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25 February 2008, Volume 28 Issue 1 Previous Issue    Next Issue

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Boundeness of Multilinear Operators Related to Fractional Integral with Rough Kernel on Hardy Spaces Han Haiyan; Lu Shanzhen Acta mathematica scientia,Series A. 2008, 28 (1):  1-011.  Abstract ( 1839 )   RICH HTML PDF (289KB) ( 1163 )   Save In this paper, the authors discuss the$(H^{1}(\rr^{n}),L^{\frac{n}{n-\alpha},\infty}(\rr^{n}))$ boundedness of the multilinear operator related to fractional integral with rough kernel \[T_{\Omega,\alpha}^{A}(f)(x)={\rm p.v.}\int_{R^{n}}P_{m}(A;x,y) \frac{\Omega(x-y)}{|x-y|^{n-\alpha+m-1}}f(y){\rm d}y.\] Related Articles | Metrics

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Fisher's Information Matrix of an Unstructured Bai Peng Acta mathematica scientia,Series A. 2008, 28 (1):  12-023.  Abstract ( 1691 )   RICH HTML PDF (310KB) ( 1075 )   Save The Fisher's information matrix of a sample in an unstructured multivariate t -model is calculated in this paper. Also, the inverse, the determinant and the trace of this matrix are obtained. Related Articles | Metrics

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A New Effective Preconditioned Method Li Jicheng Acta mathematica scientia,Series A. 2008, 28 (1):  24-034.  Abstract ( 1756 )   RICH HTML PDF (333KB) ( 1179 )   Save The paper presents a new effective preconditioned method and discusses some important properties of the new preconditioned method, and then, shows that the new preconditioned method can accelerate the convergence of Jacobi and Gauss-Seidel iterations for strictly diagonally dominant irreducible Z-matrices. Some comparison theorems proved in the paper generalized some known results. Some numerical examples illustrate its validity. Related Articles | Metrics

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On the Regular Points of Zygmund Differentiable Maps Xu Xu;Zhang Yuntao Acta mathematica scientia,Series A. 2008, 28 (1):  35-038.  Abstract ( 1582 )   RICH HTML PDF (256KB) ( 1025 )   Save The main result of this article is: For any Zygmund class $C^{p,Z}$ map $f:R^{n}\rightarrow R^{m}$ if $\frac{n-m}{2}\leq p\leq n-m-1$, then either mes$K_{f}>0$ or mes$C_{f}>0$. It provides a partial answer of the Hirsch Problem. Related Articles | Metrics

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Existence of Positive Periodic Solutions of a Prey-Predator System with Several Delays Xu Wenxiong; Zhang Tailei; Xu Zongben Acta mathematica scientia,Series A. 2008, 28 (1):  39-045.  Abstract ( 2023 )   RICH HTML PDF (276KB) ( 1199 )   Save A kind of non-autonomous prey-predator system with Holling II response function and several delays is studied. By the coincidence degree theory, the authors construct a set ofsufficient conditions to prove the existence of global positive periodic solution. Some known results are improved. Related Articles | Metrics

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The Inverse Problem of Single Photon Emission Computed Tomography Huang Hui ; Fei Pusheng ;Yuan Yuan Acta mathematica scientia,Series A. 2008, 28 (1):  46-058.  Abstract ( 2018 )   RICH HTML PDF (816KB) ( 1164 )   Save The image reconstruction processing in Single Photon Emission Computed Tomography (SPECT) is a very ill-posed inverse problem. Due to its practical importance for medical diagnostics, this problem has been addressed various times recently. In this paper, the authors discuss theoretical settings of SPECT and propose new numerical strategies based on Tikhonov-type regularization for solving it. Moreover, multilevel continuation mechanism for large-scale problems is designed. Numerical results and conclusion follow. Related Articles | Metrics

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Some Sharp Inequalities for Generalized Grotzsch Ring Function Zhang Xiaohui;Qiu Songliang;Chu Yuming ;Wang Gendi Acta mathematica scientia,Series A. 2008, 28 (1):  59-065.  Abstract ( 2080 )   RICH HTML PDF (275KB) ( 1040 )   Save For $a\in(0,1/2]$ and $r\in(0,1)$,let $\mu_a(r)$ be the so-called generalized Gr\"otzschring function which is defined by $\mu_a(r)=[\pi\K'_a(r)]/[2\sin(\pi a)\K_a(r)]$,appearing in Ramanujan's generalized modular equations.In this paper, the authors study the relations of the functions$\mu_a(r)$ and $\mu(r)$ and the monotonicity and convexity of combinations of the function $\mu_a(r)$ and some elementary functions, and obtain several sharp inequalities for $\mu_a(r)$. Some properties of the function $\mu(r)$ are generalized to the function $\mu_a(r)$. Related Articles | Metrics

