Issue 1, Volume 19, June 1994

1994 · Open access

1. SOME RESULTS ON RINGS WHOSE CYCLIC COFAITHFUL MODULES ARE GENERATORS LE VAN THUYET PDF

   3-11
2. ON THE GROWTH RATE OF SLOWLY VARYING FUNCTIONS ALLAN GUT PDF

   ▸ Abstract

   A function $L$ is slowly varying (at infinity) iff $\frac{L(tx)}{L(x)}\to 1$ as $x\to\infty$ for every $t > 0$. Motivated by two examples we investigate to what extent, if at all, the limit of the ratio equals 1 when $t$ is replaced by some function of $x$ growing to infinity.

   13-24
3. VERTEXSET CONTAINED IN LONGEST DOMINATING CYCLES IN GRAPHS VU DINH HOA PDF

   ▸ Abstract

   Let $G$ be an undirected and simple graph. A cycle $C$ in $G$ is called a {\it dominating cycle} if $V(G)-V(C)$ is an independent set of vertices in $G$. $G$ is called {\it dominable} if $G$ contains a dominating cycle $C$, and we say $G$ is {\it dominated} by $C$. In this paper we establish sets of vertices which are contained in any longest dominating cycle in $G$.

   25-30
4. A LINEAR PROGRAMMING APPROACH TO SOLVING A JOINTLY CONSTRAINED BILINEAR PROGRAMMING PROBLEM WITH SPECIAL STRUCTURE TRAN VU THIEU PDF

   ▸ Abstract

   In this paper we shall deal with the following nonconvex optimization problem: $(P)$ Minimize $c^Tz$, subject to $z\in D$ and $z_i=x_iy_i$ for all $i=1,\dots,p\leq n, x\in X, y\in S$,  where $D, S$ are polyhedrons in $\mathbb R^n$, $\mathbb R^p$ respectively, $X=\{x\in\mathbb R^p\,|\, 0 < a\leq x\leq A\}$; $a, A$ are $p$-vectors; $c$ is an $n$-vector. It is shown that $(P)$ can be reduced to a linear program whose constraints can explicitly be given in some special cases.

   31-39
5. A REDUCTION OF THE GLOBALIZATION AND U(1)-COVERING TRAN DAO DONG PDF

   ▸ Abstract

   We suggest a reduction of the globalization and multidimensional quantization to the case of reductive Lie groups by lifting to U(1)-covering. Our construction is connected with the M. Duflo's third method for algebraic groups. From a reductive datum of the givan real algebraic Lie group we firstly construct geometric complexes with respect to U(1)-covering by using the unipotent positive distributions. Then we discribe in terms of local cohomology the maximal globalization of Harish-Chandra modules which correspond to the geometric complexes.

   41-54
6. A VARIETY OF APPLICATIONS OF A THEOREM OF B.H. NEUMANN ON GROUPS T. SOUNDARARAJAN, K. VENKATACHALIENGAR PDF

   55-60
7. A CHARACTERIZATION OF SOME CUBIC $(m, n)$-METACIRCULANT GRAPHS NGO DAC TAN PDF

   ▸ Abstract

   It has been proved in [5] that if a graph $G$ is isomorphic to a cubic $(m, n)$-metacirculant graph $MC(m,n,\alpha,S_0, S_1,\dots,S_{\mu})$ with $S_0\not = \emptyset$, then $G$ is isomorphic to either a union of finitely many disjoint copies of a circulant graph $C(2\ell,S)$, where $\ell > 1$ and $S=\{1, -1, \ell\}$ or a union of finitely many disjoint copies of a generalized Petersen graph $GP(d,k)$, where $d > 2$ and $k^2\equiv \pm 1$ (mod $d$). In this paper, we prove that the converse is also true.

   61-66
8. OSCILLATION ET CONVERGENCE D'UNE MARTINGALE PHAN VIET THU PDF

   67-75
9. SEPARABLE CALIBRATIONS AND MINIMAL SURFACES HOANG XUAN HUAN PDF

   77-96
10. EFFICIENT METHODS FOR SOLVING CERTAIN BILINEAR PROGRAMMING PROBLEMS LE DUNG MUU, BUI THE TAM PDF

    ▸ Abstract

    We specialize the algorithm in [7] for solving certain nonconvex programming problems which contain indefinite quadratic and linear complementarity problems as special cases. We show that indefinite quadratic problems with a few negative eigen values and rank $k$ bilinear program with $k$ is small can be solved efficiently by this algorithm. The method is also applied for solving linear complementarity problems without any assumption on the structure of the involved matrices.

    97-110
11. STRONG CONSISTENCY OF LEAST SQUARES ESTIMATES IN POLYGONAL REGRESSION WITH RANDOM EXPLANATORY VARIABLES NGUYEN BAC VAN PDF

    ▸ Abstract

    The strong consistency of generalized least squares estimates in polygonal regression with random explanatory variables is established regardless of the projection support under minimal moment restrictions.

    111-137
12. ÉTUDE D'UN PROBLÈME DE PERTURBATION NON CLASSIQUE EN UNE DIMENSION TAOUFIG BENKIRAN PDF

    139-144
13. ON THE INTEGRAL CONVOLUTION FOR INVERSE $G$–TRANSFORMS RUDOLF GORENFLO, SEMEN B. YAKUBOVICH PDF

    ▸ Abstract

    We give a new method for constructing general integral convolutions by means of the theory of Mellin type $G$–transforms.

    145-154