (INIS)

    Di Vecchia, P.

    1989-01-01

    We describe in the case of free bosonic and fermionic theories the sewing procedure, that is a very convenient way for constructing correlation functions of these theories on an arbitrary Riemann surface from their knowledge on the sphere. The fundamental object that results from this construction is the N-point g-loop vertex. It summarizes the information of all correlation functions of the theory on an arbitrary Riemann surface. We then check explicitly the bosonization rules and derive some useful formulas. (orig.)

  6. Riemann zeta function from wave-packet dynamics

    DEFF Research Database (Denmark)

    Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.

    2010-01-01

    We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...

  7. The Riemann zeta-function theory and applications

    CERN Document Server

    Ivic, Aleksandar

    2003-01-01

    ""A thorough and easily accessible account.""-MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estim

  8. Method of construction of the Riemann function for a second-order hyperbolic equation

    Science.gov (United States)

    Aksenov, A. V.

    2017-12-01

    A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.

  9. On the $a$-points of the derivatives of the Riemann zeta function

    OpenAIRE

    Onozuka, Tomokazu

    2016-01-01

    We prove three results on the $a$-points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of the $a$-points of the derivatives of the Riemann zeta function. The second result is on certain exponential sum involving $a$-points. The third result is an analogue of the zero density theorem. We count the $a$-points of the derivatives of the Riemann zeta function in $1/2-(\\log\\log T)^2/\\log T

  10. Minimal models on Riemann surfaces: The partition functions

    International Nuclear Information System (INIS)

    Foda, O.

    1990-01-01

    The Coulomb gas representation of the A n series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius) 2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)

  11. Minimal models on Riemann surfaces: The partition functions

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)

    1990-06-04

    The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).

  12. Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions

    Energy Technology Data Exchange (ETDEWEB)

    Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)

    2009-12-31

    A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.

  13. Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

    OpenAIRE

    Biane, P.; Pitman, J.; Yor, M.

    1999-01-01

    This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.

  14. Functional models for commutative systems of linear operators and de Branges spaces on a Riemann surface

    International Nuclear Information System (INIS)

    Zolotarev, Vladimir A

    2009-01-01

    Functional models are constructed for commutative systems {A 1 ,A 2 } of bounded linear non-self-adjoint operators which do not contain dissipative operators (which means that ξ 1 A 1 +ξ 2 A 2 is not a dissipative operator for any ξ 1 , ξ 2 element of R). A significant role is played here by the de Branges transform and the function classes occurring in this context. Classes of commutative systems of operators {A 1 ,A 2 } for which such a construction is possible are distinguished. Realizations of functional models in special spaces of meromorphic functions on Riemann surfaces are found, which lead to reasonable analogues of de Branges spaces on these Riemann surfaces. It turns out that the functions E(p) and E-tilde(p) determining the order of growth in de Branges spaces on Riemann surfaces coincide with the well-known Baker-Akhiezer functions. Bibliography: 11 titles.

  15. Local Extrema of the $\\Xi(t)$ Function and The Riemann Hypothesis

    OpenAIRE

    Kobayashi, Hisashi

    2016-01-01

    In the present paper we obtain a necessary and sufficient condition to prove the Riemann hypothesis in terms of certain properties of local extrema of the function $\\Xi(t)=\\xi(\\tfrac{1}{2}+it)$. First, we prove that positivity of all local maxima and negativity of all local minima of $\\Xi(t)$ form a necessary condition for the Riemann hypothesis to be true. After showing that any extremum point of $\\Xi(t)$ is a saddle point of the function $\\Re\\{\\xi(s)\\}$, we prove that the above properties o...

  16. Quantized Dirac field in curved Riemann--Cartan background. I. Symmetry properties, Green's function

    International Nuclear Information System (INIS)

    Nieh, H.T.; Yan, M.L.

    1982-01-01

    In the present series of papers, we study the properties of quantized Dirac field in curved Riemann--Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann--Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann--Cartan background, using the Schwinger--DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background

  17. Averages of ratios of the Riemann zeta-function and correlations of divisor sums

    Science.gov (United States)

    Conrey, Brian; Keating, Jonathan P.

    2017-10-01

    Nonlinearity has published articles containing a significant number-theoretic component since the journal was first established. We examine one thread, concerning the statistics of the zeros of the Riemann zeta function. We extend this by establishing a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of Möbius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.

  18. Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function

    Directory of Open Access Journals (Sweden)

    Saker SamirH

    2010-01-01

    Full Text Available On the hypothesis that the th moments of the Hardy -function are correctly predicted by random matrix theory and the moments of the derivative of are correctly predicted by the derivative of the characteristic polynomials of unitary matrices, we establish new large spaces between the zeros of the Riemann zeta-function by employing some Wirtinger-type inequalities. In particular, it is obtained that which means that consecutive nontrivial zeros often differ by at least 6.1392 times the average spacing.

  19. Fractional parts and their relations to the values of the Riemann zeta function

    KAUST Repository

    Alabdulmohsin, Ibrahim

    2017-09-06

    A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

  20. Fractional parts and their relations to the values of the Riemann zeta function

    KAUST Repository

    Alabdulmohsin, Ibrahim

    2017-01-01

    A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

  1. Bernhard Riemann

    Indian Academy of Sciences (India)

    the basis for various fields of mathematics and the general relativity theory of Einstein. In 1857 ... This idea explained the work on algebraic ... theory, Riemann found the key to the problem of the distribution of primes, in that he associated it ...

  2. Deformations of super Riemann surfaces

    International Nuclear Information System (INIS)

    Ninnemann, H.

    1992-01-01

    Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.)

  3. Deformations of super Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Ninnemann, H [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    1992-11-01

    Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.).

  4. Conformal mapping on Riemann surfaces

    CERN Document Server

    Cohn, Harvey

    2010-01-01

    The subject matter loosely called ""Riemann surface theory"" has been the starting point for the development of topology, functional analysis, modern algebra, and any one of a dozen recent branches of mathematics; it is one of the most valuable bodies of knowledge within mathematics for a student to learn.Professor Cohn's lucid and insightful book presents an ideal coverage of the subject in five pans. Part I is a review of complex analysis analytic behavior, the Riemann sphere, geometric constructions, and presents (as a review) a microcosm of the course. The Riemann manifold is introduced in

  5. Fuzzy Riemann surfaces

    International Nuclear Information System (INIS)

    Arnlind, Joakim; Hofer, Laurent; Hoppe, Jens; Bordemann, Martin; Shimada, Hidehiko

    2009-01-01

    We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.

  6. Riemann surfaces with boundaries and string theory

    International Nuclear Information System (INIS)

    Morozov, A.Yu.; Roslyj, A.A.

    1989-01-01

    A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned

  7. Super Riemann surfaces

    International Nuclear Information System (INIS)

    Rogers, Alice

    1990-01-01

    A super Riemann surface is a particular kind of (1,1)-dimensional complex analytic supermanifold. From the point of view of super-manifold theory, super Riemann surfaces are interesting because they furnish the simplest examples of what have become known as non-split supermanifolds, that is, supermanifolds where the odd and even parts are genuinely intertwined, as opposed to split supermanifolds which are essentially the exterior bundles of a vector bundle over a conventional manifold. However undoubtedly the main motivation for the study of super Riemann surfaces has been their relevance to the Polyakov quantisation of the spinning string. Some of the papers on super Riemann surfaces are reviewed. Although recent work has shown all super Riemann surfaces are algebraic, some areas of difficulty remain. (author)

  8. Statistical properties of the zeros of zeta functions - beyond the Riemann case

    International Nuclear Information System (INIS)

    Bogomolny, E.; Leboeuf, P.

    1993-09-01

    The statistical distribution of the zeros of Dirichlet L-functions is investigated both analytically and numerically. Using the Hardy-Littlewood conjecture about the distribution of primes it is shown that the two-point correlation function of these zeros coincides with that for eigenvalues of the Gaussian unitary ensemble of random matrices, and that the distributions of zeros of different L-functions are statistically independent. Applications of these results to Epstein's zeta functions are shortly discussed. (authors) 30 refs., 3 figs., 1 tab

  9. Generalized Riemann zeta-function regularization and Casimir energy for a piecewise uniform string

    International Nuclear Information System (INIS)

    Li Xinzhou; Shi Xin; Zhang Jianzu.

    1990-12-01

    The generalized zeta-function techniques will be utilized to investigate the Casimir energy for the transverse oscillations of a piecewise uniform closed string. We find that zeta-function regularization method can lead straightforwardly to a correct result. (author). 6 refs

  10. Operator bosonization on Riemann surfaces: new vertex operators

    International Nuclear Information System (INIS)

    Semikhatov, A.M.

    1989-01-01

    A new formalism is proposed for the construction of an operator theory of generalized ghost systems (bc theories of spin J) on Riemann surfaces (loop diagrams of the theory of closed strings). The operators of the bc system are expressed in terms of operators of the bosonic conformal theory on a Riemann surface. In contrast to the standard bosonization formulas, which have meaning only locally, operator Baker-Akhiezer functions, which are well defined globally on a Riemann surface of arbitrary genus, are introduced. The operator algebra of the Baker-Akhiezer functions generates explicitly the algebraic-geometric τ function and correlation functions of bc systems on Riemann surfaces

  11. Riemann, topology, and physics

    CERN Document Server

    Monastyrsky, Michael I

    2008-01-01

    This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...

  12. Riemann quasi-invariants

    International Nuclear Information System (INIS)

    Pokhozhaev, Stanislav I

    2011-01-01

    The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.

  13. Chiral bosonization on a Riemann surface

    International Nuclear Information System (INIS)

    Eguchi, Tohru; Ooguri, Hirosi

    1987-01-01

    We point out that the basic addition theorem of θ-functions, Fay's identity, implies an equivalence between bosons and chiral fermions on Riemann surfaces with arbitrary genus. We present a rule for a bosonized calculation of correlation functions. We also discuss ghost systems of n and (1-n) tensors and derive formulas for their chiral determinants. (orig.)

  14. Interpolating and sampling sequences in finite Riemann surfaces

    OpenAIRE

    Ortega-Cerda, Joaquim

    2007-01-01

    We provide a description of the interpolating and sampling sequences on a space of holomorphic functions on a finite Riemann surface, where a uniform growth restriction is imposed on the holomorphic functions.

  15. Computational approach to Riemann surfaces

    CERN Document Server

    Klein, Christian

    2011-01-01

    This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first...

  16. The concept of a Riemann surface

    CERN Document Server

    Weyl, Hermann

    2009-01-01

    This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment

  17. Supermanifolds and super Riemann surfaces

    International Nuclear Information System (INIS)

    Rabin, J.M.

    1986-09-01

    The theory of super Riemann surfaces is rigorously developed using Rogers' theory of supermanifolds. The global structures of super Teichmueller space and super moduli space are determined. The super modular group is shown to be precisely the ordinary modular group. Super moduli space is shown to be the gauge-fixing slice for the fermionic string path integral

  18. Riemann surfaces, Clifford algebras and infinite dimensional groups

    International Nuclear Information System (INIS)

    Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.

    1990-01-01

    We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)

  19. On Riemann zeroes, lognormal multiplicative chaos, and Selberg integral

    International Nuclear Information System (INIS)

    Ostrovsky, Dmitry

    2016-01-01

    Rescaled Mellin-type transforms of the exponential functional of the Bourgade–Kuan–Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot–Bacry–Muzy. The conjecture implies that a non-trivial, log-infinitely divisible probability distribution is associated with Riemann zeroes. For application, integral moments, covariance structure, multiscaling spectrum, and asymptotics associated with the exponential functional are computed in closed form using the known meromorphic extension of the Selberg integral. (paper)

  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. Getting superstring amplitudes by degenerating Riemann surfaces

    International Nuclear Information System (INIS)

    Matone, Marco; Volpato, Roberto

    2010-01-01

    We explicitly show how the chiral superstring amplitudes can be obtained through factorisation of the higher genus chiral measure induced by suitable degenerations of Riemann surfaces. This powerful tool also allows to derive, at any genera, consistency relations involving the amplitudes and the measure. A key point concerns the choice of the local coordinate at the node on degenerate Riemann surfaces that greatly simplifies the computations. As a first application, starting from recent ansaetze for the chiral measure up to genus five, we compute the chiral two-point function for massless Neveu-Schwarz states at genus two, three and four. For genus higher than three, these computations include some new corrections to the conjectural formulae appeared so far in the literature. After GSO projection, the two-point function vanishes at genus two and three, as expected from space-time supersymmetry arguments, but not at genus four. This suggests that the ansatz for the superstring measure should be corrected for genus higher than four.

  2. The Riemann-Lovelock Curvature Tensor

    OpenAIRE

    Kastor, David

    2012-01-01

    In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

  3. A Polyakov action on Riemann surfaces

    International Nuclear Information System (INIS)

    Zucchini, R.

    1991-02-01

    A calculation of the effective action for induced conformal gravity on higher genus Riemann surfaces is presented. Our expression, generalizing Polyakov's formula, depends holomorphically on the Beltrami and integrates the diffeomorphism anomaly. A solution of the conformal Ward identity on an arbitrary compact Riemann surfaces without boundary is presented, and its remarkable properties are studied. (K.A.) 16 refs., 2 figs

  4. Riemann-Theta Boltzmann Machine arXiv

    CERN Document Server

    Krefl, Daniel; Haghighat, Babak; Kahlen, Jens

    A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.

  5. Ice cream and orbifold Riemann-Roch

    International Nuclear Information System (INIS)

    Buckley, Anita; Reid, Miles; Zhou Shengtian

    2013-01-01

    We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of K3 surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.

  6. Ice cream and orbifold Riemann-Roch

    Science.gov (United States)

    Buckley, Anita; Reid, Miles; Zhou, Shengtian

    2013-06-01

    We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of {K3} surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.

  7. The Riemann-Lovelock curvature tensor

    International Nuclear Information System (INIS)

    Kastor, David

    2012-01-01

    In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)

  8. Riemann y los Números Primos

    Directory of Open Access Journals (Sweden)

    José Manuel Sánchez Muñoz

    2011-10-01

    Full Text Available En el mes de noviembre de 1859, durante la presentación mensual de losinformes de la Academia de Berlín, el alemán Bernhard Riemann presentóun trabajo que cambiaría los designios futuros de la ciencia matemática. El tema central de su informe se centraba en los números primos, presentando el que hoy día, una vez demostrada la Conjetura de Poincaré, puede ser considerado el problema matemático abierto más importante. El presente artículo muestra en su tercera sección una traducción al castellano de dicho trabajo.

  9. Conformal algebra of Riemann surfaces

    International Nuclear Information System (INIS)

    Vafa, C.

    1988-01-01

    It has become clear over the last few years that 2-dimensional conformal field theories are a crucial ingredient of string theory. Conformal field theories correspond to vacuum solutions of strings; or more precisely we know how to compute string spectrum and scattering amplitudes by starting from a formal theory (with a proper value of central charge of the Virasoro algebra). Certain non-linear sigma models do give rise to conformal theories. A lot of progress has been made in the understanding of conformal theories. The author discusses a different view of conformal theories which was motivated by the development of operator formalism on Riemann surfaces. The author discusses an interesting recent work from this point of view

  10. Conformal scalar fields and chiral splitting on super Riemann surfaces

    International Nuclear Information System (INIS)

    D'Hoker, E.; Phong, D.H.

    1989-01-01

    We provide a complete description of correlation functions of scalar superfields on a super Riemann surface, taking into account zero modes and non-trivial topology. They are built out of chirally split correlation functions, or conformal blocks at fixed internal momenta. We formulate effective rules which determine these completely in terms of geometric invariants of the super Riemann surface. The chirally split correlation functions have non-trivial monodromy and produce single-valued amplitudes only upon integration over loop momenta. Our discussion covers the even spin structure as well as the odd spin structure case which had been the source of many difficulties in the past. Super analogues of Green's functions, holomorphic spinors, and prime forms emerge which should pave the way to function theory on super Riemann surfaces. In superstring theories, chirally split amplitudes for scalar superfields are crucial in enforcing the GSO projection required for consistency. However one really knew how to carry this out only in the operator formalism to one-loop order. Our results provide a way of enforcing the GSO projection to any loop. (orig.)

  11. Super differential forms on super Riemann surfaces

    International Nuclear Information System (INIS)

    Konisi, Gaku; Takahasi, Wataru; Saito, Takesi.

    1994-01-01

    Line integral on the super Riemann surface is discussed. A 'super differential operator' which possesses both properties of differential and of differential operator is proposed. With this 'super differential operator' a new theory of differential form on the super Riemann surface is constructed. We call 'the new differentials on the super Riemann surface' 'the super differentials'. As the applications of our theory, the existency theorems of singular 'super differentials' such as 'super abelian differentials of the 3rd kind' and of a super projective connection are examined. (author)

  12. Bosonization in a two-dimensional Riemann Cartan geometry

    International Nuclear Information System (INIS)

    Denardo, G.; Spallucci, E.

    1987-01-01

    We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)

  13. Quantum Hall effect on Riemann surfaces

    Science.gov (United States)

    Tejero Prieto, Carlos

    2009-06-01

    We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.

  14. Quantum Hall effect on Riemann surfaces

    International Nuclear Information System (INIS)

    Tejero Prieto, Carlos

    2009-01-01

    We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.

  15. Structural stability of solutions to the Riemann problem for a non-strictly hyperbolic system with flux approximation

    Directory of Open Access Journals (Sweden)

    Meina Sun

    2016-05-01

    Full Text Available We study the Riemann problem for a non-strictly hyperbolic system of conservation laws under the linear approximations of flux functions with three parameters. The approximated system also belongs to the type of triangular systems of conservation laws and this approximation does not change the structure of Riemann solutions to the original system. Furthermore, it is proven that the Riemann solutions to the approximated system converge to the corresponding ones to the original system as the perturbation parameter tends to zero.

  16. Gaussian curvature on hyperelliptic Riemann surfaces

    Indian Academy of Sciences (India)

    Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.

  17. Conformal deformation of Riemann space and torsion

    International Nuclear Information System (INIS)

    Pyzh, V.M.

    1981-01-01

    Method for investigating conformal deformations of Riemann spaces using torsion tensor, which permits to reduce the second ' order equations for Killing vectors to the system of the first order equations, is presented. The method is illustrated using conformal deformations of dimer sphere as an example. A possibility of its use when studying more complex deformations is discussed [ru

  18. Study Paths, Riemann Surfaces, and Strebel Differentials

    Science.gov (United States)

    Buser, Peter; Semmler, Klaus-Dieter

    2017-01-01

    These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…

  19. Hysteresis rarefaction in the Riemann problem

    Czech Academy of Sciences Publication Activity Database

    Krejčí, Pavel

    2008-01-01

    Roč. 138, - (2008), s. 1-10 ISSN 1742-6588. [International Workshop on Multi-Rate Processes and Hysteresis. Cork , 31.03.2008-05.04.2008] Institutional research plan: CEZ:AV0Z10190503 Keywords : Preisach hysteresis * Riemann problem Subject RIV: BA - General Mathematics http://iopscience.iop.org/1742-6596/138/1/012010

  20. Generalized Riemann problem for reactive flows

    International Nuclear Information System (INIS)

    Ben-Artzi, M.

    1989-01-01

    A generalized Riemann problem is introduced for the equations of reactive non-viscous compressible flow in one space dimension. Initial data are assumed to be linearly distributed on both sides of a jump discontinuity. The resolution of the singularity is studied and the first-order variation (in time) of flow variables is given in exact form. copyright 1989 Academic Press, Inc

  1. Explicit solution of Riemann-Hilbert problems for the Ernst equation

    Science.gov (United States)

    Klein, C.; Richter, O.

    1998-01-01

    Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.

  2. SO(N) WZNW models on higher-genus Riemann surfaces

    International Nuclear Information System (INIS)

    Alimohammadi, M.; Arfaei, H.; Bonn Univ.

    1993-08-01

    With the help of the string functions and fusion rules of SO(2N) 1 , we show that the results on SU(N) 1 correlators on higher-genus Riemann surfaces (HGRS) can be extended to the SO(2N) 1 and other level-one simply-laced WZNW models. Using modular invariance and factorization properties of Green functions we find multipoint correlators of primary and descendant fields of SO(2N+1) 1 WZNW models on higher genus Riemann surfaces. (orig.)

  3. Reassessing Riemann's paper on the number of primes less than a given magnitude

    CERN Document Server

    Dittrich, Walter

    2018-01-01

    In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized.

  4. On Lovelock analogs of the Riemann tensor

    Science.gov (United States)

    Camanho, Xián O.; Dadhich, Naresh

    2016-03-01

    It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

  5. Poisson sigma model with branes and hyperelliptic Riemann surfaces

    International Nuclear Information System (INIS)

    Ferrario, Andrea

    2008-01-01

    We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions

  6. Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis

    CERN Document Server

    Castro, C

    2004-01-01

    The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...

  7. Large chiral diffeomorphisms on Riemann surfaces and W-algebras

    International Nuclear Information System (INIS)

    Bandelloni, G.; Lazzarini, S.

    2006-01-01

    The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims

  8. The KZB equations on Riemann surfaces

    OpenAIRE

    Felder, Giovanni

    1996-01-01

    In this paper, based on the author's lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan--Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at $n$ marked points are given. The covariant derivatives are expressed in terms of ``dynamical $r$-matrices'', a notion borrowed from integrable systems. The case of marked points moving on a fixed Riemann surface is studied more closely. We prove a universa...

  9. Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

    Science.gov (United States)

    Bender, Carl M.; Brody, Dorje C.

    2018-04-01

    The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

  10. Jacob's ladders, Riemann's oscillators, quotient of two oscillating multiforms and set of metamorphoses of this system

    OpenAIRE

    Moser, Jan

    2015-01-01

    In this paper we introduce complicated oscillating system, namely quotient of two multiforms based on Riemann-Siegel formula. We prove that there is an infinite set of metamorphoses of this system (=chrysalis) on critical line $\\sigma=\\frac 12$ into a butterfly (=infinite series of M\\" obius functions in the region of absolute convergence $\\sigma>1$).

  11. Post-Quantum Cryptography: Riemann Primitives and Chrysalis

    OpenAIRE

    Malloy, Ian; Hollenbeck, Dennis

    2018-01-01

    The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first cryptographic scheme to rely on Holomorphic Learning with Errors, which is a complex form of Learning with Errors relying on the Gauss Circle Problem within the Riemann sphere. The principle security reduction proposed by this novel cryptographic scheme applies c...

  12. Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis

    International Nuclear Information System (INIS)

    Khuri, N. N.

    2002-01-01

    It is well known that the s-wave Jost function for a potential, λV, is an entire function of λ with an infinite number of zeros extending to infinity. For a repulsive V, and at zero energy, these zeros of the 'coupling constant', λ, will all be real and negative, λ n (0) n n =1/2+iγ n . Thus, finding a repulsive V whose coupling constant spectrum coincides with the Riemann zeros will establish the Riemann hypothesis, but this will be a very difficult and unguided search.In this paper we make a significant enlargement of the class of potentials needed for a generalization of the above idea. We also make this new class amenable to construction via inverse scattering methods. We show that all one needs is a one parameter class of potentials, U(s;x), which are analytic in the strip, 0≤Res≤1, Ims>T 0 , and in addition have an asymptotic expansion in powers of [s(s-1)] -1 , i.e. U(s;x)=V 0 (x)+gV 1 (x)+g 2 V 2 (x)+...+O(g N ), with g=[s(s-1)] -1 . The potentials V n (x) are real and summable. Under suitable conditions on the V n 's and the O(g N ) term we show that the condition, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx≠0, where f 0 is the zero energy and g=0 Jost function for U, is sufficient to guarantee that the zeros g n are real and, hence, s n =1/2+iγ n , for γ n ≥T 0 .Starting with a judiciously chosen Jost function, M(s,k), which is constructed such that M(s,0) is Riemann's ξ(s) function, we have used inverse scattering methods to actually construct a U(s;x) with the above properties. By necessity, we had to generalize inverse methods to deal with complex potentials and a nonunitary S-matrix. This we have done at least for the special cases under consideration.For our specific example, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx=0 and, hence, we get no restriction on Img n or Res n . The reasons for the vanishing of the above integral are given, and they give us hints on what one needs to proceed further. The problem

  13. Riemann monodromy problem and conformal field theories

    International Nuclear Information System (INIS)

    Blok, B.

    1989-01-01

    A systematic analysis of the use of the Riemann monodromy problem for determining correlators (conformal blocks) on the sphere is presented. The monodromy data is constructed in terms of the braid matrices and gives a constraint on the noninteger part of the conformal dimensions of the primary fields. To determine the conformal blocks we need to know the order of singularities. We establish a criterion which tells us when the knowledge of the conformal dimensions of primary fields suffice to determine the blocks. When zero modes of the extended algebra are present the analysis is more difficult. In this case we give a conjecture that works for the SU(2) WZW case. (orig.)

  14. The Euler–Riemann gases, and partition identities

    International Nuclear Information System (INIS)

    Chair, Noureddine

    2013-01-01

    The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice (s-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order s of the parafermions. It is also shown that these partition functions are generating functions of partitions of integers with restrictions, the Euler generating function is identified with the inverse of the graded parafermionic partition function of order 2. As a result we obtain new sequences of partitions of integers with given restrictions. If the parity of the order s is even, then mixing a system of parafermions with a system whose partition function is (IGPPF), results in a system of fermions and bosons. On the other hand, if the parity of s is odd, then, the system we obtain is still a mixture of fermions and bosons but the corresponding Fock space of states is truncated. It turns out that these partition functions are given in terms of the Jacobi theta function θ 4 , and generate sequences in partition theory. Our partition functions coincide with the overpartitions of Corteel and Lovejoy, and jagged partitions in conformal field theory. Also, the partition functions obtained are related to the Ramond characters of the superconformal minimal models, and in the counting of the Moore–Read edge spectra that appear in the fractional quantum Hall effect. The different partition functions for the Riemann gas that are the counter parts of the Euler gas are obtained by a simple change of variables. In particular the counter part of the Jacobi theta function is (ζ(2t))/(ζ(t) 2 ) . Finally, we propose two formulas which brings

  15. Quantum field theory on higher-genus Riemann surfaces

    International Nuclear Information System (INIS)

    Kubo, Reijiro; Yoshii, Hisahiro; Ojima, Shuichi; Paul, S.K.

    1989-07-01

    Quantum field theory for b-c systems is formulated on Riemann surfaces with arbitrary genus. We make use of the formalism recently developed by Krichever and Novikov. Hamiltonian is defined properly, and the Ward-Takahashi identities are derived on higher-genus Riemann surfaces. (author)

  16. Non-abelian bosonization in higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Koh, I.G.; Yu, M.

    1988-01-01

    We propose a generalization of the character formulas of the SU(2) Kac-Moody algebra to higher genus Riemann surfaces. With this construction, we show that the modular invariant partition funciton of the SO(4) k = 1 Wess-Zumino model is equivalent, in arbitrary genus Riemann surfaces, to that of free fermion theory. (orig.)

  17. Collisionless analogs of Riemann S ellipsoids with halo

    International Nuclear Information System (INIS)

    Abramyan, M.G.

    1987-01-01

    A spheroidal halo ensures equilibrium of the collisionless analogs of the Riemann S ellipsoids with oscillations of the particles along the direction of their rotation. Sequences of collisionless triaxial ellipsoids begin and end with dynamically stable members of collisionless embedded spheroids. Both liquid and collisionless Riemann S ellipsoids with weak halo have properties that resemble those of bars of SB galaxies

  18. A Riemann problem with small viscosity and dispersion

    Directory of Open Access Journals (Sweden)

    Kayyunnapara Thomas Joseph

    2006-09-01

    Full Text Available In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.

