中国科学院数学与系统科学研究院期刊网

15 November 2006, Volume 49 Issue 6
    

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  • The Problem of Simplicial Conditional Extremum in the Space of Constant Curvature
    Ding Hua YANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1201-120. https://doi.org/10.12386/A2006sxxb0149
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    The sufficient and necessary condition for positive definite quadratic form of linear constraint is obtained by using the definition of sub-eigenvalue of matrix. We also give some representations of conditional extremum of simplicial circumscribed hyperspace radius in the space of constant curvature.Using these representations,one can conclude some metric additional geometric inequality.
  • Volume Growth of Nonnegative Curvature Manifolds
    Zhen Hua JIAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1207-121. https://doi.org/10.12386/A2006sxxb0150
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    Using the properties of Busemann functions and exhaustion functions on non- negative curvature manifolds,the author gets the result of this paper:If M~n is a com- plete noncompact complex n-dimensional K■hler manifold satisfies certain nonnegative curvature conditions,then the volume growth of M satisfying:Vol (B(x_0,r))≥Cr~n. It generalizes a recent result of Chen and Zhu.
  • Ishikawa Iterative Sequences for Hemi-Contractive Mappings with Error Member
    Qi Hou LIU; Yang LIU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1213-121. https://doi.org/10.12386/A2006sxxb0151
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    In this paper,the new Theorems are presented to prove some sufficient and necessary condition of Ishikawa iterative sequence with error member for Lipschitz hemi-contraction mapping in Hilbert space converging to the fixed point.
  • Multi-Sample Testing for the Equality of Multinomial Populations Against Increasing Convex Ordering Alternative
    Yan Qin FENG; Jin De WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1217-122. https://doi.org/10.12386/A2006sxxb0152
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    Stochastic ordering among probability distributions has been widely applied in practice.Likelihood ratio testing is the most commonly used method to test hypothe- ses involving stochastic orderings.Unfortunately,statistical inference methods based on likelihood ratio principle on increasing convex ordering for more than two multino- mial populations have not been fully developed.The problem of testing the increasing convex ordering against no restriction for multi-sample case has been considered by using likelihood ratio test.However,it may be of more interest to test for the equality against the increasing convex ordering alternative among several populations.Testings for the equality againbt order-restricted alternative are most commonly considered by statisticians.This paper considers the equality against the increasing convex ordering for multi-sample case and obtains the null asymptotic distribution of the likelihood ra- tio test statistic,which is a mixture of chi-squared distributions,that is chi-bar-squared distribution.
  • Generalization of the Invariantly Cometrizable Property
    Shou Li JIANG; Zi Qin FENG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1225-123. https://doi.org/10.12386/A2006sxxb0153
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    A generalization of the invariantly cometrizable property is given for the set-open topology for function spaces.And the sufficiency and necessity condition of a function space to be invariantly cometrizable in the compact-open and point-wise convergence topology is given as a corollary.
  • Characterizations of Weakly Sequentially Retractive(LM)-Spaces
    Jing Hui QIU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1231-123. https://doi.org/10.12386/A2006sxxb0154
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    We investigate the relationships between Retakh's condition (M_0),regular- ity and weak sequential retractivity.For (LM)-spaces,weak sequential retractivity is equivalent to regularity plus a condition which lies between condition (M_0) and (Q_0). For (LN)-spaces we obtain more satisfactory result.We prove that weak sequential retractivity is equivalent to regularity plus condition (M_0) and hence is equivalent to a very weak regularity condition plus conditionc (M_0) (see [1-28]).
  • Drop Theorem in Locally Convex Separated Spaces
    Fei HE; De LIU; Cheng LUO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1239-124. https://doi.org/10.12386/A2006sxxb0155
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    In this paper,two new drop theorems are established.One of them is proper improvements of the result which is given by Jing-Hui Qiu and the result which is given by Xi-Yin Zheng (and restricted to locally convex separated spaces),the other simplifies the theorem which is proved by Jing-Hui Qiu.
  • Moore-Penrose Metric Generalized Inverse of Linear Opeartor in Arbitrary Banach Space
    Ren Xing NI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1247-125. https://doi.org/10.12386/A2006sxxb0156
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    Without geometry assumption on strictly convex space,by means of methods of geometry of Banach space,the necessary and sufficient conditions for the existence, uniqueness,minimum property and linearity of the Moore-Penrose metric generalized inverse T~+ of linear operator T are given,and some properties of T~+ are investigated. These indeed extend and improve the corresponding recent results obtained by [8] from strictly convex Banach space to arbitrary Banach space.
  • Algebraic Properties of Category of Quantale
    Zhi Bin LIU(1); Bin ZHAO(2)
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1253-125. https://doi.org/10.12386/A2006sxxb0157
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    In this paper,we discuss some properties of the category of Quantale,obtain the structures of coequalizers and free Quantale in the category of Quantale,and prove that the category of Quantale is an algebraic category.
