scholarly journals EXTREMUM PROBLEM IN CONVOLUTIONS WITH ADDITIONAL CONDITIONS ON THE AXIS

2020 ◽  
Vol 33 (2) ◽  
Author(s):  
Y.A. Hryhoriev ◽  
A.Yu. Grygoriev
Keyword(s):  
Extremum 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.

An extremum problem for the power moment of a convex polygon contained in a disc

2021 ◽  
Vol 21 (4) ◽  
pp. 599-609
Author(s):  
Irmina Herburt ◽  
Shigehiro Sakata
Keyword(s):  
Convex Polygon ◽  
Extremum Problem ◽  
Classical Theorem ◽  
Power Moment ◽  
Area Functional ◽  
The Mean

Abstract In this paper, we investigate an extremum problem for the power moment of a convex polygon contained in a disc. Our result is a generalization of a classical theorem: among all convex n-gons contained in a given disc, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the area functional. It also implies that, among all convex n-gons contained in a given disc and containing the center in those interiors, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the mean of the length of the chords passing through the center of the disc.

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

On a Geometric Extremum Problem

1965 ◽  
Vol 8 (1) ◽  
pp. 21-27 ◽  
Author(s):  
J. Schaer ◽  
A. Meir
Keyword(s):  
Extremum Problem ◽  
Unit Square

The following problem was brought to our attention by L. Moser: Locate eight points in the closed unit square so that the minimum of the distances between any two of the points should be as large as possible.

An extremum problem for distribution functions

1998 ◽  
Vol 63 (2) ◽  
pp. 279-282 ◽  
Author(s):  
V. A. Yudin
Keyword(s):  
Extremum Problem ◽  
Distribution Functions

Numerical Analysis of Inverse Problems for the Model of Transfer of Industrial Environmental Pollution in the Machine-Building

2015 ◽  
Vol 756 ◽  
pp. 353-358
Author(s):  
O.V. Soboleva ◽  
Denis V. Mashkov
Keyword(s):  
Numerical Analysis ◽  
Inverse Problems ◽  
Environmental Pollution ◽  
Numerical Experiments ◽  
Extremum Problem ◽  
Machine Building ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Lagrange Principle ◽  
Specific Cost

The model of transfer of polluting substance is considered. inverse extremum problem of identification of the coefficients in an elliptic diffusion-reaction equation is formulated. The solvability of this problem is proved, the application of Lagrange principle is justified and the optimality system is constructed for specific cost functional. The numerical algorithm based on Newton-method of nonlinear optimization of linear elliptic problems is developed and programmed on computer. The results of numerical experiments are discussed

An extremum problem for polynomials related to codes and designs

2000 ◽  
Vol 67 (4) ◽  
pp. 433-438 ◽  
Author(s):  
D. V. Gorbachev ◽  
V. I. Ivanov
Keyword(s):  
Extremum Problem
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