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Sample records for analytic function expansion

  1. A nonlinear analytic function expansion nodal method for transient calculations

    Energy Technology Data Exchange (ETDEWEB)

    Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1998-12-31

    The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

  2. Explicit transverse leakage treatment using an analytic basis function expansion

    International Nuclear Information System (INIS)

    An explicit method for calculating the transverse leakage is presented in this paper. The method is based upon the use of analytic basis functions, which represent individual eigenfunctions of the neutron diffusion equation. The intranodal flux solution is expressed as an eigenspace, and can be solved by using the already calculated surface currents and flux moments as boundary conditions. The salient feature of the method, therefore, is that no ad hoc presumptions are made with regard to the leakage shape. The individual eigenfunctions are calculated based upon already calculated parameters from the flux solution and response matrix solution, and therefore no additional parameters are introduced into the problem, which could lead to an unwanted increase in computation time. The new transverse leakage method is implemented in PSU's NEM code and is tested against the OECD/NEA 3D C5G7 rodded MOX benchmark and the C3 benchmark. (author)

  3. Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

    Energy Technology Data Exchange (ETDEWEB)

    Gao, Z. [Rice University, MS 318, 6100 Main Street, Houston, TX 77005 (United States); Xu, Y. [Argonne National Laboratory, 9700 South Case Ave., Argonne, IL 60439 (United States); Downar, T. [Department of Nuclear Engineering, University of Michigan, 2355 Bonisteel blvd., Ann Arbor, MI 48109 (United States)

    2013-07-01

    Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

  4. Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

    International Nuclear Information System (INIS)

    Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

  5. Use of analytic functions and polynomials within the framework of nodal expansion method

    International Nuclear Information System (INIS)

    A method using one-dimensional flux approximation expressed in terms of polynomials and hyperbolic functions was derived and the accuracy of the method was explored. This method called SANEM(Semi-Analytic Nodal Expansion Method) employs the same transverse leakage approximation used in NEM(Nodal Expansion Method) and flux moment balance equations to find coupling coefficients in current continuity equation. An one-dimensional flux approximation is expressed in the second order/the third order/the fourth order polynomials combined with hyperbolic functions for which several weighting functions are applied and the accuracy of methods were compared. This method has advantages of minimizing memory increase and easy implementation to a nodal code based on the conventional NEM. Benchmark calculations for the code were performed using problems such as IAEA 3D problem, NEACRP-L336 problem and EPRI-9R problem. Results show that both reactivity and assembly power density prediction by the SANEM is better than NEM for NEACRP-L336 problem, which uses MOX fuel, EPRI-9R problem, which shows characteristics of assembly in core periphery. A step function weighting applied to the third order polynomial expansion of a one-dimensional flux approximation produced better results than the polynomial weighting applied to the third order polynomial expansion for IAEA 3D problem. Furthermore, Galerkin weighting applied to the fourth order polynomial expansion shows worse results than polynomial weighting applied to the third order polynomial expansion for IAEA 3D, NEACRP-L336 and EPRI-9R problems

  6. A fast converging CMFD nonlinear iteration scheme for two-node analytic function expansion nodal methodology

    International Nuclear Information System (INIS)

    The nonlinear finite difference method (FDM) iterative scheme has been widely used as an alternative way to the core-wise response matrix formalism in modern nodal methods. This scheme turned out to be very effective in minimizing memory requirement and computing time associated with higher-order nodal methods. This conventional nonlinear FDM iterative scheme uses the modified FDM current definition with a nonlinear correction factor at an interface between two nodes. Determining the nonlinear correction factor so that the interface current should preserve the value of a higher-order nodal method makes the solution of this finite difference scheme equivalent to that of the higher-order nodal method itself. For the nonlinear FDM iterative scheme with the usual higher-order nodal methods that use the transverse-integration, this is done by solving two-node problems consisting of neighboring nodes periodically after a specified number of outer iterations of the FDM routine. Using the higher-order nodal method, the two-node problem is solved for the interface current of the two nodes with currently available node-average fluxes and transverse-leakage shapes of both nodes as boundary conditions. The nonlinear correction factor at the interface is updated by equating the resultant higher-order interface current with the modified FDM current. Then, the FDM routine is continued utilizing the updated nonlinear correction factor. The entire process is repeated until convergence of the effective multiplication factor and the node average fluxes is achieved. In this study, as an acceleration means and for the convenience of its implementation into existing FDM codes, we develop a nonlinear iterative scheme for the analytic function expansion nodal (AFEN) method. Developing a nonlinear iterative scheme for the AFEN method is not straightforward, because this method needs higher-order accurate interface and corner-point fluxes as well as interface currents in solving the two

  7. New analytic function expansion nodal (AFEN) method for solving multigroup neutron simplified P3 (SP3) equations

    International Nuclear Information System (INIS)

    Highlights: • A new AFEN code, MGANSP3, is developed for simplified P3 (SP3) calculations. • Surface averaged partial currents are used for coupling the nodes. • Coarse group rebalancing method is applied to increase the speed of calculations. • Four benchmark problems are used to examine the accuracy of the MGANSP3 code. - Abstract: In this study, a new analytic function expansion nodal (AFEN) method was developed to solve multi-group and three dimensional neutron simplified P3 equations (SP3) in reactor cores with rectangular fuel assemblies. In this method, the intranodal fluxes are expanded into a set of analytic basis functions for each group and moment. The nodes are coupled through the surface averaged partial currents at each nodal interface. Thus, six boundary conditions at each group and Legendre moments have been considered. Coarse group rebalancing (CGR) method was applied to increase the speed of code calculations. The code takes few-groups cross sections produced by a lattice code such as WIMS and calculates the effective multiplication factor, zeroth and second moments of the flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. The numerical results for different benchmark problems demonstrate that solution of SP3 equations by our AFEN method improves both effective multiplication factor (keff) and power distribution compared to our AFEN diffusion method, especially in heterogeneous geometry and mixed-oxide (MOX) fuel problems

  8. Development of a kinetics code in three-dimensional hexagonal geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    During the last decade, the analytic function expansion nodal (AFEN) method has been developed and successfully applied to the static and kinetic problems in rectangular geometry and also applied to the static problems in hexagonal geometry. Although the results of two-dimensional hexagonal problems were very accurate, the accuracy becomes poor when the current hexagonal-z method is applied to the three-dimensional hexagonal problems. In this thesis, we develop a new method which improves the accuracy in three-dimensional hexagonal geometry and computerize the method into a new kinetics code. At first we add the edge fluxes in the upper and lower planes as additional nodal unknowns in axial direction to improve the accuracy. These nodal unknowns are updated through leakage balance equations by using a simple expansion of nodal fluxes at the vicinity of the edge fluxes. The relation of delayed neutron precursor densities between time steps is obtained analytically by using the transformed fluxes and assuming linear variations of the fission rates within a time step. The code developed for the steady state is verified in the cases of 2-D VVER-1000, 3-D SNR-300, and 3-D VVER-440 benchmark problems. The results of the static problems show higher accuracy than those of the original formulations in hexagonal geometry. Finally, a kinetics code is developed and tested by introducing step changes of nodal cross sections for the VVER-440 benchmark problem. The results appear to be accurate enough for this code to be useful for analyzing realistic three-dimensional hexagonal reactors

  9. Development of a code in three-dimensional cylindrical geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)

  10. The analytic function expansion nodal (AFEN) method with half-interface averaged fluxes in mixed geometry nodes for analysis of pebble bed modular reactor (PBMR) cores

    International Nuclear Information System (INIS)

    The analytic function expansion nodal (AFEN) method has been successfully applied to the rectangular and hexagonal geometries in the cartesian coordinates system. In this paper, we extended the AFEN method to the cylindrical geometry in the R-Z coordinates for the analysis of pebble bed modular reactors (PBMRs). To treat the mixed geometry of rectangular and triangular nodes appearing in the lower periphery of the reactors, we used half-interface averaged fluxes as nodal unknowns. Numerical results obtained attest to their accuracy and applicability to practical problems. (author)

  11. Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry

    Energy Technology Data Exchange (ETDEWEB)

    Jalili Bahabadi, Mohammad Hasan; Pazirandeh, Ali; Athari, Mitra [Islamic Azad Univ., Tehran (Iran, Islamic Republic of). Dept. of Nuclear Engineering, Science and Research Branch

    2015-12-15

    In this paper, we developed a new approach of analytic function expansion nodal (AFEN) method to solve the multi-group and multi-dimensional neutron diffusion equation in reactor cores with hexagonal fuel assembly. This method represents a multidimensional intra nodal flux distribution in terms of analytic basis functions at any points in the node. New types of boundary conditions have been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. We utilized the coarse group rebalancing (CGR) method to increase the speed of code calculations. The computer code takes a few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (k{sub eff}), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for two well-known benchmark problems. The numerical results demonstrate that the new AFEN method is an accurate method for calculating k{sub eff} and power density distribution in hexagonal-z geometries.

  12. Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry

    International Nuclear Information System (INIS)

    In this paper, we developed a new approach of analytic function expansion nodal (AFEN) method to solve the multi-group and multi-dimensional neutron diffusion equation in reactor cores with hexagonal fuel assembly. This method represents a multidimensional intra nodal flux distribution in terms of analytic basis functions at any points in the node. New types of boundary conditions have been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. We utilized the coarse group rebalancing (CGR) method to increase the speed of code calculations. The computer code takes a few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (keff), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for two well-known benchmark problems. The numerical results demonstrate that the new AFEN method is an accurate method for calculating keff and power density distribution in hexagonal-z geometries.

  13. Extended Analytic Device Optimization Employing Asymptotic Expansion

    Science.gov (United States)

    Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred

    2013-01-01

    Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

  14. Asymptotic expansions of Jacobi functions

    International Nuclear Information System (INIS)

    The author presents an asymptotic expansion of the Jacobi polynomials which is based on the fact, that these polynomials are special hypergeometric functions. He uses an integral representation of these functions and expands the integrand in a power series. He derives explicit error bounds on this expansion. (HSI)

  15. Some elements of a theory of multidimensional complex variables. I - General theory. II - Expansions of analytic functions and application to fluid flows

    Science.gov (United States)

    Martin, E. Dale

    1989-01-01

    The paper introduces a new theory of N-dimensional complex variables and analytic functions which, for N greater than 2, is both a direct generalization and a close analog of the theory of ordinary complex variables. The algebra in the present theory is a commutative ring, not a field. Functions of a three-dimensional variable were defined and the definition of the derivative then led to analytic functions.

  16. An analytical model for the assessment of airline expansion strategies

    OpenAIRE

    Mauricio Emboaba Moreira

    2014-01-01

    Purpose: The purpose of this article is to develop an analytical model to assess airline expansion strategies by combining generic business strategy models with airline business models. Methodology and approach: A number of airline business models are examined, as are Porter’s (1983) industry five forces that drive competition, complemented by Nalebuff/ Brandenburger’s  (1996) sixth force, and the basic elements of the general environment in which the expansion process takes place.  A system ...

  17. An analytical model for the assessment of airline expansion strategies

    Directory of Open Access Journals (Sweden)

    Mauricio Emboaba Moreira

    2014-01-01

    Full Text Available Purpose: The purpose of this article is to develop an analytical model to assess airline expansion strategies by combining generic business strategy models with airline business models. Methodology and approach: A number of airline business models are examined, as are Porter’s (1983 industry five forces that drive competition, complemented by Nalebuff/ Brandenburger’s  (1996 sixth force, and the basic elements of the general environment in which the expansion process takes place.  A system of points and weights is developed to create a score among the 904,736 possible combinations considered. The model’s outputs are generic expansion strategies with quantitative assessments for each specific combination of elements inputted. Originality and value: The analytical model developed is original because it combines for the first time and explicitly elements of the general environment, industry environment, airline business models and the generic expansion strategy types. Besides it creates a system of scores that may be used to drive the decision process toward the choice of a specific strategic expansion path. Research implications: The analytical model may be adapted to other industries apart from the airline industry by substituting the element “airline business model” by other industries corresponding elements related to the different specific business models.

  18. Normality of Composite Analytic Functions and Sharing an Analytic Function

    OpenAIRE

    Xiao Bing; Yuan Wenjun; Wu Qifeng

    2010-01-01

    A result of Hinchliffe (2003) is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let be an analytic function, a family of analytic functions in a domain , and a transcendental entire function. If and share IM for each pair , and one of the following conditions holds: (1) has at least two distinct zeros for any ; (2) is nonconstant, and there exists such that has only one distinct zero , and su...

  19. Banach spaces of analytic functions

    CERN Document Server

    Hoffman, Kenneth

    2007-01-01

    A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f

  20. Note on trigonometric expansions of theta functions

    Science.gov (United States)

    Chouikha, A. Raouf

    2003-04-01

    We are interested in properties of coefficients of certain expansions of the classical theta functions. We show that they are solutions of a differential system derived from the heat equation. We plan to explicitly give expressions of these coefficients.

  1. Oblique photon expansion of QED structure functions

    International Nuclear Information System (INIS)

    In the oblique photon expansion, the collinear part of photon emission is summed up to all orders in perturbation theory. The number of oblique or non-collinear photons is the expansion order. Unlike in perturbation theory, every term of the expansion is both infrared finite and gauge invariant. The zero oblique photon contribution to the electromagnetic structure tensor in QED is computed in detail. The behaviors of the structure functions F1 and F2 are discussed in the soft and ultra-soft limits

  2. Analytical potential energy function for the Br + H2 system

    International Nuclear Information System (INIS)

    Analytical functions with a many-body expansion for the ground and first-excited-state potential energy surfaces for the Br+H2 system are newly presented in this work. These functions describe the abstraction and exchange reactions qualitatively well, although it has been found that the function for the ground-state potential surface is still quantitatively unsatisfactory. (author)

  3. On -Functions for Laguerre Function Expansions of Hermite Type

    Indian Academy of Sciences (India)

    Błażej Jan Wróbel

    2011-02-01

    We examine weighted $L^p$ boundedness of -functions based on semi-groups related to multi-dimensional Laguerre function expansions of Hermite type. A technique of vector-valued Calderón–Zygmund operators is used.

  4. A two-dimensional, semi-analytic expansion method for nodal calculations

    International Nuclear Information System (INIS)

    Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure

  5. Harmonic function expansion of nearly oblate systems

    CERN Document Server

    Syer, D

    1995-01-01

    We show how to develop an expansion of nearly oblate systems in terms of a set of potential-density pairs. A harmonic (multipole) structure is imposed on the potential set at infinity, and the density can be made everywhere regular. We concentrate on a set whose zeroth order functions describe the perfect oblate spheroid of de Zeeuw (1985). This set is not bi-orthogonal, but it can be shown to be complete in a weak sense. Poisson's equation can be solved approximately by truncating the expansion of the potential in such a set. A simple example of a potential which is not one of the basis functions is expanded using the symmetric members of the basis set up to fourth order. The basis functions up to first order are reconstructed approximately using 10,000 particles to show that this set could be used as part of an N-body code.

  6. Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

    CERN Document Server

    Kavanagh, Chris; Wardell, Barry

    2015-01-01

    We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of $\\ell$, and in doing so develop an efficient new method for generating the MST renormalised angular momentum, $\

  7. Space expansion and bicubic spline function approximation of magnetic field with median plane symmetry

    International Nuclear Information System (INIS)

    The space expansion of magnetic field with median plane symmetry in Taylor series is derived in cylindrical coordinate system. The expansion is expressed with the field distribution in the median plane, which may be an analytic expression or the field values at the discrete nodes. The discrete values are fitted with bicubic spline functions and the corresponding computer program is also given

  8. A Functional Analytic Approach to Group Psychotherapy

    Science.gov (United States)

    Vandenberghe, Luc

    2009-01-01

    This article provides a particular view on the use of Functional Analytical Psychotherapy (FAP) in a group therapy format. This view is based on the author's experiences as a supervisor of Functional Analytical Psychotherapy Groups, including groups for women with depression and groups for chronic pain patients. The contexts in which this approach…

  9. Edgeworth expansion for functionals of continuous diffusion processes

    DEFF Research Database (Denmark)

    Podolskij, Mark; Yoshida, Nakahiro

    2016-01-01

    This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the second order Edgeworth expansion for power variation of...... diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations....

  10. Edgeworth expansion for functionals of continuous diffusion processes

    DEFF Research Database (Denmark)

    Podolskij, Mark; Yoshida, Nakahiro

    This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes....... Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations....

  11. Analytical model for intergrain expansion and cleavage: random grain boundaries

    International Nuclear Information System (INIS)

    A description of rigid-body grain boundary relaxation and cleavage in tungsten is performed using a pair-wise Morse interatomic potential in real and reciprocal spaces. Cleavage energies and grain boundary dilatation of random grain boundaries were formulated and computed using atomic layer interaction energies. These values were determined using a model for a relaxed random grain boundary that consists of rigid grains on either side of the boundary plane that are allowed to float to reach the equilibrium position. Expressions are given that describe in real space the energy of interatomic interaction on random grain boundaries with twist orientation. It was shown that grain-boundary expansion and cleavage energies of the most widespread random grain boundaries are mainly determined by grain boundary atomic density

  12. Identification and properties of the fundamental expansion functions for neutron transport in an infinite homogeneous medium

    Energy Technology Data Exchange (ETDEWEB)

    Milgram, Michael S. [P.O. Box 1484, Deep River, Ont., K0J 1P0 (Canada)]. E-mail: mike@geometrics-unlimited.com

    2005-07-15

    Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.

  13. Explicit functions of a trigonometric series expansion of the coordinates of a perturbing body.

    Science.gov (United States)

    Emel'Yanov, N. V.

    The problem of trigonometric series expansion of a perturbing body representing coordinates as time explicit functions and occurring in the satellite motion theory and in the Earth's and Moon's rotation theories is considered. The coefficients of the series are linear in time. A specialized programming system for analytical operations with the series has been constructed. The expansions of the searched functions for the theory of satellite motion are obtained.

  14. 2D XXZ model ground state properties using an analytic Lanczos expansion

    International Nuclear Information System (INIS)

    A formalism was developed for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the t-expansion, and spin-wave theory and series expansion methods. It was found that far from the isotropic point all moment methods give essentially very similar results, but near the isotopic point the plaquette expansion is generally better than the others. 20 refs., 6 tabs

  15. Analytical method for estimating the thermal expansion coefficient of metals at high temperature

    International Nuclear Information System (INIS)

    In this paper, we propose an analytical method for estimating the thermal expansion coefficient (TEC) of metals at high-temperature ranges. Although the conventional method based on quasiharmonic approximation (QHA) shows good results at low temperatures, anharmonic effects caused by large-amplitude thermal vibrations reduces its accuracy at high temperatures. Molecular dynamics (MD) naturally includes the anharmonic effect. However, since the computational cost of MD is relatively high, in order to make an interatomic potential capable of reproducing TEC, an analytical method is essential. In our method, analytical formulation of the radial distribution function (RDF) at finite temperature realizes the estimation of the TEC. Each peak of the RDF is approximated by the Gaussian distribution. The average and variance of the Gaussian distribution are formulated by decomposing the fluctuation of interatomic distance into independent elastic waves. We incorporated two significant anharmonic effects into the method. One is the increase in the averaged interatomic distance caused by large amplitude vibration. The second is the variation in the frequency of elastic waves. As a result, the TECs of fcc and bcc crystals estimated by our method show good agreement with those of MD. Our method enables us to make an interatomic potential that reproduces the TEC at high temperature. We developed the GEAM potential for nickel. The TEC of the fitted potential showed good agreement with experimental data from room temperature to 1000 K. As compared with the original potential, it was found that the third derivative of the wide-range curve was modified, while the zeroth, first and second derivatives were unchanged. This result supports the conventional theory of solid state physics. We believe our analytical method and developed interatomic potential will contribute to future high-temperature material development. (paper)

  16. Functional integrals and 1/h expansion in the boson-fermion model

    Science.gov (United States)

    Yan, Jun

    2016-06-01

    The effective action of boson-fermion model is derived by means of the functional integrals method and Popov-Faddeev canonical transformations. The energy gap equation and excitation spectrum equation are obtained from first order and second order perturbation expansions of functional determinant. In the long wave approximation, some analytical expressions of excitation spectrum are calculated by using the 1/h expansion technique, the results showed that analytical calculation is in good agreement with the numerical calculation. Moreover, the Nambu sum rules of Higgs bosons are analyzed and discussed.

  17. [Contributions and novelties from Functional Analytic Psychotherapy].

    Science.gov (United States)

    Ferro García, Rafael; Valero Aguayo, Luis; López Bermúdez, Miguel A

    2007-08-01

    Functional Analytic Psychotherapy is based on the principles of radical behaviourism. It emphasises the impact of events occurring during therapeutic sessions, the therapist-client interaction context, functional equivalence of environments, natural reinforcement, and shaping by the therapist. Functional Analytic Psychotherapy makes use of both the basic principles of behaviour analysis: individual functional assessment and application of in vivo treatment. This paper analyses novelties and new contributions of this therapy. New contributions are classified in various categories: integration with other psychotherapies, improvement of therapeutic skills, methods for evaluation and data recording in therapy, its application to several clinical problems, and studies of its efficacy. PMID:17617985

  18. Discrete expansions of continuum Wave functions. Numerical examples

    International Nuclear Information System (INIS)

    This work is the end of two series of papers dealing with discrete expansions of continuum wave functions in a finite region. The convergence of the Weinberg expansions for S,K-matrices, continuum wave functions are investigated numerically. The case of continuum single particle states for Wood-Saxon and square well potentials is considered. Some numerical methods for solving the eigenvalue problems, corresponding to different expansions, are discussed

  19. Series Expansion of Functions with He's Homotopy Perturbation Method

    Science.gov (United States)

    Khattri, Sanjay Kumar

    2012-01-01

    Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…

  20. Analytical Properties of Credibilistic Expectation Functions

    OpenAIRE

    Shuming Wang; Bo Wang; Junzo Watada

    2014-01-01

    The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expect...

  1. On Approximate Analytical Solutions of Nonlinear Vibrations of Inextensible Beams using Parameter-Expansion Method

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo; Barari, Amin

    2010-01-01

    In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which is...... valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....

  2. An approximate analytical solution of free convection problem for vertical isothermal plate via transverse coordinate Taylor expansion

    CERN Document Server

    Leble, Sergey

    2013-01-01

    The model under consideration is based on approximate analytical solution of two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations. Approximations are based on the typical for natural convection assumptions: the fluid noncompressibility and Bousinesq approximation. We also assume that ortogonal to the plate component (x) of velocity is neglectible small. The solution of the boundary problem is represented as a Taylor Series in $x$ coordinate for velocity and temperature which introduces functions of vertical coordinate (y), as coefficients of the expansion. The correspondent boundary problem formulation depends on parameters specific for the problem: Grashoff number, the plate height (L) and gravity constant. The main result of the paper is the set of equations for the coefficient functions for example choice of expansion terms number. The nonzero velocity at the starting point of a flow appears in such approach as a development of convecntional boundary layer theory formulation.

  3. Promoting Efficacy Research on Functional Analytic Psychotherapy

    Science.gov (United States)

    Maitland, Daniel W. M.; Gaynor, Scott T.

    2012-01-01

    Functional Analytic Psychotherapy (FAP) is a form of therapy grounded in behavioral principles that utilizes therapist reactions to shape target behavior. Despite a growing literature base, there is a paucity of research to establish the efficacy of FAP. As a general approach to psychotherapy, and how the therapeutic relationship produces change,…

  4. A unified intrinsic functional expansion theory for solitary waves

    Institute of Scientific and Technical Information of China (English)

    Theodore Yaotsu Wu; John Kao; Jin E. Zhang

    2005-01-01

    A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120° down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokes's formula, F2μπ = tanμπ, relating the wave speed (the Froude number F) and the logarithmic decrement μ of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokes's basic term (singular inμ), such that 2Mμ is just somewhat beyond unity, i.e. 2Mμ (~-) 1. This fundamental criterion is fully validated by solutions for waves Dedicated to Zhemin Zheng for celebration of his Eightieth Anniversary It gives us a great pleasure to dedicate this study to Prof. Zhemin Zheng and join our distinguished colleagues and friends for the jubilant celebration of his Eightieth Anniversary. Warmest tribute is due from us, as from many others unlimited by borders and boundaries, for his contributions of great significance to science, engineering science and engineering, his tremendous influence as a source of inspiration and unerring guide to countless workers in the field, his admirable leadership in fostering the Institute of Mechanics of world renown, as well as for his untiring endeavor in promoting international interaction and cooperation between academies of various nations

  5. On the analytical development of the lunar and solar disturbing functions

    CERN Document Server

    Celletti, Alessandra; Pucacco, Giuseppe; Rosengren, Aaron J

    2015-01-01

    We provide a detailed derivation of the analytical expansion of the lunar and solar disturbing functions. We start with Kaula's expansion of the disturbing function in terms of the equatorial elements of both the perturbed and perturbing bodies. Then we provide a detailed proof of Lane's expansion, in which the elements of the Moon are referred to the ecliptic plane. Using this approach the inclination of the Moon becomes nearly constant, while the argument of perihelion, the longitude of the ascending node, and the mean anomaly vary linearly with time. We make a comparison between the different expansions and we profit from such discussion to point out some mistakes in the existing literature, which might compromise the correctness of the results. As an application, we analyze the long-term motion of the highly elliptical and critically inclined Molniya orbits subject to quadrupolar gravitational interactions. The analytical expansions presented herein are very powerful with respect to dynamical studies base...

  6. Analytical Properties of Credibilistic Expectation Functions

    Science.gov (United States)

    Wang, Bo; Watada, Junzo

    2014-01-01

    The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained. PMID:24723800

  7. The QCD analysis of xF_3 structure function based on the analytic approach

    OpenAIRE

    Sidorov, A. V.; Solovtsova, O. P.

    2013-01-01

    We apply analytic perturbation theory to the QCD analysis of the xF_3 structure function data of the CCFR collaboration. We use different approaches for the leading order Q^2 evolution of the xF_3 structure function and compare the extracted values of the parameter Lambda_QCD and the shape of the higher twistcontribution. Our consideration is based on the Jacobi polynomial expansion method of the unpolarized structure function. The analysis shows that the analytic approach provides reasonable...

  8. Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

    Institute of Scientific and Technical Information of China (English)

    甄明; 蒋志刚; 宋殿义; 刘飞

    2014-01-01

    Analytical solutions for the dynamic cylindrical cavity expansion in a com-pressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expan-sion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal’s similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.

  9. CARATHEODORY INEQUALITY FOR ANALYTIC OPERATOR FUNCTION

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Suppose H is a complex Hilbert space, AH(△) denotes the set of all analytic operator functions on △, and the set NH(△)= {f(z)|f(z) is an analytic operator function on the open uint disk △, f(z)f(ω)=f(ω)f(z),f*(z)f(z)=f(z)f*(z), z,ω∈△}. The note proves that if f(z)∈NH(△),(or AH(△) )‖f(z)‖≤1, z∈△ then ‖f'(T)‖≤(1-‖T‖2)-1‖I-f*(T)f(T)‖1/2‖I-f(T)f*(T)‖1/2,where T ∈ (H)(orT*T=TT*,respectively),‖T‖<1,Tf=fT.

  10. Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions

    Indian Academy of Sciences (India)

    BISWAJYOTI SAHA

    2016-08-01

    For an arithmetical function $f$ with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the $\\sum_{n\\leq N}$ f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.

  11. Functional expansion representations of artificial neural networks

    Science.gov (United States)

    Gray, W. Steven

    1992-01-01

    In the past few years, significant interest has developed in using artificial neural networks to model and control nonlinear dynamical systems. While there exists many proposed schemes for accomplishing this and a wealth of supporting empirical results, most approaches to date tend to be ad hoc in nature and rely mainly on heuristic justifications. The purpose of this project was to further develop some analytical tools for representing nonlinear discrete-time input-output systems, which when applied to neural networks would give insight on architecture selection, pruning strategies, and learning algorithms. A long term goal is to determine in what sense, if any, a neural network can be used as a universal approximator for nonliner input-output maps with memory (i.e., realized by a dynamical system). This property is well known for the case of static or memoryless input-output maps. The general architecture under consideration in this project was a single-input, single-output recurrent feedforward network.

  12. Approximation of Analytic Functions by Bessel's Functions of Fractional Order

    Directory of Open Access Journals (Sweden)

    Soon-Mo Jung

    2011-01-01

    Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

  13. Approximation of Analytic Functions by Bessel's Functions of Fractional Order

    OpenAIRE

    Soon-Mo Jung

    2011-01-01

    We will solve the inhomogeneous Bessel's differential equation x2y″(x)+xy′(x)+(x2-ν2)y(x)=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

  14. Analytical method of load-transfer of single pile under expansive soil swelling

    Institute of Scientific and Technical Information of China (English)

    FAN Zhen-hui; WANG Yong-he; XIAO Hong-bin; ZHANG Chun-shun

    2007-01-01

    The elastic differential equations of load-transfer of single pile either with applied loads on pile-top or only under the soil swelling were established, respectively, based on the theory of pile-soil interaction and the shear-deformation method. The derivation of analytic solution to load-transfer for single pile in expansive soil could hereby be obtained by means of superposition principle under expansive soils swelling. The comparison of two engineering examples was made to prove the credibility of the suggested method. The analyzed results show that this analytic solution can achieve high precision with few parameters required, indicating its' simplicity and practicability in engineering application. The employed method can contribute to determining the greatest tension along pile shaft resulting from expansive soils swelling and provide reliable bases for engineering design. The method can be employed to obtain various distributive curves of axial force, settlements and skin friction along the pile shaft with the changes of active depth, vertical movements of the surface and loads of pile-top.

  15. A Secure Hash Function MD-192 With Modified Message Expansion

    OpenAIRE

    Harshvardhan Tiwari; Dr. Krishna Asawa

    2010-01-01

    Cryptographic hash functions play a central role in cryptography. Hash functions were introduced in cryptology to provide message integrity and authentication. MD5, SHA1 and RIPEMD are among the most commonly used message digest algorithm. Recently proposed attacks on well known and widely used hash functions motivate a design of new stronger hash function. In this paper a new approach is presented that produces 192 bit message digest and uses a modified message expansion mechanism which gene...

  16. Using Fourier and Taylor series expansion in semi-analytical deformation analysis of thick-walled isotropic and wound composite structures

    Directory of Open Access Journals (Sweden)

    Jiran L.

    2016-06-01

    Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.

  17. A Green's function nodal expansion method for LWR diffusion calculation

    International Nuclear Information System (INIS)

    A Green's Function Nodal Expansion Method (GNEM) has been developed for the efficient numerical solution of the LWR multi-dimensional neutron diffusion equation. It is an improved version of Nodal Expansion Method (NEM) and Nodal Green's Function Method (NGFM). The code interior fluxes are approximated by a high order polynomial expansion as in NEM. The nodal surface fluxes are coupled with the net currents by using the Green's function method to improve the accuracy. A computer code GNEM has been developed and tested. The numerical results demonstrate that GNEM has the same accuracy as NGFM, while it is twice as fast as NGFM. Especially, the numerical results of TMI-1 core depletion cycles 1 and 6 demonstrate that GNEM is about two times faster than ADMARC and possesses better accuracy

  18. Ising n-fold integrals as diagonals of rational functions and integrality of series expansions

    International Nuclear Information System (INIS)

    We show that the n-fold integrals χ(n) of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the ‘Ising class’, or n-fold integrals from enumerative combinatorics, like lattice Green functions, correspond to a distinguished class of functions generalizing algebraic functions: they are actually diagonals of rational functions. As a consequence, the power series expansions of the, analytic at x = 0, solutions of these linear differential equations ‘derived from geometry’ are globally bounded, which means that after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. We also give several results showing that the unique analytical solution of Calabi–Yau ODEs and, more generally, Picard–Fuchs linear ODEs with solutions of maximal weights are always diagonals of rational functions. Besides, in a more enumerative combinatorics context, generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity of ODEs. (paper)

  19. ON STEIN-WEISS CONJUGATEHARMONIC FUNCTION ANDOCTONION ANALYTIC FUNCTION

    Institute of Scientific and Technical Information of China (English)

    Li Xingmin; Peng Lizhong

    2000-01-01

    It is shown that the Stein-Weiss conjugate harmonic funciton is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].

  20. Expansion Formulae for the Kampe De Feriet Function Involving Bessel Function

    Directory of Open Access Journals (Sweden)

    A. D. Wadhwa

    1971-01-01

    Full Text Available In this paper some integrals involving a Kampe de Feriet; function have been evaluated. These have been used to establish some expansion formulae for the Kampe de Feriet function involving Bessel function.

  1. A Secure Hash Function MD-192 With Modified Message Expansion

    CERN Document Server

    Tiwari, Harshvardhan

    2010-01-01

    Cryptographic hash functions play a central role in cryptography. Hash functions were introduced in cryptology to provide message integrity and authentication. MD5, SHA1 and RIPEMD are among the most commonly used message digest algorithm. Recently proposed attacks on well known and widely used hash functions motivate a design of new stronger hash function. In this paper a new approach is presented that produces 192 bit message digest and uses a modified message expansion mechanism which generates more bit difference in each working variable to make the algorithm more secure. This hash function is collision resistant and assures a good compression and preimage resistance.

  2. Schur function expansions of KP tau functions associated to algebraic curves

    OpenAIRE

    Enolski, V.; Harnad, J.

    2010-01-01

    The Schur function expansion of Sato-Segal-Wilson KP tau-functions is reviewed. The case of tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Pl\\"ucker coordinate coefficients appearing in the expansion are obtained in terms of directional derivatives of the Riemann theta function or Klein sigma function along the KP flow directions. Using the fundamental bi-differential, it is shown how the coefficients can be expressed as polynom...

  3. General post-Minkowskian expansion of time transfer functions

    CERN Document Server

    Teyssandier, Pierre

    2008-01-01

    Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant $G$ (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

  4. On summability of eigenfunction expansions of piecewise smooth functions

    International Nuclear Information System (INIS)

    We consider two forms of eigenfunction expansions associated with an arbitrary elliptic differential operator with constant coefficients and order m, that is the multiple Fourier series and integrals. For the multiple Fourier integrals we prove the convergence of the Riesz means of order s > (N - 3)/2 of piecewise smooth functions of N ≥ 2 variables. The same result is proved in the case of the N ≥ 3 dimensional multiple Fourier series. (author)

  5. ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    LiuXinhe

    2003-01-01

    Let r be a given positive number.Denote by D=D the closed disc in the complex plane C whose center is the origin and radius is r.For any subset K of C and any integer m ≥1,write A(Dm,K)={f|f:Dm→Kis a continuous map,and f|(Dm)*is analytic).For H∈A(Dm,C)(m≥2),f∈A(D,D)and z∈D,write ψH(f)(z)=H(z,f(z)……fm=1(x)).Suppose F,G∈A(D2n+1,C),and Hk,Kk∈A(Dk,C),k=2,……,n.In this paper,the system of functional equations {F(z,f(z),f2(ψHz(f)(z))…,fn(ψk2(g)(x))… gn(ψKn(g)(z)))=0 G(z,f(z),f2(ψH2(f)(z))…fn(ψHn(f)(z)),g(z),g2(ψk2(g)(x))…,gn(ψkn(g)(z)))=0(z∈D)is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A(D,D)are given.

  6. A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

    Institute of Scientific and Technical Information of China (English)

    C.F. Yu; K. Yan; D.Z. Liu

    2006-01-01

    Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of fuce-centered cubic (fcc) metals - Al, Cu, Ag, etc. Are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

  7. Selecting the projection functions used in an iterative Gabor expansion

    Science.gov (United States)

    Braithwaite, R. N.; Beddoes, Michael P.

    1993-11-01

    This paper discusses the selection of projection functions used in an iterative implementation of the Gabor expansion. We show that the optimal support-limited projection function corresponds to a truncated version of Bastiaans' biorthonormal projection function for the case of a harmonic lattice. For various support widths, the lower bound of the optimal convergence factor is calculated. It is shown that Gabor's original projection function, which corresponds to the central lobe of Bastiaans' biorthonormal projection function, is truncated too severely, producing a significant overlap with elementary functions from high frequency channels. As a result, the lower bound for the optimal convergence factor and the rate of convergence will approach zero as the signal bandwidth (and the highest frequency Gabor channel) is increased. This work also determines the lower bound of the optimal convergence factor for projection functions implemented using log-polar lattices. For both the harmonic and log-polar lattices, we investigate the trade-off between spread of convergence and the size of the projection function.

  8. Neural substrate expansion for the restoration of brain function

    Directory of Open Access Journals (Sweden)

    Han-Chiao Isaac Chen

    2016-01-01

    Full Text Available Restoring neurological and cognitive function in individuals who have suffered brain damage is one of the principal objectives of modern translational neuroscience. Electrical stimulation approaches, such as deep-brain stimulation, have achieved the most clinical success, but they ultimately may be limited by the computational capacity of the residual cerebral circuitry. An alternative strategy is brain substrate expansion, in which the computational capacity of the brain is augmented through the addition of new processing units and the reconstitution of network connectivity. This latter approach has been explored to some degree using both biological and electronic means but thus far has not demonstrated the ability to reestablish the function of large-scale neuronal networks. In this review, we contend that fulfilling the potential of brain substrate expansion will require a significant shift from current methods that emphasize direct manipulations of the brain (e.g., injections of cellular suspensions and the implantation of multi-electrode arrays to the generation of more sophisticated neural tissues and neural-electric hybrids in vitro that are subsequently transplanted into the brain. Drawing from neural tissue engineering, stem cell biology, and neural interface technologies, this strategy makes greater use of the manifold techniques available in the laboratory to create biocompatible constructs that recapitulate brain architecture and thus are more easily recognized and utilized by brain networks.

  9. Neural Substrate Expansion for the Restoration of Brain Function.

    Science.gov (United States)

    Chen, H Isaac; Jgamadze, Dennis; Serruya, Mijail D; Cullen, D Kacy; Wolf, John A; Smith, Douglas H

    2016-01-01

    Restoring neurological and cognitive function in individuals who have suffered brain damage is one of the principal objectives of modern translational neuroscience. Electrical stimulation approaches, such as deep-brain stimulation, have achieved the most clinical success, but they ultimately may be limited by the computational capacity of the residual cerebral circuitry. An alternative strategy is brain substrate expansion, in which the computational capacity of the brain is augmented through the addition of new processing units and the reconstitution of network connectivity. This latter approach has been explored to some degree using both biological and electronic means but thus far has not demonstrated the ability to reestablish the function of large-scale neuronal networks. In this review, we contend that fulfilling the potential of brain substrate expansion will require a significant shift from current methods that emphasize direct manipulations of the brain (e.g., injections of cellular suspensions and the implantation of multi-electrode arrays) to the generation of more sophisticated neural tissues and neural-electric hybrids in vitro that are subsequently transplanted into the brain. Drawing from neural tissue engineering, stem cell biology, and neural interface technologies, this strategy makes greater use of the manifold techniques available in the laboratory to create biocompatible constructs that recapitulate brain architecture and thus are more easily recognized and utilized by brain networks. PMID:26834579

  10. An analytic study of TTF of standing wave RF gap based on Bessel–Fourier expansion

    International Nuclear Information System (INIS)

    Transit time factor (TTF) is important in design and simulation of standing wave RF gaps. The TTF is usually constructed on the basis of a square wave model, and it is always expanded as a function of reduced velocity and structure factors. In order to express the particle's motion more authentically, the TTF is studied based on the Bessel–Fourier (B–F) expansion which is realized in BEAMPATH code. By expanding square wave electric field into harmonic electric fields, the voltage component and the TTF component of each order are obtained from corresponding harmonic electric field. The ratios of each order of voltage components and integral voltage form the weights working as coefficients of TTF components. Consequently, the effective resultant TTF depends on not only the particle's velocity and the structure factors, but also the RF phase the particle experiences. Simple expressions are derived after simplifying the complicated TTF equation in this paper

  11. High-Temperature Expansion of Supersymmetric Partition Functions

    CERN Document Server

    Ardehali, Arash Arabi; Szepietowski, Phillip

    2015-01-01

    Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($\\beta \\rightarrow 0$) behavior of supersymmetric partition functions $Z^{SUSY}(\\beta)$. Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of $\\ln Z^{SUSY}(\\beta)$ terminates at order $\\beta^0$. We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in the planar ($N \\rightarrow \\infty$) limit. Our method for regularizing the one-loop determinants of chiral and vector multiplets helps to clarify the relation between the 4d $\\mathcal{N} = 1$ superconformal index and its corresponding supersymmetric partition function obtained by path-integration.