  • a-Weyl's Theorem for Analytically Hyponormal Operators
    Xiao Hong CAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1259-126. https://doi.org/10.12386/A2006sxxb0158
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    A variant of the essential approximate point spectrum is discussed.We give the necessary and sufficient condition for T which the a-Weyl's theorem or a-Browder's theorem holds.Using the new spectrum set we define in this paper,we also consider how the a-Weyl's theorem survives for analytically hyponormal operators.
  • Generalization of Hlder Inequality and Minkowski Inequality
    Shu Hong WU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1267-127. https://doi.org/10.12386/A2006sxxb0159
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    In this paper,we make use of variational method to generalize H■der in- equality and Minkowski inequality which have several variables and do not comprise derivatives of the variables.The major significance of this method is not to prove classical inequality but to find new inequality.
  • Viscosity Approximation Methods for Continuous Pseudocontractive Mappings
    Ru Dong CHEN(1); Yi Sheng SONG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1275-127. https://doi.org/10.12386/A2006sxxb0160
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    Let K be a closed convex subset of a real reflexive Banach space E,T: K→K be a continuous pseudocontractive mapping,and f:K→K be a fixed L-Lipschitzian strongly pseudocontractive mapping.For any t∈(0,1),let x_t be the unique fixed point of tf+(1-t)T.We prove that if T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E~*,then {x_t} converges to a fixed point of T as t approaches 0.The results presented extend and improve the corresponding results of [4].
  • A Fundamental Inequality for K-Quasimeromorphic Mappings in an Angular Domain and Its Application
    Chun Hong LI; Yong Xing GU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1279-128. https://doi.org/10.12386/A2006sxxb0161
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    In this paper,we establish a fundamental inequality for K-quasimeromorphic mappings in an angular domain,and then use it to study the existence of Nevanlinna direction and T direction of the K-quasimeromorphic mappings.
  • Two Higher-Dimensional loop Algebras and Their Applications
    Yu Feng ZHANG(1); Hong Qing ZH
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1287-129. https://doi.org/10.12386/A2006sxxb0162
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    With the help of the cycled numbers,two higher-dimensional loop algebras are constructed,whose dimension numbers are 5(s+1) and 4(s+1),respectively.For the sake of simple calculation,we only take s=1 in the paper for illustrating their applications.By employing the first loop algebra ■,a generalized AKNS hierarchy is obtained,possessing 4-Hamiltonian structure,which is also reduced to the well-known AKNS hierarchy.By making use of the second loop algebra ■,a new integrable hier- archy with 4-potential functions is generated,also possessing 4-Hamiltonian structure, which is redued to a nonlinear couled Burgers equation and a coupled KdV equation, respectively.
  • On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings
    Shi Sheng ZHANG(1); Joseph Lee
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1297-130. https://doi.org/10.12386/A2006sxxb0163
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    The purpose of this paper is to study the convergence problem of the iteration scheme x_(n+1)=λ_n+1y+(1-λ_n+1)T_(n+1)x_n for a family of infinitely many nonexpansive mappings T_1,T_2,...in a Hilbert space.It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings.The results presented in this paper extend and improve the corresponding results.
  • Uniform Attractor of Non-Autonomous Schrdinger-KdV Type Equations and Estimates of Its Dimension
    Guang Gan CHEN; Zhi Lin PU; Ji
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1303-131. https://doi.org/10.12386/A2006sxxb0164
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    In this paper,we are interested in the nonlinear dynamical behavior of non- autonomous Schr■dinger-KdV type equations.Using the method of describing non- autonomous dynamical system by operator families with two parameters,we obtain the existence of their uniform attractor.Furthermore,we estimate the Hausdorff dimension of the uniform attractor.
  • On Regular WB-Rings
    Huan Yin CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1311-132. https://doi.org/10.12386/A2006sxxb0165
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    We introduce the concept of WB-rings and investigate the necessary and sufficient conditions under which a regular ring is a WB-ring.Let A be a finitely generated projective right module over a regular ring R.Suppose that M_n(R) is a WB-ring for all n∈N.If B and C are any right R-modules such that A■B≌A■C, we prove that there exist orthogonal ideals I and J such that B/BI≤■C/CI and C/CJ≤■B/BJ.This also gives some new comparable properties of modules over QB-rings.
