Issue 3, Volume 28, December 2003

2003 · Open access

1. LOCALLY BOUNDED HOLOMORPHIC FUNCTIONS AND THE MIXED HARTOGS THEOREM NGUYEN VAN KHUE, NGUYEN DINH LAN PDF

   ▸ Abstract

   This paper deals with the conditions which allow the local boundedness of every holomorphic function taking value in Frechet space. These results are also applied to get different versions of the Hartogs theorem of mixed type.

   241-258
2. GENERAL FORM OF LINEAR FUNCTIONALS ON HARDY SPACES BUI KHOI DAM PDF

   ▸ Abstract

   In this note, we give a general form of linear functionals on martingale Hardy spaces $\mathcal H_{\Phi}$, where the Young function $\Phi$ has finite power and its conjugate function $\Psi$ is of the form $\Psi(x)=\Psi_1(x^2)$ with $\Psi_1$ being also a Young function. Moreover, we discuss the relationship between the martingale Hardy space $\mathcal H_{\Phi}$ and the spaces $\mathcal K_{\Psi}$.

   259-266
3. ON HAMILTON CYCLES IN CONNECTED TETRAVALENT METACIRCULANT GRAPHS WITH NON-EMPTY FIRST SYMBOL NGO DAC TAN, TRAN MINH TUOC PDF

   ▸ Abstract

   In this paper, we show that every connected tetravalent metacirculant graph $MC(m,n,\alpha,S_0,S_1,\dots,S_{\mu})$ with $S_0\not =\emptyset$ possesses a Hamilton cycle if $m = 1$ or $2$ or $m > 2$ and both $m$ and $n$ are odd.

   267-278
4. BIFURCATION OF SOLUTIONS FOR AN ELLIPTIC DEGENERATE PROBLEM S. AMRAOUI, M. IGUERNANE PDF

   ▸ Abstract

   We investigate the existence and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation: $-x^r\Delta u=\lambda u+|u|^{p-1}u$ in $(0; 1)$; $u (0) = u(1) = 0$. This model is related to a simplified version of the nonlinear Wheeler-De Witt equation as it appears in quantum cosmological models, see [8, 9, 10].

   279-295
5. LOGARITHMIC INTEGRALS, SOBOLEV SPACES AND RADON TRANSFORM IN THE PLANE DANG VU GIANG PDF

   ▸ Abstract

   We prove that the set $\{\varphi_0,\varphi_1,\varphi_4,\dots,\varphi_{3k+1},\dots\}$ of Hermite functions is an orthogonal system in the Sobolev space $H^1(\mathbf{R}) = H_{(1)}(\mathbf{R}).$ Furthermore, the logarithmic integral of a function $f$ from the real Hardy space $\mathcal H^1(\mathbf{R})$ is exactly the primitive function of $-\tilde{f}$ (the Hilbert transform of $f$). And more interesting formulas are found for Radon transform of Hermite-like functions.

   297-307
6. ON VNR RINGS AND P-INJECTIVITY ROGER YUE CHI MING PDF

   ▸ Abstract

   This note contains the following results: (1) A is strongly regular iff every non-zero factor ring of A is a semi-prime ring containing a non-zero reduced p-injective left ideal which is a left annihilator; (2) A is an ELT von Neumann regular ring iff A is a semi-prime MELT ring whose essential right ideals are idempotent iff A is a semi-prime ELT ring such that for any essential left ideal L of A, either AA/L is p-injective or A/LA is flat; (3) If A is a semi-prime ring whose simple left modules are either YJ-injective or projective, then the Jacobson radical of A is zero. If, further, each maximal right ideal of A is either injective or a two-sided ideal of A, then A is either strongly regular or right self-injective regular. Several conditions are given for a left Noetherian ring to be left Artinian.

   309-318
7. ON SINGULAR INTEGRAL EQUATIONS WITH THE CARLEMAN SHIFTS IN THE CASE OF THE VANISHING COEFFICIENT LE HUY CHUAN, NGUYEN MINH TUAN PDF

   ▸ Abstract

   Based on the well-known necessary and sufficient condition for the linear-fractional function to be the generator of a cyclic group of $n$-terms, this paper describes the general form of all linear-fractional functions which are Carleman shifts on the unit circle. Our main result deals with the solvability in a closed form for a class of singular integral equations with Carleman shifts on the unit circle in the case where the coefficient vanishes on the curve.

   319-333
8. TYPES OF VARIETIES OF RECOGNIZABLE $\omega$-LANGUAGES AND EILENBERG CORRESPONDENCES PHAN TRUNG HUY PDF

   ▸ Abstract

   In this paper, we prove that the correspondences $\underline{V}\Rightarrow V^{\omega},$ $\underline{V}\Rightarrow \vec{V}$, proposed by D. Perrin (1982) between $M$-varieties $\underline{V}$'s of finite monoids and varieties of recognizable omega-languages $V^{\omega}$'s and $\vec{V}$'s are one-to-one. New definitions of saturation and syntactic monoid of adherences of $\omega$-languages basing on the limit operation are introduced. As consequence, a new type of varieties generated by adherences of $\omega$-languages is defined and studied.

   335-344
9. ARE SEVERAL RECENT GENERALIZATIONS OF EKELAND'S VARIATIONAL PRINCIPLE MORE GENERAL THAN THE ORIGINAL PRINCIPLE? TRUONG QUANG BAO, PHAN QUOC KHANH PDF

   ▸ Abstract

   We show that several recent results proposed as generalizations of Ekeland's variational principle are in fact equivalent to the original principle.

   345-350