scholarly journals New closed-form thermoelastostatic Green function and Poisson-type integral formula for a quarter-plane

2011 ◽  
Vol 53 (1-2) ◽  
pp. 347-358 ◽  
Author(s):  
Victor Şeremet ◽  
Guy Bonnet
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Integral Formula ◽  
Quarter Plane ◽  
Type Integral ◽  
Poisson Type

scholarly journals BAKER–AKHIEZER FUNCTION AS ITERATED RESIDUE AND SELBERG-TYPE INTEGRAL

2009 ◽  
Vol 51 (A) ◽  
pp. 59-73 ◽  
Author(s):  
GIOVANNI FELDER ◽  
ALEXANDER P. VESELOV
Keyword(s):  
Root System ◽  
Integral Formula ◽  
Explicit Evaluation ◽  
Type Integral

AbstractA simple integral formula as an iterated residue is presented for the Baker–Akhiezer function related toAn-type root system in both the rational and trigonometric cases. We present also a formula for the Baker–Akhiezer function as a Selberg-type integral and generalise it to the deformedAn,1-case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integrals.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Incomplete Bessel and Struve functions

1956 ◽  
Vol 52 (3) ◽  
pp. 431-441 ◽  
Author(s):  
W. H. Steel ◽  
Joan Y. Ward
Keyword(s):  
Type Integral ◽  
Struve Functions ◽  
Poisson Type

ABSTRACTSome properties are given of the incomplete Bessel and Struve functions defined by a Poisson-type integral. These functions are tabulated for the orders 0 and 1.

scholarly journals On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces

2019 ◽  
Vol 27 (6) ◽  
pp. 815-834
Author(s):  
Yulia Shefer ◽  
Alexander Shlapunov
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Integral Formula ◽  
Weighted Sobolev Spaces ◽  
Elliptic Systems ◽  
Fundamental Solutions ◽  
Type Integral ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Neumann Type

AbstractWe consider the ill-posed Cauchy problem in a bounded domain{\mathcal{D}}of{\mathbb{R}^{n}}for an elliptic differential operator{\mathcal{A}(x,\partial)}with data on a relatively open subsetSof the boundary{\partial\mathcal{D}}. We do it in weighted Sobolev spaces{H^{s,\gamma}(\mathcal{D})}containing the elements with prescribed smoothness{s\in\mathbb{N}}and growth near{\partial S}in{\mathcal{D}}, controlled by a real number γ. More precisely, using proper (left) fundamental solutions of{\mathcal{A}(x,\partial)}, we obtain a Green-type integral formula for functions from{H^{s,\gamma}(\mathcal{D})}. Then a Neumann-type series, constructed with the use of iterations of the (bounded) integral operators applied to the data, gives a solution to the Cauchy problem in{H^{s,\gamma}(\mathcal{D})}whenever this solution exists.

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