  12. Analytical solution to compensate for thermal expansion change in photopolymer volume holograms using a tunable laser.

    Science.gov (United States)

    Tanaka, Tomiji; Watanabe, Kenjiro

    2008-02-20

    For holographic data storage, it is necessary to adjust the wavelength and direction of the reading beam if the reading and recording temperature do not match. An analytical solution for this adjustment is derived using first-order approximations in a two-dimensional model. The optimum wavelength is a linear function of the temperature difference between recording and reading, and is independent of the direction of the reference beam. However, the optimum direction of incidence is not only a linear function of the temperature difference, but also depends on the direction of the reference beam. The retrieved image, which is produced by a diffracted beam, shrinks or expands slightly according to the temperature difference. PMID:18288226

  13. Nonlinear Riemann-Hilbert Problems for Generalized Analytic Functions

    OpenAIRE

    Efendiev, Messoud A.; Wolfgang L. Wendland

    2009-01-01

    In this study we deal with the nonlinear Riemann--Hilbert problem (in short (RHP)) for generalized analytic functions in multiply connected domains. Using a similarity principle for multiply connected domains (presented here for the first time), we reduce the nonlinear RHP for generalized analytic functions to a corresponding nonlinear RHP for holomorphic functions with Hölder continuous boundary data. Then the Newton--Kantorovič method combined with a continuation procedure as well as a new ...

  14. Superiority of Bessel function over Zernicke polynomial as base function for radial expansion in tomographic reconstruction

    Indian Academy of Sciences (India)

    A K Chattopadhyay; C V S Rao

    2003-07-01

    Here we describe the superiority of Bessel function as base function for radial expansion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev’s model for saw-tooth oscillation and real experimental x-ray data from W7-AS Stellarator.

  15. Analytic strong-coupling expansion in 1/e for the electron propagator without fermion loops in quantum electrodynamics

    International Nuclear Information System (INIS)

    Starting from the path-integral representation for the electron propagator without fermion loops in QED, we analytically investigate the strong-coupling behavior in an arbitrary background electromagnetic field through a series expansion in powers of 1/e. Contrary to the perturbation theory expansion in e the new series only contains positive powers of the derivative operator p. Due to infrared singularities in the path integral the series does not exist beyond the lowest orders, although one can build a systematic expansion in powers of p (not 1/e) which can be calculated up to any order. To handle infinities we regularize using a Pauli-Villars approach. The introduction of fermion loops would not correspond to higher orders in 1/e, so a priori our results are only pertinent to the sector of QED we have chosen. 17 refs., 1 fig

  16. Power system generation expansion planning using the maximum principle and analytical production cost model

    International Nuclear Information System (INIS)

    Historically, the electric utility demand in most countries has increased rapidly, with a doubling of approximately 10 years in the case of developing countries. In order to meet this growth in demand, the planners of expansion policies were concerned with obtaining expansion pans which dictate what new generation facilities to add and when to add them. This paper reports that, however, the practical planning problem is extremely difficult and complex, and required many hours of the planner's time even though the alternatives examined were extremely limited. In this connection, increased motivation for more sophisticated techniques of valuating utility expansion policies has been developed during the past decade. Among them, the long-range generation expansion planning is to select the most economical and reliable generation expansion plans in order to meet future power demand over a long period of time subject to a multitude of technical, economical, and social constraints

  17. An analytical wall-function for recirculating and impinging turbulent heat transfer

    International Nuclear Information System (INIS)

    Highlights: ► Improvement of the analytical wall-function is proposed. ► Strain parameter dependency is introduced to the prescribed eddy viscosity profile of the analytical wall-function. ► The model performance is evaluated in turbulent pipe, channel, back-step, abrupt expansion pipe and plane impinging flows. ► Generally improved heat transfer is obtained in all the test cases with the standard k-e model. -- Abstract: The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested

  18. Schur function expansions of KP tau functions associated to algebraic curves

    CERN Document Server

    Enolski, V

    2010-01-01

    The Schur function expansion of Sato-Segal-Wilson KP tau-functions is reviewed. The case of tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Pl\\"ucker coordinate coefficients appearing in the expansion are obtained in terms of directional derivatives of the Riemann theta function or Klein sigma function along the KP flow directions. Using the fundamental bi-differential, it is shown how the coefficients can be expressed as polynomials in terms of Klein's higher genus generalizations of Weierstrass' zeta and P functions. The cases of genus two hyperelliptic and genus three trigonal curves are detailed as illustrations of the approach developed here.

  19. Schur function expansions of KP τ-functions associated to algebraic curves

    Science.gov (United States)

    Harnad, J.; Ènol'skii, Viktor Z.

    2011-08-01

    The Schur function expansion of Sato-Segal-Wilson KP \\tau-functions is reviewed. The case of \\tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Plücker coordinate coefficients appearing in the expansion are obtained in terms of directional derivatives of the Riemann \\theta-function or Klein \\sigma-function along the KP flow directions. By using the fundamental bi-differential it is shown how the coefficients can be expressed as polynomials in terms of Klein's higher-genus generalizations of Weierstrass' \\zeta- and \\wp-functions. The cases of genus-two hyperelliptic and genus-three trigonal curves are detailed as illustrations of the approach developed here. Bibliography: 53 titles.

  20. Quasi-convolution of analytic functions with applications

    CERN Document Server

    Babalola, K O

    2010-01-01

    In this paper we define a new concept of quasi-convolution for analytic functions normalized by $f(0)=0$ and $f^\\prime(0)=1$ in the unit disk $E=\\{z\\in \\mathbb{C}\\colon |z|<1\\}$. We apply this new approach to study the closure properties of a certain class of analytic and univalent functions under some families of (known and new) integral operators.

  1. Tree based functional expansions for Feynman--Kac particle models

    OpenAIRE

    Del Moral, Pierre; Patras, Frédéric; Rubenthaler, Sylvain

    2009-01-01

    We design exact polynomial expansions of a class of Feynman–Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any order is related naturally to the number of coalescences of the trees. Our results include an extension of the Wick product formula to interacting particle systems. They also provide refined nonasymptotic propagation of chaos-type properties, as well as shar...

  2. THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.

  3. The Analytic Structure of Non-Global Logarithms: Convergence of the Dressed Gluon Expansion

    CERN Document Server

    Larkoski, Andrew J; Neill, Duff

    2016-01-01

    Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon expansion was introduced that enables an expansion of the NGL series in terms of a "dressed gluon" building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-$N_c$ master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluon expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of $\\alpha_s$log. We explain this finite radius of convergence using t...

  4. Green functions of graphene: An analytic approach

    International Nuclear Information System (INIS)

    In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is shown how the resulting GFs can be simplified from a double to a single integral form to aid computation, and that when considering off-diagonal GFs in the high symmetry directions of the lattice this single integral can be approximated very accurately by an algebraic expression. By comparing our results to the conventional first nearest neighbour model commonly found in the literature, it is apparent that the extended model leads to a sizeable change in the electronic structure away from the linear regime. As such, this article serves as a blueprint for researchers who wish to examine quantities where these considerations are important

  5. Green functions of graphene: An analytic approach

    Energy Technology Data Exchange (ETDEWEB)

    Lawlor, James A., E-mail: jalawlor@tcd.ie [School of Physics, Trinity College Dublin, Dublin 2 (Ireland); Ferreira, Mauro S. [School of Physics, Trinity College Dublin, Dublin 2 (Ireland); CRANN, Trinity College Dublin, Dublin 2 (Ireland)

    2015-04-15

    In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is shown how the resulting GFs can be simplified from a double to a single integral form to aid computation, and that when considering off-diagonal GFs in the high symmetry directions of the lattice this single integral can be approximated very accurately by an algebraic expression. By comparing our results to the conventional first nearest neighbour model commonly found in the literature, it is apparent that the extended model leads to a sizeable change in the electronic structure away from the linear regime. As such, this article serves as a blueprint for researchers who wish to examine quantities where these considerations are important.

  6. Unitarity or asymptotic completeness equations and analytic structure of the S matrix and Green functions

    International Nuclear Information System (INIS)

    Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense

  7. Complex Tanh-Function Expansion Method and Exact Solutions to Two Systems of Nonlinear Wave Equations

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jin-Liang; WANG Ming-Liang

    2004-01-01

    The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schrodinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.

  8. Complex Tanh-Function Expansion Method and Exact Solutions to Two Systems of Nonlinear Wave Equations

    Institute of Scientific and Technical Information of China (English)

    ZHANGJin-Liang; WANGMing-Liang

    2004-01-01

    The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.

  9. Subclasses of Analytic Functions Associated with Generalised Multiplier Transformations

    OpenAIRE

    Rashidah Omar; Suzeini Abdul Halim

    2012-01-01

    New subclasses of analytic functions in the open unit disc are introduced which are defined using generalised multiplier transformations. Inclusion theorems are investigated for functions to be in the classes. Furthermore, generalised Bernardi-Libera-Livington integral operator is shown to be preserved for these classes.

  10. Analytical expansion of highly focused vector beams into vector spherical harmonics and its application to Mie scattering

    Science.gov (United States)

    Orlov, S.; Peschel, U.; Bauer, T.; Banzer, P.

    2012-06-01

    The analytical expansion of linearly, azimuthally, and radially polarized rigorous beam-type solutions of Maxwell's equations into vector spherical harmonics (VSHs) is presented. We report on the dominance of higher order multipoles in highly focused radially and azimuthally polarized beams compared to linearly polarized beams under similar conditions. Furthermore, we theoretically investigate a scenario in which highly focused azimuthally and radially polarized beams interact with a linear polarizer placed in the focal plane and expand the resulting fields into VSHs. The generalized Mie theory is used afterwards to investigate the scattering of the studied beams off a spherical gold nanoparticle.

  11. Executive functioning in adult ADHD: a meta-analytic review.

    OpenAIRE

    Boonstra, A.M.; Oosterlaan, J.; Sergeant, J.A.; Buitelaar, J. K.

    2005-01-01

    textabstractBackground: Several theoretical explanations of ADHD in children have focused on executive functioning as the main explanatory neuropsychological domain for the disorder. In order to establish if these theoretical accounts are supported by research data for adults with ADHD, we compared neuropsychological executive functioning and non-executive functioning between adults with ADHD and normal controls in a meta-analytic design. Method: We compared thirteen studies that 1) included ...

  12. Functional Analytic Psychotherapy for Interpersonal Process Groups: A Behavioral Application

    Science.gov (United States)

    Hoekstra, Renee

    2008-01-01

    This paper is an adaptation of Kohlenberg and Tsai's work, Functional Analytical Psychotherapy (1991), or FAP, to group psychotherapy. This author applied a behavioral rationale for interpersonal process groups by illustrating key points with a hypothetical client. Suggestions are also provided for starting groups, identifying goals, educating…

  13. Equifinality in Functional Analytic Psychotherapy: Different Strokes for Different Folks

    Science.gov (United States)

    Darrow, Sabrina M.; Dalto, Georgia; Follette, William C.

    2012-01-01

    Functional Analytic Psychotherapy (FAP) is an interpersonal behavior therapy that relies on a therapist's ability to contingently respond to in-session client behavior. Valued behavior change in clients results from the therapist shaping more effective client interpersonal behaviors by providing effective social reinforcement when these behaviors…

  14. Some properties of two-fold symmetric analytic functions

    Directory of Open Access Journals (Sweden)

    Ali Muhammad

    2014-05-01

    Full Text Available In this paper, we introduce a new class of two-fold symmetric functions analytic in the unit disc. We prove such results as subordination and superordination properties, convolution properties, distortion theorems, and inequality properties of this new class.

  15. Treatment of a Disorder of Self through Functional Analytic Psychotherapy

    Science.gov (United States)

    Ferro-Garcia, Rafael; Lopez-Bermudez, Miguel Angel; Valero-Aguayo, Luis

    2012-01-01

    This paper presents a clinical case study of a depressed female, treated by means of Functional Analytic Psychotherapy (FAP) based on the theory and techniques for treating an "unstable self" (Kohlenberg & Tsai, 1991), instead of the classic treatment for depression. The client was a 20-year-old college student. The trigger for her problems was a…

  16. Linear circuit transfer functions an introduction to fast analytical techniques

    CERN Document Server

    Basso, Christophe P

    2016-01-01

    Linear Circuit Transfer Functions: An introduction to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical Circuits Techniques. Building on their existing knowledge of classical loop/nodal analysis, the book improves and expands their skills to unveil transfer functions in a swift and efficient manner. Starting with simple examples, the author explains step-by-step how expressing circuits time constants in different configurations leads to writing transfer functions in a compact and insightful way. By learning how to organize numerators and denominators in the fastest possible way, readers will speed-up analysis and predict the frequency resp nse of simple to complex circuits. In some cases, they will be able to derive the final expression by inspection, without writing a line of algebra. Key features: * Emphasizes analysis through employing time constant-based methods discussed in other text books but not widely us...

  17. Hemisphere Partition Function and Analytic Continuation to the Conifold Point

    CERN Document Server

    Knapp, Johanna; Scheidegger, Emanuel

    2016-01-01

    We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the K\\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces.

  18. On genus expansion of knot polynomials and hidden structure of Hurwitz tau-functions

    International Nuclear Information System (INIS)

    In the genus expansion of the HOMFLY polynomials their representation dependence is naturally captured by symmetric group characters. This immediately implies that the Ooguri-Vafa partition function (OVPF) is a Hurwitz tau-function. In the planar limit involving factorizable special polynomials, it is actually a trivial exponential tau-function. In fact, in the double scaling Kashaev limit (the one associated with the volume conjecture) dominant in the genus expansion are terms associated with the symmetric representations and with the integrability preserving Casimir operators, though we stop one step from converting this fact into a clear statement about the OVPF behavior in the vicinity of q=1. Instead, we explain that the genus expansion provides a hierarchical decomposition of the Hurwitz tau-function, similar to the Takasaki-Takebe expansion of the KP tau-functions. This analogy can be helpful to develop a substitute for the universal Grassmannian description in the Hurwitz tau-functions. (orig.)

  19. Analytical Operations Relate Structural and Functional Connectivity in the Brain

    Science.gov (United States)

    Saggio, Maria Luisa; Ritter, Petra; Jirsa, Viktor K.

    2016-01-01

    Resting-state large-scale brain models vary in the amount of biological elements they incorporate and in the way they are being tested. One might expect that the more realistic the model is, the closer it should reproduce real functional data. It has been shown, instead, that when linear correlation across long BOLD fMRI time-series is used as a measure for functional connectivity (FC) to compare simulated and real data, a simple model performs just as well, or even better, than more sophisticated ones. The model in question is a simple linear model, which considers the physiological noise that is pervasively present in our brain while it diffuses across the white-matter connections, that is structural connectivity (SC). We deeply investigate this linear model, providing an analytical solution to straightforwardly compute FC from SC without the need of computationally costly simulations of time-series. We provide a few examples how this analytical solution could be used to perform a fast and detailed parameter exploration or to investigate resting-state non-stationarities. Most importantly, by inverting the analytical solution, we propose a method to retrieve information on the anatomical structure directly from functional data. This simple method can be used to complement or guide DTI/DSI and tractography results, especially for a better assessment of inter-hemispheric connections, or to provide an estimate of SC when only functional data are available. PMID:27536987

  20. Quantum field theory in the presence of a medium: Green's function expansions

    Energy Technology Data Exchange (ETDEWEB)

    Kheirandish, Fardin [Department of Physics, Islamic Azad University, Shahreza-Branch, Shahreza (Iran, Islamic Republic of); Salimi, Shahriar [Department of Physics, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

    2011-12-15

    Starting from a Lagrangian and using functional-integration techniques, series expansions of Green's function of a real scalar field and electromagnetic field, in the presence of a medium, are obtained. The parameter of expansion in these series is the susceptibility function of the medium. Relativistic and nonrelativistic Langevin-type equations are derived. Series expansions for Lifshitz energy in finite temperature and for an arbitrary matter distribution are derived. Covariant formulations for both scalar and electromagnetic fields are introduced. Two illustrative examples are given.

  1. Analytical correlation functions for motion through diffusivity landscapes.

    Science.gov (United States)

    Roosen-Runge, Felix; Bicout, Dominique J; Barrat, Jean-Louis

    2016-05-28

    Diffusion of a particle through an energy and diffusivity landscape is a very general phenomenon in numerous systems of soft and condensed matter. On the one hand, theoretical frameworks such as Langevin and Fokker-Planck equations present valuable accounts to understand these motions in great detail, and numerous studies have exploited these approaches. On the other hand, analytical solutions for correlation functions, as, e.g., desired by experimentalists for data fitting, are only available for special cases. We explore the possibility to use different theoretical methods in the specific picture of time-dependent switching between diffusive states to derive analytical functions that allow to link experimental and simulation results to theoretical calculations. In particular, we present a closed formula for diffusion switching between two states, as well as a general recipe of how to generalize the formula to multiple states. PMID:27250281

  2. Analytic solution of certain second-order functional differential equation

    Directory of Open Access Journals (Sweden)

    Theeradach Kaewong

    2006-09-01

    Full Text Available We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x″(x[r](z=c0z2+c1(x(z2+(c2x[2](z2+⋯+cm(x[m](z2, m,r≥0.

  3. The Adler Function for Light Quarks in Analytic Perturbation Theory

    OpenAIRE

    Milton, K. A.; Solovtsov, I. L.; Solovtsova, O. P.

    2001-01-01

    The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the $\\tau$ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is ...

  4. Error estimates for Gaussian quadratures of analytic functions

    Science.gov (United States)

    Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.

    2009-12-01

    For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes [varrho]>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.

  5. Analytical methods to calculate correlation functions in quantum statistical physics

    International Nuclear Information System (INIS)

    In the work there is presented a brief but clear and quite reserved account of two analytical methods to calculate correlation functions in quantum statistical physics, proceeding from the first principles, i.e., the most broadly used at present two-time temperature Green's functions method and a new, so-called 'direct algebraic' method (DAM). The aim of this work is to show on the concrete examples of live the most broadly used models of quantum statistical physics, mathematical and technical clarity and simplicity of DAM and hence its practical value

  6. Adler function for light quarks in analytic perturbation theory

    International Nuclear Information System (INIS)

    The method of analytic perturbation theory, which avoids the problem of ghost-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the 'light' Adler function corresponding to the nonstrange vector channel of the inclusive decay of the τ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the 'experimental' Adler function down to the lowest energy scale

  7. Analytical strategies to assess the functional metabolome of vitamin E.

    Science.gov (United States)

    Torquato, Pierangelo; Ripa, Orsola; Giusepponi, Danilo; Galarini, Roberta; Bartolini, Desirée; Wallert, Maria; Pellegrino, Roberto; Cruciani, Gabriele; Lorkowski, Stefan; Birringer, Marc; Mazzini, Francesco; Galli, Francesco

    2016-05-30

    After more than 90 years from its discovery and thousands of papers published, the physiological roles of vitamin E (tocopherols and tocotrienols) are still not fully clarified. In the last few decades, the enzymatic metabolism of this vitamin has represented a stimulating subject of research. Its elucidation has opened up new horizons to the interpretation of the biological function of that class of molecules. The identification of specific properties for some of the physiological metabolites and the definition of advanced analytical techniques to assess the human metabolome of this vitamin in vivo, have paved the way to a series of hypotheses on the functional implications that this metabolism may have far beyond its catabolic role. The present review collects the available information on the most relevant analytical strategies employed to assess the status and metabolism of vitamin E in humans as well as in other model systems. A particular focus is dedicated to the analytical methods used to measure vitamin E metabolites, and particularly long-chain metabolites, in biological fluids and tissues. Preliminary information on a new LC-APCI-MS/MS method to measure these metabolites in human serum is reported. PMID:26947319

  8. On the analytic proton structure function with heavy quarks

    International Nuclear Information System (INIS)

    The analytic proton structure function including quark mass is derived in the framework of color glass condensate. To get the massive proton structure function we keep the quark mass in photon wave function in the derivation process although the calculation is much more complicated than the massless case. It shows that the quark mass plays a key role in the description of the experimental data of proton structure function, and the cross-section of γ*p scattering will be divergent without quark mass regulation. To have the right threshold behavior and a smooth transition in the limit Q2 → 0, the quark mass has to include in the cross-section. (orig.)

  9. On the analytic proton structure function with heavy quarks

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Y.; Zeng, J.; Li, Q.; Zhou, F. [Guizhou Normal University, College of Physics and Electronics Science, Guiyang (China); Zhou, D. [Huazhong Normal University, Institute of Particle physics, Wuhan (China); Xiang, W. [Guizhou Normal University, College of Physics and Electronics Science, Guiyang (China); South Dakota School of Mines and Technology, Department of Physics, Rapid City, SD (United States)

    2015-12-15

    The analytic proton structure function including quark mass is derived in the framework of color glass condensate. To get the massive proton structure function we keep the quark mass in photon wave function in the derivation process although the calculation is much more complicated than the massless case. It shows that the quark mass plays a key role in the description of the experimental data of proton structure function, and the cross-section of γ{sup *}p scattering will be divergent without quark mass regulation. To have the right threshold behavior and a smooth transition in the limit Q{sup 2} → 0, the quark mass has to include in the cross-section. (orig.)

  10. Expansion of a chromosomal repeat in Escherichia coli: roles of replication, repair, and recombination functions

    Directory of Open Access Journals (Sweden)

    Poteete Anthony R

    2009-02-01

    Full Text Available Abstract Background Previous studies of gene amplification in Escherichia coli have suggested that it occurs in two steps: duplication and expansion. Expansion is thought to result from homologous recombination between the repeated segments created by duplication. To explore the mechanism of expansion, a 7 kbp duplication in the chromosome containing a leaky mutant version of the lac operon was constructed, and its expansion into an amplified array was studied. Results Under selection for lac function, colonies bearing multiple copies of the mutant lac operon appeared at a constant rate of approximately 4 to 5 per million cells plated per day, on days two through seven after plating. Expansion was not seen in a recA strain; null mutations in recBCD and ruvC reduced the rate 100- and 10-fold, respectively; a ruvC recG double mutant reduced the rate 1000-fold. Expansion occurred at an increased rate in cells lacking dam, polA, rnhA, or uvrD functions. Null mutations of various other cellular recombination, repair, and stress response genes had little effect upon expansion. The red recombination genes of phage lambda could substitute for recBCD in mediating expansion. In the red-substituted cells, expansion was only partially dependent upon recA function. Conclusion These observations are consistent with the idea that the expansion step of gene amplification is closely related, mechanistically, to interchromosomal homologous recombination events. They additionally provide support for recently described models of RecA-independent Red-mediated recombination at replication forks.

  11. On the Hermite expansions of functions from Hardy class

    OpenAIRE

    Garg, Rahul; Thangavelu, Sundaram

    2009-01-01

    Considering functions $ f $ on $ \\R^n $ for which both $ f $ and $ \\hat{f} $ are bounded by the Gaussian $ e^{-{1/2}a|x|^2}, 0 < a < 1 $ we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for $ O(n)-$finite functions thus extending the one dimensional result of Vemuri.

  12. Polymer as a function of monomer: Analytical quantum modeling

    CERN Document Server

    Nakhaee, Mohammad

    2016-01-01

    To identify an analytical relation between the properties of polymers and their's monomer a Metal-Molecule-Metal (MMM) junction has been presented as an interesting and widely used object of research in which the molecule is a polymer which is able to conduct charge. The method used in this study is based on the Green's function approach in the tight-binding approximation using basic properties of matrices. For a polymer base MMM system, transmission, density of states (DOS) and local density of states (LDOS) have been calculated as a function of the hamiltonian of the monomer. After that, we have obtained a frequency for LDOS variations in pass from a subunit to the next one which is a function of energy.

  13. Evaluation of Analytical Modeling Functions for the Phonation Onset Process

    Science.gov (United States)

    Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael

    2016-01-01

    The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW. PMID:27066108

  14. The boundary value problem for discrete analytic functions

    KAUST Repository

    Skopenkov, Mikhail

    2013-06-01

    This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.

  15. Functional Analytic Multisensory Environmental Therapy for People with Dementia

    Directory of Open Access Journals (Sweden)

    Jason A. Staal

    2012-01-01

    Full Text Available This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment therapy. The aim of the treatment is to provide a safe and effective framework for reducing the behavioral disturbance of the disease process, increasing elder well-being, and to promote transfer of positive effects to other environments outside of the multisensory treatment room.

  16. Elements of a function analytic approach to probability.

    Energy Technology Data Exchange (ETDEWEB)

    Ghanem, Roger Georges (University of Southern California, Los Angeles, CA); Red-Horse, John Robert

    2008-02-01

    We first provide a detailed motivation for using probability theory as a mathematical context in which to analyze engineering and scientific systems that possess uncertainties. We then present introductory notes on the function analytic approach to probabilistic analysis, emphasizing the connections to various classical deterministic mathematical analysis elements. Lastly, we describe how to use the approach as a means to augment deterministic analysis methods in a particular Hilbert space context, and thus enable a rigorous framework for commingling deterministic and probabilistic analysis tools in an application setting.

  17. Functional analytic multisensory environmental therapy for people with dementia.

    Science.gov (United States)

    Staal, Jason A

    2012-01-01

    This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET) for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment therapy. The aim of the treatment is to provide a safe and effective framework for reducing the behavioral disturbance of the disease process, increasing elder well-being, and to promote transfer of positive effects to other environments outside of the multisensory treatment room. PMID:22347667

  18. Usage of analytical diagnostics when evaluating functional surface material defects

    Directory of Open Access Journals (Sweden)

    R. Frischer

    2015-10-01

    Full Text Available There are occurring defects due to defects mechanisms on parts of production devices surfaces. Outer defects pronouncement is changing throw the time with unequal speed. This variability of defect’s mechanism development cause that is impossible to evaluate technical state of the device in any moment, without the necessary underlying information. Proposed model is based on analytical diagnostics basis. Stochastic model with usage of Weibull probability distribution can assign probability of function surface defect occurrence on the operational information in any moment basis. The knowledge of defect range limiting moment, then enable when and in what range will be necessary to make renewal.

  19. On the perturbative expansion of tau hadronic spectral function moments

    CERN Document Server

    Boito, Diogo

    2013-01-01

    In the determination of alpha_s from tau decays several different moments of the hadronic spectral functions have been used. In a recent work, we performed an analysis of their perturbative behaviour under two different assumptions for the higher-order coefficients of the Adler function. We showed that the various moments can be divided in a small number of classes. We concluded that some of the moments commonly employed in alpha_s extractions should be avoided due to their bad perturbative behaviour. Furthermore, for the moments that have a good perturbative behaviour, and under reasonable assumptions for the higher-order behaviour of the Adler function, fixed-order perturbation theory (FOPT) provides the superior framework for the renormalization group improvement. Here we discuss an extension of this analysis where we consider the perturbative series for values of the hadronic invariant mass squared s_0 < m_\\tau^2. Our conclusions are not altered within a reasonable s_0 window.

  20. On the perturbative expansion of tau hadronic spectral function moments

    OpenAIRE

    Boito, Diogo

    2013-01-01

    In the determination of alpha_s from tau decays several different moments of the hadronic spectral functions have been used. In a recent work, we performed an analysis of their perturbative behaviour under two different assumptions for the higher-order coefficients of the Adler function. We showed that the various moments can be divided in a small number of classes. We concluded that some of the moments commonly employed in alpha_s extractions should be avoided due to their bad perturbative b...

  1. Perturbative Expansion of τ Hadronic Spectral Function Moments

    Science.gov (United States)

    Boito, Diogo

    2014-12-01

    In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of αs. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of the renormalon singularities of the QCD Adler function. We were able to show that within these RGI frameworks some of the commonly employed moments should be avoided due to their poor perturbative behavior. Furthermore, under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework.

  2. Perturbative expansion of tau hadronic spectral function moments

    CERN Document Server

    Boito, Diogo

    2013-01-01

    In the extraction of $\\alpha_s$ from hadronic tau decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of $\\alpha_s$. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of the renormalon singularities of the QCD Adler function. We were able to show that within these RGI frameworks some of the commonly employed moments should be avoided due to their poor perturbative behavior. Furthermore, under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework.

  3. Asymptotic expansions of integral means and applications to the ratio of gamma functions

    OpenAIRE

    Elezović, Neven; Vukšić, Lenka

    2013-01-01

    Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form $B(A(x))=C(x)$, where $B$ and $C$ have known asymptotic expansions. The results are illustrated by calculation of some important integral means connected with gamma and digamma functions.

  4. Perturbative expansion of tau hadronic spectral function moments

    OpenAIRE

    Boito, Diogo

    2013-01-01

    In the extraction of $\\alpha_s$ from hadronic tau decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of $\\alpha_s$. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The ...

  5. The Navier-Stokes equations an elementary functional analytic approach

    CERN Document Server

    Sohr, Hermann

    2001-01-01

    The primary objective of this monograph is to develop an elementary and self­ contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier­ Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin­ earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...

  6. Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

    Institute of Scientific and Technical Information of China (English)

    YAN Jun

    2008-01-01

    The free energy in ID sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strong-coupling range of fermion systems.

  7. Calculation of the multigroup space-dependent reactor transfer function using spatial eigenfunction expansion method

    International Nuclear Information System (INIS)

    The spatial eigenfunction expansion method is used to solve the multigroup time-dependent diffusion equation when the absorption cross-section in the thermal group is a function of time. An expression for the multi region reactor transfer function is obtained. Some numerical results for two energy groups are also presented. (author)

  8. BOOMERanG Constraints on Primordial Non-Gaussianity from Analytical Minkowski Functionals

    CERN Document Server

    Natoli, P; Hikage, C; Komatsu, E; Migliaccio, M; Ade, P A R; Bock, J J; Bond, J R; Borrill, J; Boscaleri, A; Contaldi, C R; Crill, B P; De Bernardis, P; De Gasperis, G; De Oliveira-Costa, A; Di Stefano, G; Hivon, E; Kisner, T S; Jones, W C; Lange, A E; Masi, S; Mauskopf, P D; MacTavish, C J; Melchiorri, A; Montroy, T E; Netterfield, C B; Pascale, E; Piacentini, F; Polenta, G; Ricciardi, S; Romeo, G; Ruhl, J E; Tegmark, M; Veneziani, M; Vittorio, N

    2009-01-01

    We use Minkowski Functionals (MF) to constrain a primordial non-Gaussian contribution to the CMB intensity field as observed in the 150 GHz and 145 GHz BOOMERanG maps from the 1998 and 2003 flights, respectively, performing for the first time a joint analysis of the two datasets. A perturbative expansion of the MF formulae in the limit of a weakly non-Gaussian field yields analytical formulae, derived by Hikage et al. (2006), which can be used to constrain the coupling parameter f_NL without the need for non-Gaussian simulations. We find -1020

  9. BOOMERanG constraints on primordial non-Gaussianity from analytical Minkowski functionals

    Science.gov (United States)

    Natoli, P.; de Troia, G.; Hikage, C.; Komatsu, E.; Migliaccio, M.; Ade, P. A. R.; Bock, J. J.; Bond, J. R.; Borrill, J.; Boscaleri, A.; Contaldi, C. R.; Crill, B. P.; de Bernardis, P.; de Gasperis, G.; de Oliveira-Costa, A.; di Stefano, G.; Hivon, E.; Kisner, T. S.; Jones, W. C.; Lange, A. E.; Masi, S.; Mauskopf, P. D.; MacTavish, C. J.; Melchiorri, A.; Montroy, T. E.; Netterfield, C. B.; Pascale, E.; Piacentini, F.; Polenta, G.; Ricciardi, S.; Romeo, G.; Ruhl, J. E.; Tegmark, M.; Veneziani, M.; Vittorio, N.

    2010-11-01

    We use Minkowski functionals (MFs) to constrain a primordial non-Gaussian contribution to the cosmic microwave background intensity field as observed in the 150- and 145-GHz BOOMERanG maps from the 1998 and 2003 flights, respectively, performing for the first time a joint analysis of the two data sets. A perturbative expansion of the MF formulae in the limit of a weakly non-Gaussian field yields analytical formulae, derived by Hikage et al., which can be used to constrain the coupling parameter fNL without the need for non-Gaussian simulations. We find -770 Troia et al. on the BOOMERanG 2003 data set. These are the best fNL limits to date for suborbital probes.

  10. A Closed-Form Approximation of Likelihood Functions for Discretely Sampled Diffusions: the Exponent Expansion

    CERN Document Server

    Capriotti, L

    2007-01-01

    In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\\Delta t$, and a series expansion of the deviation of its logarithm from that of a Gaussian distribution. Through this procedure, dubbed {\\em exponent expansion}, the transition probability is obtained as a power series in $\\Delta t$. This becomes asymptotically exact if an increasing number of terms is included, and provides remarkably accurate results even when truncated to the first few (say 3) terms. The coefficients of such expansion can be determined straightforwardly through a recursion, and involve simple one-dimensional integrals. We present several examples of financial interest, and we compare our results with the state-of-the-art approximation of discretely sampled diffusions [A\\"it-Sahalia, {\\it Journal of Finance} {\\bf 54}, 1361 (1999)]. We find that the exponent expansion prov...

  11. An analytic function approach to weak mutually unbiased bases

    Science.gov (United States)

    Olupitan, T.; Lei, C.; Vourdas, A.

    2016-08-01

    Quantum systems with variables in Z(d) are considered, and three different structures are studied. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1 /√{ k } (where k | d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. For simplicity, the case where d =p1 ×p2, where p1 ,p2 are odd prime numbers different from each other, is considered.

  12. The Navier-Stokes equations an elementary functional analytic approach

    CERN Document Server

    Sohr, Hermann

    2001-01-01

    The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...

  13. New analytical potential energy function for doubly charged diatomic molecules

    Institute of Scientific and Technical Information of China (English)

    Wang Fan-Hou; Yang Chuan-Lu; Zhu Zheng-He; Jing Fu-Qian

    2005-01-01

    A new analytical potential function for doubly charged diatomic ions is proposed as V(R)=(∑k n=0anRn-1)exp(-ak+1R)+C/R,where an, ak+1 and C are parameters, and R is the nuclear distance. This function can be used to describe the potential curves for doubly charged diatomic ions with both potential minimum and maximum, or without any stationary point. As examples, potential functions of this form for ground states of BH2+, He22+ and HF2+ have been derived.The calculations using the theoretical method QCISD with basis set 6-311++G* have shown that the potential minimum of BH2+is at Rmin=0.147nm, the maximum at Rmax=0.185nm, and ΔE = Emax - Emin=0.062 eV; for He22+Rmin=0.0736nm, Rmax=0.105nm, and ΔE = Emax - Emin=0.71 eV. It is found that the potential curve for HF2+ is one with a singly repulsive branch. The force constants and spectroscopic data for BH2+ and He22+ have also been worked out.

  14. Estimates of radiation over clouds and dust aerosols: Optimized number of terms in phase function expansion

    International Nuclear Information System (INIS)

    The bulk-scattering properties of dust aerosols and clouds are computed for the community radiative transfer model (CRTM) that is a flagship effort of the Joint Center for Satellite Data Assimilation (JCSDA). The delta-fit method is employed to truncate the forward peaks of the scattering phase functions and to compute the Legendre expansion coefficients for re-constructing the truncated phase function. Use of more terms in the expansion gives more accurate re-construction of the phase function, but the issue remains as to how many terms are necessary for different applications. To explore this issue further, the bidirectional reflectances associated with dust aerosols, water clouds, and ice clouds are simulated with various numbers of Legendre expansion terms. To have relative numerical errors smaller than 5%, the present analyses indicate that, in the visible spectrum, 16 Legendre polynomials should be used for dust aerosols, while 32 Legendre expansion terms should be used for both water and ice clouds. In the infrared spectrum, the brightness temperatures at the top of the atmosphere are computed by using the scattering properties of dust aerosols, water clouds and ice clouds. Although small differences of brightness temperatures compared with the counterparts computed with 4, 8, 128 expansion terms are observed at large viewing angles for each layer, it is shown that 4 terms of Legendre polynomials are sufficient in the radiative transfer computation at infrared wavelengths for practical applications.

  15. Functional expansion for evolution operators in a system of many fermions with many conditions

    International Nuclear Information System (INIS)

    We present a mean field expansion for many body system, using integral functionals. The problem is formulated as a initial conditions one and it is studied the effective dynamics of the body density with given initial conditions. (M.W.O.)

  16. The Expansion of the Function with Two Unknowns on the Reproducing Kernel Space

    Institute of Scientific and Technical Information of China (English)

    吴勃英

    2000-01-01

    In this paper we make use of a special procedure on the reproducing kernel space to give an expansion theorem for the function with two unknowns and a surface approximation formula. The error of the surface possesses monotonically decreasing and uniformly convergent characteristics in the sense of the norm on the space.

  17. Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

    Science.gov (United States)

    Olesov, A. V.

    2014-10-01

    New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.

  18. Hurwitz integrality of power series expansion of the sigma function for a plane curve

    OpenAIRE

    Ônishi, Yoshihiro

    2015-01-01

    This paper shows Hurwitz integrality of the coefficients of expansion at the origin of the sigma function \\(\\sigma(u)\\) associated to a certain plane curve which should be called a plane telescopic curve. For the prime \\(2\\), the expansion of \\(\\sigma(u)\\) is not Hurwitz integral, but \\(\\sigma(u)^2\\) is. This paper clarifies the precise structure of this phenomenon. Throughout the paper, computational examples for the trigonal genus three curve (\\((3,4)\\)-curve) \\(y^3+(\\mu_1x+\\mu_4)y^2+(\\mu_2...

  19. Protein SUMOylation Is Required for Regulatory T Cell Expansion and Function.

    Science.gov (United States)

    Ding, Xiao; Wang, Aibo; Ma, Xiaopeng; Demarque, Maud; Jin, Wei; Xin, Huawei; Dejean, Anne; Dong, Chen

    2016-07-26

    Foxp3-expressing regulatory T (Treg) cells are essential for immune tolerance; however, the molecular mechanisms underlying Treg cell expansion and function are still not well understood. SUMOylation is a protein post-translational modification characterized by covalent attachment of SUMO moieties to lysines. UBC9 is the only E2 conjugating enzyme involved in this process, and loss of UBC9 completely abolishes the SUMOylation pathway. Here, we report that selective deletion of Ubc9 within the Treg lineage results in fatal early-onset autoimmunity similar to Foxp3 mutant mice. Ubc9-deficient Treg cells exhibit severe defects in TCR-driven homeostatic proliferation, accompanied by impaired activation and compromised suppressor function. Importantly, TCR ligation enhanced SUMOylation of IRF4, a critical regulator of Treg cell function downstream of TCR signals, which regulates its stability in Treg cells. Our data thus have demonstrated an essential role of SUMOylation in the expansion and function of Treg cells. PMID:27425617

  20. The effects of breathing with mainly inspiration or expiration on pulmonary function and chest expansion

    OpenAIRE

    Woo, Seong-Dae; Kim, Tae-Ho; Lim, Jin-Yong

    2016-01-01

    [Purpose] This study aimed to determine the effects of inspiration- and expiration-oriented breathing on pulmonary function and chest expansion. [Subjects and Methods] Twenty healthy male university students were divided randomly into inspiration-oriented and expiration-oriented breathing groups. Their pulmonary function and chest size during inspiration or expiration were evaluated and then re-evaluated after 15 minutes of breathing exercise five times a week for four weeks. [Results] The br...

