Abstract

Let $(X, \tau)$ be a topological space and $(X, \tau^{\ast})$ its semiregularization. Then a topological property ${\Cal P}$ is semiregular provided that $\tau$ has property ${\Cal P}$ if and only if $\tau^{\ast}$ has the same property. In this work we study semiregular property of almost Lindelöf, weakly Lindelöf, nearly regular-Lindelöf, almost regular-Lindelöf and weakly regular-Lindelöf spaces. We prove that all these topological properties, on the contrary of Lindelöf property, are semiregular properties.

Keywords: Semiregular property, semiregularization topology, nearly Lindelöf, almost Lindelöf, weakly Lindelöf, nearly regular-Lindelöf, almost regular-Lindelöf and weakly regular-Lindelöf spaces.

MSC: 54A05, 54A20, 54F45

Abstract

In this note controllability of an inverse problem of the transport theory is inverstigated. They are based on an a priori estimate of the problem from our earlier paper [1].

Keywords: Controlability, inverse problem, transport theory.

MSC: 49N50

Abstract

We find bounded-degree renormalizing polynomial families for iterated repelling germs of $(C^2,0)$. These families consist in contracting mappings and yield germs whose differentials have rank two.

Keywords: Renormalizing families, holomorphic mappings, repelling fixed point.

MSC: 32H50

Abstract

We consider the global uniform convergence of spectral expansions and their derivatives, $ \sum_{n=1}^{\infty}f_n\,u_n^{(j)}(x)$, $(j=0,1,2)$, arising by an arbitrary one-dimensional self-adjoint Schrödinger operator, defined on a bounded interval $G\subset\Bbb R$. We establish the absolute and uniform convergence on $\overline G$ of the series, supposing that $f$ belongs to suitable defined subclasses of $ W_p^{(1+j)}(G)$ $(1

Keywords: Spectral expansion, uniform convergence, Schrödinger operator

MSC: 34L10, 47E05

Abstract

The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G. D. James. Hal\i c\i o{ğ}lu and Morris describe a possible extension of James' work for Weyl groups in general, where Young tableaux are interpreted in terms of root systems. In this paper, we further develop the theory and give a possible extension of this construction for finite reflection groups which cover the Weyl groups.

Keywords: Specht module, tableau, tabloid, finite reflection group.

MSC: 20C33, 20F55, 22E45

Abstract

First boundary value problem for elliptic equation with youngest coefficient containing Dirac distribution concentrated on a smooth curve is considered. For this problem a finite difference scheme on a special quasiregular grid is constructed. The finite difference scheme converges in discrete $W_2^1$ norm with the rate $O(h^{3/2})$. Convergence rate is compatible with the smoothness of input data.

Keywords: Boundary value problem, generalized solution, finite differences, rate of convergence.

MSC: 65N15