Volume 56 , issue 3$-$4 ( 2004 ) | back |

Unification of some concepts similar to the Lindelöf property | 63$-$76 |

**Abstract**

In this paper the $\varphi_{1,2}$-Lindelöf property is defined and studied with the aim of unifying various concepts related to the Lindelöf property in General Topology.

**Keywords:** Lindelöf property, operation, unification, filter,
convergence, supratopology.

**MSC:** 54D20, 54A20

Semiregular properties and generalized Lindelöf spaces | 77$-$80 |

**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

Contr\^olabilité d'un probl\`eme non-linéaire inverse de la théorie de transport | 81$-$84 |

**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

Renormalizing iterated repelling germs of $C^2$ | 85$-$90 |

**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

On uniform convergence of spectral expansions and their derivatives for functions from $W_p^1$ | 91$-$104 |

**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

The representations of finite reflection groups | 105$-$114 |

**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

On the convergence of finite difference scheme for elliptic equation with coefficients containing Dirac distribution | 115$-$123 |

**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