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20 July 2007, Volume 27 Issue 3 Previous Issue    Next Issue

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ON MIN'S ZETA-FUNCTION AND HERMITE ELLIPTIC OPERATOR Ding Xiaqi; Ding Yi Acta mathematica scientia,Series B. 2007, 27 (3):  449-455.  DOI: 10.1016/S0252-9602(07)60045-9 Abstract ( 1205 )   RICH HTML   PDF (130KB) ( 1177 )   Save In this note, the authors study some fundamental properties on a Min's zeta-function and explore its connection with Hermite elliptic operator. Related Articles | Metrics

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ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE Yu Jinghu; Shieh Narn-Rueih Acta mathematica scientia,Series B. 2007, 27 (3):  456-464.  DOI: 10.1016/S0252-9602(07)60046-0 Abstract ( 1158 )   RICH HTML   PDF (181KB) ( 1147 )   Save Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant set K for the system. In this article, the authors construct some random measure $\mu_\o$ supported on random subset $K_\o$ of $K$, $\mu_\o$ having some "non-standard" multifractal structure, which contrasts the well-known multifractal formalism for the invariant measure of system {S1,…, SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh--Taylor [14], and Morters--Shieh [12]. Related Articles | Metrics

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EQUIDISTRIBUTION OF CLOSED ORBITS OF BILLIARD FLOWS ON THE PLANE Xia Hongqiang; Ge Yunfei; Zhang Zhengjie Acta mathematica scientia,Series B. 2007, 27 (3):  465-472.  DOI: 10.1016/S0252-9602(07)60047-2 Abstract ( 1271 )   RICH HTML   PDF (173KB) ( 1074 )   Save The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed. Related Articles | Metrics

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POISSON ALGEBRA STRUCTURES ON sp2l(CQ) WITH NULLITY m Jin Quanqin; Tong Jie Acta mathematica scientia,Series B. 2007, 27 (3):  473-490.  DOI: 10.1016/S0252-9602(07)60048-4 Abstract ( 1171 )   RICH HTML   PDF (212KB) ( 1404 )   Save Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article, the noncommutative Poisson algebra structures on sp$_{2\ell}(\widetilde{\C}_Q)$ are determined. Related Articles | Metrics

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OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION: THE METHOD OF A-HARMONIC APPROXIMATION Chen Shuhong; Tan Zhong Acta mathematica scientia,Series B. 2007, 27 (3):  491-508.  DOI: 10.1016/S0252-9602(07)60049-6 Abstract ( 1614 )   RICH HTML   PDF (222KB) ( 2160 )   Save In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution. Related Articles | Metrics

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NONTRIVIAL SOLUTION FOR A CLASS OF SEMILINEAR BIHARMONIC EQUATION INVOLVING CRITICAL EXPONENTS Yao Yangxin; Wang Rongxin; Shen Yaotian Acta mathematica scientia,Series B. 2007, 27 (3):  509-514.  DOI: 10.1016/S0252-9602(07)60050-2 Abstract ( 1407 )   RICH HTML   PDF (151KB) ( 1561 )   Save In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev--Hardy inequality. Related Articles | Metrics

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LIMITING BEHAVIOR OF UNIFORM RECURSIVE TREES Su Chun; Feng Qunqiang; Liu Jie Acta mathematica scientia,Series B. 2007, 27 (3):  515-521.  Abstract ( 1223 )   RICH HTML   PDF (145KB) ( 943 )   Save The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of $\zeta_{n,m}$, the number of branches with size $m$ in a uniform recursive tree of order $n$, converges weakly to a Poisson distribution with parameter $\frac1m$ with convergence of all moments. The size of any large branch tends to infinity almost surely. Related Articles | Metrics

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SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES Ding Xieping Acta mathematica scientia,Series B. 2007, 27 (3):  522-534.  Abstract ( 1316 )   RICH HTML   PDF (145KB) ( 877 )   Save By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure. Related Articles | Metrics

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A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES J.M. Soriano; C. Ding Acta mathematica scientia,Series B. 2007, 27 (3):  535-540.  DOI: 10.1016/S0252-9602(07)60053-8 Abstract ( 1250 )   RICH HTML   PDF (138KB) ( 1258 )   Save It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectories. Related Articles | Metrics

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ON THE INVERSE IMAGE SET OF RATIONAL FUNCTIONS Sun Daochun Acta mathematica scientia,Series B. 2007, 27 (3):  541-548.  DOI: 10.1016/S0252-9602(07)60054-X Abstract ( 1191 )   RICH HTML   PDF (151KB) ( 1461 )   Save This article studies the inverse image of rational functions. Several theorems are obtained on the Julia set expressed by the inverse image, and a mistake is pointed out in H.Brolin' theorem incidentally. Related Articles | Metrics

