Issue 1, Volume 33, April 2008

2008 · Open access

1. SINGULARITY OF PROBABILITY MEASURE IN FRACTAL GEOMETRY VU THI HONG THANH, NGUYEN NHUY, LE XUAN SON PDF

   ▸ Abstract

   Let $\mu$ be the probability measure induced by $S=\sum_{i=1}^{\infty}3^{-i}X_i$, where $X_1,X_2, \dots$ are independent identically distributed random variables each taking integer values $0, 1, a$ with equal probability $1/3$, where $a$ is a parameter. Let $\alpha(s,a)$ (resp. $\underline{\alpha}(s,a)$, $\overline{\alpha}(s,a)$) denote the local dimension (resp. lower, upper local dimension) of $s\in\mathrm{supp}\mu$, and let

   $$E(a)=\{\alpha: \alpha(s,a)=\alpha \text{ for some } s\in\mathrm{supp}\mu\},$$

   $$\overline{\alpha}=\sup\{\overline{\alpha}(s,a):s\in\mathrm{supp}\mu\}; \underline{\alpha}(a)=\inf\{\underline{\alpha}(s,a): s\in\mathrm{supp}\mu\}.$$

    In this paper, we prove that for $a = 4$ we have 

   $$\overline{\alpha}(4)=1, \underline{\alpha}(4)=11-\dfrac{\log(1+\sqrt{5})-\log 2}{\log 3} \text{ and } E=[\underline{\alpha}(4),\overline{\alpha}(4)].$$

   3-16
2. EXISTENCE RESULTS FOR INITIAL VALUE PROBLEMS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL INCLUSIONS IN BANACH SPACES A. SGHIR PDF

   ▸ Abstract

   Existence results for initial value problems for neutral functional differential inclusions are given. The results are proved by direct applications of topological transversality methods based on the degree theory for $\chi$-Lipschitz multimappings.

   17-26
3. RECOGNITION OF THE LINEAR GROUPS OVER THE BINARY FIELD BY THE SET OF THEIR ELEMENT ORDERS M. R. DARAFSHEH, Y. FARJAMI, A. MAHMIANI PDF

   ▸ Abstract

   In this paper we will prove that the simple group $PSL_{14}(2)$ is recognizable by the set of its element orders, that is to say if $G$ is a 1nite group with the same set of element orders as $PSL_{14}(2)$, then $G \cong PSL_{14}(2)$.

   27-38
4. ON A PROBLEM BY N. KALTON AND THE SPACE $l^p(I)$ NUNO C. FREIRE, M. F. VEIGA PDF

   ▸ Abstract

   We prove that each infinite dimensional quasi-Banach space has a closed, proper infinite dimensional subspace, so answering the Atomic Problem by N. Kalton in the affirmative. We obtain applications concerning the structure of the separable quasi-Banach spaces and of $l^p(I)$, $0 < p < 1$.

   39-44
5. SOME PROPERTIES OF GROWTH FOR COMPOSITE ENTIRE FUNCTIONS WITH DEFICIENT FUNCTION JIANWU SUN PDF

   ▸ Abstract

   In this paper, we solve a problem of C. T. Chuang and C. C. Yang concerning the characteristic function of the composite function.

   45-52
6. LIPSCHITZ ESTIMATES FOR MULTILINEAR LITTLEWOOD-PALEY OPERATORS ON HARDY TYPE SPACES LIU LANZHE PDF

   ▸ Abstract

   In this paper, the boundedness for some multilinear operators generated by Littlewood-Paley operators and Lipschitz functions on Hardy and Herz-Hardy spaces is obtained.

   53-64
7. INEQUALITIES FOR DIRICHLET SERIES WITH POSITIVE TERMS P. CERONE, S. S. DRAGOMIR PDF

   ▸ Abstract

   Some fundamental inequalities for Dirichlet series with positive terms by utilising certain classical results due to Hölder, Cebysev, Pólya-Szegö, Grüss and others are established.

   65-84
8. ON THE DIFFERENCE EQUATION $x_{n+1}=\dfrac{\alpha x_{n-l}+\beta x_{n-k}}{Ax_{n-l}+Bx_{n-k}}$ E. M. ELABBASY, H. EL-METWALLY, E. M. ELSAYED PDF

   ▸ Abstract

   In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence $$x_{n+1}=\dfrac{\alpha x_{n-l}+\beta x_{n-k}}{Ax_{n-l}+Bx_{n-k}},\quad n=0,1,\dots$$ where the parameters $\alpha,\beta, A$ and $B$ are positive real numbers and the initial conditions $x_{-p}, x_{-p+1},\dots,x_{-1}$ and $x_0\in (0,\infty)$ where $p = \max\{l, k\}$.

   85-94