  19. E-string theory on Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Hee-Cheol; Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University, Cambridge, MA (United States); Razamat, Shlomo S. [Physics Department, Technion, Haifa (Israel); Zafrir, Gabi [Kavli IPMU (WPI), UTIAS, the University of Tokyo, Kashiwa, Chiba (Japan)

    2018-01-15

    We study compactifications of the 6d E-string theory, the theory of a small E{sub 8} instanton, to four dimensions. In particular we identify N = 1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E{sub 8} flavor symmetry. This sheds light on emergent symmetries in a number of 4d N = 1 SCFTs (including the 'E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  20. Moduli of Riemann surfaces, transcendental aspects

    International Nuclear Information System (INIS)

    Hain, R.

    2000-01-01

    These notes are an informal introduction to moduli spaces of compact Riemann surfaces via complex analysis, topology and Hodge Theory. The prerequisites for the first lecture are just basic complex variables, basic Riemann surface theory up to at least the Riemann-Roch formula, and some algebraic topology, especially covering space theory. The first lecture covers moduli in genus 0 and genus 1 as these can be understood using relatively elementary methods, but illustrate many of the points which arise in higher genus. The notes cover more material than was covered in the lectures, and sometimes the order of topics in the notes differs from that in the lectures. We have seen in genus 1 case that M 1 is the quotient Γ 1 /X 1 of a contractible complex manifold X 1 = H by a discrete group Γ 1 = SL 2 (Z). The action of Γ 1 on X 1 is said to be virtually free - that is, Γ 1 has a finite index subgroup which acts (fixed point) freely on X 1 . In this section we will generalize this to all g >= 1 - we will sketch a proof that there is a contractible complex manifold Xg, called Teichmueller space, and a group Γ g , called the mapping class group, which acts virtually freely on X g . The moduli space of genus g compact Riemann surfaces is the quotient: M g = Γ g /X g . This will imply that M g has the structure of a complex analytic variety with finite quotient singularities. Teichmueller theory is a difficult and technical subject. Because of this, it is only possible to give an overview. In this lecture, we compute the orbifold Picard group of M g for all g >= 1. Recall that an orbifold line bundle over M g is a holomorphic line bundle L over Teichmueller space X g together with an action of the mapping class group Γ g on it such that the projection L → X g is Γ g -equivariant. An orbifold section of this line bundle is a holomorphic Γ g -equivariant section X g → L of L. This is easily seen to be equivalent to fixing a level l>= 3 and considering holomorphic

  1. Transformation optics with artificial Riemann sheets

    Science.gov (United States)

    Xu, Lin; Chen, Huanyang

    2013-11-01

    The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777-80 and Pendry et al 2006 Science 312 1780-2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110-12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results.

  2. Transformation optics with artificial Riemann sheets

    International Nuclear Information System (INIS)

    Xu, Lin; Chen, Huanyang

    2013-01-01

    The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777–80 and Pendry et al 2006 Science 312 1780–2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110–12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results. (paper)

  3. From Riemann to differential geometry and relativity

    CERN Document Server

    Papadopoulos, Athanase; Yamada, Sumio

    2017-01-01

    This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

  4. From Euclidean to Minkowski space with the Cauchy-Riemann equations

    International Nuclear Information System (INIS)

    Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.

    2008-01-01

    We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)

  5. Riemann zeros and phase transitions via the spectral operator on fractal strings

    International Nuclear Information System (INIS)

    Herichi, Hafedh; Lapidus, Michel L

    2012-01-01

    The spectral operator was introduced by Lapidus and van Frankenhuijsen (2006 Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings) in their reinterpretation of the earlier work of Lapidus and Maier (1995 J. Lond. Math. Soc. 52 15–34) on inverse spectral problems and the Riemann hypothesis. In essence, it is a map that sends the geometry of a fractal string onto its spectrum. In this review, we present the rigorous functional analytic framework given by Herichi and Lapidus (2012) and within which to study the spectral operator. Furthermore, we give a necessary and sufficient condition for the invertibility of the spectral operator (in the critical strip) and therefore obtain a new spectral and operator-theoretic reformulation of the Riemann hypothesis. More specifically, we show that the spectral operator is quasi-invertible (or equivalently, that its truncations are invertible) if and only if the Riemann zeta function ζ(s) does not have any zeros on the vertical line Re(s) = c. Hence, it is not invertible in the mid-fractal case when c= 1/2 , and it is quasi-invertible everywhere else (i.e. for all c ∈ (0, 1) with c≠ 1/2 ) if and only if the Riemann hypothesis is true. We also show the existence of four types of (mathematical) phase transitions occurring for the spectral operator at the critical fractal dimension c= 1/2 and c = 1 concerning the shape of the spectrum, its boundedness, its invertibility as well as its quasi-invertibility. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)

  6. Riemann-Hilbert treatment of Liouville theory on the torus: the general case

    International Nuclear Information System (INIS)

    Menotti, Pietro

    2011-01-01

    We extend the previous treatment of Liouville theory on the torus to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We show through a group theoretic argument that the Heun parameter and a weight constant are sufficient to satisfy all monodromy conditions. We then apply the technique of differential equations on a Riemann surface to the two-point function on the torus in which one source is arbitrary and the other small. As a byproduct, we give in terms of quadratures the exact Green function on the square and on the rhombus with opening angle 2π/6 in the background of the field generated by an arbitrary charge.

  7. A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.

  8. The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems

    Science.gov (United States)

    Prykarpatsky, Yarema A.; Artemovych, Orest D.; Pavlov, Maxim V.; Prykarpatski, Anatolij K.

    2013-06-01

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.

  9. On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

    Science.gov (United States)

    Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

    2018-01-01

    The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

  10. Fermions on a Riemann surface and the Kadomtsev-Petviashvili equation

    International Nuclear Information System (INIS)

    Zabrodin, A.V.

    1989-01-01

    It is shown that the S matrix of free massless fermions on a Riemann surface of finite genus generates quasiperiodic solutions of the Kadomtsev-Petviashvili equation. An operator that changes the genus of a solution is constructed, and the law of composition of such operators is discussed. The construction is a generalization of the well-known operator approach in the case of soliton solutions to the general case of quasiperiodic τ functions

  11. Two-dimensional time dependent Riemann solvers for neutron transport

    International Nuclear Information System (INIS)

    Brunner, Thomas A.; Holloway, James Paul

    2005-01-01

    A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem

  12. The exchange algebra for Liouville theory on punctured Riemann sphere

    International Nuclear Information System (INIS)

    Shen Jianmin; Sheng Zhengmao

    1991-11-01

    We consider in this paper the classical Liouville field theory on the Riemann sphere with n punctures. In terms of the uniformization theorem of Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville fields. We find that the matrice which dominate the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (author). 10 refs

  13. Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics

    CERN Document Server

    Laugwitz, Detlef

    2008-01-01

    The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...

  14. Robinson manifolds and Cauchy-Riemann spaces

    CERN Document Server

    Trautman, A

    2002-01-01

    A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...

  15. Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems

    Science.gov (United States)

    Balsara, Dinshaw S.; Nkonga, Boniface

    2017-10-01

    Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.

  16. Solution of Riemann problem for ideal polytropic dusty gas

    International Nuclear Information System (INIS)

    Nath, Triloki; Gupta, R.K.; Singh, L.P.

    2017-01-01

    Highlights : • A direct approach is used to solve the Riemann problem for dusty ideal polytropic gas. • An analytical solution to the Riemann problem for dusty gas flow is obtained. • The existence and uniqueness of the solution in dusty gas is discussed. • Properties of elementary wave solutions of Riemann problem are discussed. • Effect of mass fraction of solid particles on the solution is presented. - Abstract: The Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady flow of an ideal polytropic gas with dust particles is solved analytically without any restriction on magnitude of the initial states. The elementary wave solutions of the Riemann problem, that is shock waves, rarefaction waves and contact discontinuities are derived explicitly and their properties are discussed, for a dusty gas. The existence and uniqueness of the solution for Riemann problem in dusty gas is discussed. Also the conditions leading to the existence of shock waves or simple waves for a 1-family and 3-family curves in the solution of the Riemann problem are discussed. It is observed that the presence of dust particles in an ideal polytropic gas leads to more complex expression as compared to the corresponding ideal case; however all the parallel results remain same. Also, the effect of variation of mass fraction of dust particles with fixed volume fraction (Z) and the ratio of specific heat of the solid particles and the specific heat of the gas at constant pressure on the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities are discussed.

  17. Conformal fields. From Riemann surfaces to integrable hierarchies

    International Nuclear Information System (INIS)

    Semikhatov, A.M.

    1991-01-01

    I discuss the idea of translating ingredients of conformal field theory into the language of hierarchies of integrable differential equations. Primary conformal fields are mapped into (differential or matrix) operators living on the phase space of the hierarchy, whereas operator insertions of, e.g., a current or the energy-momentum tensor, become certain vector fields on the phase space and thus acquire a meaning independent of a given Riemann surface. A number of similarities are observed between the structures arising on the hierarchy and those of the theory on the world-sheet. In particular, there is an analogue of the operator product algebra with the Cauchy kernel replaced by its 'off-shell' hierarchy version. Also, hierarchy analogues of certain operator insertions admit two (equivalent, but distinct) forms, resembling the 'bosonized' and 'fermionized' versions respectively. As an application, I obtain a useful reformulation of the Virasoro constraints of the type that arise in matrix models, as a system of equations on dressing (or Lax) operators (rather than correlation functions, i.e., residues or traces). This also suggests an interpretation in terms of a 2D topological field theory, which might be extended to a correspondence between Virasoro-constrained hierarchies and topological theories. (orig.)

  18. Riemann solvers and undercompressive shocks of convex FPU chains

    International Nuclear Information System (INIS)

    Herrmann, Michael; Rademacher, Jens D M

    2010-01-01

    We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions

  19. The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

    Science.gov (United States)

    Shao, Zhiqiang

    2018-04-01

    The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

  20. Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

    International Nuclear Information System (INIS)

    Ernst, Frederick J

    2007-01-01

    metric tensor components. The first two chapters of this book are devoted to some basic ideas: in the introductory chapter 1 the authors discuss the concept of integrability, comparing the integrability of the vacuum Ernst equation with the integrability of nonlinear equations of Korteweg-de Vries (KdV) type, while in chapter 2 they describe various circumstances in which the vacuum Ernst equation has been determined to be relevant, not only in connection with gravitation but also, for example, in the construction of solutions of the self-dual Yang-Mills equations. It is also in this chapter that one of several equivalent linear systems for the Ernst equation is described. The next two chapters are devoted to Dmitry Korotkin's concept of algebro-geometric solutions of a linear system: in chapter 3 the structure of such solutions of the vacuum Ernst equation, which involve Riemann theta functions of hyperelliptic algebraic curves of any genus, is contrasted with the periodic structure of such solutions of the KdV equation. How such solutions can be obtained, for example, by solving a matrix Riemann-Hilbert problem and how the metric tensor of the associated spacetime can be evaluated is described in detail. In chapter 4 the asymptotic behaviour and the similarity structure of the general algebro-geometric solutions of the Ernst equation are described, and the relationship of such solutions to the perhaps more familiar multi-soliton solutions is discussed. The next three chapters are based upon the authors' own published research: in chapter 5 it is shown that a problem involving counter-rotating infinitely thin disks of matter can be solved in terms of genus two Riemann theta functions, while in chapter 6 the authors describe numerical methods that facilitate the construction of such solutions, and in chapter 7 three-dimensional graphs are displayed that depict all metrical fields of the associated spacetime. Finally, in chapter 8, the difficulties associated with

  1. BRST quantization of superconformal theories on higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Leman Kuang

    1992-01-01

    A complex contour integral method is constructed and applied to the Becchi-Rouet-Stora-Tyutin (BRST) quantization procedure of string theories on higher genus Riemann surfaces with N=0 and 1 Krichever-Novikov (KN) algebras. This method makes calculations very simple. It is shown that the critical spacetime dimension of the string theories on a genus-g Riemann surface equals that of the string theories on a genus-zero Riemann surface, and that the 'Regge intercepts' in the genus-g case are α(g)=1-3/4g-9/8g 2 and 1/2-3/4g-17/16g 2 for bosonic strings and superstrings, respectively. (orig.)

  2. Compact Riemann surfaces an introduction to contemporary mathematics

    CERN Document Server

    Jost, Jürgen

    2006-01-01

    Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

  3. Line operators from M-branes on compact Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Amariti, Antonio [Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY 10031 (United States); Orlando, Domenico [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Reffert, Susanne, E-mail: sreffert@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

    2016-12-15

    In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. The latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.

  4. Riemann-Hilbert approach to the time-dependent generalized sine kernel

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K.

    2010-12-15

    We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)

  5. Integrability of Liouville system on high genus Riemann surface: Pt. 1

    International Nuclear Information System (INIS)

    Chen Yixin; Gao Hongbo

    1992-01-01

    By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface

  6. On an isospectrality question over compact Riemann surfaces

    International Nuclear Information System (INIS)

    Srinivas Rau, S.

    1990-01-01

    It is proved that for a generic compact Riemann surface X of genus g>1,(i) there are at most 2 2g unitary characters of π 1 (X) whose associated line bundles have laplacians of identical spectrum, (ii) generating cycles for π 1 (X) can be chosen to be closed geodesics whose length multiplicity is 1. (author). 5 refs

  7. Quantum Riemann surfaces. Pt. 2; The discrete series

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, S. (Dept. of Mathematics, IUPUI, Indianapolis, IN (United States)); Lesniewski, A. (Dept. of Physics, Harvard Univ., Cambridge, MA (United States))

    1992-02-01

    We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of C{sup *}-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional C{sup *}-algebras. (orig.).

  8. Colliding holes in Riemann surfaces and quantum cluster algebras

    Science.gov (United States)

    Chekhov, Leonid; Mazzocco, Marta

    2018-01-01

    In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.

  9. Weyl transforms associated with the Riemann-Liouville operator

    Directory of Open Access Journals (Sweden)

    N. B. Hamadi

    2006-01-01

    Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.

  10. Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2007-01-01

    This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established

  11. Toeplitz operators on higher Cauchy-Riemann spaces

    Czech Academy of Sciences Publication Activity Database

    Engliš, Miroslav; Zhang, G.

    2017-01-01

    Roč. 22, č. 22 (2017), s. 1081-1116 ISSN 1431-0643 Institutional support: RVO:67985840 Keywords : Toeplitz operator * Hankel operator * Cauchy-Riemann operators Subject RIV: BA - General Math ematics OBOR OECD: Pure math ematics Impact factor: 0.800, year: 2016 https://www. math .uni-bielefeld.de/documenta/vol-22/32.html

  12. The beauty of the Riemann-Silberstein vector

    International Nuclear Information System (INIS)

    Bialynicki-Birula, I.

    2005-01-01

    Beams of light carrying angular momentum have recently been widely studied theoretically and experimentally. In my talk I will show that the description of these beams in terms of the Riemann-Silberstein vector offers many advantages. In particular, it provides a natural bridge between the classical and the quantum description. (author)

  13. Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems

    Science.gov (United States)

    Harada, Hiromitsu; Mouchet, Amaury; Shudo, Akira

    2017-10-01

    The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann surface provides complete information on the topology of complex paths, which allows us to enumerate all the possible candidates contributing to the semiclassical sum formula for tunnelling splittings. This naturally leads to action relations among classically disjoined regions, revealing entirely non-local nature in the quantization condition. The importance of the proper treatment of Stokes phenomena is also discussed in Hamiltonians in the normal form.

  14. Approximate Riemann solver for the two-fluid plasma model

    International Nuclear Information System (INIS)

    Shumlak, U.; Loverich, J.

    2003-01-01

    An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves

  15. Exploration and extension of an improved Riemann track fitting algorithm

    Science.gov (United States)

    Strandlie, A.; Frühwirth, R.

    2017-09-01

    Recently, a new Riemann track fit which operates on translated and scaled measurements has been proposed. This study shows that the new Riemann fit is virtually as precise as popular approaches such as the Kalman filter or an iterative non-linear track fitting procedure, and significantly more precise than other, non-iterative circular track fitting approaches over a large range of measurement uncertainties. The fit is then extended in two directions: first, the measurements are allowed to lie on plane sensors of arbitrary orientation; second, the full error propagation from the measurements to the estimated circle parameters is computed. The covariance matrix of the estimated track parameters can therefore be computed without recourse to asymptotic properties, and is consequently valid for any number of observation. It does, however, assume normally distributed measurement errors. The calculations are validated on a simulated track sample and show excellent agreement with the theoretical expectations.

  16. Pseudo-periodic maps and degeneration of Riemann surfaces

    CERN Document Server

    Matsumoto, Yukio

    2011-01-01

    The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

  17. Towards a theory of chaos explained as travel on Riemann surfaces

    International Nuclear Information System (INIS)

    Calogero, F; Santini, P M; Gomez-Ullate, D; Sommacal, M

    2009-01-01

    We investigate the dynamics defined by a set of three coupled first-order ODEs. It is shown that the system can be reduced to quadratures which can be expressed in terms of elementary functions. Despite the integrable character of the model, the general solution is a multiple-valued function of time (considered as a complex variable), and we investigate the position and nature of its branch points. In the semi-symmetric case (g 1 = g 2 ≠ g 3 ), for rational values of the coupling constants the system is isochronous and explicit formulae for the period of the solutions can be given. For irrational values, the motions are confined but feature aperiodic motion with sensitive dependence on initial conditions. The system shows a rich dynamical behaviour that can be understood in quantitative detail since a global description of the Riemann surface associated with the solutions can be achieved. The details of the description of the Riemann surface are postponed to a forthcoming publication. This toy model is meant to provide a paradigmatic first step towards understanding a certain novel kind of chaotic behaviour

  18. Non-supersymmetric matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces

    International Nuclear Information System (INIS)

    Billo, M.; D'Adda, A.; Provero, P.

    2000-01-01

    We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S N and U(1) N . By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon

  19. Quantum field theory on higher-genus Riemann surfaces, 2

    International Nuclear Information System (INIS)

    Kubo, Reijiro; Ojima, Shuichi.

    1990-08-01

    Quantum field theory for closed bosonic string systems is formulated on arbitrary higher-genus Riemann surfaces in global operator formalism. Canonical commutation relations between bosonic string field X μ and their conjugate momenta P ν are derived in the framework of conventional quantum field theory. Problems arising in quantizing bosonic systems are considered in detail. Applying the method exploited in the preceding paper we calculate Ward-Takahashi identities. (author)

  20. A contribution to the great Riemann solver debate

    Science.gov (United States)

    Quirk, James J.

    1992-01-01

    The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.

  1. Submaximal Riemann-Roch expected curves and symplectic packing.

    Directory of Open Access Journals (Sweden)

    Wioletta Syzdek

    2007-06-01

    Full Text Available We study Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ in the context of the Nagata-Biran conjecture. This conjecture predicts that for sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$. We construct examples verifying to the effect that the assertions of the Nagata-Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $mathbb{P}^1 imes mathbb{P}^1$ and a relatively smallnumber of points. The solutions geometrically correspond to Riemann-Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of mathbb{P}^1 imes mathbb{P}^1. In fact we conjecture that it can be replaced by a lower number and we provide evidence justifying this conjecture.

  2. Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral

    Directory of Open Access Journals (Sweden)

    Weijing Zhao

    2014-01-01

    Full Text Available The derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses 2 derivative values at the endpoints. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated.

  3. Integrable systems twistors, loop groups, and Riemann surfaces

    CERN Document Server

    Hitchin, NJ; Ward, RS

    2013-01-01

    This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu

  4. Riemann-Roch Spaces and Linear Network Codes

    DEFF Research Database (Denmark)

    Hansen, Johan P.

    We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal...... number of points for curves of their respective genera. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang %\\cite{DBLP:journals/tit/KoetterK08} introduced...... in the above metric making them suitable for linear network coding....

  5. Extended KN algebras and extended conformal field theories over higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Ceresole, A.; Huang Chaoshang

    1990-01-01

    A global operator formalism for extended conformal field theories over higher genus Riemann surfaces is introduced and extended KN algebra are obtained by means of the KN bases. The BBSS construction of the spin-3 operator is carried out for Kac-Moody algebra A 2 over a Riemann surface of arbitrary genus. (orig.)

  6. Superconformal structures and holomorphic 1/2-superdifferentials on N=1 super Riemann surfaces

    International Nuclear Information System (INIS)

    Kachkachi, H.; Kachkachi, M.

    1992-07-01

    Using the Super Riemann-Roch theorem we give a local expression for a holomorphic 1/2-superdifferential in a superconformal structure parametrized by special isothermal coordinates on an N=1 Super Riemann Surface (SRS). This construction is done by choosing a suitable origin for these coordinates. The holomorphy of the latter with respect to super Beltrami differentials is proven. (author). 26 refs

  7. Superconformal algebra on meromorphic vector fields with three poles on super-Riemann sphere

    International Nuclear Information System (INIS)

    Wang Shikun; Xu Kaiwen.

    1989-07-01

    Based upon the Riemann-Roch theorem, we construct superconformal algebra of meromorphic vector fields with three poles and the relevant abelian differential of the third kind on super Riemann sphere. The algebra includes two Ramond sectors as subalgebra, and implies a picture of interaction of three superstrings. (author). 14 refs

  8. Two-Loop Scattering Amplitudes from the Riemann Sphere

    CERN Document Server

    Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr

    2016-01-01

    The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.

  9. Zeros da função zeta de Riemann e o teorema dos números primos

    OpenAIRE

    Oliveira, Willian Diego [UNESP

    2013-01-01

    We studied various properties of the Riemann’s zeta function. Three proofs of the Prime Number Theorem were provides. Classical results on zero-free region of the zeta function, as well as their relation to the error term in the Prime Number Theorem, were studied in details Estudamos várias propriedades da função zeta de Riemann. Três provas do Teorema dos Números Primos foram fornecidas. Resultados clássicos sobre regiões livres de zeros da função zeta, bem como sua relação com o termo do...

  10. A Riemann-Hilbert formulation for the finite temperature Hubbard model

    Energy Technology Data Exchange (ETDEWEB)

    Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Cornagliotto, Martina [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mattelliano, Massimo; Tateo, Roberto [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy)

    2015-06-03

    Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

  11. A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

    Science.gov (United States)

    Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

    2014-06-01

    Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

  12. Riemann surfaces and algebraic curves a first course in Hurwitz theory

    CERN Document Server

    Cavalieri, Renzo

    2016-01-01

    Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

  13. Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis.

    Science.gov (United States)

    Lapidus, Michel L

    2015-08-06

    This research expository article not only contains a survey of earlier work but also contains a main new result, which we first describe. Given c≥0, the spectral operator [Formula: see text] can be thought of intuitively as the operator which sends the geometry onto the spectrum of a fractal string of dimension not exceeding c. Rigorously, it turns out to coincide with a suitable quantization of the Riemann zeta function ζ=ζ(s): a=ζ(∂), where ∂=∂(c) is the infinitesimal shift of the real line acting on the weighted Hilbert space [Formula: see text]. In this paper, we establish a new asymmetric criterion for the Riemann hypothesis (RH), expressed in terms of the invertibility of the spectral operator for all values of the dimension parameter [Formula: see text] (i.e. for all c in the left half of the critical interval (0,1)). This corresponds (conditionally) to a mathematical (and perhaps also, physical) 'phase transition' occurring in the midfractal case when [Formula: see text]. Both the universality and the non-universality of ζ=ζ(s) in the right (resp., left) critical strip [Formula: see text] (resp., [Formula: see text]) play a key role in this context. These new results are presented here. We also briefly discuss earlier joint work on the complex dimensions of fractal strings, and we survey earlier related work of the author with Maier and with Herichi, respectively, in which were established symmetric criteria for the RH, expressed, respectively, in terms of a family of natural inverse spectral problems for fractal strings of Minkowski dimension D∈(0,1), with [Formula: see text], and of the quasi-invertibility of the family of spectral operators [Formula: see text] (with [Formula: see text]). © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  14. Contribution of non integer integro-differential operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

    International Nuclear Information System (INIS)

    Le Mehaute, Alain; El Kaabouchi, Abdelaziz; Nivanen, Laurent

    2008-01-01

    Advances in fractional analysis suggest a new way for the physics understanding of Riemann's conjecture. It asserts that, if s is a complex number, the non trivial zeros of zeta function 1/(ζ(s)) =Σ n=1 ∞ (μ(n))/(n s ) in the gap [0, 1], is characterized by s=1/2 (1+2iθ). This conjecture can be understood as a consequence of 1/2-order fractional differential characteristics of automorph dynamics upon opened punctuated torus with an angle at infinity equal to π/4. This physical interpretation suggests new opportunities for revisiting the cryptographic methodologies

  15. Polynomials, Riemann surfaces, and reconstructing missing-energy events

    CERN Document Server

    Gripaios, Ben; Webber, Bryan

    2011-01-01

    We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.

  16. Supersymmetric Dirac particles in Riemann-Cartan space-time

    International Nuclear Information System (INIS)

    Rumpf, H.

    1981-01-01

    A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of h/2π and thus complete the partial results of previous WKB calculations. The author also considers such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass. (Auth.)

  17. A New Riemann Type Hydrodynamical Hierarchy and its Integrability Analysis

    International Nuclear Information System (INIS)

    Golenia, Jolanta Jolanta; Bogolubov, Nikolai N. Jr.; Popowicz, Ziemowit; Pavlov, Maxim V.; Prykarpatsky, Anatoliy K.

    2009-12-01

    Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible co-symplectic structures and Lax type representations for the special cases N = 2, 3 and N = 4 are constructed. (author)

  18. The Picard group of the moduli space of r-Spin Riemann surfaces

    DEFF Research Database (Denmark)

    Randal-Williams, Oscar

    2012-01-01

    An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford...... conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles....

  19. Structural stability of Riemann solutions for strictly hyperbolic systems with three piecewise constant states

    Directory of Open Access Journals (Sweden)

    Xuefeng Wei

    2016-12-01

    Full Text Available This article concerns the wave interaction problem for a strictly hyperbolic system of conservation laws whose Riemann solutions involve delta shock waves. To cover all situations, the global solutions are constructed when the initial data are taken as three piecewise constant states. It is shown that the Riemann solutions are stable with respect to a specific small perturbation of the Riemann initial data. In addition, some interesting nonlinear phenomena are captured during the process of constructing the solutions, such as the generation and decomposition of delta shock waves.

  20. The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime

    International Nuclear Information System (INIS)

    Sierra, Germán

    2014-01-01

    We construct a Hamiltonian H R whose discrete spectrum contains, in a certain limit, the Riemann zeros. H R is derived from the action of a massless Dirac fermion living in a domain of Rindler spacetime, in 1 + 1 dimensions, which has a boundary given by the world line of a uniformly accelerated observer. The action contains a sum of delta function potentials that can be viewed as partially reflecting moving mirrors. An appropriate choice of the accelerations of the mirrors, provide primitive periodic orbits that are associated with the prime numbers p, whose periods, as measured by the observer's clock, are logp. Acting on the chiral components of the fermion χ ∓ , H R becomes the Berry–Keating Hamiltonian ±(x p-hat + p-hat x)/2, where x is identified with the Rindler spatial coordinate and p-hat with the conjugate momentum. The delta function potentials give the matching conditions of the fermion wave functions on both sides of the mirrors. There is also a phase shift e iϑ for the reflection of the fermions at the boundary where the observer sits. The eigenvalue problem is solved by transfer matrix methods in the limit where the reflection amplitudes become infinitesimally small. We find that, for generic values of ϑ, the spectrum is a continuum where the Riemann zeros are missing, as in the adelic Connes model. However, for some values of ϑ, related to the phase of the zeta function, the Riemann zeros appear as discrete eigenvalues that are immersed in the continuum. We generalize this result to the zeros of Dirichlet L-functions, which are associated to primitive characters, that are encoded in the reflection coefficients of the mirrors. Finally, we show that the Hamiltonian associated to the Riemann zeros belongs to class AIII, or chiral GUE, of the Random Matrix Theory. (paper)

  1. Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

    OpenAIRE

    Loveridge, Lee C.

