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25 December 2008, Volume 28 Issue 6 Previous Issue    Next Issue

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Null Controllability of a Cascade System of Degenerate Parabolic Equations Liu Xu|Gao Hang|Lin Ping Acta mathematica scientia,Series A. 2008, 28 (6):  985-996.  Abstract ( 1844 )   RICH HTML PDF (313KB) ( 1456 )   Save This paper deals with null controllability of a cascade system governed by a semilinear heat equation and degenerate parabolic equation under appropriate assumptions. The control acts on only one equation . The critical point is to establish suitable observability inequalities. Related Articles | Metrics

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The Extension of Isometries Between Unit Spheres Li Lei Acta mathematica scientia,Series A. 2008, 28 (6):  997-001.  Abstract ( 1554 )   RICH HTML PDF (258KB) ( 1275 )   Save In this paper, the author studies the extension of isometries between unit spheres of real normed spaces. The author considers a new space E#, which is called the positively homogeneous dual space, and studies it under a new topology σ(E#, E). Then, the author shows that a class of surjective isometries between unit spheres of real normed spaces can be linearly isometrically extended to the whole space. Related Articles | Metrics

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Nonlinear Stability of Generalized Eady Problem in Finite Periodic Channel Cai Jingjing|Liu Yongming Acta mathematica scientia,Series A. 2008, 28 (6):  1002-1014.  Abstract ( 1866 )   RICH HTML PDF (347KB) ( 1311 )   Save Nonlinear stability criterion for the generalized Eady model is improved by establishing an optimal Poincaréinequality. The inequality is derived from a variational calculation considering an additional constraint of invariant of zonal momentum. Two cases that ρ(z)=ρ0 and ρ(z)=ρ0e-z/H are discussed, respectively, where ρ(z) is the prescribed reference-state density and ρ0 is a constant. The improved nonlinear stability criteria are the same as the linear ones provided that the ratios of the meridional width to the channel length are less than or equal to 0.84402 for the case one and 0.86068 for the case two, respectively. Related Articles | Metrics

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Jordan Hǒlder Theorem and Saturated Homomorphs Bai Ruipu Acta mathematica scientia,Series A. 2008, 28 (6):  1015-1022.  Abstract ( 1334 )   RICH HTML PDF (259KB) ( 1252 )   Save In this paper, we proved the Jordan-Hǒlder Theorem for n-Lie algebras. And the saturated homomorphs of n-Lie algebras are systematically studied. Related Articles | Metrics

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Fixed Point Theorems of u0 - concave Operators and Applications Zhai Chengbo;Li Yongjin Acta mathematica scientia,Series A. 2008, 28 (6):  1023-1028.  Abstract ( 2078 )   RICH HTML PDF (271KB) ( 1236 )   Save In this paper, the existence and uniqueness of positive fixed points for u0-concave operators is obtained by means of the properties of cone and monotone iterative technique. The results extend and improve the corresponding results. As an application, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for a class of Hammerstein integral equations. Related Articles | Metrics

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Rectifiability Properties of Varifolds Zhao Peibiao|Yang Xiaoping Acta mathematica scientia,Series A. 2008, 28 (6):  1029-1037.  Abstract ( 1210 )   RICH HTML PDF (387KB) ( 1526 )   Save The authors prove the following theorem: given a varifold V with the property that 0r→0uV(Cr(x))/rn<∞ for μV a.e. x∈ SptV , then V is rectifiable. Related Articles | Metrics

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The Sufficient and Necessary Conditions for Trigonometric Series Belonging to Ba Spaces Yu Dansheng|Zhou Songping Acta mathematica scientia,Series A. 2008, 28 (6):  1038-1045.  Abstract ( 1660 )   RICH HTML PDF (297KB) ( 1416 )   Save The present paper gives a sufficient and necessary condition for sine series and cosine series, with their coefficients satisfying NBV condition, belonging to Ba spaces. This is the first result on Ba spaces and can be regarded as an essential generalization of that on Lp spaces. Related Articles | Metrics

