Issue 2, Volume 23, December 1998

1998 · Open access

1. GLOBAL STABILITY IN A MODEL OF SINGLE-SPECIES POPULATION DYNAMICS IN A PERIODIC PATCHY ENVIRONMENT TRINH TUAN ANH PDF

   ▸ Abstract

   We consider a model of single-species population dynamics in a periodic patchy environment and prove a sufficient condition for the
   existence of a globally asymptotically stable, strictly positive (component-wise) and periodic solution.

   185-193
2. STRONG CONSISTENCY OF LEAST SQUARES ESTIMATES AND MEAN SQUARE REGRESSION NGUYEN BAC VAN PDF

   ▸ Abstract

   We prove that the least squares estimates of regression parameters are strongly consistent if and only if the regression is the mean
   square one.

   195-205
3. SEPARATELY HOLOMORPHIC FUNCTIONS ON COMPACT SETS NGUYEN THAI SON PDF

   ▸ Abstract

   The main aim of this paper is to give a characterization for $\mathcal H(Z)$ to have the property $(DN)$, where $Z$ is a Stein space, and to give conditions for a compact set $K$ in a locally irreducible Stein space not to be pluripolar in every irreducible branch of all neighbourhoods of $K$.

   207-216
4. ON COHEN-MACAULAYNESS AND GORENSTEINNESS OF REES ALGEBRAS OF INTERGRALLY CLOSED FILTRATIONS OF HEIGHT TWO EQUIMULTIPLE IDEALS DUONG QUOC VIET PDF

   217-229
5. SEMI-TRACES AND PROCESSES OF PETRI NETS TRAN VAN DUNG PDF

   ▸ Abstract

   It is well known that the processes of a Petri net represent its true concurrent behaviour [11]. For the safe nets, the processes can
   be replaced by traces on firing sequences [2, 3]. In the present paper we generalize this result for a special class of nets which is strictly larger than the class of safe nets. Namely, we prove that the processes of such nets can be replaced by some semi-traces on firing sequences. We also show that for a net in which every final process has a global observation, some set of its final semi-traces on firing sequences forms a prime event structure, and hence its induced finitary algebraic domain is equivalent to the one generated by the set of processes.

   231-246
6. ON $F$-DISCRETE DISTRIBUTION PHAM XUAN BINH PDF

   ▸ Abstract

   We investigate a new family of discrete distributions which are called $F$-discrete distributions. A moment recursion formula and some limit theorems for these distributions are proved. These results are similar to those for the well-known $F$-distributions in the continuous case.

   247-256
7. NORMAL STRUCTURE AND FIXED POINT PROPERTY IN LINEAR METRIC SPACES T. D. NARANG PDF

   257-262
8. RELATIVE PRIMENESS OF ENTIRE FUNCTIONS JIAZHANG ZHOU, XIN-HOU HUA PDF

   ▸ Abstract

   In this note, we will discuss the relative primeness of entire functions. In particular, we will answer a problem due to C. C. Yang.

   263-267
9. HOPF'S FORMULA FOR LIPSCHITZ SOLUTIONS OF HAMILTON-JACOBI EQUATIONS WITH CONCAVE-CONVEX HAMILTONIAN HA TIEN NGOAN PDF

   ▸ Abstract

   We extend Hopf's formula for Lipschitz solutions of Hamilton-Jacobi equation to the case where the Hamiltonian $H(p) = H^\prime(p^\prime, p^{\prime\prime})$ is a concave-convex function.

   269-293
10. A CLASSIFICATION OF CONTRACTIVE MAPPINGS IN PROBABILISTIC METRIC SPACES DO HONG TAN PDF

    ▸ Abstract

    In this work we define some classes of contractive mappings in probabilistic metric spaces, establish the relation between them and prove a fixed point theorem.

    295-302
11. FRECHET-VALUED MEROMORPHIC FUNCTIONS ON COMPACT SETS IN $\mathbb C^n$ NGUYEN VAN DONG PDF

    ▸ Abstract

    Let $F$ be a Frechet space. The main aim of this paper is to prove that $[F^*_{bor}]^*\in (LB_{\infty})$ if and only if $M(X,[F^*_{bor}]^*)=M_{\omega}(X,[F^*_{bor}]^*)$ for every compact uniqueness subset $X$ of $\mathbb C^n$ . We also prove that a compact set $X$ in $\mathbb C^n$ is pluripolar if and only if $X$ is unique and $M(X, F) = M_{\omega}(X, F)$ for every Frechet space $F \in (DN)$.

    303-316
12. WEAKLY HOLOMORPHIC EXTENSIONS AND THE CONDITION (L) NGUYEN VAN HAO, BUI DAC TAC PDF

    ▸ Abstract

    In this note we investigate relations between the condition (L) and weakly holomorphic extensions and separately holomorphic functions in indinite dimension.

    317-323
13. INTÉGRATION STOCHASTIQUE MULTIVOQUE ET INCLUSIONS DIFFÉRENTIELLES STOCHASTIQUES RÉTROGRADES A. BOUCHEN, A. EL ARNI, Y. OUKNINE, M. N'ZI PDF

    ▸ Abstract

    We will present several results concerning multivalued stochastic integration and the existence of solution for some backward stochastic differential inclusion under various conditions, including non-Lipschitz case.

    325-345
14. APPROXIMATION ORDERS IN THE CONDITIONAL CENTRAL LIMIT THEOREM FOR WEAKLY DEPENDENT RANDOM VARIABLES BUI KHOI DAM PDF

    ▸ Abstract

    Let $(X_n)_{n\geq 1}$ be a stationary, strong mixing sequence of random variables with $EX_n=0$, $EX^2_n=1$ and let $B\in\sigma(X_1,X_2,\dots,X_n,\dots)$ with $P(B) > 0$. In this note we establish an estimation for the quantity
    $$\Delta_n(B)=\sup\limits_{t\in R}|P(S_n.(ES_n^2)^{-1/2} < t|B)-\Phi(t),$$
    where $\Phi(t)$ is a standard normal distribution function and $S_n=\sum_{i=1}^nX_i$.

    347-358