On the Direct Cauchy Theorem in Widom Domains: Positive and Negative Examples Peter Yuditskii

2012 ◽  
Vol 11 (2) ◽  
pp. 395-414 ◽  
Author(s):  
Peter Yuditskii
Keyword(s):  
Cauchy Theorem

scholarly journals Direct Cauchy theorem and Fourier integral in Widom domains

2020 ◽  
Vol 141 (1) ◽  
pp. 411-439
Author(s):  
Peter Yuditskii
Keyword(s):  
Fourier Integral ◽  
Cauchy Theorem

Color science applications of the Binet-Cauchy theorem

2002 ◽  
Vol 27 (5) ◽  
pp. 310-315 ◽  
Author(s):  
Michael H. Brill
Keyword(s):  
Color Science ◽  
Cauchy Theorem

scholarly journals The Cauchy theorem for functions on closed sets

1942 ◽  
Vol 48 (12) ◽  
pp. 912-917
Author(s):  
Philip T. Maker
Keyword(s):  
Closed Sets ◽  
Cauchy Theorem

scholarly journals A characterization of the permanent function by the Binet-Cauchy theorem

1988 ◽  
Vol 101 ◽  
pp. 49-72 ◽  
Author(s):  
Konrad J. Heuvers ◽  
L.J. Cummings ◽  
K.P.S. Bhaskara Rao
Keyword(s):  
Cauchy Theorem ◽  
Permanent Function

scholarly journals A Picard-Maclaurin theorem for initial value PDEs

2000 ◽  
Vol 5 (1) ◽  
pp. 47-63 ◽  
Author(s):  
G. Edgar Parker ◽  
James S. Sochacki
Keyword(s):  
Differential Equation ◽  
Series Solution ◽  
Initial Conditions ◽  
Broad Class ◽  
Picard Iteration ◽  
Power Series Solution ◽  
Initial Value ◽  
Arbitrary Degree ◽  
Cauchy Theorem ◽  
Analogous Theorem

In 1988, Parker and Sochacki announced a theorem which proved that the Picard iteration, properly modified, generates the Taylor series solution to any ordinary differential equation (ODE) onℜnwith a polynomial generator. In this paper, we present an analogous theorem for partial differential equations (PDEs) with polynomial generators and analytic initial conditions. Since the domain of a solution of a PDE is a subset ofℜn, we identify one component of the domain to achieve the analogy with ODEs. The generator for the PDE must be a polynomial and autonomous with respect to this component, and no partial derivative with respect to this component can appear in the domain of the generator. The initial conditions must be given in the designated component at zero and must be analytic in the nondesignated components. The power series solution of such a PDE, whose existence is guaranteed by the Cauchy theorem, can be generated to arbitrary degree by Picard iteration. As in the ODE case these conditions can be met, for a broad class of PDEs, through polynomial projections.

Application of the Cauchy theorem to the location of zeros of sectionally analytic functions

1984 ◽  
Vol 35 (5) ◽  
pp. 705-711 ◽  
Author(s):  
E. G. Anastasselou ◽  
N. I. Ioakimidis
Keyword(s):  
Analytic Functions ◽  
Cauchy Theorem ◽  
Location Of Zeros

scholarly journals Using Cauchy theorem to compute complicated real integrals

2021 ◽  
Vol 2012 (1) ◽  
pp. 012064
Author(s):  
Jiarui Song ◽  
Zhanhua Shi ◽  
Haotao Wang
Keyword(s):  
Cauchy Theorem

scholarly journals STEEP UNSTEADY WATER WAVES: AN EFFICIENT COMPUTATIONAL SCHEME

1984 ◽  
Vol 1 (19) ◽  
pp. 65 ◽  
Author(s):  
J.W. Dold ◽  
D.H. Peregrine
Keyword(s):  
Water Waves ◽  
Water Surface ◽  
Unsteady Motion ◽  
Boundary Integral ◽  
Computational Scheme ◽  
Multiple Time ◽  
Numerical Implementation ◽  
Surface Motion ◽  
Cauchy Theorem ◽  
Derivatives Of

A new method for computing the unsteady motion of a water surface, including the overturning of water waves as they break, has been developed. It is based on a Cauchy theorem boundary integral for the evaluation of multiple time derivatives of the surface motion. The numerical implementation of the method is efficient, accurate and stable.

Cauchy Theorem

2005 ◽  
Keyword(s):  
Cauchy Theorem
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