Explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs

1998 ◽  
pp. 105-110 ◽  
Author(s):  
Mitchell Rothstein
Keyword(s):  
Explicit Formulas

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

On a generalization of the Rényi–Srivastava characterization of the Poisson law

2021 ◽  
Vol 58 (1) ◽  
pp. 68-82
Author(s):  
Jean-Renaud Pycke
Keyword(s):  
Life Insurance ◽  
Collective Model ◽  
New Method ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Compound Distributions ◽  
Poisson Law ◽  
Pierre Loti

AbstractWe give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

On the Number of Representations of Integers by Quadratic Forms in Twelve Variables

1998 ◽  
Vol 5 (6) ◽  
pp. 545-564
Author(s):  
G. Lomadze
Keyword(s):  
Quadratic Forms ◽  
Explicit Formulas ◽  
Representations Of Integers ◽  
Positive Integers

Abstract A way of finding exact explicit formulas for the number of representations of positive integers by quadratic forms in 12 variables with integral coefficients is suggested.

scholarly journals Computation of several Hessenberg determinants

2020 ◽  
Vol 70 (6) ◽  
pp. 1521-1537
Author(s):  
Feng Qi ◽  
Omran Kouba ◽  
Issam Kaddoura
Keyword(s):  
Linear Algebra ◽  
Simple Formula ◽  
Binomial Coefficients ◽  
Explicit Formulas ◽  
Methods And Techniques

AbstractIn the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternatively and simply recover some known results.

scholarly journals DETERMINING EQUATIONS FOR HIGHER-ORDER DECOMPOSITIONS OF EXPONENTIAL OPERATORS

1995 ◽  
Vol 09 (25) ◽  
pp. 3241-3268 ◽  
Author(s):  
ZENGO TSUBOI ◽  
MASUO SUZUKI
Keyword(s):  
General Scheme ◽  
Higher Order ◽  
Explicit Formulas ◽  
Decomposition Theory ◽  
Lyndon Words

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.

scholarly journals The Chowla–Selberg formula for abelian CM fields and Faltings heights

2015 ◽  
Vol 152 (3) ◽  
pp. 445-476 ◽  
Author(s):  
Adrian Barquero-Sanchez ◽  
Riad Masri
Keyword(s):  
Gamma Function ◽  
Abelian Varieties ◽  
Modular Function ◽  
Rational Numbers ◽  
Explicit Formulas ◽  
Arithmetic Properties ◽  
Hilbert Modular ◽  
Cm Points ◽  
Analogous Function

In this paper we establish a Chowla–Selberg formula for abelian CM fields. This is an identity which relates values of a Hilbert modular function at CM points to values of Euler’s gamma function ${\rm\Gamma}$ and an analogous function ${\rm\Gamma}_{2}$ at rational numbers. We combine this identity with work of Colmez to relate the CM values of the Hilbert modular function to Faltings heights of CM abelian varieties. We also give explicit formulas for products of exponentials of Faltings heights, allowing us to study some of their arithmetic properties using the Lang–Rohrlich conjecture.

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (2) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

New explicit formulas for the effective piezoelectric coefficients of binary 0-3 composites

2006 ◽  
Vol 16 (4) ◽  
pp. 283-288 ◽  
Author(s):  
C. H. Ho ◽  
Y. M. Poon ◽  
F. G. Shin
Keyword(s):  
Explicit Formulas
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