  • A Geometric Result for Approximating Fixed Points of Nonlinear Mappings by Iteration Sequence
    Yong Fu SU(1); Hai Yun ZHOU(2)
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1321-132. https://doi.org/10.12386/A2006sxxb0166
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    LetE be a Hilbert space,T:D(T)→R(T) be a nonlinear mapping with nonempty set of fixed points.For a lot of nonlinear mappings,the fixed points can be approximating by iteration sequence{x_n}.In the approximating process,a geometric result can be expressed as lim sup_(n→+∞)〈p-p_0,(x_n-p_o)/(||x_n-p_o||)≤0,■p∈F(T).Equvalently, puttingθ_n(p)=arccos〈(p-p_o)/(||p-p_o||),(x_n-p_o)/(||x_n-p_o||)〉,■p∈F(T).then limsup_(n→∞)θ_n(p)≥π/2. This geometric result is said to be an obtuse angle principle.In the relevant condition, the obtuse angle principle holds for nonexpansive mappings,asymptotically nonex- pansive mappings,Lipschitz mappings,accretive mappings,pseudocontractive map- pings,asymptotically pseudocontractive mappings,strictly pseudocontractive map- pings,strongly pseudocontractive mapping,etc.
  • On Some Inequalities for the New Geometric BodyΓ__pK
    Wei Dong WANG(1); Gang Song LE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1327-133. https://doi.org/10.12386/A2006sxxb0167
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    In this paper,some inequalities including the bodyΓ_(-p)K associated with L_p-centroid body and L_p John ellipsoid,and the monotonicity ofΓ_(-p)K are shown, respecyively.In partcular,an isolated form of L_p-Busemann-Petty centroid inequality is obtained.
  • On Linear Extension of Isometries Between Unit Spheres
    Rui Dong WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1335-133. https://doi.org/10.12386/A2006sxxb0168
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    we study the extension of isometries between the unit spheres S_1 (E) and S_1 (F),where E and F are both real normed spaces.We obtain that if the non-surjective isometry V_0 from S_1 (E) to S_1 (F) satisfy some properties,the V_0 can be extended to be real linearly isometric map V of E into F.This is the first time we study Tingley' problem without the condition of surjectivity.
  • An Extension of Kemperman Structure Theorem
    Xue Sheng CHEN(1); Ping Zhi YU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1339-134. https://doi.org/10.12386/A2006sxxb0169
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    In this paper,we investigate the structure of the those pairs(A,B)of finite subsets of an Abelian group satisfying|A+B|=|A|+|B|+k(k■-1),and extend the Kemperman structure theorem.
  • Existence and Uniqueness of Periodic Solutions for a Class of First Order Neutral Functional Differential Equations
    Bing Wen LIU(1); Li HOng HUANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1347-135. https://doi.org/10.12386/A2006sxxb0170
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    In this paper,we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the first order neutral functional differential equation of the form(x(t)+Bx(t-δ))′=gl(t,x(t))+g2(t,x(t-τ(t)))+p(t).
  • The Matching Equivalence Classes of Graphs with the Maximum Matching Root Less Than or Equal to 2
    Hai Cheng MA
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1355-136. https://doi.org/10.12386/A2006sxxb0171
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    The 16 matching equivalence relations(called the matching equivalence bridges)are obtained.For two graphs,with maximum matching root less than or equal to 2,they are matching equivalent if and only if they can be equivalently trans- formed by the 16 matching equivalence bridges.Meanwhile,the matching equivalence classes of their complementary graphs are characterized.All matching unique graphs are obtained for a graph in which the maximum matching root less than or equal to 2 or its complement graphs.
  • X_d Frames and Reisz Bases for a Banach Space
    Chun Yan LI(1); Huai Xin CAO(2
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1361-136. https://doi.org/10.12386/A2006sxxb0172
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    In this paper,we introduce and discuss X_d frames,X_d Bessel sequences, tight X_d frames,independent X_d frames and X_d Riesz basis for a Banach space.We give a necessary and sufficent condition for a Banach space X to have an X_d frame or to have an X_d Riesz basis,and a necessary and sufficent condition for an X_d frame to have a dual frame.We also discuss some relations among basis,X_d frame and X_d Riesz basis in a Banach space.
  • Graded Morita Contexts and Graded Radicals
    Yao WANG; Yan Li REN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1367-137. https://doi.org/10.12386/A2006sxxb0173
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    LetM={A=■_(g∈G)A_g,V=■_(g∈G)V_g,W=■_(g∈G)W_g,B=■_(g∈G)B_g} and(,),[,]be a G-graded Morita Context with(V,W)=A and[W,V]=B,where A and B are graded ring with 1.We show that r_G(B)=[W,r_G(A)V]=[Wr_G(A),V],r_G(A)=(V,r_G(B)W)=(Vr_G(B),W), where r_G is one of the following graded radicals:the graded prime radical;the graded Jacobson radical;the graded Koethe radical;the graded Levitzki radical;the graded strongly prime radical;the graded uniformly strongly prime radical.
