Issue 2, Volume 33, August 2008

2008 · Open access

1. SOLVING DELAY DIFFERENTIAL EQUATIONS USING EMBEDDED SINGLY DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FUDZIAH ISMAIL, RAED ALI AL-KHASSAWNEH PDF

   ▸ Abstract

   In this paper we used three embedded diagonally implicit RungeKutta methods to solve a standard set of delay differential equations. Some of the methods share the FSAL (first stage as last) property and the same stage order. The Q-stability polynomials of the methods are obtained and their stability regions presented. Numerical results are tabulated and compared, from which we can conclude that the method with the highest order and the higher stage order is the most efficient.

   95-105
2. ON THE POLYCONVOLUTION FOR THE FOURIER COSINE AND FOURIER SINE TRANSFORMS NGUYEN XUAN THAO, NGUYEN DUC HAU PDF

   ▸ Abstract

   In this paper we introduce the polyconvolution for the Fourier cosine and Fourier sine integral transforms. It is applied for solving integral equations and systems of integral equations.

   107-122
3. A CLASS OF DELTA-PLURISUBHARMONIC FUNCTIONS AND THE COMPLEX MONGE-AMPERE OPERATOR NGUYEN QUANG DIEU, DAU HOANG HUNG PDF

   ▸ Abstract

   The aim of this note is to extend some fundamental properties of the complex Monge-Ampère operator for plurisubharmonic functions to the class of delta-plurisubharmonic functions. The main result is an analogue of the celebrated Bedford-Taylor comparision for plurisubharmonic functions.

   123-132
4. THE EXTREME VALUES OF LOCAL DIMENSION IN FRACTAL GEOMETRY VU THI HONG THANH PDF

   ▸ Abstract

   Let $\mu$ be the probability measure induced by $S=\sum_{i=0}^{\infty}q^{-i}X_i$, where $m \geqslant q \geqslant 2$ are integers and $X_0, X_1, \dots$ a sequence of independent identically distributed random variables each taking integer values $0, 1, \dots, m$ with equal probability $p = 1/(m + 1)$. Let $\alpha(s)$ (resp. $\alpha_*(s), \alpha^*(s)$) denote the local dimension (resp. lower, upper local dimension) of $s \in \mathrm{supp}\mu$, and let $$\alpha^*=\sup\{\alpha^*(s):s\in\mathrm{supp}\mu\}; \alpha_*=\inf\{\alpha_*(s):s\in \mathrm{supp}\mu\}.$$ We show that $$\alpha_*=\dfrac{\log(m+1)-\log(r+\sqrt{r^2+4(l+1)})+\log 2}{\log q}$$ for $rq\leqslant m < rq + r$; $r = 1,\dots, q − 1$ and $l = m − rq$.

   The special case of our result, $m = rq$ $(l = 0)$, was obtained earlier in [6].

   133-142
5. PRODUCT PROPERTIES IN WEIGHTED PLURIPOTENTIAL THEORY PHAM HOANG HIEP, PHUNG VAN MANH PDF

   ▸ Abstract

   In this article we study product properties in weighted pluripotential theory.

   143-153
6. SOME SUBCLASSES OF ANALYTIC FUNCTIONS WITH RESPECT TO $k$-SYMMETRIC POINTS ZHI-GANG WANG, DI SONG PDF

   ▸ Abstract

   In the present paper, we introduce two new subclasses $\mathcal P^{(k)}(\lambda, \alpha)$ and $\mathcal Q^{(k)}(\lambda, \alpha)$ of analytic functions with respect to $k$-symmetric points. Such results as integral representations, convolution properties and coefficient inequalities for these function classes are proven.

   155-161
7. ON THE ASSOCIATED PRIMES AND THE SUPPORT OF GENERALIZED LOCAL COHOMOLOGY MODULES NGUYEN VAN HOANG PDF

   ▸ Abstract

   In this note, we prove the following results: (1) if $\dim (N) \geqslant 3$ then $\mathrm{Ass}(H_I^i(M, N))$ is finite for all $i\geqslant 0$; (2) Let $d = \dim(R)$ and $s(I, M) = \mathrm{depth}(M/I^nM)$ for some large $n$. If $N$ has finite injective dimension then we have $H_I^i(M, N) = 0$ for all $i > d − s(I, M),$ $H_I^d(M, N)$ is Artinian, and $\mathrm{Supp}(H_I^{d−1}(M, N))$ is finite.

   163-171
8. THE GENERALIZED DISCRETIZED SEQUENTIAL PROBABILITY RATIO TEST AND ITS APPLICATION IN INSURANCE MATHEMATICS VOLKER MAMMITZSCH PDF

   ▸ Abstract

   WALD’s famous sequential probability ratio test for comparing two simple hypotheses $P_1$ and $P_2$ is extended to the case when instead of successive observations of i.i.d. random variables general observations can be taken and final decisions are allowed at a discrete series of pre-assigned time points. It is shown that the following properties are equivalent:

   (a) Each test of that type is closed.

   (b) The errors of first and second kind of those tests can be made arbitrarily small.

   (c) $P_1$ and $P_2$ are orthogonal probability measures.

   This result is applied to the risk process in insurance mathematics and a uniqueness problem is discussed.

   173-180
9. UNIQUENESS THEOREMS AND UNIQUENESS POLYNOMIALS FOR $p$-ADIC HOLOMORPHIC CURVES VU HOAI AN, TRAN DINH DUC PDF

   ▸ Abstract

   In this paper, using the techniques of value distribution theory in the $p$-adic case, we prove uniqueness theorems for nonconstant $p$-adic holomorphic curves and the existence of a class of strong uniqueness polynomials for algebraically nondegenerate $p$-adic holomorphic curves. It is shown that if $X$ is a hypersurface defined by a polynomial in this class, then $X$ is a unique range set for algebraically nondegenerate $p$-adic holomorphic curves.

   181-195
10. ON COFINITELY $\delta$-SEMIPERFECT MODULES L. V. THUYET, M. T. KOŞAN, T. C. QUYNH PDF

    ▸ Abstract

    Supplemented modules and $\oplus$-supplemented modules are useful in characterizing semiperfect modules and rings. Recently, the notion of cofinitely supplemented modules and $\delta$-supplemented modules were introduced as generalizations of supplemented modules. In this paper, $\oplus − co f_{\delta}$- supplemented and cofinitely δ-semiperfect modules are defined as generalizations of $\oplus$-cofinitely supplemented modules and cofinitely semiperfect modules. Several properties of these modules are obtained.

    197-207