    2004-01-01

    Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

  2. Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Johnny Henderson

    2016-01-01

    Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

  3. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

    National Research Council Canada - National Science Library

    Derbyshire, John

    2003-01-01

    .... Is the hypothesis true or false?Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic defining a precise formula to track and identify the occurrence...

  4. Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition

    Directory of Open Access Journals (Sweden)

    Ge-Feng Yang

    2012-01-01

    differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.

  5. A variational approach to closed bosonic strings on bordered Riemann surfaces

    International Nuclear Information System (INIS)

    Ohrndorf, T.

    1987-01-01

    Polyakov's path integral for bosonic closed strings defined on a bordered Riemann surface is investigated by variational methods. It is demonstrated that boundary variations are generated by the Virasoro operators. The investigation is performed for both, simply connected Riemann surfaces as well as ringlike domains. It is shown that the form of the variational operator is the same on both kinds of surfaces. The Virasoro algebra arises as a consistency condition for the variation. (orig.)

  6. Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

    Directory of Open Access Journals (Sweden)

    Ming Li

    2013-01-01

    Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

  7. Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective

    Science.gov (United States)

    Bernard, Julien

    2018-02-01

    I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.

  8. RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

    International Nuclear Information System (INIS)

    Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

    2010-01-01

    We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

  9. Numerical implication of Riemann problem theory for fluid dynamics

    International Nuclear Information System (INIS)

    Menikoff, R.

    1988-01-01

    The Riemann problem plays an important role in understanding the wave structure of fluid flow. It is also crucial step in some numerical algorithms for accurately and efficiently computing fluid flow; Godunov method, random choice method, and from tracking method. The standard wave structure consists of shock and rarefaction waves. Due to physical effects such as phase transitions, which often are indistinguishable from numerical errors in an equation of state, anomalkous waves may occur, ''rarefaction shocks'', split waves, and composites. The anomalous waves may appear in numerical calculations as waves smeared out by either too much artificial viscosity or insufficient resolution. In addition, the equation of state may lead to instabilities of fluid flow. Since these anomalous effects due to the equation of state occur for the continuum equations, they can be expected to occur for all computational algorithms. The equation of state may be characterized by three dimensionless variables: the adiabatic exponent γ, the Grueneisen coefficient Γ, and the fundamental derivative G. The fluid flow anomalies occur when inequalities relating these variables are violated. 18 refs

  10. Deduction of Einstein equation from homogeneity of Riemann spacetime

    Science.gov (United States)

    Ni, Jun

    2012-03-01

    The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).

  11. Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time

    Science.gov (United States)

    Jumarie, Guy

    2013-04-01

    By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.

  12. On membrane interactions and a three-dimensional analog of Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Kovacs, Stefano [Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); ICTP South American Institute for Fundamental Research, IFT-UNESP,São Paulo, SP 01440-070 (Brazil); Sato, Yuki [National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the Witwartersrand,Wits 2050 (South Africa); Shimada, Hidehiko [Okayama Institute for Quantum Physics,Okayama (Japan)

    2016-02-08

    Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of ℝ{sup 3} connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

  13. On membrane interactions and a three-dimensional analog of Riemann surfaces

    International Nuclear Information System (INIS)

    Kovacs, Stefano; Sato, Yuki; Shimada, Hidehiko

    2016-01-01

    Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of ℝ"3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

  14. The Equation Δ u + ∇φ· ∇u = 8πc(1-heu) on a Riemann Surface

    International Nuclear Information System (INIS)

    Wang Meng

    2009-12-01

    Let M be a compact Riemann surface, h(x) a positive smooth function on M, and φ(x) a smooth function on M which satisfies that ∫ M e φ dV g = 1. In this paper, we consider the functional J(u) = 2 1 ∫ M |∇u| 2 e φ dV g +8πc ∫ M ue φ dV g -8πclog ∫ M he u+φ dV g . We give a sufficient condition under which J achieves its minimum for c ≤ inf xelement ofM Φ(x). (author)

  15. The continuous determination of spacetime geometry by the Riemann curvature tensor

    International Nuclear Information System (INIS)

    Rendall, A.D.

    1988-01-01

    It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)

  16. Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

    Science.gov (United States)

    Chiodaroli, Elisabetta; Kreml, Ondřej

    2018-04-01

    We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.

  17. Modular transformations of conformal blocks in WZW models on Riemann surfaces of higher genus

    International Nuclear Information System (INIS)

    Miao Li; Ming Yu.

    1989-05-01

    We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilson line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g > 0 Riemann surfaces depend only on those for g ≤ 3. (author). 13 refs, 15 figs

  18. A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

    Science.gov (United States)

    Ghil, M.; Balgovind, R.

    1979-01-01

    The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

  19. Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies

    Science.gov (United States)

    Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.

  20. Riemann problems and their application to ultra-relativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Plohr, B.J.; Sharp, D.H.

    1986-07-01

    Heavy ion collisions at sufficiently high energies to form quark-gluon plasma are considered. The phase transformation from a quark-gluon phase to hadrons as the nuclear matter cools is modeled as a hydrodynamical flow. Nonlinear waves are the predominant feature of this type of flow and the Riemann problem of a relativistic gas undergoing a phase transformation is explored as a method to numerically model this phase transition process in nuclear matter. The solution of the Riemann problem is outlined and results of preliminary numerical computations of the flow are presented. 10 refs., 2 figs

  1. Reduction of 4-dim self dual super Yang-Mills onto super Riemann surfaces

    International Nuclear Information System (INIS)

    Mendoza, A.; Restuccia, A.; Martin, I.

    1990-05-01

    Recently self dual super Yang-Mills over a super Riemann surface was obtained as the zero set of a moment map on the space of superconnections to the dual of the super Lie algebra of gauge transformations. We present a new formulation of 4-dim Euclidean self dual super Yang-Mills in terms of constraints on the supercurvature. By dimensional reduction we obtain the same set of superconformal field equations which define self dual connections on a super Riemann surface. (author). 10 refs

  2. Super-quasi-conformal transformation and Schiffer variation on super-Riemann surface

    International Nuclear Information System (INIS)

    Takahasi, Wataru

    1990-01-01

    A set of equations which characterizes the super-Teichmueller deformations is proposed. It is a supersymmetric extension of the Beltrami equation. Relations between the set of equations and the Schiffer variations with the KN bases are discussed. This application of the KN bases shows the powerfulness of the KN theory in the study of super-Riemann surfaces. (author)

  3. The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integrals

    Science.gov (United States)

    Sealey, Vicki; Engelke, Nicole

    2012-01-01

    The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

  4. Riemann type algebraic structures and their differential-algebraic integrability analysis

    Directory of Open Access Journals (Sweden)

    Prykarpatsky A.K.

    2010-06-01

    Full Text Available The differential-algebraic approach to studying the Lax type integrability of generalized Riemann type equations is devised. The differentiations and the associated invariant differential ideals are analyzed in detail. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.

  5. Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model

    International Nuclear Information System (INIS)

    Hao Sanru; Li Wei

    1989-01-01

    This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed

  6. Superconformal algebra and central extension of meromorphic vector fields with multipoles on super-Riemann sphere

    International Nuclear Information System (INIS)

    Wang Shikun; Xu Kaiwen.

    1989-12-01

    The superconformal algebras of meromorphic vector fields with multipoles, the central extension and the relevant abelian differential of the third kind on super Riemann sphere were constructed. The background of our theory is concerned with the interaction of closed superstrings. (author). 9 refs

  7. Seeley-De Witt coefficients in a Riemann-Cartan manifold

    International Nuclear Information System (INIS)

    Cognola, G.; Zerbini, S.; Istituto Nazionale di Fisica Nucleare, Povo

    1988-01-01

    A new derivation of the first two coefficients of the heat kernel expansion for a second-order elliptic differential operator on a Riemann-Cartan manifold with arbitrary torsion is given. The expressions are presented in a very compact and tractable form useful for physical applications. Comparisons with other similar results that appeared in the literature are briefly discussed. (orig.)

  8. Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

    International Nuclear Information System (INIS)

    Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.

    1984-09-01

    The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)

  9. Representation theory of current algebra and conformal field theory on Riemann surfaces

    International Nuclear Information System (INIS)

    Yamada, Yasuhiko

    1989-01-01

    We study conformal field theories with current algebra (WZW-model) on general Riemann surfaces based on the integrable representation theory of current algebra. The space of chiral conformal blocks defined as solutions of current and conformal Ward identities is shown to be finite dimensional and satisfies the factorization properties. (author)

  10. Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

    International Nuclear Information System (INIS)

    Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

    1995-01-01

    The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

  11. Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)

    International Nuclear Information System (INIS)

    Shen Jianmin; Sheng Zhengmao; Wang Zhonghua

    1992-02-01

    We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs

  12. Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere

    International Nuclear Information System (INIS)

    Sabbah, C

    2004-01-01

    It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin

  13. Modification of the Riemann problem and the application for the boundary conditions in computational fluid dynamics

    Directory of Open Access Journals (Sweden)

    Kyncl Martin

    2017-01-01

    Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some

  14. Selberg trace formula for bordered Riemann surfaces: Hyperbolic, elliptic and parabolic conjugacy classes, and determinants of Maass-Laplacians

    International Nuclear Information System (INIS)

    Bolte, J.

    1992-08-01

    The Selberg trace formula for automorphic forms of weight m ε- Z, on bordered Riemann surfaces is developed. The trace formula is formulated for arbitrary Fuchsian groups of the first kind which include hyperbolic, elliptic and parabolic conjugacy classes. In the case of compact bordered Riemann surfaces we can explicitly evaluate determinants of Maass-Laplacians for both Dirichlet and Neumann boundary-conditions, respectively. Some implications for the open bosonic string theory are mentioned. (orig.)

  15. Generalization of the fejer-hadamard type inequalities for p-convex functions via k-fractional integrals

    Directory of Open Access Journals (Sweden)

    Ghulam Farid

    2017-10-01

    Full Text Available The aim of this paper is to obtain some more general fractional integral inequalities of Fejer Hadamard type for p-convex functions via Riemann-Liouville k-fractional integrals. Also in particular fractional inequalities for p-convex functions via Riemann-Liouville fractional integrals have been deduced.

  16. A variational principle giving gravitational 'superpotentials', the affine connection, Riemann tensor, and Einstein field equations

    International Nuclear Information System (INIS)

    Stachel, J.

    1977-01-01

    A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)

  17. An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

    Energy Technology Data Exchange (ETDEWEB)

    Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-03-05

    This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.

  18. Ship-induced solitary Riemann waves of depression in Venice Lagoon

    International Nuclear Information System (INIS)

    Parnell, Kevin E.; Soomere, Tarmo; Zaggia, Luca; Rodin, Artem; Lorenzetti, Giuliano; Rapaglia, John; Scarpa, Gian Marco

    2015-01-01

    We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope

  19. Instanton calculus without equations of motion: semiclassics from monodromies of a Riemann surface

    Science.gov (United States)

    Gulden, Tobias; Janas, Michael; Kamenev, Alex

    2015-02-01

    Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely attainable. A prime example are spin-coherent states which are used e.g. to describe single molecule magnets (SMM). We use this example to develop instanton calculus which does not rely on explicit solutions of the classical equations of motion. Energy conservation restricts the complex phase space to a Riemann surface of complex dimension one, allowing to deform integration paths according to Cauchy’s integral theorem. As a result, the semiclassical actions can be evaluated without knowing actual classical paths. Furthermore we show that in many cases such actions may be solely derived from monodromy properties of the corresponding Riemann surface and residue values at its singular points. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.

  20. Ship-induced solitary Riemann waves of depression in Venice Lagoon

    Energy Technology Data Exchange (ETDEWEB)

    Parnell, Kevin E. [College of Marine and Environmental Sciences and Centre for Tropical Environmental and Sustainability Sciences, James Cook University, Queensland 4811 (Australia); Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Soomere, Tarmo, E-mail: soomere@cs.ioc.ee [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn (Estonia); Zaggia, Luca [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rodin, Artem [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Lorenzetti, Giuliano [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rapaglia, John [Sacred Heart University Department of Biology, 5151 Park Avenue, Fairfield, CT 06825 (United States); Scarpa, Gian Marco [Università Ca' Foscari, Dorsoduro 3246, 30123 Venice (Italy)

    2015-03-06

    We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope.

  1. Flux quantization and quantum mechanics on Riemann surfaces in an external magnetic field

    International Nuclear Information System (INIS)

    Bolte, J.; Steiner, F.

    1990-10-01

    We investigate the possibility to apply an external constant magnetic field to a quantum mechanical system consisting of a particle moving on a compact or non-compact two-dimensional manifold of constant negative Gaussian curvature and of finite volume. For the motion on compact Riemann surfaces we find that a consistent formulation is only possible if the magnetic flux is quantized, as it is proportional to the (integrated) first Chern class of a certain complex line bundle over the manifold. In the case of non-compact surfaces of finite volume we obtain the striking result that the magnetic flux has to vanish identically due to the theorem that any holomorphic line bundle over a non-compact Riemann surface is holomorphically trivial. (orig.)

  2. Integral relations for invariants constructed from three Riemann tensors and their applications in quantum gravity

    International Nuclear Information System (INIS)

    van Nieuwenhuizen, P.; Wu, C.C.

    1977-01-01

    The lowest order quantum corrections to pure gravitation are finite because there exists an integral relation between products of two Riemann tensors (the Gauss--Bonnet theorem). In this article several algebraic and integral relations are determined between products of three Riemann tensors in four- and six-dimensional spacetime. In both cases, one is left with only one invariant when R/sub μ//sub ν/=0, viz., ∫ (-g) 1 / 2 (R/sub b//sub β//sub μ//sub ν/R/sup μ//sup ν//sup rho//sup sigma/R/sub rho//sub sigma/ /sup α//sup β/).It is explicitly shown that this invariant does not vanish, even when R/sub μ//sub ν/=0. Consequently, the two-loop quantum corrections to pure gravitation will only be finite if, due to miraculous cancellation, the coefficient of this invariant vanishes

  3. Multi-loop string amplitudes and Riemann surfaces

    International Nuclear Information System (INIS)

    Taylor, J.G.

    1986-01-01

    The paper was presented at the workshop on 'Supersymmetry and its applications', Cambridge, United Kingdom, 1985. Super-string theory is discussed under the following topic headings: the functional approach to the string amplitude, Rieman surfaces, the determinants Δsub(epsilon)(1) and Δsub(epsilon)(2), Green's functions, total amplitude, and divergence analysis. (U.K.)

  4. Quantum Riemann surfaces. Pt. 1. The unit disc

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, S.; Lesniewski, A. (Harvard Univ., Cambridge, MA (United States))

    1992-05-01

    We construct a non-commutative C{sup *}-algebra C{sub {mu}}(anti U) which is a quantum deformation of the algebra of continuous functions on the closed unit disc anti U.C{sub {mu}}(anti U) is generated by the Toeplitz operators on a suitable Hilbert space of holomorphic functions on U. (orig.).

  5. Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy

    OpenAIRE

    Neagu, Mircea

    2007-01-01

    The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.

  6. Temperature duality on Riemann surface and cosmological solutions for genus g = 1 and 2

    International Nuclear Information System (INIS)

    Yan Jun; Wang Shunjin

    1999-01-01

    A bosonic string model at finite temperature on the gravitation g μν and the dilaton φ background field is examined. Moreover, the duality relation of energy momentum tensor on high genus Riemann surface is derived. At the same time, the temperature duality invariance for the action of string gas matter is proved in 4-D Robertson-Walker metric, the string cosmological solutions and temperature duality of the equations of motion for genus g = 1 and 2 are also investigated

  7. Stability of the isentropic Riemann solutions of the full multidimensional Euler system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Kreml, Ondřej; Vasseur, A.

    2015-01-01

    Roč. 47, č. 3 (2015), s. 2416-2425 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * isentropic solutions * Riemann problem * rarefaction wave Subject RIV: BA - General Mathematics Impact factor: 1.486, year: 2015 http://epubs.siam.org/doi/abs/10.1137/140999827

  8. Codomains for the Cauchy-Riemann and Laplace operators in ℝ2

    Directory of Open Access Journals (Sweden)

    Lloyd Edgar S. Moyo

    2008-01-01

    Full Text Available A codomain for a nonzero constant-coefficient linear partial differential operator P(∂ with fundamental solution E is a space of distributions T for which it is possible to define the convolution E*T and thus solving the equation P(∂S=T. We identify codomains for the Cauchy-Riemann operator in ℝ2 and Laplace operator in ℝ2 . The convolution is understood in the sense of the S′-convolution.

  9. Representation of symmetric metric connection via Riemann-Christoffel curvature tensor

    International Nuclear Information System (INIS)

    Selikhov, A.V.

    1989-01-01

    Bivector σ-bar μ ν ' which is the Jacoby matrix of the transformation to the Riemanian coordinates is considered in the paper. Basing on the dual nature of σ-bar μ ν ' the representation of metric connection (Christoffel symbols) have been obtained at the Riemanian coordinates via Riemann-Christoffel curvature tensor; the covariant conserved four-momentum in the general theory of relativity have been constructed. 11 refs

  10. The mass-damped Riemann problem and the aerodynamic surface force calculation for an accelerating body

    International Nuclear Information System (INIS)

    Tan, Zhiqiang; Wilson, D.; Varghese, P.L.

    1997-01-01

    We consider an extension of the ordinary Riemann problem and present an efficient approximate solution that can be used to improve the calculations of aerodynamic forces on an accelerating body. The method is demonstrated with one-dimensional examples where the Euler equations and the body motion are solved in the non-inertial co-ordinate frame fixed to the accelerating body. 8 refs., 6 figs

  11. A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces

    International Nuclear Information System (INIS)

    Soda, Jiro

    1991-02-01

    We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)

  12. Cálculo de áreas mediante la suma de Riemann con la TI-83

    OpenAIRE

    Lupiáñez, José Luis

    2002-01-01

    En este artículo presentamos una actividad para introducir el cálculo del área que encierra una curva, basada en la Suma de Riemann, y que puede realizarse con la calculadora TI-83. El planteamiento de la actividad permite estudiar varias funciones sin perder tiempo en tediosos cálculos, con idea de observar lo acertado de este método de aproximación.

  13. Vertex operators, non-abelian orbifolds and the Riemann-Hilbert problem

    International Nuclear Information System (INIS)

    Gato, B.; Massachusetts Inst. of Tech., Cambridge

    1990-01-01

    We show how to construct the oscillator part of vertex operators for the bosonic string moving on non-abelian orbifolds, using the conserved charges method. When the three-string vertices are twisted by non-commuting group elements, the construction of the conserved charges becomes the Riemann-Hilbert problem with monodromy matrices given by the twists. This is solvable for any given configuration and any non-abelian orbifold. (orig.)

  14. Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

    Czech Academy of Sciences Publication Activity Database

    Chiodaroli, E.; Kreml, Ondřej

    2018-01-01

    Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/ article /10.1088/1361-6544/aaa10d/meta

  15. Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

    Czech Academy of Sciences Publication Activity Database

    Chiodaroli, E.; Kreml, Ondřej

    2018-01-01

    Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6544/aaa10d/meta

  16. Integrable equations, addition theorems, and the Riemann-Schottky problem

    International Nuclear Information System (INIS)

    Buchstaber, Viktor M; Krichever, I M

    2006-01-01

    The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.

  17. Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The Composite Riemann Problem and its numerical solution

    Science.gov (United States)

    Rosatti, Giorgio; Zugliani, Daniel

    2015-03-01

    In a two-phase free-surface flow, the transition from a mobile-bed condition to a fixed-bed one (and vice versa) occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly. This leads to the possibility of conceiving a new type of Riemann Problem (RP), which we have called Composite Riemann Problem (CRP), where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity. In this paper, we present a strategy for solving a CRP by reducing it to a standard RP of a single, composite system of equations. This can be obtained by combining the two original systems by means of a suitable weighting function, namely the erodibility variable, and the introduction of an appropriate differential equation for this quantity. In this way, the CRP problem can be analyzed theoretically with standard methods, and the features of the solutions can be clearly identified. In particular, a stationary contact wave is able to correctly describe the sharp transition between mobile- and fixed-bed conditions. A finite volume scheme based on the Multiple Averages Generalized Roe approach (Rosatti and Begnudelli (2013) [22]) was used to numerically solve the fixed-mobile CRP. Several test cases demonstrate the effectiveness, exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model.

  18. Multidimensional Riemann problem with self-similar internal structure. Part II - Application to hyperbolic conservation laws on unstructured meshes

    Science.gov (United States)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-04-01

    Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we

  19. Study of the Riemann problem and construction of multidimensional Godunov-type schemes for two-phase flow models

    International Nuclear Information System (INIS)

    Toumi, I.

    1990-04-01

    This thesis is devoted to the study of the Riemann problem and the construction of Godunov type numerical schemes for one or two dimensional two-phase flow models. In the first part, we study the Riemann problem for the well-known Drift-Flux, model which has been widely used for the analysis of thermal hydraulics transients. Then we use this study to construct approximate Riemann solvers and we describe the corresponding Godunov type schemes for simplified equation of state. For computation of complex two-phase flows, a weak formulation of Roe's approximate Riemann solver, which gives a method to construct a Roe-averaged jacobian matrix with a general equation of state, is proposed. For two-dimensional flows, the developed methods are based upon an approximate solver for a two-dimensional Riemann problem, according to Harten-Lax-Van Leer principles. The numerical results for standard test problems show the good behaviour of these numerical schemes for a wide range of flow conditions [fr

  20. Riemann solvers for multi-component gas mixtures with temperature dependent heat capacities

    International Nuclear Information System (INIS)

    Beccantini, A.

    2001-01-01

    This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)

  1. A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

    Science.gov (United States)

    Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun

    2018-03-01

    Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a

  2. Loss of hyperbolicity changes the number of wave groups in Riemann problems

    OpenAIRE

    Vítor Matos; Julio D. Silva; Dan Marchesin

    2016-01-01

    Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve ...

  3. The motion of a classical spinning point particle in a Riemann-Cartan space-time

    International Nuclear Information System (INIS)

    Amorim, R.

    1983-01-01

    A consistent set of equations of motion for classical charged point particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a generalized Lagrangean formalism. The equations avoid the spurius free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are paralell in this theory, where the condition of orthogonality between the spin and the 4-velocity is treated as a non-holonomic one. (Author) [pt

  4. A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

    Science.gov (United States)

    Its, A.; Sukhanov, V.

    2016-05-01

    The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

  5. The transition from regular to irregular motions, explained as travel on Riemann surfaces

    International Nuclear Information System (INIS)

    Calogero, F; Santini, P M; Gomez-Ullate, D; Sommacal, M

    2005-01-01

    We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a three-body problem in the (complex) plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riemann surfaces. The interest of this phenomenology-illustrating the onset in a deterministic context of irregular motions-is underlined by its generality, suggesting its eventual relevance to understand natural phenomena and experimental investigations. Here only some of our main findings are reported, without detailing their proofs: a more complete presentation will be published elsewhere

  6. Arithmetical Fourier and Limit values of elliptic modular functions

    Indian Academy of Sciences (India)

    2

    In order to remove singularities, Riemann used a well-known device of taking the odd part (3.2) or an alternate sum (3.3) to be stated in §3. In §2 of this note we shall reveal that the limit values of elliptic modular functions in Riemann's fragment II evaluated by the differences of polyloga- rithm function l1(x) of order 1 (cf.

  7. Do extended objects move along the geodesics in the Riemann space-time

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

    1981-01-01

    Movement of an extended self-gravitating body in the gravitational field of another distant body is studied in the postnewtonian approximation of arbitrary metrical gravitational theory. Comparison of the mass center acceleration of the extended body with the acceleration of a point body moving in the Riemann space-time, the metrics of which is formally equivalent to the metrics of two moving extended bodies, shows that in any metrical gravitation theory with conservation laws of energy and momentum of the matter and gravitational field taken together, the mass center of the extended body does not, in general case, move along the geodesics of the Riemann space-time. Application of the general formulas obtained to the system Sun-Earth combined with the experimental data of the lunar laser ranging, shows that the Earth in its orbital motion is oscillating with respect to reference geodesics, with the period about one hour and the amplitude not less than 10 -2 cm. This amplitude is of the postnewtonian magnitude and as a consequence, the deviation of the Earth movement from the geodesical movement can be observed in the experiment possessing the postnewtonian accuracy. The difference between the acceleration of the Earth mass center and that of a test body in the postnewtonian approximation is equal to 10 -7 part of the Earth acceleration. The ratio of the passive gravitational mass of the Earth (defined according to Will) and its inert mass differs from 1 by 10 -8 approximately [ru

  8. Riemann Integration

    Indian Academy of Sciences (India)

    and that this should be true, no matter how the in- terval [a, b] is subdivided. ..... Moreover, J: 1 is the unique number with this property. We do not know which ..... as some of our previous demonstrations illustrate, the details of the argument ...

  9. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow; Solveurs de Riemann approches et schemas de decentrement de flux pour les ecoulements diphasiques

    Energy Technology Data Exchange (ETDEWEB)

    Toumi, I.; Kumbaro, A.; Paillere, H

    1999-07-01

    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  10. Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg-de Vries hydrodynamical equations

    Energy Technology Data Exchange (ETDEWEB)

    Prykarpatsky, Anatoliy K [Department of Mining Geodesy, AGH University of Science and Technology, Cracow 30059 (Poland); Artemovych, Orest D [Department of Algebra and Topology, Faculty of Mathematics and Informatics of the Vasyl Stefanyk Pre-Carpathian National University, Ivano-Frankivsk (Ukraine); Popowicz, Ziemowit [Institute of Theoretical Physics, University of Wroclaw (Poland); Pavlov, Maxim V, E-mail: pryk.anat@ua.f, E-mail: artemo@usk.pk.edu.p, E-mail: ziemek@ift.uni.wroc.p, E-mail: M.V.Pavlov@lboro.ac.u [Department of Mathematical Physics, P.N. Lebedev Physical Institute, 53 Leninskij Prospekt, Moscow 119991 (Russian Federation)

    2010-07-23

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.

  11. Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg-de Vries hydrodynamical equations

    International Nuclear Information System (INIS)

    Prykarpatsky, Anatoliy K; Artemovych, Orest D; Popowicz, Ziemowit; Pavlov, Maxim V

    2010-01-01

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.

  12. Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

    OpenAIRE

    Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol

    2013-01-01

    This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.

  13. Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction

    CERN Document Server

    Sauloy, Jacques

    2017-01-01

    Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equat...

  14. A boundary-fitted staggered difference method for incompressible flow using Riemann geometry

    International Nuclear Information System (INIS)

    Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.

    1990-01-01

    A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)

  15. Riemann-Liouville integrals of fractional order and extended KP hierarchy

    International Nuclear Information System (INIS)

    Kamata, Masaru; Nakamula, Atsushi

    2002-01-01

    An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators

  16. Scattering analysis of asymmetric metamaterial resonators by the Riemann-Hilbert approach

    DEFF Research Database (Denmark)

    Kaminski, Piotr Marek; Ziolkowski, Richard W.; Arslanagic, Samel

    2016-01-01

    This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell with an ap......This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell...... with an aperture. Exact analytical solution of the problem is derived; it is based on the n-series approach which is casted into the equivalent Riemann-Hilbert problem. The examined configuration leads to large enhancements of the radiated field and to steerable Huygens-like directivity patterns. Particularly...

  17. Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

    Science.gov (United States)

    Pelinovsky, Dmitry E.; Sulem, Catherine

    A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

  18. Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

    International Nuclear Information System (INIS)

    Li Jiequan; Li Qibing; Xu Kun

    2011-01-01

    The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an

  19. On the fractional calculus of Besicovitch function

    International Nuclear Information System (INIS)

    Liang Yongshun

    2009-01-01

    Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

  20. Implicit approximate Riemann solver for two fluid two phase flow models

    International Nuclear Information System (INIS)

    Raymond, P.; Toumi, I.; Kumbaro, A.

    1993-01-01

    This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by

  1. Formulation of dynamical theory of X-ray diffraction for perfect crystals in the Laue case using the Riemann surface.

    Science.gov (United States)

    Saka, Takashi

    2016-05-01

    The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.

