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25 December 2010, Volume 30 Issue 6 Previous Issue    Next Issue

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Irreducible Modules for Special Algebra S (3, 1) SHAN Cui-Ping, JIANG Zhi-Hong Acta mathematica scientia,Series A. 2010, 30 (6):  1383-1393.  Abstract ( 1289 )   RICH HTML PDF (328KB) ( 1017 )   Save In this paper,  the authors study the irreducible modules by determining the maximal weight vector which generates the minimal left ideal of the reduced enveloping algebra. They obtain a complete set of non-isomorphic irreducible modules for Special algebra $S(3, {\bf 1})$ when the height of the characters is not larger than 0 and characteristic of the field is 2, and determine their dimension. References | Related Articles | Metrics

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Strong Law for Moving Average Processes of Arrays CHEN Ping-Yan, GUAN Zong-Ping Acta mathematica scientia,Series A. 2010, 30 (6):  1394-1401.  Abstract ( 1358 )   RICH HTML PDF (233KB) ( 903 )   Save In this paper, the sufficient and necessary conditions of the law of logarithm law for the moving average processes of array of independent identically distributed random variables are obtained, which extend some well-known results. References | Related Articles | Metrics

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Left-symmetric Structures on Lie Superalgebra W(m, n, t ) WEI Zhu, ZHANG Qiang-Cheng Acta mathematica scientia,Series A. 2010, 30 (6):  1402-1412.  Abstract ( 1210 )   RICH HTML PDF (377KB) ( 1032 )   Save This paper discusses some properties about etale superaffine representation by defining the left-symmetric superalgebra. Let W:=W(m, n, t ) be the general module Lie superalgebra of Cartan type. Under certain conditions, translative isomorphisms induce left-symmetric structures on W. On the other hand, the mixed product theorems are generalized. References | Related Articles | Metrics

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The Asymptotic Solutions of Delay Singularly Perturbed Differential Difference Equations NI Ming-Kang, LIN Wu-Zhong Acta mathematica scientia,Series A. 2010, 30 (6):  1413-1423.  Abstract ( 1355 )   RICH HTML PDF (376KB) ( 990 )   Save For a class of nonlinear singularly perturbed differential difference equations, with the method of boundary layer functions, the authors construct the uniformly valid asymptotic solutions. Because  the deviating factor, confirming boundary layer functions was difficulty, but with the method of splice, the author not only gave the smooth solution's existence proof, but also the remainder estimation was done. References | Related Articles | Metrics

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On the Approximation for Bernstein-Durrmeyer-Bézier Operators in Lp Spaces GUO Shun-Sheng, LIU Guo-Fen, SONG Zhan-Jie Acta mathematica scientia,Series A. 2010, 30 (6):  1424-1434.  Abstract ( 1219 )   RICH HTML PDF (261KB) ( 936 )   Save In this paper, the direct and inverse approximation theorems and equivalent theorem for Bernstein-Durrmeyer-B\'ezier Operators with first order Ditzian-Totik moduli of smoothness are given References | Related Articles | Metrics

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The Commutant of Bm, n(Ω) and Its K0 Group HE Hua, HAN Bing, DONG Yun-Bai Acta mathematica scientia,Series A. 2010, 30 (6):  1435-1443.  Abstract ( 1315 )   RICH HTML PDF (278KB) ( 943 )   Save In the paper,  the authors caculate  the commutant of  Cowen-Douglas operator with two indexes and also the Jacobson radical of the commutant. And it is showed that the commutant of a strongly irreducible Cowen-Douglas operator with two indexes is essentially commutative  by the tools of algebra techniques and spectral theory, and  the K0 group of the commutant is  isomorphic to the  integer group Z. References | Related Articles | Metrics