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BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES Liu Yue; Wang Zhengping Acta mathematica scientia,Series B. 2007, 27 (3):  549-560.  DOI: 10.1016/S0252-9602(07)60055-1 Abstract ( 1281 )   RICH HTML   PDF (188KB) ( 1957 )   Save This article considers the equation △2 u =f(x,u) with boundary conditions either $u|_{\partial\Omega}=\frac{\partial u}{\partial n}|_{\partial\Omega}=0 $ or $u|_{\partial\Omega}=\bigtriangleup u|_{\partial\Omega}=0$, where $f(x,t)$ is asymptotically linear with respect to t at infinity, and $\Omega$ is a smooth bounded domain in RN, N >4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x,t). Related Articles | Metrics

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THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET Hu Dihe; Zhang Xiaomin Acta mathematica scientia,Series B. 2007, 27 (3):  561-573.  DOI: 10.1016/S0252-9602(07)60056-3 Abstract ( 1350 )   RICH HTML   PDF (191KB) ( 1299 )   Save In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end. Related Articles | Metrics

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KAMENEV-TYPE OSCILLATION CRITERIA FOR DELAY DIFFERENCE EQUATIONS Cheng Jinfa Acta mathematica scientia,Series B. 2007, 27 (3):  574-580.  DOI: 10.1016/S0252-9602(07)60057-5 Abstract ( 1255 )   RICH HTML   PDF (138KB) ( 1399 )   Save Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △ (pn (△ (xn + cn xn - τ) )γ ) + qnxn - σβ = 0,n = 0, 1, 2,… which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10]. Related Articles | Metrics

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SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION Yao Zheng'an; Zhou Wenshu Acta mathematica scientia,Series B. 2007, 27 (3):  581-601.  DOI: 10.1016/S0252-9602(07)60058-7 Abstract ( 1421 )   RICH HTML   PDF (220KB) ( 1321 )   Save In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed. Related Articles | Metrics

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SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS E.M.E. Zayed; M.A. El-Moneam Acta mathematica scientia,Series B. 2007, 27 (3):  602-610.  DOI: 10.1016/S0252-9602(07)60059-9 Abstract ( 1338 )   RICH HTML   PDF (145KB) ( 1644 )   Save The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))'+δ1p(t)x'(t)+δ2q(t)f(x(g(t)))=0, for 0≤ t0 ≤t, where δ1=± 1 and δ2=± 1. The functions p,q,g:[t0,∞ )→R, f:R→R are continuous, a(t)>0, p(t)≥0,q(t)≥0 for t≥t0,limt→∞g(t)=∞, and q is not identically zero on any subinterval of [t0,∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable. Related Articles | Metrics

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GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD Xie Naqing; Xu Hongwei Acta mathematica scientia,Series B. 2007, 27 (3):  611-618.  DOI: 10.1016/S0252-9602(07)60060-5 Abstract ( 1263 )   RICH HTML   PDF (147KB) ( 1132 )   Save This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form. Related Articles | Metrics

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LOOMIS-WHITNEY'S INEQUALITY ABOUT MIXED BODY Si Lin; Leng Gangsong Acta mathematica scientia,Series B. 2007, 27 (3):  619-624.  DOI: 10.1016/S0252-9602(07)60061-7 Abstract ( 1167 )   RICH HTML   PDF (135KB) ( 1185 )   Save In this article, the authors establish two theorems for mixed body, which are the generalizations of the well-known Loomis--Whitney's inequality. Related Articles | Metrics

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UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS Chen Zhihua; Li Yanhua; Yan Qiming Acta mathematica scientia,Series B. 2007, 27 (3):  625-634.  DOI: 10.1016/S0252-9602(07)60062-9 Abstract ( 1279 )   RICH HTML   PDF (172KB) ( 1380 )   Save In this article, two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved. Related Articles | Metrics

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FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS Yu Hongwang; Wang Zhiming Acta mathematica scientia,Series B. 2007, 27 (3):  635-644.  DOI: 10.1016/S0252-9602(07)60063-0 Abstract ( 1282 )   RICH HTML   PDF (169KB) ( 1170 )   Save In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level. Related Articles | Metrics

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STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE Yu Yumei; Wang Wendi Acta mathematica scientia,Series B. 2007, 27 (3):  645-655.  DOI: 10.1016/S0252-9602(07)60064-2 Abstract ( 1426 )   RICH HTML   PDF (171KB) ( 1379 )   Save In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems. Related Articles | Metrics

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OSCILLATION OF SOLUTIONS OF THE SYSTEMS OF QUASILINEAR HYPERBOLIC EQUATION UNDER NONLINEAR BOUNDARY CONDITION Deng Lihu; Mu Chunlai Acta mathematica scientia,Series B. 2007, 27 (3):  656-662.  DOI: 10.1016/S0252-9602(07)60065-4 Abstract ( 1294 )   RICH HTML   PDF (138KB) ( 1358 )   Save Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition. Related Articles | Metrics

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SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC#br# EQUATIONS OF SECOND ORDER Wen Guochun Acta mathematica scientia,Series B. 2007, 27 (3):  663-672.  DOI: 10.1016/S0252-9602(07)60066-6 Abstract ( 1336 )   RICH HTML   PDF (177KB) ( 1196 )   Save The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved. Related Articles | Metrics