  2. Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem

    CERN Document Server

    Gaydashev, D G

    2006-01-01

    The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...

  3. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow

    International Nuclear Information System (INIS)

    Toumi, I.; Kumbaro, A.; Paillere, H.

    1999-01-01

    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  4. A geometric construction of the Riemann scalar curvature in Regge calculus

    Science.gov (United States)

    McDonald, Jonathan R.; Miller, Warner A.

    2008-10-01

    The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.

  5. 3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity

    International Nuclear Information System (INIS)

    Loubere, Raphael; Maire, Pierre-Henri; Vachal, Pavel

    2013-01-01

    The aim of the present work is the 3D extension of a general formalism to derive a staggered discretization for Lagrangian hydrodynamics on unstructured grids. The classical compatible discretization is used; namely, momentum equation is discretized using the fundamental concept of subcell forces. Specific internal energy equation is obtained using total energy conservation. The subcell force is derived by invoking the Galilean invariance and thermodynamic consistency. A general form of the subcell force is provided so that a cell entropy inequality is satisfied. The subcell force consists of a classical pressure term plus a tensorial viscous contribution proportional to the difference between the node velocity and the cell-centered velocity. This cell-centered velocity is an extra degree of freedom solved with a cell-centered approximate Riemann solver. The second law of thermodynamics is satisfied by construction of the local positive definite subcell tensor involved in the viscous term. A particular expression of this tensor is proposed. A more accurate extension of this discretization both in time and space is also provided using a piecewise linear reconstruction of the velocity field and a predictor-corrector time discretization. Numerical tests are presented in order to assess the efficiency of this approach in 3D. Sanity checks show that the 3D extension of the 2D approach reproduces 1D and 2D results. Finally, 3D problems such as Sedov, Noh, and Saltzman are simulated. (authors)

  6. A geometric construction of the Riemann scalar curvature in Regge calculus

    International Nuclear Information System (INIS)

    McDonald, Jonathan R; Miller, Warner A

    2008-01-01

    The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas

  7. On the properties of torsions in Riemann-Cartan space-times

    International Nuclear Information System (INIS)

    Baker, W.M.; Atkins, W.K.; Davis, W.R.

    1978-01-01

    This paper is the first paper in a series of three papers dealing with the physical properties of torsions in Riemann-Cartan space-times (U 4 ). Paper one deals with the particular types of torsion that can be associated with the U 4 reinterpretation of a special class of null electromagnetic solutions of the standard form of Einstein's equations. In particular, for plane null electromagnetic solutions, three types of torsion solutions are associated with this type of reinterpretation. Two of these solutions, the trivector and semi-symmetric torsions, although rather special, serve as examples of what could be done to find the associated torsions in terms of simple requirements on identities in U 4 . The third class is obtained by relating the contorsion to the Lanczos ''spin'' tensor. Paper two, dealing with gravitational radiation, provides the proper background relating to the physical significance of the Lanczos tensor. This series of papers is primarily concerned with the question of the possible physical role of all types of torsion, compatible with an extension or an U 4 reinterpretation of Einstein's theory, consistent with the broadest possible interpretation of the present form of the Einstein-Cartan-Sciama-Kibble theory. However, in paper three some consideration will be given on theories with simpler metrical generalizations of U 4 and the related types of torsion. We emphasize that the content of paper one and two should be viewed mainly as special formal results that introduce the more general considerations of paper three

  8. Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

    Energy Technology Data Exchange (ETDEWEB)

    Duca, Vittorio Del [Institute for Theoretical Physics, ETH Zürich,Hönggerberg, 8093 Zürich (Switzerland); Druc, Stefan; Drummond, James [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Duhr, Claude [Theoretical Physics Department, CERN,Route de Meyrin, CH-1211 Geneva 23 (Switzerland); Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Dulat, Falko [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Marzucca, Robin [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Papathanasiou, Georgios [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Verbeek, Bram [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium)

    2016-08-25

    We show that scattering amplitudes in planar N=4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L+4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

  9. AdS5 solutions from M5-branes on Riemann surface and D6-branes sources

    Energy Technology Data Exchange (ETDEWEB)

    Bah, Ibrahima [Department of Physics and Astronomy, University of Southern California,Los Angeles, CA 90089 (United States); Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France)

    2015-09-24

    We describe the gravity duals of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a punctured Riemann surface. The internal geometry, normal to the AdS{sub 5} factor, generically preserves two U(1)s, with generators (J{sup +},J{sup −}), that are fibered over the Riemann surface. The metric is governed by a single potential that satisfies a version of the Monge-Ampère equation. The spectrum of N=1 punctures is given by the set of supersymmetric sources of the potential that are localized on the Riemann surface and lead to regular metrics near a puncture. We use this system to study a class of punctures where the geometry near the sources corresponds to M-theory description of D6-branes. These carry a natural (p,q) label associated to the circle dual to the killing vector pJ{sup +}+qJ{sup −} which shrinks near the source. In the generic case the world volume of the D6-branes is AdS{sub 5}×S{sup 2} and they locally preserve N=2 supersymmetry. When p=−q, the shrinking circle is dual to a flavor U(1). The metric in this case is non-degenerate only when there are co-dimension one sources obtained by smearing M5-branes that wrap the AdS{sub 5} factor and the circle dual the superconformal R-symmetry. The D6-branes are extended along the AdS{sub 5} and on cups that end on the co-dimension one branes. In the special case when the shrinking circle is dual to the R-symmetry, the D6-branes are extended along the AdS{sub 5} and wrap an auxiliary Riemann surface with an arbitrary genus. When the Riemann surface is compact with constant curvature, the system is governed by a Monge-Ampère equation.

  10. Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

    International Nuclear Information System (INIS)

    Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

    2007-01-01

    We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

  11. Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions

    International Nuclear Information System (INIS)

    Rudaz, S.

    1990-01-01

    Asymptotic series for the Hurwitz zeta function, its derivative, and related functions (including the Riemann zeta function of odd integer argument) are derived as an illustration of a simple, direct method of broad applicability, inspired by the calculus of finite differences

  12. Algebraic functions

    CERN Document Server

    Bliss, Gilbert Ames

    1933-01-01

    This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t

  13. Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics

    International Nuclear Information System (INIS)

    Kraczek, B.; Miller, S.T.; Haber, R.B.; Johnson, D.D.

    2010-01-01

    We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numerical stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1dxtime and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals in

  14. Riemann solvers for multi-component gas mixtures with temperature dependent heat capacities; Solveurs de riemann pour des melanges de gaz parfaits avec capacites calorifiques dependant de la temperature

    Energy Technology Data Exchange (ETDEWEB)

    Beccantini, A

    2001-07-01

    This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)

  15. Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I

    International Nuclear Information System (INIS)

    McLaughlin, K. T.-R.; Vartanian, A. H.; Zhou, X.

    2008-01-01

    Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert problems on R, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method

  16. On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability

    Directory of Open Access Journals (Sweden)

    Jolanta Golenia

    2010-01-01

    Full Text Available Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N=3 are constructed.

  17. Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

    Science.gov (United States)

    Bui-Thanh, T.; Girolami, M.

    2014-11-01

    We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint

  18. (Anti-) selfdual Riemann curvature tensor in four spacelike compactified dimensions, O5 isometry group and chiral fermion zero modes

    International Nuclear Information System (INIS)

    Minkowski, P.

    1986-01-01

    The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form Rsup(+-)sub(μνsigmatau)=(1/2a 2 )(gsub(μsigma)gsub(νtau) - gsub(μtau)gsub(νsigma)+-√g epsilonsub(μνsigmatau)). The metric with euclidean signature (++++) describes a sphere S 4 with radius a, i.e. admits the isometry group O5. For selfdual (antiselfdual) curvature tensor the contorsion tensor is given by the antiselfdual (selfdual) instanton configuration with respect to the spin gauge group SU2sub(R) (SU2sub(L)). The selfdual (antiselfdual) Riemann tensor admits two covariantly constant right-handed (left-handed) spin 1/2 fermion zero modes, one J=1/2 and one J=3/2 right-handed (left-handed) multiplet corresponding to L=1, transforming as a pseudoreal representation of O4 (SU2sub(R(L))). The hermitean Dirac equation retains only the two constant chiral modes. (orig.)

  19. A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces

    CERN Document Server

    Pioline, Boris

    2016-01-01

    The Kawazumi-Zhang invariant $\\varphi$ for compact genus-two Riemann surfaces was recently shown to be a eigenmode of the Laplacian on the Siegel upper half-plane, away from the separating degeneration divisor. Using this fact and the known behavior of $\\varphi$ in the non-separating degeneration limit, it is shown that $\\varphi$ is equal to the Theta lift of the unique (up to normalization) weak Jacobi form of weight $-2$. This identification provides the complete Fourier-Jacobi expansion of $\\varphi$ near the non-separating node, gives full control on the asymptotics of $\\varphi$ in the various degeneration limits, and provides a efficient numerical procedure to evaluate $\\varphi$ to arbitrary accuracy. It also reveals a mock-type holomorphic Siegel modular form of weight $-2$ underlying $\\varphi$. From the general relation between the Faltings invariant, the Kawazumi-Zhang invariant and the discriminant for hyperelliptic Riemann surfaces, a Theta lift representation for the Faltings invariant in genus two ...

  20. La notion husserlienne de multiplicité : au-delà de Cantor et Riemann

    Directory of Open Access Journals (Sweden)

    Carlo Ierna

    2012-04-01

    Full Text Available En raison du rôle changeant qu’il joue dans les différents ouvrages de Husserl, le concept de Mannigfaltigkeit afait l’objet de nombreuses interprétations. La présence de ce terme a notamment induit en erreur plusieurs commentateurs, qui ont cru en déterminer l’origine dans les années de Halle, à l’époque où Husserl, ami et collègue de Cantor, rédigeait la Philosophie de l’arithmétique. Mais force est de constater qu’à cette époque Husserl s’était déjà ouvertement éloigné de la définition cantorienne de Mannigfaltigkeit en s’approchant plutôt de Riemann, comme le montrent les nombreuses études et leçons qui lui sont consacrées. La Mannigfaltigkeitslehre de Husserl semble donc plus proche de la topologie que de la théorie des ensembles de Cantor. Ainsi, dans les Prolégomènes, Husserl introduit l’idée d’une Mannigfaltigkeitslehre pure en tant qu’entreprise méta-théorique dont le but est d’étudier les relations entre théories, à savoir la manière par laquelle une théorie est dérivée ou fondée à partir d’une autre. Dès lors, lorsque Husserl affirme que le meilleur exemple d’une telle théorie pure des multiplicités se trouve dans les mathématiques, cela risque donc de prêter à confusion. En effet, la théorie pure des théories ne saurait être simplement identifiée aux mathématiques qui relèvent de la topologie, mais considérée en tant que mathesis universalis. Bien qu’une telle position ne fût sans doute pas entièrement claire en 1900-01, Husserl ne tardera pas à relier explicitement théorie des multiplicités et mathesis universalis.En ce sens, la mathesis universalis, théorie des théories en général, est une discipline formelle, apriori et analytique qui a pour but l’analyse des catégories sémantiques suprêmes et des catégories d’objets qui leur sont corrélées. Dans cet article j’essayerai de comprendre le développement de la notion de

  1. Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

    Science.gov (United States)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-10-01

    Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on

  2. On calculation of zeta function of integral matrix

    Czech Academy of Sciences Publication Activity Database

    Janáček, Jiří

    2009-01-01

    Roč. 134, č. 1 (2009), s. 49-58 ISSN 0862-7959 R&D Projects: GA AV ČR(CZ) IAA100110502 Institutional research plan: CEZ:AV0Z50110509 Keywords : Epstein zeta function * integral lattice * Riemann theta function Subject RIV: BA - General Mathematics

  3. Effective action and β-functions for the heterotic string

    International Nuclear Information System (INIS)

    Foakes, A.P.; Mohammedi, N.; Ross, D.A.

    1988-01-01

    The results of the calculation of the metric β-function for the heterotic string sigma model up to three loops are presented and it is shown that although this β-function is non vanishing it is compatible with an O((α') 2 ) effective action in which there are no terms cubic in the Riemann tensor or gauge field strength. (orig.)

  4. Extension problem for generalized multi-monogenic functions in Clifford analysis

    International Nuclear Information System (INIS)

    Tran Quyet Thang.

    1992-10-01

    The main purpose of this paper is to extend some properties of multi-monogenic functions, which is a generalization of monogenic functions in higher dimensions, for a class of functions satisfying Vekua-type generalized Cauchy-Riemann equations in Clifford Analysis. It is proved that the Hartogs theorem is valid for these functions. (author). 7 refs

  5. Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

    Science.gov (United States)

    Carraro, F.; Valiani, A.; Caleffi, V.

    2018-03-01

    Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

  6. Fractional derivative of the Hurwitz ζ-function and chaotic decay to zero

    Directory of Open Access Journals (Sweden)

    C. Cattani

    2016-01-01

    Full Text Available In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivative. Some interesting properties of the fractional derivative of the Riemann zeta function are also investigated to show that there is a chaotic decay to zero (in the Gaussian plane and a promising expression as a complex power series.

  7. On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

    International Nuclear Information System (INIS)

    Manakov, S V; Santini, P M

    2008-01-01

    We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking

  8. On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

    Energy Technology Data Exchange (ETDEWEB)

    Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)

    2008-02-08

    We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.

  9. Extending the Riemann-Solver-Free High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme (DG-CVS) to Solve Compressible Magnetohydrodynamics Equations

    Science.gov (United States)

    2016-06-08

    Ideal Magnetohydrodynamics,” J. Com- put. Phys., Vol. 153, No. 2, 1999, pp. 334–352. [14] Tang, H.-Z. and Xu, K., “A high-order gas -kinetic method for...notwithstanding any other provision of law , no person shall be subject to any penalty for failing to comply with a collection of information if it does...Riemann-solver-free spacetime discontinuous Galerkin method for general conservation laws to solve compressible magnetohydrodynamics (MHD) equations. The

  10. Functional geometric method for solving free boundary problems for harmonic functions

    Energy Technology Data Exchange (ETDEWEB)

    Demidov, Aleksander S [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

    2010-01-01

    A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann-Hilbert problems. An extensive list of open questions is presented. Bibliography: 124 titles.

  11. Complex function theory

    CERN Document Server

    Sarason, Donald

    2007-01-01

    Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Co

  12. Changing gauge of second type for the election of Landau and tangential Cauchy-Riemann equations

    International Nuclear Information System (INIS)

    Laville, Guy

    1980-01-01

    For any type choice of gauge it is possible to get an equality between the Hamiltonian of a charge particle and an operator of second order which is associated with the boundary values of holomorphic functions of two complex variables [fr

  13. 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.

  14. The Riemann Surface of Static Limit Dispersion Relation and Projective Spaces

    CERN Document Server

    Majewski, M; Meshcheryakov, D V; Tran Quang Tuyet

    2004-01-01

    The rigorous Bogoliubov's prove of the dispersion relations (DR) for pion-nucleon scattering is a good foundation for the static models. DR contain the small parameter (ratio of the pion-nucleon masses). The static models arise when this parameter goes to zero. The S-matrix in the static models has a block structure. Each block of the S-matrix has a finite order N\\times N and is a matrix of meromorphic functions of the light particle energy \\omega in the complex plane with cuts (-\\inf,-1], [+1, +\\inf). In the elastic case, it reduces to N functions S_{i}(\\omega) connected by N\\times N the crossing-symmetry matrix A. The unitarity and the crossing symmetry are the base for the system of nonlinear boundary value problems. It defines the analytical continuation of S_{i}(\\omega) from the physical sheet to the unphysical ones and can be treated as a system of nonlinear difference equations. The problem is solvable for any 2\\times 2 crossing-symmetry matrix A that permits one to calculate the Regge trajectories for...

  15. The Riemann surface of static limit dispersion relation and projective spaces

    International Nuclear Information System (INIS)

    Majewski, M.; Meshcheryakov, V.A.; Meshcheryakov, D.V.; Tran Quang Tuyet

    2004-01-01

    The rigorous Bogolyubov's proof of the dispersion relations (DR) for pion-nucleon scattering is a good foundation for the static models. DR contain a small parameter (ratio of the pion-nucleon masses). The static models arise when this parameter goes to zero. The S-matrix in the static models has a block structure. Each block of the S-matrix has a finite order NxN and is a matrix of meromorphic functions of the light particle energy ω in the complex plane with cuts (-∞, -1], [+1,+∞). In the elastic case, it reduces to N functions S i (ω) connected by the NxN crossing-symmetry matrix A. The unitarity and the crossing symmetry are the base for the system of nonlinear boundary value problems. It defines the analytical continuation of S i (ω) from the physical sheet to the unphysical ones and can be treated as a system of nonlinear difference equations. The problem is solvable for any 2x2 crossing-symmetry matrix A that permits one to calculate the Regge trajectories for the SU(2) static model. It is shown that global analyses of this system can be carried out effectively in projective spaces P N-1 and P N . The connection between the spaces P N-1 and P N is discussed. Some particular solutions of the system are found

  16. Controlling lightwave in Riemann space by merging geometrical optics with transformation optics.

    Science.gov (United States)

    Liu, Yichao; Sun, Fei; He, Sailing

    2018-01-11

    In geometrical optical design, we only need to choose a suitable combination of lenses, prims, and mirrors to design an optical path. It is a simple and classic method for engineers. However, people cannot design fantastical optical devices such as invisibility cloaks, optical wormholes, etc. by geometrical optics. Transformation optics has paved the way for these complicated designs. However, controlling the propagation of light by transformation optics is not a direct design process like geometrical optics. In this study, a novel mixed method for optical design is proposed which has both the simplicity of classic geometrical optics and the flexibility of transformation optics. This mixed method overcomes the limitations of classic optical design; at the same time, it gives intuitive guidance for optical design by transformation optics. Three novel optical devices with fantastic functions have been designed using this mixed method, including asymmetrical transmissions, bidirectional focusing, and bidirectional cloaking. These optical devices cannot be implemented by classic optics alone and are also too complicated to be designed by pure transformation optics. Numerical simulations based on both the ray tracing method and full-wave simulation method are carried out to verify the performance of these three optical devices.

  17. Two-loop superstring partition function

    International Nuclear Information System (INIS)

    Morozov, A.Y.

    1988-01-01

    Is it possible to choose the odd moduli on super-Riemann surfaces of genus p≥2 in such a way that the corresponding contributions to the superstring partition function vanish before the integration over the space of the moduli? It is shown that, at least for p = 2, the answer to this question is affirmative, and in this case the odd moduli should be localized at branch points

  18. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

    Science.gov (United States)

    Owolabi, Kolade M.

    2018-03-01

    In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

  19. Isomonodromic tau-functions from Liouville conformal blocks

    International Nuclear Information System (INIS)

    Iorgov, N.; Lisovyy, O.

    2014-01-01

    The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c=1. This implies a similar representation for the isomonodromic tau-function. In the case n=4 we thereby get a proof of the relation between tau-functions and conformal blocks discovered in O. Gamayun, N. Iorgov, and O. Lisovyy (2012). We briefly discuss a possible application of our results to the study of relations between certain N=2 supersymmetric gauge theories and conformal field theory.

  20. Bernoulli numbers and zeta functions

    CERN Document Server

    Arakawa, Tsuneo; Kaneko, Masanobu

    2014-01-01

    Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...

  1. Riemann-Hypothesis Millennium-Problem(MP) Physics Proof via CATEGORY-SEMANTICS(C-S)/F =C Aristotle SQUARE-of-OPPOSITION(SoO) DEduction-LOGIC DichotomY

    Science.gov (United States)

    Baez, Joao-Joan; Lapidaryus, Michelle; Siegel, Edward Carl-Ludwig

    2013-03-01

    Riemann-hypothesis physics-proof combines: Siegel-Antono®-Smith[AMS Joint Mtg.(2002)- Abs.973-03-126] digits on-average statistics HIll[Am. J. Math 123, 3, 887(1996)] logarithm-function's (1,0)- xed-point base =units =scale-invariance proven Newcomb [Am. J. Math. 4, 39(1881)]-Weyl[Goett. Nachr.(1914); Math. Ann.7, 313(1916)]-Benford[Proc. Am. Phil. Soc. 78, 4, 51(1938)]-law [Kac,Math. of Stat.-Reasoning(1955); Raimi, Sci. Am. 221, 109(1969)] algebraic-inversion to ONLY Bose-Einstein quantum-statistics(BEQS) with digit d = 0 gapFUL Bose-Einstein Condensation(BEC) insight that digits are quanta are bosons because bosons are and always were quanta are and always were digits, via Siegel-Baez category-semantics tabular list-format matrix truth-table analytics in Plato-Aristotle classic ''square-of-opposition'' : FUZZYICS =CATEGORYICS/Category-Semantics, with Goodkind Bose-Einstein Condensation (BEC) ABOVE ground-state with/and Rayleigh(cut-limit of ''short-cut method''1870)-Polya(1922)-''Anderson''(1958) localization [Doyle and Snell,Random-Walks and Electrical-Networks, MAA(1981)-p.99-100!!!] in Brillouin[Wave-Propagation in Periodic-Structures(1946) Dover(1922)]-Hubbard-Beeby[J.Phys.C(1967)] Siegel[J.Nonxline-Sol.40,453(1980)] generalized-disorder collective-boson negative-dispersion mode-softening universality-principle(G...P) first use of the ``square-of-opposition'' in physics since Plato and Aristote!!!

  2. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    Liu, Dayan; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

  3. Integral approximants for functions of higher monodromic dimension

    Energy Technology Data Exchange (ETDEWEB)

    Baker, G.A. Jr.

    1987-01-01

    In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.

  4. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    Liu, Dayan

    2015-02-01

    This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

  5. On Montgomery's pair correlation conjecture to the zeros of Riedmann zeta function

    OpenAIRE

    Li, Pei

    2005-01-01

    In this thesis, we are interested in Montgomery's pair correlation conjecture which is about the distribution of.the spacings between consecutive zeros of the Riemann Zeta function. Our goal is to explain and study Montgomery's pair correlation conjecture and discuss its connection with the random matrix theory. In Chapter One, we will explain how to define the Ftiemann Zeta function by using the analytic continuation. After this, several classical properties of the Ftiemann Zeta function wil...

  6. Conformal scalar field on the hyperelliptic curve and critical Ashkin-Teller multipoint correlation functions

    International Nuclear Information System (INIS)

    Zamolodchikov, A.B.

    1987-01-01

    A multipoint conformal block of Ramond states of the two-dimensional free scalar field is calculated. This function is related to the free energy of the scalar field on the hyperelliptic Riemann surface under a particular choice of boundary conditions. Being compactified on the circle this field leads to the crossing symmetric correlation functions with a discrete spectrum of scale dimensions. These functions are supposed to describe multipoint spin correlations of the critical Ashkin-Teller model. (orig.)

  7. Exp-function method for solving fractional partial differential equations.

    Science.gov (United States)

    Zheng, Bin

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

  8. 1-loop partition function in AdS{sub 3}/CFT{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Wu, Jie-qiang [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China)

    2015-12-16

    The 1-loop partition function of the handlebody solutions in the AdS{sub 3} gravity have been derived some years ago using the heat kernel techniques and the method of images. In the semiclassical limit, such partition function should correspond to the order O(c{sup 0}) part in the partition function of dual conformal field theory(CFT) on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, the CFT is effectively free in the sense that to the leading order of c the multi-point function is further simplified to be a summation over the products of two-point functions of single-particle states. Correspondingly in the bulk, the graviton is freely propagating without interaction. Furthermore the product of the two-point functions may define the links, each of which is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the multiplier of the element in the conjugacy class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity and its dual CFT.

  9. Mayer Transfer Operator Approach to Selberg Zeta Function

    DEFF Research Database (Denmark)

    Momeni, Arash; Venkov, Alexei

    . In a special situation the dynamical zeta function is defined for a geodesic flow on a hyperbolic plane quotient by an arithmetic cofinite discrete group. More precisely, the flow is defined for the corresponding unit tangent bundle. It turns out that the Selberg zeta function for this group can be expressed...... in terms of a Fredholm determinant of a classical transfer operator of the flow. The transfer operator is defined in a certain space of holomorphic functions and its matrix representation in a natural basis is given in terms of the Riemann zeta function and the Euler gamma function....

  10. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2013-01-01

    Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

  11. Scalar field Green functions on causal sets

    International Nuclear Information System (INIS)

    Nomaan Ahmed, S; Surya, Sumati; Dowker, Fay

    2017-01-01

    We examine the validity and scope of Johnston’s models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2-dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker’s continuum Green function. We find that the same prescription can also be used for de Sitter spacetime and the conformally flat patch of anti-de Sitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston’s model for the Green function for a causal set approximated by 3-dimensional flat spacetime. (paper)

  12. 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.

  13. 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)

  14. Renormalization in quantum field theory and the Riemann-Hilbert problem. I. Hopf algebra structure of graphs and the main theorem

    International Nuclear Information System (INIS)

    Connes, A.; Kreimer, D.

    2000-01-01

    This paper gives a complete selfcontained proof of our result (1999) showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra H which is commutative asan algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra G whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of H. We show then that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop γ(z) element of G, z element of C, where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ + of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. (orig.)

  15. Integration a functional approach

    CERN Document Server

    Bichteler, Klaus

    1998-01-01

    This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might...

  16. Orthogonal Polynomials and Special Functions

    CERN Document Server

    Assche, Walter

    2003-01-01

    The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.

  17. The method of images and Green's function for spherical domains

    International Nuclear Information System (INIS)

    Gutkin, Eugene; Newton, Paul K

    2004-01-01

    Motivated by problems in electrostatics and vortex dynamics, we develop two general methods for constructing Green's function for simply connected domains on the surface of the unit sphere. We prove a Riemann mapping theorem showing that such domains can be conformally mapped to the upper hemisphere. We then categorize all domains on the sphere for which Green's function can be constructed by an extension of the classical method of images. We illustrate our methods by several examples, such as the upper hemisphere, geodesic triangles, and latitudinal rectangles. We describe the point vortex motion in these domains, which is governed by a Hamiltonian determined by the Dirichlet Green's function

  18. A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

    International Nuclear Information System (INIS)

    Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho

    2016-01-01

    In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is

  19. A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

    Energy Technology Data Exchange (ETDEWEB)

    Balsara, Dinshaw S., E-mail: dbalsara@nd.edu [Physics Department, University of Notre Dame (United States); Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, Tokyo 113-0033 (Japan); Garain, Sudip, E-mail: sgarain@nd.edu [Physics Department, University of Notre Dame (United States); Kim, Jinho, E-mail: jkim46@nd.edu [Physics Department, University of Notre Dame (United States)

    2016-08-01

    In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is

  20. A Walsh Function Module Users' Manual

    Science.gov (United States)

    Gnoffo, Peter A.

    2014-01-01

    The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

  1. Particle in the magnetic field: 2D Riemann spherical space and complex analogue of the Poincare half-plane

    International Nuclear Information System (INIS)

    Red'kov, V.M.; Ovsiyuk, E.M.; Ishkhanyan, A.M.

    2013-01-01

    The Schrodinger particle on the background of the 2D space of the constant positive curvature S 2 , a sphere in the 3D Euclidean space, is considered in the external magnetic field. By analogy with the case of the hyperbolic Lobachevsky plane H 2 , where quasi-Cartesian coordinates exist with the realization of H 2 as the Poincare half-plane, a specific system of quasi-Cartesian coordinates (x, y) in S 2 is introduced. It turns out that it is possible only if the two coordinates are complex and obey an additional restriction in order to present a real 2D space. The Schrodinger equation is solved using the method of separation of the variables in the both coordinate systems, cylindrical and quasi-Cartesian, the energy spectrum is the same. For parametrization of the space S 2 , one can use the coordinates (x, x*) or (y, y*), however, in this case the separability of the variables in the wave functions is lost. Constructed solutions may be of interest for describing charged particles in magnetic fields in the context of cosmological models, and for simulating the behavior of the particles in a specific field-configuration in the nano-physics. (authors)

  2. String operator formalism and functional intergal in the holomorphic representation

    International Nuclear Information System (INIS)

    Losev, A.S.; Morozov, A.Yu.; Rislyj, A.A.; Shatashvili, S.L.

