Cauchy’s Theorem: How to Show a Number Is Greater Than 1

Algebra ◽  
2018 ◽  
pp. 37-44
Keyword(s):  
Cauchy's Theorem

A Note on Cauchy's Theorem

1953 ◽  
Vol 60 (2) ◽  
pp. 110
Author(s):  
Harry Lass
Keyword(s):  
Cauchy's Theorem

scholarly journals Numerical Steepest Descent Method for Hankel Type of Hypersingular Oscillatory Integrals in Electromagnetic Scattering Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Qinghua Wu ◽  
Mengjun Sun
Keyword(s):  
Electromagnetic Scattering ◽  
High Efficiency ◽  
Integral Formula ◽  
Main Idea ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Scattering Problems ◽  
Hypersingular Integrals ◽  
Cauchy's Theorem ◽  
Highly Oscillatory

We present a fast and accurate numerical scheme for approximating hypersingular integrals with highly oscillatory Hankel kernels. The main idea is to first change the integration path by Cauchy’s theorem, transform the original integral into an integral on a , + ∞ , and then use the generalized Gauss Laguerre integral formula to calculate the corresponding integral. This method has the advantages of high-efficiency, fast convergence speed. Numerical examples show the effect of this method.

scholarly journals On the refinement of Cauchy's theorem and Pellet's theorem

2004 ◽  
Vol 291 (1) ◽  
pp. 262-269
Author(s):  
Zifang Zhang ◽  
Daoyi Xu ◽  
Jianren Niu
Keyword(s):  
Cauchy's Theorem

scholarly journals Conservation laws in anisotropic elasticity I. Basic framework

1993 ◽  
Vol 443 (1917) ◽  
pp. 139-151 ◽  
Keyword(s):  
Conservation Laws ◽  
General Procedure ◽  
Anisotropic Elasticity ◽  
Two Dimensional ◽  
Real Form ◽  
Elastic Materials ◽  
Complete Class ◽  
First Order ◽  
Cauchy's Theorem ◽  
Anisotropic Elastic

A complete class of first order conservation laws for two dimensional deformations in general anisotropic elastic materials is derived. The derivations are based on Stroh’s formalism for anisotropic elasticity. The general procedure proposed by P. J. Olver for the construction of conservation integrals is followed. It is shown that the conservation laws are intimately connected with Cauchy’s theorem for complex analytic functions. Real-form conservation laws that are valid for degenerate or non-degenerate materials are given.

Sign in / Sign up

Export Citation Format

Share Document