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On the Complex Oscillation Theory of Linear Differential Equations with Analytic Coefficients in the Unit Disc Cao Tingbin|Yi Hongxun Acta mathematica scientia,Series A. 2008, 28 (6):  1046-1057.  Abstract ( 2236 )   RICH HTML PDF (352KB) ( 1580 )   Save The complex oscillation theory of linear differential equations of the form L(f)=f(k)+Ak-1(z)f(k-1)+ … + A0(z)f=F(z)(k∈ N) is investigated, where the coefficients Aj(z) (j=0, … , k-1) and F(z) are analytic functions in the unit disc △={z:|z|<1}. The authors obtain several precise theorems about the hyper order, the hyper convergence exponent of zero points and fixed points of solutions of differential equations. Related Articles | Metrics

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The Uniqueness of the Decomposition of Lie Supertriple Systems Pan Yuxia|Zhang Qingcheng Acta mathematica scientia,Series A. 2008, 28 (6):  1058-1066.  Abstract ( 1673 )   RICH HTML PDF (297KB) ( 1369 )   Save This paper first shows the decomposition of the center, the derivation superalgebras and inner derivation superalgebras respectively according to the decomposition of Lie supertriple systems. It maily consider the decomposition of Lie supertriple systems with trivial center and uniqueness and the extension of the automorphism of a Lie supertriple system. Related Articles | Metrics

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Alternative Doi-Hopf Modules over Weak Hopf Algebras Jia Ling|Li Fang Acta mathematica scientia,Series A. 2008, 28 (6):  1067-1076.  Abstract ( 1687 )   RICH HTML PDF (274KB) ( 1081 )   Save In this paper, we first introduce the notion of weak alternative Doi-Hopf modules, and then mainly give the construction of adjoint functor to the functor from the category of weak alternative Doi-Hopf modules to the category of modules (resp. comodules) disregarding the coaction (resp. the action). Related Articles | Metrics

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Ringel-Hall Algebra of A∞&infin|_ type Hou Ruchen;Ye Yu Acta mathematica scientia,Series A. 2008, 28 (6):  1077-1087.  Abstract ( 1741 )   RICH HTML PDF (385KB) ( 1263 )   Save This is the first one of two papers studying the quantum group of sl ∞∞ type via the Ringel-Hall algebra of A∞∞ type. For this we need to deal with finite-dimensional representations of the infinite-dimensional path algebra kA∞∞ over any field k. In the present paper, we first study the category of the finite-dimensional representations of kA∞∞ by determining all its indecomposable objects and their extensions explicitly ; then we investigate the Ringel-Hall algebra H(kA∞∞) for a finite field k. The main viewpoint of this investigation is to regard H(kA∞∞) as the direct limit of the Ringel-Hall algebra H(kA∞) and H(kA∞) as the direct limit of the Ringel-Hall algebra H(kAn). In particular, we get a PBW-basis of H(kA∞∞) and show that H(kA∞∞) coincides with its composition subalgebra. Related Articles | Metrics

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Inertial Manifolds with Delays and Approximate Inertial Manifolds of a Class of Non-autonomous Retarded Evolution Equations with Quasi-Periodic Terms Li Xiang|Zhu Jianmin|Huang Jianhua Acta mathematica scientia,Series A. 2008, 28 (6):  1088-1096.  Abstract ( 1760 )   RICH HTML PDF (340KB) ( 1348 )   Save The present paper deals with the long-time behavior of a class of non-autonomous retarded evolution equations with quasi-periodic terms. First we prove the existence of the inertial manifolds with delay of the systems, then we construct the approximate inertial manifolds of the systems. Related Articles | Metrics

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The Semigroup Structure of Orthorings Zhou Yuanlan; Guo Yuqi; Wang zhengpan Acta mathematica scientia,Series A. 2008, 28 (6):  1097-1102.  Abstract ( 1668 )   RICH HTML PDF (236KB) ( 1189 )   Save A semiring is an orthoring, if it is the disjoint union of subrings and the set of its additive idempotents is a band semiring. An orthoring is called a T rthoring, if the set of its additive idempotents is a T band semiring. The semigroup structures of orthorings and some T orthorings are studied. Related Articles | Metrics