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A New Method to Solve a Kind of Nonlinear Singular Integral Equation HUANG Xin-Min Acta mathematica scientia,Series A. 2010, 30 (6):  1444-1450.  Abstract ( 2033 )   RICH HTML PDF (295KB) ( 916 )   Save In this paper, the problem discussed in  [1] is extended, that is, the general solution of the nonlinear singular  integral equation a(t)Φ2(t)+b(t)/πi ∫LΦ(τ)/τ-t dτ+c(t)=0,     t ∈L, is solved in H\"older\ continuous space, where a(t),b(t), c(t) are polynomials and a(t)b(t) ≠0. The complex plane is divided into a region S+ and an open set(or a region)S- by L, L being  a simple closed contour in the complex plane, or a simple arc, or a set of some simple arcs, or a  set of curves consisting of some simple closed contours and simple arcs. A new method is used which is different from that in [1], the problem is transformed to a Riemann boundary value problem, then it is solved. References | Related Articles | Metrics

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Perturbation of g-frames and Atomic Resolution WANG Jing, GAO De-Zhi Acta mathematica scientia,Series A. 2010, 30 (6):  1451-1456.  Abstract ( 1372 )   RICH HTML PDF (267KB) ( 1009 )   Save This paper  improves the stability of g-frames. Firstly,  some results on perturbations of g-frames are given, including the compact perturbation property. Secondly, the relation between g-frames and atomic resolution of the identity is discussed.    References | Related Articles | Metrics

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Non-oscillation and Oscillation |in Solutions of Nonlinear Stochastic Differential Equations with Bounded Delay WANG hong-Chu, HU Shi-Geng, ZHU Quan-Xin Acta mathematica scientia,Series A. 2010, 30 (6):  1457-1464.  Abstract ( 1957 )   RICH HTML PDF (307KB) ( 1056 )   Save This paper studies non-oscillation and oscillation in solutions of a nonlinear stochastic delay differential equation, in which the delay is time varying and  bounded. Depending on the properties of the drift and the diffusion of the equation, positive solutions may exist with positive probability for suitable selected initial process, and a sufficient condition for the almost sure oscillation of the solutions is also established. References | Related Articles | Metrics

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The Properties of Normed Lattice H Implication Algebras LAI Jia-Jun, XU Yang, QIN Ke-Yun Acta mathematica scientia,Series A. 2010, 30 (6):  1465-1473.  Abstract ( 1533 )   RICH HTML PDF (330KB) ( 901 )   Save Firstly, in this paper, under a norm situation,  the notion of lattice H implication algebra L[15] is extended (i.e., normed lattice H implication algebras), and some properties are discussed. Secondly, with the properties of implication distance d→, v -distance dv and ∧-distance d in normed lattice H implication algebras L investigated, the authors also define norned implication epimorphism、normed lattice H implication homomorphism、normed lattice H implication isomorphism and normed isomorphism by using of a mapping f which has two normed lattice H implication algebras L1 and L2 together with its properties studied. Finally,  the authors  further probe into the boundedness of convergence sequence, showing that sequences operations (i.e., $\otimes$, $\oplus$, ∨, ∧, →) to implication distance is bounded. References | Related Articles | Metrics

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Properties of Superdiffusions with Singular Branching Mechanism ZHANG Jing, REN Yan-Xia Acta mathematica scientia,Series A. 2010, 30 (6):  1474-1484.  Abstract ( 1409 )   RICH HTML PDF (299KB) ( 896 )   Save Suppose X is a superdiffusion on domain $D\subseteq\textrm{R}^{d}$, whose underlying motion ζ is a diffusion process with absorption at the boundary corresponding to generator   $$L=\frac{1}{2}\sum\limits_{i,j=1}^{d}a_{i,j}(x)\frac{\partial^{2}}{\partial x_{i}\partial x_{j}}+\sum\limits_{i=1}^{d}b_{i}(x)\frac{\partial}{\partial x_{i}},$$  whose  branching rate function is dt, and branching mechanism is of the form ψ(x, z) =α(x)z2, x ∈D, α∈Cη(D)(0<η≤1), and α(x)≡0 on D0(D0 is a bounded domain in D), α>0 on D\D0. The authors prove criteria for extinction, compact support property and global support being compact. References | Related Articles | Metrics

