Acta Mathematica Vietnamica
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Issue 1, Volume 20, June 1995
1995 · Open access
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SYSTEMATIC BUILDING OF A DISTRIBUTED RECURSIVE ALGORITHM EXAMPLE: THE SHORTEST PATH ALGORITHM G. FLORIN, R. GÓMEX, I. LAVALLÉE PDF3-30
▸ Abstract
Designers of distributed algorithms must deal with a variety of issues including sequential algorithms design, communication protocols, fault tolerance. The distributed design must also include a proof step of the whole algorithm features. This paper gives a new scheme for the design of distributed algorithms. In this approach the design step is performed simultaneously with the proof step. Our distributed design method is mainly based on parallel recursive schemes, but recursivity is used in a distributed environment, so we use two existing and widely available tools: remote procedure call, and the PAR instruction parallel execution of threads.
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31-41
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THE IRREDUCIBLE MODULAR REPRESENTATIONS OF SEMIGROUPS OF ALL MATRICES TON THAT TRI PDF43-53
▸ Abstract
Let $M_n=M(n, F_q)$ be the semigroup of all $n\times n$ matrices over the field $F_q$ of $q$ elements. By using Dickson's invariants we construct a complete set of $q^n$ distinct irreducible $F_q[M_n]$ modules, called $H_{\beta}$ and give isomorphisms between them and the modules $F^{\alpha}$ which were constructed in [3] by the ''Weyl module'' construction.
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REMARKS ON KALTON'S PAPER: ''COMPACT CONVEX SETS AND COMPLEX CONVEXITY'' TRAN VAN AN, NGUYEN NHUY, LE HOANG TRI PDF55-66
▸ Abstract
Kalton [K] constructed compact convex sets which cannot be affinely embedded into the space $L_0$ of all measurable functions. This paper proves that compact convex sets constructed by Kalton's method have the fixed point property.
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PROPERTY $\overline{\overline{\Omega}}$ AND HOLOMORPHIC FUNCTIONS WITH VALUES IN A PSEUDOCONVEX SPACE HAVING A STEIN MORPHISM INTO A COMPLEX LIE GROUP NGUYEN MINH HA, THAI THUAN QUANG PDF67-83
▸ Abstract
It is shown that a Fréchet-Schwartz space $E$ with an absolute basis has the property $\overline{\overline{\Omega}}$ if and only if every holomorphic function on $D\times E$ with values in a pseudoconvex space having a Stein morphism into a complex Lie group, where $D$ is a Stein space, is of uniform type. In the scalar case, where $E$ is a nuclear Fréchet space, the result was established by Meise and Vogt [5].
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SPLINE COLLOCATION METHODS FOR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS OF SECOND ORDER NGUYEN MINH CHUONG, NGUYEN VAN TUAN PDF85-98
▸ Abstract
A spline collocation method is used to solve approximately a general class of boundary value problem for integro-differential equations of second order. Theorem of existence and uniqueness of approximant via diagonally dominant matrix is shown. Theorem of convergence rate of second order for approximate solutions is obtained,
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POLYHEDRAL ANNEXATION VS OUTER APPROXIMATION FOR THE DECOMPOSITION OF MONOTONIC QUASICONCAVE MINIMIZATION PROBLEMS HOANG TUY, BUI THE TAM PDF99-114
▸ Abstract
We discuss polyhedral annexation and outer approximation methods for the decomposition of linearly constrained quasiconcave minimization problems with a special structure of monotonicity. We show that polyhedral annexation is generally superior, except when the problem has some additional structure.
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HYPERSURFACES IN (DFC)-SPACES LE MAU HAI PDF129-143
▸ Abstract
It is shown that every hypersurface $H$ in a (DFM)-space $E$ is of uniform type. This means that there exist a continuous semi-norm $\rho$ on $E$ and a hypersurface $\widehat{H}$ in $E_{\rho}$, the Banach space associated to $\rho$, such that $H=\omega_{\rho}^{-1}(\widehat{H})$, where $\omega_{\rho}: E\to E_{\rho}$ is the canonical map.