  1. Semi-analytical calculations for parameters of boiling layer in isetropic expansion of warm dense matter with van der Waals equation of state

    OpenAIRE

    Borovikov, Dmitry; Iosilevskiy, Igor

    2012-01-01

    Features and parameters of \\boiling" liquid layer, which arises under conditions of isentropic expansion of warm dense matter (WDM), are stud- ied with the use of simplest van der Waals equation of state (EOS). Advan- tage of this EOS is possibility of demonstrable and semi-analytical descrip- tion of thermo- and hydrodynamics of the process. Idealized self-similar case of behavior of matter on interception of equilibrium (not metastable) isoentropic curve and boundary of gas-liquid coexisten...

  2. (G'/G)-Expansion Method Equivalent to Extended Tanh Function Method

    Institute of Scientific and Technical Information of China (English)

    LIU Chun-Ping

    2009-01-01

    In a recent article [Physics Letters A 372 (2008) 417], Wang et al. proposed a method, which is called the (G'/G)-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the (G'/G)-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the (G'/G)-expansion method is equivalent to the extended tanh function method.

  3. Applying fuzzy analytic network process in quality function deployment model

    Directory of Open Access Journals (Sweden)

    Mohammad Ali Afsharkazemi

    2012-08-01

    Full Text Available In this paper, we propose an empirical study of QFD implementation when fuzzy numbers are used to handle the uncertainty associated with different components of the proposed model. We implement fuzzy analytical network to find the relative importance of various criteria and using fuzzy numbers we calculate the relative importance of these factors. The proposed model of this paper uses fuzzy matrix and house of quality to study the products development in QFD and also the second phase i.e. part deployment. In most researches, the primary objective is only on CRs to implement the quality function deployment and some other criteria such as production costs, manufacturing costs etc were disregarded. The results of using fuzzy analysis network process based on the QFD model in Daroupat packaging company to develop PVDC show that the most important indexes are being waterproof, resistant pill packages, and production cost. In addition, the PVDC coating is the most important index in terms of company experts’ point of view.

  4. Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

    Science.gov (United States)

    Zylka, Christian; Vojta, Guenter

    1993-01-01

    The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

  5. Many-body Expanded Analytical Potential Energy Function for Ground State PuOH Molecule

    Institute of Scientific and Technical Information of China (English)

    LI Yue-Xun; GAO Tao; ZHU Zheng-He

    2006-01-01

    Using the density functional method B3LYP with relativistic effective core potential (RECP) for Pu atom, the low-lying excited states (4∑+, 6∑+, 8∑+) for three structures of PuOH molecule were optimized. The results show that the ground state is X6∑+of the linear Pu-O-H (C∞v), its corresponding equilibrium geometry and dissociation energy are RPu-O=0.20595 nm, RO-H=0.09581 nm and -8.68 eV, respectively. At the same time, two other metastable structures [PuOH (Cs) and H-Pu-O (C∞v)] were found. The analytical potential energy function has also been derived for whole range using the many-body expansion method. This potential energy function represents the considerable topographical features of PuOH molecule in detail, which is adequately accurate in the whole potential surface and can be used for the molecular reaction dynamics research.

  6. DIRECT EXPANSIONS FOR THE DISTRIBUTION FUNCTIONS AND DENSITY FUNCTIONS OF x2-TYPE AND t-TYPE DISTRIBUTED RANDOM VARIABLES

    Institute of Scientific and Technical Information of China (English)

    ZHENGZUKANG

    1996-01-01

    Suppose that Z1,Z2…,Zn are independent normal random variables with common mean μ and variance σ2. Then S2=∑n n=1 (zi-z)2/σ2 and T =(n-1的平方根)-Z/(S2/n的平方根) have x2n-1 distribution and tn-1 distribution respectively. If the normal assumption fails, there will be the remainders of the distribution functions and density functions. This paper gives the direct expansions of distribution functions and density functions of S2 and T up to o(n-1). They are more intuitive and convenient than usual Edgeworth expansions.

  7. Analytical representation of time correlation functions and application to relaxation problems

    International Nuclear Information System (INIS)

    Two analytical representations of the Laplace transform of the time autocorrelation of a dynamical variable, namely the moment expansion and Mori's continued fraction expansion, are investigated from the point of view of structure and convergence properties, and the relation between them is established. The general theory is applied first to a dynamical model exactly solvable, the isotopic impurity in a linear chain of coupled harmonic oscillators, and then to two stochastic models recently introduced by Gordon for the rotational diffusion of molecules. In the latter case, the continued fraction expansion yields simple analytical expressions for the infrared absorption band shapes, showing that these models contain all the features of observed shapes in compressed gases, liquids and solutions. (author)

  8. Boundary-value problems for x-analytical functions with weighted boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Kapshivyi, A.A. [Kiev Univ. (Ukraine)

    1994-11-10

    We consider boundary-value problems for x-analytical functions of a complex variable z = x + iy in a number of domains. Limit values with the weight (ln x){sup {minus}1} are given for the real part of the x-analytical function on the sections of the boundary that follow the imaginary axis, and simple limits are given for the real part of the x-analytical functions on the part of the boundary outside the imaginary axis. The apparatus of integral representations of x-analytical functions is applied to obtain a solution of the problem in quadratures.

  9. The molecular structure and the analytical potential energy function of S-2 and S-3

    Institute of Scientific and Technical Information of China (English)

    Liu Yu-Fang; Li Jun-Yu; Han Xiao-Qin; Sun Jin-Feng

    2007-01-01

    In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S-2 and S-3 have been calculated at QCISD/6-311++G(3d2f) and B3P86/6-311++G(3d2f) level. The S-2 ground state is of 2Ⅱg, the S-3 ground state is of 2B1 and S-3 has a bent (C2V) structure with an angle of 115.65° The results are in good agreement with these reported in other literature. For S-3 ion, the vibration frequencies and the force constants have also been calculated. Base on the general principles of microscopic reversibility, the dissociation limits has been deduced. The Murrell-Sorbie potential energy function for S-2 has been derived according to the ab initio data through the leastsquares fitting. The force constants and spectroscopic data for S-2 have been calculated, then compared with other theoretical data. The analytical potential energy function of S-3 have been obtained based on the many-body expansion theory. The structure and energy can correctly reappear on the potential surface.

  10. Lymph vessel expansion and function in the development of hepatic fibrosis and cirrhosis.

    OpenAIRE

    Vollmar, B; Wolf, B.; Siegmund, S.; Katsen, A. D.; Menger, M. D.

    1997-01-01

    The process of lymph vessel expansion and function in the development of CCl4-induced hepatic fibrosis and cirrhosis was studied using intravital fluorescence microscopy of the rat liver. The unique aspect of our approach was the use of high molecular fluorescein-isothiocyanate-labeled dextran (MW, 150,000) as fluorescent marker, which allowed for simultaneous assessment of both 1) the macromolecular blood hepatocytic exchange from the sinusoidal microvasculature (extra-/intrasinusoidal gray ...

  11. Harmonic expansion of the effective potential in Functional Renormalization Group at finite chemical potential

    CERN Document Server

    Barnafoldi, G G; Posfay, P

    2016-01-01

    In this paper we propose a method to study the Functional Renormalization Group at finite chemical potential. The method consists of mapping the FRG equations within the Fermi surface into a differential equation defined on a rectangle with zero boundary conditions. To solve this equation we use an expansion of the potential in a harmonic basis. With this method we determined the phase diagram of a simple Yukawa-type model; as expected, the bosonic fluctuations decrease the strength of the transition.

  12. Effects of Lung Expansion Therapy on Lung Function in Patients with Prolonged Mechanical Ventilation

    OpenAIRE

    Yen-Huey Chen; Ming-Chu Yeh; Han-Chung Hu; Chung-Shu Lee; Li-Fu Li; Ning-Hung Chen; Chung-Chi Huang; Kuo-Chin Kao

    2016-01-01

    Common complications in PMV include changes in the airway clearance mechanism, pulmonary function, and respiratory muscle strength, as well as chest radiological changes such as atelectasis. Lung expansion therapy which includes IPPB and PEEP prevents and treats pulmonary atelectasis and improves lung compliance. Our study presented that patients with PMV have improvements in lung volume and oxygenation after receiving IPPB therapy. The combination of IPPB and PEEP therapy also results in inc...

  13. Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Olesov, A V [G.I. Nevelskoi Maritime State University, Vladivostok (Russian Federation)

    2014-10-31

    New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.

  14. Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

    International Nuclear Information System (INIS)

    New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles

  15. Application of wavelet scaling function expansion continuous-energy resonance calculation method to MOX fuel problem

    International Nuclear Information System (INIS)

    More and more MOX fuels are used in all over the world in the past several decades. Compared with UO2 fuel, it contains some new features. For example, the neutron spectrum is harder and more resonance interference effects within the resonance energy range are introduced because of more resonant nuclides contained in the MOX fuel. In this paper, the wavelets scaling function expansion method is applied to study the resonance behavior of plutonium isotopes within MOX fuel. Wavelets scaling function expansion continuous-energy self-shielding method is developed recently. It has been validated and verified by comparison to Monte Carlo calculations. In this method, the continuous-energy cross-sections are utilized within resonance energy, which means that it's capable to solve problems with serious resonance interference effects without iteration calculations. Therefore, this method adapts to treat the MOX fuel resonance calculation problem natively. Furthermore, plutonium isotopes have fierce oscillations of total cross-section within thermal energy range, especially for 240Pu and 242Pu. To take thermal resonance effect of plutonium isotopes into consideration the wavelet scaling function expansion continuous-energy resonance calculation code WAVERESON is enhanced by applying the free gas scattering kernel to obtain the continuous-energy scattering source within thermal energy range (2.1 eV to 4.0 eV) contrasting against the resonance energy range in which the elastic scattering kernel is utilized. Finally, all of the calculation results of WAVERESON are compared with MCNP calculation. (authors)

  16. On the Gibbs phenomenon 3: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

    Science.gov (United States)

    Gottlieb, David; Shu, Chi-Wang

    1993-01-01

    The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.

  17. Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of the S U (Nc) conformal anomaly and studies of the conformal symmetry limit

    Science.gov (United States)

    Cvetič, Gorazd; Kataev, A. L.

    2016-07-01

    We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.

  18. Asymptotic Expansions in the CLT in Free Probability

    CERN Document Server

    Chistyakov, G P

    2011-01-01

    We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution. We apply these results to the expansion of densities to derive expansions for the free entropic distance of sums to the Wigner law.

  19. Analytic structure of many-body Coulombic wave functions

    DEFF Research Database (Denmark)

    Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas; Sørensen, Thomas Østergaard

    2009-01-01

    We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a...

  20. On the analytical structure of the Bogolubov generating functional method in classical statistical physics and related 'collective' variables and Wigner transforms

    International Nuclear Information System (INIS)

    We show that the N.N. Bogolubov generating functional method is a very effective tool for studying distribution functions of both equilibrium and non equilibrium states of classical many-particle dynamical systems. In some cases the Bogolubov generating functionals can be represented by means of infinite Ursell-Mayer diagram expansions, whose convergence holds under some additional constraints on statistical system. The classical Bogolubov idea to use the Wigner density operator transformation for studying the non equilibrium distribution functions is developed and new analytic non-stationary solution to the classical N.N. Bogolubov evolution functional equation is constructed. (author)

  1. Determination of the exchange interaction energy from the polarization expansion of the wave function

    CERN Document Server

    Gniewek, Piotr

    2016-01-01

    The exchange contribution to the energy of the hydrogen atom interacting with a proton is calculated from the polarization expansion of the wave function using the conventional surface-integral formula and two formulas involving volume integrals: the formula of the symmetry-adapted perturbation theory (SAPT) and the variational formula recommended by us. At large internuclear distances $R$, all three formulas yield the correct expression $-(2/e)Re^{-R}$, but approximate it with very different convergence rates. In the case of the SAPT formula, the convergence is geometric with the error falling as $3^{-K}$, where $K$ is the order of the applied polarization expansion. The error of the surface-integral formula decreases exponentially as $a^K/(K+1)!$, where $a=\\ln2 -\\tfrac{1}{2}$. The variational formula performs best, its error decays as $K^{1/2} [a^{ K}/(K+1)!]^2$. These convergence rates are much faster than those resulting from approximating the wave function through the multipole expansion. This shows the ...

  2. Algebraic and analyticity properties of the n-point function in quantum field theory

    International Nuclear Information System (INIS)

    The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author)

  3. On Certain Subclasses of Analytic and Univalent Functions based on an Extension of Salagean Operator

    Directory of Open Access Journals (Sweden)

    T.V. Sudharsan

    2012-09-01

    Full Text Available There is many subclasses of analytic and univalent functions. A class T of functions with negative coefficients introduced by Silverman [8] opened up a new and fruitful line of research in the theory of univalent functions. Following the works of Khairnar and Meena More [3], Aghalary and Kulkarni [1], Silverman and Silvia [8] and Owa and Nishiwaki [5] on analytic and univalent functions, in this paper we introduce two new classes for a family of analytic function with negative coefficients. We have attempted to obtain coefficient estimate, distortion theorem and extreme points for the class

  4. Analytic Continuation of Hypergeometric Functions in the Resonant Case

    CERN Document Server

    Scheidegger, Emanuel

    2016-01-01

    We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant case, there are necessarily logarithmic solutions. We apply the result to Picard-Fuchs equations of certain one--parameter families of Calabi--Yau manifolds, known as the mirror quartic and the mirror quintic.

  5. Parametric analyticity of functional variations of Dirichlet-Neumann operators

    OpenAIRE

    Fazioli, Carlo; Nicholls, David P.

    2008-01-01

    One of the important open questions in the theory of free--surface ideal fluid flows is the dynamic stability of traveling wave solutions. In a spectral stability analysis, the first variation of the governing Euler equations is required which raises both theoretical and numerical issues. With Zakharov and Craig and Sulem's formulation of the Euler equations in mind, this paper addresses the question of analyticity properties of first (and higher) variations of the Dirichlet--N...

  6. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    International Nuclear Information System (INIS)

    Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes

  7. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    Energy Technology Data Exchange (ETDEWEB)

    Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu [Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)

    2015-08-15

    Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

  8. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    Directory of Open Access Journals (Sweden)

    Adib Samin

    2015-08-01

    Full Text Available Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

  9. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    Science.gov (United States)

    Samin, Adib; Lahti, Erik; Zhang, Jinsuo

    2015-08-01

    Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

  10. Growth Type and Functional Trajectories: An Empirical Study of Urban Expansion in Nanjing, China

    Science.gov (United States)

    Yuan, Feng

    2016-01-01

    Drawing upon the Landsat satellite images of Nanjing from 1985, 1995, 2001, 2007, and 2013, this paper integrates the convex hull analysis and common edge analysis at double scales, and develops a comprehensive matrix analysis to distinguish the different types of urban land expansion. The results show that Nanjing experienced rapid urban expansion, dominated by a mix of residential and manufacturing land from 1985 to 2013, which in turn has promoted Nanjing’s shift from a compact mononuclear city to a polycentric one. Spatial patterns of three specific types of growth, namely infilling, extension, and enclave were quite different in four consecutive periods. These patterns result primarily from the existing topographic constraints, as well as government-oriented urban planning and policies. By intersecting the function maps, we also reveal the functional evolution of newly-developed urban land. Moreover, both self-enhancing and mutual promotion of the newly developed functions are surveyed over the last decade. Our study confirms that the integration of a multi-scale method and multi-perspective analysis, such as the spatiotemporal patterns and functional evolution, helps us to better understand the rapid urban growth in China. PMID:26845155

  11. Growth Type and Functional Trajectories: An Empirical Study of Urban Expansion in Nanjing, China.

    Science.gov (United States)

    Chen, Jianglong; Gao, Jinlong; Yuan, Feng

    2016-01-01

    Drawing upon the Landsat satellite images of Nanjing from 1985, 1995, 2001, 2007, and 2013, this paper integrates the convex hull analysis and common edge analysis at double scales, and develops a comprehensive matrix analysis to distinguish the different types of urban land expansion. The results show that Nanjing experienced rapid urban expansion, dominated by a mix of residential and manufacturing land from 1985 to 2013, which in turn has promoted Nanjing's shift from a compact mononuclear city to a polycentric one. Spatial patterns of three specific types of growth, namely infilling, extension, and enclave were quite different in four consecutive periods. These patterns result primarily from the existing topographic constraints, as well as government-oriented urban planning and policies. By intersecting the function maps, we also reveal the functional evolution of newly-developed urban land. Moreover, both self-enhancing and mutual promotion of the newly developed functions are surveyed over the last decade. Our study confirms that the integration of a multi-scale method and multi-perspective analysis, such as the spatiotemporal patterns and functional evolution, helps us to better understand the rapid urban growth in China. PMID:26845155

  12. Growth Type and Functional Trajectories: An Empirical Study of Urban Expansion in Nanjing, China.

    Directory of Open Access Journals (Sweden)

    Jianglong Chen

    Full Text Available Drawing upon the Landsat satellite images of Nanjing from 1985, 1995, 2001, 2007, and 2013, this paper integrates the convex hull analysis and common edge analysis at double scales, and develops a comprehensive matrix analysis to distinguish the different types of urban land expansion. The results show that Nanjing experienced rapid urban expansion, dominated by a mix of residential and manufacturing land from 1985 to 2013, which in turn has promoted Nanjing's shift from a compact mononuclear city to a polycentric one. Spatial patterns of three specific types of growth, namely infilling, extension, and enclave were quite different in four consecutive periods. These patterns result primarily from the existing topographic constraints, as well as government-oriented urban planning and policies. By intersecting the function maps, we also reveal the functional evolution of newly-developed urban land. Moreover, both self-enhancing and mutual promotion of the newly developed functions are surveyed over the last decade. Our study confirms that the integration of a multi-scale method and multi-perspective analysis, such as the spatiotemporal patterns and functional evolution, helps us to better understand the rapid urban growth in China.

  13. Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit

    OpenAIRE

    Cvetič, Gorazd; Kataev, A. L.

    2016-01-01

    We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the non-singlet part of the $e^+e^-$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering $C_{ns}^{Bjp}$, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is a two-fold series in terms of powers of the conformal anomaly and of $SU(N_c)$ coupling $\\alpha_s$. Explicit expressions are obtaine...

  14. High-rate production of functional nanostructured films and devices by coupling flame spray pyrolysis with supersonic expansion

    International Nuclear Information System (INIS)

    The fabrication of functional thin films and devices by direct deposition of nanoparticles from the gas phase is a promising approach enabling, for instance, the integration of complex analytical and sensing capabilities on microfabricated platforms. Aerosol-based techniques ensure large-scale nanoparticle production and they are potentially suited for this goal. However, they are not adequate in terms of fine control over the lateral resolution of the coatings, mild processing conditions (avoiding high temperature and aggressive chemicals), low contamination and compatibility with microfabrication processes. Here we report the high-rate and efficient production of functional nanostructured films by nanoparticle assembling obtained by the combination of flame spray pyrolysis and supersonic expansion. Our approach merges the advantages of flame spray pyrolysis for bulk nanopowders such as process stability and wide material library availability with those of supersonic cluster beam deposition in terms of lateral resolution and of direct integration of nanomaterials on devices. We efficiently produced nanostructured films and devices (such as gas sensors) using metal oxide, pure noble metal and oxide-supported noble metal nanoparticles. (paper)

  15. Expansion and functions of myeloid-derived suppressor cells in the tumor microenvironment.

    Science.gov (United States)

    Qu, Peng; Wang, Li-Zhen; Lin, P Charles

    2016-09-28

    Myeloid derived suppressor cells (MDSCs) are a group of immature myeloid cells accumulated in most cancer patients and mouse tumor models. MDSCs suppress host immune response and concurrently promote tumor angiogenesis, thereby promote tumor growth and progression. In this review, we discuss recent progresses in expansion and activity of tumor MDSCs, and describe new findings about immunosuppressive function of different subtypes of MDSCs in cancer. We also discussed tumor angiogenic activities and pro-tumor invasion/metastatic roles of MDSCs in tumor progression. PMID:26519756

  16. Expansion of amphibian intronless interferons revises the paradigm for interferon evolution and functional diversity.

    Science.gov (United States)

    Sang, Yongming; Liu, Qinfang; Lee, Jinhwa; Ma, Wenjun; McVey, D Scott; Blecha, Frank

    2016-01-01

    Interferons (IFNs) are key cytokines identified in vertebrates and evolutionary dominance of intronless IFN genes in amniotes is a signature event in IFN evolution. For the first time, we show that the emergence and expansion of intronless IFN genes is evident in amphibians, shown by 24-37 intronless IFN genes in each frog species. Amphibian IFNs represent a molecular complex more complicated than those in other vertebrate species, which revises the established model of IFN evolution to facilitate re-inspection of IFN molecular and functional diversity. We identified these intronless amphibian IFNs and their intron-containing progenitors, and functionally characterized constitutive and inductive expression and antimicrobial roles in infections caused by zoonotic pathogens, such as influenza viruses and Listeria monocytogenes. Amphibians, therefore, may serve as overlooked vectors/hosts for zoonotic pathogens, and the amphibian IFN system provides a model to study IFN evolution in molecular and functional diversity in coping with dramatic environmental changes during terrestrial adaption. PMID:27356970

  17. High-frequency expansion of memory function in classical simple liquids, 3

    International Nuclear Information System (INIS)

    Collective modes in liquid metals are studied by applying the memory function formalism to a generalized Langevin equation satisfied by the density fluctuation of ions. A high-frequency expansion of the memory function is used to make a systematic analysis of the dynamical structure factor S(k, ω). Numerical calculations of the dispersion curves of collective modes are made for liquid Na, Rb and Pb by using suitable model pseudo-potentials. The characteristics of the dispersion curves are shown to be similar to these of liquid Ar. These are compared with the results of the inelastic neutron scattering measurements in the vicinity of the first peak of the static structure factor and good agreement is obtained. It is shown that the contribution from the terms containing the three-body correlation function seems to be different from the case of liquid Ar. (auth.)

  18. Application of expansion of the variables in hierarchical functions for solution of Navier-Stokes equations for incompressible fluids

    International Nuclear Information System (INIS)

    This work applied of the expansion of the variables in hierarchical functions for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. This work is based on the finite element method. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desire degree. This method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature are analyze. The results show the method capacity in supplying precise results. (author)

  19. Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

    OpenAIRE

    Gori-Giorgi, Paola; Sacchetti, Francesco; Bachelet, Giovanni B.

    1999-01-01

    We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real...

  20. Computing the hadronic vacuum polarization function by analytic continuation

    CERN Document Server

    Feng, Xu; Hotzel, Grit; Jansen, Karl; Petschlies, Marcus; Renner, Dru B

    2013-01-01

    We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the space-like and time-like regions. We provide two independent derivations of this method showing that it leads to the desired hadronic vacuum polarization function in Minkowski space-time. We show with the example of the leading- order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.

  1. Computing the hadronic vacuum polarization function by analytic continuation

    Energy Technology Data Exchange (ETDEWEB)

    Feng, Xu [KEK National High Energy Physics, Tsukuba (Japan); Hashimoto, Shoji [KEK National High Energy Physics, Tsukuba (Japan); The Graduate Univ. for Advanced Studies, Tsukuba (Japan). School of High Energy Accelerator Science; Hotzel, Grit [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Petschlies, Marcus [The Cyprus Institute, Nicosia (Cyprus); Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

    2013-07-15

    We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the space-like and time-like regions. We provide two independent derivations of this method showing that it leads to the desired hadronic vacuum polarization function in Minkowski space-time. We show with the example of the leading- order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.

  2. Moment expansion to the memory function for generalized Drude scattering rate

    Science.gov (United States)

    Bhalla, Pankaj; Das, Nabyendu; Singh, Navinder

    2016-05-01

    The memory function formalism is an important tool to evaluate the frequency dependent electronic conductivity. It is previously used within some approximations in the case of electrons interacting with various other degrees of freedom in metals with great success. However, one needs to go beyond those approximations as the interaction strengths become stronger. In this work, we propose a systematic expansion of the memory function involving its various moments. We calculate the higher order contribution to the generalized Drude scattering rate in case of electron-impurity interactions. Further we compare our results with the results from previously studied lowest order calculations. We find larger contributions from the higher moments in the low frequency regime and also in the case of larger interaction strength.

  3. Fermi surface in local-density-functional theory and in gradient expansions

    Science.gov (United States)

    Mearns, Daniel; Kohn, Walter

    1989-05-01

    It has recently been shown that the Kohn-Sham (KS) equations, even with the exact exchange-correlation potential, vxc(r), in general do not yield the exact physical Fermi surface (FS). The latter may be obtained either from the discontinuities of the momentum distribution in the exact ground state or, equally well, from the locus of singularities in q space of the exact density-density response function, χ(q,q) (Kohn effect). The present paper considers approximations in which the exact exchange-correlation energy functional is replaced by a gradient expansion of arbitrary finite order m [e.g., Exc(2)[n] =Fd3 [exc(n(r))n(r)+gxc (n(r))||∇n(r)||2

  4. Interpretation of semiclassical transition moments through wave function expansion of dipole moment functions with applications to the OH stretching spectra of simple acids and alcohols.

    Science.gov (United States)

    Takahashi, Hirokazu; Takahashi, Kaito; Yabushita, Satoshi

    2015-05-21

    Semiclassical description of molecular vibrations has provided us with various computational approximations and enhanced our conceptual understanding of quantum mechanics. In this study, the transition moments of the OH stretching fundamental and overtone intensities (Δv = 1-6) of some alcohols and acids are calculated by three kinds of semiclassical methods, correspondence-principle (CP) approximation, quasiclassical approximation, and uniform WKB approximation, and their respective transition moments are compared to those by the quantum theory. On the basis of the local mode picture, the one-dimensional potential energy curves and the dipole moment functions (DMFs) were obtained by density functional theory calculations and then fitted to Morse functions and sixth-order polynomials, respectively. It was shown that both the transition energies and the absorption intensities derived in the semiclassical methods reproduced their respective quantum values. In particular, the CP approximation reproduces the quantum transition moments if the formula given by Naccache is used for the action integral value. On the basis of these semiclassical results, we present a picture to understand the small variance in the overtone intensities of these acids and alcohols. Another important result is the ratios of semiclassical-to-quantum transition moment are almost independent of the applied molecules even with a great molecular variance of the DMFs, and they depend only on the nature of the semiclassical approximations and the quantum number. The difference between the semiclassical and quantum transition moments was analyzed in terms of a hitherto unrecognized concept that the Fourier expansion of the time dependent DMF in the CP treatment is a kind of the wave function expansion method using trigonometric functions as the quotient functions. For a Morse oscillator, we derive the analytic and approximate expressions of the quotient functions in terms of the bond displace

  5. Histone deacetylase 11: A novel epigenetic regulator of myeloid derived suppressor cell expansion and function.

    Science.gov (United States)

    Sahakian, Eva; Powers, John J; Chen, Jie; Deng, Susan L; Cheng, Fengdong; Distler, Allison; Woods, David M; Rock-Klotz, Jennifer; Sodre, Andressa L; Youn, Je-In; Woan, Karrune V; Villagra, Alejandro; Gabrilovich, Dmitry; Sotomayor, Eduardo M; Pinilla-Ibarz, Javier

    2015-02-01

    Myeloid-derived suppressor cells (MDSCs), a heterogeneous population of cells capable of suppressing anti-tumor T cell function in the tumor microenvironment, represent an imposing obstacle in the development of cancer immunotherapeutics. Thus, identifying elements essential to the development and perpetuation of these cells will undoubtedly improve our ability to circumvent their suppressive impact. HDAC11 has emerged as a key regulator of IL-10 gene expression in myeloid cells, suggesting that this may represent an important targetable axis through which to dampen MDSC formation. Using a murine transgenic reporter model system where eGFP expression is controlled by the HDAC11 promoter (Tg-HDAC11-eGFP), we provide evidence that HDAC11 appears to function as a negative regulator of MDSC expansion/function in vivo. MDSCs isolated from EL4 tumor-bearing Tg-HDAC11-eGFP display high expression of eGFP, indicative of HDAC11 transcriptional activation at steady state. In striking contrast, immature myeloid cells in tumor-bearing mice display a diminished eGFP expression, implying that the transition of IMC to MDSC's require a decrease in the expression of HDAC11, where we postulate that it acts as a gate-keeper of myeloid differentiation. Indeed, tumor-bearing HDAC11-knockout mice (HDAC11-KO) demonstrate a more suppressive MDSC population as compared to wild-type (WT) tumor-bearing control. Notably, the HDAC11-KO tumor-bearing mice exhibit enhanced tumor growth kinetics when compare to the WT control mice. Thus, through a better understanding of this previously unknown role of HDAC11 in MDSC expansion and function, rational development of targeted epigenetic modifiers may allow us to thwart a powerful barrier to efficacious immunotherapies. PMID:25155994

  6. Analytic flux formulas and tables of shielding functions

    International Nuclear Information System (INIS)

    Hand calculations of radiation flux and dose rates are often useful in evaluating radiation shielding and in determining the scope of a problem. The flux formulas appropriate to such calculations are almost always based on the point kernel and allow for at most the consideration of laminar slab shields. These formulas often require access to tables of values of integral functions for effective use. Flux formulas and function tables appropriate to calculations involving homogeneous source regions with the shapes of lines, disks, slabs, truncated cones, cylinders, and spheres are presented. Slab shields may be included in most of these calculations, and the effect of a cylindrical shield surrounding a cylindrical source may be estimated. Detector points may be located axially, laterally, or interior to a cylindrical source. Line sources may be tilted with respect to a slab shield. All function tables are given for a wide range of arguments

  7. Analytic flux formulas and tables of shielding functions

    Energy Technology Data Exchange (ETDEWEB)

    Wallace, O.J.

    1981-06-01

    Hand calculations of radiation flux and dose rates are often useful in evaluating radiation shielding and in determining the scope of a problem. The flux formulas appropriate to such calculations are almost always based on the point kernel and allow for at most the consideration of laminar slab shields. These formulas often require access to tables of values of integral functions for effective use. Flux formulas and function tables appropriate to calculations involving homogeneous source regions with the shapes of lines, disks, slabs, truncated cones, cylinders, and spheres are presented. Slab shields may be included in most of these calculations, and the effect of a cylindrical shield surrounding a cylindrical source may be estimated. Detector points may be located axially, laterally, or interior to a cylindrical source. Line sources may be tilted with respect to a slab shield. All function tables are given for a wide range of arguments.

  8. Variational characterizations for eigenfunctions of analytic self-adjoint operator functions

    OpenAIRE

    Georgios Katsouleas; John Maroulas

    2013-01-01

    In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.

  9. ORBITALES. A program for the calculation of wave functions with an analytical central potential

    International Nuclear Information System (INIS)

    In this paper is described the objective, basis, carrying out in FORTRAN language and use of the program ORBITALES. This program calculate atomic wave function in the case of ths analytical central potential (Author) 8 refs

  10. On Eneström–Kakeya Theorem and Related Analytic Functions

    Indian Academy of Sciences (India)

    W M Shah; A Liman

    2007-08-01

    We prove some extensions of the classical results concerning the Eneström–Kakeya theorem and related analytic functions. Besides several consequences, our results considerably improve the bounds by relaxing and weakening the hypothesis in some cases.

  11. Analytic height correlation function of rough surfaces derived from light scattering

    CERN Document Server

    Zamani, M; Fazeli, S M; Downer, M C; Jafari, G R

    2015-01-01

    We obtain an analytic expression for the height correlation function of a rough surface based on the inverse wave scattering method of Kirchhoff theory. The expression directly relates the height correlation function to diffuse scattered intensity. We test the solution by measuring the angular distribution of light scattered from rough silicon surfaces, solving for the height correlation functions, and comparing them to functions derived from AFM measurements. The results show good agreement. The advantages of this method are its accurate analytical equation for the height correlation function and the simplicity of the experimental setup required to measure it.

  12. Functional calculus for generators of analytic semigroups of operators

    OpenAIRE

    Lopushansky O.V.; Sharyn S.V.

    2012-01-01

    We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty)$. Domain of constructed calculus isdense in the Banach space.

  13. Functional calculus for generators of analytic semigroups of operators

    Directory of Open Access Journals (Sweden)

    Lopushansky O.V.

    2012-06-01

    Full Text Available We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty$. Domain of constructed calculus isdense in the Banach space.

  14. Constructing and Deriving Reciprocal Trigonometric Relations: A Functional Analytic Approach

    Science.gov (United States)

    Ninness, Chris; Dixon, Mark; Barnes-Holmes, Dermot; Rehfeldt, Ruth Anne; Rumph, Robin; McCuller, Glen; Holland, James; Smith, Ronald; Ninness, Sharon K.; McGinty, Jennifer

    2009-01-01

    Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed…

  15. Newton Algorithms for Analytic Rotation: An Implicit Function Approach

    Science.gov (United States)

    Boik, Robert J.

    2008-01-01

    In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

  16. Function of nuclear analytical techniques in Interuniverinteruniversity research cooperation

    International Nuclear Information System (INIS)

    The interuniversity institute was established in 1957 with the instruction to use its major research tool - the nuclear research reactor - in cooperation with and for the benefit of all universities in the Netherlands. Developments in the institute have resulted in two forms of neutron activation analysis currently applied on routine basis. A highly sophisticated automated instrumental multi-element analysis is mostly applied to samples containing elements in the ppm-range and in which no strongly dominating activity is formed. These conditions are fulfilled in general for silicous materials as encountered in geological and archeological samples and in soils and sediments. An automated destructive multi-element analysis involving chemical separations is used for samples with element concentrations in the ppb-range containing some type of dominating activities. This occurs in biological and environmental samples where Na, Fe and Br are mostly available in high concentrations. The institute has been asked many times to help in setting up radio-tracer experiments in various fields including analytical chemistry (isotope dilution, radio immuno assay), physical chemistry (adsorption, diffusion and exchange reactions between solids and liquids during crystallization, corrosion), chemical engineering (determination of contact times and their distribution), biomedical engineering (diffusion processes in membranes for artificial kidneys), biology (uptake of chemical by fish, measurement of displacement habits of animals) etc. Special attention is being paid to the behaviour of trace-elements in metabolic processes, which has been initiated by the medical interest in pathological deviations of copper metabolism in Wilson's and Menkes' diseases. (T.G.)

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

    International Nuclear Information System (INIS)

    We prove the following theorems: 1) The Laurent expansions in ε of the Gauss hypergeometric functions 2F1(I1+aε,I2+bε;I3+(p)/(q)+cε;z), 2F1(I1+(p)/(q)+aε,I2+(p/q)+bε;I3+(p)/(q)+cε;z) and 2F1(I1+(p)/(q)+ aε,I2+bε;I3+(p)/(q)+cε;z), where I1,I2,I3,p,q are arbitrary integers, a,b,c are arbitrary numbers and ε is an infinitesimal parameter, are expressible in terms of multiple polylogarithms of q-roots of unity with coefficients that are ratios of polynomials; 2) The Laurent expansion of the Gauss hypergeometric function 2F1(I1+(p)/(q)+aε,I2+bε;I3+cε;z) is expressible in terms of multiple polylogarithms of q-roots of unity times powers of logarithm with coefficients that are ratios of polynomials; 3) The multiple inverse rational sums Σ∞j=1(Γ(j))/(Γ(1+j-(p)/(q))) (zj)/(jc) Sa1(j-1).. Sap(j-1) and the multiple rational sums Σ∞j=1 (Γ(j+(p)/(q)))/(Γ(1+j)) (zj)/(jc) Sa1(j-1).. Sap(j-1), where Sa(j)=Σjk=1(1)/(ka) is a harmonic series and c is an arbitrary integer, are expressible in terms of multiple polylogarithms; 4) The generalized hypergeometric functions pFp.1(vectorA+vectoraε;vectorB+vectorbε,(p)/(q)+Bp-1;z) and pFp-1(vectorA+vectoraε,(p)/(q)+Ap;vectorB+vectorbε; z) are expressible in terms of multiple polylogarithms with coefficients that are ratios of polynomials. (orig.)

  18. Exchange splitting of the interaction energy and the multipole expansion of the wave function

    CERN Document Server

    Gniewek, Piotr

    2015-01-01

    The exchange splitting $J$ of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula $J_{\\textrm{surf}}[\\varphi]$, the volume-integral formula of the symmetry-adapted perturbation theory $J_{\\textrm{SAPT}}[\\varphi]$, and a variational volume-integral formula $J_{\\textrm{var}}[\\varphi]$. The calculations are based on the multipole expansion of the wave function $\\varphi$, which is divergent for any internuclear distance $R$. Nevertheless, the resulting approximations to the leading coefficient $j_0$ in the large-$R$ asymptotic series $J(R) = 2 e^{-R-1} R ( j_0 + j_1 R^{-1} + j_2 R^{-2} +\\cdots ) $ converge, with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the $J_{\\textrm{var}}[\\varphi]$, $J_{\\textrm{surf}}[\\varphi]$, and $J_{\\textrm{SAPT}}[\\varphi]$ formulas are used, respectively. Additionally, we observe that also the higher $j_k$ coefficients are predicted correctly when the multipole expansion is used in the $J_{...

  19. Exchange splitting of the interaction energy and the multipole expansion of the wave function

    International Nuclear Information System (INIS)

    The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula Jsurf[Φ], the volume-integral formula of the symmetry-adapted perturbation theory JSAPT[Φ], and a variational volume-integral formula Jvar[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j0 in the large-R asymptotic series J(R) = 2e−R−1R(j0 + j1R−1 + j2R−2 + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the Jvar[Φ], Jsurf[Φ], and JSAPT[Φ] formulas are used, respectively. Additionally, we observe that also the higher jk coefficients are predicted correctly when the multipole expansion is used in the Jvar[Φ] and Jsurf[Φ] formulas. The symmetry adapted perturbation theory formula JSAPT[Φ] predicts correctly only the first two coefficients, j0 and j1, gives a wrong value of j2, and diverges for higher jn. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general

  20. External Volume Expansion Modulates Vascular Growth and Functional Maturation in a Swine Model

    Science.gov (United States)

    Kao, Huang-Kai; Hsu, Hsiang-Hao; Chuang, Wen-Yu; Chen, Sheng-Chih; Chen, Bin; Wu, Shinn-Chih; Guo, Lifei

    2016-01-01

    Despite increasing application of the pre-grafting expansion during autologous fat transplantation in breast reconstruction, little is known about its mechanism of action. To address that, ventral skins of miniature pigs were treated over a 10-day or 21-day period, with continuous suction at −50 mm Hg via a 7-cm diameter rubber-lined suction-cup device. Soft tissue thickness increased immediately after this external volume expansion (EVE) treatment, such increase completely disappeared by the next day. In the dermis and subcutaneous fat, the EVE treated groups showed significant increases in blood vessel density evident by CD31 staining as well as in vascular networks layered with smooth muscle cells when compared with the control group. This finding was corroborated by the increased percentage of endothelial cells present in the treatment groups. There was no significant difference in the percentages of proliferating basal keratinocytes or adipocytes, nor in epidermal thickness. Moreover, the EVE had no effect on proliferation or differentiation potential of adipose stem cells. Taken together, the major effects of EVE appeared to be vascular remodeling and maturation of functional blood vessels. This understanding may help clinicians optimize the vascularity of the recipient bed to further improve fat graft survival. PMID:27174509

  1. Analytical theory of the probability distribution function of structure formation

    OpenAIRE

    Anderson, Johan; Kim, Eun-Jin

    2009-01-01

    The probability distribution function (PDF) tails of the zonal flow structure formation and the PDF tails of momentum flux by incorporating effect of a shear flow in ion-temperature-gradient (ITG) turbulence are computed in the present paper. The bipolar vortex soliton (modon) is assumed to be the coherent structure responsible for bursty and intermittent events driving the PDF tails. It is found that stronger zonal flows are generated in ITG turbulence than Hasegawa-Mima (HM) turbulence as w...