    1989-01-01

    Connection between the continual integral over open Riemann surfaces and the operator formalism on closed Riemann surfaces is discussed. States of the operator formalism are the holomorphic representation of the continual integral

  3. Geometric function theory: a modern view of a classical subject

    International Nuclear Information System (INIS)

    Crowdy, Darren

    2008-01-01

    Geometric function theory is a classical subject. Yet it continues to find new applications in an ever-growing variety of areas such as modern mathematical physics, more traditional fields of physics such as fluid dynamics, nonlinear integrable systems theory and the theory of partial differential equations. This paper surveys, with a view to modern applications, open problems and challenges in this subject. Here we advocate an approach based on the use of the Schottky–Klein prime function within a Schottky model of compact Riemann surfaces. (open problem)

  4. Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

    Directory of Open Access Journals (Sweden)

    Rahmatullah

    2018-03-01

    Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

  5. Conditions for bound states in a periodic linear chain, and the spectra of a class of Toeplitz operators in terms of polylogarithm functions

    International Nuclear Information System (INIS)

    Prunele, E de

    2003-01-01

    Conditions for bound states for a periodic linear chain are given within the framework of an exactly solvable non-relativistic quantum-mechanical model in three-dimensional space. These conditions express the strength parameter in terms of the distance between two consecutive centres of the chain, and of the range interaction parameter. This expression can be formulated in terms of polylogarithm functions, and, in some particular cases, in terms of the Riemann zeta function. An interesting mathematical result is that these expressions also correspond to the spectra of Toeplitz complex symmetric operators. The non-trivial zeros of the Riemann zeta function are interpreted as multiple points, at the origin, of the spectra of these Toeplitz operators

  6. Certain fractional integral formulas involving the product of generalized Bessel functions.

    Science.gov (United States)

    Baleanu, D; Agarwal, P; Purohit, S D

    2013-01-01

    We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

  7. Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

    Science.gov (United States)

    Baleanu, D.; Agarwal, P.; Purohit, S. D.

    2013-01-01

    We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions. PMID:24379745

  8. Dynamics on the Riemann Sphere

    DEFF Research Database (Denmark)

    Petersen, Carsten Lunde

    Collection of research papers on holomorphic dynamical systems with an introduction to Bodil Branners works on the field. Contributions: John Milnor: On Lattès Maps. Carsten Lunde Petersen and Tan Lei: Branner-Hubbard motions and attracting dynamics. Artur Avila and Mikhail Lyubich: Examples...

  9. Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution - Part II, higher order FVTD schemes

    Science.gov (United States)

    Balsara, Dinshaw S.; Garain, Sudip; Taflove, Allen; Montecinos, Gino

    2018-02-01

    The Finite Difference Time Domain (FDTD) scheme has served the computational electrodynamics community very well and part of its success stems from its ability to satisfy the constraints in Maxwell's equations. Even so, in the previous paper of this series we were able to present a second order accurate Godunov scheme for computational electrodynamics (CED) which satisfied all the same constraints and simultaneously retained all the traditional advantages of Godunov schemes. In this paper we extend the Finite Volume Time Domain (FVTD) schemes for CED in material media to better than second order of accuracy. From the FDTD method, we retain a somewhat modified staggering strategy of primal variables which enables a very beneficial constraint-preservation for the electric displacement and magnetic induction vector fields. This is accomplished with constraint-preserving reconstruction methods which are extended in this paper to third and fourth orders of accuracy. The idea of one-dimensional upwinding from Godunov schemes has to be significantly modified to use the multidimensionally upwinded Riemann solvers developed by the first author. In this paper, we show how they can be used within the context of a higher order scheme for CED. We also report on advances in timestepping. We show how Runge-Kutta IMEX schemes can be adapted to CED even in the presence of stiff source terms brought on by large conductivities as well as strong spatial variations in permittivity and permeability. We also formulate very efficient ADER timestepping strategies to endow our method with sub-cell resolving capabilities. As a result, our method can be stiffly-stable and resolve significant sub-cell variation in the material properties within a zone. Moreover, we present ADER schemes that are applicable to all hyperbolic PDEs with stiff source terms and at all orders of accuracy. Our new ADER formulation offers a treatment of stiff source terms that is much more efficient than previous ADER

  10. Hexagonalization of correlation functions

    Energy Technology Data Exchange (ETDEWEB)

    Fleury, Thiago [Instituto de Física Teórica, UNESP - University Estadual Paulista,ICTP South American Institute for Fundamental Research,Rua Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP (Brazil); Komatsu, Shota [Perimeter Institute for Theoretical Physics,31 Caroline St N Waterloo, Ontario N2L 2Y5 (Canada)

    2017-01-30

    We propose a nonperturbative framework to study general correlation functions of single-trace operators in N=4 supersymmetric Yang-Mills theory at large N. The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases, the results are in perfect agreement with the perturbative data. We also suggest that our method can be a useful tool to study conformal integrals, and show it explicitly for the case of ladder integrals.

  11. A pedagogical introduction to theta functions

    International Nuclear Information System (INIS)

    Koh, I.G.; Shin, H.J.

    1988-01-01

    This paper reports on revolutions in physics that have been frequently accompanied by new developments in mathematics. In seventeenth century, Newton has initiated a program of describing celestial motion by classical mechanics. Integral and differential calculus was essential tool. Orbits of the moon and the earth are given by solving the differential equation of Newton's equation. Imagine a situation where one tries to solve such orbits without integral and differential calculus. Similar revolutions in understanding quantum gravity and in making deep connections between statistical and string physics are under progresses. One of indispensible tools are the theory of theta functions on Riemann surfaces. Since the literature of theta functions is mainly written by professional mathematician, physicists feel somewhat uneasy to begin to read a long chapters of lemmas and theorems, but it is now generally accepted that theta function is essential in understanding two-dimensional conformal field theory as the integral and differential calculus was indispensible in Newtonian mechanics

  12. Signed zeros of Gaussian vector fields - density, correlation functions and curvature

    CERN Document Server

    Foltin, G

    2003-01-01

    We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.

  13. 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.

  14. 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)

  15. Justification of the zeta-function renormalization in rigid string model

    International Nuclear Information System (INIS)

    Nesterenko, V.V.; Pirozhenko, I.G.

    1997-01-01

    A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein-Hurwitz zeta-functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy

  16. Singular integral equations boundary problems of function theory and their application to mathematical physics

    CERN Document Server

    Muskhelishvili, N I

    2011-01-01

    Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem

  17. Genus two partition functions of extremal conformal field theories

    International Nuclear Information System (INIS)

    Gaiotto, Davide; Yin Xi

    2007-01-01

    Recently Witten conjectured the existence of a family of 'extremal' conformal field theories (ECFTs) of central charge c = 24k, which are supposed to be dual to three-dimensional pure quantum gravity in AdS 3 . Assuming their existence, we determine explicitly the genus two partition functions of k = 2 and k = 3 ECFTs, using modular invariance and the behavior of the partition function in degenerating limits of the Riemann surface. The result passes highly nontrivial tests and in particular provides a piece of evidence for the existence of the k = 3 ECFT. We also argue that the genus two partition function of ECFTs with k ≤ 10 are uniquely fixed (if they exist)

  18. Hexagon functions and the three-loop remainder function

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance J.; Drummond, James M.; von Hippel, Matt; Pennington, Jeffrey

    2013-12-01

    We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.

  19. Lecture notes: string theory and zeta-function

    Energy Technology Data Exchange (ETDEWEB)

    Toppan, Francesco [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: toppan@cbpf.br

    2001-11-01

    These lecture notes are based on a revised and LaTexed version of the Master thesis defended at ISAS. The research part being omitted, they included a review of the bosonic closed string a la Polyakov and of the one-loop background field method of quantisation defined through the zeta-function. In an appendix some basic features of the Riemann zeta-function are also reviewed. The pedagogical aspects of the material here presented are particularly emphasized. These notes are used, together with the Scherk's article in Rev. Mod. Phys. and the first volume of the Polchinski book, for the mini-course on String Theory (16-hours of lectures) held at CBPF. In this course the Green-Schwarz-Witten two-volumes book is also used for consultative purposes. (author)

  20. Fractionalization of the complex-valued Brownian motion of order n using Riemann-Liouville derivative. Applications to mathematical finance and stochastic mechanics

    International Nuclear Information System (INIS)

    Jumarie, Guy

    2006-01-01

    The (complex-valued) Brownian motion of order n is defined as the limit of a random walk on the complex roots of the unity. Real-valued fractional noises are obtained as fractional derivatives of the Gaussian white noise (or order two). Here one combines these two approaches and one considers the new class of fractional noises obtained as fractional derivative of the complex-valued Brownian motion of order n. The key of the approach is the relation between differential and fractional differential provided by the fractional Taylor's series of analytic function f(z+h)=E α (h α D z α ).f(z), where E α is the Mittag-Leffler function on the one hand, and the generalized Maruyama's notation, on the other hand. Some questions are revisited such as the definition of fractional Brownian motion as integral w.r.t. (dt) α , and the exponential growth equation driven by fractional Brownian motion, to which a new solution is proposed. As a first illustrative example of application, in mathematical finance, one proposes a new approach to the optimal management of a stochastic portfolio of fractional order via the Lagrange variational technique applied to the state moment dynamical equations. In the second example, one deals with non-random Lagrangian mechanics of fractional order. The last example proposes a new approach to fractional stochastic mechanics, and the solution so obtained gives rise to the question as to whether physical systems would not have their own internal random times

  1. Zeta functions for the spectrum of the non-commutative harmonic oscillators

    CERN Document Server

    Ichinose, T

    2004-01-01

    This paper investigates the spectral zeta function of the non-commutative harmonic oscillator studied in \\cite{PW1, 2}. It is shown, as one of the basic analytic properties, that the spectral zeta function is extended to a meromorphic function in the whole complex plane with a simple pole at $s=1$, and further that it has a zero at all non-positive even integers, i.e. at $s=0$ and at those negative even integers where the Riemann zeta function has the so-called trivial zeros. As a by-product of the study, both the upper and the lower bounds are also given for the first eigenvalue of the non-commutative harmonic oscillator.

  2. Bosonization on higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Alvarez-Gaume, L.; Moore, G.; Nelson, P.; Vafa, C.

    1987-01-01

    We prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions. The theories have fields of arbitrary spin on compact surfaces with any number of handles. Global considerations required that we add new topological terms to the bosonic action. The proof that our prescritpion is correct relies on methods of complex algebraic geometry. (orig.)

  3. The Einstein tensor characterizing some Riemann spaces

    International Nuclear Information System (INIS)

    Rahman, M.S.

    1993-07-01

    A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs

  4. 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.

  5. The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications

    Directory of Open Access Journals (Sweden)

    Fuquan Jiang

    2013-01-01

    Full Text Available We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t+f(t,u(t+e(t=0,0Riemann-Liouville derivative. Here our nonlinearity f may be singular at u=0. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.

  6. An introduction to bicomplex variables and functions; Introduzione ai sistemi ipercomplessi commutativi a quattro unita

    Energy Technology Data Exchange (ETDEWEB)

    Catoni, Francesco; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Servizio Centralizzato Informatica e Reti; Catoni, Vincenzo; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Unita tecnico scientifica Fonti Rinnovabili e Cicli Energetici Innovativi

    2005-08-15

    The commutative quaternions introduced by C. Segre are similar to the Hamilton quaternions but, thanks to their commutativity, allow to introduce the functions. This property opens new ways far applications. [Italian] E noto da un teorema di Scheffers che per i sistemi ipercomplessi com-mutativi esiste il calcolo integrodifferenziale che permette di definire le loro funzioni in modo perfettamente analogo alle funzioni di variabili complesse. Questa proprieta rende questi sistemi, potenzialmente utilizzabili in nuovi campi, rispetto ai quaternioni noncommutativi di Hamilton. In questo lavoro introduciamo due di questi sistemi con le loro proprieta algebriche, le condizioni differenziali (condizioni di Cauchy-Riemann generalizzate) a cui devono soddisfare le loro funzioni e, infine, sono date le espressioni delle funzioni elementari.

  7. Identification of fractional order systems using modulating functions method

    KAUST Repository

    Liu, Dayan

    2013-06-01

    The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

  8. 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.

  9. Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions

    International Nuclear Information System (INIS)

    Jumarie, Guy

    2009-01-01

    A probability distribution of fractional (or fractal) order is defined by the measure μ{dx} = p(x)(dx) α , 0 α (D x α h α )f(x) provided by the modified Riemann Liouville definition, one can expand a probability calculus parallel to the standard one. A Fourier's transform of fractional order using the Mittag-Leffler function is introduced, together with its inversion formula; and it provides a suitable generalization of the characteristic function of fractal random variables. It appears that the state moments of fractional order are more especially relevant. The main properties of this fractional probability calculus are outlined, it is shown that it provides a sound approach to Fokker-Planck equation which are fractional in both space and time, and it provides new results in the information theory of non-random functions.

  10. Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

    Science.gov (United States)

    Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

    2018-03-01

    We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

  11. Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

    Science.gov (United States)

    Li, Q; He, Y L; Wang, Y; Tao, W Q

    2007-11-01

    A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

  12. Supersymmetric partition functions and the three-dimensional A-twist

    Energy Technology Data Exchange (ETDEWEB)

    Closset, Cyril [Theory Department, CERN,CH-1211, Geneva 23 (Switzerland); Kim, Heeyeon [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, N2L 2Y5, Ontario (Canada); Willett, Brian [Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106 (United States)

    2017-03-14

    We study three-dimensional N=2 supersymmetric gauge theories on M{sub g,p}, an oriented circle bundle of degree p over a closed Riemann surface, Σ{sub g}. We compute the M{sub g,p} supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round S{sup 3} can be understood as the expectation value of a so-called “fibering operator” on S{sup 2}×S{sup 1} with a topological twist. More generally, we show that the 3d N=2 supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on M{sub g,p} are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimensional supersymmetric dualities.

  13. The bosonic thermal Green function, its dual, and the fermion correlators of the massive Thirring model at finite temperature

    International Nuclear Information System (INIS)

    Mondaini, Leonardo; Marino, E.C.

    2011-01-01

    Full text: Despite the fact that quantum field theories are usually formulated in coordinate space, calculations, in both T = 0 and T ≠ 0 cases, are almost always performed in momentum space. However, when we are faced with the exact calculation of correlation functions we are naturally led to the problem of finding closed-form expressions for Green functions in coordinate space. In the present work, we derive an exact closed-form representation for the Euclidian thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a variable that conformally maps the infinite strip -∞ < x < ∞ (0 < τ < β of the z = x + iτ (τ: imaginary time) plane into the upper-half-plane. Use of the Cauchy-Riemann conditions, then allows us to identify the dual thermal Green function as the imaginary part of that function. Using both the thermal Green function and its dual, we obtain an explicit series expression for the fermionic correlation functions of the massive Thirring model (MTM) at a finite temperature. (author)

  14. More on zeta-function regularization of high-temperature expansions

    International Nuclear Information System (INIS)

    Actor, A.

    1987-01-01

    A recent paper using the Riemann ζ-function to regularize the (divergent) coefficients occurring in the high-temperature expansions of one-loop thermodynamic potentials is extended. This method proves to be a powerful tool for converting Dirichlet-type series Σ m a m (x i )/m s into power series in the dimensionless parameters x i . The coefficients occurring in the power series are (proportional to) ζ-functions evaluated away from their poles - this is where the regularization occurs. High-temperature expansions are just one example of this highly-nontrivial rearrangement of Dirichlet series into power series form. We discuss in considerable detail series in which a m (x i ) is a product of trigonometric, algebraic and Bessel function factors. The ζ-function method is carefully explained, and a large number of new formulae are provided. The means to generalize these formulae are also provided. Previous results on thermodynamic potentials are generalized to include a nonzero constant term in the gauge potential (time component) which can be used to probe the electric sector of temperature gauge theories. (author)

  15. Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

    Science.gov (United States)

    Gnoffo, Peter A.

    2015-01-01

    Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

  16. Asymptotic expansion of a partition function related to the sinh-model

    CERN Document Server

    Borot, Gaëtan; Kozlowski, Karol K

    2016-01-01

    This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...

  17. Generalized functions

    CERN Document Server

    Gelfand, I M; Graev, M I; Vilenkin, N Y; Pyatetskii-Shapiro, I I

    Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.

  18. Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations

    International Nuclear Information System (INIS)

    Calzetta, E.; Habib, S.; Hu, B.L.

    1988-01-01

    We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G 1 (x 1 ,x 2 ) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x 1 -x 2 on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for G 1 a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covariant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum kinetic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe

  19. Riemann-Cartan geometry of nonlinear disclination mechanics

    KAUST Repository

    Yavari, A.; Goriely, A.

    2012-01-01

    In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining

  20. Riemann Geometric Color-Weak Compensationfor Individual Observers

    OpenAIRE

    Kojima, Takanori; Mochizuki, Rika; Lenz, Reiner; Chao, Jinhui

    2014-01-01

    We extend a method for color weak compensation based on the criterion of preservation of subjective color differences between color normal and color weak observers presented in [2]. We introduce a new algorithm for color weak compensation using local affine maps between color spaces of color normal and color weak observers. We show howto estimate the local affine map and how to determine correspondences between the origins of local coordinates in color spaces of color normal and color weak ob...

  1. An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

    CERN Document Server

    Schlichenmaier, Martin

    2007-01-01

    This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role nowadays in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches. At the end of each chapter suggestions for further reading are given to allow the reader to study the touched topics in greater detail. This second edition of the book contains two additional more advanced geometric techniques: (1) The modern language and modern view of Algebraic Geometry and (2) Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture. Graduate students of theoretical and mathematical physics will appreciate this book as textbook. Students of mathematics who are looking for a short introduction to the various aspects of modern geometry and their interplay will also find it useful. Researchers will esteem the book as reliable ...

  2. Riemann-Cartan geometry of nonlinear disclination mechanics

    KAUST Repository

    Yavari, A.

    2012-03-23

    In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

  3. A Polyakov action on Riemann surfaces. Pt. 2

    International Nuclear Information System (INIS)

    Zucchini, R.

    1991-11-01

    The model independent study of the Polyakov action is continued on an arbitrary compact surface without boundary of genus larger than 2 as the general solution of the relevant conformal Ward identity. A general formula for the Polyakov action and an explicit calculation of the energy-momentum tensor density is provided. The general geometric setting of the construction is described in detail. It is shown that the Polyakov action defines a distribution of finite dimensional directions in the holomorphic tangent bundle of the manifold of Beltrami differentials. It is further argued that motions parallel to such distribution correspond to Polyakov's SL(2,C) symmetry transformations. Owing to the existence of renormalization ambiguities on a topologically non-trivial surface, the energy-momentum tensor needs not be invariant under the full SL(2,C) symmetry. The residual SL(2,C) symmetry is characterized geometrically. (author) 31 refs

  4. Beltrami algebra and symmetry of Beltrami equation on Riemann surfaces

    International Nuclear Information System (INIS)

    Guo Hanying; Xu Kaiwen; Shen Jianmin; Wang Shikun

    1989-12-01

    It is shown that the Beltrami equation has an infinite dimensional symmetry, namely the Beltrami algebra, on its solution spaces. The Beltrami algebra with central extension and its supersymmetric version are explicitly found. (author). 12 refs

  5. Functional Boxplots

    KAUST Repository

    Sun, Ying

    2011-01-01

    This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve, and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. This article has supplementary material online. © 2011 American Statistical Association.

  6. Staircase functions, spectral regidity and a rule for quantizing chaos

    International Nuclear Information System (INIS)

    Aurich, R.; Steiner, F.

    1991-07-01

    Considering the Selberg trace formula as an exact version of Gutzwiller's semiclassical periodic-orbit theory in the case of the free motion on compact Riemann surfaces with constant negative curvature (Hadamard-Gutzwiller model), we study two complementary basic problems in quantum chaology: the computation of the calssical staircase N(l), the number of periodic orbits with length shorter than l, in terms of the quantal energy spectrum {E n }, the computation of the spectral staircase N (E), the number of quantal energies below the energy E, in terms of the length spectrum {l n } of the classical periodic orbits. A formulation of the periodic-orbit theory is presented which is intrinsically unsmoothed, but for which an effective smoothing arises from the limited 'input data', i.e. from the limited knowledge of the periodic orbits in the case of N(E) and the limited knowledge of quantal energies in the case of N(l). Based on the periodic-orbit formula for N(E), we propose a new rule for quantizing chaos, which simply states that the quantal energies are determined by the zeros of the function ξ 1 (E) = cos (πN(E)). The formulas for N(l) and N(E) as well as the new quantization condition are tested numerically. Furthermore, it is shown that the staircase N(E) computed from the length spectrum yields (up to a constant) a good description of the spectral rigidity Δ 3 (L), being the first numerical attempt to compute a statistical property of the quantal energy spectrum of a chaotic system from classical periodic orbits. (orig.)

  7. Orbit Functions

    Directory of Open Access Journals (Sweden)

    Anatoliy Klimyk

    2006-01-01

    Full Text Available In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E_n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group in the entire Euclidean space E_n. Orbit functions are solutions of the corresponding Laplace equation in E_n, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points.

  8. Conference on Commutative rings, integer-valued polynomials and polynomial functions

    CERN Document Server

    Frisch, Sophie; Glaz, Sarah; Commutative Algebra : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions

    2014-01-01

    This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: ·    Homological dimensions of Prüfer-like rings ·    Quasi complete rings ·    Total graphs of rings ·    Properties of prime ideals over various rings ·    Bases for integer-valued polynomials ·    Boolean subrings ·    The portable property of domains ·    Probabilistic topics in Intn(D) ·    Closure operations in Zariski-Riemann spaces of valuation domains ·    Stability of do...

  9. Functional displays

    International Nuclear Information System (INIS)

    Angelis De, F.; Haentjens, J.

    1995-01-01

    The Functional Displays are directly derived from the Man-Machine Design key document: Function-Based Task Analysis. The presentation defines and describes the goals-means structure of the plant function along with applicable control volumes and parameters of interest. The purpose of the subject is to show, through an example of a preliminary design, what the main parts of a function are. (3 figs.)

  10. Functional Programming

    OpenAIRE

    Chitil, Olaf

    2009-01-01

    Functional programming is a programming paradigm like object-oriented programming and logic programming. Functional programming comprises both a specific programming style and a class of programming languages that encourage and support this programming style. Functional programming enables the programmer to describe an algorithm on a high-level, in terms of the problem domain, without having to deal with machine-related details. A program is constructed from functions that only map inputs to ...

  11. Functionalized amphipols

    DEFF Research Database (Denmark)

    Della Pia, Eduardo Antonio; Hansen, Randi Westh; Zoonens, Manuela

    2014-01-01

    Amphipols are amphipathic polymers that stabilize membrane proteins isolated from their native membrane. They have been functionalized with various chemical groups in the past years for protein labeling and protein immobilization. This large toolbox of functionalized amphipols combined with their...... surfaces for various applications in synthetic biology. This review summarizes the properties of functionalized amphipols suitable for synthetic biology approaches....

  12. Lightness functions

    DEFF Research Database (Denmark)

    Campi, Stefano; Gardner, Richard; Gronchi, Paolo

    2012-01-01

    Variants of the brightness function of a convex body K in n-dimensional Euclidean are investigated. The Lambertian lightness function L(K; v , w ) gives the total reflected light resulting from illumination by a light source at infinity in the direction w that is visible when looking...... in the direction v . The partial brightness function R( K ; v , w ) gives the area of the projection orthogonal to v of the portion of the surface of K that is both illuminated by a light source from the direction w and visible when looking in the direction v . A class of functions called lightness functions...... is introduced that includes L(K;.) and R(K;.) as special cases. Much of the theory of the brightness function like uniqueness, stability, and the existence and properties of convex bodies of maximal and minimal volume with finitely many function values equal to those of a given convex body, is extended...

  13. Functional analysis

    CERN Document Server

    Kantorovich, L V

    1982-01-01

    Functional Analysis examines trends in functional analysis as a mathematical discipline and the ever-increasing role played by its techniques in applications. The theory of topological vector spaces is emphasized, along with the applications of functional analysis to applied analysis. Some topics of functional analysis connected with applications to mathematical economics and control theory are also discussed. Comprised of 18 chapters, this book begins with an introduction to the elements of the theory of topological spaces, the theory of metric spaces, and the theory of abstract measure space

  14. Functional Boxplots

    KAUST Repository

    Sun, Ying; Genton, Marc G.

    2011-01-01

    data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve, and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central

  15. Functional coma.

    Science.gov (United States)

    Ludwig, L; McWhirter, L; Williams, S; Derry, C; Stone, J

    2016-01-01

    Functional coma - here defined as a prolonged motionless dissociative attack with absent or reduced response to external stimuli - is a relatively rare presentation. In this chapter we examine a wide range of terms used to describe states of unresponsiveness in which psychologic factors are relevant to etiology, such as depressive stupor, catatonia, nonepileptic "pseudostatus," and factitious disorders, and discuss the place of functional or psychogenic coma among these. Historically, diagnosis of functional coma has sometimes been reached after prolonged investigation and exclusion of other diagnoses. However, as is the case with other functional disorders, diagnosis should preferably be made on the basis of positive findings that provide evidence of inconsistency between an apparent comatose state and normal waking nervous system functioning. In our review of physical signs, we find some evidence for the presence of firm resistance to eye opening as reasonably sensitive and specific for functional coma, as well as the eye gaze sign, in which patients tend to look to the ground when turned on to one side. Noxious stimuli such as Harvey's sign (application of high-frequency vibrating tuning fork to the nasal mucosa) can also be helpful, although patients with this disorder are often remarkably unresponsive to usually painful stimuli, particularly as more commonly applied using sternal or nail bed pressure. The use of repeated painful stimuli is therefore not recommended. We also discuss the role of general anesthesia and other physiologic triggers to functional coma. © 2016 Elsevier B.V. All rights reserved.

  16. Rhinoplasty (Functional)

    Science.gov (United States)

    ... RESOURCES Medical Societies Patient Education About this Website Font Size + - Home > TREATMENTS > Rhinoplasty (Functional) Nasal/Sinus Irrigation ... performed to restore breathing, it typically necessitates some type of change to the appearance of the nose. ...

  17. Functional tremor.

    Science.gov (United States)

    Schwingenschuh, P; Deuschl, G

    2016-01-01

    Functional tremor is the commonest reported functional movement disorder. A confident clinical diagnosis of functional tremor is often possible based on the following "positive" criteria: a sudden tremor onset, unusual disease course, often with fluctuations or remissions, distractibility of the tremor if attention is removed from the affected body part, tremor entrainment, tremor variability, and a coactivation sign. Many patients show excessive exhaustion during examination. Other somatizations may be revealed in the medical history and patients may show additional functional neurologic symptoms and signs. In cases where the clinical diagnosis remains challenging, providing a "laboratory-supported" level of certainty aids an early positive diagnosis. In rare cases, in which the distinction from Parkinson's disease is difficult, dopamine transporter single-photon emission computed tomography (DAT-SPECT) can be indicated. © 2016 Elsevier B.V. All rights reserved.

  18. Cognitive Function

    Science.gov (United States)

    Because chemicals can adversely affect cognitive function in humans, considerable effort has been made to characterize their effects using animal models. Information from such models will be necessary to: evaluate whether chemicals identified as potentially neurotoxic by screenin...

  19. Functional unparsing

    DEFF Research Database (Denmark)

    Danvy, Olivier

    2000-01-01

    A string-formatting function such as printf in C seemingly requires dependent types, because its control string determines the rest of its arguments. Examples: formula here We show how changing the representation of the control string makes it possible to program printf in ML (which does not allow...... dependent types). The result is well typed and perceptibly more efficient than the corresponding library functions in Standard ML of New Jersey and in Caml....