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Statistical Inference for the Burr Type XII Distribution Wang Bingxing Acta mathematica scientia,Series A. 2008, 28 (6):  1103-1108.  Abstract ( 1447 )   RICH HTML PDF (284KB) ( 1385 )   Save This paper obtains the new point estimate and interval estimate for the two-parameter Burr type XII distribution based on the progressively type II censored sample. Using Monte Carlo method, we compare the proposed estimators with the maximum likelihood estimators. The simulation results show that the proposed estimators outperform the maximum likelihood estimators. Finally, a numerical example is presented to illustrate the methods discussed in this paper. Related Articles | Metrics

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The M/M/2 Repairable Queue System with Two Repairmen Lv Shengli|Li Jingbo|Yue Dequan Acta mathematica scientia,Series A. 2008, 28 (6):  1109-1118.  Abstract ( 1463 )   RICH HTML PDF (330KB) ( 1138 )   Save In this paper, we consider the M/M/2 queueing system with service interruptions. The rates of server breakdown are different between busy time and idle time, and there are two repairmen in the system. We obtain the steady-state probabilities of the states, the steady-state availability and the steady-state queueing length, give the condition for the existence of the steady-state probabilities. Related Articles | Metrics

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Initial Value Problems for the Systems of Second Order Integro-differential Equations in Banach Space Song Guangxing|Wang Xiurong|Pai Xinying|Liang Shuxia Acta mathematica scientia,Series A. 2008, 28 (6):  1119-1127.  Abstract ( 1820 )   RICH HTML PDF (251KB) ( 1264 )   Save In this paper, by use of new comparison result, the existence of solutions of initial value problems for the systems of second order integro-differential equations in Bandch spaces is discussed. The results are new even in finite dimensional spaces. Related Articles | Metrics

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The Asymptotic Behavior of Solution for a Class of Nonlinear Singularly Perturbed Robin Problem Tang Rongrong Acta mathematica scientia,Series A. 2008, 28 (6):  1128-1132.  Abstract ( 1833 )   RICH HTML PDF (281KB) ( 1288 )   Save In this paper, by using the singular perturbation theory and the method for differential inequality, the asymptotic behavior for a class of nonlinear singularly perturbed Robin problems are considered. The existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary nth-order are obtained. Related Articles | Metrics

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Feedback Stabilization of a Class of Parabolic Systems with Neumann Boundary Conditions Dong Wangyuan Acta mathematica scientia,Series A. 2008, 28 (6):  1133-1149.  Abstract ( 1545 )   RICH HTML PDF (386KB) ( 1177 )   Save In this paper, the author studies internal stabilization of steady-state solutions to a class of semi-linear parabolic systems including three equations via finite-dimensional feedback controllers. The main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers are provided by considering LQ problems associated with the linearized systems at steady-state solutions, and they are added to one, two or three equations, depending on the considered steady-state solutions. Related Articles | Metrics

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Discussion on the Quantum Tunneling Characteristics of Stationary NUT- Kerr-Newman Black Hole Li Huiling|Cai Min|Lin Rong|Yang Shuzheng|Qi Dejiang Acta mathematica scientia,Series A. 2008, 28 (6):  1150-1156.  Abstract ( 1825 )   RICH HTML PDF (347KB) ( 1538 )   Save Adopting Parikh’s mode of quantum radiation as tunneling, the tunneling radiation characteristics of NUT- Kerr- Newman black hole is studyed. When energy conservation and angular momentum conservation are taken into account, the real spectrum of stationary NUT- Kerr- Newman black hole is not precisely thermal at all and the tunneling rate of the particle on the event horizon relates to the change of Bekenstein- Hawking entropy, which is consistent with underlying unitary quantum theory. Related Articles | Metrics

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Quasi Sure Convergence Rate of the Modulus of Continuity for Brownian Motion Liu Yonghong|Li Luoqing Acta mathematica scientia,Series A. 2008, 28 (6):  1157-1163.  Abstract ( 1654 )   RICH HTML PDF (250KB) ( 1229 )   Save In this paper, the authors obtain the rate of convergence in the functional limit for modulus of continuity of Brownian motion in terms of the Cr, p- capacity. Related Articles | Metrics

