Volume 47 , issue 3$-$4 ( 1995 ) | back |

Index of imprimitivity of the non-complete extended $p$-sum of digraphs | 57$-$60 |

**Abstract**

We prove that all components of the non-complete extended $p$-sum (NEPS) of strongly connected digraphs have the same index of imprimitivity. This index is given in dependence of the indices of imprimitivity of digraphs on which the operation is performed.

**Keywords:** Index of imprimitivity, product of digraphs.

**MSC:** 05C40, 05C20

An object model for natural language document | 61$-$84 |

**Abstract**

An object model of a text is defined, and structural and manipulative aspects of the model are presented. The model proposed supports text in its general sence (as a natural language document), which comprises structural, syntactic, semantic, orthographic, stylistic properties of both the underlying natural language and the text itself. Extended class algebra is defined as a basis for manipulative part of the model. Set of classes is then proved to be closed under the operations of the extended class algebra.

**Keywords:** Object model, natural language document.

**MSC:** 68S05

On uniform convergence of spectral expansions and their derivatives corresponding to self-adjoint extensions of Schrödinger operator | 85$-$92 |

**Abstract**

In this paper we consider problem of the global uniform convergence of spectral expansions and their derivatives generated by arbitrary non-negative self-adjoint extensions of the Schrödinger operator $$ \Cal L(u)(x)=-u^{\prime\prime}(x)+q(x)u(x) \tag 1 $$ with discrete spectrum, for functions in the Sobolev class $\overset\circ\to{W}_p^{(k)}(G)$ ($p>1$) defined on a finite interval $G\subset R$. Assuming that the potential $q(x)$ of the operator $\Cal L$ belongs to the class $L_p(G)$ ($1

**Keywords:** Spectral expansion, self-adjoint extension, Schrödinger operator.

**MSC:** 34L10, 47E05

On the convergence of a three-level vector SOR scheme | 93$-$98 |

**Abstract**

In this paper we consider a vector alternating directions difference scheme for solving multidimensional wave equation. The scheme reduces to a modified block successive overrelaxation (SOR) algorithm. The stability and the convergence of the scheme are investigated.

**Keywords:** Vector SOR scheme

**MSC:** 65M12

On fixed points in a metric space over Tychonoff semifield | 99$-$102 |

**Abstract**

A theorem is proved which generalizes some fixed point theorems about functions on metric spaces over Tychonoff semifield.

**Keywords:** Tychonoff semifield, fixed point.

**MSC:** 54H25, 47H10

Flow-oriented difference scheme for multidimensional convection- diffusion equation | 103$-$111 |

**Abstract**

In this paper one flow-oriented difference scheme for multidimensional convection-diffusion equation is constructed and analysed. The order of the accuracy is $O(\Delta x^2)$, except for convection dominant case when it decreased by one. The stability depends on the diffusion coefficient $D$, and for the square grid the stability condition is $D\,\Delta t/\Delta x^2\le 0.25$. Some examples are presented to illustrate that the scheme is especially applicable for dominantly convection problems and problems with not enough smooth solutions.

**Keywords:** Finite difference scheme, convection-diffusion equation.

**MSC:** 65C20, 76R99