Issue 3, Volume 31, December 2006

2006 · Open access

1. ON COLORINGS OF SPLIT GRAPHS NGO DAC TAN, LE XUAN HUNG PDF

   ▸ Abstract

   A graph $G = (V,E)$ is called a split graph if there exists a partition $V = I \cup K$ such that the subgraphs of $G$ induced by $I$ and $K$ are empty and complete graphs, respectively. In this paper, we determine chromatic polynomials for split graphs and characterize chromatically unique split graphs. Some sufficient conditions for split graphs to be Class one are also proved. In particular, we prove that the conjecture posed by Hilton and Zhao is true for split graphs.

   195-204
2. AN OPTIMIZATION PROBLEM IN MATRIX DATA DEPENDENCE ANALYSIS NGUYEN BAC VAN PDF

   ▸ Abstract

   The paper treats the problem of stepwise maximizing a sum of squared bilinear forms which stems from the dependence analysis of several data matrices. A constructive approach is presented which leads to clear-cut properties of the maximization process.

   205-217
3. THE WEIGHTED RELATIVE EXTREMAL FUNCTIONS AND WEIGHTED CAPACITY LE MAU HAI, NGUYEN VAN KHUE, PHAM HOANG HIEP PDF

   ▸ Abstract

   The aim of the present paper is to investigate the weighted relative extremal functions and weighted capacities with weights in the Cegrell classes $\mathcal F$ and $\mathcal E$. Some results on the connection between the weighted capacities with the weighted relative extremal functions are established. Moreover, we give a characterization of weighted capacities $C_{n,u}$ through $u$ and prove the absolute continuity of $C_{n,u}$ with respect to the Sadullaev’s weighted capacity $\mathcal P_{n,u}$.

   219-230
4. ENDPOINT BOUNDEDNESS FOR SOME MULTILINEAR OPERATORS REN YUPING PDF

   ▸ Abstract

   In this paper, we prove the endpoint estimates for some multilinear operators related to the Littlewood-Paley operator and Marcinkiewiecz integral operator.

   231-247
5. ON THE PLANCHEREL THEOREM FOR THE OLEVSKII TRANSFORM SEMYON B. YAKUBOVICH PDF

   ▸ Abstract

   We deal here with a class of integral transformations with respect to parameters of hypergeometric functions or the index transforms. In particular, we treat the familiar Olevskii transform, which is associated with the Gauss hypergeometric function as a kernel. It involves, in turn, as particular cases index transforms of the Mehler-Fock type which are used in the mathematical theory of elasticity. Boundedness $L_2$- properties for the Olevskii transform are investigated. The Plancherel theorem is proved. It shows that the Olevskii transform is an isometric isomorphism between two weighted $L_2$ - spaces. More examples of such isomorphisms are exhibited for the Mehler-Fock type transforms.

   249-260
6. ON LEVY’S CONVERGENCE THEOREMS OF TWO-PARAMETER MULTIVALUED RANDOM PROCESSES NGO HOANG LONG, VU VIET YEN PDF

   ▸ Abstract

   In this paper we prove the Levy’s upward and downward theorems for the convergence of two-parameter multivalued random processes in Hausdorff’s sense.

   261-267
7. INEQUALITIES FOR MULTILINEAR LITTLEWOOD-PALEY OPERATORS ON CERTAIN HARDY SPACES LIU LANZHE PDF

   ▸ Abstract

   In this paper, the boundedness for the multilinear Littlewood-Paley operators on certain Hardy and Herz-Hardy spaces are obtained.

   269-281
8. TIKHONOV REGULARIZATION ALGORITHM FOR PSEUDOMONOTONE VARIATIONAL INEQUALITIES NGUYEN THANH HAO PDF

   ▸ Abstract

   We establish a convergence theorem for the Tikhonov regularization algorithm applied to finite-dimensional pseudomonotone variational inequalities. Thus the open question stated by Facchinei and Pang in [1, p. 1129] is answered in affirmative. Several examples are given to analyze the obtained results.

   283-289
9. SOME INEQUALITIES FOR NORMAL OPERATORS IN HILBERT SPACES S. S. DRAGOMIR PDF

   ▸ Abstract

   Some inequalities for normal operators in Hilbert spaces are given. For this purpose, some results for vectors in inner product spaces due to Buzano, Dunkl-Williams, Hile, Goldstein-Ryff-Clarke, Dragomir-Sándor and the author are employed.

   291-300