On a coefficient problem for schlicht functions

1976 ◽  
pp. 79-91 ◽  
Author(s):  
Albert Pfluger
Keyword(s):  
Coefficient Problem

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

scholarly journals Coefficients problems for families of holomorphic functions related to hyperbola

2020 ◽  
Vol 70 (3) ◽  
pp. 605-616
Author(s):  
Stanisława Kanas ◽  
Vali Soltani Masih ◽  
Ali Ebadian
Keyword(s):  
Unit Disk ◽  
Holomorphic Functions ◽  
Hankel Determinant ◽  
Coefficient Problem

AbstractWe consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation $\begin{array}{} \frac{1}{\rho}=\left( 2\cos\frac{\varphi}{s}\right)^s\quad (0 \lt s\le 1,\, |\varphi| \lt (\pi s)/2). \end{array}$ We mainly study a coefficient problem of the families of functions for which zf′/f or 1 + zf″/f′ map the unit disk onto a subset of ℍ(s) . We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant.

Research of Volterra Series Kernel Coefficient Calculation Method

2011 ◽  
Vol 255-260 ◽  
pp. 2967-2971
Author(s):  
Yu Chen ◽  
Xin Ling Wen ◽  
Jin Tao Meng
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Volterra Series ◽  
Simple Calculation ◽  
Difficult Problem ◽  
Coefficient Problem ◽  
Memory Length ◽  
Non Linear ◽  
Non Linear System ◽  
Space Method

Volterra series kernel coefficient calculation of non-linear system is a difficult problem. In this paper, we introduce some way, which can get kernel coefficient. With the increasing of memory length and identification order, it can make calculation complex and hard to rebuild system non-linear model. This article introduces some conventional Volterra series kernel calculation ways, and introduces a kind of method to get Volterra series kernel through using Hilbert space method emphasis, this method can transform Volterra series kernel coefficient calculation problem into reproducing kernel coefficient problem, which has largely simple calculation rate and can get any order Volterra series kernel coefficient in theory.

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