  2. Adler function and Bjorken polarized sum rule: perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit

    CERN Document Server

    Cvetič, Gorazd

    2016-01-01

    We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\\{\\beta\\}$-expanded perturbation coefficients at $O(\\alpha_s^4)$ level in $\\overline{\\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\\{\\beta\\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations are pres...

  3. On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

    Science.gov (United States)

    Gottlieb, David; Shu, Chi-Wang

    1994-01-01

    We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

  4. Sub-critical reactor kinetics analysis using incomplete gamma functions and binomial expansions

    International Nuclear Information System (INIS)

    Point reactor kinetics equations with one group of delayed neutrons are solved analytically to determine the neutron population as a function of time for any ramp reactivity insertion in the presence of external neutron source using prompt jump approximation. With the time dependent neutron population the other important kinetic parameters such as the reactor period also can be derived. Analytical solutions are available in the literatures for any ramp reactivity insertion into a critical reactor without considering the source term. Analytical solutions available in the literature by considering the source term also to study sub-critical reactor kinetics. But such a solutions either uses constant source approximation which under predicts the solution, or the available solution is not useful for all kind of sub-critical reactivity and external ramp reactivity insertion combination due to the computer precision incompatibility. In the present work, analyses are carried out to determine the reactivity boundary to which the existing results can converge to a true solution, beyond where the precision incompatibility arises. A new series solution is recommended in the region where existing solution converges to false solution due to precision incompatibility.

  5. Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.

    Science.gov (United States)

    Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz

    2016-02-01

    Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system. PMID:26906812

  6. Examining the Analytic Structure of Green's Functions: Massive Parallel Complex Integration using GPUs

    CERN Document Server

    Windisch, Andreas; Haase, Gundolf; Liebmann, Manfred

    2012-01-01

    Graphics Processing Units (GPUs) are employed for a numerical determination of the analytic structure of two-point correlation functions of Quantum Field Theories. These functions are represented through integrals in d-dimensional Euclidean momentum space. Such integrals can in general not be solved analytically, and therefore one has to rely on numerical procedures to extract their analytic structures if needed. After describing the general outline of the corresponding algorithm we demonstrate the procedure by providing a completely worked-out example in four dimensions for which an exact solution exists. We resolve the analytic structure by highly parallel evaluation of the correlation functions momentum space integral in the complex plane. The (logarithmically) divergent integral is regularized by applying a BPHZ-like Taylor subtraction to the integrand. We find perfect agreement with the exact solution. The fact that each point in the complex plane does not need any information from other points makes thi...

  7. Partition function expansion on region graphs and message-passing equations

    International Nuclear Information System (INIS)

    Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)

  8. The evolutionary strata of DARPP-32 tail implicates hierarchical functional expansion in higher vertebrates

    Indian Academy of Sciences (India)

    Choong Yong Ung; Teow Chong Teoh

    2014-06-01

    DARPP-32 (dopamine and adenosine 3′,5′-monophosphate-regulated phosphoprotein of 32 kDa), which belongs to PPP1R1 gene family, is known to act as an important integrator in dopamine-mediated neurotransmission via the inhibition of protein phosphatase-1 (PP1). Besides its neuronal roles, this protein also behaves as a key player in pathological and pharmacological aspects. Use of bioinformatics and phylogenetics approaches to further characterize the molecular features of DARPP-32 can guide future works. Predicted phosphorylation sites on DARPP-32 show conservation across vertebrates. Phylogenetics analysis indicates evolutionary strata of phosphorylation site acquisition at the C-terminus, suggesting functional expansion of DARPP-32, where more diverse signalling cues may involve in regulating DARPP-32 in inhibiting PP1 activity. Moreover, both phylogenetics and synteny analyses suggest de novo origination of PPP1R1 gene family via chromosomal rearrangement and exonization.

  9. Reexamination of molecular integrals arising from the Dirac equation. Analytical evaluation of molecular auxiliary functions integrals

    CERN Document Server

    Bagci, A

    2016-01-01

    The author in his previous works were presented a numerical integration method, namely, global-adaptive with the Gauss-Kronrod numerical integration extension in order to accurate calculation of molecular auxiliary functions integrals involve power functions with non-integer exponents. They are constitute elements of molecular integrals arising in Dirac equation when Slater-type orbitals with non-integer principal quantum numbers are used. Binomial series representation of power functions method, so far, is used for analytical evaluation of the molecular auxiliary function integrals however, intervals of integration cover areas beyond the condition of convergence. In the present study, analytical evaluation of these integrals is re-examined. They are expressed via prolate spheroidal coordinates. An alternative analytical approximation are derived. Slowly convergent binomial series representation formulae for power functions is investigated through nonlinear sequence transformations for the acceleration of con...

  10. Resonant state expansions

    International Nuclear Information System (INIS)

    The completeness properties of the discrete set of bound state, virtual states and resonances characterizing the system of a single nonrelativistic particle moving in a central cutoff potential is investigated. From a completeness relation in terms of these discrete states and complex scattering states one can derive several Resonant State Expansions (RSE). It is interesting to obtain purely discrete expansion which, if valid, would significantly simplify the treatment of the continuum. Such expansions can be derived using Mittag-Leffler (ML) theory for a cutoff potential and it would be nice to see if one can obtain the same expansions starting from an eigenfunction theory that is not restricted to a finite sphere. The RSE of Greens functions is especially important, e.g. in the continuum RPA (CRPA) method of treating giant resonances in nuclear physics. The convergence of RSE is studied in simple cases using square well wavefunctions in order to achieve high numerical accuracy. Several expansions can be derived from each other by using the theory of analytic functions and one can the see how to obtain a natural discretization of the continuum. Since the resonance wavefunctions are oscillating with an exponentially increasing amplitude, and therefore have to be interpreted through some regularization procedure, every statement made about quantities involving such states is checked by numerical calculations.Realistic nuclear wavefunctions, generated by a Wood-Saxon potential, are used to test also the usefulness of RSE in a realistic nuclear calculation. There are some fundamental differences between different symmetries of the integral contour that defines the continuum in RSE. One kind of symmetry is necessary to have an expansion of the unity operator that is idempotent. Another symmetry must be used if we want purely discrete expansions. These are found to be of the same form as given by ML. (29 refs.)

  11. Search for analytic extensions of combinations of thermal two-point functions at one loop

    International Nuclear Information System (INIS)

    Full text: In this paper, we study the analytic properties of two and three-point amplitudes at Finite Temperature in the Closed Time Path formalism at one loop. In [Phys. Rev. D 71, 036002 (2005)], Weldon has shown the impossibility of analytic continuation for the 2n different n-points functions that appear in the Real Time Formalism in Quantum Field Theory at Finite Temperature, due to the presence of branch cuts at various energy values. Even though none of these functions alone can be extended to complex regions he has found the particular combination of these n-point functions which admit analytic extension to complex energies. In his work, he has considered general properties of thermal average of field operators to analyse the results. On the other hand, at one loop in the perturbation theory more analytic structures appear inside the loop integrals and it is not clear how these results will appear. Here, we consider the λφ3 and the Schwinger Models and study how these analytic properties manifest specifically inside a loop integral. We explicitly extract the branch cuts of the various amplitudes for the self-energies and vertex corrections and show which combinations of them admit analytic continuation for complex energy values. We will extend this paper of n-point functions. (author)

  12. Analytical functions in non-canonical two dimensional algebras; Funzioni analitiche nelle algebre a due componenti

    Energy Technology Data Exchange (ETDEWEB)

    Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione

    1997-10-01

    Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.

  13. Applying the expansion method in hierarchical functions to the solution of Navier-Stokes equations for incompressible fluids

    International Nuclear Information System (INIS)

    This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)

  14. Analytical approach to the current correlation function in dissipative two-state systems

    Institute of Scientific and Technical Information of China (English)

    Qin WANG; Cheng JIANG; Hang ZHENG

    2008-01-01

    Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipa-tive two-state systems with the view of understanding the ef-fects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations.

  15. Optimization of Quantum Monte Carlo Wave Functions Using Analytical Energy Derivatives

    CERN Document Server

    Lin, X; Rappe, A M; Lin, Xi; Zhang, Hongkai; Rappe, Andrew M.

    1999-01-01

    An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational principle yields significantly low er energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A g eneral theorem is presented, which substantially simplifies the analytic expressions of de rivatives in the case of wave function optimization. To demonstrate the method, the ground state energies of the first-row elements are calculated.

  16. Exchange splitting of the interaction energy and the multipole expansion of the wave function

    Energy Technology Data Exchange (ETDEWEB)

    Gniewek, Piotr, E-mail: pgniewek@tiger.chem.uw.edu.pl; Jeziorski, Bogumił, E-mail: jeziorsk@chem.uw.edu.pl [Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw (Poland)

    2015-10-21

    The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.

  17. The Challenge of Developing a Universal Case Conceptualization for Functional Analytic Psychotherapy

    Science.gov (United States)

    Bonow, Jordan T.; Maragakis, Alexandros; Follette, William C.

    2012-01-01

    Functional Analytic Psychotherapy (FAP) targets a client's interpersonal behavior for change with the goal of improving his or her quality of life. One question guiding FAP case conceptualization is, "What interpersonal behavioral repertoires will allow a specific client to function optimally?" Previous FAP writings have suggested that a therapist…

  18. Simple analytical expression for work function in the 'nearest neighbour' approximation

    Energy Technology Data Exchange (ETDEWEB)

    Chrzanowski, J. [Institute of Physics, Maritime University of Szczecin, 1-2 Waly Chrobrego, Szczecin 70-500 (Poland); Kravtsov, Yu.A., E-mail: y.kravtsov@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, 1-2 Waly Chrobrego, Szczecin 70-500 (Poland); Space Research Institute, Profsoyuznaya St. 82/34, Moscow 117997 (Russian Federation)

    2011-01-17

    Nonlocal operator of potential is suggested, based on the 'nearest neighbour' approximation (NNA) for single electron wave function in metals. It is shown that Schroedinger equation with nonlocal potential leads to quite simple analytical expression for work function, which surprisingly well fits to experimental data.

  19. Simple analytical expression for work function in the “nearest neighbour” approximation

    Science.gov (United States)

    Chrzanowski, J.; Kravtsov, Yu. A.

    2011-01-01

    Nonlocal operator of potential is suggested, based on the “nearest neighbour” approximation (NNA) for single electron wave function in metals. It is shown that Schrödinger equation with nonlocal potential leads to quite simple analytical expression for work function, which surprisingly well fits to experimental data.

  20. Analytic eigenenergies of Dirac equation under a confining linear potential using basis functions localized in spacetime

    CERN Document Server

    Fukushima, Kimichika

    2015-01-01

    This paper presents analytical eigenenergies for a pair of confined fundamental fermion and antifermion under a linear potential derived from the Wilson loop for the non-Abelian Yang-Mills field. We use basis functions localized in spacetime, and the Hamiltonian matrix of the Dirac equation is analytically diagonalized. The squared system eigenenergies are proportional to the string tension and the absolute value of the Dirac's relativistic quantum number related to the total angular momentum, consistent with the expectation.

  1. Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    CERN Document Server

    Stefańska, Patrycja

    2016-01-01

    The Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\\/~Szmytkowski, J.\\ Phys.\\ B \\textbf{30}, 825 (1997); \\textbf{30}, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric functions ${}_3F_2$ of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with $1 \\leqslant Z \\leqslant 137$ and compare them with data available in the literature.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2008-07-15

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

  3. Effects of Lung Expansion Therapy on Lung Function in Patients with Prolonged Mechanical Ventilation

    Directory of Open Access Journals (Sweden)

    Yen-Huey Chen

    2016-01-01

    Full Text Available Common complications in PMV include changes in the airway clearance mechanism, pulmonary function, and respiratory muscle strength, as well as chest radiological changes such as atelectasis. Lung expansion therapy which includes IPPB and PEEP prevents and treats pulmonary atelectasis and improves lung compliance. Our study presented that patients with PMV have improvements in lung volume and oxygenation after receiving IPPB therapy. The combination of IPPB and PEEP therapy also results in increase in respiratory muscle strength. The application of IPPB facilitates the homogeneous gas distribution in the lung and results in recruitment of collapsed alveoli. PEEP therapy may reduce risk of respiratory muscle fatigue by preventing premature airway collapse during expiration. The physiologic effects of IPPB and PEEP may result in enhancement of pulmonary function and thus increase the possibility of successful weaning from mechanical ventilator during weaning process. For patients with PMV who were under the risk of atelectasis, the application of IPPB may be considered as a supplement therapy for the enhancement of weaning outcome during their stay in the hospital.

  4. Expanded functional diversity of shaker K(+ channels in cnidarians is driven by gene expansion.

    Directory of Open Access Journals (Sweden)

    Timothy Jegla

    Full Text Available The genome of the cnidarian Nematostella vectensis (starlet sea anemone provides a molecular genetic view into the first nervous systems, which appeared in a late common ancestor of cnidarians and bilaterians. Nematostella has a surprisingly large and diverse set of neuronal signaling genes including paralogs of most neuronal signaling molecules found in higher metazoans. Several ion channel gene families are highly expanded in the sea anemone, including three subfamilies of the Shaker K(+ channel gene family: Shaker (Kv1, Shaw (Kv3 and Shal (Kv4. In order to better understand the physiological significance of these voltage-gated K(+ channel expansions, we analyzed the function of 18 members of the 20 gene Shaker subfamily in Nematostella. Six of the Nematostella Shaker genes express functional homotetrameric K(+ channels in vitro. These include functional orthologs of bilaterian Shakers and channels with an unusually high threshold for voltage activation. We identified 11 Nematostella Shaker genes with a distinct "silent" or "regulatory" phenotype; these encode subunits that function only in heteromeric channels and serve to further diversify Nematostella Shaker channel gating properties. Subunits with the regulatory phenotype have not previously been found in the Shaker subfamily, but have evolved independently in the Shab (Kv2 family in vertebrates and the Shal family in a cnidarian. Phylogenetic analysis indicates that regulatory subunits were present in ancestral cnidarians, but have continued to diversity at a high rate after the split between anthozoans and hydrozoans. Comparison of Shaker family gene complements from diverse metazoan species reveals frequent, large scale duplication has produced highly unique sets of Shaker channels in the major metazoan lineages.

  5. Tailored functional materials with controlled thermal expansion and excellent thermal conductivity

    International Nuclear Information System (INIS)

    Engineering materials are mainly used for structures. Therefore high-strength, stiffness and sufficient toughness are of prime importance. For a long time engineers thought first in terms of metals. Material scientists developed alloys tailored to the needs of industry. Ceramics are known to be brittle and therefore not suitable in the first place for structural application under stress. Polymers with their low modulus became attractive when reinforced with high-strength fibres. Composites processed by polymer, metal or ceramic matrices and high-strength reinforcements have been introduced into many sectors of industry. Engineering materials for structural applications fulfil a function: they withstand high stresses, temperatures, fatigue, creep etc. But usually we do not call them functional materials. Functional materials serve applications apart from classical engineering fields. Electricity conducting materials, semi conductors, memory alloys and many others are called functional materials. Because of the fact that the basic physical properties cannot be changed in single-phase materials, the combination of two and more materials with different properties lead to components with new and tailored properties. A few techniques for preparation are described as powder metallurgy, infiltration of prepegs and compaction of precoated fibres/particles. The lecture is focusing on carbon fibre/particle reinforced Metal Matrix Materials. The achievable properties, in particular the thermal conductivity originating from the base materials is depending on the orientation of the fibres and interfacial contacts in the composite. The carefully controlled expansion behaviour is the most important property to use the material as a heat sink in electronic assemblies. (author)

  6. Efficient time-dependent density functional theory approximations for hybrid density functionals: Analytical gradients and parallelization

    Science.gov (United States)

    Petrenko, Taras; Kossmann, Simone; Neese, Frank

    2011-02-01

    In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ˜26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ˜27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ˜24 on 30 processors. The

  7. Analytic Solutions of a Second-Order Iterative Functional Differential Equations

    Science.gov (United States)

    Liu, Lingxia

    In this paper, the existence of analytic solutions of an iterative functional differential equation is studied. We reduce this problem to finding analytic solutions of a functional differential equation without iteration of the unknown function. For technical reasons, in previous work the constant α given in Schröder transformation is required to fulfill that α is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we break the restraint of the Diophantine condition and obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.

  8. Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization

    OpenAIRE

    Stoitsov, M.; Kortelainen, M.; Bogner, S. K.; Duguet, T.; Furnstahl, R. J.; Gebremariam, B.; Schunck, N.

    2010-01-01

    In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the dens...

  9. The resonance expansion for the Green's function of the Schroedinger and wave equations

    International Nuclear Information System (INIS)

    We give a survey of some recent mathematical work on resonances, in particular on perturbation series, low energy expansions and on resonances for point interactions. Expansions of the kernels of esup(-it)√sup(H+) and esup(-itH) in terms of resonances are also given (where Hsub(+) is the positive part of the Hamiltonian). (orig.)

  10. Output Tracking Control of Switched Hybrid Systems: A Fliess Functional Expansion Approach

    Directory of Open Access Journals (Sweden)

    Fenghua He

    2013-01-01

    Full Text Available The output tracking problem is investigated for a nonlinear affine system with multiple modes of continuous control inputs. We convert the family of nonlinear affine systems under consideration into a switched hybrid system by introducing a multiple-valued logic variable. The Fliess functional expansion is adopted to express the input and output relationship of the switched hybrid system. The optimal switching control is determined for a multiple-step output tracking performance index. The proposed approach is applied to a multitarget tracking problem for a flight vehicle aiming for one real target with several decoys flying around it in the terminal guidance course. These decoys appear as apparent targets and have to be distinguished with the approaching of the flight vehicle. The guidance problem of one flight vehicle versus multiple apparent targets should be considered if no large miss distance might be caused due to the limitation of the flight vehicle maneuverability. The target orientation at each time interval is determined. Simulation results show the effectiveness of the proposed method.

  11. Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time

    CERN Document Server

    Kamikado, Kazuhiko; Uchino, Shun

    2016-01-01

    Motivated by experiments with cold atoms, we investigate a mobile impurity immersed in a Fermi sea in three dimensions at zero temperature by means of the functional renormalization group. We first perform the derivative expansion of the effective action to calculate the ground state energy and Tan's contact across the polaron-molecule transition for several mass imbalances. Next we study quasiparticle properties of the impurity by using a real-time method recently developed in nuclear physics, which allows one to go beyond the derivative expansion. We obtain the spectral function of the polaron, the effective mass and quasiparticle weight of attractive and repulsive polarons, and clarify how they are affected by mass imbalances.

  12. Analytic integration of a common set of microwave beam intensity functions

    Energy Technology Data Exchange (ETDEWEB)

    Potter, S.D. [New York Univ., New York, NY (United States)

    1994-12-31

    When designing a wireless power transmission system, a virtually limitless number of aperture illumination functions are available. However, a commonly-used set of beam tapers results in received intensities that involve Bessel functions. This family of intensities is convenient to study and compare systematically. A cosntraint on the calculation of reception efficiency is the need to write numerical routines to integrate such functions. It is shown that these functions can be integrated analytically, resulting in a concise formula for reception efficiency as a function of rectifying antenna (rectenna) diameter.

  13. Semi-analytical calculations for parameters of boiling layer in isetropic expansion of warm dense matter with van der Waals equation of state

    CERN Document Server

    Borovikov, Dmitry

    2012-01-01

    Features and parameters of \\boiling" liquid layer, which arises under conditions of isentropic expansion of warm dense matter (WDM), are stud- ied with the use of simplest van der Waals equation of state (EOS). Advan- tage of this EOS is possibility of demonstrable and semi-analytical descrip- tion of thermo- and hydrodynamics of the process. Idealized self-similar case of behavior of matter on interception of equilibrium (not metastable) isoentropic curve and boundary of gas-liquid coexistence curve (binodal) is analyzed. The possibility of formation of such "liquid layer" was studied previously in [1] during solving the problem of ablation of metal surface under the action of strong laser radiation. Peculiarity of such "freezing" of finite portion of expanding matter in the state, which corresponds to the binodal of gas-liquid or/and other phase transitions|so called "phase freezeout"and prospects of applications of this phenomenon for intended generation of uniform and extensive zone of previously unexplor...

  14. Differential Sandwich Theorems for some Subclasses of Analytic Functions Involving a Linear Operator

    Directory of Open Access Journals (Sweden)

    S. Sivasubramanian

    2007-10-01

    Full Text Available By making use of the familiar Carlson-Shaffer operator,the authors derive derive some subordination and superordination results for certain normalized analytic functions in the open unit disk. Relevant connections ofthe results, which are presented in this paper, with various other known results are also pointed out.

  15. On the analyticity of periodic gravity water waves with integrable vorticity function

    OpenAIRE

    Escher, Joachim; Matioc, Bogdan-Vasile

    2013-01-01

    We prove that the streamlines and the profile of periodic gravity water waves traveling over a flat bed with wavespeed which exceeds the horizontal velocity of all fluid particles are real-analytic graphs if the vorticity function is merely integrable.

  16. An Example of a Hakomi Technique Adapted for Functional Analytic Psychotherapy

    Science.gov (United States)

    Collis, Peter

    2012-01-01

    Functional Analytic Psychotherapy (FAP) is a model of therapy that lends itself to integration with other therapy models. This paper aims to provide an example to assist others in assimilating techniques from other forms of therapy into FAP. A technique from the Hakomi Method is outlined and modified for FAP. As, on the whole, psychotherapy…

  17. Prop erties for Certain Sub classes of Analytic Functions Asso ciated with Generalized Multiplier Transformation

    Institute of Scientific and Technical Information of China (English)

    LI Zong-tao; GUO Dong

    2014-01-01

    In this paper, we introduce certain new subclasses of analytic functions defined by generalized multiplier transformation. By using the differential subordination, we study and investigate various inclusion properties of these classes. Also inclusion properties of these classes involving the integral operator are considered.

  18. Functional analytic background for a theory of infinite-dimensional reductive Lie groups

    OpenAIRE

    Beltita, Daniel

    2007-01-01

    Motivated by the interesting and yet scattered developments in representation theory of Banach-Lie groups, we discuss several functional analytic issues which should underlie the notion of infinite-dimensional reductive Lie group: norm ideals, triangular integrals, operator factorizations, and amenability.

  19. Interpersonal Mindfulness Informed by Functional Analytic Psychotherapy: Findings from a Pilot Randomized Trial

    Science.gov (United States)

    Bowen, Sarah; Haworth, Kevin; Grow, Joel; Tsai, Mavis; Kohlenberg, Robert

    2012-01-01

    Functional Analytic Psychotherapy (FAP; Kohlenberg & Tsai, 1991) aims to improve interpersonal relationships through skills intended to increase closeness and connection. The current trial assessed a brief mindfulness-based intervention informed by FAP, in which an interpersonal element was added to a traditional intrapersonal mindfulness…

  20. Functional Analytic Psychotherapy (FAP) in Ibero-America: Review of Current Status and Some Proposals

    Science.gov (United States)

    Munoz-Martinez, Amanda; Novoa-Gomez, Monica; Gutierrez, Rochy Vargas

    2012-01-01

    Functional Analytic Psychotherapy (FAP) has been making an important rise in Ibero-America in recent years. This paper presents a review of different contributions, problems and some proposals. Three principal topics are reviewed: (a) general characteristics and theoretical bases of FAP, (b) the uses of FAP and its relationship with other…

  1. Functional Analytic Psychotherapy (FAP): A Review of Publications from 1990 to 2010

    Science.gov (United States)

    Mangabeira, Victor; Kanter, Jonathan; Del Prette, Giovana

    2012-01-01

    Functional Analytic Psychotherapy (FAP), a therapy based on radical behaviorism, establishes the priority of the therapeutic interaction as a mechanism of change in psychotherapy. Since the first book on FAP appeared in 1991, it has been the focus of many papers and has been incorporated by the community of behavior therapists. This paper is a…

  2. Closed analytical expressions for some useful sums and integrals involving Legendre function

    International Nuclear Information System (INIS)

    Simple closed analytical expressions are obtained for some integrals and infinite sums involving Legendre functions. They are lacking in the mathematical literature. The limiting values of these expressions pass into the known ones. The obtained expressions for the above sums and integrals may be useful for the calculation of the magnetic fields with configurations close to the toroidal ones (tokamak devices)

  3. A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    J.Dziok

    2011-01-01

    In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination.Coefficient estimates,distortion theorems,integral means inequalities,and the radii of convexity and starlikeness are investigated.Convolution properties are also pointed out.

  4. External Volume Expansion Modulates Vascular Growth and Functional Maturation in a Swine Model

    OpenAIRE

    Kao, Huang-Kai; Hsu, Hsiang-Hao; Chuang, Wen-Yu; Chen, Sheng-Chih; Chen, Bin; Wu, Shinn-Chih; Guo, Lifei

    2016-01-01

    Despite increasing application of the pre-grafting expansion during autologous fat transplantation in breast reconstruction, little is known about its mechanism of action. To address that, ventral skins of miniature pigs were treated over a 10-day or 21-day period, with continuous suction at −50 mm Hg via a 7-cm diameter rubber-lined suction-cup device. Soft tissue thickness increased immediately after this external volume expansion (EVE) treatment, such increase completely disappeared by the...

  5. Edgeworth expansion for the survival function estimator in the Koziol-Green model

    Institute of Scientific and Technical Information of China (English)

    SUN; Liuquan(孙六全); WU; Guofu(吴国富)

    2002-01-01

    In the KozioI-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studen tized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.

  6. Structure and analytical potential energy function for the ground state of the BCx (x=0, -1)

    Institute of Scientific and Technical Information of China (English)

    Geng Zhen-Duo; Zhang Yan-Song; Fan Xiao-Wei; Lu Zhan-Sheng; Luo Gai-Xia

    2006-01-01

    In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data (αe, ωe and ωeXe) of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.

  7. Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

    Science.gov (United States)

    Izacard, Olivier

    2016-08-01

    In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it

  8. Assessing Impairment of Executive Function and Psychomotor Speed in Premanifest and Manifest Huntington's Disease Gene-expansion Carriers

    DEFF Research Database (Denmark)

    Unmack Larsen, Ida; Vinther-Jensen, Tua; Gade, Anders;

    2015-01-01

    Executive functions (EF) and psychomotor speed (PMS) has been widely studied in Huntington's disease (HD). Most studies have focused on finding markers of disease progression by comparing group means at different disease stages. Our aim was to investigate performances on nine measures of EF and PMS...... in a group of premanifest and manifest HD-gene expansion carriers and to investigate which measures were most sensitive for assessment of individual patients by analyzing frequencies of impaired performances relative to healthy controls. We recruited HD gene-expansion carriers, 48 manifest and 50...... premanifest and as controls 39 healthy gene-expansion negative individuals. All participants underwent neurological examination and neuropsychological testing with nine cognitive measures. The frequency of impairment was investigated using cutoff scores. In group comparisons the manifest HD gene...

  9. On the analytical evaluation of the partition function for unit hypercubes in four dimensions

    International Nuclear Information System (INIS)

    The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)

  10. The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps

    OpenAIRE

    Lehner, Sabrina

    2016-01-01

    The well-known Riemann Mapping Theorem states the existence of a conformal map of a simply connected proper domain of the complex plane onto the upper half plane. One of the main topics in geometric function theory is to investigate the behaviour of the mapping functions at the boundary of such domains. In this work, we always assume that a piecewise analytic boundary is given. Hereby, we have to distinguish regular and singular boundary points. While the asymptotic behaviour for regular boun...

  11. Certain Subclasses of Analytic and Bi-Univalent Functions Involving Double Zeta Functions

    Directory of Open Access Journals (Sweden)

    Saibah Siregar

    2012-01-01

    Full Text Available In the present paper, we introduce two new subclasses of the functions class Σ of bi-univalent functions involving double zeta functions in the open unit disc U={z:zEC, |z|<1}. The estimates on the coefficients |a2| and |a3| for functions in these new subclasses of the function class Σ are obtained in our investigation.

  12. The functional connectivity of the human caudate: An application of meta-analytic connectivity modeling with behavioral filtering

    OpenAIRE

    Robinson, Jennifer L.; Laird, Angela R.; Glahn, David C.; Blangero, John; Sanghera, Manjit K.; Pessoa, Luiz; Fox, P. Mickle; Uecker, Angela; Friehs, Gerhard; Young, Keith A.; Griffin, Jennifer L.; LOVALLO, WILLIAM R.; Fox, Peter T

    2011-01-01

    Meta-analysis based techniques are emerging as powerful, robust tools for developing models of connectivity in functional neuroimaging. Here, we apply meta-analytic connectivity modeling to the human caudate to 1) develop a model of functional connectivity, 2) determine if meta-analytic methods are sufficiently sensitive to detect behavioral domain specificity within region-specific functional connectivity networks, and 3) compare meta-analytic driven segmentation to structural connectivity p...

  13. Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

    International Nuclear Information System (INIS)

    Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented

  14. Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method.

    Science.gov (United States)

    Nakata, Hiroya; Fedorov, Dmitri G; Zahariev, Federico; Schmidt, Michael W; Kitaura, Kazuo; Gordon, Mark S; Nakamura, Shinichiro

    2015-03-28

    Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented. PMID:25833559

  15. Analytic Structure of the SCFT Energy Functional of Multicomponent Block Copolymers

    CERN Document Server

    Jiang, Kai; Zhang, Pingwen

    2013-01-01

    This paper concerns the analytic structure of the self-consistent field theory (SCFT) energy functional of multicomponent block copolymer systems which contain more than two chemically distinct blocks. The SCFT has enjoyed considered success and wide usage in investigation of the complex phase behavior of block copolymers. It is well-known that the physical solutions of the SCFT equations are saddle points, however, the analytic structure of the SCFT energy functional has received little attention over the years. A recent work by Fredrickson and collaborators [see the monograph by Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers, (2006), pp. 203-209] has analysed the mathematical structure of the field energy functional for polymeric systems, and clarified the index-1 saddle point nature of the problem produced by the incompressibility constraint. In this paper, our goals are to draw further attention to multicomponent block copolymers utilizing the Hubbard-Stratonovich transformation used by Fre...

  16. Analyticity properties of three-point functions in QCD beyond leading order

    International Nuclear Information System (INIS)

    The removal of unphysical singularities in the perturbatively calculable part of the pion form factor - a classical example of a three-point function in QCD - is discussed. Different 'analytization' procedures in the sense of Shirkov and Solovtsov are examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a whole, as proposed before by Karanikas and Stefanis, one can make infrared finite not only the strong running coupling and its powers, but also cure potentially large logarithms (that first appear in the next-to-leading order) containing the factorization scale and modifying the discontinuity across the cut along the negative real axis. The scheme used here generalizes the Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer powers of the strong coupling and diminishes the dependence of QCD hadronic quantities on all perturbative scheme and scale-setting parameters, including the factorization scale

  17. An alternative analytical formulation for the Voigt function applied to resonant effects in nuclear processes

    International Nuclear Information System (INIS)

    The Voigt function H(a,v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.

  18. An alternative analytical formulation for the Voigt function applied to resonant effects in nuclear processes

    Energy Technology Data Exchange (ETDEWEB)

    Palma, Daniel A.P., E-mail: dpalmaster@gmail.com [CNEN-Comissao Nacional de Energia Nuclear, 22290-901, Rio de Janeiro (Brazil); Goncalves, Alessandro da C; Martinez, Aquilino S. [COPPE/UFRJ-Programa de Engenharia Nuclear, 21941-972, Rio de Janeiro (Brazil)

    2011-10-21

    The Voigt function H(a,v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.

  19. An alternative analytical formulation for the Voigt function applied to resonant effects in nuclear processes

    Science.gov (United States)

    Palma, Daniel A. P.; Gonçalves, Alessandro da C.; Martinez, Aquilino S.

    2011-10-01

    The Voigt function H( a, v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.

  20. Application of the Multi-Peaked Analytically Extended Function to Representation of Some Measured Lightning Currents

    CERN Document Server

    Lundengård, Karl; Javor, Vesna; Silvestrov, Sergei

    2016-01-01

    A multi-peaked form of the analytically extended function (AEF) is used for approximation of lightning current waveforms in this paper. The AEF function's parameters are estimated using the Marquardt least-squares method (MLSM), and the general procedure for fitting the $p$-peaked AEF function to a waveform with an arbitrary (finite) number of peaks is briefly described. This framework is used for obtaining parameters of 2-peaked waveforms typically present when measuring first negative stroke currents. Advantages, disadvantages and possible improvements of the approach are also discussed.

  1. VECTOR-VALUED HOLOMORPHIC FUNCTIONS ON THE COMPLEX BALL AND THE ANALYTIC RADON-NIKODYM PROPERTY

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The complex Banach spaces X with values in which every bounded holomorphic function in the unit ball B of Cd(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property.The proof is based on inner Hardy martingales introduced here.The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.

  2. Expansion of amphibian intronless interferons revises the paradigm for interferon evolution and functional diversity

    Science.gov (United States)

    Interferons (IFNs) are key cytokines identified in vertebrates, and evolutionary dominance of intronless IFN genes in amniotes is a signature event in IFN evolution. For the first time, we show that the emergence and expansion of intronless IFN genes is evident in amphibians, shown by 24-37 intronle...

  3. Foundations of predictive analytics

    CERN Document Server

    Wu, James

    2012-01-01

    Drawing on the authors' two decades of experience in applied modeling and data mining, Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications, such as consumer behavior modeling, risk and marketing analytics, and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods, from distributions to cumulant and copula functions to Cornish--Fisher expansion and o

  4. Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube

    International Nuclear Information System (INIS)

    Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states are investigated. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected significantly by the material nonhomogeneity. Different modes of plasticization may take place unlike the homogeneous case. It is also shown mathematically that the nonhomogeneous elastoplastic solution presented here reduces to that of a homogeneous one by appropriate choice of the material parameters

  5. Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

    CERN Document Server

    Rassias, Michael

    2014-01-01

    This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

  6. Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

    International Nuclear Information System (INIS)

    We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities

  7. Aptamer functionalized lipid multilayer gratings for label free detection of specific analytes

    Science.gov (United States)

    Prommapan, Plengchart; Lowry, Troy W.; van Winkle, David; Lenhert, Steven

    2015-03-01

    Lipid multilayer gratings have been formed on surfaces with a period of 700 nm. When illuminated with white light incident at about 50°, these gratings diffract green light perpendicular to their surface. We demonstrate the potential of these gratings as sensors for analytes by monitoring changes in the diffracted light due to the changes in the size and shape of the grating in response to analyte binding. To demonstrate this potential application, a lipid multilayer grating was functionalized with a thrombin binding aptamer. The selectivity of our aptamer functionalized lipid gratings was confirmed both by monitoring the diffracted light intensity and by fluorescence microscopy. Furthermore, the results show that the binding activity between the aptamer and thrombin depends on the relative composition of a zwitterionic lipid (DOPC) and a cationic lipid (DOTAP). This work shows that nanostructured lipid multilayers on surfaces are a promising nanomaterial for label-free bio-sensing applications.

  8. UNIFORM ANALYTIC CONSTRUCTION OF WAVELET ANALYSIS FILTERS BASED ON SINE AND COSINE TRIGONOMETRIC FUNCTIONS

    Institute of Scientific and Technical Information of China (English)

    李建平; 唐远炎; 严中洪; 张万萍

    2001-01-01

    Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When/N = 2k- 1 and N = 2k , the unified analytic constructions of orthogonal wavelet filters are put forward,respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.

  9. Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model

    Directory of Open Access Journals (Sweden)

    Houyu Zhao

    2012-01-01

    Full Text Available We study the existence of analytic solutions of a functional differential equation (z(s+α2z'(s=β(z(s+z(s-z(s which comes from traffic flow model. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constant λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition.

  10. An Analytically-Derived, Parametric Transfer-Function Model for Ideal, Packed, Binary Distillation Columns

    OpenAIRE

    Edwards, J B; Guilandoust, M

    1980-01-01

    Partial differential equations and boundary conditions are derived for the large-and-small-signal behaviour of compositions in an ideal, symmetrical spatially-continuous (packed) distillation column separating a binary mixture. A precise paramemtric transfer-function matrix (T.F.M.) for the system is derived completely analytically so allowing the calculation of parameters of the T.F.M. directly from those of the plant. It is shown that the correct choice of input and output vectors yields a ...

  11. Integration Quality Function Deployment and Analytic Hierarchy Process Methods to Improve Service Quality

    OpenAIRE

    Shun-Hsing Chen; Fei-Yun Chen; Tsu-Ming Yeh

    2015-01-01

    Customer needs regarding product and service quality are rising. Because of the economic recession, the food and beverage industry faces strong competition. Customer needs can be satisfied only by understanding their needs. Therefore, this study uses Quality Function Deployment (QFD) and the Analytic Hierarchy Process (AHP) to clarify customer needs and to explore the most effective options to improve service quality in the vegetarian foods industry. This study primary objective included: (1)...

  12. Analytic cubic and quartic force fields using density-functional theory

    OpenAIRE

    Ringholm, Magnus; Jonsson, Dan; Bast, Radovan; Gao, Bin; Thorvaldsen, Andreas J; Ekström, Ulf; Helgaker, Trygve; Ruud, Kenneth

    2014-01-01

    We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kern...

  13. Proof of Analytic Extension Theorem for Zeta Function Using Abel Transformation and Euler Product

    Directory of Open Access Journals (Sweden)

    Mbaitiga Zacharie

    2010-01-01

    Full Text Available Problem statement: In the prime number the Riemann zeta function is unquestionable and undisputable one of the most important questions in mathematics whose many researchers are still trying to find answer to some unsolved problems such as Riemann Hypothesis. In this study we proposed a new method that proves the analytic extension theorem for zeta function. Approach: Abel transformation was used to prove that the extension theorem is true for the real part of the complex variable that is strictly greater than one and consequently provides the required analytic extension of the zeta function to the real part greater than zero and Euler product was used to prove the real part of the complex that are less than zero and greater or equal to one. Results: From this proposed study we noted that the real values of the complex variable are lying between zero and one which may help to understand the relation between zeta function and its properties and consequently can pay the way to solve some complex arithmetic problems including the Riemann Hypothesis. Conclusion: The combination of Abel transformation and Euler product is a powerful tool for proving theorems and functions related to Zeta function including other subjects such as radio atmospheric occultation.

  14. Semi-Analytical Solution of Functionally Graded Circular Short Hollow Cylinder Subject to Transient Thermal Loading

    Directory of Open Access Journals (Sweden)

    Eskandari Jam Jafar

    2014-12-01

    Full Text Available In this paper, by using a semi-analytical solution based on multi-layered approach, the authors present the solutions of temperature, displacements, and transient thermal stresses in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Time variations of the temperature, displacements, and stresses are obtained by employing series solving method for ordinary differential equation, Laplace transform techniques and a numerical Laplace inversion.

