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20 July 2005, Volume 25 Issue 3 Previous Issue    Next Issue

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INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES A. Azizi Acta mathematica scientia,Series B. 2005, 25 (3):  385-394.  Abstract ( 837 )   RICH HTML PDF (178KB) ( 3843 )   Save The aim of this paper is to study the conditions by which a P-prime sub- module can be expressed as a ¯nite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given. References | Related Articles | Metrics

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ON THE PRODUCT OF G\^ATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES CHEN Chi-Sheng, CHENG Li-Xin Acta mathematica scientia,Series B. 2005, 25 (3):  395-400.  Abstract ( 600 )   RICH HTML PDF (107KB) ( 881 )   Save A locally convex space is said to be a Gˆateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gˆateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Fr´echet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS. References | Related Articles | Metrics

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COINCIDENCE THEOREMS IN PRODUCT G-CONVEX SPACES DING XIEPING Acta mathematica scientia,Series B. 2005, 25 (3):  401-407.  Abstract ( 560 )   RICH HTML PDF (119KB) ( 1125 )   Save By applying the technique of continuous partition of unity, some new co- incidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature. Related Articles | Metrics

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(r,s)-STABILITY OF UNFOLDING OF |$\Gamma$-EQUIVARIANT PROBLEM LIU Heng-Xin, ZHANG San-Mu Acta mathematica scientia,Series B. 2005, 25 (3):  408-418.  Abstract ( 615 )   RICH HTML PDF (296KB) ( 759 )   Save In this paper,the $\Gamma$-equivariant $(s,t)$-equivalence  relation and $\Gamma$-equivariant infinitesimally  $(r,s)$-stability of $\Gamma$-equivariant bifurcation problem are defined. The criterion for $\Gamma$-equivariant infinitesimally $(r,s)$-stability is proven when $\Gamma$ is a compact finite Lie group . Transversality condition is used to characterize the stability. References | Related Articles | Metrics

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ON THE BOREL SUMMABILITY OF FORMAL SOLUTIONS FOR SOME FIRST ORDER SINGULAR PDES WITH IRREGULAR SINGULARITY CHEN Hua, ZHANG Zhi-Xiong Acta mathematica scientia,Series B. 2005, 25 (3):  419-426.  Abstract ( 955 )   RICH HTML PDF (123KB) ( 1000 )   Save In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a enumerable directions, the formal solutions are Borel summable. References | Related Articles | Metrics

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FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE Yuan-Yi-Rang Acta mathematica scientia,Series B. 2005, 25 (3):  427-438.  Abstract ( 633 )   RICH HTML PDF (357KB) ( 1289 )   Save Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite dif- ference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thoroughly and completely solved. References | Related Articles | Metrics

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COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE FANG Gen-Sun, XIE Pei-Xin Acta mathematica scientia,Series B. 2005, 25 (3):  439-448.  Abstract ( 565 )   RICH HTML PDF (153KB) ( 1012 )   Save The order of computational complexity of all bounded linear functional approximation problem is determined for the generalized Sobolev class W p (Id), Nikolskii class Hk 1(Id) in the worst (deterministic), stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes W p (Id) and Hk 1(Id) is intractable in worst case setting, but is tractable with respect to stochastic and average case setting. References | Related Articles | Metrics

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LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS Park Chun-Gil Acta mathematica scientia,Series B. 2005, 25 (3):  449-454.  Abstract ( 621 )   RICH HTML PDF (177KB) ( 902 )   Save It is shown that for a derivation $$f(x_1 \circ \cdots \circ x_{j-1}\circ x_j\circ  x_{j+1} \circ \cdots \circ x_k)= \sum_{j=1}^k x_1\circ \cdots \circ x_{j-1}\circ x_{j+1}\circ \cdots\circ x_k \circ f(x_j)$$ on a $JB^*$-algebra ${\cal B}$, there exists a unique ${\Bbb C}$-linear $*$-derivation $D : {\cal B} \rightarrow {\cal B}$ near the derivation. References | Related Articles | Metrics

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EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP Hn 1 SONG Ying-Qing, YANG Xiao-Beng, QIN Jiao-Hua Acta mathematica scientia,Series B. 2005, 25 (3):  455-469.  Abstract ( 631 )   RICH HTML PDF (208KB) ( 848 )   Save The purpose of this paper is to prove existence of minimisers of the functional $$J(K,u):=\int_{\Omega\setminus K}f(L_u){\rm d}x+\alpha  \int_{\Omega\setminus K}|u-g|^q {\rm d}x+\beta \sdqe(K\cap\Omega),$$ where $\Omega$ is an open set of the Heisenberg group $\hn$, $K$ runs over all closed sets of $\hn$, $u$ varies in $C_H^1(\Omega\setminus K)$, $\alpha$, $\beta >0,q\ge 1,g\in  L^q(\Omega)\cap L^\infty(\Omega)$ and $f:R^{2n} \rightarrow R$ is a convex function  satisfying some  structure conditions (H$_1$)(H$_2)$(H$_3)$ (see below). References | Related Articles | Metrics

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THE COMPARISON OF GREEN FUNCTION |FOR QUASI-LINEAR ELLIPTIC EQUATION ZHENG Shen-Zhou, KANG Xiu-Yang Acta mathematica scientia,Series B. 2005, 25 (3):  470-480.  Abstract ( 560 )   RICH HTML PDF (152KB) ( 1020 )   Save A generalization of the usual Green function to a kind of nonlinear elliptic equation of divergence form is discussed. The regularity and comparison principle of Green function in the sense of distribution are shown. References | Related Articles | Metrics