  20. Functional Unparsing

    DEFF Research Database (Denmark)

    Danvy, Olivier

    1998-01-01

    A string-formatting function such as printf in C seemingly requires dependent types, because its control string determines the rest of its arguments. We show how changing the representation of the control string makes it possible to program printf in ML (which does not allow dependent types......). The result is well typed and perceptibly more efficient than the corresponding library functions in Standard ML of New Jersey and in Caml....

  1. Overlap functions

    Czech Academy of Sciences Publication Activity Database

    Bustince, H.; Fernández, J.; Mesiar, Radko; Montero, J.; Orduna, R.

    2010-01-01

    Roč. 72, 3-4 (2010), s. 1488-1499 ISSN 0362-546X R&D Projects: GA ČR GA402/08/0618 Institutional research plan: CEZ:AV0Z10750506 Keywords : t-norm * Migrative property * Homogeneity property * Overlap function Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2009/E/mesiar-overlap functions.pdf

  2. Bessel functions

    CERN Document Server

    Nambudiripad, K B M

    2014-01-01

    After presenting the theory in engineers' language without the unfriendly abstraction of pure mathematics, several illustrative examples are discussed in great detail to see how the various functions of the Bessel family enter into the solution of technically important problems. Axisymmetric vibrations of a circular membrane, oscillations of a uniform chain, heat transfer in circular fins, buckling of columns of varying cross-section, vibrations of a circular plate and current density in a conductor of circular cross-section are considered. The problems are formulated purely from physical considerations (using, for example, Newton's law of motion, Fourier's law of heat conduction electromagnetic field equations, etc.) Infinite series expansions, recurrence relations, manipulation of expressions involving Bessel functions, orthogonality and expansion in Fourier-Bessel series are also covered in some detail. Some important topics such as asymptotic expansions, generating function and Sturm-Lioville theory are r...

  3. Functional inequalities

    CERN Document Server

    Ghoussoub, Nassif

    2013-01-01

    The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of...

  4. Functional dyspepsia

    NARCIS (Netherlands)

    Kleibeuker, JH; Thijs, JC

    2004-01-01

    Purpose of review Functional dyspepsia is a common disorder, most of the time of unknown etiology and with variable pathophysiology. Therapy has been and still is largely empirical. Data from recent studies provide new clues for targeted therapy based on knowledge of etiology and pathophysiologic

  5. Functional Literacy

    Directory of Open Access Journals (Sweden)

    Fani Nolimal

    2000-12-01

    Full Text Available The author first defines literacy as the ability of co-operation in all fields of life and points at the features of illiterate or semi-literate individuals. The main stress is laid upon the assessment of literacy and illiteracy. In her opinion the main weak­ ness of this kind of evaluation are its vague psycho-metric characteristics, which leads to results valid in a single geographical or cultural environment only. She also determines the factors causing illiteracy, and she states that the level of functional literacy is more and more becoming a national indicator of successfulness.

  6. Lung function

    International Nuclear Information System (INIS)

    Sorichter, S.

    2009-01-01

    The term lung function is often restricted to the assessment of volume time curves measured at the mouth. Spirometry includes the assessment of lung volumes which can be mobilised with the corresponding flow-volume curves. In addition, lung volumes that can not be mobilised, such as the residual volume, or only partially as FRC and TLC can be measured by body plethysmography combined with the determination of the airway resistance. Body plethysmography allows the correct positioning of forced breathing manoeuvres on the volume-axis, e.g. before and after pharmacotherapy. Adding the CO single breath transfer factor (T LCO ), which includes the measurement of the ventilated lung volume using He, enables a clear diagnosis of different obstructive, restrictive or mixed ventilatory defects with and without trapped air. Tests of reversibility and provocation, as well as the assessment of inspiratory mouth pressures (PI max , P 0.1 ) help to classify the underlying disorder and to clarify treatment strategies. For further information and to complete the diagnostic of disturbances of the ventilation, diffusion and/or perfusion (capillar-)arterial bloodgases at rest and under physical strain sometimes amended by ergospirometry are recommended. Ideally, lung function measurements are amended by radiological and nuclear medicine techniques. (orig.) [de

  7. Functional phlebology

    International Nuclear Information System (INIS)

    Weber, J.; May, R.; Biland, L.; Endert, G.; Gottlob, R.; Justich, E.; Luebcke, P.; Mignon, G.; Moltz, L.; Partsch, H.; Petter, A.; Ritter, H.; Soerensen, R.; Widmer, L.K.; Widmer, M.T.; Zemp, E.

    1990-01-01

    The book presents a complete survey of the problems occurring in the venous system of the legs, pelvis, and abdomen. The material is arranged in the following main chapters: (1) Introduction to the phlebology of the low-pressure system in the lower part of the body; (2) Phlebographic methods; (3) Instrumented function studies and methods; (4) Pathologic findings; (5) Diagnostic methods and vein therapy; (6) Interventional radiology; (7) Expert opinions on venous lesions including insurance aspects. The first chapter encompasses a section briefly discussing the available instrumented diagnostic imaging methods. In view of the novel imaging methods, namely digital subtraction phlebology, sonography, CT and MRI, the classical phlebography remains the gold standard, so to speak: all currently available phlebographic methods for imaging the venes in the legs, pelvis and abdomen are explained and comparatively evaluated. Instrumented function tests such as Doppler effect ultrasound testing, plethysmography, peripheral and central phlebodynamometry (venous pressure measurement) are analysed for their diagnostic value and as alternative or supplementing techniques in comparison to phlebology. (orig./MG) With 843 figs., 101 tabs [de

  8. Functional Credentials

    Directory of Open Access Journals (Sweden)

    Deuber Dominic

    2018-04-01

    Full Text Available A functional credential allows a user to anonymously prove possession of a set of attributes that fulfills a certain policy. The policies are arbitrary polynomially computable predicates that are evaluated over arbitrary attributes. The key feature of this primitive is the delegation of verification to third parties, called designated verifiers. The delegation protects the privacy of the policy: A designated verifier can verify that a user satisfies a certain policy without learning anything about the policy itself. We illustrate the usefulness of this property in different applications, including outsourced databases with access control. We present a new framework to construct functional credentials that does not require (non-interactive zero-knowledge proofs. This is important in settings where the statements are complex and thus the resulting zero-knowledge proofs are not efficient. Our construction is based on any predicate encryption scheme and the security relies on standard assumptions. A complexity analysis and an experimental evaluation confirm the practicality of our approach.

  9. Functional Angioplasty

    Directory of Open Access Journals (Sweden)

    Rohit Tewari

    2013-01-01

    Full Text Available Coronary angiography underestimates or overestimates lesion severity, but still remains the cornerstone in the decision making for revascularization for an overwhelming majority of interventional cardiologists. Guidelines recommend and endorse non invasive functional evaluation ought to precede revascularization. In real world practice, this is adopted in less than 50% of patients who go on to have some form of revascularization. Fractional flow reserve (FFR is the ratio of maximal blood flow in a stenotic coronary relative to maximal flow in the same vessel, were it normal. Being independent of changes in heart rate, BP or prior infarction; and take into account the contribution of collateral blood flow. It is a majorly specific index with a reasonably high sensitivity (88%, specificity (100%, positive predictive value (100%, and overall accuracy (93%. Whilst FFR provides objective determination of ischemia and helps select appropriate candidates for revascularization (for both CABG and PCI in to cath lab itself before intervention, whereas intravascular ultrasound/optical coherence tomography guidance in PCI can secure the procedure by optimizing stent expansion. Functional angioplasty simply is incorporating both intravascular ultrasound and FFR into our daily Intervention practices.

  10. Cavalieri Integration | Ackermann | Quaestiones Mathematicae

    African Journals Online (AJOL)

    We also present two methods of evaluating a Cavalieri integral by first transforming it to either an equivalent Riemann or Riemann-Stieltjes integral by using special transformation functions h(x) and its inverse g(x), respectively. Interestingly enough it is often very difficult to find the transformation function h(x), whereas it is ...

  11. Thyroid Function Tests

    Science.gov (United States)

    ... Home » Thyroid Function Tests Leer en Español Thyroid Function Tests FUNCTION HOW DOES THE THYROID GLAND FUNCTION? ... Cancer Thyroid Nodules in Children and Adolescents Thyroid Function Tests Resources Thyroid Function Tests Brochure PDF En ...

  12. Functional materials

    International Nuclear Information System (INIS)

    Park, J. Y.; Hong, G. W.; Lee, H. J.

    2002-05-01

    Development of fabrication process of functional ceramic materials, evaluation of characteristics and experiments for understanding of irradiation behavior of ceramics were carried out for application of ceramics to the nuclear industry. The developed processes were the SiC surface coating technology with large area for improvement of wear resistance and corrosion resistance, the fabrication technology of SiC composites for excellent irradiation resistance, performance improvement technology of SiC fiber and nano-sized powder processing by combustion ignition and spray. Typical results were CVD SiC coating with diameter of 25cm and thickness of 100μm, highly dense SiC composite by F-CVI, heat-treating technology of SiC fiber using B4C power, and nano-sized powders of ODS-Cu, Li-based breeding materials, Ni-based metal powders with primary particle diameter of 20∼50nm. Furthermore, test equipment, data productions and damage evaluations were performed to understand corrosion resistance and wear resistance of alumina, silicon carbide and silicon nitride under PWR or PHWR operation conditions. Experimental procedures and basic technologies for evaluation of irradiation behavior were also established. Additionally, highly reactive precursor powders were developed by various technologies and the powders were applied to the fabrication of 100 m long Ag/Bi-2223 multi-filamentary wires. High Tc magnets and fly wheel for energy storage were developed, as well

  13. 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.

  14. Functional Programming in R

    DEFF Research Database (Denmark)

    Mailund, Thomas

    Master functions and discover how to write functional programs in R. In this book, you'll make your functions pure by avoiding side-effects; you’ll write functions that manipulate other functions, and you’ll construct complex functions using simpler functions as building blocks. In Functional...... Programming in R, you’ll see how we can replace loops, which can have side-effects, with recursive functions that can more easily avoid them. In addition, the book covers why you shouldn't use recursion when loops are more efficient and how you can get the best of both worlds. Functional programming...... functions by combining simpler functions. You will: Write functions in R including infix operators and replacement functions Create higher order functions Pass functions to other functions and start using functions as data you can manipulate Use Filer, Map and Reduce functions to express the intent behind...

  15. Resummed coefficient function for the shape function

    OpenAIRE

    Aglietti, U.

    2001-01-01

    We present a leading evaluation of the resummed coefficient function for the shape function. It is also shown that the coefficient function is short-distance-dominated. Our results allow relating the shape function computed on the lattice to the physical QCD distributions.

  16. Time functions function best as functions of multiple times

    NARCIS (Netherlands)

    Desain, P.; Honing, H.

    1992-01-01

    This article presents an elegant way of representing control functions at an abstractlevel. It introduces time functions that have multiple times as arguments. In this waythe generalized concept of a time function can support absolute and relative kinds of time behavior. Furthermore the

  17. Wave-function functionals for the density

    International Nuclear Information System (INIS)

    Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht

    2011-01-01

    We extend the idea of the constrained-search variational method for the construction of wave-function functionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals ψ[χ] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W=Σ i r i n , n=-2,-1,1,2, W=Σ i δ(r i ) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2)Σ i ∇ i 2 , the two-particle operators W=Σ n u n , n=-2,-1,1,2, where u=|r i -r j |, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.

  18. Nonlocal kinetic energy functionals by functional integration

    Science.gov (United States)

    Mi, Wenhui; Genova, Alessandro; Pavanello, Michele

    2018-05-01

    Since the seminal studies of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting kinetic energy, Ts[ρ], the subject of this work. The typical paradigm is to first approximate the energy functional and then take its functional derivative, δ/Ts[ρ ] δ ρ (r ) , yielding a potential that can be used in orbital-free DFT or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for Ts[ρ] is prescribed [which we dub Mi-Genova-Pavanello (MGP)] having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential is derived from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (body-centered cubic, face-centered cubic) and semiconducting (crystal diamond) phases of silicon as well as of III-V semiconductors. The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm. MGP's computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.

  19. Generalized Probability Functions

    Directory of Open Access Journals (Sweden)

    Alexandre Souto Martinez

    2009-01-01

    Full Text Available From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs. A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.

  20. Functionality and homogeneity.

    NARCIS (Netherlands)

    2011-01-01

    Functionality and homogeneity are two of the five Sustainable Safety principles. The functionality principle aims for roads to have but one exclusive function and distinguishes between traffic function (flow) and access function (residence). The homogeneity principle aims at differences in mass,

  1. Extraocular muscle function testing

    Science.gov (United States)

    ... medlineplus.gov/ency/article/003397.htm Extraocular muscle function testing To use the sharing features on this page, please enable JavaScript. Extraocular muscle function testing examines the function of the eye muscles. ...

  2. Congenital platelet function defects

    Science.gov (United States)

    ... pool disorder; Glanzmann's thrombasthenia; Bernard-Soulier syndrome; Platelet function defects - congenital ... Congenital platelet function defects are bleeding disorders that cause reduced platelet function. Most of the time, people with these disorders have ...

  3. Hepatic (Liver) Function Panel

    Science.gov (United States)

    ... Educators Search English Español Blood Test: Hepatic (Liver) Function Panel KidsHealth / For Parents / Blood Test: Hepatic (Liver) ... kidneys ) is working. What Is a Hepatic (Liver) Function Panel? A liver function panel is a blood ...

  4. Platelet Function Tests

    Science.gov (United States)

    ... Patient Resources For Health Professionals Subscribe Search Platelet Function Tests Send Us Your Feedback Choose Topic At ... Also Known As Platelet Aggregation Studies PFT Platelet Function Assay PFA Formal Name Platelet Function Tests This ...

  5. On Poisson functions

    OpenAIRE

    Terashima, Yuji

    2008-01-01

    In this paper, defining Poisson functions on super manifolds, we show that the graphs of Poisson functions are Dirac structures, and find Poisson functions which include as special cases both quasi-Poisson structures and twisted Poisson structures.

  6. Investigating body function

    International Nuclear Information System (INIS)

    Monks, R.; Riley, A.L.M.

    1981-01-01

    This invention relates to the investigation of body function, especially small bowel function but also liver function, using bile acids and bile salts or their metabolic precursors labelled with radio isotopes and selenium or tellurium. (author)

  7. Functional bowel disorders and functional abdominal pain

    OpenAIRE

    Thompson, W; Longstreth, G; Drossman, D; Heaton, K; Irvine, E; Muller-Lissner, S

    1999-01-01

    The Rome diagnostic criteria for the functional bowel disorders and functional abdominal pain are used widely in research and practice. A committee consensus approach, including criticism from multinational expert reviewers, was used to revise the diagnostic criteria and update diagnosis and treatment recommendations, based on research results. The terminology was clarified and the diagnostic criteria and management recommendations were revised. A functional bowel disorder (FBD) is diagnosed ...

  8. Functional microorganisms for functional food quality.

    Science.gov (United States)

    Gobbetti, M; Cagno, R Di; De Angelis, M

    2010-09-01

    Functional microorganisms and health benefits represent a binomial with great potential for fermented functional foods. The health benefits of fermented functional foods are expressed either directly through the interactions of ingested live microorganisms with the host (probiotic effect) or indirectly as the result of the ingestion of microbial metabolites synthesized during fermentation (biogenic effect). Since the importance of high viability for probiotic effect, two major options are currently pursued for improving it--to enhance bacterial stress response and to use alternative products for incorporating probiotics (e.g., ice cream, cheeses, cereals, fruit juices, vegetables, and soy beans). Further, it seems that quorum sensing signal molecules released by probiotics may interact with human epithelial cells from intestine thus modulating several physiological functions. Under optimal processing conditions, functional microorganisms contribute to food functionality through their enzyme portfolio and the release of metabolites. Overproduction of free amino acids and vitamins are two classical examples. Besides, bioactive compounds (e.g., peptides, γ-amino butyric acid, and conjugated linoleic acid) may be released during food processing above the physiological threshold and they may exert various in vivo health benefits. Functional microorganisms are even more used in novel strategies for decreasing phenomenon of food intolerance (e.g., gluten intolerance) and allergy. By a critical approach, this review will aim at showing the potential of functional microorganisms for the quality of functional foods.

  9. The Interpretive Function

    DEFF Research Database (Denmark)

    Agerbo, Heidi

    2017-01-01

    Approximately a decade ago, it was suggested that a new function should be added to the lexicographical function theory: the interpretive function(1). However, hardly any research has been conducted into this function, and though it was only suggested that this new function was relevant...... to incorporate into lexicographical theory, some scholars have since then assumed that this function exists(2), including the author of this contribution. In Agerbo (2016), I present arguments supporting the incorporation of the interpretive function into the function theory and suggest how non-linguistic signs...... can be treated in specific dictionary articles. However, in the current article, due to the results of recent research, I argue that the interpretive function should not be considered an individual main function. The interpretive function, contrary to some of its definitions, is not connected...

  10. Every storage function is a state function

    NARCIS (Netherlands)

    Trentelman, H.L.; Willems, J.C.

    1997-01-01

    It is shown that for linear dynamical systems with quadratic supply rates, a storage function can always be written as a quadratic function of the state of an associated linear dynamical system. This dynamical system is obtained by combining the dynamics of the original system with the dynamics of

  11. Persistent Functional Languages: Toward Functional Relational Databases

    NARCIS (Netherlands)

    Wevers, L.

    2014-01-01

    Functional languages provide new approaches to concurrency control, based on techniques such as lazy evaluation and memoization. We have designed and implemented a persistent functional language based on these ideas, which we plan to use for the implementation of a relational database system. With

  12. Museums and Their Functions.

    Science.gov (United States)

    Osborne, Harold

    1985-01-01

    Historical background concerning the nature and function of museums is provided, and the aesthetic functions of museums are discussed. The first major aesthetic function of museums is to preserve the artistic heritage of mankind and to make it widely available. The second major function is patronage. (RM)

  13. Hierarchical wave functions revisited

    International Nuclear Information System (INIS)

    Li Dingping.

    1997-11-01

    We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasi electron excitation on a torus, is also solved in this paper. (author)

  14. Functional Programming in R

    DEFF Research Database (Denmark)

    Mailund, Thomas

    Master functions and discover how to write functional programs in R. In this book, you'll make your functions pure by avoiding side-effects; you’ll write functions that manipulate other functions, and you’ll construct complex functions using simpler functions as building blocks. In Functional...... Programming in R, you’ll see how we can replace loops, which can have side-effects, with recursive functions that can more easily avoid them. In addition, the book covers why you shouldn't use recursion when loops are more efficient and how you can get the best of both worlds. Functional programming...... is a style of programming, like object-oriented programming, but one that focuses on data transformations and calculations rather than objects and state. Where in object-oriented programming you model your programs by describing which states an object can be in and how methods will reveal or modify...

  15. Functional Programming in R

    DEFF Research Database (Denmark)

    Mailund, Thomas

    2017-01-01

    Master functions and discover how to write functional programs in R. In this book, you'll make your functions pure by avoiding side-effects; you’ll write functions that manipulate other functions, and you’ll construct complex functions using simpler functions as building blocks. In Functional...... Programming in R, you’ll see how we can replace loops, which can have side-effects, with recursive functions that can more easily avoid them. In addition, the book covers why you shouldn't use recursion when loops are more efficient and how you can get the best of both worlds. Functional programming...... is a style of programming, like object-oriented programming, but one that focuses on data transformations and calculations rather than objects and state. Where in object-oriented programming you model your programs by describing which states an object can be in and how methods will reveal or modify...

  16. Teager Correlation Function

    DEFF Research Database (Denmark)

    Bysted, Tommy Kristensen; Hamila, R.; Gabbouj, M.

    1998-01-01

    A new correlation function called the Teager correlation function is introduced in this paper. The connection between this function, the Teager energy operator and the conventional correlation function is established. Two applications are presented. The first is the minimization of the Teager error...... norm and the second one is the use of the instantaneous Teager correlation function for simultaneous estimation of TDOA and FDOA (Time and Frequency Difference of Arrivals)....

  17. Properties of Ambiguity Functions

    OpenAIRE

    Mulcahy-Stanislawczyk, John

    2014-01-01

    The use of ambiguity functions in radar signal design and analysis is very common. Understanding the various properties and meanings of ambiguity functions allow a signal designer to understand the time delay and doppler shift properties of a given signal. Through the years, several different versions of the ambiguity function have been used. Each of these functions essentially have the same physical meaning; however, the use of different functions makes it difficult to be sure that certai...

  18. Ergotic / epistemic / semiotic functions

    OpenAIRE

    Luciani , Annie

    2007-01-01

    International audience; Claude Cadoz has introduced a typology of human-environment relation, identifying three functions. This typology allows characterizing univocally, i.e. in a non-redundant manner, the computer devices and interfaces that allow human to interact with environment through and by computers. These three functions are: the epistemic function, the semiotic function, the ergotic function. Conversely to the terms epistemic and semiotic that are usual, the term ergotic has been s...

  19. Variational functionals which admit discontinuous trial functions

    International Nuclear Information System (INIS)

    Nelson, P. Jr.

    1975-01-01

    It is argued that variational synthesis with discontinuous trial functions requires variational principles applicable to equations involving operators acting between distinct Hilbert spaces. A description is given of a Roussopoulos-type variational principle generalized to cover this situation. This principle is suggested as the basis for a unified approach to the derivation of variational functionals. In addition to esthetics, this approach has the advantage that the mathematical details increase the understanding of the derived functional, particularly the sense in which a synthesized solution should be regarded as an approximation to the true solution. By way of illustration, the generalized Roussopoulos principle is applied to derive a class of first-order diffusion functionals which admit trial functions containing approximations at an interface. These ''asymptotic'' interface quantities are independent of the limiting approximations from either side and permit use of different trial spectra at and on either side of an interface. The class of functionals derived contains as special cases both the Lagrange multiplier method of Buslik and two functionals of Lambropoulos and Luco. Some numerical results for a simple two-group model confirm that the ''multipliers'' can closely approximate the appropriate quantity in the region near an interface. (U.S.)

  20. A Blue Lagoon Function

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2007-01-01

    We consider a specific function of two variables whose graph surface resembles a blue lagoon. The function has a saddle point $p$, but when the function is restricted to any given straight line through $p$ it has a {\\em{strict local minimum}} along that line at $p$.......We consider a specific function of two variables whose graph surface resembles a blue lagoon. The function has a saddle point $p$, but when the function is restricted to any given straight line through $p$ it has a {\\em{strict local minimum}} along that line at $p$....

  1. Quality function deployment

    International Nuclear Information System (INIS)

    1981-10-01

    This book indicates quality function deployment with quality and deployment of quality function, process and prospect of quality function deployment and development, product process and conception of quality table, deployment of quality demand, design of quality table and application of concurrent multi design, progress design and quality development, main safe part and management of important function part, quality development and deployment of method of construction, quality deployment and economics, total system of quality function deployment and task of quality function deployment in the present and future.

  2. Functional Object Analysis

    DEFF Research Database (Denmark)

    Raket, Lars Lau

    We propose a direction it the field of statistics which we will call functional object analysis. This subfields considers the analysis of functional objects defined on continuous domains. In this setting we will focus on model-based statistics, with a particularly emphasis on mixed......-effect formulations, where the observed functional signal is assumed to consist of both fixed and random functional effects. This thesis takes the initial steps toward the development of likelihood-based methodology for functional objects. We first consider analysis of functional data defined on high...

  3. High spin structure functions

    International Nuclear Information System (INIS)

    Khan, H.

    1990-01-01

    This thesis explores deep inelastic scattering of a lepton beam from a polarized nuclear target with spin J=1. After reviewing the formation for spin-1/2, the structure functions for a spin-1 target are defined in terms of the helicity amplitudes for forward compton scattering. A version of the convolution model, which incorporates relativistic and binding energy corrections is used to calculate the structure functions of a neutron target. A simple parameterization of these structure functions is given in terms of a few neutron wave function parameters and the free nucleon structure functions. This allows for an easy comparison of structure functions calculated using different neutron models. (author)

  4. From functional architecture to functional connectomics.

    Science.gov (United States)

    Reid, R Clay

    2012-07-26

    "Receptive Fields, Binocular Interaction and Functional Architecture in the Cat's Visual Cortex" by Hubel and Wiesel (1962) reported several important discoveries: orientation columns, the distinct structures of simple and complex receptive fields, and binocular integration. But perhaps the paper's greatest influence came from the concept of functional architecture (the complex relationship between in vivo physiology and the spatial arrangement of neurons) and several models of functionally specific connectivity. They thus identified two distinct concepts, topographic specificity and functional specificity, which together with cell-type specificity constitute the major determinants of nonrandom cortical connectivity. Orientation columns are iconic examples of topographic specificity, whereby axons within a column connect with cells of a single orientation preference. Hubel and Wiesel also saw the need for functional specificity at a finer scale in their model of thalamic inputs to simple cells, verified in the 1990s. The difficult but potentially more important question of functional specificity between cortical neurons is only now becoming tractable with new experimental techniques. Copyright © 2012 Elsevier Inc. All rights reserved.

  5. Functional Median Polish

    KAUST Repository

    Sun, Ying

    2012-08-03

    This article proposes functional median polish, an extension of univariate median polish, for one-way and two-way functional analysis of variance (ANOVA). The functional median polish estimates the functional grand effect and functional main factor effects based on functional medians in an additive functional ANOVA model assuming no interaction among factors. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, Canadian temperature data, U. S. precipitation observations and outputs of global and regional climate models are considered, which can facilitate the research on the close link between local climate and the occurrence or severity of some diseases and other threats to human health. © 2012 International Biometric Society.

  6. Hearing the music of the primes: auditory complementarity and the siren song of zeta

    International Nuclear Information System (INIS)

    Berry, M V

    2012-01-01

    A counting function for the primes can be rendered as a sound signal whose harmonies, spanning the gamut of musical notes, are the Riemann zeros. But the individual primes cannot be discriminated as singularities in this ‘music’, because the intervals between them are too short. Conversely, if the prime singularities are detected as a series of clicks, the Riemann zeros correspond to frequencies too low to be heard. The sound generated by the Riemann zeta function itself is very different: a rising siren howl, which can be understood in detail from the Riemann–Siegel formula. (fast track communication)

  7. Operations Between Functions

    DEFF Research Database (Denmark)

    Gardner, Richard J.; Kiderlen, Markus

    A structural theory of operations between real-valued (or extended-real-valued) functions on a nonempty subset A of Rn is initiated. It is shown, for example, that any operation ∗ on a cone of functions containing the constant functions, which is pointwise, positively homogeneous, monotonic......, and associative, must be one of 40 explicitly given types. In particular, this is the case for operations between pairs of arbitrary, or continuous, or differentiable functions. The term pointwise means that (f ∗g)(x) = F(f(x), g(x)), for all x ∈ A and some function F of two variables. Several results in the same...... spirit are obtained for operations between convex functions or between support functions. For example, it is shown that ordinary addition is the unique pointwise operation between convex functions satisfying the identity property, i.e., f ∗ 0 = 0 ∗ f = f, for all convex f, while other results classify Lp...

  8. Kidney function tests

    Science.gov (United States)

    Kidney function tests are common lab tests used to evaluate how well the kidneys are working. Such tests include: ... Oh MS, Briefel G. Evaluation of renal function, water, electrolytes ... and Management by Laboratory Methods . 23rd ed. Philadelphia, ...

  9. Liver Function Tests

    Science.gov (United States)

    ... digest food, store energy, and remove poisons. Liver function tests are blood tests that check to see ... as hepatitis and cirrhosis. You may have liver function tests as part of a regular checkup. Or ...

  10. Functionalized diamond nanoparticles

    KAUST Repository

    Beaujuge, Pierre M.; El Tall, Omar; Raja, Inam U.

