Acta Mathematica Vietnamica
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Issue 2, Volume 21, December 1996
1996 · Open access
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ON ITO STOCHASTIC INTEGRAL WITH RESPECT TO VECTOR STABLE RANDOM MEASURES DANG HUNG THANG PDF171-181
▸ Abstract
Let $Z_p$ be a vector $p$-stable random measure with values in a $q$-smoothable Banach space, where $p > q$ if $p < 2$ and $q = 2$ if $p = 2$. It is shown that the stochastic integral $\int_0^1udZ_p$ can be defined for processes $u$ which are non-anticipating with respect to $Z_p$.
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WEAK EXTENSION OF FRECHET-VALUED HOLOMORPHIC FUNCTIONS ON COMPACT SETS AND LINEAR TOPOLOGICAL INVARIANTS LE MAU HAI PDF183-199
▸ Abstract
It is shown that every holomorphic function on a nuclear Frechet space $E$ with values in a Frechet space $F$ is of uniform type if
$E$ has the linear topological invariant $(\tilde{\Omega})$ and $F$ has the linear topological invariant $(DN)$ respectively. Based on the obtained result the equivalence of the holomorphicity and the weak holomorphicity of Frechet-valued functions on $\tilde{L}$-regular compact subsets in a nuclear Frechet space is established. -
ON A CLASS OF SINGULAR INTEGRAL EQUATIONS WITH ROTATIONS NGUYEN MINH TUAN PDF201-211
▸ Abstract
The paper deals with the singular integral equation
$$a(t)\varphi(t)+b(t)[S+MP_{\ell}\varphi](t)=f(t),$$
where $a(t) =\prod_{i=1}^m(t-\alpha_i)^{r_i}s(t)$. We will reduce the equation to the well-known Riemann boundary value problem and then describe all solution of the indicate problem in a closed form. -
ON A CLASS OF NONLINEAR ELLIPTIC EQUATIONS AND BOUNDARY VALUE PROBLEMS IN THE LIMIT DOMAIN HOANG QUOC TOAN PDF253-267
▸ Abstract
In this paper we study the boundary value problem for a class of high order nonlinear elliptic equations in the bounded domain $G_0$ with smooth boundary $\Gamma_0$ in the space $\mathbf{R}^n$ where the domain $G_0$ is considered as a limit (in some sense) of the family of domain $\{G_t\}$ which depend smoothly on a parameter $t\in [0; T]$ in S. G. Krein's sense when $t$ tends to 0.
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ON THE GEOMETRIC COMPOSED VARIABLE AND THE ESTIMATE OF THE STABLE DEGREE OF THE RENYI'S CHARACTERISTIC THEOREM TRAN KIM THANH, NGUYEN HUU BAO PDF269-277
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A PROPERTY OF FINITE MAXIMAL CODES NGUYEN HUONG LAM PDF279-287
▸ Abstract
We establish a property of finite maximal codes relating exponent $m$ such that $b^m$ is in the code for some letter $b$ to a structure pertaining to certain specific codewords. Consequently, we are able to propose some classes of finite codes that cannot be included in any finite maximal codes for almost all given exponents.
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A REMARK ON DIFFERENTIAL OPERATORS OF INFINITE ORDER HA HUY BANG PDF289-294
▸ Abstract
In this paper we give a necessary and sufficient condition for a linear differential operator of infinite order to act invariantly in the space of distributions with compact support.
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MODULES WITH FLAT SOCLES AND ALMOST EXCELLENT EXTENSIONS WANG DINGGUO PDF295-301
▸ Abstract
Modules (resp. rings) with flat socles are called FS-modules (resp. FS-rings) which are preserved by Morita equivalences and (almost) excellent extensions. One result of Xue Weimin [7] is generalized. We show that when $S$ is an almost excellent extension of $R$, if either ring is (i) left SF-ring, or (ii) right coherent, or (iii) left semi-hereditary, or (iv) left perfect, then so is another. This answers a question of Xue Weimin [8] in the affirmative.
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ON THE TWO-SIDED PREDICTABLE APPROXIMATION FOR STOCHASTIC PROCESSES NGUYEN MINH DUC PDF303-307
▸ Abstract
The two-sided predictable stochastic processes are introduced to show that they can approximate every bounded measurable stochastic process $(X_t(\omega), 0 < t\leq 1)\ P$-almost surely uniformly in $t$. Consequently, it is proved that the two-sided predictable algebra also generates the product $\sigma$-field $\mathcal B((0; 1])\otimes \mathcal F$.
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349-367