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Some New Results about Asymptotic Properties of Additive Functionals of Brownian Motion CHEN Chuan-Zhong, HAN Xin-Fang, MA Li Acta mathematica scientia,Series A. 2010, 30 (6):  1485-1494.  Abstract ( 1716 )   RICH HTML PDF (351KB) ( 982 )   Save Let $\textbf{B=}(\Omega,{{\cal F}},({{\cal F}}_{t})_{t\geq0},(B_{t})_{t\geq0},(P_{x})_{x\inR^{d}})$ be the classical Brownian motion on $L^{2}(R^{d},m)$, which is associated with a symmetric Dirichlet form $({{\cal E}},{{\cal D}}({{\cal E}}))$. For $u\in{{\cal D}}({{\cal E}})$,  $\tilde{u}(B_{t})-\tilde{u}(B_{0})=M^{u}_{t}+N^{u}_{t}$ is Fukushima decomposition, where $\tilde{u}$ is a quasi-continuous version of $u$, $M^{u}_{t}$ the martingale part and $N^{u}_{t}$  the zero energy part. In this paper, the authors first study transformed process $\widehat{B}$ of B, which is determined by the supermartingale $L^{-u}_{t}:=e^{M^{-u}_{t}-\frac{1}{2}\langle M^{-u}\rangle_{t}}$, they get some properties of its transition semigroup; Then, they study the asymptotic properties of $N^{u}_{t}$, they get that if $L^{-u}_{t}$  is a martingale, $u$ is bounded and $\nabla u\in K_{d-1}$, $||E_{.}(e^{M^{-u}_{t}})||_{q}<\infty$, then for every $x\in R^{d}$,  $$\begin{eqnarray*} \lim_{t\rightarrow \infty}\frac{1}{t} \log E_{x}(e^{N^{u}_{t}}) =-\inf_{{f\in {{\cal D}}({\cal E})_{b}}\atop{\| f \| _{L^{2}(R^{d},m)}=1}}({{\cal E}}(f,f)+{{\cal E}}(f^{2},u)), \end{eqnarray*}$$ where  ${{\cal D}}({{\cal E}})_{b}={{\cal D}}({{\cal E}})\cap L^{\infty}(R^{d},m)$. References | Related Articles | Metrics

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Positive Solutions of Nonlinear Third-order Periodic Boundary Value Problems YAO Qiang-Liu Acta mathematica scientia,Series A. 2010, 30 (6):  1495-1502.  Abstract ( 1750 )   RICH HTML PDF (294KB) ( 1068 )   Save The positive solutions for a nonlinear third-order periodic boundary value problem are considered. By making use of a suitable transformation the problem is transfered into an integral equation. By applying the Guo-Lakshmikantham fixed point index theorem on cone, the existence of single or multiple positive solutions is established. References | Related Articles | Metrics

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Nontrivial Solutions of Multi-point Boundary Value Problems with Sign-changing Nonlinear Terms LUAN Shi-Xia, WAN Fei-Fei, ZHANG Xin-Guang Acta mathematica scientia,Series A. 2010, 30 (6):  1503-1513.  Abstract ( 1498 )   RICH HTML PDF (343KB) ( 994 )   Save In this paper, the authors consider a class of m-point  boundary value problems with changing sign nonlinearity $$\left\{\begin{array}{l} (p(t)u'(t))'-q(t)u(t)+ h(t)f(t,u(t))=0,\quad 0<t<1, \disp au(0)-bp(0)u'(0)=\sum_{i=1}^{m-2}\alpha_{i}u(\xi_{i}),\\[3mm]\disp cu(1)+dp(1)u'(1)=\sum_{i=1}^{m-2}\beta_{i}u(\xi_{i}), \end{array}\right.$$ where f ∈ C([0,1]×(-∞,+∞),(-∞,+∞)) is a sign-changing function, not necessarily nonnegative and bounded from below. By establishing a more general Leray-Schauder degree theory, and computing the topological degree of a completely continuous field, some existence results of nontrival solutions are obtained. References | Related Articles | Metrics