  15. Boundary and expansion effects on two-pion correlation functions in relativistic heavy-ion collisions

    OpenAIRE

    Ayala, Alejandro; Sanchez, Angel

    2001-01-01

    We examine the effects that a confining boundary together with hydrodynamical expansion play on two-pion distributions in relativistic heavy-ion collisions. We show that the effects arise from the introduction of further correlations due both to collective motion and the system's finite size. As is well known, the former leads to a reduction in the apparent source radius with increasing average pair momentum K. However, for small K, the presence of the boundary leads to a decrease of the appa...

  16. Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function

    Institute of Scientific and Technical Information of China (English)

    LIU Wen; SHAN Rui

    2009-01-01

    Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lamè solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.

  17. Constraints on the nuclear energy density functional and new possible analytical forms

    International Nuclear Information System (INIS)

    The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are: 1) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, 2) the tedious analytical derivation of the functional and of the associated one-body fields, 3) the implementation of the latter in existing codes, and 4) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as the state-of-the-art (quasi) bilinear functionals. (author)

  18. Federalism. Theory and Neo-Functionalism: Elements for an analytical framework

    DEFF Research Database (Denmark)

    Dosenrode, Søren

    2010-01-01

    The purpose of this article is to propose a draft for an analytical frame for analyzing regional integration consisting of federalism theory and neo-functionalism. It starts out discussing the concept of regional integration setting up a stagiest model for categorizing it.Then follows an analysis...... of federalism theory and neo-functionalism. One argument of this article is to understand federalism theory as a regional integration theory. Another is to look at federalism theory as complementary to neo-functionalism when trying to explain regional integration. Federalism theory, in an extended...... Riker-McKayian way, is able to explain the cases of ‘big bang’ integration (USA, Australia, Canada), but not an ‘organic’ integration process. Neo-functionalism, on the other hand, is not able to explain this relatively fast form of integration, but it is – in its new version - able to analyze and...

  19. Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system

    International Nuclear Information System (INIS)

    In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.

  20. Analytical environmental nanotechnology. Functional and chemical multielemental speciation in natural and engineered nanoparticles

    International Nuclear Information System (INIS)

    Complete text of publication follows. Nanoscale materials find use in a variety of different areas such as electronic, biomedical, sensing sciences, pharmaceutical, cosmetic, energy, environmental, catalytic and material applications. The environmental nanoparticles (NPs) can be classified in two groups: Natural NPs and Engineered or Anthropogenic NPs. Today the development of analytical methods for physical and chemical characterization of nanoparticles is still in its infancy .The natural and the engineered NPs can be investigated with an integrated analytical methodology by using several complementary techniques . We will show our experimental results on new analytical methodology to investigate the rol of the elements Cd, Cr, Cu, Hg, Ni, Pb, Zn, As, Co, Mo, Al, B, Fe, Mn, Sb, Sn, Ti, V in Organic and Inorganic Nanoparticles, by using specially hyphenated techniques like as: AsFIFFF-ICP-MS, AsFIFFF-UV.VIS, HPLC-SEC-UV.VIS-ICP-MS, PAGE-ICP-MS, PAGE-LA-ICP-MS, and Solid NPs Voltametry . The application of mathematical deconvolution to the fractograms to refine analytical signals provides a high resolution and the determination of polydispersity of particles as a very interesting information. The obtained results give a useful information about the Bioavailability, Mobility and Toxicity of the elements associated to nanoparticles. We will show also the experimental results and conclusions about the use of these hyphenated techniques to develop analytical methodology from three important point of view: Particle Size-Particle Kind and Chemical Composition, to establish a model of Functional Speciation of engineered nanoparticles like colloidal silver, and several nano-biocolloids from aquatic pseudo-multiphases. The work has been supported by Spanish Department of Science (Project CTQ 2006-00894 BQU).

  1. Analytical Energy Gradients in Range-Separated Hybrid Density Functional Theory with Random Phase Approximation

    CERN Document Server

    Mussard, Bastien; Ángyán, János G

    2015-01-01

    Analytical forces have been derived in the Lagrangian framework for several random phase approximation (RPA) correlated total energy methods based on the range separated hybrid (RSH) approach, which combines a short-range density functional approximation for the short-range exchange-correlation energy with a Hartree-Fock-type long-range exchange and RPA long-range correlation. The RPA correlation energy has been expressed as a ring coupled cluster doubles (rCCD) theory. The resulting analytical gradients have been implemented and tested for geometry optimization of simple molecules and intermolecular charge transfer complexes, where intermolecular interactions are expected to have a non-negligible effect even on geometrical parameters of the monomers.

  2. Expressing self-absorption in the analytical function of inductively coupled plasma atomic emission spectrometry

    Science.gov (United States)

    Kántor, Tibor; Bartha, András

    2015-11-01

    The self-absorption of spectral lines was studied with up to date multi-element inductively coupled plasma atomic emission spectrometry (ICP-AES) instrumentation using radial and axial viewing of the plasma, as well, performing line peak height and line peak area measurements. Two resonance atomic and ionic lines of Cd and Mg were studied, the concentration range was extended up to 2000 mg/L. At the varying analyte concentration, constant matrix concentration of 10,000 mg/L Ca was ensured in the pneumatically nebulized solutions. The physical and the phenomenological formulation of the emission analytical function is overviewed and as the continuity of the earlier results the following equation is offered:

  3. Towards an Analytical Age-Dependent Model of Contrast Sensitivity Functions for an Ageing Society

    Science.gov (United States)

    Joulan, Karine; Brémond, Roland

    2015-01-01

    The Contrast Sensitivity Function (CSF) describes how the visibility of a grating depends on the stimulus spatial frequency. Many published CSF data have demonstrated that contrast sensitivity declines with age. However, an age-dependent analytical model of the CSF is not available to date. In this paper, we propose such an analytical CSF model based on visual mechanisms, taking into account the age factor. To this end, we have extended an existing model from Barten (1999), taking into account the dependencies of this model's optical and physiological parameters on age. Age-dependent models of the cones and ganglion cells densities, the optical and neural MTF, and optical and neural noise are proposed, based on published data. The proposed age-dependent CSF is finally tested against available experimental data, with fair results. Such an age-dependent model may be beneficial when designing real-time age-dependent image coding and display applications. PMID:26078994

  4. New Dirac delta function based methods with applications to perturbative expansions in quantum field theory

    International Nuclear Information System (INIS)

    We derive new all-purpose methods that involve the Dirac delta distribution. Some of the new methods use derivatives in the argument of the Dirac delta. We highlight potential avenues for applications to quantum field theory and we also exhibit a connection to the problem of blurring/deblurring in signal processing. We find that blurring, which can be thought of as a result of multi-path evolution, is, in Euclidean quantum field theory without spontaneous symmetry breaking, the strong coupling dual of the usual small coupling expansion in terms of the sum over Feynman graphs. (paper)

  5. On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

    Science.gov (United States)

    Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Herve

    1992-01-01

    It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

  6. An analytic distribution function for a massless cored stellar system in a cuspy dark matter halo

    CERN Document Server

    Breddels, Maarten A

    2013-01-01

    We demonstrate the existence of distribution functions that can be used to represent spherical massless cored stellar systems embedded in cuspy dark matter halos with constant mildly tangential velocity anisotropy. In particular, we derive analytically the functional form of the distribution function for a Plummer stellar sphere in a Hernquist dark halo, for \\beta_0 = -0.5 and for different degrees of embedding. This particular example satisfies the condition that the central logarithmic slope of the light profile \\gamma_0 > 2 \\beta_0. Our models have velocity dispersion profiles similar to those observed in nearby dwarf spheroidal galaxies. Hence they can be used to generate initial conditions for a variety of problems, including N-body simulations that may represent dwarf galaxies in the Local Group.

  7. Analytic function theory of several variables elements of Oka’s coherence

    CERN Document Server

    Noguchi, Junjiro

    2016-01-01

    The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps). The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appear...

  8. Multifractal Analysis of Some Inhomogeneous Multinomial Measures with Distinct Analytic Olsen's and Functions

    Science.gov (United States)

    Shen, Shuang

    2015-06-01

    We construct exact dimensional measures whose support is the whole interval and whose Olsen's multifractal functions and are real analytic and agree at two points only. These measures satisfy an extended multifractal formalism in the sense that, for in some interval, the Hausdorff dimension of the level sets of the local Hölder exponent of is the Legendre transform of whereas their packing dimension is the Legendre transform of . We first construct such measures on a symbolic space. Then we obtain the measures by projecting on after composition with a Gray code.

  9. Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity

    OpenAIRE

    Hurley, J. R.; Pols, O. R.; Tout, C. A.

    2000-01-01

    We present analytic formulae that approximate the evolution of stars for a wide range of mass and metallicity. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main-sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5% of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar ...

  10. Gradually-varied flow profiles in open channels analytical solutions by using Gaussian hypergeometric function

    CERN Document Server

    Jan, Chyan-Deng

    2014-01-01

    Gradually-varied flow (GVF) is a steady non-uniform flow in an open channel with gradual changes in its water surface elevation. The evaluation of GVF profiles under a specific flow discharge is very important in hydraulic engineering. This book proposes a novel approach to analytically solve the GVF profiles by using the direct integration and Gaussian hypergeometric function. Both normal-depth- and critical-depth-based dimensionless GVF profiles are presented. The novel approach has laid the foundation to compute at one sweep the GVF profiles in a series of sustaining and adverse channels, w

  11. Experimental validation of an analytical method to obtain the response function of an alpha particle spectrometer

    International Nuclear Information System (INIS)

    In a previous paper, one of the authors suggested an analytical method for calculation of the response function of an alpha spectrometer for the case of large solid angles. This paper describes the experimental verification of the method. Spectra of a well-known natural uranium sample were measured with a 450 mm2 Si detector and compared to the theoretical predictions. The measurements were carried out with two different geometrical configurations. In both cases a good agreement was observed between experimental and theoretical results

  12. Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations

    Energy Technology Data Exchange (ETDEWEB)

    Moawad, S. M., E-mail: smmoawad@hotmail.com [Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt)

    2015-02-15

    In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.

  13. Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations

    Science.gov (United States)

    Moawad, S. M.

    2015-02-01

    In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.

  14. Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations

    International Nuclear Information System (INIS)

    In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics

  15. Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    CERN Document Server

    Szmytkowski, Radosław

    2016-01-01

    The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$-polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825, erratum: 30 (1997) 2747] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities --- the polarizabilities $\\alpha_{L}$, electric-to-magnetic cross-susceptibilities $\\alpha_{\\mathrm{E}L\\to\\mathrm{M}(L\\mp1)}$ and electric-to-toroidal-magnetic cross-susceptibilities $\\alpha_{\\mathrm{E}L\\to\\mathrm{T}L}$ --- are found to be expressible in terms of one or two non-terminating generalized hypergeometric functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities --- the electric nuclear shielding constants $\\sigma_{\\mathrm{E}L\\to\\m...

  16. Expansions of τ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

    Science.gov (United States)

    Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel; Fischer, Jan

    2013-08-01

    The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling αs and other QCD parameters from the hadronic decays of the τ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called “reference model,” including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

  17. First-principles cluster expansion study of functionalization of black phosphorene via fluorination and oxidation

    Science.gov (United States)

    Nahas, Suhas; Ghosh, Barun; Bhowmick, Somnath; Agarwal, Amit

    2016-04-01

    Predicting the ground states for surface adsorption is a challenging problem because the number of degrees of freedom involved in the process is very high. Most of the studies deal with some specific arrangements of adsorbates on a given surface, but very few of them actually attempt to find the ground states for different adatom coverage. In this work, we show the effectiveness of the cluster expansion method to predict the "ground states" resulting from chemisorption of oxygen and fluorine atom on the surface of monolayer black phosphorus or phosphorene. For device applications, we find that in addition to band-gap tuning, controlled chemisorption can change the unique anisotropic carrier effective mass for both the electrons and holes and even rotate them by 90∘, which can be useful for exploring unusual quantum Hall effect and electronic devices based on phosphorene.

  18. Biomass, stem basic density and expansion factor functions for five exotic conifers grown in Denmark

    DEFF Research Database (Denmark)

    Nord-Larsen, Thomas; Nielsen, Anders Tærø

    2015-01-01

    five species were estimated simultaneously using a linear, mixed effects model that allowed contemporaneous correlations between the different tree components. Models differed among species and included dbh and tree height. The models explained more than 98% of the variation in above-ground biomass and...... reflected differences in the allometry between tree species. Stem density differed among species but generally declined with increasing site index and dbh. The overall model for predicting stem basic density included dbh, H100 and site index and explained 66% of the total variation. Expansion factors...... decreased from 1.8–2.0 in small trees (dbh < 10 cm) to 1.1–1.2 for large trees (dbh > 25 cm), but differed among species. The overall model explained 86% of the variation and included quadratic mean diameter and dbh....

  19. Analytical singlet α{/s 4} QCD contributions into the e + e --annihilation Adler function and the generalized Crewther relations

    Science.gov (United States)

    Kataev, A. L.

    2012-02-01

    The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. These relations follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle amplitude in two regions, adjoining to the angle sides ( x, y) (or p 2, q 2). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation expression for two products of the coefficient functions of annihilation and deepinelastic scattering processes in the non-singlet and vector channels. This feature explains the conformal symmetry motivated cancellations between the singlet α{/s 3} corrections to the Gross-Llewellyn Smith sum rule S GLS of ν N deep inelastic scattering and the singlet α{/s 3} correction to the e + e --annihilation Adler function D {/A V } in the product of the corresponding perturbative series. Taking into account the Baikov-Chetyrkin-Kuhn fourth order result for S GLS and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the analytical contribution to the singlet α{/s 4} correction to the D {/A V } function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet fourth order corrections to D {/A V } function demonstrates the coincidence of the predicted and obtained ζ{3/2}-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation. Therefore, on the contrary to previous belief, the appearance of ζ3-terms in the perturbative series in quantum field theory gauge models does not contradict to the property of the conformal symmetry and can be considered as regular feature. The Banks-Zaks motivated relation between our predicted and the obtained directly fourth order corrections is mentioned. It confirms the expectation, previously made by Baikov

  20. ON THE COMPETITION BETWEEN RADIAL EXPANSION AND COULOMB COLLISIONS IN SHAPING THE ELECTRON VELOCITY DISTRIBUTION FUNCTION: KINETIC SIMULATIONS

    International Nuclear Information System (INIS)

    We present numerical simulations of the solar wind using a fully kinetic model which takes into account the effects of particle's binary collisions in a quasi-neutral plasma in spherical expansion. Starting from an isotropic Maxwellian velocity distribution function for the electrons, we show that the combined effect of expansion and Coulomb collisions leads to the formation of two populations: a collision-dominated cold and dense population almost isotropic in velocity space and a weakly collisional, tenuous field-aligned and antisunward drifting population generated by mirror force focusing in the radially decreasing magnetic field. The relative weights and drift velocities for the two populations observed in our simulations are in excellent agreement with the relative weights and drift velocities for both core and strahl populations observed in the real solar wind. The radial evolution of the main moments of the electron velocity distribution function is in the range observed in the solar wind. The electron temperature anisotropy with respect to the magnetic field direction is found to be related to the ratio between the collisional time and the solar wind expansion time. Even though collisions are found to shape the electron velocity distributions and regulate the properties of the strahl, it is found that the heat flux is conveniently described by a collisionless model where a fraction of the electron thermal energy is advected at the solar wind speed. This reinforces the currently largely admitted fact that collisions in the solar wind are clearly insufficient to force the electron heat flux obey the classical Spitzer-Härm expression where heat flux and temperature gradient are proportional to each other. The presented results show that the electron dynamics in the solar wind cannot be understood without considering the role of collisions.

  1. Integrasi Taguchi Loss Function dengan Fuzzy Analytical Hierarchy Process dalam Pemilih Pemasok

    Directory of Open Access Journals (Sweden)

    Ahmad S. Indrapriyatna

    2011-01-01

    Full Text Available One important issue in the line production is the selection of the company's best supplier. Various criteria should be considered for determining the best supplier. Answering to that challenge, we apply Taguchi loss function- Analytical Hierarchy Process Fuzzy-Linear Programming (Taguchi loss function-Fuzzy AHP to find out the best supplier. Moreover, we also consider multiple criteria, i.e., goods’ completeness, quality, delivery, and quality loss in that analysis. By maximizing the suppliers’ performances based on each criterion and aggregated the suppliers’ performances based on the overall criteria, we selected the best one. Applying this method for selecting the best pressure gauge’s supplier in PT. Coca Cola Bottling Indonesia Central Sumatera (PT. CCBICS, we found out that among three suppliers, the second supplier is the best one.

  2. An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra.

    Science.gov (United States)

    Bruce, S D; Higinbotham, J; Marshall, I; Beswick, P H

    2000-01-01

    The approximation of the Voigt line shape by the linear summation of Lorentzian and Gaussian line shapes of equal width is well documented and has proved to be a useful function for modeling in vivo (1)H NMR spectra. We show that the error in determining peak areas is less than 0.72% over a range of simulated Voigt line shapes. Previous work has concentrated on empirical analysis of the Voigt function, yielding accurate expressions for recovering the intrinsic Lorentzian component of simulated line shapes. In this work, an analytical approach to the approximation is presented which is valid for the range of Voigt line shapes in which either the Lorentzian or Gaussian component is dominant. With an empirical analysis of the approximation, the direct recovery of T(2) values from simulated line shapes is also discussed. PMID:10617435

  3. Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

    Science.gov (United States)

    Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing

    2015-10-01

    Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.

  4. Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions

    OpenAIRE

    Beneke, Martin; Boito, Diogo; Jamin, Matthias

    2012-01-01

    Various moments of the hadronic spectral functions have been employed in the determination of the strong coupling alpha_s from tau decays. In this work we study the behaviour of their perturbative series under different assumptions for the large-order behaviour of the Adler function, extending previous work on the tau hadronic width. We find that the moments can be divided into a small number of classes, whose characteristics depend only on generic features of the moment weight function and A...

  5. On Equiconvergence of Expansions in Trigonometric Fourier Series and in Principal Functions of Ordinary Differential Operators

    Science.gov (United States)

    Vagabov, A. I.

    1985-06-01

    A regularity concept is given for ordinary differential pencils of a general form in a space of vector-valued functions, and this concept is subjected to analysis. Theorems are established asserting that the Fourier series of an arbitrary vector-valued function in the system of eigenelements of the pencils is equiconvergent with the usual trigonometric Fourier series of the components of this vector-valued function. Bibliography: 7 titles.

  6. Discrete Jacobi elliptic function expansion method for nonlinear differential-difference equations

    International Nuclear Information System (INIS)

    In this paper, an improved algorithm is devised to derive exact travelling wave solutions of nonlinear differential-difference equations (DDEs) by means of Jacobi elliptic functions. With the aid of symbolic computation, we choose the integrable discrete nonlinear Schroedinger equation to illustrate the validity and advantages of the method. As a result, new and more general Jacobi elliptic function solutions are obtained, from which hyperbolic function solutions and trigonometric function solutions are derived when the modulus m→1 and 0. It is shown that the proposed method provides a more effective mathematical tool for nonlinear DDEs in mathematical physics.

  7. Analytic trigonometry

    CERN Document Server

    Bruce, William J; Maxwell, E A; Sneddon, I N

    1963-01-01

    Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions

  8. Expansion of X-ray form factor for close shell using uncorrelated wave function

    Energy Technology Data Exchange (ETDEWEB)

    AL-Robayi, Enas M. [Babylon University , College of Science for Women, laser Physics Department, Hilla (Iraq)

    2013-12-16

    The atomic scattering factor has been studied for Be+ve, and B+2ve ions using the uncorrelated wave function (Hartree-Fock (HF)) for inter particle electronic shells. The physical importance of this factor appears in its relation to several important atomic properties as, the coherent scattering intensity, the total scattering intensity, the incoherent scattering function, the coherent scattering cross section, the total incoherent cross section, the nuclear magnetic shielding constant, the geometrical structure factor. Also there is one atomic properties the one particle radial density distribution function D(r)has been studied using the partitioning technique.

  9. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    OpenAIRE

    Adib Samin; Erik Lahti; Jinsuo Zhang

    2015-01-01

    Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using th...

  10. Generic smooth connection functions: a new analytic approach to Hermite interpolation

    International Nuclear Information System (INIS)

    We present a new analytic approach to Hermite's interpolation problem in two dimensions. The interpolating curves are the exact solutions of a variational problem that is invariant under translations and rotations. We study the general case of functionals that are given by the integral of the curvature raised to some power ν along the curve. The parameter ν determines the importance of minimal curvature with respect to minimal length. The boundary conditions are given by the initial and final points of the curve and the tangent vectors at these points. In order to find the family of functions that obtain the minimal weight, we use extensively notions that are well known in classical mechanics. The minimization of the weight functional via the Euler-Lagrange formalism leads to a highly non-trivial differential equation. Using the symmetries of the problem it is possible to find conserved quantities that help to simplify the problem to a level where the solution functions can be written in a closed form for any given ν. (author)

  11. Univalence and Starlikeness of Nonlinear Integral Transform of Certain Class of Analytic Functions

    Indian Academy of Sciences (India)

    M Obradović; S Ponnusamy; P Vasundhra

    2009-11-01

    Let $\\mathcal{U}(, )$ denote the class of all normalized analytic functions in the unit disk $|z| < 1$ satisfying the condition \\begin{equation*}\\frac{f(z)}{z}≠ 0\\quad\\text{and}\\quad\\left|f'(z)\\left(\\frac{z}{f(z)}\\right)^{ +1}-1\\right| < ,\\quad |z| < 1.\\end{equation*} For $f\\in\\mathcal{U}(, )$ with ≤ 1 and $0≠_1≤ 1$, and for a positive real-valued integrable function defined on [0,1] satisfying the normalized condition $\\int^1_0\\varphi(t)dt=1$, we consider the transform $G_\\varphi f(z)$ defined by \\begin{equation*}G_\\varphi f(z)=z\\left[\\int^1_0\\varphi(t)\\left(\\frac{zt}{f(tz)}\\right)^ dt\\right]^{-1/ 1},\\quad z\\in.\\end{equation*} In this paper, we find conditions on the range of parameters and so that the transform $G_\\varphi f$ is univalent or star-like. In addition, for a given univalent function of certain form, we provide a method of obtaining functions in the class $\\mathcal{U}(, )$.

  12. Non-linear Dynamics and Mass Function of Cosmic Structures; 1, Analytical Results

    CERN Document Server

    Audit, E; Teyssier, R; Audit, Edouard; Teyssier, Romain

    1997-01-01

    We investigate some modifications to the Press & Schechter (1974) (PS) prescription resulting from shear and tidal effects. These modifications rely on more realistic treatments of the collapse process than the standard approach based on the spherical model. First, we show that the mass function resulting from a new approximate Lagrangian dynamic (Audit & Alimi 96), contains more objects at high mass, than the classical PS mass function and is well fitted by a PS-like function with a threshold density of $\\delta_c \\simeq 1.4$. However, such a Lagrangian description can underestimate the epoch of structure formation since it defines it as the collapse of the first principal axis. We therefore suggest some analytical prescriptions, for computing the collapse time along the second and third principal axes, and we deduce the corresponding mass functions. The collapse along the third axis is delayed by the shear and the number of objects of high mass then decreases. Finally, we show that the shear also str...

  13. Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions

    CERN Document Server

    Beneke, Martin; Jamin, Matthias

    2012-01-01

    Various moments of the hadronic spectral functions have been employed in the determination of the strong coupling alpha_s from tau decays. In this work we study the behaviour of their perturbative series under different assumptions for the large-order behaviour of the Adler function, extending previous work on the tau hadronic width. We find that the moments can be divided into a small number of classes, whose characteristics depend only on generic features of the moment weight function and Adler function series. Some moments that are commonly employed in alpha_s analyses from tau decays should be avoided because of their perturbative instability. This conclusion is corroborated by a simplified alpha_s extraction from individual moments. Furthermore, under reasonable assumptions for the higher-order behaviour of the perturbative series, fixed-order perturbation theory (FOPT) provides the preferred framework for the renormalization group improvement of all moments that show good perturbative behaviour. Finally...

  14. A singularity free surface hopping expansion for the multistate wave function.

    Science.gov (United States)

    Herman, Michael F

    2009-12-01

    A version of a surface hopping wave function for nonadiabatic multistate problems, which is free of turning point singularities, is derived and tested. The primitive semiclassical form of the particular surface hopping method considered has been shown to be highly accurate, even for classically forbidden processes. However, this semiclassical wave function displays the usual singular behavior at turning points and caustics in the classical motion. Numerical data has shown that this somewhat reduces its accuracy when the energy is near the crossing energy of the diabatic electronic surfaces. The singularity free version of this surface hopping wave function is derived by partitioning the x-axis into a large number of small steps for one dimensional problems. The adiabatic electronic energy surfaces are approximated to be linear functions within each step. The matching conditions required by the continuity of the wave function and its derivative at each step boundary provide the needed conditions to obtain the amplitudes for changes in electronic state and/or reflection of the trajectory for the motion of the nuclei. This leads to a form of the surface hopping wave function that is free of turning point singularities. The method is tested for a one dimensional model problem, and it is found to be highly accurate at all energies considered, even when the energy is near the crossing energy. PMID:19968338

  15. Cognitive-analytical therapy for a patient with functional neurological symptom disorder-conversion disorder (psychogenic myopia: A case study

    Directory of Open Access Journals (Sweden)

    Hamid Nasiri

    2015-01-01

    Full Text Available Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-old boy with the diagnosed functional neurological symptom disorder (psychogenic myopia was put under a cognitive-analytical treatment. The outcome of this treatment modality was proved successful.

  16. Perturbative expansion of τ hadronic spectral function moments and α s extractions

    Science.gov (United States)

    Beneke, Martin; Boito, Diogo; Jamin, Matthias

    2013-01-01

    Various moments of the hadronic spectral functions have been employed in the determination of the strong coupling α s from tau decays. In this work we study the behaviour of their perturbative series under different assumptions for the large-order behaviour of the Adler function, extending previous work on the tau hadronic width. We find that the moments can be divided into a small number of classes, whose characteristics depend only on generic features of the moment weight function and Adler function series. Some moments that are commonly employed in α s analyses from τ decays should be avoided because of their perturbative instability. This conclusion is corroborated by a simplified α s extraction from individual moments. Furthermore, under reasonable assumptions for the higher-order behaviour of the perturbative series, fixed-order perturbation theory (FOPT) provides the preferred framework for the renormalization group improvement of all moments that show good perturbative behaviour. Finally, we provide further evidence for the plausibility of the description of the Adler function in terms of a small number of leading renormalon singularities.

  17. Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity

    CERN Document Server

    Hurley, J R; Tout, C A

    2000-01-01

    We present analytic formulae that approximate the evolution of stars for a wide range of mass and metallicity. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main-sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5% of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar properties, and in particular for use in combination with N-body codes. We describe a mass loss prescription that can be used with these formulae and investigate the resulting stellar remnant distribution.

  18. Performance Analytical Model of IEEE 802.11 Distributed Coordination Function

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    IEEE 802.11 distributed coordination function (DCF) is a distributed medium access scheme based on carrier sense multiple access with collision avoidance (CSMA/CA) protocol. Many literatures have analyzed the performance of IEEE 802.11 DCF. However, such literatures either used simulation methods or built the analytical models under the assumption that the saturation condition was satisfied. To overcome such a problem, in this paper, a bi-dimensional Markovian model has been introduced to depict the DCF mechanism. The proposed model introduced an idle stage and a discrete time M/G/1 queue to deduce the channel throughput under finite load traffic. Simulation results proved the accuracy of the proposed model.

  19. Analytic cubic and quartic force fields using density-functional theory.

    Science.gov (United States)

    Ringholm, Magnus; Jonsson, Dan; Bast, Radovan; Gao, Bin; Thorvaldsen, Andreas J; Ekström, Ulf; Helgaker, Trygve; Ruud, Kenneth

    2014-01-21

    We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree-Fock results. The Hartree-Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants. PMID:25669359

  20. Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc

    Directory of Open Access Journals (Sweden)

    Ze-Hua Zhou

    2009-01-01

    Full Text Available This paper gives some estimates of the essential norm for the difference of composition operators induced by φ and ψ acting on the space, H∞(Dn, of bounded analytic functions on the unit polydisc Dn, where φ and ψ are holomorphic self-maps of Dn. As a consequence, one obtains conditions in terms of the Carathéodory distance on Dn that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on H∞(Dn is compact.

  1. Application of the generating functional method to the radionuclides expansion problem

    International Nuclear Information System (INIS)

    It is offered a generalized approach to the description of air pollution sources located within the same region. Sources themselves can be both fixed and mobile, and their number, location and mode of operation may be probabilistic in nature. The approach is based on the concept of probabilistic behavior of particles of pollution. As the mathematical tools the method of generating functional is used

  2. Improved Green’s function measurement for hybridization expansion quantum Monte Carlo

    Czech Academy of Sciences Publication Activity Database

    Augustinský, Pavel; Kuneš, Jan

    2013-01-01

    Roč. 184, č. 9 (2013), s. 2119-2126. ISSN 0010-4655 Institutional support: RVO:68378271 Keywords : continuous time quantum Monte Carlo method * Green function estimator Subject RIV: BE - Theoretical Physics Impact factor: 2.407, year: 2013

  3. Capacity Expansion and Reliability Evaluation on the Networks Flows with Continuous Stochastic Functional Capacity

    Directory of Open Access Journals (Sweden)

    F. Hamzezadeh

    2014-01-01

    Full Text Available In many systems such as computer network, fuel distribution, and transportation system, it is necessary to change the capacity of some arcs in order to increase maximum flow value from source s to sink t, while the capacity change incurs minimum cost. In real-time networks, some factors cause loss of arc’s flow. For example, in some flow distribution systems, evaporation, erosion or sediment in pipes waste the flow. Here we define a real capacity, or the so-called functional capacity, which is the operational capacity of an arc. In other words, the functional capacity of an arc equals the possible maximum flow that may pass through the arc. Increasing the functional arcs capacities incurs some cost. There is a certain resource available to cover the costs. First, we construct a mathematical model to minimize the total cost of expanding the functional capacities to the required levels. Then, we consider the loss of flow on each arc as a stochastic variable and compute the system reliability.

  4. Molecular structure and analytical potential energy function of SeCO

    International Nuclear Information System (INIS)

    The density functional method (B3P86/6-311G) is used for calculating the possible structures of SeC, SeO, and SeCO molecules. The result shows that the ground state of the SeC molecule is 1Σ, the equilibrium nuclear distance is RSeC = 0.1699 nm, and the dissociation energy is De = 8.7246 eV. The ground state of the SeO molecule is 3Σ, with equilibrium nuclear distance RSeO = 0.1707 nm and dissociation energy De = 7.0917 eV. There are two structures for the ground state of the SeCO molecule: Se=C=O and Se=O=C. The linear Se=C=O is 1Σ. Its equilibrium nuclear distances and dissociation energy are RSeC = 0.1715 nm, RCO = 0.1176 nm and 18.8492 eV, respectively. The other structure Se=O=C is 1Σ. Its equilibrium nuclear distances and dissociation energy are RCO = 0.1168 nm, RSeO = 0.1963 nm and 15.5275 eV, respectively. The possible dissociative limit of the SeCO molecule is analyzed. The potential energy function for the SeCO molecule has been obtained from the many-body expansion theory. The contour of the potential energy curve describes the structure characters of the SeCO molecule. Furthermore, contours of the molecular stretching vibration based on this potential energy function are discussed. (atomic and molecular physics)

  5. Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution

    Science.gov (United States)

    Mukhin, S. I.; Galimzyanov, T. R.

    2012-06-01

    An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (Mukhin, 2009, 2011) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.

  6. Expansions of the pair distribution function and the second-order density matrix in terms of homogeneous functionals

    Science.gov (United States)

    Liu, Shubin

    1996-12-01

    It has been shown previously that under certain circumstances the correlation energy density functional Ec[ρ] and its kinetic Tc[ρ] and potential Vc[ρ] components can be expanded in terms of homogeneous functionals An[ρ], with n=1,2,3,..., and where An[ρ] is homogeneous of degree (1-n) with respect to coordinate scaling. In this paper, we extend the analysis to expand similarly the pair distribution function gxc([ρ]r1,r2) and the second-order density matrix ρ2(r1,r2). It is found that both of them can be expanded under certain circumstances in terms of functionals an([ρ]r1,r2), with n=1,2,3,..., that are homogeneous of degree -n in coordinate scaling. The An[ρ] are explicitly obtained in terms of the an([ρ]r1,r2).

  7. Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion

    Energy Technology Data Exchange (ETDEWEB)

    Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu; Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu [Iowa State University, Center for Nondestructive Evaluation, 1915 Scholl Road, Ames, IA 50011 (United States)

    2015-03-31

    We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.

  8. Shell Corrections for Finite-Depth Deformed Potentials Green's Function Oscillator Expansion Method

    CERN Document Server

    Vertse, T; Nazarewicz, W

    2000-01-01

    Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.

  9. Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion

    International Nuclear Information System (INIS)

    We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme

  10. A new thermostatic expansion valve controlling high pressure for R744 with OP as safety function; Ein neuartiges hochdruckregelndes thermostatisches Expansionsventil fuer R744 mit MOP als Sicherheitsfunktion

    Energy Technology Data Exchange (ETDEWEB)

    Aguilar, J.; Maurer, R.; Robin, J.J. [Otto Egelhof GmbH, Fellbach (Germany)

    2007-07-01

    This work reports on the development of a new thermostatic expansion valve, which permits to control the high-pressure of an automotive A/C-System with R744, using the outlet-temperature of the high-pressure line of its internal heat exchanger. At the same time this expansion valve offers a safety function against too high pressures without requiring other mechanically driven bypasses or external control units. (orig.)

  11. The Expansion and Functional Diversification of the Mammalian Ribonuclease A Superfamily Epitomizes the Efficiency of Multigene Families at Generating Biological Novelty

    OpenAIRE

    Goo, Stephen M.; Cho, Soochin

    2013-01-01

    The ribonuclease (RNase) A superfamily is a vertebrate-specific gene family. Because of a massive expansion that occurred during the early mammalian evolution, extant mammals in general have much more RNase genes than nonmammalian vertebrates. Mammalian RNases have been associated with diverse physiological functions including digestion, cytotoxicity, angiogenesis, male reproduction, and host defense. However, it is still uncertain when their expansion occurred and how a wide array of functio...

  12. Histone deacetylase 11: A novel epigenetic regulator of myeloid derived suppressor cell expansion and function

    OpenAIRE

    Sahakian, Eva; Powers, John J.; Chen, Jie; Deng, Susan L.; Cheng, Fengdong; Distler, Allison; Woods, David M.; Rock-Klotz, Jennifer; Laino, Andressa Sodre'; Youn, Je-In; Woan, Karrune V.; Villagra, Alejandro; Gabrilovich, Dmitry,; Sotomayor, Eduardo M.; Pinilla-Ibarz, Javier

    2014-01-01

    Myeloid-derived suppressor cells (MDSC's), a heterogeneous population of cells capable of suppressing anti-tumor T cell function in the tumor microenvironment, represent an imposing obstacle in the development of cancer immunotherapeutics. Thus, identifying elements essential to the development and perpetuation of these cells will undoubtedly improve our ability to circumvent their suppressive impact. HDAC11 has emerged as a key regulator of IL-10 gene expression in myeloid cells, suggesting ...

  13. Continuation of the wave function for higher angular momentum states to D dimensions I. The generalized Schwartz expansion

    International Nuclear Information System (INIS)

    Extending the techniques of dimensional scaling to higher angular momentum states of multi-electron atoms requires the derivation, from the Schroedinger equation, of a tractable set of differential equations which admit continuation in the spatial dimension D. This derivation centers on open-quote open-quote factoring out,close-quote close-quote in D dimensions, the rotational degrees of freedom from the internal degrees of freedom in the wave function. A solution to this problem, by generalizing the Schwartz expansion (Schwartz, Phys. Rev. 123, 1700 (1961)) to N electrons in D dimensions, is presented. The generalization to systems with particles of arbitrary masses is straightforward. Copyright copyright 1996 Academic Press, Inc

  14. Human purified CD8+ T cells: Ex vivo expansion model to generate a maximum yield of functional cytotoxic cells.

    Science.gov (United States)

    Al-Shanti, Nasser; Aldahoudi, Ziyad

    2007-01-01

    CD8+ T cells are a critical component of the cellular immune response. They play an important role in the control of viral infection and eliminating cells with malignant potential. However, attempts to generate and expand human CD8+ T cells in vitro for an adoptive immunotherapy have been conducted with limitation of the very low frequency of CD8+ T cells in blood. Therefore, several expansion protocols have been developed to obtain large and efficient numbers of human CD8+ T cells for use in adoptive immunotherapies. In this study various common culture conditions using different cytokines IL-2, IL-4, IL-7, IL-10, IL-12 and IL-15 and autologous feeders and sera were investigated to expand human purified CD8+ T cells. The importance and the influence of these factors on the growth and phenotype of CD8+ T cell were assessed by serially sampling cultures using flow cytometry. We demonstrated that combination of IL-2 (50 U/ml) and autologous feeders induced maximal CD8+ T cell proliferation (40-50 folds) compared to other cytokines. Immunophenotypic analysis of cultured cells showed that expanded CD8+ T cells were activated and differentiated. Furthermore our expansion model also demonstrated that expanded CD8+ T cells are functionally cytotoxic active by killing Allogeneic LCLs cells. In conclusion, we have developed a reliable, simple method that uses minimal cell numbers to generate a high yield of functional cytotoxic CD8+ T cells, which can be used for the development of cellular immunotherapies. PMID:17190652

  15. Molecular evolution and the role of oxidative stress in the expansion and functional diversification of cytosolic glutathione transferases

    Directory of Open Access Journals (Sweden)

    Vasconcelos Vítor

    2010-09-01

    Full Text Available Abstract Background Cytosolic glutathione transferases (cGST are a large group of ubiquitous enzymes involved in detoxification and are well known for their undesired side effects during chemotherapy. In this work we have performed thorough phylogenetic analyses to understand the various aspects of the evolution and functional diversification of cGSTs. Furthermore, we assessed plausible correlations between gene duplication and substrate specificity of gene paralogs in humans and selected species, notably in mammalian enzymes and their natural substrates. Results We present a molecular phylogeny of cytosolic GSTs that shows that several classes of cGSTs are more ubiquitous and thus have an older ancestry than previously thought. Furthermore, we found that positive selection is implicated in the diversification of cGSTs. The number of duplicate genes per class is generally higher for groups of enzymes that metabolize products of oxidative damage. Conclusions 1 Protection against oxidative stress seems to be the major driver of positive selection in mammalian cGSTs, explaining the overall expansion pattern of this subfamily; 2 Given the functional redundancy of GSTs that metabolize xenobiotic chemicals, we would expect the loss of gene duplicates, but by contrast we observed a gene expansion of this family, which likely has been favored by: i the diversification of endogenous substrates; ii differential tissue expression; and iii increased specificity for a particular molecule; 3 The increased availability of sequence data from diversified taxa is likely to continue to improve our understanding of the early origin of the different cGST classes.

