The topological degree applied to some problems in approximation theory

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

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Topological degree and application to a parabolic variational inequality problem

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171201004306 ◽

2001 ◽

Vol 25 (4) ◽

pp. 273-287 ◽

Cited By ~ 3

Author(s):

A. Addou ◽

B. Mermri

Keyword(s):

Variational Inequality ◽

Topological Degree ◽

Variational Inequality Problem ◽

Maximal Monotone ◽

Maximal Monotone Operators ◽

Monotone Operators ◽

Parabolic Variational Inequality ◽

Inequality Problem ◽

Monotone Map ◽

New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

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Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-021-00618-7 ◽

2021 ◽

Vol 23 (4) ◽

Author(s):

Jifeng Chu ◽

Kateryna Marynets

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Conditions ◽

Topological Degree ◽

Antarctic Circumpolar Current ◽

Fixed Point Theorems ◽

Nonlinear Differential Equations ◽

Existence Results ◽

Circumpolar Current ◽

The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

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Mkhitar Djrbashian and his contribution to Fractional Calculus

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2020-0089 ◽

2020 ◽

Vol 23 (6) ◽

pp. 1797-1809

Author(s):

Sergei Rogosin ◽

Maryna Dubatovskaya

Keyword(s):

Cauchy Problem ◽

Fractional Calculus ◽

Fractional Order ◽

Approximation Theory ◽

Fractional Derivatives ◽

Complex Analysis ◽

Integral Transforms ◽

Modern Theory ◽

Survey Paper ◽

The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

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