    2014-01-01

    A diamond nanoparticle can be functionalized with a substituted dienophile under ambient conditions, and in the absence of catalysts or additional reagents. The functionalization is thought to proceed through an addition reaction.

  11. Smart hydrogel functional materials

    CERN Document Server

    Chu, Liang-Yin; Ju, Xiao-Jie

    2014-01-01

    This book systematically introduces smart hydrogel functional materials with the configurations ranging from hydrogels to microgels. It serves as an excellent reference for designing and fabricating artificial smart hydrogel functional materials.

  12. Integrals of Bessel functions

    OpenAIRE

    Babusci, D.; Dattoli, G.; Germano, B.; Martinelli, M. R.; Ricci, P. E.

    2011-01-01

    We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.

  13. Functional Python programming

    CERN Document Server

    Lott, Steven

    2015-01-01

    This book is for developers who want to use Python to write programs that lean heavily on functional programming design patterns. You should be comfortable with Python programming, but no knowledge of functional programming paradigms is needed.

  14. Functionalized diamond nanoparticles

    KAUST Repository

    Beaujuge, Pierre M.

    2014-10-21

    A diamond nanoparticle can be functionalized with a substituted dienophile under ambient conditions, and in the absence of catalysts or additional reagents. The functionalization is thought to proceed through an addition reaction.

  15. Ecological Functions of Landscapes

    Science.gov (United States)

    Kiryushin, V. I.

    2018-01-01

    Ecological functions of landscapes are considered a system of processes ensuring the development, preservation, and evolution of ecosystems and the biosphere as a whole. The concept of biogeocenosis can be considered a model that integrates biotic and environmental functions. The most general biogeocenotic functions specify the biodiversity, biotic links, self-organization, and evolution of ecosystems. Close interaction between biocenosis and the biotope (ecotope) is ensured by the continuous exchange of matter, energy, and information. Ecotope determines the biocenosis. The group of ecotopic functions includes atmospheric (gas exchange, heat exchange, hydroatmospheric, climate-forming), lithospheric (geodynamic, geophysical, and geochemical), hydrologic and hydrogeologic functions of landscape and ecotopic functions of soils. Bioecological functions emerge as a result of the biotope and ecotope interaction; these are the bioproductive, destructive, organoaccumulative, biochemical (gas, concentration, redox, biochemical, biopedological), pedogenetic, and energy functions

  16. Functional Median Polish

    KAUST Repository

    Sun, Ying; Genton, Marc G.

    2012-01-01

    polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science

  17. Hybrid functional pseudopotentials

    Science.gov (United States)

    Yang, Jing; Tan, Liang Z.; Rappe, Andrew M.

    2018-02-01

    The consistency between the exchange-correlation functional used in pseudopotential construction and in the actual density functional theory calculation is essential for the accurate prediction of fundamental properties of materials. However, routine hybrid density functional calculations at present still rely on generalized gradient approximation pseudopotentials due to the lack of hybrid functional pseudopotentials. Here, we present a scheme for generating hybrid functional pseudopotentials, and we analyze the importance of pseudopotential density functional consistency for hybrid functionals. For the PBE0 hybrid functional, we benchmark our pseudopotentials for structural parameters and fundamental electronic gaps of the Gaussian-2 (G2) molecular dataset and some simple solids. Our results show that using our PBE0 pseudopotentials in PBE0 calculations improves agreement with respect to all-electron calculations.

  18. Photon structure function - theory

    International Nuclear Information System (INIS)

    Bardeen, W.A.

    1984-12-01

    The theoretical status of the photon structure function is reviewed. Particular attention is paid to the hadronic mixing problem and the ability of perturbative QCD to make definitive predictions for the photon structure function. 11 references

  19. Monotone Boolean functions

    International Nuclear Information System (INIS)

    Korshunov, A D

    2003-01-01

    Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years

  20. and chebyshev functions

    Directory of Open Access Journals (Sweden)

    Mohsen Razzaghi

    2000-01-01

    Full Text Available A direct method for finding the solution of variational problems using a hybrid function is discussed. The hybrid functions which consist of block-pulse functions plus Chebyshev polynomials are introduced. An operational matrix of integration and the integration of the cross product of two hybrid function vectors are presented and are utilized to reduce a variational problem to the solution of an algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.

  1. Functional Task Test (FTT)

    Science.gov (United States)

    Bloomberg, Jacob J.; Mulavara, Ajitkumar; Peters, Brian T.; Rescheke, Millard F.; Wood, Scott; Lawrence, Emily; Koffman, Igor; Ploutz-Snyder, Lori; Spiering, Barry A.; Feeback, Daniel L.; hide

    2009-01-01

    This slide presentation reviews the Functional Task Test (FTT), an interdisciplinary testing regimen that has been developed to evaluate astronaut postflight functional performance and related physiological changes. The objectives of the project are: (1) to develop a set of functional tasks that represent critical mission tasks for the Constellation Program, (2) determine the ability to perform these tasks after space flight, (3) Identify the key physiological factors that contribute to functional decrements and (4) Use this information to develop targeted countermeasures.

  2. Pseudolinear functions and optimization

    CERN Document Server

    Mishra, Shashi Kant

    2015-01-01

    Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems.The book describes the characterizations of solution sets of various optimization problems. It examines multiobjective pseudolinear, multiobjective fractional pseudolinear, static minmax pseudolinear, and static minmax fractional pseudolinear optimization problems and their results. The authors extend these results to locally

  3. Photon wave function

    OpenAIRE

    Bialynicki-Birula, Iwo

    2005-01-01

    Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, t...

  4. On Functional Calculus Estimates

    NARCIS (Netherlands)

    Schwenninger, F.L.

    2015-01-01

    This thesis presents various results within the field of operator theory that are formulated in estimates for functional calculi. Functional calculus is the general concept of defining operators of the form $f(A)$, where f is a function and $A$ is an operator, typically on a Banach space. Norm

  5. Phylogenetic molecular function annotation

    International Nuclear Information System (INIS)

    Engelhardt, Barbara E; Jordan, Michael I; Repo, Susanna T; Brenner, Steven E

    2009-01-01

    It is now easier to discover thousands of protein sequences in a new microbial genome than it is to biochemically characterize the specific activity of a single protein of unknown function. The molecular functions of protein sequences have typically been predicted using homology-based computational methods, which rely on the principle that homologous proteins share a similar function. However, some protein families include groups of proteins with different molecular functions. A phylogenetic approach for predicting molecular function (sometimes called 'phylogenomics') is an effective means to predict protein molecular function. These methods incorporate functional evidence from all members of a family that have functional characterizations using the evolutionary history of the protein family to make robust predictions for the uncharacterized proteins. However, they are often difficult to apply on a genome-wide scale because of the time-consuming step of reconstructing the phylogenies of each protein to be annotated. Our automated approach for function annotation using phylogeny, the SIFTER (Statistical Inference of Function Through Evolutionary Relationships) methodology, uses a statistical graphical model to compute the probabilities of molecular functions for unannotated proteins. Our benchmark tests showed that SIFTER provides accurate functional predictions on various protein families, outperforming other available methods.

  6. New Similarity Functions

    DEFF Research Database (Denmark)

    Yazdani, Hossein; Ortiz-Arroyo, Daniel; Kwasnicka, Halina

    2016-01-01

    spaces, in addition to their similarity in the vector space. Prioritized Weighted Feature Distance (PWFD) works similarly as WFD, but provides the ability to give priorities to desirable features. The accuracy of the proposed functions are compared with other similarity functions on several data sets....... Our results show that the proposed functions work better than other methods proposed in the literature....

  7. Two Functions of Language

    Science.gov (United States)

    Feldman, Carol Fleisher

    1977-01-01

    Author advocates the view that meaning is necessarily dependent upon the communicative function of language and examines the objections, particularly those of Noam Chomsky, to this view. Argues that while Chomsky disagrees with the idea that communication is the essential function of language, he implicitly agrees that it has a function.…

  8. Automatic differentiation of functions

    International Nuclear Information System (INIS)

    Douglas, S.R.

    1990-06-01

    Automatic differentiation is a method of computing derivatives of functions to any order in any number of variables. The functions must be expressible as combinations of elementary functions. When evaluated at specific numerical points, the derivatives have no truncation error and are automatically found. The method is illustrated by simple examples. Source code in FORTRAN is provided

  9. Nonparametric Transfer Function Models

    Science.gov (United States)

    Liu, Jun M.; Chen, Rong; Yao, Qiwei

    2009-01-01

    In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. PMID:20628584

  10. Weakly clopen functions

    International Nuclear Information System (INIS)

    Son, Mi Jung; Park, Jin Han; Lim, Ki Moon

    2007-01-01

    We introduce a new class of functions called weakly clopen function which includes the class of almost clopen functions due to Ekici [Ekici E. Generalization of perfectly continuous, regular set-connected and clopen functions. Acta Math Hungar 2005;107:193-206] and is included in the class of weakly continuous functions due to Levine [Levine N. A decomposition of continuity in topological spaces. Am Math Mon 1961;68:44-6]. Some characterizations and several properties concerning weakly clopenness are obtained. Furthermore, relationships among weak clopenness, almost clopenness, clopenness and weak continuity are investigated

  11. Implementing function spreadsheets

    DEFF Research Database (Denmark)

    Sestoft, Peter

    2008-01-01

    : that of turning an expression into a named function. Hence they proposed a way to define a function in terms of a worksheet with designated input and output cells; we shall call it a function sheet. The goal of our work is to develop implementations of function sheets and study their application to realistic...... examples. Therefore, we are also developing a simple yet comprehensive spreadsheet core implementation for experimentation with this technology. Here we report briefly on our experiments with function sheets as well as other uses of our spreadsheet core implementation....

  12. Transfer function combinations

    KAUST Repository

    Zhou, Liang; Schott, Mathias; Hansen, Charles

    2012-01-01

    Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions, are not always effective for all data sets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnitude for boundary location and statistical, occlusion, or size metrics. In this paper, we present a novel transfer function method which can provide more specificity for data classification by combining different transfer function spaces. In this work, a 2D transfer function can be combined with 1D transfer functions which improve the classification. Specifically, we use the traditional 2D scalar/gradient magnitude, 2D statistical, and 2D occlusion spectrum transfer functions and combine these with occlusion and/or size-based transfer functions to provide better specificity. We demonstrate the usefulness of the new method by comparing to the following previous techniques: 2D gradient magnitude, 2D occlusion spectrum, 2D statistical transfer functions and 2D size based transfer functions. © 2012 Elsevier Ltd.

  13. Transfer function combinations

    KAUST Repository

    Zhou, Liang

    2012-10-01

    Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions, are not always effective for all data sets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnitude for boundary location and statistical, occlusion, or size metrics. In this paper, we present a novel transfer function method which can provide more specificity for data classification by combining different transfer function spaces. In this work, a 2D transfer function can be combined with 1D transfer functions which improve the classification. Specifically, we use the traditional 2D scalar/gradient magnitude, 2D statistical, and 2D occlusion spectrum transfer functions and combine these with occlusion and/or size-based transfer functions to provide better specificity. We demonstrate the usefulness of the new method by comparing to the following previous techniques: 2D gradient magnitude, 2D occlusion spectrum, 2D statistical transfer functions and 2D size based transfer functions. © 2012 Elsevier Ltd.

  14. Functional Maximum Autocorrelation Factors

    DEFF Research Database (Denmark)

    Larsen, Rasmus; Nielsen, Allan Aasbjerg

    2005-01-01

    MAF outperforms the functional PCA in concentrating the interesting' spectra/shape variation in one end of the eigenvalue spectrum and allows for easier interpretation of effects. Conclusions. Functional MAF analysis is a useful methods for extracting low dimensional models of temporally or spatially......Purpose. We aim at data where samples of an underlying function are observed in a spatial or temporal layout. Examples of underlying functions are reflectance spectra and biological shapes. We apply functional models based on smoothing splines and generalize the functional PCA in......\\verb+~+\\$\\backslash\\$cite{ramsay97} to functional maximum autocorrelation factors (MAF)\\verb+~+\\$\\backslash\\$cite{switzer85,larsen2001d}. We apply the method to biological shapes as well as reflectance spectra. {\\$\\backslash\\$bf Methods}. MAF seeks linear combination of the original variables that maximize autocorrelation between...

  15. The Riemann Solution for the Injection of Steam and Nitrogen in a Porous Medium

    NARCIS (Netherlands)

    Lambert, W.; Marchesin, D.; Bruining, J.

    2009-01-01

    We solve the model for the flow of nitrogen, vapor, and water in a porous medium, neglecting compressibility, heat conductivity, and capillary effects. Our choice of injection conditions is determined by the application to clean up polluted sites. We study all mathematical structures, such as

  16. Study of the Issues of Computational Aerothermodynamics Using a Riemann Solver

    Science.gov (United States)

    2008-07-01

    should satisfy positiv - ity and not violate the Second Law of Thermodynamics (commonly called the entropy condition). Positivity preserving schemes...can be seen that N2 starts to dissociate around 6000 K - 12,000 K. 5.3 Conclusion This work has produced quantitative dividing lines between a regime...This figure provides a great deal of quantitative information and should be very useful to the high-speed flow CFD community. This work has also

  17. Quantum Yang-Mills theory of Riemann surfaces and conformal field theory

    International Nuclear Information System (INIS)

    Killingback, T.P.

    1989-01-01

    It is shown that Yang-Mills theory on a smooth surface, when suitably quantized, is a topological quantum field theory. This topological gauge theory is intimately related to two-dimensional conformal field theory. It is conjectured that all conformal field theories may be obtained from Yang-Mills theory on smooth surfaces. (orig.)

  18. Differential geometry for physicists and mathematicians moving frames and differential forms : from Euclid past Riemann

    CERN Document Server

    Vargas, José G

    2014-01-01

    This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative - almost like a story being told - that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas

  19. Geometry of the fundamental interactions on Riemann's legacy to high energy physics and cosmology

    CERN Document Server

    Maia, M D

    2011-01-01

    The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles. Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field. This book presents...

  20. The holographic dual of a Riemann problem in a large number of dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Herzog, Christopher P.; Spillane, Michael [C.N. Yang Institute for Theoretical Physics, Department of Physics and Astronomy,Stony Brook University, Stony Brook, NY 11794 (United States); Yarom, Amos [Department of Physics, Technion,Haifa 32000 (Israel)

    2016-08-22

    We study properties of a non equilibrium steady state generated when two heat baths are initially in contact with one another. The dynamics of the system we study are governed by holographic duality in a large number of dimensions. We discuss the “phase diagram” associated with the steady state, the dual, dynamical, black hole description of this problem, and its relation to the fluid/gravity correspondence.

  1. Asymptotic behavior of monodromy singularly perturbed differential equations on a Riemann surface

    CERN Document Server

    Simpson, Carlos

    1991-01-01

    This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.

  2. Riemann solvers and numerical methods for fluid dynamics a practical introduction

    CERN Document Server

    Toro, Eleuterio F

    2009-01-01

    High resolution upwind and centred methods are a mature generation of computational techniques applicable to a range of disciplines, Computational Fluid Dynamics being the most prominent. This book gives a practical presentation of this class of techniques.

  3. E-Orbit Functions

    Directory of Open Access Journals (Sweden)

    Jiri Patera

    2008-01-01

    Full Text Available We review and further develop the theory of $E$-orbit functions. They are functions on the Euclidean space $E_n$ obtained from the multivariate exponential function by symmetrization by means of an even part $W_{e}$ of a Weyl group $W$, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. They are closely related to symmetric and antisymmetric orbit functions which are received from exponential functions by symmetrization and antisymmetrization procedure by means of a Weyl group $W$. The $E$-orbit functions, determined by integral parameters, are invariant withrespect to even part $W^{aff}_{e}$ of the affine Weyl group corresponding to $W$. The $E$-orbit functions determine a symmetrized Fourier transform, where these functions serve as a kernel of the transform. They also determine a transform on a finite set of points of the fundamental domain $F^{e}$ of the group $W^{aff}_{e}$ (the discrete $E$-orbit function transform.

  4. Antisymmetric Orbit Functions

    Directory of Open Access Journals (Sweden)

    Anatoliy Klimyk

    2007-02-01

    Full Text Available In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group $G$ of rank $n$. Up to a sign, values of antisymmetric orbit functions are repeated on copies of the fundamental domain $F$ of the affine Weyl group (determined by the initial Weyl group in the entire Euclidean space $E_n$. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in $E_n$, vanishing on the boundary of the fundamental domain $F$. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group $G$. They also determine a transform on a finite set of points of $F$ (the discrete antisymmetric orbit function transform. Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.

  5. Mathematical modelling and numerical simulation of casting processes

    DEFF Research Database (Denmark)

    Hattel, Jesper Henri

    1998-01-01

    The control volume method applied to numerical modelling of castning. Analytical solutions based on the error function.Riemann-temperature. Modelling of release of latent heat with the enthalpy method....

  6. B Plant function analysis report

    International Nuclear Information System (INIS)

    Lund, D.P.

    1995-09-01

    The document contains the functions, function definitions, function interfaces, function interface definitions, Input Computer Automated Manufacturing Definition (IDEFO) diagrams, and a function hierarchy chart that describe what needs to be performed to deactivate B Plant

  7. Rδ-Supercontinuous Functions

    Directory of Open Access Journals (Sweden)

    Kohli J. K.

    2014-06-01

    Full Text Available A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl- supercontinuous functions (Demonstratio Math. 46(1 (2013, 229-244 and so includes all Rcl-supercontinuous (≡clopen continuous functions (Applied Gen. Topol. 8(2 (2007, 293-300; Indian J. Pure Appl. Math. 14(6 (1983, 767-772 and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3 (2010, 703-723.

  8. Intrinsic-density functionals

    International Nuclear Information System (INIS)

    Engel, J.

    2007-01-01

    The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals

  9. Functional analysis and applications

    CERN Document Server

    Siddiqi, Abul Hasan

    2018-01-01

    This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse pro...

  10. Counting with symmetric functions

    CERN Document Server

    Mendes, Anthony

    2015-01-01

    This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics.  It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions.  Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions.  Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4.  The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...

  11. Relativistic plasma dispersion functions

    International Nuclear Information System (INIS)

    Robinson, P.A.

    1986-01-01

    The known properties of plasma dispersion functions (PDF's) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF's required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF's relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived

  12. dftools: Distribution function fitting

    Science.gov (United States)

    Obreschkow, Danail

    2018-05-01

    dftools, written in R, finds the most likely P parameters of a D-dimensional distribution function (DF) generating N objects, where each object is specified by D observables with measurement uncertainties. For instance, if the objects are galaxies, it can fit a mass function (D=1), a mass-size distribution (D=2) or the mass-spin-morphology distribution (D=3). Unlike most common fitting approaches, this method accurately accounts for measurement in uncertainties and complex selection functions.

  13. Entropy and wigner functions

    Science.gov (United States)

    Manfredi; Feix

    2000-10-01

    The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

  14. Entropy and Wigner Functions

    OpenAIRE

    Manfredi, G.; Feix, M. R.

    2002-01-01

    The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions

  15. Time functions revisited

    Science.gov (United States)

    Fathi, Albert

    2015-07-01

    In this paper we revisit our joint work with Antonio Siconolfi on time functions. We will give a brief introduction to the subject. We will then show how to construct a Lipschitz time function in a simplified setting. We will end with a new result showing that the Aubry set is not an artifact of our proof of existence of time functions for stably causal manifolds.

  16. SPLINE, Spline Interpolation Function

    International Nuclear Information System (INIS)

    Allouard, Y.

    1977-01-01

    1 - Nature of physical problem solved: The problem is to obtain an interpolated function, as smooth as possible, that passes through given points. The derivatives of these functions are continuous up to the (2Q-1) order. The program consists of the following two subprograms: ASPLERQ. Transport of relations method for the spline functions of interpolation. SPLQ. Spline interpolation. 2 - Method of solution: The methods are described in the reference under item 10

  17. Hadron structure functions

    International Nuclear Information System (INIS)

    Martin, F.

    1981-03-01

    The x dependence of hadron structure functions is investigated. If quarks can exist in very low mass states (10 MeV for d and u quarks) the pion structure function is predicted to behave like (1-x) and not (1-x) 2 in a x-region around 1. Relativistic and non-relativistic quark bound state pictures of hadrons are considered together with their relation with the Q 2 evolution of structure functions. Good agreement with data is in general obtained

  18. Calculus of bivariant function

    OpenAIRE

    PTÁČNÍK, Jan

    2011-01-01

    This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, inc...

  19. Functional esophageal disorders

    OpenAIRE

    Clouse, R; Richter, J; Heading, R; Janssens, J; Wilson, J

    1999-01-01

    The functional esophageal disorders include globus, rumination syndrome, and symptoms that typify esophageal diseases (chest pain, heartburn, and dysphagia). Factors responsible for symptom production are poorly understood. The criteria for diagnosis rest not only on compatible symptoms but also on exclusion of structural and metabolic disorders that might mimic the functional disorders. Additionally, a functional diagnosis is precluded by the presence of a pathology-based motor disorder or p...

  20. Functional Programming With Relations

    OpenAIRE

    Hutton, Graham

    1991-01-01

    While programming in a relational framework has much to offer over the functional style in terms of expressiveness, computing with relations is less efficient, and more semantically troublesome. In this paper we propose a novel blend of the functional and relational styles. We identify a class of "causal relations", which inherit some of the bi-directionality properties of relations, but retain the efficiency and semantic foundations of the functional style.

  1. Photon structure function

    International Nuclear Information System (INIS)

    Bardeen, W.A.

    1980-11-01

    Theoretical understanding of the photon structure function is reviewed. As an illustration of the pointlike component, the parton model is briefly discussed. However, the systematic study of the photon structure function is presented through the framework of the operator product expansion. Perturbative QCD is used as the theoretical basis for the calculation of leading contributions to the operator product expansion. The influence of higher order QCD effects on these results is discussed. Recent results for the polarized structure functions are discussed

  2. Nonrespiratory lung function

    International Nuclear Information System (INIS)

    Isawa, Toyoharu

    1994-01-01

    The function of the lungs is primarily the function as a gas exchanger: the venous blood returning to the lungs is arterialized with oxygen in the lungs and the arterialized blood is sent back again to the peripheral tissues of the whole body to be utilized for metabolic oxygenation. Besides the gas exchanging function which we call ''respiratory lung function'' the lungs have functions that have little to do with gas exchange itself. We categorically call the latter function of the lungs as ''nonrespiratory lung function''. The lungs consist of the conductive airways, the gas exchanging units like the alveoli, and the interstitial space that surrounds the former two compartments. The interstitial space contains the blood and lymphatic capillaries, collagen and elastic fibers and cement substances. The conductive airways and the gas exchanging units are directly exposed to the atmosphere that contains various toxic and nontoxic gases, fume and biological or nonbiological particles. Because the conductive airways are equipped with defense mechanisms like mucociliary clearance or coughs to get rid of these toxic gases, particles or locally produced biological debris, we are usually free from being succumbed to ill effects of inhaled materials. By use of nuclear medicine techniques, we can now evaluate mucociliary clearance function, and other nonrespiratory lung functions as well in vivo

  3. Subordination by convex functions

    Directory of Open Access Journals (Sweden)

    Rosihan M. Ali

    2006-01-01

    Full Text Available For a fixed analytic function g(z=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ denote the class of all analytic functions f(z=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ, a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.

  4. Renormalization Group Functional Equations

    CERN Document Server

    Curtright, Thomas L

    2011-01-01

    Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

  5. Perceptual Audio Hashing Functions

    Directory of Open Access Journals (Sweden)

    Emin Anarım

    2005-07-01

    Full Text Available Perceptual hash functions provide a tool for fast and reliable identification of content. We present new audio hash functions based on summarization of the time-frequency spectral characteristics of an audio document. The proposed hash functions are based on the periodicity series of the fundamental frequency and on singular-value description of the cepstral frequencies. They are found, on one hand, to perform very satisfactorily in identification and verification tests, and on the other hand, to be very resilient to a large variety of attacks. Moreover, we address the issue of security of hashes and propose a keying technique, and thereby a key-dependent hash function.

  6. Nonrespiratory lung function

    Energy Technology Data Exchange (ETDEWEB)

    Isawa, Toyoharu [Tohoku University Research Institute for Chest Disease and Cancer, Sendai (Japan)

    1994-07-01

    The function of the lungs is primarily the function as a gas exchanger: the venous blood returning to the lungs is arterialized with oxygen in the lungs and the arterialized blood is sent back again to the peripheral tissues of the whole body to be utilized for metabolic oxygenation. Besides the gas exchanging function which we call ''respiratory lung function'' the lungs have functions that have little to do with gas exchange itself. We categorically call the latter function of the lungs as ''nonrespiratory lung function''. The lungs consist of the conductive airways, the gas exchanging units like the alveoli, and the interstitial space that surrounds the former two compartments. The interstitial space contains the blood and lymphatic capillaries, collagen and elastic fibers and cement substances. The conductive airways and the gas exchanging units are directly exposed to the atmosphere that contains various toxic and nontoxic gases, fume and biological or nonbiological particles. Because the conductive airways are equipped with defense mechanisms like mucociliary clearance or coughs to get rid of these toxic gases, particles or locally produced biological debris, we are usually free from being succumbed to ill effects of inhaled materials. By use of nuclear medicine techniques, we can now evaluate mucociliary clearance function, and other nonrespiratory lung functions as well in vivo.

  7. Control functions in MFM

    DEFF Research Database (Denmark)

    Lind, Morten

    2011-01-01

    Multilevel Flow Modeling (MFM) has been proposed as a tool for representing goals and functions of complex industrial plants and suggested as a basis for reasoning about control situations. Lind presents an introduction to MFM but do not describe how control functions are used in the modeling....... The purpose of the present paper is to serve as a companion paper to this introduction by explaining the basic principles used in MFM for representation of control functions. A theoretical foundation for modeling control functions is presented and modeling examples are given for illustration....

  8. Regulated functions and integrability

    Directory of Open Access Journals (Sweden)

    Ján Gunčaga

    2009-04-01

    Full Text Available Properties of functions defined on a bounded closed interval, weaker than continuity, have been considered by many mathematicians. Functions having both sides limits at each point are called regulated and were considered by J. Dieudonné [2], D. Fraňková [3] and others (see for example S. Banach [1], S. Saks [8]. The main class of functions we deal with consists of piece-wise constant ones. These functions play a fundamental role in the integration theory which had been developed by Igor Kluvanek (see Š. Tkacik [9]. We present an outline of this theory.

  9. Introduction to functional methods

    International Nuclear Information System (INIS)

    Faddeev, L.D.

    1976-01-01

    The functional integral is considered in relation to Feynman diagrams and phase space. The holomorphic form of the functional integral is then discussed. The main problem of the lectures, viz. the construction of the S-matrix by means of the functional integral, is considered. The functional methods described explicitly take into account the Bose statistics of the fields involved. The different procedure used to treat fermions is discussed. An introduction to the problem of quantization of gauge fields is given. (B.R.H.)

  10. The gamma function

    CERN Document Server

    Artin, Emil

    2015-01-01

    This brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, ""I feel that this monograph will help to show that the gamma function can be thought of as one of the elementary functions, and that all of its basic properties can be established using elementary methods of the calculus."" Generations of teachers

  11. Normal Functions As A New Way Of Defining Computable Functions

    Directory of Open Access Journals (Sweden)

    Leszek Dubiel

    2004-01-01

    Full Text Available Report sets new method of defining computable functions. This is formalization of traditional function descriptions, so it allows to define functions in very intuitive way. Discovery of Ackermann function proved that not all functions that can be easily computed can be so easily described with Hilbert’s system of recursive functions. Normal functions lack this disadvantage.

  12. Normal Functions as a New Way of Defining Computable Functions

    Directory of Open Access Journals (Sweden)

    Leszek Dubiel

    2004-01-01

    Full Text Available Report sets new method of defining computable functions. This is formalization of traditional function descriptions, so it allows to define functions in very intuitive way. Discovery of Ackermann function proved that not all functions that can be easily computed can be so easily described with Hilbert's system of recursive functions. Normal functions lack this disadvantage.