  16. First Steps in FAP: Experiences of Beginning Functional Analytic Psychotherapy Therapist with an Obsessive-Compulsive Personality Disorder Client

    Science.gov (United States)

    Manduchi, Katia; Schoendorff, Benjamin

    2012-01-01

    Practicing Functional Analytic Psychotherapy (FAP) for the first time can seem daunting to therapists. Establishing a deep and intense therapeutic relationship, identifying FAP's therapeutic targets of clinically relevant behaviors, and using contingent reinforcement to help clients emit more functional behavior in the therapeutic relationship all…

  17. Coefficient Estimates for New Subclasses of Analytic and Bi-Univalent Functions Defined by Al-Oboudi Differential Operator

    Directory of Open Access Journals (Sweden)

    Serap Bulut

    2013-01-01

    Full Text Available We introduce and investigate two new subclasses and of analytic and bi-univalent functions in the open unit disk For functions belonging to these classes, we obtain estimates on the first two Taylor-Maclaurin coefficients and

  18. Study on the Explicit Formula of the Triangular Flat Shell Element Based on the Analytical Trial Functions for Anisotropy Material

    OpenAIRE

    Xiang-Rong Fu; Li-Na Ge; Ge Tian; Ming-Wu Yuan

    2013-01-01

    This paper presents a novel way to formulate the triangular flat shell element. The basic analytical solutions of membrane and bending plate problem for anisotropy material are studied separately. Combining with the conforming displacement along the sides and hybrid element strategy, the triangular flat shell elements based on the analytical trial functions (ATF) for anisotropy material are formulated. By using the explicit integral formulae of the triangular element, the matrices used in pro...

  19. Expansion of the Kano model to identify relevant customer segments and functional requirements

    DEFF Research Database (Denmark)

    Atlason, Reynir Smari; Stefansson, Arnaldur Smari; Wietz, Miriam;

    2016-01-01

    The Kano model of customer satisfaction has been widely used to analyse perceived needs of customers. The model provides product developers valuable information about if, and then how much a given functional requirement (FR) will impact customer satisfaction if implemented within a product, system...... more than one combined customer segment. It further shows which segments provide the highest possibility for high satisfaction of combined sets of FRs. We demonstrate the usefulness of this approach in a case study involving customers’ preference for outdoor sports equipment....

  20. Radial expansion for spinning conformal blocks

    CERN Document Server

    Costa, Miguel$uPorto U.; Penedones, João; Trevisani, Emilio

    2016-01-01

    This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we explain how to write closed form recursion relations for the coefficients of the expansions. We study three examples of four point functions in detail: one vector and three scalars; two vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the case of two external vectors, we also provide a more efficient way to generate the series expansion using the analytic structure of the blocks as a function of the scaling dimension of the exchanged operator.

  1. An Analytical Model for the Prediction of a Micro-Dosimeter Response Function

    Science.gov (United States)

    Badavi, Francis F.; Xapsos, Mike

    2008-01-01

    A rapid analytical procedure for the prediction of a micro-dosimeter response function in low Earth orbit (LEO), correlated with the Space Transportation System (STS, shuttle) Tissue Equivalent Proportional Counter (TEPC) measurements is presented. The analytical model takes into consideration the energy loss straggling and chord length distribution of the detector, and is capable of predicting energy deposition fluctuations in a cylindrical micro-volume of arbitrary aspect ratio (height/diameter) by incoming ions through both direct and indirect (ray) events. At any designated (ray traced) target point within the vehicle, the model accepts the differential flux spectrum of Galactic Cosmic Rays (GCR) and/or trapped protons at LEO as input. On a desktop PC, the response function of TEPC for each ion in the GCR/trapped field is computed at the average rate of 30 seconds/ion. The ionizing radiation environment at LEO is represented by O'Neill fs GCR model (2004), covering charged particles in the 1 less than or equal to Z less than or equal to 28. O'Neill's free space GCR model is coupled with the Langley Research Center (LaRC) angular dependent geomagnetic cutoff model to compute the transmission coefficient in LEO. The trapped proton environment is represented by a LaRC developed time dependent procedure which couples the AP8MIN/AP8MAX, Deep River Neutron Monitor (DRNM) and F10.7 solar radio frequency measurements. The albedo neutron environment is represented by the extrapolation of the Atmospheric Ionizing Radiation (AIR) measurements. The charged particle transport calculations correlated with STS 51 and 114 flights are accomplished by using the most recent version (2005) of the LaRC deterministic High charge (Z) and Energy TRaNsport (HZETRN) code. We present the correlations between the TEPC model predictions (response function) and TEPC measured differential/integral spectra in the lineal energy (y) domain for both GCR and trapped protons, with the conclusion

  2. Analytical theory for the initial mass function: III time dependence and star formation rate

    CERN Document Server

    Hennebelle, Patrick

    2013-01-01

    The present paper extends our previous theory of the stellar initial mass function (IMF) by including the time-dependence, and by including the impact of magnetic field. The predicted mass spectra are similar to the time independent ones with slightly shallower slopes at large masses and peak locations shifted toward smaller masses by a factor of a few. Assuming that star-forming clumps follow Larson type relations, we obtain core mass functions in good agreement with the observationally derived IMF, in particular when taking into account the thermodynamics of the gas. The time-dependent theory directly yields an analytical expression for the star formation rate (SFR) at cloud scales. The SFR values agree well with the observational determinations of various Galactic molecular clouds. Furthermore, we show that the SFR does not simply depend linearly on density, as sometimes claimed in the literature, but depends also strongly on the clump mass/size, which yields the observed scatter. We stress, however, that ...

  3. Cognitive-analytical therapy for a patient with functional neurological symptom disorder-conversion disorder (psychogenic myopia): A case study

    OpenAIRE

    Hamid Nasiri; Amrollah Ebrahimi; Arash Zahed; Mostafa Arab; Rahele Samouei

    2015-01-01

    Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-ol...

  4. Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    CERN Document Server

    Stefańska, Patrycja

    2016-01-01

    We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless and of charge Ze. Calculations are based on the Sturmian expansion of the generalized Dirac- Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); erratum 30, 2747 (1997)], combined with the theory of hypergeometric functions. The final result is of an elementary form and agrees with corresponding formulas obtained earlier by other authors for some particular states of the atom.

  5. Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    Science.gov (United States)

    Stefańska, Patrycja

    2016-07-01

    We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Z e . Calculations are based on the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997), 10.1088/0953-4075/30/4/007; erratum R. Szmytkowski, J. Phys. B 30, 2747(E) (1997), 10.1088/0953-4075/30/11/023], combined with the theory of hypergeometric functions. The final result is of an elementary form and agrees with corresponding formulas obtained earlier by other authors for some particular states of the atom.

  6. The QCD analysis of the combined set for the F_3 structure function data based on the analytic approach

    OpenAIRE

    Sidorov, A. V.; Solovtsova, O. P.

    2014-01-01

    We apply analytic perturbation theory to the QCD analysis of the xF_3(x,Q^2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Lambda_{QCD}, the parameters of the form of the xF_3 structure function, and the x-shape of the higher twist contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the exper...

  7. Polarized nonsinglet {Delta q}_3 and nonsinglet fragmentation function D^{pi+}_{u_v} in the analytic approach to QCD

    OpenAIRE

    Sidorov, A. V.; Solovtsova, O. P.

    2014-01-01

    We discuss the application of an analytic approach called the analytic perturbation theory (APT) to the QCD analysis of DIS data. In particular, the results of the QCD analysis of a set of `fake' data on the polarized nonsinglet Delta{q3} and the nonsinglet fragmentation function D^{pi+}_{u_v} by using the Q^2-evolution within the APT are considered. The `fake' data are constructed based on parametrization of the polarized PDF and nonsinglet combination of the pion fragmentation functions. We...

  8. On the relation between the Lebesgue integral means and Nevanlinna characteristic of analytic functions in the unit disc

    Directory of Open Access Journals (Sweden)

    Ya. V. Vasyl’kiv

    2011-07-01

    Full Text Available The best possible asymptotic estimates for Lebesgue integral means $m_{p}(r,log f, 1 leq p$ of logarithms of analytic functions $f(z$ in the unit disc in terms of their Nevanlinna characteristic $T(r,f$ are obtained. We get sharp relation between the order of $T(r,f$ and the order of $m_{p}(r,log f$ for an analytic function $f(z$ of finite order $alpha(f.$ This generalizes well-known results of L.~R.~Sons and C.~N.~Linden.

  9. Expansions of $\\tau$ hadronic spectral function moments in a non-power QCD perturbation theory with tamed large order behaviour

    CERN Document Server

    Abbas, Gauhar; Caprini, Irinel; Fischer, Jan

    2013-01-01

    The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling $\\alpha_s$ and other QCD parameters from the hadronic decays of the $\\tau$ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behaviour of these moments in the framework of a QCD non-power perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large order behaviour. Two recently proposed models of the Adler function are employed to generate the higher order coefficients of the required perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved and the renormalization-group-summed non-power perturbation theories have very good con vergence properties for a large class...

  10. Wave-function frozen-density embedding: Approximate analytical nuclear ground-state gradients.

    Science.gov (United States)

    Heuser, Johannes; Höfener, Sebastian

    2016-05-01

    We report the derivation of approximate analytical nuclear ground-state uncoupled frozen density embedding (FDEu) gradients for the resolution of identity (RI) variant of the second-order approximate coupled cluster singles and doubles (RICC2) as well as density functional theory (DFT), and an efficient implementation thereof in the KOALA program. In order to guarantee a computationally efficient treatment, those gradient terms are neglected which would require the exchange of orbital information. This approach allows for geometry optimizations of single molecules surrounded by numerous molecules with fixed nuclei at RICC2-in-RICC2, RICC2-in-DFT, and DFT-in-DFT FDE level of theory using a dispersion correction, required due to the DFT-based treatment of the interaction in FDE theory. Accuracy and applicability are assessed by the example of two case studies: (a) the Watson-Crick pair adenine-thymine, for which the optimized structures exhibit a maximum error of about 0.08 Å for our best scheme compared to supermolecular reference calculations, (b) carbon monoxide on a magnesium oxide surface model, for which the error amount up to 0.1 Å for our best scheme. Efficiency is demonstrated by successively including environment molecules and comparing to an optimized conventional supermolecular implementation, showing that the method is able to outperform conventional RICC2 schemes already with a rather small number of environment molecules, gaining significant speed up in computation time. © 2016 Wiley Periodicals, Inc. PMID:26804310

  11. Using analytic derivatives to assess the impact of phase function Fourier decomposition technique on the accuracy of a radiative transfer model

    International Nuclear Information System (INIS)

    Fourier decomposition of the phase function is essential to decouple the azimuthal component of the radiative transfer equation for multiple scattering calculations. This decomposition can be carried out by means of a direct numerical method based on the definition of the Fourier transform (numFT), or by an expansion of the phase function in terms of spherical Legendre polynomials (sphFT). numFT requires interpolation of the phase function between discrete angles, leading to spurious errors in the final computations. This error is difficult to quantify by means of intensity-only computations, since it is hard to determine the absolute accuracy of any given approach. We show that a linearization (analytic computation of derivatives) of the intensity with respect to parameters governing the phase function can be compared against results using the finite difference method, thereby providing a self-consistency test for characterizing and quantifying the error. We have applied this approach to two linearized versions of the Matrix Operator Method, which are identical in all respects except that one uses numFT while the other uses sphFT. In both cases, we compute the derivatives of the intensity with respect to aerosol parameters governing scattering in the simulated atmosphere. Comparison of the derivatives against their finite difference estimates shows a reduction of error by several orders of magnitude when Legendre polynomials are employed. We have also examined the effect of the angular resolution of the phase function on the error due to the numFT technique. A general reduction of error is seen with increasing angular resolution, indicating that interpolation is indeed the major error source. Also, we have pointed out a related source of error in numFT computations that occurs when Fourier decomposition is carried out on the composite phase function of a layer consisting of more than one scatterer. We conclude that an expansion of the phase function in terms of

  12. Effect of Strong Acid Functional Groups on Electrode Rise Potential in Capacitive Mixing by Double Layer Expansion

    KAUST Repository

    Hatzell, Marta C.

    2014-12-02

    © 2014 American Chemical Society. The amount of salinity-gradient energy that can be obtained through capacitive mixing based on double layer expansion depends on the extent the electric double layer (EDL) is altered in a low salt concentration (LC) electrolyte (e.g., river water). We show that the electrode-rise potential, which is a measure of the EDL perturbation process, was significantly (P = 10-5) correlated to the concentration of strong acid surface functional groups using five types of activated carbon. Electrodes with the lowest concentration of strong acids (0.05 mmol g-1) had a positive rise potential of 59 ± 4 mV in the LC solution, whereas the carbon with the highest concentration (0.36 mmol g-1) had a negative rise potential (-31 ± 5 mV). Chemical oxidation of a carbon (YP50) using nitric acid decreased the electrode rise potential from 46 ± 2 mV (unaltered) to -6 ± 0.5 mV (oxidized), producing a whole cell potential (53 ± 1.7 mV) that was 4.4 times larger than that obtained with identical electrode materials (from 12 ± 1 mV). Changes in the EDL were linked to the behavior of specific ions in a LC solution using molecular dynamics and metadynamics simulations. The EDL expanded in the LC solution when a carbon surface (pristine graphene) lacked strong acid functional groups, producing a positive-rise potential at the electrode. In contrast, the EDL was compressed for an oxidized surface (graphene oxide), producing a negative-rise electrode potential. These results established the linkage between rise potentials and specific surface functional groups (strong acids) and demonstrated on a molecular scale changes in the EDL using oxidized or pristine carbons.

  13. Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities

    OpenAIRE

    Gori-Giorgi, Paola; Perdew, John P.

    2002-01-01

    We construct analytic formulas that represent the coupling-constant-averaged pair distribution function $\\gxcav(r_s,\\zeta, k_Fu)$ of a uniform electron gas with density parameter $r_s =(9\\pi/4)^{1/3}/k_F$ and relative spin polarization $\\zeta$ over the whole range $0

  14. Translating the Theoretical into Practical: A Logical Framework of Functional Analytic Psychotherapy Interactions for Research, Training, and Clinical Purposes

    Science.gov (United States)

    Weeks, Cristal E.; Kanter, Jonathan W.; Bonow, Jordan T.; Landes, Sara J.; Busch, Andrew M.

    2012-01-01

    Functional analytic psychotherapy (FAP) provides a behavioral analysis of the psychotherapy relationship that directly applies basic research findings to outpatient psychotherapy settings. Specifically, FAP suggests that a therapist's in vivo (i.e., in-session) contingent responding to targeted client behaviors, particularly positive reinforcement…

  15. A Single-Case Experimental Demonstration of Functional Analytic Psychotherapy with Two Clients with Severe Interpersonal Problems

    Science.gov (United States)

    Oshiro, Claudia Kami Bastos; Kanter, Jonathan; Meyer, Sonia Beatriz

    2012-01-01

    Functional Analytic Psychotherapy (FAP) is emerging as an effective psychotherapy for psychiatric clinical cases. However, there is little research demonstrating the process of change of FAP. The present study evaluated the introduction and withdrawal of FAP interventions on therapy-interfering verbal behaviors of two participants who were in…

  16. Analytical, Creative, and Practical Intelligence as Predictors of Self-reported Adaptive Functioning: A Case Study in Russia.

    Science.gov (United States)

    Grigorenko, Elena L.; Sternberg, Robert J.

    2001-01-01

    Studied the efficacy of the triarchic theory of intelligence as a basis for predicting adaptive functioning in a rapidly changing society, that of Russia. Results of intelligence measures administered to 452 women and 293 men show that analytical, practical, and creative intelligence all relate in some degree to self-reported everyday adaptive…

  17. Jacobi elliptic function solutions of nonlinear wave equations via the new sinh-Gordon equation expansion method

    International Nuclear Information System (INIS)

    In this paper, based on the well-known sinh-Gordon equation, a new sinh-Gordon equation expansion method is developed. This method transforms the problem of solving nonlinear partial differential equations into the problem of solving the corresponding systems of algebraic equations. With the aid of symbolic computation, the procedure can be carried out by computer. Many nonlinear wave equations in mathematical physics are chosen to illustrate the method such as the KdV-mKdV equation, (2+1)-dimensional coupled Davey-Stewartson equation, the new integrable Davey-Stewartson-type equation, the modified Boussinesq equation, (2+1)-dimensional mKP equation and (2+1)-dimensional generalized KdV equation. As a consequence, many new doubly-periodic (Jacobian elliptic function) solutions are obtained. When the modulus m → 1 or 0, the corresponding solitary wave solutions and singly-periodic solutions are also found. This approach can also be applied to solve other nonlinear differential equations

  18. Development of the learning-training lessons for functional-analytical training facility of NPP with WWER-1000 reactor

    International Nuclear Information System (INIS)

    General principles of construction of functional-analytical training facility of a NPP, which represents the computation system consisting of the ES-1045 type computer and personal computers, are considered. The KIPR program used for the ES computer describes stationary and dynamic regimes of a power unit real time operation. The personal computers perform service functions of displaying the information required by an operator. The high efficiency of the algorithms used for NPP operator training is proved

  19. On the Riemann-Hilbert problem for analytic functions in circular domains

    OpenAIRE

    Efimushkin, A. S.; Ryazanov, V. I.

    2015-01-01

    It is proved the existence of single-valued analytic solutions in the unit disk and multivalent analytic solutions in domains bounded by a finite collection of circles for the Riemann-Hilbert problem with coefficients of sigma-finite variation and with boundary data that are measurable with respect to logarithmic capacity. It is shown that these spaces of solutions have the infinite dimension.

  20. 再生核空间二元函数展开%The Expansion of the Function with Two Unknowns on the Reproducing Kernel Space

    Institute of Scientific and Technical Information of China (English)

    吴勃英

    2000-01-01

    In this paper we make use of a special procedure on the reproducing kernel space to give an expansion theorem for the function with two unknowns and a surface approximation formula. The error of the surface possesses monotonically decreasing and uniformly convergent characteristics in the sense of the norm on the space.

  1. Study on the Explicit Formula of the Triangular Flat Shell Element Based on the Analytical Trial Functions for Anisotropy Material

    Directory of Open Access Journals (Sweden)

    Xiang-Rong Fu

    2013-01-01

    Full Text Available This paper presents a novel way to formulate the triangular flat shell element. The basic analytical solutions of membrane and bending plate problem for anisotropy material are studied separately. Combining with the conforming displacement along the sides and hybrid element strategy, the triangular flat shell elements based on the analytical trial functions (ATF for anisotropy material are formulated. By using the explicit integral formulae of the triangular element, the matrices used in proposed shell element are calculated efficiently. The benchmark examples showed the high accuracy and high efficiency.

  2. An Analytical Study of the Nonsinglet Spin Structure Function g1NS(x,t) Up to NLO in the DGLAP Approach at Small x

    International Nuclear Information System (INIS)

    A next-to-leading order QCD calculation of nonsinglet spin structure function g1NS(x,t) at small x is presented using the analytical methods: Lagrange’s method and method of characteristics. The compatibility of these analytical approaches is tested by comparing the analytical solutions with the available polarized global fits

  3. Two-loop two-point functions with masses asymptotic expansions and Taylor series, in any dimension

    CERN Document Server

    Broadhurst, D J; Tarasov, O V

    1993-01-01

    In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.

  4. Is it possible to check urgently the 5-loop analytical results for the e+e--annihilation Adler function?

    International Nuclear Information System (INIS)

    Considering the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED β-function we emphasize that to our point of view it is important to perform their independent cross-checks. We propose one of the ways of these cross-check. It is based on the application of the original Crewther relation. We derive the new analytical expressions for the CF4αs4-contributions to the Bjorken polarized sum rule. If results of possible direct calculations will agree with the presented expression, then the appearance of ζ3-term in the 5-loop correction to the QED β-function and in the CF4αs4 contribution into the e+e- annihilation Adler function will get independent support and may be analysed within the framework of the recently introduced concept of 'maximal transcendentality'

  5. Fisher–Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain

    International Nuclear Information System (INIS)

    Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher–Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painlevé equations. We present explicit results up to the 11th order and compare them with a numerical example. (paper)

  6. The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group

    International Nuclear Information System (INIS)

    We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model. (paper)

  7. On the analytic representation of the correlation function of linear random vibration systems

    OpenAIRE

    Gruner, J; Scheidt, J. vom; Wunderlich, R.

    1998-01-01

    This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result...

  8. Differential effects of inhibitors of the PI3K/mTOR pathway on the expansion and functionality of regulatory T cells.

    Science.gov (United States)

    Huijts, Charlotte M; Santegoets, Saskia J; Quiles Del Rey, Maria; de Haas, Richard R; Verheul, Henk M; de Gruijl, Tanja D; van der Vliet, Hans J

    2016-07-01

    The PI3K/mTOR pathway is commonly deregulated in cancer. mTOR inhibitors are registered for the treatment of several solid tumors and novel inhibitors are explored clinically. Notably, this pathway also plays an important role in immunoregulation. While mTOR inhibitors block cell cycle progression of conventional T cells (Tconv), they also result in the expansion of CD4(+)CD25(hi)FOXP3(+) regulatory T cells (Tregs), and this likely limits their clinical antitumor efficacy. Here, we compared the effects of dual mTOR/PI3K inhibition (using BEZ235) to single PI3K (using BKM120) or mTOR inhibition (using rapamycin and everolimus) on Treg expansion and functionality. Whereas rapamycin, everolimus and BEZ235 effected a relative expansion benefit for Tregs and increased their overall suppressive activity, BKM120 allowed for similar expansion rates of Tregs and Tconv without altering their overall suppressive activity. Therefore, PI3K inhibition alone might offer antitumor efficacy without the detrimental selective expansion of Tregs associated with mTOR inhibition. PMID:27189717

  9. Ergodicity testing using an analytical formula for a dynamical functional of alpha-stable autoregressive fractionally integrated moving average processes

    Science.gov (United States)

    Loch, Hanna; Janczura, Joanna; Weron, Aleksander

    2016-04-01

    In this paper we study asymptotic behavior of a dynamical functional for an α -stable autoregressive fractionally integrated moving average (ARFIMA) process. We find an analytical formula for this important statistics and show its usefulness as a diagnostic tool for ergodic properties. The obtained results point to the very fast convergence of the dynamical functional and show that even for short trajectories one may obtain reliable conclusions on the ergodic properties of the ARFIMA process. Moreover we use the obtained theoretical results to illustrate how the dynamical functional statistics can be used in the verification of the proper model for an analysis of some biophysical experimental data.

  10. A spectral analytic discrete-ordinates transport method based on infinite medium green's function for multiplying fission source problems

    International Nuclear Information System (INIS)

    Analytic solutions of the multigroup discrete ordinates transport equation with linearly anisotropic scattering and fission source for multi-layered slab problems are obtained by using the infinite medium Green's function (IMGF) and Placzek's lemma. In this approach, the infinite medium Green's function is derived analytically by using the spectral analysis for the multigroup discrete ordinates transport equation and its transposed equation, and this infinite medium solution is related to the finite medium solution by Placzek's lemma. In eigenvalue problems having fission source, complex eigenvalues can occur. As such equations involve the k eigenvalue as a non-linear parameter, to obtain criticality Newton's chord method combined with bisection is used. The resulting equation leads to an exact relation that represents the outgoing angular fluxes in terms of the incoming angular fluxes and fission source for each slab. For heterogeneous problems having multi-layered slabs, the slabs are coupled through the interface angular fluxes. Since all derivations are performed analytically, the method gives exact solution with no truncation error. After the interface angular fluxes are calculated by using an iterative method, the continuous spatial distribution of the angular flux (i.e. analytic solution) in each slab is given straightforwardly in terms of the IMGF and the boundary angular fluxes. Therefore, in our method, the number of meshes that is equal to the number of the homogeneous slabs is sufficient

  11. Thermal expansion

    International Nuclear Information System (INIS)

    Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)

  12. The expansion and functional diversification of the mammalian ribonuclease a superfamily epitomizes the efficiency of multigene families at generating biological novelty.

    Science.gov (United States)

    Goo, Stephen M; Cho, Soochin

    2013-01-01

    The ribonuclease (RNase) A superfamily is a vertebrate-specific gene family. Because of a massive expansion that occurred during the early mammalian evolution, extant mammals in general have much more RNase genes than nonmammalian vertebrates. Mammalian RNases have been associated with diverse physiological functions including digestion, cytotoxicity, angiogenesis, male reproduction, and host defense. However, it is still uncertain when their expansion occurred and how a wide array of functions arose during their evolution. To answer these questions, we generate a compendium of all RNase genes identified in 20 complete mammalian genomes including the platypus, Ornithorhynchus anatinus. Using this, we delineate 13 ancient RNase gene lineages that arose before the divergence between the monotreme and the other mammals (∼220 Ma). These 13 ancient gene lineages are differentially retained in the 20 mammals, and the rate of protein sequence evolution is highly variable among them, which suggest that they have undergone extensive functional diversification. In addition, we identify 22 episodes of recent expansion of RNase genes, many of which have signatures of adaptive functional differentiation. Exemplifying this, bursts of gene duplication occurred for the RNase1, RNase4, and RNase5 genes of the little brown bat (Myotis lucifugus), which might have contributed to the species' effective defense against heavier pathogen loads caused by its communal roosting behavior. Our study illustrates how host-defense systems can generate new functions efficiently by employing a multigene family, which is crucial for a host organism to adapt to its ever-changing pathogen environment. PMID:24162010

  13. Special Issue: “q-Series and Related Topics in Special Functions and Analytic Number Theory”—Foreword

    OpenAIRE

    Hari M. Srivastava

    2013-01-01

    It is indeed a fairly common practice for scientific research journals and scientific research periodicals to publish special issues as well as conference proceedings. Quite frequently, these special issues are devoted exclusively to specific topics and/or are dedicated respectfully to commemorate the celebrated works of renowned research scientists. The following Special Issue: “q-Series and Related Topics in Special Functions and Analytic Number Theory” (see [1–8] below) is an outcome of th...

  14. Public Key Infrastructure (PKI) And Virtual Private Network (VPN) Compared Using An Utility Function And The Analytic Hierarchy Process (AHP)

    OpenAIRE

    Wagner, Edward Dishman

    2002-01-01

    This paper compares two technologies, Public Key Infrastructure (PKI) and Virtual Private Network (VPN). PKI and VPN are two approaches currently in use to resolve the problem of securing data in computer networks. Making this comparison difficult is the lack of available data. Additionally, an organization will make their decision based on circumstances unique to their information security needs. Therefore, this paper will illustrate a method using a utility function and the Analytic Hie...

  15. The s-ordered expansions of the operator function about the combined quadrature μX + νP

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    A general framework applicable to deriving the s-ordered operator expansions is presented in this paper.We firstly deduce the s-ordered operator expansion formula of density operator ρ a?,a and introduce the technique of integration within the sordered product of operators (IWSOP).Based on the deduction and the technique,we derive the s-ordered expansions of operators (μX + νP)n and Hn (μX + νP) (linear combinations of the coordinate operator X and the momentum operator P,Hn (x) is Hermite polynomial),respectively,and discuss some special cases of s=1,0,-1.Some new useful operator identities are obtained as well.

  16. Simple analytical approximations to the integrals of the Bessel functions Jν: application to the transmittance of a circular aperture

    International Nuclear Information System (INIS)

    Two accurate, yet simple, analytic approximations to the integral of the Bessel function J0 are presented. These first and second-order approximations are obtained by improving on the recently developed method known as two-point quasi-rational approximations. The accuracy of the first-order approximant is better than 0.05. The second-order approximant is practically indistinguishable from the true integral, even for very large values of the argument (overall accuracy is better than 0.002 05). Our approximants are, in addition, analytic and therefore replace with significant advantages both the well known power series and the asymptotic formulae of the integral. Approximants to the transmittance function of a plane wave through a circular aperture are derived, a problem which arises in diffraction theory and particle scattering. The second-order approximant to the transmittance is analytic too, and can be evaluated for small and large values of the argument, just with a hand-calculator. Its accuracy is better than 0.0011. As an extension, two first-order approximations to the integrals of the Bessel functions Jν, of fractional order ν, are derived. (author)

  17. EXTREME POINTS AND SUPPORT POINTS OF A CLASS OF ANALYTIC FUNCTIONS

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Suppose that {bn} and {cn} are two positive sequences.Let F({bn},{cn})={f(z) :f(z) is analytic in |z|<1,f(z) = z-∑+∞n=2 anzn,an 0,∑+∞n=2 bnan 1 and ∑+∞n=2 cnan ≤1}.This article obtains the extreme points and support points of F({bn},{cn}).

  18. Analytic expression for the proton structure function in deep inelastic scattering

    Institute of Scientific and Technical Information of China (English)

    XIANG Wen-Chang; ZHOU Dai-Cui; WAN Ren-Zhuo; YUAN Xian-Bao

    2009-01-01

    The analytic expression of proton in deep inelastic scattering is studied by using the color glass condensate model and the dipole picture. We get a better description of the HERA DIS data than the CBW model which was inspired by the Glauber model. We find that our model satisfies the unitarity limit and Froissart Bound which refers to an energy dependence of the total cross-section rising no more rapidly than ln2s.

  19. Analytic Evaluation of some 2-, 3- and 4- Electron Atomic Integrals Containing Exponentially Correlated Functions of $r_{ij}$

    CERN Document Server

    Padhy, Bholanath

    2016-01-01

    A simple method is outlined for analytic evaluation of the basic 2-electron atomic integral with integrand containing products of atomic s-type Slater orbitals and exponentially correlated function of the form $r_{ij} exp(-\\lambda_{ij}r_{ij})$, by employing the Fourier representation of $exp(-\\lambda_{ij}r_{ij})/r_{ij}$ without the use of either the spherical harmonic addition theorem or the Feynman technique. This method is applied to obtain closed-form expressions, in a simple manner, for certain other 2-,3- and 4-electron atomic integrals with integrands which are products of exponentially correlated functions and atomic s-type Slater orbitals.

  20. Multipole expansions in magnetostatics

    International Nuclear Information System (INIS)

    Multipole expansions of the magnetic field of a spatially restricted system of stationary currents and those for the potential function of such currents in an external magnetic field are studied using angular momentum algebraic techniques. It is found that the expansion for the magnetic induction vector is made identical to that for the electric field strength of a neutral system of charges by substituting electric for magnetic multipole moments. The toroidal part of the multipole expansion for the magnetic field vector potential can, due to its potential nature, be omitted in the static case. Also, the potential function of a system of currents in an external magnetic field and the potential energy of a neutral system of charges in an external electric field have identical multipole expansions. For axisymmetric systems, the expressions for the field and those for the potential energy of electric and magnetic multipoles are reduced to simple forms, with symmetry axis orientation dependence separated out. (methodological notes)

  1. Multipole expansions in magnetostatics

    Energy Technology Data Exchange (ETDEWEB)

    Agre, Mark Ya [National University of ' Kyiv-Mohyla Academy' , Kyiv (Ukraine)

    2011-02-28

    Multipole expansions of the magnetic field of a spatially restricted system of stationary currents and those for the potential function of such currents in an external magnetic field are studied using angular momentum algebraic techniques. It is found that the expansion for the magnetic induction vector is made identical to that for the electric field strength of a neutral system of charges by substituting electric for magnetic multipole moments. The toroidal part of the multipole expansion for the magnetic field vector potential can, due to its potential nature, be omitted in the static case. Also, the potential function of a system of currents in an external magnetic field and the potential energy of a neutral system of charges in an external electric field have identical multipole expansions. For axisymmetric systems, the expressions for the field and those for the potential energy of electric and magnetic multipoles are reduced to simple forms, with symmetry axis orientation dependence separated out. (methodological notes)

  2. The devil is in the methods: lineage tracing, functional screens and sequencing, hormones, tumour-stroma interactions, and expansion of human breast tumours as xenografts

    OpenAIRE

    dM Vivanco, María; Stingl, John; Clarke, Robert B.; Bentires-Alj, Mohamed

    2011-01-01

    The meeting of the European Network for Breast Development and Cancer (ENBDC) on 'Methods in Mammary Gland Development and Cancer' has become an annual international rendezvous for scientists with interests in the normal and neoplastic breast. The third meeting in this series, held in April-May 2011 in Weggis, Switzerland, focussed on functional screens and sequencing, hormones, lineage tracing, tumor-stroma interactions and the expansion of human breast tumours as xenografts.

  3. Analytical Hessian of electronic excited states in time-dependent density functional theory with Tamm-Dancoff approximation.

    Science.gov (United States)

    Liu, Jie; Liang, WanZhen

    2011-07-01

    We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values. PMID:21744894

  4. Resonances and analyticity of scattering wave function for square-well-type potentials

    International Nuclear Information System (INIS)

    In this paper we extend our previous analysis of the scattering of wave packets in one dimension to the case of the square-well potential. The analytic properties of the general scattering solution are emphasized thereby making the analysis useful as introductory material for a more sophisticated S-matrix treatment. The square-well model is particularly interesting because of its application to the deuteron problem. Resonance scattering, barrier penetration, time delay, and line shape are discussed at the level of the first-year graduate student

  5. Functional-analytical capabilities of GIS technology in the study of water use risks

    Science.gov (United States)

    Nevidimova, O. G.; Yankovich, E. P.; Yankovich, K. S.

    2015-02-01

    Regional security aspects of economic activities are of great importance for legal regulation in environmental management. This has become a critical issue due to climate change, especially in regions where severe climate conditions have a great impact on almost all types of natural resource uses. A detailed analysis of climate and hydrological situation in Tomsk Oblast considering water use risks was carried out. Based on developed author's techniques an informational and analytical database was created using ArcGIS software platform, which combines statistical (quantitative) and spatial characteristics of natural hazards and socio-economic factors. This system was employed to perform areal zoning according to the degree of water use risks involved.

  6. Functions of diffraction correction and analytical solutions in nonlinear acoustic measurement

    CERN Document Server

    Alliès, Laurent; Nadi, M

    2008-01-01

    This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction applied to fundamental, makes it possible to obtain simple solutions for the second harmonic of the average acoustic pressure, but sufficiently precise for measuring the parameter of nonlinearity B/A in a finite amplitude method. Comparison with other expressions requiring numerical integration, show the solutions are precise in the nearfield.

  7. Nonuniversality of the dispersion interaction: analytic benchmarks for van der Waals energy functionals

    OpenAIRE

    Dobson, John F.; Rubio, Angel

    2005-01-01

    We highlight the non-universality of the asymptotic behavior of dispersion forces, such that a sum of inverse sixth power contributions is often inadequate. We analytically evaluate the cross-correlation energy Ec between two pi-conjugated layers separated by a large distance D within the electromagnetically non-retarded Random Phase Approximation, via a tight-binding model. For two perfect semimetallic graphene sheets at T=0K we find Ec = C D^{-3}, in contrast to the "insulating" D^{-4} depe...

  8. An analytical electron distribution function for inelastic collisions in a uniform gas with time varying electric field

    International Nuclear Information System (INIS)

    The desire for improved control over electric discharge phenomena in a wide variety of scientific, technological, manufacturing, and waste processing activities spurs the development of non-equilibrium, non-uniform, and time dependent models. This paper addresses the situation of slightly ionized, spatially uniform gas with a time varying electric field, and in which inelastic collisions occur. The purpose here is to present a reasonably consistent, and reasonably accessible analytical result for the electron kinetics in a gas discharge regime of technological interest. This paper will be structured as follows. First, the analytical result for the time dependent electron distribution function is stated. Second, a summary of the solution procedure with its attendant assumptions is given. Lastly, examples of the solution are given for an idealized nitrogen-like gas where the electric field ramps between static conditions, and then for sinusoidal behavior

  9. Analytical solution to a non-autonomous second order differential equation with modified hyperbolic tangent function

    International Nuclear Information System (INIS)

    The solution to a non-autonomous second order ordinary differential equation is presented. The real function, dependent on the differentiation variable, is a squared hyperbolic tangent function plus a term that involves the quotient of hyperbolic functions. This function varies from one limiting value to another without having any singularities. The solution is remarkably simple and involves only trigonometric and hyperbolic trigonometric functions. The solution is analyzed in the context of wave propagation in an inhomogeneous one-dimensional medium. The profile is shown to act as a perfect anti-reflection interface, providing a possible alternative route to the fabrication of reflectionless surfaces. (paper)

  10. Simplex and duplex event-specific analytical methods for functional biotech maize.

    Science.gov (United States)

    Lee, Seong-Hun; Kim, Su-Jeong; Yi, Bu-Young

    2009-08-26

    Analytical methods are very important in the control of genetically modified organism (GMO) labeling systems or living modified organism (LMO) management for biotech crops. Event-specific primers and probes were developed for qualitative and quantitative analysis for biotech maize event 3272 and LY 038 on the basis of the 3' flanking regions, respectively. The qualitative primers confirmed the specificity by a single PCR product and sensitivity to 0.05% as a limit of detection (LOD). Simplex and duplex quantitative methods were also developed using TaqMan real-time PCR. One synthetic plasmid was constructed from two taxon-specific DNA sequences of maize and two event-specific 3' flanking DNA sequences of event 3272 and LY 038 as reference molecules. In-house validation of the quantitative methods was performed using six levels of mixing samples, from 0.1 to 10.0%. As a result, the biases from the true value and the relative deviations were all within the range of +/-30%. Limits of quantitation (LOQs) of the quantitative methods were all 0.1% for simplex real-time PCRs of event 3272 and LY 038 and 0.5% for duplex real-time PCR of LY 038. This study reports that event-specific analytical methods were applicable for qualitative and quantitative analysis for biotech maize event 3272 and LY 038. PMID:19650633

  11. Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

    Science.gov (United States)

    Sharma, Pankaj; Parashar, Sandeep Kumar

    2016-05-01

    The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d15 effect. In piezoelectric actuators, the potential use of d15 effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d31 and d33. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton`s principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

  12. On the Equisummability of Hermite and Fourier Expansions

    Indian Academy of Sciences (India)

    E K Narayanan; S Thangavelu

    2001-02-01

    We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.

  13. Expansion and functional properties of extruded snacks enriched with nutrition sources from food processing by-products.

    Science.gov (United States)

    Korkerd, Sopida; Wanlapa, Sorada; Puttanlek, Chureerat; Uttapap, Dudsadee; Rungsardthong, Vilai

    2016-01-01

    Rich sources of protein and dietary fiber from food processing by-products, defatted soybean meal, germinated brown rice meal, and mango peel fiber, were added to corn grit at 20 % (w/w) to produce fortified extruded snacks. Increase of total dietary fiber from 4.82 % (wb) to 5.92-17.80 % (wb) and protein from 5.03 % (wb) to 5.46-13.34 % were observed. The product indicated high expansion and good acceptance tested by sensory panels. There were 22.33-33.53 and 5.30-11.53 fold increase in the phenolics and antioxidant activity in the enriched snack products. The effects of feed moisture content, screw speed, and barrel temperature on expansion and nutritional properties of the extruded products were investigated by using response surface methodology. Regression equations describing the effect of each variable on the product responses were obtained. The snacks extruded with feed moisture 13-15 % (wb) and extrusion temperature at 160-180 °C indicated the products with high preference in terms of expansion ratio between insoluble dietary fiber and soluble dietary fiber balance. The results showed that the by-products could be successfully used for nutritional supplemented expanded snacks. PMID:26787975

  14. Analytical method for the evaluation of sulfur functionalities in American coals. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Attar, A.

    1983-05-01

    This investigation consisted of the following 6 tasks: (1) improve the instrumentation for the sulfur functional groups analysis and make it more reliable. (2) create a set of reference standards of sulfur-containing compounds. (3) examine the sulfur groups distribution in untreated and desulfurized coals. (4) examine the sulfur functionalities in raw and processed coals, i.e., liquefied coals. (5) determine the distribution of sulfur functionalities in modified coals. (6) prepare computer programs for calculations related to the distribution of sulfur functional groups in coal. Each task is discussed and results are presented. Appendix A contains the computer program used to interpret the data. 31 references, 56 figures, 17 tables.

