scholarly journals The argument principle and holomorphic extendibility

2004 ◽  
Vol 94 (1) ◽  
pp. 385-395 ◽  
Author(s):  
Josip Globevnik
Keyword(s):  
Argument Principle ◽  
Holomorphic Extendibility

Locating complex eigenvalues for analytical eddy-current models used to detect flaws

2019 ◽  
Vol 38 (6) ◽  
pp. 1800-1809
Author(s):  
Grzegorz Tytko ◽  
Łukasz Dawidowski
Keyword(s):  
Eddy Current ◽  
Design Methodology ◽  
Complex Function ◽  
Precise Determination ◽  
Argument Principle ◽  
Content Type ◽  
Conductive Material ◽  
Complex Roots ◽  
Complex Eigenvalues

Purpose Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function. Design/methodology/approach The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them. Findings The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time. Originality/value The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.

The Argument Principle

2019 ◽  
pp. 151-168
Author(s):  
Steven G. Krantz
Keyword(s):  
Argument Principle

scholarly journals Partial and Local Argument Properties of Holomorphic and Meromorphic Complex Functions in Several Variables

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jun Zhou ◽  
Zhaoxia Duan
Keyword(s):  
Cauchy Integral ◽  
Argument Principle ◽  
General Argument ◽  
Numerical Examples ◽  
Argument Analysis ◽  
Several Variables ◽  
Analysis Technique ◽  
Complex Functions ◽  
Variable Domains ◽  
Integral Contour

The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply n-variable complex functions with n≥2. Argument analytic relationships for n-variable complex functions with significance similar to the argument principle for one-variable ones are retrieved partially and locally. More precisely, argument analysis in n-variable complex functions is carried out one-by-one in terms of each and all variables, namely, partially, so that argument-principle-like relations are established in poly-disc neighborhoods of the variable domains, namely locally. The technique is applicable graphically with loci plotting, independent of Cauchy integral contour and locus orientations; it is also numerically tractable without loci plotting via argument incremental integration. Numerical examples are included to illustrate the main results.

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