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On Super f- Edge Cover-Coloring of Multigraphs Xin Yongxun;Liu Guizhen Acta mathematica scientia,Series A. 2008, 28 (6):  1164-1172.  Abstract ( 1696 )   RICH HTML PDF (327KB) ( 1250 )   Save An edge cover-coloring of a graph G is called a super f-edge cover-coloring, if each color appears at each vertex v at least f(v) times and multiple edges receive different colors. Let χHfc denote the maximum positive integer k for which by using k colors a super f-edge cover-coloring of G exists. The existence of χHfc is discussed and its lower bound is obtained. Related Articles | Metrics

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Convexity and Geometrical Convexity of the Identic and Logarithmic Means in N Variables Zheng Ningguo;Zhang Xiaoming;Chu Yuming Acta mathematica scientia,Series A. 2008, 28 (6):  1173-1180.  Abstract ( 1406 )   RICH HTML PDF (305KB) ( 1166 )   Save In this paper, we study the Schur convexity and Schur geometrical convexity of identric and logarithmic means in n variables. We prove the following results: (1) The identric mean is Schur concave and S-geometrically convex; (2) The first-logarithmic mean is Schur concave; (3) The second-logarithmic mean is Schur convex. At last we give two open problems. Related Articles | Metrics

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Functional Representation Theorem for Polynomially Bounded Operators on a Banach Space Liu Mingxue Acta mathematica scientia,Series A. 2008, 28 (6):  1181-1186.  Abstract ( 1844 )   RICH HTML PDF (266KB) ( 1251 )   Save In this paper, the author introduces a transformation by scalar multiplication of the independent variable in the disc algebra, finds the connection between the Riesz functional calculus of polynomially bounded operators and the polynomial calculus of polynomially bounded operators, and obtains the functional representation theorem for (general) polynomially bounded operators on a Banach space. Related Articles | Metrics

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Global Existence and Blow-up of Solutions to a Quasi-linear Degenerate Parabolic System Li Fucai Acta mathematica scientia,Series A. 2008, 28 (6):  1187-1193.  Abstract ( 1945 )   RICH HTML PDF (288KB) ( 1256 )   Save This paper investigates the nonnegative solutions of quasi-linear degenerate parabolic system ut-div(|▽u|p-2 ▽u) =avα, vt-div(|▽v|q-2 ▽v) =buβ with zero Dirichlet boundary conditions in a smooth bounded domain Ω( RN (N≥ 1), where p, q>2, α, β ≥ 1, a, b>0 are constants. It is obtained that whether the solution blows up in finite time or not depends on the initial data, the coefficients a and b, and the relation between αβ and (p-1)(q-1). Related Articles | Metrics

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Multiplication-Preserving Maps On Matrix Algebras An Guimei|Hou Jinchuan Acta mathematica scientia,Series A. 2008, 28 (6):  1194-1205.  Abstract ( 1682 )   RICH HTML PDF (339KB) ( 1127 )   Save In this paper, we give some structure features of the multiplicative maps and the rank preserving multiplicative maps on matrix algebra Mn(F), where F is a field. By applying these results, we get some characterizations of the multiplicative maps on complex matrix algebras which preserve any one of the spectral radius, numerical radius, numerical range, positivity, self-adjointness, normality and unitarity of matrices. Related Articles | Metrics

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Automorphism Group, Central Extension and Derivations for a Lie Algebra over Quantum Torus Zheng Zhaojuan Acta mathematica scientia,Series A. 2008, 28 (6):  1206-1217.  Abstract ( 1780 )   RICH HTML PDF (331KB) ( 1282 )   Save Let q be generic and Cq:=x±11, x±12] be an associative torus algebra, and D(Cq) the set of derivations of Cq. Set Lq to be the derived Lie subalgebra of Cq㈩ D (Cq). In this paper, we study the automorphism group, central extension and derivations of the Lie algebra Lq. Related Articles | Metrics