  15. Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Padé approximant

    Science.gov (United States)

    Sergeev, A.; Alharbi, F. H.; Jovanovic, R.; Kais, S.

    2016-04-01

    The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke’s law model for two-electron atoms.

  16. Analytic results for scaling function and moments for a different type of avalanche in the Bak-Sneppen evolution model

    Science.gov (United States)

    Li, W.; Cai, X.

    2000-12-01

    Starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the Bak-Sneppen evolution model, we derive the exact formula of the scaling function describing the probability distribution of avalanches. The scaling function displays features required by the scaling ansatz and verified by simulations. Using the scaling function we investigate the avalanche moment, denoted by Δf¯. It is found that for any non-negative integer k, Δf¯ diverges as Δf¯-k, which gives an infinite group of exact critical exponents. Simulation outcomes of avalanche moments with k=1,2,3, are found to be consistent with the corresponding analytical results.

  17. Functional-analytical capabilities of GIS technology in the study of water use risks

    International Nuclear Information System (INIS)

    Regional security aspects of economic activities are of great importance for legal regulation in environmental management. This has become a critical issue due to climate change, especially in regions where severe climate conditions have a great impact on almost all types of natural resource uses. A detailed analysis of climate and hydrological situation in Tomsk Oblast considering water use risks was carried out. Based on developed author's techniques an informational and analytical database was created using ArcGIS software platform, which combines statistical (quantitative) and spatial characteristics of natural hazards and socio-economic factors. This system was employed to perform areal zoning according to the degree of water use risks involved

  18. Analytical Derivation of Three Dimensional Vorticity Function for wave breaking in Surf Zone

    CERN Document Server

    Dutta, R

    2015-01-01

    In this report, Mathematical model for generalized nonlinear three dimensional wave breaking equations was de- veloped analytically using fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The three dimensional equations for vorticity distributions are developed from Reynold based stress equations. Vorticity transport equations are also developed for wave breaking zone. This equations are basic model tools for numerical simulation of surf zone to explain wave breaking phenomena. The model reproduces most of the dynamics in the surf zone. Non linearity for wave height predictions is also shown close to the breaking both in shoaling as well as surf zone. Keyword Wave breaking, Boussinesq equation, shallow water, surf zone. PACS : 47.32-y

  19. Analytic derivation of the longitudinal component of the three-dimensional point-spread function in coded-aperture laminography

    Science.gov (United States)

    Accorsi, Roberto

    2005-10-01

    Near-field coded-aperture data from a single view contain information useful for three-dimensional (3D) reconstruction. A common approach is to reconstruct the 3D image one plane at a time. An analytic expression is derived for the 3D point-spread function of coded-aperture laminography. Comparison with computer simulations and experiments for apertures with different size, pattern, and pattern family shows good agreement in all cases considered. The expression is discussed in the context of the completeness conditions for projection data and is applied to explain an example of nonlinear behavior inherent in 3D laminographic imaging.

  20. THE EXTREME POINTS OF A CLASS OF ANALYTIC FUNCTIONS WITH POSITIVE REAL PART AND A PRESCRIBED SET OF VALUES

    Institute of Scientific and Technical Information of China (English)

    Peng Zhigang

    2012-01-01

    Let ζ=(0,z1,z2,...,zn)with|zj|<≤ 1for 1≤j ≤n,ω=(1,w1,w2,...,wn),and P(ζ,w) denote the set of functions p(z) that are analytic in D ={z:|z| < 1} and satisfy Rep(z) ≥ 0 (|z| < 1),p(0) =1,p(zj) =wj,j =1,2,…,n.In this article we investigate the extreme points of P(ζ,w).

  1. An Examination of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Channel-Base Currents

    CERN Document Server

    Lundengård, Karl; Javor, Vesna; Silvestrov, Sergei

    2016-01-01

    A multi-peaked version of the analytically extended function (AEF) intended for approximation of multi-peaked lightning current wave-forms will be presented along with some of its basic properties. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a given charge trans-fer and specific energy will also be described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach will be discussed.

  2. On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

    Science.gov (United States)

    Gottlieb, David; Shu, Chi-Wang

    1994-01-01

    The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

  3. The toroidal block and the genus expansion

    CERN Document Server

    Kashani-Poor, Amir-Kian

    2012-01-01

    We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via geometric engineering from the topological string. This point of view uncovers modular properties of the one-point conformal block on a torus with complexified intermediate momenta: in the large intermediate weight limit, it is a power series whose coefficients are quasi-modular forms. The all-genus viewpoint that the conformal field theory approach lends to the topological string yields insight into the analytic structure of the topological string partition function.

  4. The Effect of Contingent Reinforcement on Target Variables in Outpatient Psychotherapy for Depression: A Successful and Unsuccessful Case Using Functional Analytic Psychotherapy

    Science.gov (United States)

    Kanter, Jonathan W.; Landes, Sara J.; Busch, Andrew M.; Rusch, Laura C.; Brown, Keri R.; Baruch, David E.; Holman, Gareth I.

    2006-01-01

    The current study investigated a behavior-analytic treatment, functional analytic psychotherapy (FAP), for outpatient depression utilizing two single-subject A/A+B designs. The baseline condition was cognitive behavioral therapy. Results demonstrated treatment success in 1 client after the addition of FAP and treatment failure in the 2nd. This…

  5. Analytical Formulation of the Single-visit Completeness Joint Probability Density Function

    Science.gov (United States)

    Garrett, Daniel; Savransky, Dmitry

    2016-09-01

    We derive an exact formulation of the multivariate integral representing the single-visit obscurational and photometric completeness joint probability density function for arbitrary distributions for planetary parameters. We present a derivation of the region of nonzero values of this function, which extends previous work, and discuss the time and computational complexity costs and benefits of the method. We present a working implementation and demonstrate excellent agreement between this approach and Monte Carlo simulation results.

  6. Analytical formulation of the single-visit completeness joint probability density function

    CERN Document Server

    Garrett, Daniel

    2016-01-01

    We derive an exact formulation of the multivariate integral representing the single-visit obscurational and photometric completeness joint probability density function for arbitrary distributions for planetary parameters. We present a derivation of the region of nonzero values of this function which extends previous work, and discuss time and computational complexity costs and benefits of the method. We present a working implementation, and demonstrate excellent agreement between this approach and Monte Carlo simulation results

  7. Worldsheet operator product expansions and p-point functions in AdS{sub 3}/CFT{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Kirsch, Ingo [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Wirtz, Tim [Siegen Univ. (Germany). Fachbereich Physik

    2011-06-15

    We construct the operator product expansions (OPE) of the chiral primary operators in the worldsheet theory for strings on AdS{sub 3} x S{sup 3} x T{sup 4}. As an interesting application, we will use the worldsheet OPEs to derive a recursion relation for a particular class of extremal p-point correlators on the sphere. We compare our result with the corresponding recursion relation previously found in the symmetric orbifold theory on the boundary of AdS{sub 3}. (orig.)

  8. Analytical study on system identification of fixed base transfer functions for an embedded reactor building

    International Nuclear Information System (INIS)

    System identification method proposed by the authors to estimate the dynamic characteristic of a building itself, under an imaginary fixed base condition in the other words, is studied for buildings with large soil-structure interaction (SSI) effect. The applicability of the method to buildings with embedment is studied in this paper. The assumed system model for the method is slightly different from the actual SSI system. This difference as well as the additional input to the underground wall may produce some system identification error. For these reasons, the proposed method and other spectral analysis procedures as well as the ARX method are applied to the response of an analytical model and results are compared. The benefit of the use of such model response instead of actual measured data is that the causality is very clear. In result, relative merits and demerits of the methods, cause and mechanism of them become clear. Furthermore, the applicability of the proposed method is confirmed. Such a method can be used to check the change of dynamic characteristics of the buildings after large earthquakes or long-term service. (author)

  9. Application of ANFIS for analytical modeling of tensile strength of functionally graded steels

    Directory of Open Access Journals (Sweden)

    Ali Nazari

    2012-06-01

    Full Text Available In the present study, the tensile strength of ferritic and austenitic functionally graded steels produced by electroslag remelting has been modeled. To produce functionally graded steels, two slices of plain carbon steel and austenitic stainless steels were spot welded and used as electroslag remelting electrode. Functionally graded steel containing graded layers of ferrite and austenite may be fabricated via diffusion of alloying elements during remelting stage. Vickers microhardness profile of the specimen has been obtained experimentally and modeled with adaptive network-based fuzzy inference systems (ANFIS. To build the model for graded ferritic and austenitic steels, training, testing and validation using respectively 174 and 120 experimental data were conducted. According to the input parameters, in the ANFIS model, the Vickers microhardness of each layer was predicted. A good fit equation which correlates the Vickers microhardness of each layer to its corresponding chemical composition was achieved by the optimized network for both ferritic and austenitic graded steels. Afterwards; the Vickers microhardness of each layer in functionally graded steels was related to the yield stress of the corresponding layer and by assuming Holloman relation for stress-strain curve of each layer, they were acquired. Finally, by applying the rule of mixtures, tensile strength of functionally graded steels configuration was found through a numerical method. The obtained results from the proposed model are in good agreement with those acquired from the experiments.

  10. Tokamak plasma shape identification with a Legendre-Fourier expansion of the vacuum poloidal flux function in the toroidal coordinates

    International Nuclear Information System (INIS)

    A new method is proposed for identification of the outermost magnetic surface of tokamak plasmas. The method is based on the analytical solution of the Grad-Shafranov equation in a vacuum region under the toroidal coordinates. This method is applicable to accurate feedback control and real-time visualization of various plasma configurations, and robust to the loss of sensors or the existence of signal noise. (author)

  11. ORBITALES. A program for the calculation of wave functions with an analytical central potential; ORBITALES. Programa de calculo de Funciones de Onda para una Potencial Central Analitico

    Energy Technology Data Exchange (ETDEWEB)

    Yunta Carretero; Rodriguez Mayquez, E.

    1974-07-01

    In this paper is described the objective, basis, carrying out in FORTRAN language and use of the program ORBITALES. This program calculate atomic wave function in the case of ths analytical central potential (Author) 8 refs.

  12. Some Applications of a Lemma Concerning Analytic Functions Having Positive Real Parts in the Unit Disk

    CERN Document Server

    Opoola, T O

    2009-01-01

    In this paper we give some applications of a lemma of Babalola and Opoola \\cite{BO}, which is a classical extension of an earlier one by Lewandowski, Miller and Zlotkiewicz \\cite{LMZ}. The applications were given via a new generalization of some well-known subclasses of univalent functions, and they unify many known results.

  13. Weakly Non-Linear Gaussian Fluctuations and the Edgeworth Expansion

    OpenAIRE

    Juszkiewicz, R.; Weinberg, D; Amsterdamski, P.; Chodorowski, M.; Bouchet, F.

    1993-01-01

    We calculate the cosmological evolution of the 1-point probability distribution function (PDF), using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion of the PDF. Our method applies directly to a smoothed mass density field or to the divergence of a smoothed peculiar velocity field, provided that rms fluctuations are small compared to unity on the smoothing scale, and that the primordial fluctuations that seed the growth of structure are G...

  14. An Analytical Approach to Document Clustering Based on Internal Criterion Function

    CERN Document Server

    Ranjan, Alok; Kandpal, Eatesh; Dhar, Joydip

    2010-01-01

    Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a goal of creating good quality clusters, a variety of algorithms have been developed having quality-complexity trade-offs. Among these, some algorithms seek to minimize the computational complexity using certain criterion functions which are defined for the whole set of clustering solution. In this paper, we are proposing a novel document clustering algorithm based on an internal criterion function. Most commonly used partitioning clustering algorithms (e.g. k-means) have some drawbacks as they suffer from local optimum solutions and creation of empty clusters as a clustering solution. The proposed algorithm usually does not suffer from these problems and converge to a global optimum, its performance enhances with the increase in number of clusters. We have checked our algor...

  15. Fractional Calculus of Analytic Functions Concerned with Möbius Transformations

    Directory of Open Access Journals (Sweden)

    Nicoleta Breaz

    2016-01-01

    Full Text Available Let A be the class of functions f(z in the open unit disk U with f(0=0 and f′(0=1. Also, let w(ζ be a Möbius transformation in U for some z∈U. Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals of f(z∈A. Also, some interesting examples for fractional calculus are given.

  16. A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels

    Energy Technology Data Exchange (ETDEWEB)

    Zahedinejad, P. [Department of Mechanical Engineering, Islamic Azad University, Branch of Shiraz, Shiraz (Iran, Islamic Republic of); Malekzadeh, P., E-mail: malekzadeh@pgu.ac.i [Department of Mechanical Engineering, Persian Gulf University, Persian Gulf University Boulevard, Bushehr 75168 (Iran, Islamic Republic of); Center of Excellence for Computational Mechanics, Shiraz University, Shiraz (Iran, Islamic Republic of); Farid, M. [Department of Mechanical Engineering, Islamic Azad University, Branch of Shiraz, Shiraz (Iran, Islamic Republic of); Karami, G. [Department of Mechanical Engineering and Applied Mechanics, North Dakota State University, Fargo, ND 58105-5285 (United States)

    2010-08-15

    Based on the three-dimensional elasticity theory, free vibration analysis of functionally graded (FG) curved thick panels under various boundary conditions is studied. Panel with two opposite edges simply supported and arbitrary boundary conditions at the other edges are considered. Two different models of material properties variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential distribution of the material properties through the thickness are considered. Differential quadrature method in conjunction with the trigonometric functions is used to discretize the governing equations. With a continuous material properties variation assumption through the thickness of the curved panel, differential quadrature method is efficiently used to discretize the governing equations and to implement the related boundary conditions at the top and bottom surfaces of the curved panel and in strong form. The convergence of the method is demonstrated and to validate the results, comparisons are made with the solutions for isotropic and FG curved panels. By examining the results of thick FG curved panels for various geometrical and material parameters and subjected to different boundary conditions, the influence of these parameters and in particular, those due to functionally graded material parameters are studied.

  17. Interrupting CD28 costimulation before antigen rechallenge affects CD8(+) T-cell expansion and effector functions during secondary response in mice.

    Science.gov (United States)

    Fröhlich, Monika; Gogishvili, Tea; Langenhorst, Daniela; Lühder, Fred; Hünig, Thomas

    2016-07-01

    The role of CD28-mediated costimulation in secondary CD8(+) T-cell responses remains controversial. Here, we have used two tools - blocking mouse anti-mouse CD28-specific antibodies and inducible CD28-deleting mice - to obtain definitive answers in mice infected with ovalbumin-secreting Listeria monocytogenes. We report that both blockade and global deletion of CD28 reveal its requirement for full clonal expansion and effector functions such as degranulation and IFN-γ production during the secondary immune response. In contrast, cell-intrinsic deletion of CD28 in transferred TCR-transgenic CD8(+) T cells before primary infection leads to impaired clonal expansion but an increase in cells able to express effector functions in both primary and secondary responses. We suggest that the proliferation-impaired CD8(+) T cells respond to CD28-dependent help from their environment by enhanced functional differentiation. Finally, we report that cell-intrinsic deletion of CD28 after the peak of the primary response does not affect the establishment, maintenance, or recall of long-term memory. Thus, if given sufficient time, the progeny of primed CD8(+) T cells adapt to the absence of this costimulator. PMID:27122236

  18. New Dirac Delta function based methods with applications to perturbative expansions in quantum field theory and beyond

    CERN Document Server

    Kempf, Achim; Morales, Alejandro H

    2014-01-01

    The Dirac delta distribution serves as a useful tool in many areas of science and engineering. Here, we derive further properties of the Dirac Delta which involve derivatives in its argument and which can serve as all-purpose methods in a variety of fields from science to engineering. We highlight potential avenues for applications to quantum field theory and we also exhibit a connection to the problem of blurring/deblurring in signal processing. We find that blurring, which may be thought of as a result of multi-path evolution, is in quantum field theory the strong coupling dual of the usual small coupling expansion in terms of the sum over Feynman graphs.

  19. Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities

    Science.gov (United States)

    Gori-Giorgi, Paola; Perdew, John P.

    2002-10-01

    We construct analytic formulas that represent the coupling-constant-averaged pair distribution function gxc(rs,ζ,kFu) of a three-dimensional nonrelativistic ground-state electron gas constrained to a uniform density with density parameter rs=(9π/4)1/3/kF and relative spin polarization ζ over the whole range 0∞) oscillations averaged out. The pair distribution function gxc at the physical coupling constant is then given by differentiation with respect to rs. Our formulas are constructed using only known theoretical constraints plus the correlation energy ɛc(rs,ζ), and accurately reproduce the gxc of the quantum Monte Carlo method and of the fluctuation-dissipation theorem with the Richardson-Ashcroft dynamical local-field factor. Our gxc is correct even in the high-density (rs-->0) and low-density (rs-->∞) limits. When the spin resolution of ɛc into ↑↑, ↓↓, and ↑↓ contributions is known, as it is in the high- and low-density limits, our formulas also yield the spin resolution of gxc. Because of these features, our formulas may be useful for the construction of density functionals for nonuniform systems. We also analyze the kinetic energy of correlation into contributions from density fluctuations of various wave vectors. The exchange and long-range correlation parts of our gxc(rs,ζ,kFu)-1 are analytically Fourier transformable, so that the static structure factor Sxc(rs,ζ,k/kF) is easily evaluated.

  20. Analytical approach for the excited-state Hessian in time-dependent density functional theory: Formalism, implementation, and performance

    Science.gov (United States)

    Liu, Jie; Liang, WanZhen

    2011-11-01

    The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations.

  1. Analytical Phase Equilibrium Function for Mixtures Obeying Raoult's and Henry's Laws

    Science.gov (United States)

    Hayes, Robert

    When a mixture of two substances exists in both the liquid and gas phase at equilibrium, Raoults and Henry's laws (ideal solution and ideal dilute solution approximations) can be used to estimate the gas and liquid mole fractions at the extremes of either very little solute or solvent. By assuming that a cubic polynomial can reasonably approximate the intermediate values to these extremes as a function of mole fraction, the cubic polynomial is solved and presented. A closed form equation approximating the pressure dependence on mole fraction of the constituents is thereby obtained. As a first approximation, this is a very simple and potentially useful means to estimate gas and liquid mole fractions of equilibrium mixtures. Mixtures with an azeotrope require additional attention if this type of approach is to be utilized. This work supported in part by federal Grant NRC-HQ-84-14-G-0059.

  2. Sum rules for the exchange-correlation energy functional of the extended constrained-search theory: Application to checking the validity of the vorticity expansion approximation of the current-density functional theory

    International Nuclear Information System (INIS)

    We present four kinds of sum rules for the exchange-correlation energy functional of the extended constrained-search theory. They are applicable even to the conventional density functional theory. As an application of these sum rules, we utilize them to check the validity of the vorticity expansion approximation (VEA) of the current-density functional theory (CDFT). The VEA formula fulfils three of them, though the local density approximation formula of the CDFT fulfills only one. The validity of the VEA formula is thus confirmed successfully from the viewpoint of the sum rules.

  3. Laplacian-level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory

    CERN Document Server

    Laricchia, S; Fabiano, E; Della Sala, F

    2014-01-01

    We test Laplacian-level meta-generalized gradient approximation (meta-GGA) non-interacting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We consider several well known Laplacian-level meta-GGAs from literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin [Phys. Rev. B \\textbf{75},155109 (2007)]), as well as two newly designed Laplacian-level kinetic energy functionals (named L0.4 and L0.6). First, a general assessment of the different functionals is performed, testing them for model systems (one-electron densities, Hooke's atom and different jellium systems), atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assess, for the first time, the performance of the different functionals for Subsystem Density Functional Theory (DFT) calculations on non-covalently interacting systems. We find that the different Laplacian-level meta-GGA kinetic functionals may improve the descript...

  4. Discussion on Function Expansion of Internal Audit after Financial Crisis%金融危机后内部审计功能拓展探讨

    Institute of Scientific and Technical Information of China (English)

    张雨桐

    2012-01-01

    Combining with background of social economic envimrmaent of later global financial crisis period, specific contents of function expansion of internal audit were discussed. It was thought that internal audit should break through the limit of traditional value keeping activities and work center should transfer to activities of helping enterprises realize value increasing. Three challenges that the expansion function of internal audit will meet when it plays its role were proposed, including status, personnel and technology.%结合全球金融危机后期的经济环境背景,讨论了内部审计功能拓展的具体内容.认为内部审计应当突破传统保值活动的界限,将工作重心转移到帮助企业实现增值的活动中,并指出内部审计拓展功能的发挥面临着地位、人员和技术方面的三大挑战.

  5. Analytic investigation of effect of electric field on elasto-plastic response of a functionally graded piezoelectric hollow sphere

    Energy Technology Data Exchange (ETDEWEB)

    Atai, Ali Asghar [University of Tehran, Tehran (Iran, Islamic Republic of); Lak, Davaod [National Iranian Oil Co., Tehran (Iran, Islamic Republic of)

    2016-01-15

    In this work, the effect of electric potential on the mechanical (Stresses, strains, displacement) and electrical (electrical displacement and intensity) response of a Functionally graded piezoelectric (FGP) hollow sphere is analytically investigated. The sphere is under the action of internal/external pressure and temperature gradient as well. The inhomogeneity is based on power law in radial direction. The analysis is done in two parts: elastic response and plastic response, using Tresca yield criterion. It is shown by illustrative example that under internal pressure and assumed model parameters, the commencement of plastic region is from outside surface towards inside in the plastic zone is extended with the increase of electric potential. Interestingly, radial stress and displacement have an extreme not on the boundaries, but on the inside.

  6. Probing primordial non Gaussianity in the BOOMERanG CMB maps: an analysis based on analytical Minkowski functionals

    International Nuclear Information System (INIS)

    Minkowski functionals are a powerful tool to constrain the Gaussianity of the Cosmic Microwave Background (CMB). In the limit of a weakly non Gaussian field, a perturbative approach can be derived [Hikage C., Komatsu E., and Matsubara T., 2006, ApJ, 653, 11] that is completely based on analytical formulae without requiring computationally intensive, dedicated Monte Carlo non Gaussian simulations of the CMB anisotropy. We apply this machinery to an intensity map derived from the 1998 and 2003 flights of BOOMERanG, analyzed here together for the first time. We set limits on the non-linear coupling parameter fNL as -1020NL<390 at 95% CL, markedly improving the previous constraints set by [De Troia G. et al., 2007, ApJ, 670, L73] whose analysis was limited to the BOOMERanG 2003 dataset. These limits are the most stringent ever set among suborbital experiments.

  7. Probing primordial non Gaussianity in the BOOMERanG CMB maps: an analysis based on analytical Minkowski functionals

    Energy Technology Data Exchange (ETDEWEB)

    Migliaccio, M.; Natoli, P.; De Troia, G. [Dipartimento di Fisica, Universita di Roma ' Tor Vergata' , Via della Ricerca Scientifica, 1 I-00133 Roma (Italy); Hikage, C. [School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA (United Kingdom); Komatsu, E. [Texas Cosmology Center, University of Texas at Austin, 1 University Station, C1400, Austin, TX 78712 (United States); Ade, P.A.R. [School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA (United Kingdom); Bock, J.J. [Jet Propulsion Laboratory, Pasadena, CA (United States); Bond, J.R. [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario (Canada); Borrill, J. [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Boscaleri, A. [IFAC-CNR, Firenze (Italy); Contaldi, C.R. [Theoretical Physics Group, Imperial College, London (United Kingdom); Crill, B.P. [Jet Propulsion Laboratory, Pasadena, CA (United States); Bernardis, P. de [Dipartimento di Fisica, Universita La Sapienza, Roma (Italy); Gasperis, G. de [Dipartimento di Fisica, Universita di Roma ' Tor Vergata' , Via della Ricerca Scientifica, 1 I-00133 Roma (Italy); Oliveira-Costa, A. de [Department of Physics, MIT, Cambridge, MA 02139 (United States); Di Stefano, G. [Istituto Nazionale di Geofisica e Vulcanologia, 00143 Rome (Italy); Hivon, E. [Institut d' Astrophysique, Paris (France); Kisner, T.S. [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Jones, W.C. [Department of Physics, Princeton University, Princeton, NJ 0854 (United States); Lange, A.E. [Observational Cosmology, California Institute of Technology, Pasadena, CA (United States)

    2009-10-15

    Minkowski functionals are a powerful tool to constrain the Gaussianity of the Cosmic Microwave Background (CMB). In the limit of a weakly non Gaussian field, a perturbative approach can be derived [Hikage C., Komatsu E., and Matsubara T., 2006, ApJ, 653, 11] that is completely based on analytical formulae without requiring computationally intensive, dedicated Monte Carlo non Gaussian simulations of the CMB anisotropy. We apply this machinery to an intensity map derived from the 1998 and 2003 flights of BOOMERanG, analyzed here together for the first time. We set limits on the non-linear coupling parameter f{sub NL} as -1020

  8. Probing primordial non Gaussianity in the BOOMERanG CMB maps: an analysis based on analytical Minkowski functionals

    Science.gov (United States)

    Migliaccio, M.; Natoli, P.; De Troia, G.; Hikage, C.; Komatsu, E.; Ade, P. A. R.; Bock, J. J.; Bond, J. R.; Borrill, J.; Boscaleri, A.; Contaldi, C. R.; Crill, B. P.; de Bernardis, P.; de Gasperis, G.; de Oliveira-Costa, A.; Di Stefano, G.; Hivon, E.; Kisner, T. S.; Jones, W. C.; Lange, A. E.; Masi, S.; Mauskopf, P. D.; MacTavish, C. J.; Melchiorri, A.; Montroy, T. E.; Netterfield, C. B.; Pascale, E.; Piacentini, F.; Polenta, G.; Ricciardi, S.; Romeo, G.; Ruhl, J. E.; Tegmark, M.; Veneziani, M.; Vittorio, N.

    2009-10-01

    Minkowski functionals are a powerful tool to constrain the Gaussianity of the Cosmic Microwave Background (CMB). In the limit of a weakly non Gaussian field, a perturbative approach can be derived [Hikage C., Komatsu E., & Matsubara T., 2006, ApJ, 653, 11] that is completely based on analytical formulae without requiring computationally intensive, dedicated Monte Carlo non Gaussian simulations of the CMB anisotropy. We apply this machinery to an intensity map derived from the 1998 and 2003 flights of BOOMERanG, analyzed here together for the first time. We set limits on the non-linear coupling parameter f as -1020Troia G. et al., 2007, ApJ, 670, L73] whose analysis was limited to the BOOMERanG 2003 dataset. These limits are the most stringent ever set among suborbital experiments.

  9. Development and application of functional-analytic simulator in the training of nuclear power plant operating personnel

    International Nuclear Information System (INIS)

    The experience is reviewed from the development and utilization of a functional-analytic training simulator used in the USSR for training the personnel of nuclear power plants with WWER-1000 reactors. The training facility consists of a central ES 1066 computer where the mathematical model of the power unit is implemented, and of four teaching workplaces with Elektronika-85 personal computers. An Elektronika-60 computer links these computers to the central unit. The training facility enables reactor operators to practise in understanding dynamic power unit characteristics and relations between dynamic parameters, to gain basic skills for unit control with respect to limitations following from nuclear safety requirements, to master non-standard situations and to perform analyses of accidents. The facility is also used to check the professional skills of operators and to provide preliminary training prior to switching over to full-scale training facilities. (Z.M.). 2 refs

  10. Prediction and optimization of the performance of parabolic solar dish concentrator with sphere receiver using analytical function

    CERN Document Server

    Huang, Weidong; Hu, Peng; Chen, Zeshao

    2011-01-01

    Parabolic solar dish concentrator with sphere receiver is less studied. We present an analytic function to calculate the intercept factor of the system with real sun bright distribution and Gaussian distribution, the results indicate that the intercept factor is related to the rim angle of reflector and the ratio of open angle of receiver at the top of reflector to optical error when the optical error is larger than or equal to 5 mrad, but is related to the rim angle, open angle and optical error in less than 5 mrad optical error. Furthermore we propose a quick process to optimize the system to provide the maximum solar energy to net heat efficiency for different optical error under typical condition. The results indicate that the parabolic solar dish concentrator with sphere receiver has rather high solar energy to net heat efficiency which is 20% more than solar trough and tower system including higher cosine factor and lower heat loss of the receiver.

  11. Functional data analytic approach of modeling ECG T-wave shape to measure cardiovascular behavior

    CERN Document Server

    Zhou, Yingchun; 10.1214/09-AOAS273

    2010-01-01

    The T-wave of an electrocardiogram (ECG) represents the ventricular repolarization that is critical in restoration of the heart muscle to a pre-contractile state prior to the next beat. Alterations in the T-wave reflect various cardiac conditions; and links between abnormal (prolonged) ventricular repolarization and malignant arrhythmias have been documented. Cardiac safety testing prior to approval of any new drug currently relies on two points of the ECG waveform: onset of the Q-wave and termination of the T-wave; and only a few beats are measured. Using functional data analysis, a statistical approach extracts a common shape for each subject (reference curve) from a sequence of beats, and then models the deviation of each curve in the sequence from that reference curve as a four-dimensional vector. The representation can be used to distinguish differences between beats or to model shape changes in a subject's T-wave over time. This model provides physically interpretable parameters characterizing T-wave sh...

  12. Asymptotic expansions for the Gaussian unitary ensemble

    DEFF Research Database (Denmark)

    Haagerup, Uffe; Thorbjørnsen, Steen

    2012-01-01

    Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean and...

  13. On the Fourier expansion method for highly accurate computation of the Voigt/complex error function in a rapid algorithm

    CERN Document Server

    Abrarov, S M

    2012-01-01

    In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified representation of the proposed complex error function approximation makes possible further algorithmic optimization resulting in a considerable computational acceleration without compromise on accuracy.

  14. Au-ionic liquid functionalized reduced graphene oxide immunosensing platform for simultaneous electrochemical detection of multiple analytes.

    Science.gov (United States)

    Liu, Na; Ma, Zhanfang

    2014-01-15

    In this work, an Au-ionic liquid functionalized reduced graphene oxide nanocomposite (IL-rGO-Au) was fabricated via the self-assembly of ionic liquid functionalized reduced graphene oxide (IL-rGO) and gold nanoparticles (AuNPs) by electrostatic interaction. The IL-rGO can be synthesized and stabilized by introducing the cations of the amine-terminated ionic liquids (IL-NH2) into the graphene oxide (GO). With the assistance of IL-NH2, AuNPs were uniformly and densely absorbed on the surfaces of the IL-rGO. The proposed IL-rGO-Au nanocomposite can be used as an immunosensing platform because it can not only facilitate the electrons transfer of the electrode surface but also provide a large accessible surface area for the immobilization of abundant antibody. To assess the performance of the IL-rGO-Au nanocomposite, a sandwich-type electrochemical immunosensor was designed for simultaneous multianalyte detection (carcinoembryonic antigen (CEA) and alpha-fetoprotein (AFP) as model analytes). The chitosan (CS) coated prussian blue nanoparticles (PBNPs) or cadmium hexacyanoferrate nanoparticles (CdNPs) and loaded with AuNPs were used as distinguishable signal tags. The resulting immunosensor exhibited high selectivity and sensitivity in simultaneous determination of CEA and AFP in a single run. The linear ranges were from 0.01 to 100 ng mL(-1) for both CEA and AFP. The detection limits reached 0.01 ng mL(-1) for CEA and 0.006 ng mL(-1) for AFP, respectively. No obvious nonspecific adsorption and cross-talk was observed during a series of analyses to detect target analytes. In addition, for the detection of clinical serum samples, it is well consistent with the data determined by the ELISA, indicating that the immunosensor provides a possible application for the simultaneous multianalyte determination of CEA and AFP in clinical diagnostics. PMID:23962704

  15. Fractal analytical approach of urban form based on spatial correlation function

    International Nuclear Information System (INIS)

    Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning

  16. Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    CERN Document Server

    Stefańska, Patrycja

    2016-01-01

    We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997)], we derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.

  17. On genus expansion of superpolynomials

    CERN Document Server

    Mironov, A; Sleptsov, A; Smirnov, A

    2013-01-01

    Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present letter we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis:the Casimir operators are beta-deformed to Hamiltonians of the Calogero-Moser-Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is rather straightforward only for the thin knots. Beyond this family additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpol...

  18. On genus expansion of superpolynomials

    OpenAIRE

    Mironov, Andrei; Morozov, Alexei; Sleptsov, Alexei; Smirnov, Andrey(ITEP, Moscow, 117218, Russia)

    2013-01-01

    Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present letter we claim that the superpolynomials are not functions of such a type: symmetric group characters do ...

  19. Critical Crossover Functions for Simple Fluids: Non-Analytical Scaling Determination of the Ising-Like Crossover Parameter

    Science.gov (United States)

    Garrabos, Yves; Lecoutre, Carole; Marre, Samuel; LeNeindre, Bernard

    2016-08-01

    A non-analytical scaling determination of the Ising-like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature. The mean crossover functions, estimated from the bounded results of the massive renormalization scheme in field theory applied to the ( Φ 2) d2( n) model in three dimensions (d=3) and scalar order parameter (n=1), are used to formulate the corresponding scaling equations valid in two well-defined temperature ranges from the critical temperature. The validity range and the Ising-like nature of the corresponding crossover description are discussed in terms of a single Ising-like scale factor characterizing the critical isochore. The asymptotic value of this scale factor can be predicted within the Ising-like preasymptotic domain. Unfortunately, the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible. A contrario, from our scaling equations and the use of precise measurements performed at finite distance from the critical point, its local value can be estimated beyond the Ising-like preasymptotic domain. This non-analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids. This latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor-liquid critical point of each fluid are known. Xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the Ising-like crossover parameter. With the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain, and the vapor-liquid coexisting densities in the

  20. Synthesis and analytical characterization of reactive functionalized ketenes and their application in host-guest chemistry

    International Nuclear Information System (INIS)

    .-butyl by O-CH3) was found, which led to a new stable α-oxoketene. The oxoketenes also only differ by one methoxygroup and were generated from their furandiones at about the same reaction conditions: Sublimed together, the α-oxoketenes were formed simultaneously already during FV-pyrolysis, guaranteeing a perfect mixture. By warming up, these oxoketenes dimerize slowly via [2+4] cycloaddition reaction in another unusual way, since one oxoketene adds onto the carbonyl double bond of the other oxoketene to afford a new dimer with ketene-functionality. Its structure was determined by several spectroscopic measurements, including IR, 2D-NMR and a x-ray analysis. Scope and limitations of the chemistry of this novel α -oxoketene is discussed in detail. (author)

  1. Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

    Czech Academy of Sciences Publication Activity Database

    Abbas, G.; Ananthanarayan, B.; Caprini, I.; Fischer, Jan

    2013-01-01

    Roč. 88, č. 3 (2013), "034026-1"-"034026-16". ISSN 1550-7998 Institutional support: RVO:68378271 Keywords : Borel transformation * asymptotic series * Adler function Subject RIV: BE - Theoretical Physics Impact factor: 4.864, year: 2013

  2. Exponential Expansion in Evolutionary Economics

    DEFF Research Database (Denmark)

    Frederiksen, Peter; Jagtfelt, Tue

    2013-01-01

    this problem is proposed in the form of a model of exponential expansion. The model outlines the overall structure and function of the economy as exponential expansion. The pictographic model describes four axiomatic concepts and their exponential nature. The interactive, directional, emerging and...

  3. The super Weierstrass ζ-function and operator product expansions in 2D-induced supergravity on the supertorus

    International Nuclear Information System (INIS)

    In order to solve the superBeltrami equations (SBE) on the supertorus, we construct the quasielliptic Weierstrass ζ-function as the δ-Cuachy kernel thereon. Using this solution we compute the stress-energy tensor, and Green functions corresponding to induced supergravity in Polyakov's path integral formalism. This allows us to recover the corresponding results on the supercomplex plane and the torus. Finally, we discuss generalizations to super Riemann surfaces of higher genus. (author). 16 refs

  4. Design and analysis of a multi-backend database system for performance improvement, functionality expansion and capacity growth. Part I

    OpenAIRE

    Hsiao, David K.; Menon, M. Jaishankar

    1983-01-01

    It is generally known that the use of a single general-purpose digital computer with dedicated software for database management as a backend to offload the mainframe host computer from database management tasks yields no appreciable gains in performance and functionality. Research is therefore being pursued to replace this software backend approach to database management with an architecture approach which will yield good performance and new functionality. The aim of the pro...

  5. Thermal expansion of mullite-type Bi2Al4O9: A study by X-ray diffraction, vibrational spectroscopy and density functional theory

    International Nuclear Information System (INIS)

    Polycrystalline Bi2Al4O9 powder samples were synthesized using the glycerine method. Single crystals were produced from the powder product in a Bi2O3 melt. The lattice thermal expansion of the mullite-type compound was studied using X-ray diffraction, Raman spectroscopy and density functional theory (DFT). The metric parameters were modeled using Grüneisen approximation for the zero pressure equation of state, where the temperature-dependent vibrational internal energy was calculated from the Debye characteristic frequency. Both the first-order and second-order Grüneisen approximations were applied for modeling the volumetric expansion, and the second-order approach provided physically meaningful axial parameters. The phonon density of states as well as phonon dispersion guided to set the characteristic frequency for simulation. The experimental infrared and Raman phonon bands were compared with those calculate from the DFT calculations. Selective Raman modes were analyzed for the thermal anharmonic behaviors using simplified Klemens model. The respective mode Grüneisen parameters were calculated from the pressure-dependent Raman spectra. - Graphical abstract: Crystal structure of mullite-type Bi2Al4O9 showing the edge-sharing AlO6 octahedra running parallel to the c-axis. - Highlights: • Thermal expansion of Bi2Al4O9 was studied using XRD, FTIR, Raman and DFT. • Metric parameters were modeled using Grüneisen approximation. • Phonon DOS and phonon dispersion helped to set the Debye frequency. • Mode Grüneisen parameters were calculated from the pressure-dependent Raman spectra. • Anharmonicity was analyzed for some selective Raman modes

  6. Analytical model for temperature distribution of an end diode-pumped laser slab with Robin boundary conditions by Green’s function method

    Science.gov (United States)

    Moghtader Dindarlu, M. H.; Kavosh Tehrani, M.; Saghafifar, H.; Maleki, A.

    2016-05-01

    In this paper, an analytical model is introduced for temperature distribution of an end diode-pumped laser slab by Green’s function method. To solve the heat equation, Robin boundary conditions are considered because four lateral faces of the slab are cooled by water. An analytical model is extracted for single and dual end-pumping configuration. For an example, the 2D and 3D temperature distributions are plotted and our analytical model is validated by numerical solution based on the finite element method (FEM). The results show that our model has very good agreement with numerical solution. Furthermore, dependence of the temperature distribution on absorbed pump power is shown.

  7. Gradient expansion for anisotropic hydrodynamics

    CERN Document Server

    Florkowski, Wojciech; Spaliński, Michał

    2016-01-01

    We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of non-hydrodynamic modes.

  8. Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models

    OpenAIRE

    Van der Hofstad, R.; Hara, T.; Slade, G

    2000-01-01

    We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on ${\\mathbb{Z}^d}$, having long finite-range connections, above their upper critical dimensions $d=4$ (self-avoiding walk), $d=6$ (percolation) and $d=8$ (trees and animals). The two-point functions for these models are respectively the generating function for self-avoiding walks from the origin to $x \\in {\\mathbb{Z}^d}$, the probability of a connection from 0 to x, and the generatin...

