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Explicit iteration methods for a class of variational inequalities in Banach spaces
Allerton Press - Tập 59 - Trang 16-22 - 2015
In this paper, in order to solve a variational inequality problem over the set
of common fixed points of an infinite family of nonexpansive mappings on real
reflexive and strictly convex Banach spaces with a uniformlyGâteaux
differentiable norm, we introduce two new explicit iteration methods.
On the Number of Linearly Independent Solutions of the Riemann Boundary Value Problem on the Riemann Surface of an Algebraic Function
Allerton Press - Tập 65 - Trang 10-30 - 2021
We suggest a modified solution to the Riemann boundary value problem on a
Riemann surface of an algebraic function of genus $\rho$ . This allows us to to
reduce the problem of finding the number l of linearly independent algebraic
functions (LIAF), that are multiples of a fractional divisor Q, to finding the
number of LIAF that are multiples of an effective divisor J (
$\operatorname{ord}\,J = \rh...
Conditions for the Qualified Convergence of Finite Difference Methods and the Quasi-Reversibility Method for Solving Linear Ill-Posed Cauchy Problems in a Hilbert Space
Allerton Press - Tập 63 - Trang 40-54 - 2019
We study finite difference methods and the quasi-reversibility method in
application to linear ill-posed Cauchy problems with a self-adjoint operator in
a Hilbert space with exact data. We prove that for these problems, it is
possible to strengthen our earlier results on the convergence of the mentioned
methods in a general case of a Banach space. We establish close to each other
necessary and suf...
The Dirichlet problem for telegraph equation in a rectangular domain
Allerton Press - Tập 61 - Trang 39-48 - 2017
We investigate the Dirichlet problem for the telegraph equation in a rectangular
domain. We establish a criterion of uniqueness of solution to the problem. The
solution is constructed as the sum of an orthogonal series. In substantiation of
convergence of the series, the problem of small denominators occurs. In
connection with this, we establish estimates ensuring separation from zero of
denominat...
On tracking solutions of parabolic equations
Allerton Press - Tập 56 - Trang 35-42 - 2011
We consider a control problem for a parabolic equation. It consists in
constructing an algorithm for finding a feedback control such that a solution of
a given equation should track a solution of another equation generated by an
unknown right-hand side. We propose two noise-resistant solution algorithms for
the indicated problem. They are based on the method of extremal shift well-known
in the gua...
On the Stability of Spline Collocation Difference Scheme for Linear Multidimensional Differential-Algebraic Systems
Allerton Press - Tập 66 - Trang 56-65 - 2023
An initial-boundary value problem is considered for a linear multidimensional
differential-algebraic system of first-order equations with variable matrix
coefficients of a special form. A spline collocation method is used to solve it
numerically. Unlike splitting methods, this method allows taking into account
the structural features of all matrix coefficients of the system in total and
has a high...
On Inductive Limits for Systems of C*-Algebras
Allerton Press - Tập 62 - Trang 68-73 - 2018
We consider a covariant functor from the category of an arbitrary partially
ordered set into the category of C*-algebras and their *-homomorphisms. In this
case one has inductive systems of algebras over maximal directed subsets. The
article deals with properties of inductive limits for those systems. In
particular, for a functor whose values are Toeplitz algebras, we show that each
such an induct...
The elastic semi-space consolidation under the normal load on a square area
Allerton Press - Tập 60 - Trang 64-66 - 2016
We investigate the elastic saturated semi-space consolidation under the uniform
normal load on a square area. The analytical forms for the fluid pressure and
the semi-space surface settlement are found by the solutions to the Dirichlet
problem for the Laplace equation and the first boundary-value problem for the
heat equation.
Uniqueness of the Kernel Determination Problem in a Integro-Differential Parabolic Equation with Variable Coefficients
Allerton Press - - 2024
We investigate the inverse problem of determining the time and space dependent
kernel of the integral term in the $$n$$ -dimensional integro-differential
equation of heat conduction from the known solution of the Cauchy problem for
this equation. First, the original problem is replaced by the equivalent problem
in which an additional condition contains the unknown kernel without integral.
We study...
Isomorphisms of Endomorphism Semigroups of Mixed Abelian Groups
Allerton Press - - 2018
We study abelian groups whose endomorphism rings are rings with unique addition.
This means that there exists a unique binary operation of addition on the
endomorphism semigroup which turns it into a ring. We also solve some close
problems.
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