Plemelj Formula of Cauchy-Type Integral of Random Process with Second Order Moment

Plemelj Formula of Cauchy-Type Integral of Random Process with Second Order Moment

The research is Supported by Natural Science Foundation of Fujian Province, China (2007J0183). Abstract Under the condition of arc-wise smooth path of integration, the Plemelj formula of Cauchy-type integral on random process with second order moment is obtained.

A Cauchy integral formula in superspace

In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal Clifford analysis. After introducing Clifford algebra valued surfaceand volume-elements first a purely fermionic Cauchy formula is proven. Combining this formula ...

An effective method for approximating the solution of singular integral equations with Cauchy kernel type

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

The plemelj formulas with unrestricted approach, and the continuity of cauchy-type integrals.

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...