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20 April 2007, Volume 27 Issue 2 Previous Issue    Next Issue

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CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES#br# OF AM-SPACES Ding Guanggui Acta mathematica scientia,Series B. 2007, 27 (2):  225-231.  DOI: 10.1016/S0252-9602(07)60021-6 Abstract ( 1555 )   RICH HTML PDF (141KB) ( 1406 )   Save This article presents a novel method to prove that: let E be an AM-space and if dim E≥ 3, then there does not exist any odd subtractive isometric mapping from the unit sphere S(E) into $S[L(\Omega,\mu)]$. In particular, there does not exist any real linear isometry from E into $L(\Omega,\mu)$. Related Articles | Metrics

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THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR Wu Changchun; Zhang Runchu Acta mathematica scientia,Series B. 2007, 27 (2):  232-242.  DOI: 10.1016/S0252-9602(07)60022-8 Abstract ( 1255 )   RICH HTML PDF (169KB) ( 845 )   Save Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error. Related Articles | Metrics

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A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE--STEP NONINTERIOR#br# CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS Zhang Liping Acta mathematica scientia,Series B. 2007, 27 (2):  243-253.  DOI: 10.1016/S0252-9602(07)60023-X Abstract ( 1200 )   RICH HTML PDF (174KB) ( 1321 )   Save A noninterior continuation method is proposed for semidefinite complementarity problem (SDCP). This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are: (i) it is well defined for the monotones SDCP; (ii) it has to solve just one linear system of equations at each step; (iii) it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions. Related Articles | Metrics

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SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m Harun Polat; Feyzi Basar Acta mathematica scientia,Series B. 2007, 27 (2):  254-266.  DOI: 10.1016/S0252-9602(07)60024-1 Abstract ( 1365 )   RICH HTML PDF (206KB) ( 2699 )   Save Kizmaz [13] studied the difference sequence spaces $\ell_\infty(\Delta),~c(\Delta)$, and $c_0(\Delta)$. Several article dealt with the sets of sequences of $m$-th order difference of which are bounded, convergent, or convergent to zero. Altay and Ba\c sar [5] and Altay, Ba\c sar, and Mursaleen [7] introduced the Euler sequence spaces $e_0^r$, $e_c^r$, and $e_\infty^r$, respectively. The main purpose of this article is to introduce the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$, and $e_\infty^r(\Delta^{(m)})$ consisting of all sequences whose $m^{th}$ order differences are in the Euler spaces $e_0^r$, $e_c^r$, and $e_\infty^r$, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the $\alpha$-, $\beta$-, and $\gamma$-duals of the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$, and $e_\infty^r(\Delta^{(m)})$, and the Schauder basis of the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space $e_c^r(\Delta^{(m)})$. Related Articles | Metrics

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THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET Hu Dihe; Zhang Xiaomin Acta mathematica scientia,Series B. 2007, 27 (2):  267-273.  DOI: 10.1016/S0252-9602(07)60025-3 Abstract ( 1282 )   RICH HTML PDF (151KB) ( 1225 )   Save First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators. Related Articles | Metrics

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THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS Wang Yang Acta mathematica scientia,Series B. 2007, 27 (2):  274-282.  DOI: 10.1016/S0252-9602(07)60026-5 Abstract ( 986 )   RICH HTML PDF (173KB) ( 1405 )   Save This article consider, for the following heat equation $$\left\{ \begin{array}{ll} \displaystyle\frac{u_t}{|x|^s}-\Delta_p u=u^q ,\ \ &(x,t) \in \Omega \times (0,T),\\ u(x,t)= 0 ,&(x,t) \in \partial \Omega\times(0,T) ,\\ u(x,0)=u_0(x) ,& u_0(x)\ge 0,\quad u_0(x)\not\equiv0 \end{array} \right.$$ the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, where $\Omega$ is a smooth bounded domain in $R^N(N >p)$, $0\in \Omega ,\Delta_p u={\rm div}(|\nabla u|^{p-2}\nabla u),0\le s\le 2, p\ge 2, p-1 Related Articles | Metrics