  9. Monkeypox Virus Infection of Rhesus Macaques Induces Massive Expansion of Natural Killer Cells but Suppresses Natural Killer Cell Functions

    OpenAIRE

    Song, Haifeng; Josleyn, Nicole; Janosko, Krisztina; Skinner, Jeff; Reeves, R. Keith; Cohen, Melanie; Jett, Catherine; Johnson, Reed; Blaney, Joseph E.; Bollinger, Laura; Jennings, Gerald; Jahrling, Peter B

    2013-01-01

    Natural killer (NK) cells play critical roles in innate immunity and in bridging innate and adaptive immune responses against viral infection. However, the response of NK cells to monkeypox virus (MPXV) infection is not well characterized. In this intravenous challenge study of MPXV infection in rhesus macaques (Macaca mulatta), we analyzed blood and lymph node NK cell changes in absolute cell numbers, cell proliferation, chemokine receptor expression, and cellular functions. Our results show...

  10. Expansion of Functions and Rights of Accountants of Agricultural Sector and Consolidation of the Rules of Professional Ethics and Conduct

    OpenAIRE

    Volodymyr Metelytsia

    2015-01-01

    The article describes the implementation measures of the Development strategy of the accounting profession in the agricultural sector as part of its functional and ethical direction. It grounds the necessity of legislative regulation of the rights of the chief accountant or the person holding the duty of business bookkeeping. It is proved the necessity of introducing the sole responsibility of the person who is entrusted with the task of the organization of accounting at the corporate level (...

  11. Expansions of $\\tau$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

    OpenAIRE

    Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel; Fischer, Jan

    2013-01-01

    The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling $\\alpha_s$ and other QCD parameters from the hadronic decays of the $\\tau$ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mapp...

  12. The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion

    International Nuclear Information System (INIS)

    The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z (α,β) takes a form where, besides trivial dependences, α and β only appear through a statistical factor Fk- = [1 + e-α+βεk0-βWk]-1. Wk is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z (α,β) under variations of Fk-. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author)

  13. Analytic expression of the chirped sampled function used to produce the equal chirp in the specific reflection channel in uniform period fiber Bragg gratings

    Institute of Scientific and Technical Information of China (English)

    LIU Yu-min; YU Zhong-yuan; YANG Hong-bo; ZHANG Na

    2005-01-01

    The general analytic expression of the chirped sampled function is derived based on coupled mode theory. This function can be used to describe how to use uniform period fiber Bragg grating to produce the equal chirp at will in the specific reflection channel. As an example,the exact sampled function expression that produces a linear chirped at the +4 channel is given. The simulation results by using the transfer-matrix show that the theory is correct.

  14. Analytic structure of QCD propagators in Minkowski space

    CERN Document Server

    Siringo, Fabio

    2016-01-01

    Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles.The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is equivalent to the standard perturbation theory in the UV. By dimensional regularization, all diverging mass terms cancel exactly without including mass counterterms that would spoil the gauge and chiral symmetry of the Lagrangian. Universal scaling properties are predicted for the inverse dressing functions and shown to be satisfied by the lattice data. Complex conjugated poles are found for the gluon propagator, in agre...

  15. Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-Function

    Directory of Open Access Journals (Sweden)

    Javier Cubas

    2014-06-01

    Full Text Available Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation..., it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage–I-V–curve at different levels of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer’s datasheet.

  16. Single functional magnetic-bead as universal biosensing platform for trace analyte detection using SERS-nanobioprobe.

    Science.gov (United States)

    Xiao, R; Wang, C W; Zhu, A N; Long, F

    2016-05-15

    SERS biosensor has demonstrated remarkable potential to analyze various bio/chemical targets with ultrahigh sensitivity. However, the development of universal SERS biosensing platforms with a uniform and reproducible structure that can quantitatively detect a broad range of trace analytes remains a significant challenge. The production of SERS nanotags with abundant Raman reporters and rational structure to conjugate with detection biomolecules is another key to design SERS-nanobioprobes. Here, we introduce a facile single magnetic-bead biosensing platform, formed by combining the captured antibodies/antigens conjugated magnetic-beads and the Au@Raman-Reporters@Ag sandwich-based nanorod tags labeled nanobioprobes. The advantage of the robust sandwich-structure-based nanotags is attributed not only to the high density Raman reporters contained inside, with high EF value because of enhanced electromagnetic field density, but also to the flexibility for bioconjugation of the detection biomolecules. The 3-D structure of the functional magnetic-bead provides a perfect platform to rapidly capture and enrich biomolecules. Ultrasensitive detection of two small molecules and a protein was achieved in samples, respectively. PMID:26765530

  17. ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS%泛函方程组的解析解

    Institute of Scientific and Technical Information of China (English)

    刘新和

    2003-01-01

    Let r be a given positive numberDenote by D=Dr the closed disc in the complexplane C whose center is the origin and radius is rFor any subset K of C and any integer m≥1,write A(Dm,K)= {f|f: Dm→K is a continuous map, and f| (Dm)° is analytic}For H∈A(Dm,C)(m≥2),f∈A(D,D)and z∈D,write ΨH(f)(z)=H(z,f(z),...,fm-1(z)).Suppose F,G∈A(D2n+1,C),and Hk,Kk∈A(Dk,C),k=2,...,n.In this paper,the system of functional equations F(z,f(z),f2(ΨH2(f)(z)),...,fn(ΨHn(f)(z)),g(z),g2(ΨK2(g)(z)),...,gn(ΨKn(g)(z))=0 G(z,f(z),f2(ΨH2(f)(z)),...,fn(ΨHn(f)(z)),g(z),g2(ΨK2(g)(z)),...,gn(ΨKn(g)(z))=0 (z∈D) is studied and some conditions for the system of equations to have a solution or a uniquesolution in A(D,D)×A(D,D) are given.

  18. Identification of Epoxide Functionalities in Protonated Monofunctional Analytes by Using Ion/Molecule Reactions and Collision-Activated Dissociation in Different Ion Trap Tandem Mass Spectrometers

    Science.gov (United States)

    Eismin, Ryan J.; Fu, Mingkun; Yem, Sonoeun; Widjaja, Fanny; Kenttämaa, Hilkka I.

    2012-01-01

    A mass spectrometric method has been delineated for the identification of the epoxide functionalities in unknown monofunctional analytes. This method utilizes gas-phase ion/molecule reactions of protonated analytes with neutral trimethyl borate (TMB) followed by collision-activated dissociation (CAD) in an ion trapping mass spectrometer (tested for a Fourier-transform ion cyclotron resonance and a linear quadrupole ion trap). The ion/molecule reaction involves proton transfer from the protonated analyte to TMB, followed by addition of the analyte to TMB and elimination of methanol. Based on literature, this reaction allows the general identification of oxygen-containing analytes. Vinyl and phenyl epoxides can be differentiated from other oxygen-containing analytes, including other epoxides, based on the loss of a second methanol molecule upon CAD of the addition/methanol elimination product. The only other analytes found to undergo this elimination are some amides but they also lose O = B-R (R = group bound to carbonyl), which allows their identification. On the other hand, other epoxides can be differentiated from vinyl and phenyl epoxides and from other monofunctional analytes based on the loss of (CH3O)2BOH or formation of protonated (CH3O)2BOH upon CAD of the addition/methanol elimination product. For propylene oxide and 2,3-dimethyloxirane, the (CH3O)2BOH fragment is more basic than the hydrocarbon fragment, and the diagnostic ion (CH3O)2BOH{2/+} is formed. These reactions involve opening of the epoxide ring. The only other analytes found to undergo (CH3O)2BOH elimination are carboxylic acids, but they can be differentiated from the rest based on several published ion/molecule reaction methods. Similar results were obtained in the Fourier-transform ion cyclotron resonance and linear quadrupole ion trap mass spectrometer.

  19. Completeness relations and resonant state expansions

    International Nuclear Information System (INIS)

    The completeness properties of the discrete set of bound states, virtual states, and resonant states characterizing the system of a single nonrelativistic particle moving in a central cutoff potential are investigated. We do not limit ourselves to the restricted form of completeness that can be obtained from Mittag-Leffler theory in this case. Instead we will make use of the information contained in the asymptotic behavior of the discrete states to get a new approach to the question of eventual overcompleteness. Using the theory of analytic functions we derive a number of completeness relations in terms of discrete states and complex continuum states and give some criteria for how to use them to form resonant state expansions of functions, matrix elements, and Green's functions. In cases where the integral contribution vanishes, the discrete part of the expansions is of the same form as that given by Mittag-Leffler theory but with regularized inner products. We also consider the possibility of using the discrete states as basis in a matrix representation

  20. Relatively light general anesthesia is more effective than fluid expansion in reducing the severity of epinephrine-induced hypotension during functional endoscopic sinus surgery

    Institute of Scientific and Technical Information of China (English)

    LI Wei-yan; ZHOU Zhi-qiang; JI Jun-feng; LI Ze-qing; YANG Jian-jun; SHANG Ruo-jing

    2007-01-01

    Background Epinephrine infiltration of the nasal mucosa causes hypotension during functional endoscopic sinus surgery (FESS) under general anesthesia. A prospective randomized-controlled study was designed to determine whether relatively light general anesthesia is superior to fluid expansion in reducing epinephrine-induced hypotension during FESS.Methods Ninety patients undergoing elective FESS under general anesthesia were randomly assigned to three groups with 30 patients in each. Each patient received local infiltration with adrenaline-containing (5 μg/ml) lidocaine (1%,4 ml) under different conditions. For Group Ⅰ, anesthesia was maintained with propofol 2 μg/ml and rimifentanil 2 ng/ml by TCI. Group Ⅱ (control group) and Group Ⅲ received propofol 4 μg/ml and rimifentanil 4 ng/ml, respectively. In Groups Ⅰ and Ⅱ, fluid expansion was performed with hetastarch 5 mi/kg within 20 minutes; hetastarch 10 ml/kg was used in Group Ⅲ. Mean arterial pressure (MAP) and heart rate (HR) were recorded at 30-second-intervals for 5 minutes after the beginning of local infiltration. Simultaneously, the lowest and the highest MAP were recorded to calculate the mean maximum increase or decrease percent in MAP for all patients in each group. Data analysis was performed by χ2 test,one-way analysis of variance, or one-way analysis of covariance.Results Hemodynamic changes, particularly a decrease in MAP accompanied by an increase in HR at 1.5 minutes(P<0.05), were observed in all groups. The mean maximum decrease in MAP below baseline was 14% in Group Ⅰ, 24% in Group Ⅲ and 26% in Group Ⅱ. There were statistically significant differences between Group Ⅰ and Groups Ⅱ and Ⅲ(P<0.05). The mean maximum increase in MAP above baseline was 9% in Group Ⅰ, 6% in Group Ⅲ and 2% in Group Ⅱ.Conclusion Relatively light general anesthesia can reduce the severity of epinephrine-induced hypotension more effectively than fluid expansion during FESS under general

  1. Affine transformations and analytic capacities

    OpenAIRE

    Dowling, Thomas; O'Farrell, Anthony G.

    1995-01-01

    Analytic capacities are set functions defined on the plane which may be used in the study of removable singularities, boundary smoothness and approximation of analytic functions belonging to some function space. The symmetric concrete Banach spaces form a class of function spaces that include most spaces usually studied. The Beurling transform is a certain singular integral operator that has proved useful in analytic function theory. It is shown that the analytic capacity associated to ...

  2. Analytical calculation of boozer magnetic coordinates for axisymmetric MHD equilibria

    International Nuclear Information System (INIS)

    A new analytical technique for extracting the Boozer magnetic coordinates in axisymmetric MHD equilibria is described. The method is based upon the correspondence between the expansion of the flux function in toroidal multipolar moments and the expansion in toroidal axisymmetric harmonics of the magnetic scalar potential χ0, which appears in the covariant representation B=∇χ0+β∇ψ-T of the magnetic field. An example of calculation of Boozer magnetic coordinates is given for an experimental highly shaped high β equilibrium of DIIID

  3. On the maximal terms of succesive Gelfond-Leont’ev-Salagen and Gelfond- Leont’ev-Ruscheweyh derivatives of a function analytic in the unit disc

    Directory of Open Access Journals (Sweden)

    M. M. Sheremeta

    2012-03-01

    Full Text Available For a function analytic in the unit disc the concepts of Gelfond-Leont'ev-Salagen and Gelfond-Leont'ev-Ruscheweyh derivatives of n-th order are introduced and the asymptotic behaviour of the maximal terms of their power development as n→+∞ is investigated.

  4. Three-loop QED photon vacuum polarization function: small Q2 limit

    International Nuclear Information System (INIS)

    The first three Taylor coefficients in small q2 expansion for QED photon polarization function were calculated analytically on three-loop level. The corresponding contribution to the four-loop muon anomalous magnetic moment was estimated

  5. 3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

    OpenAIRE

    António, Julieta; Tadeu, António

    2002-01-01

    This paper presents analytical solutions for computing the 3D displacements in a flat solid elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Greens functions in a boundary element method code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries.

  6. Selberg supertrace formula for super Riemann surfaces, analytic properties of Selberg super zeta-functions and multiloop contributions for the fermionic string

    Energy Technology Data Exchange (ETDEWEB)

    Grosche, C. (Hamburg Univ. (Germany, F.R.). 2. Inst. fuer Theoretische Physik)

    1990-11-01

    In this paper a complete derivation of the Selberg supertrace fomula for super Riemann surfaces and a discussion of the analytic properties of the Selberg super zeta-functions is presented. The Selberg supertrace formula is based on Laplace-Dirac operators square {sub m} of weight m on super Riemann surfaces. The trace formula for all m{epsilon}Z is derived and it is shown that one must discriminate between even and odd m. Particularly the term in the trace formula proportional to the identity transformation is sensititve to this discrimination. The analytic properties of the two Selberg super zeta-functions are discussed in detail, first with, and the second without consideration of the spin structure. As it is shown the Selberg super zeta-functions have a similar zero structure as the ordinary Selberg zeta-function. Also functional equations for the two Selberg super zeta-functions are derived. The results are applied to discuss the spectrum of the Laplace-Dirac operators and to calculate their determinants. For the spectrum it is found that the nontrivial Eigenvalues are the same for square{sub m} and square{sub 0} up to a constant depending on m, which is analogous to the bosonic case. The analytic properties of the determinants can be deduced from the analytic properties of the Selberg super zeta-functions, and it is shown that they are well-defined. Special cases (m=0, 2) for the determinants are important in the Polyakov approach for the fermionic string. With these results it is deduced that the fermionic string integrand of the Polyakov functional integral is well-defined. (orig.).

  7. Selberg supertrace formula for super Riemann surfaces, analytic properties of Selberg super zeta-functions and multiloop contributions for the fermionic string

    International Nuclear Information System (INIS)

    In this paper a complete derivation of the Selberg supertrace fomula for super Riemann surfaces and a discussion of the analytic properties of the Selberg super zeta-functions is presented. The Selberg supertrace formula is based on Laplace-Dirac operators □m of weight m on super Riemann surfaces. The trace formula for all mεZ is derived and it is shown that one must discriminate between even and odd m. Particularly the term in the trace formula proportional to the identity transformation is sensititve to this discrimination. The analytic properties of the two Selberg super zeta-functions are discussed in detail, first with, and the second without consideration of the spin structure. As it is shown the Selberg super zeta-functions have a similar zero structure as the ordinary Selberg zeta-function. Also functional equations for the two Selberg super zeta-functions are derived. The results are applied to discuss the spectrum of the Laplace-Dirac operators and to calculate their determinants. For the spectrum it is found that the nontrivial Eigenvalues are the same for □m and □0 up to a constant depending on m, which is analogous to the bosonic case. The analytic properties of the determinants can be deduced from the analytic properties of the Selberg super zeta-functions, and it is shown that they are well-defined. Special cases (m=0, 2) for the determinants are important in the Polyakov approach for the fermionic string. With these results it is deduced that the fermionic string integrand of the Polyakov functional integral is well-defined. (orig.)

  8. Argument Estimate of Analytic Functions Defined by Linear Operator%由算子定义的解析函数的辐角估计

    Institute of Scientific and Technical Information of China (English)

    陈建兰

    2011-01-01

    The paper defines the operator transformation by means of Hadamard product. It introduces a novel class of analytic functions in the open unit disk and studies the argument estimate of the new functions.%通过Hadamard卷积定义了算子变换,利用其得到了单位开圆内解析函数类的新子类并研究了新函数类的辐角估计性质.

  9. Gradually-varied open-channel flow profiles normalized by critical depth and analytically solved by using Gaussian hypergeometric functions

    Directory of Open Access Journals (Sweden)

    C. D. Jan

    2012-10-01

    Full Text Available The equation of one-dimensional gradually-varied flow (GVF in sustaining and non-sustaining open channels is normalized using the critical depth, hc, and then analytically solved by the direct integration method with the use of the Gaussian hypergeometric function (GHF. The GHF-based solution so obtained from the hc-based dimensionless GVF equation is more useful and versatile than its counterpart from the GVF equation normalized by the normal depth, hn, because the GHF-based solutions of the hc-based dimensionless GVF equation for the mild (M and adverse (A profiles can asymptotically reduce to the hc-based dimensionless horizontal (H profiles as hc/hn → 0. An in-depth analysis of the hc-based dimensionless profiles expressed in terms of the GHF for GVF in sustaining and adverse wide channels has been conducted to discuss the effects of hc/hn and the hydraulic exponent N on the profiles This paper has laid the foundation to compute at one sweep the hc-based dimensionless GVF profiles in a series of sustaining and adverse channels, which have horizontal slopes sandwiched in between them, by using the GHF-based solutions.

  10. The toroidal block and the genus expansion

    Science.gov (United States)

    Kashani-Poor, Amir-Kian; Troost, Jan

    2013-03-01

    We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of {N}={2^{*}} gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via geometric engineering from the topological string. This point of view uncovers modular properties of the one-point conformal block on a torus with complexified intermediate momenta: in the large intermediate weight limit, it is a power series whose coefficients are quasimodular forms. The all-genus viewpoint that the conformal field theory approach lends to the topological string yields insight into the analytic structure of the topological string partition function in the field theory limit.

  11. 基于中弧线-厚度函数的翼型形状解析构造法%Analytic expression method of airfoil profile shape based on a mean camber and thickness function

    Institute of Scientific and Technical Information of China (English)

    姜海波; 赵云鹏

    2013-01-01

    复杂翼型几何形状的解析表达对叶片的优化设计有重要的意义,文章研究了用解析函数构造复杂翼型形状的方法.通过对儒科夫斯基翼型函数的简化,得到用中弧线-厚度函数表示翼型型线的解析表达式,对式中的相关系数和指数进行重新定义和变换,构造出包括儒科夫斯基翼型的一般翼型型线的解析表达式;通过进一步分离上、下型线并进行重新组合的方法可构造出更复杂翼型的形状;再通过增加一个独立的厚度函数项的方法,可构造出具有光滑尾缘形状的翼型.研究表明,复杂翼型的几何形状可通过有限个参数的解析函数表达,这些参数不仅具有明确的几何意义,而且使用方便,便于调整翼型的局部形状.文中给出了用翼型、弦长和扭角函数构造风力机叶片解析函数的应用示例.%It is important that the geometric shape of a complex airfoil contour be expressed by an analytic formula, In this paper, the method to construct airfoil contour by analytic functions is discussed. Joukowsky airfoil contour function is simplified to a straightforward expression with mean camber function and thickness function. Many airfoil contours can be constructed by redefining and transforming the coefficients and indexes in the expansion, and more complex airfoil contours can be obtained through separating and resetting the upper and lower contours. Also, the contour function of any airfoil with smooth trailing edge is obtained by adding an independent thickness function. It is shown that a complex airfoil contour can be expressed by an analytic function with limited parameters which have clear geometric meaning, and can be used to adjust the local shape easily. As an example of application, the paper also gives a method to construct analytic function of blade with an airfoil contour, a chord and a twist functions.

  12. A transition from a decelerated to an accelerated phase of the universe expansion from the simplest non-trivial polynomial function of T in the f(R,T) formalism

    CERN Document Server

    Moraes, P H R S; Correa, R A C

    2016-01-01

    In this work we present cosmological solutions from the simplest non-trivial $T$-dependence in $f(R,T)$ theory of gravity, with $R$ and $T$ standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Although such an approach yields a highly non-linear differential equation for the scale factor, we show that it is possible to obtain analytical solutions for the cosmological parameters. For some values of the free parameters, the model is able to predict a transition from a decelerated to an accelerated expansion of the universe.

  13. Accuracy of numerical functional transforms applied to derive Molière series terms and comparison with analytical results

    Science.gov (United States)

    Takahashi, N.; Okei, K.; Nakatsuka, T.

    Accuracies of numerical Fourier and Hankel transforms are examined with the Takahasi-Mori theory of error evaluation. The higher Moliere terms both for spatial and projected distributions derived by these methods agree very well with those derived analytically. The methods will be valuable to solve other transport problems concerning fast charged particles.

  14. Intermediate algebra & analytic geometry

    CERN Document Server

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

  15. Ultracold neutral plasma expansion in two dimensions

    CERN Document Server

    Cummings, E A; Durfee, D S; Bergeson, S D

    2005-01-01

    We extend an isothermal thermal model of ultracold neutral plasma expansion to systems without spherical symmetry, and use this model to interpret new fluorescence measurements on these plasmas. By assuming a self-similar expansion, it is possible to solve the fluid equations analytically and to include velocity effects to predict the fluorescence signals. In spite of the simplicity of this approach, the model reproduces the major features of the experimental data.

  16. Asymptotic Expansions of the Probability Density Function and the Distribution Function of Chi-Square Distribution%卡方分布密度函数与分布函数的渐近展开

    Institute of Scientific and Technical Information of China (English)

    陈刚; 王梦婕

    2014-01-01

    通过对χ2分布概率密度函数的自变量进行标准化变换,将其展开成如下形式:2nχ2( x;n)=1+r1(t)n +r2(t)n +r3(t)n n +r4(t)n2éëùûφ(t)+o 1n2(),其中n为自由度,φ(t)为标准正态分布的密度函数,ri(t)(1≤i≤4)均为关于t的多项式。从该展开式得到χ2分布密度函数的一个近似计算公式。进一步建立φ( t)的幂系数积分递推关系,得到χ2分布函数的渐近展开式。最后通过数值计算验证了这些结果在实际应用中的有效性。%Through the transformation of the independent variable of χ2 distribution probability density function,degree of freedom of which is n,the equation can be expanded as follows: 2nχ2(x;n)=f(t;n)= 1+r1(t)n +r2(t)n +r3(t)n n +r4(t)n2éë ùûφ(t)+o 1n2( ) ,here,φ(t) is a density function of standard normal distribution;ri(t) is a 3i order polynomial of t(1≤i≤4). An approximate formula can be obtained from the expansion of the distribution density function. We further establish the integral recurrence relations of the power coefficients of the standard normal density function and obtain the asymptotic expansion of the distribution function ofχ2 . Finally,the effectiveness of these results in practical application was verified by the numerical calculations.

  17. Vibronic interactions proceeding from combined analytical and numerical considerations: Covalent functionalization of graphene by benzene, distortions, electronic transitions

    Science.gov (United States)

    Krasnenko, V.; Boltrushko, V.; Hizhnyakov, V.

    2016-04-01

    Chemically bound states of benzene molecules with graphene are studied both analytically and numerically. The states are formed by switching off intrabonds of π-electrons in C6 rings to interbonds. A number of different undistorted and distorted structures are established both with aligned and with transversal mutual orientation of benzene and graphene. The vibronic interactions causing distortions of bound states are found, by using a combination of analytical and numerical considerations. This allows one to determine all electronic transitions of π-electrons without explicit numerical calculations of excited states, to find the conical intersections of potentials, and to show that the mechanism of distortions is the pseudo-Jahn-Teller effect. It is found that the aligned distorted benzene molecule placed between two graphene sheets makes a chemical bond with both of them, which may be used for fastening of graphene sheets together.

  18. QCD analytic perturbation theory. From integer powers to any power of the running coupling

    International Nuclear Information System (INIS)

    A new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes is proposed. We construct non-power series expansions for the analytic images of the running coupling and its powers for any fractional (real) power and complete the linear space of these solutions by constructing the index derivative. Using the Laplace transformation in conjunction with dispersion relations, we are able to derive at the one-loop order closed-form expressions for the analytic images in terms of the Lerch function. At the two-loop order we provide approximate analytic images of products of powers of the running coupling and logarithms - typical in higher-order perturbative calculations and when including evolution effects. Moreover, we supply explicit expressions for the two-loop analytic coupling and the analytic images of its powers in terms of one-loop quantities that can strongly simplify two-loop calculations. It is also shown how to resum powers of the running coupling while maintaining analyticity, a procedure that captures the generic features of Sudakov resummation. The algorithmic rules to obtain analytic coupling expressions within the proposed Fractional Analytic Perturbation Theory from the standard QCD power-series expansion are supplied ready for phenomenological applications and numerical comparisons are given for illustration

  19. Thermal Expansion of Polyurethane Foam

    Science.gov (United States)

    Lerch, Bradley A.; Sullivan, Roy M.

    2006-01-01

    expansion tests and the response of the microstructure. A novel optical method is described which is appropriate for measuring thermal expansion at high temperatures without influencing the thermal expansion measurement. Detailed microstructural investigations will also be described which show cell expansion as a function of temperature. Finally, a phenomenological model on thermal expansion will be described.

  20. On genus expansion of superpolynomials

    Energy Technology Data Exchange (ETDEWEB)

    Mironov, Andrei, E-mail: mironov@itep.ru [Lebedev Physics Institute, Moscow 119991 (Russian Federation); ITEP, Moscow 117218 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Morozov, Alexei, E-mail: morozov@itep.ru [ITEP, Moscow 117218 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Sleptsov, Alexei, E-mail: sleptsov@itep.ru [ITEP, Moscow 117218 (Russian Federation); Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk 454001 (Russian Federation); KdVI, University of Amsterdam (Netherlands); Smirnov, Andrey, E-mail: asmirnov@math.columbia.edu [ITEP, Moscow 117218 (Russian Federation); Columbia University, Department of Mathematics, New York (United States)

    2014-12-15

    Recently it was shown that the (Ooguri–Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present paper we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are β-deformed to Hamiltonians of the Calogero–Moser–Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials. However, even for the thin knots the beta-deformation is non-innocent: already in the simplest examples it seems inconsistent with the positivity of colored superpolynomials in non-(anti)symmetric representations, which also happens in I. Cherednik's (DAHA-based) approach to the torus knots.

  1. On genus expansion of superpolynomials

    International Nuclear Information System (INIS)

    Recently it was shown that the (Ooguri–Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present paper we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are β-deformed to Hamiltonians of the Calogero–Moser–Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials. However, even for the thin knots the beta-deformation is non-innocent: already in the simplest examples it seems inconsistent with the positivity of colored superpolynomials in non-(anti)symmetric representations, which also happens in I. Cherednik's (DAHA-based) approach to the torus knots

  2. Thermal expansion in the garnet-type solid electrolyte (Li7−xAlx/3)La3Zr2O12 as a function of Al content

    International Nuclear Information System (INIS)

    Highlights: • Thermal expansion (TE) coefficients of LLZ found up to 700°. • The aluminum content of LLZ has a small impact on the thermal expansion. • Typical thermal expansion values were around, 16 × 10−6 K−1. • The TE is approximately double other garnet-type structures. - Abstract: The thermal expansion (TE) coefficients of the lithium-stable lithium-ion conducting garnet lithium lanthanum zirconium oxide (LLZ) and the effect of aluminum substitution were measured from room temperature up to 700 °C by a synchrotron-based X-ray diffraction. The typical TE value measured for the most reported composition (LLZ doped with 0.3 wt.% or 0.093 mol% aluminum) was 15.498 × 10−6 K−1, which is approximately twice the value reported for other garnet-type structures. As the Al(III) concentration has been observed to strongly affect the structure observed and the ionic conductivity, we also assessed its role on thermal expansion and noted only a small variation with increasing dopant concentration. The materials implications for using LLZ in a solid state battery are discussed

  3. An Expansion of the Free Energy of Anharmonic Oscillator Based on the Variational Result

    CERN Document Server

    Lu, W F; Bak, J; Kim, C K; Nahm, K; Lu, Wen-Fa; You, Sang Koo; Bak, Jino; Kim, Chul Koo; Nahm, Kyun

    2002-01-01

    Based on the variational result, we performed a Taylor series expansion of the free energy of an anharmonic oscillator within the functional integral formalism. The variationally extremized condition makes Cactus Feynman diagrams disappear from any higher-order diagrams, and accordingly Feynman diagrams are simplified. We obtained the analytical expression of the free energy up to the fourth order, and compared our results with exact, accurate and variational results.

  4. Investigation of analytical potential energy function, harmonic frequency and vibrational levels for the X2∑+ and A2∏ states of CN radical

    Institute of Scientific and Technical Information of China (English)

    Wang Jian-Kun; Wu Zhen-Sen

    2008-01-01

    This paper calculates the equilibrium structure and the potential energy functions of the ground state (X2∑+) and the low lying excited electronic state (A2∏) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency (ωe) and other spectroscopic constants (ωeχe, βe and αe) are calculated by employing the Rydberg-Klein-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional Schrodinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

  5. Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B1П of 7LiH

    Institute of Scientific and Technical Information of China (English)

    Shi De-Heng; Liu Yu-Fang; Sun Jin-Feng; Zhu Zun-Lùe; Yang Xiang-Dong

    2006-01-01

    The reasonable dissociation limit of the second excited singlet state B1П of 7LiH molecule is obtained. The obtained over the internuclear distance ranging from about 0.10 nm to 0.54 nm, and has a least-square fit to the analytic compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition.comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more theories.

  6. Long-Range Monthly Discharge Forecast Method Based on Empirical Orthogonal Function Repeatedly Analytic Method%基于EOF迭代的月径流长期预报

    Institute of Scientific and Technical Information of China (English)

    李杰友; 熊学农; 刘秀玉

    2001-01-01

    应用经验正交函数分析方法,以月平均500hPa,100hPa高度场及月平均海温场为预报因子,对广东省氵翁江流域的月径流进行预报.结果表明,基于EOF迭代的预报方法是一种有效的月径流长期预报新方法,具有明显的应用价值.%Based on the empirical orthogonal function analytical method,500hPa,100hPa and the North Pacific sea surface temperature are used as forecast factors and quantitative model of monthly discharge is established.The forecast results illustrate that the empirical orthogonal fuction repeatedly analytic method is a right way for long range monthly discharge forecast and is of practical value.

  7. Task Analytic Models to Guide Analysis and Design: Use of the Operator Function Model to Represent Pilot-Autoflight System Mode Problems

    Science.gov (United States)

    Degani, Asaf; Mitchell, Christine M.; Chappell, Alan R.; Shafto, Mike (Technical Monitor)

    1995-01-01

    Task-analytic models structure essential information about operator interaction with complex systems, in this case pilot interaction with the autoflight system. Such models serve two purposes: (1) they allow researchers and practitioners to understand pilots' actions; and (2) they provide a compact, computational representation needed to design 'intelligent' aids, e.g., displays, assistants, and training systems. This paper demonstrates the use of the operator function model to trace the process of mode engagements while a pilot is controlling an aircraft via the, autoflight system. The operator function model is a normative and nondeterministic model of how a well-trained, well-motivated operator manages multiple concurrent activities for effective real-time control. For each function, the model links the pilot's actions with the required information. Using the operator function model, this paper describes several mode engagement scenarios. These scenarios were observed and documented during a field study that focused on mode engagements and mode transitions during normal line operations. Data including time, ATC clearances, altitude, system states, and active modes and sub-modes, engagement of modes, were recorded during sixty-six flights. Using these data, seven prototypical mode engagement scenarios were extracted. One scenario details the decision of the crew to disengage a fully automatic mode in favor of a semi-automatic mode, and the consequences of this action. Another describes a mode error involving updating aircraft speed following the engagement of a speed submode. Other scenarios detail mode confusion at various phases of the flight. This analysis uses the operator function model to identify three aspects of mode engagement: (1) the progress of pilot-aircraft-autoflight system interaction; (2) control/display information required to perform mode management activities; and (3) the potential cause(s) of mode confusion. The goal of this paper is twofold

  8. GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

    Institute of Scientific and Technical Information of China (English)

    陈泽乾

    2002-01-01

    A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators (e)t and its dual, creation operators (e)*t.

  9. Calculation of integrals for the LCAO MO method in a basis of hydrogen functions

    International Nuclear Information System (INIS)

    The authors give an algorithm for the analytical calculation of multicenter quantum chemical integrals in a basis of hydrogenic AO's. A characteristic feature of the algorithm involves expansion of two-center distributions with respect to one-center functions, which leads to a more compact expression for the multicenter integral than does the use of an expansion of AO's relative to another center. They obtain recurrence relations for the expansion coefficients

  10. Analytical potential energy function for the ground state(1A1) of hydrogen isotopic D2O molecule

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The present work is to construct the potential energy function of isotopic molecules. The so-called molecular potential energy function is the electronic energy function under Born-Oppenheimer approximation,in which the nuclear motions(translational,rotational and vibration motions) are not included,therefore,its nuclear vibration motion and isotopic effect need to be considered. Based on group theory and atomic and molecular reactive statics(AMRS),the reasonable dissociation limits of D2O(1A1)are determined,its equilibrium geometry and dissociation energy are calculated by density-functional theory(DFT) B3lyp,and then,using the many-body expansion method the potential energy function of D2O(1A1) is obtained for the first time. The potential contours are drawn,in which it is found that the reactive channel D + OD→D2O has no threshold energy,so it is a free radical reaction. But the reactive channel O + DD→D2O has a saddle point. The study of collision for D2O(1A1) is under way.

  11. Analytical potential energy function for the ground state (~X1A1) of hydrogen isotopic D2O molecule

    Institute of Scientific and Technical Information of China (English)

    RUAN Wen; LUO WenLang; ZHANG Li; ZHU ZhengHe

    2009-01-01

    The present work is to construct the potential energy function of Isotopic molecules. The so-called molecular potential energy function is the electronic energy function under Born-Oppenheimer ap-proximation, in which the nuclear motions (translational, rotational and vibration motions) are not in-cluded, therefore, its nuclear vibration motion and isotopic effect need to be considered. Based on group theory and atomic and molecular reactive statics (AMRS), the reasonable dissociation limits of D2O(~X1A1) are determined, its equilibrium geometry and dissociation energy are calculated by den-sity-functional theory (DFT) B3lyp, and then, using the many-body expansion method the potential en-ergy function of D2O (~X1A1) Is obtained for the first time. The potential contours are drawn, in which It is found that the reactive channel D + OD→D2O has no threshold energy, so it is a free radical reaction. But the reactive channel O + DD→D2P has a saddle point. The study of collision for D2O (~X1A1) is under way.

  12. Local cubic vertex functions for three massless higher even spin fields on spaces AdSD: An analytic approach

    International Nuclear Information System (INIS)

    Local cubic vertex functions of three higher even spin fields on AdSD are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV divergence as the residue of the highest order pole in the dimensional regularization parameter ϵ. In fact N-point Green functions of such conserved currents produce a series of poles up to the order N−1. The method works for even D and maintains covariance at any step. The resulting formula is quite concise

  13. Whole-brain analytic measures of network communication reveal increased structure-function correlation in right temporal lobe epilepsy

    Directory of Open Access Journals (Sweden)

    Jonathan Wirsich

    2016-01-01

    In rTLE patients, we found a widespread hypercorrelated functional network. Network communication analysis revealed greater unspecific branching of the shortest path (search information in the structural connectome and a higher global correlation between the structural and functional connectivity for the patient group. We also found evidence for a preserved structural rich-club in the patient group. In sum, global augmentation of structure-function correlation might be linked to a smaller functional repertoire in rTLE patients, while sparing the central core of the brain which may represent a pathway that facilitates the spread of seizures.

  14. Analytical solution for Klein-Gordon equation and action function of the solution for Dirac equation in counter-propagating laser waves

    CERN Document Server

    Hu, Huayu

    2015-01-01

    Nonperturbative calculation of QED processes participated by a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the usage of analytical solutions of the particle dynamical equation, such as the Klein-Gordon equation and Dirac equation. However only for limited field configurations such as a plane-wave field could the equations be solved analytically. Studies have shown significant interests in QED processes in a strong field composed of two counter-propagating laser waves, but the exact solutions in such a field is out of reach. In this paper, inspired by the observation of the structure of the solutions in a plane-wave field, we develop a new method and obtain the analytical solution for the Klein-Gordon equation and equivalently the action function of the solution for the Dirac equation in this field, under a largest dynamical parameter condition that there exists an inertial frame in which the particl...

  15. Analytic Evaluation of Three Different Five-Electron Atomic Integrals Involving Exponentially Correlated Functions of $r_{ij}$ With $r_{ij}$'s Not Forming A Closed Loop

    CERN Document Server

    Padhy, B

    2016-01-01

    The simple method outlined in our earlier paper [B.Padhy, Orissa Journal of Physics, vol.19, No.1, p.1, February 2012] has been utilized here for analytic evaluation of three different five-electron atomic integrals with integrands involving products of s Slater-type orbitals and exponentially correlated functions of the form $r_{ij} exp(-\\lambda_{ij} r_{ij})$. Only products of those $r_{ij}$'s which do not form a closed loop by themselves, are considered.

  16. Application of the (G'/G)-expansion method to nonlinear blood flow in large vessels

    International Nuclear Information System (INIS)

    As is widely known today, Navier-Stokes equations are used to describe blood flow in large vessels. In the past several decades, and even in very recent works, these equations have been reduced to Korteweg-de Vries (KdV), modified KdV or Boussinesq equations. In this paper, we avoid such simplifications and investigate the analytical traveling wave solutions of the one-dimensional generic Navier-Stokes equations, through the (G ' /G)-expansion method. These traveling wave solutions include hyperbolic functions, trigonometric functions and rational functions. Since some of them are not yet explored in the study of blood flow, we pay attention to hyperbolic function solutions and we show that the (G ' /G)-expansion method presents a wider applicability that allows us to bring out the widely known blood flow behaviors. The biological implications of the found solutions are discussed accordingly.

  17. Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function

    OpenAIRE

    Ghosh, Uttam; Sengupta, Srijan; Sarkar, Susmita; Das, Shantanu

    2015-01-01

    There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays...

  18. Virial expansion coefficients in the harmonic approximation

    DEFF Research Database (Denmark)

    R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.;

    2012-01-01

    The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to...

  19. A New Analytical Expression for the Relationship Between the Charpy Impact Energy and Notch Tip Position for Functionally Graded Steels

    Institute of Scientific and Technical Information of China (English)

    H.Samareh Salavati Pour; F.Berto; Y.Alizadeh

    2013-01-01

    The effect of the distance between the notch tip and the position of the middle phase in the FGSs on the Charpy impact energy is investigated in the present paper.The results show that when the notch apex is close to the middle layer,the Charpy impact energy reaches its maximum value.This is due to the increment of the absorbed energy by plastic deformation ahead of the notch tip.On the other hand,when the notch tip is far from the middle layer,the Charpy impact energy strongly decreases.Another fundamental motivation of the present work is that for crack arrester configuration,no accurate mathematical or analytical modelling is available up to now.By considering the relationship between the Charpy impact energy and the plastic volume size,a new theoretical model has been developed to link the Charpy impact energy with the distance from the notch apex to the middle phase.This model is a simplified one and the effect of different shapes of the layers and the effect of microstructure on the mechanical properties and plastic region size will be considered in further investigation.The results of the new developed closed form expression show a sound agreement with some recent experimental results taken from the literature.

  20. ON CONVERGENCE OF WAVELET PACKET EXPANSIONS

    Institute of Scientific and Technical Information of China (English)

    Morten Nielsen

    2002-01-01

    It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 <q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1<p<∞, converges in norm and pointwise almost everywhere.