Issue 2, Volume 18, December 1993

1993 · Open access

1. PURSUIT PROBLEMS WITHOUT DISCRIMINATION OF EVASION OBJECT IN LINEAR DIFFERENTIAL GAMES NGUYEN VAN CHAU, PHAN HUY KHAI PDF

   173-190
2. LOCALLY LIPSCHITZ SET-VALUED MAPS ON TOPOLOGICAL VECTOR SPACES AND SURJECTIVITY THEOREMS DUONG TRONG NHAN PDF

   191-202
3. ON THE ACTION OF THE STEENROD ALGEBRA ON THE MODULAR INVARIANTS OF SPECIAL LINEAR GROUP NGUYEN SUM PDF

   203-213
4. A SUFFICIENT CONDITION FOR BIJECTIVITY OF POLYNOMIAL MAPS ON THE REAL PLANE NGUYEN VAN CHAU PDF

   ▸ Abstract

   It is shown that the non-singular polynomial map $f$ of $R^2$ into itself is a global diffeomorphism of $R^2$ if $0\not\in Co\{Df(x)v\| \|x\| > Const.\}$ for a vector $v$. This result is a variant of a theorem of Olech and Meister [3, 6] for the polynomial case.

   215-218
5. A NEW INTEGRAL CONTAINING THE JACOBI POLYNOMIAL S. D. BAJPAI PDF

   ▸ Abstract

   A new integral containing the Jacobi polynomials is given with an elementary multiplier function.

   219-223
6. ON THE ROCKAFELLAR DERIVATIVE OF MARGINAL FUNCTIONS AND APPLICATIONS DO VAN LUU PDF

   ▸ Abstract

   In this paper, some evaluations of the directional Rockafellar derivative of a function defined by $\varphi_F(x)=\mathrm{inf}\{f(x,y)\,|\, y\in F(x)\}$ via the directional Clarke and Rockafellar derivative of $f$ are shown. These evaluations are applied to find necessary optimality conditions for generalized optimal control problems governed by hemivariational inequalities.

   225-236
7. A SUBCLASSIFICATION OF UNIMODAL DISTRIBUTIONS NGUYEN VAN THU PDF

   ▸ Abstract

   We introduce and study classes $\mathcal P_{\alpha}$,  $\alpha > 0$, of $\alpha$-times unimodal distributions. Various characterizations of these distributions are obtained and relations between them and fractional calculus are established.

   237-249
8. THE SOLUTION OF A CLASS OF DUAL INTEGRAL EQUATIONS INVOLVING HANKEL TRANSFORM NGUYEN VAN NGOC PDF

   251-263
9. MODULAR INVARIANTS AND THE mod $p$ COHOMOLOGY ALGEBRA OF THE INFINITE SYMMETRIC GROUP NGUYEN HUU VIET HUNG PDF

   ▸ Abstract

   We determine the mod $p$ cohomology algebra of the infinite symmetric group for $p$ an odd prime by using what we call the Dickson characteristic classes. These classes are constructed by means of the Dickson-Mùi invariants of $GL(n,\mathbb Z_p)$ on the algebra $E(x_1,\dots,x_n)\otimes \mathbb Z_p[y_1,\dots,y_n]$. They are closely related to the classical Chern classes.

   265-294
10. AN IMPROVEMENT FOR PARALLEL-ITERATED RUNGE-KUTTA-NYSTRÖM METHODS NGUYEN HUU CONG PDF

    ▸ Abstract

    This paper deals with predictor-corrector (PC) iteration of Runge-Kutta-Nyström (RKN) methods for integrating initial-value problems for special second-order, ordinary differential equations. We consider RKN correctors based on direct collocation techniques with high stage-order so that the stage-values can be used by extrapolation techniques to construct high-order predictior methods with no additional sequential right-hand side evaluations and without increasing number of processors. Having the high-order predictor in addition with the small convergence factor and error constant, the parallel-iterated PC methods based on direct collocation RKN correctors considered in this paper show the improved efficiency when they are compared to the PIRKN methods available in the literature.

    295-307
11. ON THE CALCULATION OF GENERALIZED GRADIENTS FOR A MARGINAL FUNCTION PHAM HUY DIEN, DINH THE LUC PDF

    309-326