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ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES Gan Shixin; Chen Pingyan Acta mathematica scientia,Series B. 2007, 27 (2):  283-290.  DOI: 10.1016/S0252-9602(07)60027-7 Abstract ( 1218 )   RICH HTML PDF (151KB) ( 1409 )   Save Let {Xni, 1≤ n,i<∞} be an array of rowwise NA random variables and {an,n≥1} a sequence of constants with 0n↑∞. The limiting behavior of maximum partial sums $\frac{1}{a_n}\max\limits_{1\leq k\leq n}|\sum\limits^k_{i=1}X_{ni}|$ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2]. Related Articles | Metrics

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DEFICIENT FUNCTIONS OF RANDOM DIRICHLET SERIES Zhou Junying; Sun Daochun Acta mathematica scientia,Series B. 2007, 27 (2):  291-296.  DOI: 10.1016/S0252-9602(07)60028-9 Abstract ( 1181 )   RICH HTML PDF (137KB) ( 949 )   Save In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely(a.s.) no deficient functions is proved. Related Articles | Metrics

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QUASI-PERMUTATION REPRESENTATIONS OF ALTERNATING AND SYMMETRIC GROUPS Houshang Behravesh; Mohammad Hossein Jafari Acta mathematica scientia,Series B. 2007, 27 (2):  297-300.  DOI: 10.1016/S0252-9602(07)60029-0 Abstract ( 1089 )   RICH HTML PDF (122KB) ( 1060 )   Save The quantities c(G), q(G) and p(G) for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group A{n} and the symmetric group S{n} are calculated. It is shown that [c(G)=q(G)=p(G)=n,] when G= A{n} or S{n}. Related Articles | Metrics

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ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS Du Zhihua; Du Jinyuan Acta mathematica scientia,Series B. 2007, 27 (2):  301-307.  DOI: 10.1016/S0252-9602(07)60030-7 Abstract ( 1479 )   RICH HTML PDF (136KB) ( 1248 )   Save In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu. Related Articles | Metrics

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GALERKIN-PETROV METHODS OF TOEPLITZ OPERATORS ON DIRICHLET SPACE Wang Xiaofeng; Cao Guangfu Acta mathematica scientia,Series B. 2007, 27 (2):  308-316.  DOI: 10.1016/S0252-9602(07)60031-9 Abstract ( 1124 )   RICH HTML PDF (167KB) ( 1167 )   Save The convergence of several Galerkin--Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry. Related Articles | Metrics

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COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE#br# ORTHOGONAL GROUPS Wang Dengyin Acta mathematica scientia,Series B. 2007, 27 (2):  317-328.  DOI: 10.1016/S0252-9602(07)60032-0 Abstract ( 989 )   RICH HTML PDF (182KB) ( 989 )   Save All parabolic subgroups and Borel subgroups of $P\Omega(2m+1,F)$ over a linearable field F of characteristic 0 are shown to be complete groups, provided m>3. Related Articles | Metrics

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THE EIGENVALUE PROBLEM FOR THE LAPLACIAN EQUATIONS Shao Zhiqiang; Hong Jiaxing Acta mathematica scientia,Series B. 2007, 27 (2):  329-337.  DOI: 10.1016/S0252-9602(07)60033-2 Abstract ( 1693 )   RICH HTML PDF (157KB) ( 2145 )   Save This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u=-λu, $x\in \Omega$, $u=0$, $x\in\partial\Omega$, where $\Omega\subset R^{n}$ is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T. Yau et al. Related Articles | Metrics

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BOUNDEDNESS AND CONVERGENCE FOR THE NON-LIENARD TYPE DIFFERENTIAL EQUATION Zhao Liqin Acta mathematica scientia,Series B. 2007, 27 (2):  338-346.  DOI: 10.1016/S0252-9602(07)60034-4 Abstract ( 1277 )   RICH HTML PDF (167KB) ( 1506 )   Save In this article, the author studies the boundedness and convergence for the non--Lienard type differential equation x' = a(y)-f(x), y' =b(y)β(x)-g(x)+e(t), where a(y), b(y), f(x), g(x), β(x) are real continuous functions in y∈ R or x ∈ R, β(x)≥ 0 for all x and e(t) is a real continuous function on R+={t: t≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended. Related Articles | Metrics

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ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR HYPERBOLIC-ELLIPTIC COUPLED SYSTEM IN RADIATING GAS Ruan Lizhi; Zhang Jing Acta mathematica scientia,Series B. 2007, 27 (2):  347-360.  DOI: 10.1016/S0252-9602(07)60035-6 Abstract ( 1344 )   RICH HTML PDF (176KB) ( 1551 )   Save In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one--dimensional system of the radiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L2-energy method. Related Articles | Metrics

