scholarly journals Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

2021 ◽  
Vol 10 (02) ◽  
pp. 81-90
Author(s):  
Nurgul Bedelova ◽  
Avyt Asanov ◽  
Zhypar Orozmamatova ◽  
Zhypargul Abdullaeva
Keyword(s):  
Integral Equation ◽  
Stieltjes Integral ◽  
The Third

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

scholarly journals Existence of Solutions for Functional Integral Equation Involving the Henstock-Kurzweil-Stieltjes Integral

2017 ◽  
Vol 9 (5) ◽  
pp. 46
Author(s):  
Hui Mei ◽  
Guoju Ye ◽  
Wei Liu ◽  
Yanrong Chen
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Stieltjes Integral

In this paper, we apply the method associated with the technique of measure of noncompactness and some generalizations of Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile, an example is provided to illustrate our results.

Some Useful Approximations for the Availability Function

2015 ◽  
Vol 22 (02) ◽  
pp. 1550008 ◽  
Author(s):  
Viswanathan Arunachalam ◽  
Alvaro Calvache ◽  
Ayşe Tansu
Keyword(s):  
Communication Network ◽  
Integral Equation ◽  
Analytical Solution ◽  
Reliability Analysis ◽  
Test Cases ◽  
Channel Access ◽  
The Third ◽  
Access Scheme ◽  
Opportunistic Channel Access ◽  
Functional Forms

Availability function which forms an important part of reliability analysis is expressed in terms of an integral equation. The analytical solution of such an equation is possible only in very simple cases and hence approximations are the only tools available; very few such approximations are available in the literature. This paper proposes three useful approximations, two of which are based only on the first few moments of the underlying distributions and do not require their functional forms. The third approximation uses the Riemannian sum to approximate the integral equation. Numerical illustrations based on test cases are provided to show the efficacy of the approximations. As an application, the problem of an opportunistic channel access scheme in a communication network is used to test the approximations.

scholarly journals The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks

2006 ◽  
Vol 2006 ◽  
pp. 1-14
Author(s):  
Dagmar Medková
Keyword(s):  
Integral Equation ◽  
Laplace Equation ◽  
Smooth Boundary ◽  
Single Layer ◽  
Double Layer Potential ◽  
Jump Conditions ◽  
Single Layer Potential ◽  
Layer Potential ◽  
The Third ◽  
Planar Domains

This paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition∂u/∂n+hu=fis given on the boundary of the domain. The skip of the functionu+−u−=gand the modified skip of the normal derivatives(∂u/∂n)+−(∂u/∂n)−+hu+=fare given on cracks. The solution is looked for in the form of the sum of a modified single-layer potential and a double-layer potential. The solution of the corresponding integral equation is constructed.

scholarly journals On Monotonic and Nonnegative Solutions of a Nonlinear Volterra-Stieltjes Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tomasz Zając
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Bounded Variation ◽  
Fractional Integral ◽  
Functions Of Bounded Variation ◽  
Stieltjes Integral ◽  
Measures Of Noncompactness ◽  
Bounded Interval ◽  
Nonnegative Solutions ◽  
Real Functions

We study the existence of monotonic and nonnegative solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous on a bounded interval. The main tools used in our considerations are the technique of measures of noncompactness in connection with the theory of functions of bounded variation and the theory of Riemann-Stieltjes integral. The obtained results can be easily applied to the class of fractional integral equations and Volterra-Chandrasekhar integral equations, among others.

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