  • Relationships Among Markov ChAins in Random Environments and Joint Markov Chains
    Ying Qiu LI(1); Su Ming WANG(1
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1373-138. https://doi.org/10.12386/A2006sxxb0174
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    Relationships among Markov chains in single infinite random environments, Markov chains in bi-infinite random environments,joint Markov chains and original processes are solved more satisfactorily.Especially,some misunderstandings are clar- ified,and the wrong conclusions among them are corrected.These offer very distinct basic concepts for the further study of Markov chains in random environments.
  • One-Dimensional Global Attractor for Strongly Damped Wave Equations with Neumann Boundary Condition
    Hong Yan LI; Sheng Fan ZHOU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1381-138. https://doi.org/10.12386/A2006sxxb0175
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    In this paper,we consider the existence of global attractor of strongly damped wave equations under homogeneous Neumann boundary condition.By the property of limit set of asymptotic time-periodic differential equations,we prove that in a cer- tain parameter region,the system has a one-dimensional global attractor,which is a horizontal curve.
  • Boundedness Properties for Commutators of Multipliers
    Pu ZHANG(1); Jie Cheng CHEN(2)
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1387-139. https://doi.org/10.12386/A2006sxxb0176
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    In this paper,the authors study the commutators generalized by multipliers and a Lipschitz function.The boundedness properties on Lebesgue spaces and Hardy spaces are established.
  • Extension of Isometries and(λ,ψ,2)-Isometries on the Unit Spheres
    Xiu Zhong YANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1397-140. https://doi.org/10.12386/A2006sxxb0177
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    We first obtain some sufficient conditions for an isometric mapping defined on the unit sphere(or ball)of aβ-normed space(0＜β■1)can bc extended to be a linear isometry on the whole space.Secondly,in aβ-normed space E,we study the extension problem of(λ,Ψ,2)-isometry.The main result says that positively ho- mogeneous mapping V_0:B_1(E)→B_1(E)is(1,Ψ,2)-isometry if and only if‖V_0x‖■‖x‖,■x∈B_1(E),hence this result generalizes the corresponding result in Zhang L.
  • Admissibility of Linear Estimators in Linear Models with Respect to Inequality Constraints
    Jian Hong Wu(1); Xue Qin Chen(
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1403-141. https://doi.org/10.12386/A2006sxxb0178
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    Admissibility of both homogeneous and inhomogeneous linear estimators is investigated in linear models with respect to inequality constraints.The relation between admissibility of the two types of estimators is derived.Under some condi- tious,sufficient and necessary conditions for the admissibility of inhomogeneous linear estimators with respect to inequality constraints are given.
  • 2-Local Derivations on Digraph Algebras
    Jian Hua ZHANG; Hong Xia LI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1411-141. https://doi.org/10.12386/A2006sxxb0179
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    In this paper,we prove that every 2-local derivation from any symmetric digraph algebra into itself is a derivation.Moreover,we give an example to show that the conclusion may not be true if it has not the condition of symmetry.
  • Strong Consistency of Wavelet Estimation in Semiparametric Regression Models
    Hong Chang HU; Di He HU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1417-142. https://doi.org/10.12386/A2006sxxb0180
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    Consider the semiparametric regression model y_i~(n)=X_i~((n)T)β+g(t_i~(n))+ε_i~(n)(1■i■n)whereβis a d×1 unknown parametric vector,g(t)is an unknown Borel function on[0,1],X_i~(n)is a d×1 random design vector,random error sequences {ε_i~(n)}are martingale difference sequences,{t_i~(n)}is a constant sequence on[0,1].In this paper,the estimators of parameter and nonparameter are established by wavelet method,and the strong consistency of wavelet estimators is studied.
  • Vector Equilibrium Problems with Coercivity Conditions
    LOng Guang HUANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1425-143. https://doi.org/10.12386/A2006sxxb0181
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    The vector equilibrium problems with coercivity conditions for cone-pseudo- monotone,cone-quasiconvex and upper cone-continuous mappings are dealt with.The interrelations between coercivity conditions and solution sets of vector equilibrium problems are presented.The nonemptiness conditions on solution sets of vector equilib- rium problems,and property that local solution set of dual vector equilibrium problem is contained in that of vector equilibrium problem are derived.An equivalence is stated between the nonemptiness and boundedness of solution set and those coercivity conditions in the cone-pseudomonotone,cone-quasiconvex and upper cone-continuous setting.
  • A New Kind of Solutions to Modularity Condition Equations
    Feng QIN; Bin ZHAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(6): 1433-144. https://doi.org/10.12386/A2006sxxb0182
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    The modularity condition equations only involved idempotent uninorms and t-operators are investigated.The three following cases are proved:(i)A t-operator with an idempotent uninorm is modular if and only if there exists uniquely a kind of new non-trivial solutions;(ii)An idempotent uninorm with a t-operator is modular if and only if there exists uniquely a kind of new non-trivial solutions also;(iii)the necessary and sufficient conditions are given when two idempotent uninorms satisfy the modularity condition equation.
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