Issue 2, Volume 31, August 2006

2006 · Open access

1. SOME PROPERTIES OF GENERALIZED LOCAL COHOMOLOGY MODULES AMIR MAFI PDF

   ▸ Abstract

   Let $R$ be a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R, M$ and N be two finitely generated $R$-modules. Let $t$ be a positive integer. We prove that if $R$ is local with maximal ideal $\mathfrak{m}$ and $M \otimes_R N$ is of finite length then $H^t_{\mathfrak{m}}(M,N)$ is of finite length for all $t \geq 0$ and
   $$l_R(H^t_{\mathfrak{m}}(M,N))\leq \sum\limits_{i=0}^tl_R(\mathrm{Ext}_R^i(M,H^{t-i}_{\mathfrak{m}}(N))).$$

   This yields $l_R(H^t_{\mathfrak{m}}(M,N))=l_R(\mathrm{Ext}^t_R(M,N))$.

   Additionally, we show that $\mathrm{Ext}^i_R(R/\mathfrak{a},N)$ is Artinian for all $i \leq t$ if and only if $H^i_{\mathfrak{a}}(M,N)$ is Artinian for all $i \leq t$. Moreover, we show that whenever $\dim(R/\mathfrak{a}) = 0$ then $H^t_{\mathfrak{a}}(M,N)$ is Artinian for all $t \geq 0$.

   99-102
2. SOME REMARKS ON APPROXIMATION OF PLURISUBHARMONIC FUNCTIONS NGUYEN QUANG DIEU PDF

   103-108
3. CONVERGENCE OF TWO-PARAMETER MULTIVALUED MARTINGALES IN THE LIMIT VU VIET YEN PDF

   ▸ Abstract

   In this paper, some convergence results of two-parameter multivalued martingales in the limit are presented.

   109-114
4. COMPORTEMENT ASYMPTOTIQUE DE LA SOLUTION D’UNE SORTE D’EQUATION INTEGRALE STOCHASTIQUE DANS $\mathbf{R}^n$ HISAO FUJITA YASHIMA, ANNA GIANESINI PDF

   ▸ Abstract

   We consider a stochastic integral equation in $\mathbf{R}^n$, i.e. integral equation to which a stochastic perturbation is added. In the first place we consider the linear equation with constant coefficients. For this equation, first of all, we establish the uniform boundedness of the solution and, by using this uniform boundedness and by considering the solution in a suitable Hilbert space, we prove the existence of an invariant measure for this equation; the invariant measure will be proved to be unique. In the second place we consider the non-linear equation with suitable conditions and, by using a method developed for the linear equation, we prove the existence of an invariant measure for this non-linear equation.

   115-129
5. SOLVABLE SUBGROUPS IN THE DIVISION RING OF REAL QUATERNIONS BUI XUAN HAI, LE KHAC HUYNH PDF

   ▸ Abstract

   Maximal solvable subgroups of the multiplicative group $H^*$ of the division ring $H$ of real quaternions were described in [2]. In this paper we study the structure of the solvable subgroups of $H^*$.

   131-136
6. ON CERTAIN SUBCLASS OF MULTIVALENT FUNCTIONS OF COMPLEX ORDER HALIT ORHAN, ELIF GUNES, MASLINA DARUS PDF

   ▸ Abstract

   The aim of the present paper is to show several properties of functions belonging to a subclass $M^p_{n,\Omega}(A,B,\lambda,b)$ (where $b$ is complex number with $\mathbf{Re}(b) > 0$ and $A$ ve $B$ are two arbitrary constants with $−1\leq B < A \leq 1$). Coefficient estimates and some distortion theorems for this class of functions are obtained. For this class we also derive the radii of close-to-convexity, starlikeness, and convexity. Further, an application involving fractional calculus for functions in $M^p_{n,\Omega}(A,B,\lambda,b)$ is given.

   137-148
7. THE UNIQUENESS OF VISCOSITY SOLUTIONS OF SECOND ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS IN A HILBERT SPACE OF TWO-DIMENSIONAL FUNCTIONS TRAN VAN BANG PDF

   ▸ Abstract

   In this paper we prove the uniqueness of viscosity solutions of the second order nonlinear partial differential equations associated with the Stokes and Euler operators in a Hilbert space of two-dimensional functions.

   149-165
8. ON THE FUNCTIONAL EQUATION $P(f) = Q(g)$ IN NON-ARCHIMEDEAN FIELD NGUYEN TRONG HOA PDF

   ▸ Abstract

   In this paper, we study the existence of non-constant meromorphic solutions $f$ and $g$ of the functional equation $P(f) = Q(g)$, where $P(z)$ and $Q(z)$ are given nonlinear polynomials with coefficients in the non-Archimedean field $\mathbb K$.

   167-180
9. SHARP WEIGHTED INEQUALITIES FOR MULTILINEAR INTEGRAL OPERATORS LANZHE LIU PDF

   ▸ Abstract

   A sharp inequality for some multilinear operator related to a certain integral operator is obtained. The operator includes the Littlewood-Paley operator, the Marcinkiewicz operator and the Bochner-Riesz operator. As an application, we derive the weighted $L^p$ $(p > 1)$ norm inequalities and $L \log L$ type estimate for the multilinear operator.

   181-194