integration formula
1.When the strength obeys Weibull distribution and the stress obeys Gauss distribution,the integration interval of calculation reliability is subdivided to some subdomain. In the subdomain of the integration the numerical integration formula of Gauss Lagendre is applied. The adaptive algorithm is presented in this paper at the request of the calculation reliability accuracy,which can autonomously adjudge the calculation number of time.
2.Through mathematic integration a formula of volume-pressure relatonship asP=b/(1+Ce~(-Mv))(C and M are contants,b is the maximal value of ICP after thevolume increases continuously)was derived.
3.This paper presents a comprehensive formula that computes basic solution matrix of linear homogeneous differential equations with constant coefficients. Contour integration by Cauchy integral formula formula is used. The formula is more pithy and distinct than previously.
4.Numerical calculation results are compared with those obtained by direct integration of the Collins formula Wen’s method.
5.Then the paper discusses the integration methods of it and elicit Cauchy integral formula by constructing an assistant function.
6.In this note, the well-known Bertrand-Poincare formula for changing order of integration related to singular intergrals with Cauchy kernel has been extended to some cases related to singular integrals of high order.
7.In this paper,the cauchy principal value integrals of the form is discussed. The finite-pair intrgration of singlar integrals is defined,and the formula for the Cauchy principal value integrals by finite-part integration is gerived.