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THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS ON WEIGHTED SPACES#br# AND HERZ-TYPE SPACES Zhou Weijun; Ma Bolin; Xu Jingshi Acta mathematica scientia,Series B. 2007, 27 (2):  361-372.  DOI: 10.1016/S0252-9602(07)60036-8 Abstract ( 1271 )   RICH HTML PDF (188KB) ( 1410 )   Save The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon--Zygmund kernel on Herz-type spaces is also considered. Related Articles | Metrics

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EVENTUAL STABILITY OF IMPULSIVE DIFFERENTIAL SYSTEMS Zhang Yu; Sun Jitao Acta mathematica scientia,Series B. 2007, 27 (2):  373-380.  DOI: 10.1016/S0252-9602(07)60037-X Abstract ( 1220 )   RICH HTML PDF (152KB) ( 1306 )   Save In this article, criteria of eventual stability are established for impulsive differential systems using piecewise continuous Lyapunov functions. The sufficient conditions that are obtained significantly depend on the moments of impulses. An example is discussed to illustrate the theorem. Related Articles | Metrics

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SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS II, NONLINEAR CAUSTIC Yuan Mingsheng Acta mathematica scientia,Series B. 2007, 27 (2):  381-394.  DOI: 10.1016/S0252-9602(07)60038-1 Abstract ( 1181 )   RICH HTML PDF (205KB) ( 891 )   Save This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions. Related Articles | Metrics

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SOME DUAL KINEMATIC FORMULAS Xie Fengfan; Li Deyi Acta mathematica scientia,Series B. 2007, 27 (2):  395-404.  DOI: 10.1016/S0252-9602(07)60039-3 Abstract ( 1381 )   RICH HTML PDF (156KB) ( 1415 )   Save In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals. Related Articles | Metrics

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OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION Dong Lingzhen; Chen Lansun; Sun Lihua Acta mathematica scientia,Series B. 2007, 27 (2):  405-412.  DOI: 10.1016/S0252-9602(07)60040-X Abstract ( 1257 )   RICH HTML PDF (156KB) ( 1615 )   Save This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort. Related Articles | Metrics

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A NOVEL FIXED POINT THEOREM AND ITS APPLICATIONS Zhai Chengbo; Guo Chunmei Acta mathematica scientia,Series B. 2007, 27 (2):  413-420.  DOI: 10.1016/S0252-9602(07)60041-1 Abstract ( 1695 )   RICH HTML PDF (148KB) ( 1426 )   Save In this article, a novel fixed point theorem in C[0,1] space is established by using the properties of fixed point index. This theorem is then applied to prove the existence of positive solutions for three-point boundary value problems and generalizes some previous results. Related Articles | Metrics

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GLOBALLY BOUNDED IN-TIME SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM#br# MODELLING CHEMOTAXIS Zhong Xinhua; Jiang Song Acta mathematica scientia,Series B. 2007, 27 (2):  421-429.  DOI: 10.1016/S0252-9602(07)60042-3 Abstract ( 1050 )   RICH HTML PDF (155KB) ( 1095 )   Save In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller--Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained. Related Articles | Metrics

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EXISTENCE OF GLOBAL SMOOTH SOLUTION FOR SCALAR CONSERVATION LAWS WITH DEGENERATE VISCOSITY IN 2-DIMENSIONAL SPACE Chen Jing; Xu Xuewen Acta mathematica scientia,Series B. 2007, 27 (2):  430-436.  DOI: 10.1016/S0252-9602(07)60043-5 Abstract ( 1233 )   RICH HTML PDF (146KB) ( 984 )   Save This article concerns the existence of global smooth solution for scalar conservation laws with degenerate viscosity in 2-dimensional space. The analysis is based on successive approximation and maximum principle. Related Articles | Metrics

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RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN #br# SEMICONDUCTOR SCIENCE Li Yong Acta mathematica scientia,Series B. 2007, 27 (2):  437-448.  DOI: 10.1016/S0252-9602(07)60044-7 Abstract ( 1274 )   RICH HTML PDF (182KB) ( 1610 )   Save In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler--Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales. Related Articles | Metrics