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Perturbation in a Free Boundary Problem in R3 LIU Wei-Ming, ZHANG Zheng-Jie Acta mathematica scientia,Series A. 2010, 30 (6):  1514-1522.  Abstract ( 1516 )   RICH HTML PDF (284KB) ( 937 )   Save In this paper, the authors  use the perturbation method to consider the following free boundary problem { -Δu=λ+εg(u))H(u-1),  x ∈Ω,   ul ∂Ω=0.  where λ is a constant and Ω is the unit ball in R3, H(t)={ 1,    t ≥ 0,  0,   t<0.  Under some conditions, the authors  prove that there is a positive constant ε0 >0, if 0< ε < ε0 there is at least one solution for above problem and some results for the solution as ε tend to zero. References | Related Articles | Metrics

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Martingale Transforms between Hardy Spaces and Hardy-Orlicz Spaces of Martingales MENG Wei-Wei, YU Lin Acta mathematica scientia,Series A. 2010, 30 (6):  1523-1527.  Abstract ( 1402 )   RICH HTML PDF (243KB) ( 975 )   Save The martingale transform techniques are used to show that, given any Young function Φ with finite power pΦ, the corresponding Hardy-Orlicz space HsΦ is the martingale transform of Hardy spaces Hs1,  and the converse result is also true. The results obtained here extend the corresponding results in literature. References | Related Articles | Metrics

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Generalized Vector F-implicit Complementarity Problems in Topological Vector Spaces FENG Shi-Qiang, GAO Da-Feng, LI Jun Acta mathematica scientia,Series A. 2010, 30 (6):  1528-1533.  Abstract ( 1466 )   RICH HTML PDF (284KB) ( 980 )   Save In this work, the authors introduce a new class of vector F-implicit complementarity problems (for short, GVF-ICP) and two classes of  (strong and weak) vector F-implicit variational inequalities (for short, (GVF-IVI)1 and (GVF-IVI)2, respectively) in topological vector spaces. They present the equivalence between (GVF-ICP) and (GVF-IVI)1 under homogeneity. They also derive some new existence theorems of solutions for (GVF-IVI)2 by using the KKM theorem under some suitable assumptions. References | Related Articles | Metrics

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Limit-point and Limit-circle Classification of |Singular Sturm-Liouville Equations with Complex Coefficients JING Hai-Bin, QI Jian-Gang, YUE Chong-Shan Acta mathematica scientia,Series A. 2010, 30 (6):  1534-1541.  Abstract ( 1568 )   RICH HTML PDF (319KB) ( 1019 )   Save By using limit-point(circle) classification theory of symmetric Hamiltonian differential systems, different from the method used by B.M.Brown et al, the paper gives the Sims classification of singular Sturm-Liouville equations with complex coefficients: limit-point-1 case, limit-point-2 case and limit-circle case. Then two limit-point-1 case criteria are obtained. Furthermore, the authors give an affirmative answer to the open problem of B.M.Brown et al by an example. References | Related Articles | Metrics

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Error Estimates for the Finite Element Approximation of Nonlinear Parabolic Optimal Control Problems FU Hong-Fei, RUI Hong-Xing Acta mathematica scientia,Series A. 2010, 30 (6):  1542-1554.  Abstract ( 1634 )   RICH HTML PDF (2481KB) ( 969 )   Save In this paper, the finite element approximation to a class of nonlinear optimal control problems with two different kinds of control constrained sets is investigated, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. Some a priori error estimates are derived for both control and state approximations. It is proven that these approximations have convergence order O(hU+h+k), where hU and h are the spatial mesh-sizes for control and state, respectively, and k is the time increment. Numerical examples are given to show the efficiency of the present scheme. References | Related Articles | Metrics

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Some Lower Bounds of Centered L2-discrepancy on Foldover Designs LEI Yi-Ju, QIN Hong, ZOU Na Acta mathematica scientia,Series A. 2010, 30 (6):  1555-1561.  Abstract ( 1587 )   RICH HTML PDF (359KB) ( 941 )   Save Foldover is a classic technique that reverses the sign(s) of one or more factors in the initial design for the follow-up experiment (called a foldover design). The full design obtained by joining the runs in the foldover design to those of the initial design is called a combined design. In this paper, under the full foldover plan and fractional foldover plans, some lower bounds of the combined designs in terms of centered L2 discrepancy are obtained, which can be used as a benchmark for searching optimal foldover plans. The results provide a theoretical justification for optimal foldover plans based on uniformity criterion. References | Related Articles | Metrics

