Issue 2, Volume 19, December 1994

1994 · Open access

1. A VERSION AT INFINITY OF THE KUIPER-KUO THEOREM HA HUY VUI PDF

   ▸ Abstract

   We prove that if $P(x)$ is a tame polynomial of several variables and if $Q(x)$ is a polynomial of degree lower than one plus the Lojasiewicz number at infinity of $P(x)$, then the Milnor fibrations at infinity of $P(x)$ and $P(x)+Q(x)$ are equivalent. This fact can be considered as a version at infinity of the Kuiper-Kuo theorem. We also relate the  Lojasiewicz number at infinity to the phenomenon of singularities at infinity.

   3-12
2. SOME RESULTS ON QUASI-CONTINUOUS MODULES NGO SI TUNG PDF

   ▸ Abstract

   In [5] Mohamed and Müller introduced and gave some characterizations of quasi-continuous modules. Here we characterize these modules by extending property of uniform submodules. The following theorem is proven: Let $M=\oplus_{i\in I}M_i$ such that: (i) all $M_i$ are uniform; (ii) this decomposition of $M$ complements uniform direct summands; (iii) for all $i, j\in I, i\not = j, M_i$ can not be proper embedded in $M_j$; and (iv) $M$ has $1-C_1$. Then $M$ is a quasi-continuous module. As an application we show that, a ring $R$ is QF iff $R$ is semiperfect right continuous and every projective right $R$-module has $(1-C_1)$.

   13-17
3. ON SUBGROUPS OF THE GENERAL LINEAR GROUP OVER A COMMUTATIVE VON NEUMANN REGULAR RING BUI XUAN HAI, TRAN NGOC HOI PDF

   ▸ Abstract

   Let $R$ be a commutative von Neumann regular ring. In this paper we study the lattice of subgroups of the general linear group $G=GL_n(R)$ containing the group $D=D_n(R)$ of diagonal matrices. We show that if $R$ satisfies some conditions (see Definition 2.4 in the text), then for every such subgroup $H$ there is a uniquely determined $D$-net $\sigma$ of ideals such that $G(\sigma)\leq H\leq N(\sigma)$, where $N(\sigma)$ is the normalizer of a $D$-net subgroup $G(\sigma)$.

   19-30
4. ON A GENERALIZATION OF EXCELLENT EXTENSIONS WEIMIN XUE PDF

   ▸ Abstract

   We introduce almost excellent extensions of rings. If $S\geq R$ is such an extension, we study (1) the relation between properties of an $S$-module $M_S$ and the $R$-module $M_R$; and (2) the relation between properties of the ring $S$ and the ring $R$.

   31-38
5. ESTIMATES OF THE SIZES OF RELATIONS IN RELATIONAL DATAMODEL VU DUC THI PDF

   39-49
6. MORE ON APPLICATIONS AND EXTENSIONS OF P-COERCIVE VARIATIONAL INEQUALITIES DANG DINH ANG, LE KY VY PDF

   51-70
7. A REMARK ON THE BERNSTEIN-NIKOLSKII INEQUALITY HA HUY BANG PDF

   ▸ Abstract

   Certain criteria for a function from an arbitrary Orlicz space having its spectrum contained in parallelepiped $\Delta_{\sigma}=\{\xi\, :\, |\xi_j|\leq \sigma_j, j=1,\dots,n\}$ are established in this note.

   71-78
8. ON CONVERGENCE FOR SOME DIFFERENTIAL OPERATORS OF DISTRIBUTIONS HOANG DINH DUNG PDF

   ▸ Abstract

   This convergence of classical differential operators was considered by several authors (see, for instance, [1-4]). This work deals with the convergence for some differential operators of distributions.

   79-84
9. ESPACE À POIDS $H_a^s(G)$ ET PROBLÈME AUX LIMITES ELLIPTIQUE HOANG QUOC TOAN PDF

   85-96
10. ON THE EXPONENTIAL DICHOTOMY OF THE SOLUTIONS OF COUNTABLE SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS CAN VAN TUAT PDF

    97-109
11. ON THE EXPLICIT REPRESENTATION OF GLOBAL SOLUTIONS OF THE CAUCHY PROBLEM FOR HAMILTON-JACOBI EQUATIONS TRAN DUC VAN, NGUYEN HOANG, NGUYEN DUY THAI SON PDF

    111-120
12. EXISTENCE OF GLOBAL MINIMAX SOLUTIONS OF THE CAUCHY PROBLEM FOR SYSTEMS OF FIRST-ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS TRAN DUC VAN, NGUYEN DAC LIEM PDF

    121-135
13. ON THE SUBDIFFEENTIAL OF AN UPPER ENVELOPE OF CONVEX FUNCTIONS M. VOLLE PDF

    ▸ Abstract

    We extend a Rockefellers result for the subdifferential of the upper envelope $j=\sup\limits_{1\leq i\leq n}f$, of a finite collection $f_1,\dots,f_r$ of convex proper functionals on a locally convex Hausdorff topological space $X$. Assuming that $f_1,\dots,f_{n-1}$ are finite and continuous at a point $x_0$ of $X$ where $f_n$ is finite, we show that, for any point $x$ of $X$ such that $f(x)$ is finite \begin{equation}\partial f(x)=\mathrm{co}\{\partial f_k(x)\,:\, f_k(x)=f(x)\}+\sum\limits_{i=1}^n N(\mathrm{dom\ }f_i, x),\tag{*}\end{equation} where co stands for the convex hull and $N(\mathrm{dom\ }f_i, x)$ for the normal cone to the domain dom $f_i$ of $f_i$ at $x$. We also give an application of (*) to asymptotical analysis related to a result by Choquet, and prove that (*) remains true when the epigraph of the Legendre-Fenchel conjugate of $f$ is weak* complete and pointed, and the $f_i$ are lower-semicontinuous.

    137-148
14. ON THE EXISTENCE OF BAYESIAN ESTIMATES IN NONLINEAR STATISTICAL MODELS WITH COMPACT PARAMETER SPACE UNG NGOC QUANG PDF

    149-160