The points of maximum modulus of a univalent function

The Yukawa Potential Function and Reciprocal Univalent Function

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v3i2.2072 ◽

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.

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Nonlinear conservation laws for the Schrödinger boundary value problems of second order

Boundary Value Problems ◽

10.1186/s13661-019-01311-5 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 3

Author(s):

Ming Ren ◽

Shiwei Yun ◽

Zhenping Li

Keyword(s):

Cauchy Problem ◽

Conservation Laws ◽

Boundary Value Problems ◽

Boundary Value ◽

Maximum Modulus ◽

Second Order ◽

Nonlinear Conservation Laws ◽

The Cauchy Problem ◽

Modulus Method ◽

Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

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SHARP LOGARITHMIC DERIVATIVE ESTIMATES WITH APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS IN THE UNIT DISC

Journal of the Australian Mathematical Society ◽

10.1017/s1446788710000029 ◽

2010 ◽

Vol 88 (2) ◽

pp. 145-167 ◽

Cited By ~ 10

Author(s):

I. CHYZHYKOV ◽

J. HEITTOKANGAS ◽

J. RÄTTYÄ

Keyword(s):

Differential Equations ◽

Unit Disc ◽

Logarithmic Derivative ◽

Maximum Modulus ◽

Exceptional Set ◽

Proximate Order ◽

Upper Density ◽

Linear Differential ◽

Logarithmic Derivatives ◽

Growth Of Solutions

AbstractNew estimates are obtained for the maximum modulus of the generalized logarithmic derivatives f(k)/f(j), where f is analytic and of finite order of growth in the unit disc, and k and j are integers satisfying k>j≥0. These estimates are stated in terms of a fixed (Lindelöf) proximate order of f and are valid outside a possible exceptional set of arbitrarily small upper density. The results obtained are then used to study the growth of solutions of linear differential equations in the unit disc. Examples are given to show that all of the results are sharp.

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Trial Study on Methods of Damage Extent Identification Based on Wavelet Transform of Strain Signal

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.163-167.2543 ◽

2010 ◽

Vol 163-167 ◽

pp. 2543-2548

Author(s):

Jin Fan ◽

Hong Po Liu

Keyword(s):

Wavelet Transform ◽

Wavelet Coefficient ◽

Maximum Modulus ◽

Steel Beam ◽

Simply Supported ◽

Relative Damage ◽

Damage Extent ◽

Strain Signal

Wavelet transform of strain signal can be used in the damage relative damage extent identification. The proposed method is validated by trial on a simply supported steel beam. And meanwhile the relative damage extent can be identified by drawing the curve of the maximum modulus of the wavelet coefficient and damage extent.

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