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A New Trust Region Algorithm with Simple Quadratic Models and Line Search SUN Qing-Ying, DONG Jie-Hong, SANG Zhao-Yang Acta mathematica scientia,Series A. 2010, 30 (6):  1562-1574.  Abstract ( 1352 )   RICH HTML PDF (426KB) ( 798 )   Save The authors propose a new trust region algorithm with simple quadratic models and larger Armijo line search rule. The global convergence property of the  new method is proved under the condition that the gradient of function is uniformly continuous. Numerical results show that the new algorithm is efficient, and attractive for large-scale optimization problems. References | Related Articles | Metrics

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Categories and Functions of Weak Relative Hopf Modules ZHANG Liang-Yun Acta mathematica scientia,Series A. 2010, 30 (6):  1575-1581.  Abstract ( 1265 )   RICH HTML PDF (265KB) ( 987 )   Save In this paper, the author  gives relations between the category of coinvariant modules and the category of weak relative Hopf modules, and gives some applications of the coinvariant  functor (•)coH and the induced  functor Ind==•\otimesBA. Moreover, it is showed  that the category A M H* of weak relative Hopf modules is isomorphic to the category A#H M of weak smash product modules. References | Related Articles | Metrics

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The Roper-Suffridge Extension Operator in Complex Banach Space ZU Juan Acta mathematica scientia,Series A. 2010, 30 (6):  1582-1591.  Abstract ( 1575 )   RICH HTML PDF (313KB) ( 980 )   Save In this paper, the author extends the Roper-Suffridge operator to some domains in complex Banach space, and it is proved that certain extended Roper-Suffridge operator preserves spirallikeness of type α on the relevant domain, while another extended Roper-Suffridge operator preserves starlikeness of order α on the unit ball in a complex Banach space. Some results of Liu T S , Liu X S and Feng S X in Hilbert space are extended to Banach spaces. References | Related Articles | Metrics

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Existence of Multiple Symmetric Positive Solutions of Higher Order Sturm-Liouville-type Boundary Value Problem PANG Hui-Hui, ZHAO Jun-Fang, GE Wei-Gao Acta mathematica scientia,Series A. 2010, 30 (6):  1592-1603.  Abstract ( 1463 )   RICH HTML PDF (305KB) ( 934 )   Save In this paper, the authors consider the following higher order Sturm-Liouville-type four-point boundary value problem {u(2m)(t)=f(t, u(t), u'(t), … , u{(2m-1)(t)),  u{(2i)(0)-αu(2i+1)(ξ)=0, u(2i)}(1)+αu(2i+1)(η)=0, 0≤ i ≤ m-1,  where nonlinear f depends on all lower order derivatives of u. Sufficient conditions of existence of at least three symmetric positive solutions are established by applying five-functional fixed point theorem. References | Related Articles | Metrics

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B-valued Bi-random Dirichlet Series WANG Hui-Jian, SUN Dao-Chun Acta mathematica scientia,Series A. 2010, 30 (6):  1604-1611.  Abstract ( 1447 )   RICH HTML PDF (317KB) ( 894 )   Save By studying the convergence and the growth of bi-random Dirichlet series ∑∞n=0anXn(ω)e-λn(ω)s in with coefficients {Xn}(ω): n≥0, being unidentically distributed B-valued φ-mixing random sequences, satisfying d p σnp \triangleq d pE ll Xnllp≤ Epll Xnll< ∞ (p>1, d>0), under centain suitable conditions, the authors obtain such results: on the whole plane, the bi-random Dirichlet series and some Dirichlet series almost surely have the same abscissa of convergence (uniform convergence, or absolute convergence), the same order of growth and (p, q)(R)-order, and the necessary and sufficient conditions of the bi-random Dirichlet series almost surely with the same order after rearrangement of the coefficients. References | Related Articles | Metrics

