Sentence examples for multiple integral equations from inspiring English sources

Some mixed boundary value problems of the mathematical theory of elasticity are solved by reducing them to multiple integral equations.

We also derive many properties and formulae for our -Euler polynomials of higher order by using the multiple integral equations on.

In other words, the distribution of the random vector U n can be found by the traditional combinatorial analysis when F=G. Unfortunately, when F≠G, we will not be able to establish the distribution of U n through Equation (7) as solving the multiple integral in Equation (8) is either tedious given some appropriate alternative distribution function or difficult.

The complex variable function method is used to formulate the multiple curved crack problems into hypersingular integral equations.

The existence of multiple positive solutions of systems of singular Hammerstein integral equations is studied, where the nonlinearities involved are allowed to have singularities in their second variables and satisfy weaker conditions involving the first eigenvalues of the corresponding linear Hammerstein integral operators.

This paper studies a numerical solution of multiple crack problem in a finite plate using coupled integral equations.

The dislocation solution is utilized to formulate integral equations for the strip weakened by multiple smooth cracks under anti-plane deformation.

In this paper, we present a systemic study of some families of multiple Carlitz's type -Bernoulli numbers and polynomials by using the integral equations of -adic -integrals on.

Equations vary in complexity from simple algebraic equations (involving only addition or multiplication) to differential equations, exponential equations (involving exponential expressions), and integral equations.

It focuses on vector spaces, matrix algebra, differential equations (especially for boundary value problems), integral equations, integral transforms, infinite series, and complex variables.

Bolza's later lectures on his function theory and integral equations were collected by William V. Lovitt and published in 1924 as Linear Integral Equations.