  13. Function spaces, 1

    CERN Document Server

    Pick, Luboš; John, Oldrich; Fucík, Svatopluk

    2012-01-01

    This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volum

  14. F-supercontinuous functions

    Directory of Open Access Journals (Sweden)

    J.K. Kohli

    2009-04-01

    Full Text Available A strong variant of continuity called ‘F-supercontinuity’ is introduced. The class of F-supercontinuous functions strictly contains the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33 (7 (2002, 1097–1108 which in turn properly contains the class of cl-supercontinuous functions ( clopen maps (Appl. Gen. Topology 8 (2 (2007, 293–300; Indian J. Pure Appl. Math. 14 (6 (1983, 762–772. Further, the class of F-supercontinuous functions is properly contained in the class of R-supercontinuous functions which in turn is strictly contained in the class of continuous functions. Basic properties of F-supercontinuous functions are studied and their place in the hierarchy of strong variants of continuity, which already exist in the mathematical literature, is elaborated. If either domain or range is a functionally regular space (Indagationes Math. 15 (1951, 359–368; 38 (1976, 281–288, then the notions of continuity, F-supercontinuity and R-supercontinuity coincide.

  15. Photon strength functions

    International Nuclear Information System (INIS)

    Bergqvist, I.

    1976-01-01

    Methods for extracting photon strength functions are briefly discussed. We follow the Brink-Axel approach to relate the strength functions to the giant resonances observed in photonuclear work and summarize the available data on the E1, E2 and M1 resonances. Some experimental and theoretical problems are outlined. (author)

  16. A Functional HAZOP Methodology

    DEFF Research Database (Denmark)

    Liin, Netta; Lind, Morten; Jensen, Niels

    2010-01-01

    A HAZOP methodology is presented where a functional plant model assists in a goal oriented decomposition of the plant purpose into the means of achieving the purpose. This approach leads to nodes with simple functions from which the selection of process and deviation variables follow directly...

  17. Functional Magnetic Resonance Imaging

    Science.gov (United States)

    Voos, Avery; Pelphrey, Kevin

    2013-01-01

    Functional magnetic resonance imaging (fMRI), with its excellent spatial resolution and ability to visualize networks of neuroanatomical structures involved in complex information processing, has become the dominant technique for the study of brain function and its development. The accessibility of in-vivo pediatric brain-imaging techniques…

  18. Cryptographic Hash Functions

    DEFF Research Database (Denmark)

    Gauravaram, Praveen; Knudsen, Lars Ramkilde

    2010-01-01

    functions, also called message authentication codes (MACs) serve data integrity and data origin authentication in the secret key setting. The building blocks of hash functions can be designed using block ciphers, modular arithmetic or from scratch. The design principles of the popular Merkle...

  19. Functional Assessment Inventory Manual.

    Science.gov (United States)

    Crewe, Nancy M.; Athelstan, Gary T.

    This manual, which provides extensive new instructions for administering the Functional Assessment Inventory (FAI), is intended to enable counselors to begin using the inventory without undergoing any special training. The first two sections deal with the need for functional assessment and issues in the development and use of the inventory. The…

  20. Functional and cognitive grammars

    Institute of Scientific and Technical Information of China (English)

    Anna Siewierska

    2011-01-01

    This paper presents a comprehensive review of the functional approach and cognitive approach to the nature of language and its relation to other aspects of human cognition. The paper starts with a brief discussion of the origins and the core tenets of the two approaches in Section 1. Section 2 discusses the similarities and differences between the three full-fledged structural functional grammars subsumed in the functional approach: Halliday's Systemic Functional Grammar (SFG), Dik's Functional Grammar (FG), and Van Valin's Role and Reference Grammar (RRG). Section 3 deals with the major features of the three cognitive frameworks: Langacker's Cognitive Grammar (CG), Goldberg's Cognitive Construction Grammar (CCG), and Croft's Radical Construction Grammar (RCG). Section 4 compares the two approaches and attempts to provide a unified functional-cognitive grammar. In the last section, the author concludes the paper with remarks on the unidirectional shift from functional grammar to cognitive grammar that may indicate a reinterpretation of the traditional relationship between functional and cognitive models of grammar.

  1. Heterogeneity in kinesin function

    NARCIS (Netherlands)

    Reddy, Babu J N; Tripathy, Suvranta; Vershinin, Michael; Tanenbaum, Marvin E; Xu, Jing; Mattson-Hoss, Michelle; Arabi, Karim; Chapman, Dail; Doolin, Tory; Hyeon, Changbong; Gross, Steven P

    2017-01-01

    The kinesin family proteins are often studied as prototypical molecular motors; a deeper understanding of them can illuminate regulation of intracellular transport. It is typically assumed that they function identically. Here we find that this assumption of homogeneous function appears incorrect:

  2. Thermal dielectric function

    International Nuclear Information System (INIS)

    Moneta, M.

    1999-01-01

    Thermal dielectric functions ε(k,ω) for homogeneous electron gas were determined and discussed. The ground state of the gas is described by the Fermi-Dirac momentum distribution. The low and high temperature limits of ε(k,ω) were related to the Lindhard dielectric function and to ε(k, omega) derived for Boltzmann and for classical momentum distributions, respectively. (author)

  3. Monadic Functional Reactive Programming

    NARCIS (Netherlands)

    A.J. van der Ploeg (Atze); C Shan

    2013-01-01

    htmlabstractFunctional Reactive Programming (FRP) is a way to program reactive systems in functional style, eliminating many of the problems that arise from imperative techniques. In this paper, we present an alternative FRP formulation that is based on the notion of a reactive computation: a

  4. The Grindahl Hash Functions

    DEFF Research Database (Denmark)

    Knudsen, Lars Ramkilde; Rechberger, Christian; Thomsen, Søren Steffen

    2007-01-01

    to the state. We propose two concrete hash functions, Grindahl-256 and Grindahl-512 with claimed security levels with respect to collision, preimage and second preimage attacks of 2^128 and 2^256, respectively. Both proposals have lower memory requirements than other hash functions at comparable speeds...

  5. Neurophysiology of functional imaging

    NARCIS (Netherlands)

    van Eijsden, Pieter; Hyder, Fahmeed; Rothman, Douglas L.; Shulman, Robert G.

    2009-01-01

    The successes of PET and fMRI in non-invasively localizing sensory functions had encouraged efforts to transform the subjective concepts of cognitive psychology into objective physical measures. The assumption was that mental functions could be decomposed into non-overlapping, context-independent

  6. properties and luminosity functions

    Directory of Open Access Journals (Sweden)

    Hektor Monteiro

    2007-01-01

    Full Text Available In this article, we present an investigation of a sample of 1072 stars extracted from the Villanova Catalog of Spectroscopically Identified White Dwarfs (2005 on-line version, studying their distribution in the Galaxy, their physical properties and their luminosity functions. The distances and physical properties of the white dwarfs are determined through interpolation of their (B-V or (b-y colors in model grids. The solar position relative to the Galactic plane, luminosity function, as well as separate functions for each white dwarf spectral type are derived and discussed. We show that the binary fraction does not vary significantly as a function of distance from the Galactic disk out to 100 pc. We propose that the formation rates of DA and non-DAs have changed over time and/or that DAs evolve into non-DA types. The luminosity functions for DAs and DBs have peaks possibly related to a star burst event.

  7. The triad value function

    DEFF Research Database (Denmark)

    Vedel, Mette

    2016-01-01

    the triad value function. Next, the applicability and validity of the concept is examined in a case study of four closed vertical supply chain triads. Findings - The case study demonstrates that the triad value function facilitates the analysis and understanding of an apparent paradox; that distributors...... are not dis-intermediated in spite of their limited contribution to activities in the triads. The results indicate practical adequacy of the triad value function. Research limitations/implications - The triad value function is difficult to apply in the study of expanded networks as the number of connections...... expands exponentially with the number of ties in the network. Moreover, it must be applied in the study of service triads and open vertical supply chain triads to further verify the practical adequacy of the concept. Practical implications - The triad value function cannot be used normatively...

  8. Pair Correlation Function Integrals

    DEFF Research Database (Denmark)

    Wedberg, Nils Hejle Rasmus Ingemar; O'Connell, John P.; Peters, Günther H.J.

    2011-01-01

    We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long......-distance behavior of radial distribution functions is determined by requiring that the corresponding direct correlation functions follow certain approximations at long distances. We have briefly described the method and tested its performance in previous communications [R. Wedberg, J. P. O’Connell, G. H. Peters......, and J. Abildskov, Mol. Simul. 36, 1243 (2010); Fluid Phase Equilib. 302, 32 (2011)], but describe here its theoretical basis more thoroughly and derive long-distance approximations for the direct correlation functions. We describe the numerical implementation of the method in detail, and report...

  9. Managing Functional Power

    DEFF Research Database (Denmark)

    Rosenstand, Claus Andreas Foss; Laursen, Per Kyed

    2013-01-01

    How does one manage functional power relations between leading functions in vision driven digital media creation, and this from idea to master during the creation cycle? Functional power is informal, and it is understood as roles, e.g. project manager, that provide opportunities to contribute...... to the product quality. The area of interest is the vision driven digital media industry in general; however, the point of departure is the game industry due to its aesthetic complexity. The article's contribution to the area is a power graph, which shows the functional power of the leading functions according...... to a general digital media creation cycle. This is used to point out potential power conflicts and their consequences. It is concluded that there is normally more conflict potential in vision driven digital media creation than in digital media creation in general or in software development. The method...

  10. Functional data analysis

    CERN Document Server

    Ramsay, J O

    1997-01-01

    Scientists today collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drwan from growth analysis, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researc...

  11. The function of introns

    Directory of Open Access Journals (Sweden)

    Liran eCarmel

    2012-04-01

    Full Text Available The intron-exon architecture of many eukaryotic genes raises the intriguing question of whether this unique organization serves any function, or is it simply a result of the spread of functionless introns in eukaryotic genomes. In this review, we show that introns in contemporary species fulfill a broad spectrum of functions, and are involved in virtually every step of mRNA processing. We propose that this great diversity of intronic functions supports the notion that introns were indeed selfish elements in early eukaryotes, but then independently gained numerous functions in different eukaryotic lineages. We suggest a novel criterion of evolutionary conservation, dubbed intron positional conservation, which can identify functional introns.

  12. A phased translation function

    International Nuclear Information System (INIS)

    Read, R.J.; Schierbeek, A.J.

    1988-01-01

    A phased translation function, which takes advantage of prior phase information to determine the position of an oriented mulecular replacement model, is examined. The function is the coefficient of correlation between the electron density computed with the prior phases and the electron density of the translated model, evaluated in reciprocal space as a Fourier transform. The correlation coefficient used in this work is closely related to an overlap function devised by Colman, Fehlhammer and Bartels. Tests with two protein structures, one of which was solved with the help of the phased translation function, show that little phase information is required to resolve the translation problem, and that the function is relatively insensitive to misorientation of the model. (orig.)

  13. Submodular functions and optimization

    CERN Document Server

    Fujishige, Satoru

    2005-01-01

    It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics. Key features: - Self-contained exposition of the theory of submodular ...

  14. Time Functions as Utilities

    Science.gov (United States)

    Minguzzi, E.

    2010-09-01

    Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K + relation (Seifert’s relation). By exploiting this analogy, we are able to import some mathematical results, most notably Peleg’s and Levin’s theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover the K + (or Seifert) relation which indeed turns out to be the intersection of the time or temporal orderings. This result tells us in which circumstances it is possible to recover the chronological or causal relation starting from the set of time or temporal functions allowed by the spacetime. Moreover, it is proved that a chronological spacetime in which the closure of the causal relation is transitive (for instance a reflective spacetime) admits a semi-time function. Along the way a new proof avoiding smoothing techniques is given that the existence of a time function implies stable causality, and a new short proof of the equivalence between K-causality and stable causality is given which takes advantage of Levin’s theorem and smoothing techniques.

  15. Multidisciplinary team functioning.

    Science.gov (United States)

    Kovitz, K E; Dougan, P; Riese, R; Brummitt, J R

    1984-01-01

    This paper advocates the need to move beyond interdisciplinary team composition as a minimum criterion for multidisciplinary functioning in child abuse treatment. Recent developments within the field reflect the practice of shared professional responsibility for detection, case management and treatment. Adherence to this particular model for intervention requires cooperative service planning and implementation as task related functions. Implicitly, this model also carries the potential to incorporate the supportive functioning essential to effective group process. However, explicit attention to the dynamics and process of small groups has been neglected in prescriptive accounts of multidisciplinary child abuse team organization. The present paper therefore focuses upon the maintenance and enhancement aspects of multidisciplinary group functioning. First, the development and philosophy of service for the Alberta Children's Hospital Child Abuse Program are reviewed. Second, composition of the team, it's mandate for service, and the population it serves are briefly described. Third, the conceptual framework within which the program functions is outlined. Strategies for effective group functioning are presented and the difficulties encountered with this model are highlighted. Finally, recommendations are offered for planning and implementing a multidisciplinary child abuse team and for maintaining its effective group functioning.

  16. The Enzyme Function Initiative†

    Science.gov (United States)

    Gerlt, John A.; Allen, Karen N.; Almo, Steven C.; Armstrong, Richard N.; Babbitt, Patricia C.; Cronan, John E.; Dunaway-Mariano, Debra; Imker, Heidi J.; Jacobson, Matthew P.; Minor, Wladek; Poulter, C. Dale; Raushel, Frank M.; Sali, Andrej; Shoichet, Brian K.; Sweedler, Jonathan V.

    2011-01-01

    The Enzyme Function Initiative (EFI) was recently established to address the challenge of assigning reliable functions to enzymes discovered in bacterial genome projects; in this Current Topic we review the structure and operations of the EFI. The EFI includes the Superfamily/Genome, Protein, Structure, Computation, and Data/Dissemination Cores that provide the infrastructure for reliably predicting the in vitro functions of unknown enzymes. The initial targets for functional assignment are selected from five functionally diverse superfamilies (amidohydrolase, enolase, glutathione transferase, haloalkanoic acid dehalogenase, and isoprenoid synthase), with five superfamily-specific Bridging Projects experimentally testing the predicted in vitro enzymatic activities. The EFI also includes the Microbiology Core that evaluates the in vivo context of in vitro enzymatic functions and confirms the functional predictions of the EFI. The deliverables of the EFI to the scientific community include: 1) development of a large-scale, multidisciplinary sequence/structure-based strategy for functional assignment of unknown enzymes discovered in genome projects (target selection, protein production, structure determination, computation, experimental enzymology, microbiology, and structure-based annotation); 2) dissemination of the strategy to the community via publications, collaborations, workshops, and symposia; 3) computational and bioinformatic tools for using the strategy; 4) provision of experimental protocols and/or reagents for enzyme production and characterization; and 5) dissemination of data via the EFI’s website, enzymefunction.org. The realization of multidisciplinary strategies for functional assignment will begin to define the full metabolic diversity that exists in nature and will impact basic biochemical and evolutionary understanding, as well as a wide range of applications of central importance to industrial, medicinal and pharmaceutical efforts. PMID

  17. The Enzyme Function Initiative.

    Science.gov (United States)

    Gerlt, John A; Allen, Karen N; Almo, Steven C; Armstrong, Richard N; Babbitt, Patricia C; Cronan, John E; Dunaway-Mariano, Debra; Imker, Heidi J; Jacobson, Matthew P; Minor, Wladek; Poulter, C Dale; Raushel, Frank M; Sali, Andrej; Shoichet, Brian K; Sweedler, Jonathan V

    2011-11-22

    The Enzyme Function Initiative (EFI) was recently established to address the challenge of assigning reliable functions to enzymes discovered in bacterial genome projects; in this Current Topic, we review the structure and operations of the EFI. The EFI includes the Superfamily/Genome, Protein, Structure, Computation, and Data/Dissemination Cores that provide the infrastructure for reliably predicting the in vitro functions of unknown enzymes. The initial targets for functional assignment are selected from five functionally diverse superfamilies (amidohydrolase, enolase, glutathione transferase, haloalkanoic acid dehalogenase, and isoprenoid synthase), with five superfamily specific Bridging Projects experimentally testing the predicted in vitro enzymatic activities. The EFI also includes the Microbiology Core that evaluates the in vivo context of in vitro enzymatic functions and confirms the functional predictions of the EFI. The deliverables of the EFI to the scientific community include (1) development of a large-scale, multidisciplinary sequence/structure-based strategy for functional assignment of unknown enzymes discovered in genome projects (target selection, protein production, structure determination, computation, experimental enzymology, microbiology, and structure-based annotation), (2) dissemination of the strategy to the community via publications, collaborations, workshops, and symposia, (3) computational and bioinformatic tools for using the strategy, (4) provision of experimental protocols and/or reagents for enzyme production and characterization, and (5) dissemination of data via the EFI's Website, http://enzymefunction.org. The realization of multidisciplinary strategies for functional assignment will begin to define the full metabolic diversity that exists in nature and will impact basic biochemical and evolutionary understanding, as well as a wide range of applications of central importance to industrial, medicinal, and pharmaceutical efforts.

  18. Polysheroidal periodic functions

    International Nuclear Information System (INIS)

    Truskova, N.F.

    1985-01-01

    Separation of variables in the Helmholtz N-dimensional (N≥4) equation in polyspheroidal coordinate systems leads to the necessity of solving equations going over into equations for polyspheroidal periodic functions used for solving the two-centre problem in quantum mechanics, the three-body problem with Coulomb interaction, etc. For these functions the expansions are derived in terms of the Jacobi polynomials and Bessel functions. Their basic properties, asymptotics are considered. The algorithm of their computer calculations is developed. The results of numerical calculations are given

  19. cl-Supercontinuous Functions

    Directory of Open Access Journals (Sweden)

    D. Singh

    2007-10-01

    Full Text Available Basic properties of cl-supercontinuity, a strong variant of continuity, due to Reilly and Vamanamurthy [Indian J. Pure Appl. Math., 14 (1983, 767–772], who call such maps clopen continuous, are studied. Sufficient conditions on domain or range for a continuous function to be cl-supercontinuous are observed. Direct and inverse transfer of certain topological properties under cl-supercontinuous functions are studied and existence or nonexistence of certain cl-supercontinuous function with specified domain or range is outlined.

  20. Mean-periodic functions

    Directory of Open Access Journals (Sweden)

    Carlos A. Berenstein

    1980-01-01

    Full Text Available We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn. This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.

  1. Functional Amyloids in Reproduction.

    Science.gov (United States)

    Hewetson, Aveline; Do, Hoa Quynh; Myers, Caitlyn; Muthusubramanian, Archana; Sutton, Roger Bryan; Wylie, Benjamin J; Cornwall, Gail A

    2017-06-29

    Amyloids are traditionally considered pathological protein aggregates that play causative roles in neurodegenerative disease, diabetes and prionopathies. However, increasing evidence indicates that in many biological systems nonpathological amyloids are formed for functional purposes. In this review, we will specifically describe amyloids that carry out biological roles in sexual reproduction including the processes of gametogenesis, germline specification, sperm maturation and fertilization. Several of these functional amyloids are evolutionarily conserved across several taxa, including human, emphasizing the critical role amyloids perform in reproduction. Evidence will also be presented suggesting that, if altered, some functional amyloids may become pathological.

  2. THE PSEUDO-SMARANDACHE FUNCTION

    OpenAIRE

    David Gorski

    2007-01-01

    The Pseudo-Smarandache Function is part of number theory. The function comes from the Smarandache Function. The Pseudo-Smarandache Function is represented by Z(n) where n represents any natural number.

  3. Coded Network Function Virtualization

    DEFF Research Database (Denmark)

    Al-Shuwaili, A.; Simone, O.; Kliewer, J.

    2016-01-01

    Network function virtualization (NFV) prescribes the instantiation of network functions on general-purpose network devices, such as servers and switches. While yielding a more flexible and cost-effective network architecture, NFV is potentially limited by the fact that commercial off......-the-shelf hardware is less reliable than the dedicated network elements used in conventional cellular deployments. The typical solution for this problem is to duplicate network functions across geographically distributed hardware in order to ensure diversity. In contrast, this letter proposes to leverage channel...... coding in order to enhance the robustness on NFV to hardware failure. The proposed approach targets the network function of uplink channel decoding, and builds on the algebraic structure of the encoded data frames in order to perform in-network coding on the signals to be processed at different servers...

  4. Functional Use Database (FUse)

    Data.gov (United States)

    U.S. Environmental Protection Agency — There are five different files for this dataset: 1. A dataset listing the reported functional uses of chemicals (FUse) 2. All 729 ToxPrint descriptors obtained from...

  5. Contributing to Functionality

    DEFF Research Database (Denmark)

    Törpel, Bettina

    2006-01-01

    The objective of this paper is the design of computer supported joint action spaces. It is argued against a view of functionality as residing in computer applications. In such a view the creation of functionality is equivalent to the creation of computer applications. Functionality, in the view...... advocated in this paper, emerges in the specific dynamic interplay of actors, objectives, structures, practices and means. In this view, functionality is the result of creating, harnessing and inhabiting computer supported joint action spaces. The successful creation and further development of a computer...... supported joint action space comprises a whole range of appropriate design contributions. The approach is illustrated by the example of the creation of the computer supported joint action space "exchange network of voluntary union educators". As part of the effort a group of participants created...

  6. Liver Function Tests

    Science.gov (United States)

    ... Liver Function Tests Clinical Trials Liver Transplant FAQs Medical Terminology Diseases of the Liver Alagille Syndrome Alcohol-Related ... the Liver The Progression of Liver Disease FAQs Medical Terminology HOW YOU CAN HELP Sponsorship Ways to Give ...

  7. Introduction to structure functions

    International Nuclear Information System (INIS)

    Kwiecinski, J.

    1996-07-01

    The theory of deep inelastic scattering structure functions is reviewed with an emphasis put on the QCD expectations of their behaviour in the region of small values of Bjorken parameter x. (author). 56 refs

  8. Bioprinting: Functional droplet networks

    Science.gov (United States)

    Durmus, Naside Gozde; Tasoglu, Savas; Demirci, Utkan

    2013-06-01

    Tissue-mimicking printed networks of droplets separated by lipid bilayers that can be functionalized with membrane proteins are able to spontaneously fold and transmit electrical currents along predefined paths.

  9. Center for Functional Nanomaterials

    Data.gov (United States)

    Federal Laboratory Consortium — The Center for Functional Nanomaterials (CFN) explores the unique properties of materials and processes at the nanoscale. The CFN is a user-oriented research center...

  10. density functional theory approach

    Indian Academy of Sciences (India)

    YOGESH ERANDE

    2017-07-27

    Jul 27, 2017 ... a key role in all optical switching devices, since their optical properties can be .... optimized in the gas phase using Density Functional Theory. (DFT).39 The ...... The Mediation of Electrostatic Effects by Sol- vents J. Am. Chem.

  11. Reasoning about Function Objects

    Science.gov (United States)

    Nordio, Martin; Calcagno, Cristiano; Meyer, Bertrand; Müller, Peter; Tschannen, Julian

    Modern object-oriented languages support higher-order implementations through function objects such as delegates in C#, agents in Eiffel, or closures in Scala. Function objects bring a new level of abstraction to the object-oriented programming model, and require a comparable extension to specification and verification techniques. We introduce a verification methodology that extends function objects with auxiliary side-effect free (pure) methods to model logical artifacts: preconditions, postconditions and modifies clauses. These pure methods can be used to specify client code abstractly, that is, independently from specific instantiations of the function objects. To demonstrate the feasibility of our approach, we have implemented an automatic prover, which verifies several non-trivial examples.

  12. Normal Functioning Family

    Science.gov (United States)

    ... Spread the Word Shop AAP Find a Pediatrician Family Life Medical Home Family Dynamics Adoption & Foster Care ... Español Text Size Email Print Share Normal Functioning Family Page Content Article Body Is there any way ...

  13. Fundamentals of functional analysis

    CERN Document Server

    Farenick, Douglas

    2016-01-01

    This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner,...

  14. Smooth functions statistics

    International Nuclear Information System (INIS)

    Arnold, V.I.

    2006-03-01

    To describe the topological structure of a real smooth function one associates to it the graph, formed by the topological variety, whose points are the connected components of the level hypersurface of the function. For a Morse function, such a graph is a tree. Generically, it has T triple vertices, T + 2 endpoints, 2T + 2 vertices and 2T + 1 arrows. The main goal of the present paper is to study the statistics of the graphs, corresponding to T triple points: what is the growth rate of the number φ(T) of different graphs? Which part of these graphs is representable by the polynomial functions of corresponding degree? A generic polynomial of degree n has at most (n - 1) 2 critical points on R 2 , corresponding to 2T + 2 = (n - 1) 2 + 1, that is to T = 2k(k - 1) saddle-points for degree n = 2k

  15. Structure function monitor

    Science.gov (United States)

    McGraw, John T [Placitas, NM; Zimmer, Peter C [Albuquerque, NM; Ackermann, Mark R [Albuquerque, NM

    2012-01-24

    Methods and apparatus for a structure function monitor provide for generation of parameters characterizing a refractive medium. In an embodiment, a structure function monitor acquires images of a pupil plane and an image plane and, from these images, retrieves the phase over an aperture, unwraps the retrieved phase, and analyzes the unwrapped retrieved phase. In an embodiment, analysis yields atmospheric parameters measured at spatial scales from zero to the diameter of a telescope used to collect light from a source.

  16. Sexual Function Across Aging.

    Science.gov (United States)

    Clayton, Anita H; Harsh, Veronica

    2016-03-01

    Women experience multiple changes in social and reproductive statuses across the life span which can affect sexual functioning. Various phases of the sexual response cycle may be impacted and can lead to sexual dysfunction. Screening for sexual problems and consideration of contributing factors such as neurobiology, reproductive life events, medical problems, medication use, and depression can help guide appropriate treatment and thereby improve the sexual functioning and quality of life of affected women. Treatment options include psychotropic medications, hormone therapy, and psychotherapy.

  17. Inequalities for Humbert functions

    Directory of Open Access Journals (Sweden)

    Ayman Shehata

    2014-04-01

    Full Text Available This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications.

  18. Functionally graded materials

    CERN Document Server

    Mahamood, Rasheedat Modupe

    2017-01-01

    This book presents the concept of functionally graded materials as well as their use and different fabrication processes. The authors describe the use of additive manufacturing technology for the production of very complex parts directly from the three dimension computer aided design of the part by adding material layer after layer. A case study is also presented in the book on the experimental analysis of functionally graded material using laser metal deposition process.

  19. [Functional (psychogenic) vertigo].

    Science.gov (United States)

    Diukova, G M; Zamergrad, M V; Golubev, V L; Adilova, S M; Makarov, S A

    Psychogenic (functional) vertigo is in second place by frequency after benign positional paroxysmal vertigo. It is often difficult to make the diagnosis, diagnostic program is expensive and traditional treatment often is not effective. This literature review covers current concepts on the terminology, clinical signs, pathogenesis and treatment approaches with regard to functional vertigo. Special attention is given to cerebral mechanisms of the pathogenesis including cognitive aspects.

  20. NEUROFEEDBACK USING FUNCTIONAL SPECTROSCOPY

    OpenAIRE

    Hinds, Oliver; Wighton, Paul; Tisdall, M. Dylan; Hess, Aaron; Breiter, Hans; van der Kouwe, André

    2014-01-01

    Neurofeedback based on real-time measurement of the blood oxygenation level-dependent (BOLD) signal has potential for treatment of neurological disorders and behavioral enhancement. Commonly employed methods are based on functional magnetic resonance imaging (fMRI) sequences that sacrifice speed and accuracy for whole-brain coverage, which is unnecessary in most applications. We present multi-voxel functional spectroscopy (MVFS): a system for computing the BOLD signal from multiple volumes of...