Some Remarks on Schwarz–Christoffel Transformations from the Unit Disk to a Regular Polygon and their Numerical Computation

2004 ◽  
Vol 49 (4) ◽  
pp. 271-284 ◽  
Author(s):  
Damiano Bonciani * ◽  
Fabio Vlacci
Keyword(s):  
Numerical Computation ◽  
Unit Disk ◽  
Regular Polygon

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

ABOUT INVARIANCE OF ANGLE NOISE DISTRIBUTION PARAMETERS BY AN ARBITRARY N-POINT GEOMETRIC MODEL TO VIEWING ANGLE

2019 ◽  
pp. 32-35
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Regular Polygon ◽  
Geometric Model ◽  
Sea Surface ◽  
Noise Distribution ◽  
Viewing Angle ◽  
Distributed Objects ◽  
Software Complex ◽  
The Earth ◽  
Distribution Parameters ◽  
Equal Power

In this article we consider a problem of reliable modeling of echo signals and angle noise of distributed objects using twodimensional geometric models with random statistically unrelated signals. The conditions that ensure the invariance of distribution parameters of the angle noise generated by an arbitrary N-point configuration of a two-dimensional geometric model are obtained. In the particular case of a model whose emitters are supplied with signals of equal power, the conditions of invariance are reduced to the location of the model points on the plane in the form of a regular polygon. These results can be used to synthesize mathematical models used for simulating reflections from distributed objects and for developing a hardware-software complex for the simulation of electromagnetic fields reflected from the Earth surface, atmospheric inhomogeneities, the sea surface, etc.

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