Issue 2, Volume 28, August 2003

2003 · Open access

1. NEW INEQUALITIES FOR CSISZÁR DIVERGENCE AND APPLICATIONS S. S. DRAGOMIR PDF

   ▸ Abstract

   In this paper we point out some new inequalities for Csiszár $f$-divergence and apply them for particular instances of distances between two probability distributions.

   123-134
2. SUPPLY-DEMAND THEOREMS FOR FINITE PROBABILISTIC AUTOMATA PHAM TRA AN PDF

   ▸ Abstract

   In this paper, we show that there are supply-demand theorems for finite probabilistic automata, but here the notion of state is understood in a rather general sense. It is notion of hyperstate.

   135-145
3. ON NON-LINEAR APPROXIMATIONS OF PERIODIC FUNCTIONS OF BESOV CLASSES USING WAVELET DECOMPOSITIONS MAI XUAN THAO PDF

   ▸ Abstract

   In the present paper, we extend results of Dinh Dung [5] on nonlinear $n$-term $L_q$-approximation and non-linear widths to the Besov class $SB^{\omega}_{p,\theta}$ where $1\leq p, q\leq \infty, 0 < \theta \leq \infty$, and $\omega$ is a given function of modulus of smoothness type.

   147-157
4. ON THE GENERALIZED CONVOLUTION FOR I-TRANSFORM NGUYEN XUAN THAO, TRINH TUAN PDF

   ▸ Abstract

   An I-transform and a generalized convolution for this transform are introduced and their properties are considered

   159-174
5. GROWTH OF A CLASS OF COMPOSITE ENTIRE FUNCTIONS JIANWU SUN PDF

   ▸ Abstract

   In this paper, we obtain the following results:
   Let $f_1, f_2$ and $g_1, g_2$ be four transcendental entire functions with $T(r, f_1) = O^{\ast}((\log r)^{\nu}e^{(\log r)^{\alpha}})$ and $T(r, g_1) = O^{\ast}((\log r)^{\beta})$ (i.e., there exist four positive constants $K_1, K_2, K_3$ and $K_4$ such that $K_1\leq \frac{T(r,f_1)}{(\log r)^{\nu}e^{(\log r)^{\alpha}}}\leq K_2$ and $K_3\leq \frac{T(r,g_1)}{(\log r)^{\beta}}\leq K_4$).
   If $T(r, f_1) \thicksim T(r, f_2),$ $T(r, g_1) \thicksim T(r, g_2)$ $(r \to\infty)$, then
   $$T(r,f_1(g_1))\thicksim T(r,f_2(g_2))\quad (r\to\infty, r\not\in E)$$
   where $\nu > 0, 0 < \alpha < 1, \beta > 1$ and $\alpha \beta < 1$ and $E$ is a set of finite logarithmic measure.
   We solved a problem due to C. C. Yang concerning the characteristic functions of the composite functions.

   175-183
6. A DISCRETE LOCATION PROBLEM HOANG TUY, NGUYEN DUC NGHIA, LE SI VINH PDF

   ▸ Abstract

   An efficient algorithm based on discrete monotonic optimization is proposed for finding the largest ball centered in a given $\underline{\text{finite}}$ $S\subset \mathbb R^n$ and disjoint from any of $m$ given balls in $\mathbb R^n$.

   185-199
7. BAYESIAN ESTIMATION UNDER ESTIMATION CONSTRAINT PHAM GIA THU, TRAN LOC HUNG PDF

   ▸ Abstract

   We suppose that a constraint is imposed on the value of the estimator in Bayesian Estimation Theory and study the distribution of this estimator under various hypotheses, using the two main loss functions: the absolute value and the quadratic.

   201-207
8. A SIMPLE PROOF OF JUNG’S THEOREM ON POLYNOMIAL AUTOMORPHISMS OF $\mathbf{C}^2$ NGUYEN VAN CHAU PDF

   ▸ Abstract

   The Automorphism Theorem, discovered first by Jung in 1942, asserts that if $k$ is a field, then every polynomial automorphism of $k^2$ is a finite product of linear automorphisms and automorphisms of the form $(x, y) \mapsto (x + p(y), y)$ for $p \in k[y]$. We present here a simple proof for the case $k = \mathbf{C}$ by using Newton-Puiseux expansions.

   209-214
9. OPTIMALITY CONDITIONS IN REVERSE CONVEX OPTIMIZATION M. LAGHDIR PDF

   ▸ Abstract

   Necessary and sufficient optimality conditions associated with the problem of minimizing a convex function subject to a reverse convex constraint are obtained in this paper.

   215-223
10. STRONG MINIMALITY OF GAUSSIAN-SUMMING NORM V. TARIELADZE, R. VIDAL PDF

    ▸ Abstract

    By means of a sequence $\varphi_{\cdot}:= (\varphi_n)_{n\in\mathbb N}$ of square-integrable functions a notion of a $\varphi_{\cdot}$-summing operator is defined. It is shown that if $\inf_n\|\varphi_n\|_2 > 0$, then any $\varphi_{\cdot}$-summing operator is Gaussian-summing. This recovers a previously known result, which asserts the same in case when $\varphi_{\cdot}:= (\varphi_n)_{n\in\mathbb N}$ is an orthonormal sequence.

    225-240