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PERSISTENCE OF RESONANT INVARIANT TORI WITH NON-HAMILTONIAN PERTURBATION BAI Yu-Zhen, SHU De-Meng Acta mathematica scientia,Series B. 2005, 25 (3):  481-491.  Abstract ( 582 )   RICH HTML PDF (144KB) ( 862 )   Save A persistence theorem for resonant invariant tori with non-Hamiltonian per- turbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method. The results obtained are extensions of Chicone’s for the three dimensional non-Hamiltonian systems. References | Related Articles | Metrics

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THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES CHU Yu-Meng Acta mathematica scientia,Series B. 2005, 25 (3):  492-504.  Abstract ( 597 )   RICH HTML PDF (156KB) ( 874 )   Save The main aim of this paper is to discuss the following  two problems:  \\  Problem I: Given  $X\in H^{n\times m}$ (the set of all $n\times m$ quaternion matrices),  $\Lambda={\rm diag}(\lambda_1, \cdots$, $\lambda_m)\in H^{m\times m}$,  find $A\in BSH_\geq^{n\times n}$  such that $AX=X\Lambda$, where $BSH_\geq^{n\times n}$   denotes the set of all $n\times n$ quaternion matrices which are bi-self-conjugate and nonnegative definite.\\  ProblemⅡ: Given  $B\in H^{n\times m}$, find $\overline{B}\in S_E$  such that  $\|B-\overline{B}\|_Q=\min_{A\in S_E}\|B-A\|_{Q},$  where $S_{E}$ is the solution set of problem Ⅰ,  $\|\cdot\|_Q$ is the  quaternion matrix norm. The necessary and sufficient conditions for $S_E$  being nonempty are obtained.  The general form of elements in  $S_E$ and the expression of the unique solution $\overline{B}$   of problem Ⅱ are given.   References | Related Articles | Metrics

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SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES Li Xiaoyan,Leng Gangsong Acta mathematica scientia,Series B. 2005, 25 (3):  505-510.  Abstract ( 627 )   RICH HTML PDF (105KB) ( 1283 )   Save The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.   References | Related Articles | Metrics

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EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES M.R. Pournaki,M. Tousi Acta mathematica scientia,Series B. 2005, 25 (3):  511-514.  Abstract ( 623 )   RICH HTML PDF (173KB) ( 1133 )   Save Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p) 6= 0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R=p. References | Related Articles | Metrics

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TWO PROBLEMS ABOUT COMPOSITION OPERATORS ON HARDY SPACE TUN Shu-Hong, WANG Mao-Fa, LIU Pei-De Acta mathematica scientia,Series B. 2005, 25 (3):  515-524.  Abstract ( 594 )   RICH HTML PDF (148KB) ( 1082 )   Save In this paper, two problems about composition operator on Hardy space are considered. Firstly, a new estimation of the norm of a class of composition operators is given. Secondly, the cyclic behavior of the adjoint operator of a composition operator is discussed. References | Related Articles | Metrics

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ON THE STRONG LAW OF LARGE NUMBERS QIU De-Hua, GAN Shi-Xin Acta mathematica scientia,Series B. 2005, 25 (3):  525-532.  Abstract ( 559 )   RICH HTML PDF (123KB) ( 1001 )   Save This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general random variable sequences. As applications of the result the authors characterize p-smoothableness of Banach space. Some generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann- Jørgensen and Pisier theorem are obtained. References | Related Articles | Metrics

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EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS HAN Pi-Gong Acta mathematica scientia,Series B. 2005, 25 (3):  533-544.  Abstract ( 573 )   RICH HTML PDF (157KB) ( 851 )   Save This paper deals with the existence of solutions to the elliptic equation − u− µ u |x|2 = u + |u|2∗−2u + f(x, u) in , u = 0 on @ , where  is a bounded domain in RN(N ≥ 3), 0 ∈ , 2 = 2N N−2 ,  > 0,  6∈ µ, µ is the spectrum of the operator − − µI |x|2 with zero Dirichlet boundary condition, 0 < µ < ¯µ, ¯µ = (N−2)2 4 , f(x, u) is an asymmetric lower order perturbation of |u|2∗−1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved. References | Related Articles | Metrics

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ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS HU Guo-En Acta mathematica scientia,Series B. 2005, 25 (3):  545-554.  Abstract ( 554 )   RICH HTML PDF (140KB) ( 1008 )   Save Lp(Rn) (1 < p < 1) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1 < p < 1) and the weak type (H1(Rn), L1(Rn)) boundedness for the corresponding commutators. A new interpolation theorem is also established. References | Related Articles | Metrics

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THE DECOMPOSITION OF STATE SPACE FOR MARKOV CHAIN IN RANDOM ENVIRONMENT HU Di-He Acta mathematica scientia,Series B. 2005, 25 (3):  555-568.  Abstract ( 560 )   RICH HTML PDF (165KB) ( 1091 )   Save This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples. References | Related Articles | Metrics

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MULTIPLICATION OF WEAK FUNCTIONS DING Jia-Qi, WANG Zhen Acta mathematica scientia,Series B. 2005, 25 (3):  569-576.  Abstract ( 557 )   RICH HTML PDF (104KB) ( 926 )   Save This paper is a contionuation of [1] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions in [2]. References | Related Articles | Metrics