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Making the Category of Group Entwined Modules into a Bradied Monoidal Category LIU Ling, WANG Shuan-Hong Acta mathematica scientia,Series A. 2010, 30 (6):  1612-1620.  Abstract ( 1352 )   RICH HTML PDF (290KB) ( 841 )   Save The authors investigate how the category of group entwined modules can be made into a monoidal category[11]. It suffices that the algebra and π-coalgebra in question are bialgebra and semi-Hopf π-coalgebra, with some extra compatibility relation. Braidings on a monoidal category of π-entwined modules are constructed. The construction unifies quasitriangular and coquasitriangular Hopf algebras (Hopf π-coalgebras), Doi-Hopf  π-modules. References | Related Articles | Metrics

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Admissibility of Matrix Nonhomogeneous Linear Estimators in Multivariate Linear Models ZHOU Zai-Ying Acta mathematica scientia,Series A. 2010, 30 (6):  1621-1628.  Abstract ( 1408 )   RICH HTML PDF (296KB) ( 989 )   Save This paper studies the admissibility of matrix nonhomogeneous linear estimators of an estimable parameter matrix linear function in multivariate linear models with completely unknown covariance matrix under a quadratic matrix loss function. A necessary and sufficient condition is given for a matrix nonhomogeneous linear estimator to be admissible in the class of all matrix linear estimators without normality assumption. Under normality assumption, a sufficient condition that a matrix nonhomogeneous linear estimator is admissible in the class of all matrix estimators is derived. References | Related Articles | Metrics

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The Subrepresentation Theorems of the Conjugate Cones of Real Locally p-convex Spaces l p and Lp(μ)(0<p <|1) WANG Jian-Yong Acta mathematica scientia,Series A. 2010, 30 (6):  1629-1639.  Abstract ( 1428 )   RICH HTML PDF (327KB) ( 932 )   Save This paper falls into the category of non-locally convex analysis. In this paper the author deals with the representation problems of the normed conjugate cones (l p)p* and [Lp(μ)]p* of real locally p-convex spaces l p and Lp(μ) (0<p< 1), obtains (l p)p*\simeq m+×m+ and [Lp(μ)]p*\simeq M+(μ)×M+(μ), called the subrepresentation theorems of (l p)p* and [Lp(μ)]p* respectively. References | Related Articles | Metrics

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A Singular Radius of Quasimeromorphic Mappings on Some Type-functions in the Unit Disc KONG Yin-Ying Acta mathematica scientia,Series A. 2010, 30 (6):  1640-1647.  Abstract ( 1560 )   RICH HTML PDF (332KB) ( 1021 )   Save A singular radius of quasimeromorphic mappings on some Type-functions in the unit disc is studied in the present paper. Some results on the existence of Borel radius, the largest type Borel radius (with their multiple values) and S radius of such mappings  are investigated and their relations are obtained. References | Related Articles | Metrics

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On a New Extension of a Hilbert-type Integral Inequality XIN Dong-Mei, YANG Bi-Cheng Acta mathematica scientia,Series A. 2010, 30 (6):  1648-1653.  Abstract ( 1463 )   RICH HTML PDF (245KB) ( 1143 )   Save By introducing two independent parameters λ, α and two pairs of conjugate exponents (p, q), (r, s), we obtain a new extension of a Hilbert-type integral inequality connecting two base Hilbert-type integral inequalities with the best constant factor. The authors  also consider its equivalent form and some particular results. References | Related Articles | Metrics

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Stability of a Ring Neural Network with Delays ZOU Shao-Fen, WANG Yao-Na, HUANG Li-Hong Acta mathematica scientia,Series A. 2010, 30 (6):  1654-1665.  Abstract ( 1675 )   RICH HTML PDF (1101KB) ( 860 )   Save A system of ring neural network with self-feedback and multiple delays is considered. Conditions for the stability  and unstability of the trivial solution of this system are completely represented in a parameter space. According to the regulation of the variation of the number of eigenvalues with positive real parts, for different parameters, the authors investigate the boundary of the largest stability set,  improve and complete the former conclusions References | Related Articles | Metrics