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On Two Point Homogeneous Finsler Spaces Deng Shaoqiang Acta mathematica scientia,Series A. 2008, 28 (6):  1218-1221.  Abstract ( 1529 )   RICH HTML PDF (265KB) ( 1125 )   Save In this note, we prove that a two point homogeneous Finsler space is a Riemannian space. As a byproduct, we generalize a classical result of Mazur in functional analysis, asserting that a finite-dimensional transitive reversible normed linear space is a Euclidean space to the case of a non-reversible Minkowski space. Related Articles | Metrics

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π-quasinormality of the Maximal Subgroups of a Sylow Subgroup in a Local Subgroup Guo Xiuyun|Zhao Xianhe Acta mathematica scientia,Series A. 2008, 28 (6):  1222-1226.  Abstract ( 1410 )   RICH HTML PDF (257KB) ( 1218 )   Save A subgroup of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, which was firstly posed by Kegel. Since then, a long series of papers deal with π-quasinormality well located in G. In this paper we localize the above conditions in the G-normalizer of Sylow subgroups of the group G. Related Articles | Metrics

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Power Stably Free Modules over Noetherian Rings Chen Huanyin|Zhang Wei Acta mathematica scientia,Series A. 2008, 28 (6):  1227-1231.  Abstract ( 1575 )   RICH HTML PDF (204KB) ( 1065 )   Save Let I be a projective ideal of a noetherian ring R and Im=In for some m≠n. We prove that every finitely generated projective right R-module is power stably free if and only if (1) there exists a ring S such that I|m-n|( S ( R and every finitely generated projective right S-module is power stably free, and (2)every finitely generated projective right R/I|m-n|-module is power stably free. Related Articles | Metrics

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Triple Positive Symmetric Solutions of Two-Point BVPs for p-Laplacian Dynamic Equations on Time Scales Su Youhui;Li Wantong Acta mathematica scientia,Series A. 2008, 28 (6):  1232-1241.  Abstract ( 2010 )   RICH HTML PDF (324KB) ( 1362 )   Save This paper is concerned with the p-Laplacian boundary value problem (g(u△(t)))▽+a(t)f(t, u(t))=0 for t ∈ [ 0, T]T, u(0)=u(T)=w, u△(0)=-u△(T), where w is a nonnegative real number and g(ν)=lν|p-2ν with p>1 . By using symmetry technique and a five functionals fixed-point theorem, we prove that the boundary value problem has at least three positive symmetric solutions. As application, an example is given to illustrate our result. Related Articles | Metrics

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Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation Yang Xiangdong;Deng Guantie Acta mathematica scientia,Series A. 2008, 28 (6):  1242-1250.  Abstract ( 1889 )   RICH HTML PDF (296KB) ( 1687 )   Save In this paper, we prove that analytic functions in the right half plane with some restricted growth can be represented by a sum of its weighted Blaschke product and its integral on the boundary of the half plane. As its applications, we also investigate the completeness of complex exponential polynomials in Cα, where Cα is a weighted Banach space of complex continuous functions f on the real axis R with f(t)exp(-α(t)) vanishing at infinity, in the uniform norm with respect to the weight α(t). Related Articles | Metrics

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Quasi-compact Elements and Continuous Lattices Li Qingguo; Li Jibo Acta mathematica scientia,Series A. 2008, 28 (6):  1251-1255.  Abstract ( 1668 )   RICH HTML PDF (246KB) ( 1135 )   Save The concept of quasi-compact elements in continuous lattices is introduced. After introducing a quasi-base and investigating characterizations of quasi-bases of continuous lattices, a representation for continuous lattices is formulated by certain family of subsets of a given set. Related Articles | Metrics

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Positive Solutions to a Three-species Predator-prey Model Chen Bin; Wang Minxing Acta mathematica scientia,Series A. 2008, 28 (6):  1256-1266.  Abstract ( 1968 )   RICH HTML PDF (365KB) ( 1336 )   Save This paper is concerned with a diffusive three-species predator-prey model subject to the homogeneous Dirichlet boundary condition. Using the local and global bifurcation theory, the existence, mniqueness, stability and multiplicity of positive solutions are obtained. Related Articles | Metrics