scholarly journals A Higher Order Painlevé System in Two Variables and Extensions of the Appell Hypergeometric Functions F1, F2 and F3

2018 ◽  
Vol 61 (1) ◽  
pp. 81-107
Author(s):  
Takao Suzuki
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order

scholarly journals TRANSCENDENCE OF SPECIAL VALUES OF POCHHAMMER FUNCTIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 667-677
Author(s):  
MARVIN D. TRETKOFF ◽  
PAULA TRETKOFF
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Algebraic Numbers ◽  
Special Values

In this paper, we examine the set of algebraic numbers at which higher order hypergeometric functions take algebraic values. In particular, we deduce criteria for this set to be finite and for it to be infinite.

scholarly journals The higher-order matching polynomial of a graph

2005 ◽  
Vol 2005 (10) ◽  
pp. 1565-1576 ◽  
Author(s):  
Oswaldo Araujo ◽  
Mario Estrada ◽  
Daniel A. Morales ◽  
Juan Rada
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Disjoint Paths ◽  
Hosoya Index ◽  
Matching Polynomial ◽  
Similarities And Differences

Given a graphGwithnvertices, letp(G,j)denote the number of waysjmutually nonincident edges can be selected inG. The polynomialM(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial ofG, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of disjoint paths of lengtht, denoted bypt(G,j). We compare this higher-order matching polynomial with the usual one, establishing similarities and differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found.

scholarly journals Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions

2020 ◽  
Author(s):  
Feng Qi ◽  
Chuan-Jun Huang
Keyword(s):  
Hypergeometric Function ◽  
General Formula ◽  
Differentiable Function ◽  
Inversion Formula ◽  
Hypergeometric Functions ◽  
Beta Function ◽  
Higher Order ◽  
Gauss Hypergeometric Function ◽  
Partial Derivatives ◽  
Real Academia

In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. This preprint has been formally published as "Feng Qi and Chuan-Jun Huang, Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas, Vol. 114, Paper No. 191, 9 pages (2020); available online at https://doi.org/10.1007/s13398-020-00927-y."

scholarly journals Riccati Generalized Resonant States of Higher-order Nonlinear Schrӧdinger Equation With Pӧschl-teller Potential

2021 ◽  
Author(s):  
Nisha Kadian ◽  
Sanjana Bhatia ◽  
Shailza Pathania ◽  
Amit Goyal ◽  
Nagaraja Kumar Choragudi
Keyword(s):  
Hypergeometric Functions ◽  
Resonant State ◽  
Higher Order ◽  
Hamiltonian Approach ◽  
Localized Solutions ◽  
Resonant States

Abstract We present resonant state solutions of the higher-order nonlinear Schrӧdinger model, with Pӧschl-Teller (PT) potential, under certain parametric conditions. It is found that the localized solutions can be expressed in terms of the hypergeometric functions F(a, b, c; z). The dynamics of these resonant states and their control using isospectral Hamiltonian approach is well illustrated for PT potential, which is analytically tractable.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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