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Iterative Approximation to Common |Fixed Points of An Infinite Family of Non-self Non-expansive Maps and Strong Convergence of Cesàro Mean Iterations RAO Ruo-Feng Acta mathematica scientia,Series A. 2010, 30 (6):  1666-1676.  Abstract ( 1619 )   RICH HTML PDF (356KB) ( 967 )   Save The author  introduces and studies an iteration with  infinitely many non-expansive nonself mappings in the framework of reflexive and strictly convex Banach spaces. A new strong convergence theorem  is obtained, which immediately extends the main result obtained by Zhang-Lee-Chan  in 2007 from non-expanive  self-mapping to non-expanive non-self-mapping, from Hilbert spaces to Banach spaces. In addition, other main results of this paper extend the main result obtained by R. Wangkeeree in 2007 from  Cesàro mean iteration with one non-expansive mapping to Cesàro mean iteration with two ones. Finally, an interesting new result about the set of fixed points of non-expansive mappings  is given. References | Related Articles | Metrics

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Liouville Theorems of F-Stationary Maps ZHOU Zhen-Rong Acta mathematica scientia,Series A. 2010, 30 (6):  1677-1685.  Abstract ( 1182 )   RICH HTML PDF (316KB) ( 941 )   Save In this paper, the author discusses theorems of Liouville type for F-stationary maps, and proves that $F$-stationary maps with finite F-energy must be constant, if the sectional curvatures of the initial manifolds satisfy some nonpositive conditions and  F obeys the F-p-condition. The author also investigates a class of special F-stationary maps, i.e., maps obeying the integral F-conservation law, and proves similar theorems of Liouville type, under the same curvature conditions and the F-p-condition, but replacing the finiteness of F-energy by the slowly divergent F-energies. References | Related Articles | Metrics

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Additive Maps Satisfying [Φ(A2), Φ(A)] = 0 on the Space of Self-adjoint Operators QI Xiao-Fei, DU Quan-Ping, HOU Jin-Chuan Acta mathematica scientia,Series A. 2010, 30 (6):  1686-1692.  Abstract ( 1380 )   RICH HTML PDF (311KB) ( 933 )   Save Let $H$ be a complex Hilbert space with dimension greater than 2 and ${\mathcal B}_{s}(H)$ the space of all self-adjoint operators in ${\mathcal B}(H)$. A characterization is given for additive bijective map $\Phi$ on ${\mathcal B}_{s}(H)$ satisfying $[\Phi(A^2),\Phi(A)]=0$ for all $A\in {\mathcal B}_s(H)$. It is showed that, if $\Phi({\mathcal F}_{s}(H)) \not\subseteq {\mathbb R}I$ or  ${\mathbb R}I\subseteq\Phi({\mathbb R}I)$, then $\Phi$ has the form $\Phi(A)=cUAU^*+f(A)I, ~ \forall  A \in {\mathcal B}_{s}(H),$ where $c\in {\mathbb R},$ $c\neq 0$, $U:H\rightarrow H$ is an unitary or conjugate unitary operator, and $f$ is an additive real functional of ${\mathcal B}_{s}(H)$. References | Related Articles | Metrics

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Regularity Criteria for a Two-fluid Model of the Truncated Euler Equations SUN Jian-Zhu, FAN Ji-Shan Acta mathematica scientia,Series A. 2010, 30 (6):  1693-1698.  Abstract ( 1877 )   RICH HTML PDF (222KB) ( 1039 )   Save The authors study a two-fluid model of the truncated Euler equations with partial viscosity. Some regularity criteria of the strong solutions in homogeneous Besov spaces are proved. References | Related Articles | Metrics

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The Upper Bound of Second Order Item Coefficients of Homogeneous Expansion for Close-to-starlike Mappings CHANG Shui-Zhen, LIU Hao Acta mathematica scientia,Series A. 2010, 30 (6):  1699-1703.  Abstract ( 1667 )   RICH HTML PDF (264KB) ( 1009 )   Save In this thesis, on the unit ball Bn in Cn, firstly,  the better upper bound of second order item coefficients of homogeneous expansion for normalized starlike mappings is attained; Secondly, with the properties of Loewner chains, the upper bound of second order item coefficients of homogeneous expansion for close-to-starlike mappings is  obtained. References | Related Articles | Metrics