Published in Lobachevskii Journal of Mathematics
In this paper, some known background results of bi-ideals for our studies are introduced. Then we give some characterizations of (0-)minimal and maximal bi-ideals in semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu[7].
Published in Lobachevskii Journal of Mathematics
In [7] the authors introduced a generalized integral operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{I}_{b,\lambda ,\mu }^n f $$\end{document}. Using...
Published in Lobachevskii Journal of Mathematics
Here we present a justification of a Galerkin method for solving the linear singular integro-differential equations with Cauchy kernel on an interval. The proofs of the convergence and the error estimations are given.
Published in Lobachevskii Journal of Mathematics
In this paper, we give some characterizations of spaces with locally countable weak bases and prove that spaces with locally countable weak bases are preserved by some maps.
Published in Lobachevskii Journal of Mathematics
In this paper we define fuzzy bi-ideal subsets and fuzzy bi-filters in ordered semigroups and characterize ordered semigroups in terms of fuzzy bi-ideal subsets and fuzzy bi-filters. We also define fuzzy left filters and fuzzy prime left ideals in ordered semigroups and characterize ordered semigroups in terms of these notions.
Published in Lobachevskii Journal of Mathematics
The concept of residual finiteness with respect to automorphic equivalence, a property generalizing residual finiteness and conjugacy separability is introduced. A sufficient condition for a group G to be residually finite with respect to automorphic equivalence is proven (Theorem). It is then used to give some examples of automorphic equivalent re...
Published in Lobachevskii Journal of Mathematics
In this paper we define the notions of rough sub-acts and give some properties of such sub-acts and rough fuzzy sub-acts. We discuss approximations of a subset in acts with respect to Green’s relations. Relationship between upper [lower] rough sub-acts [bi-acts] and upper [lower] aproximations of their homomorphic images are discussed. We also disc...
Published in Lobachevskii Journal of Mathematics
Published in Lobachevskii Journal of Mathematics
In this paper, we study an a priori error analysis for the quadratic optimal control problems governed by nonlinear elliptic partial differential equations using mixed finite element methods. The state and the costate are approximated by the lowest order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise consta...
Published in Lobachevskii Journal of Mathematics
This paper deals with singular integral operators with a reverting orientation Carleman shift defined on the classic Lebesgue space and having essentially bounded functions as coefficients. We will use similarity relations to show that the mentioned operators are equivalent tomatrix Toeplitz plus Hankel operators acting on the corresponding Hardy s...