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On the Law of the Iterated Logarithm for Products of Sums Chen Pingyan Acta mathematica scientia,Series A. 2008, 28 (1):  66-072.  Abstract ( 1927 )   RICH HTML PDF (233KB) ( 1147 )   Save Let $\{X,X_n,n\geq1\}$ be a stationary stochastic sequence of independent, or $\varphi$-mixing, or $\rho$-mixing positive random variables, or $\{X,X_n,n\geq1\}$ be a positive random variable sequence such that $\{X_n-EX,n\geq1\}$ is a stationary ergodic martingale differences, and set $S_n=\sum\limits^n_{j=1}X_j$ for $n\geq1 $. This paper proves certain law of the iterated logarithm for properly normalized products of the partial sums, $\prod\limits^n_{j=1}S_j/n!\mu^n$ when $EX=\mu>0$ and $0<{\rm Var}(X)<\infty$. Related Articles | Metrics

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The Existence of Positive Solutions to Boundary Value Problems of Second Order Singular Differential Equations Kang Ping; Liu Lishan Acta mathematica scientia,Series A. 2008, 28 (1):  73-080.  Abstract ( 2009 )   RICH HTML PDF (281KB) ( 1189 )   Save In this paper, by constructing a special cone and using the fixed point theorems of cone expansion and cone compression, the existence of two positive solutions to a class of boundary value problem of second order singular differential equations is investigated. The results presented here improve some recent results. Related Articles | Metrics

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Probabilistic Numerical Method for Boundary Value Problems Tang Li ; Yang Wensheng Acta mathematica scientia,Series A. 2008, 28 (1):  81-085.  Abstract ( 2076 )   RICH HTML PDF (276KB) ( 1290 )   Save In this paper a kind of numerical method for boundary value problems over bounded or unbounded domains is investigated by probability theory. It's main idea is as follows: Firstly, represent the solution of the boundary value problem as the stochastic representations. Secondly, construct an auxiliary ball and subdivide the boundaries of the domains to make the problem discretized. Finally, by using the strong Markov property and the distributions of the time and place of hitting spheres for Brownian motion with drift, obtain the solutions to the discretized problems. Related Articles | Metrics

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Analysis of Solitary-wave Shape and Solutions of the Generalized Strong Nonlinear Boussinesq Equation zhangWeiguo; Tao Tao Acta mathematica scientia,Series A. 2008, 28 (1):  86-92.  Abstract ( 2162 )   RICH HTML PDF (329KB) ( 1544 )   Save In this paper, the relations among dissipation term, speed of wave, asymptotic value and wave shape are established for generalized strong nonlinear Boussinesq equation. Their kink or bell shape solitary-wave solutions are obtained by proper transformation and undetermined assumption method. The authors also obtain the periodic wave solutions of cosine function for the generalized Boussinesq equation without dissipation term, which have not been reported before. Moreover, a conclusion with respect to wave speed's influence on wave shape is shown, i.e., for ``good'' Boussinesq equation travalling wave solution changes to cosine periodic wave solution from bell shape solitary-wave solution as wave speed varies from small to large; for ``bad'' Boussinesq equation travalling wave solution changes to bell shape solitary-wave solution from cosine periodic wave solution as wave speed varies from small to large. Related Articles | Metrics

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Lagrangian Globalization Projection Methods for Nonlinear Constrained Equations Tong Xiaojiao ;He Wei Acta mathematica scientia,Series A. 2008, 28 (1):  96-108.  Abstract ( 1939 )   RICH HTML PDF (411KB) ( 1045 )   Save To solve constrained nonlinear equations based on optimization algorithms is suffered a difficulty that the authors obtain just a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. Then the arising problem is how to get a better point from the stationary point or the local minimizer point. By using a projection-type method, this paper extends the Lagrangian globalization (LG) method [8, 9] to a system of nonlinear equations with bounded constraints. The authors prove that from a stationary point, the LG projection method can find a better point. Numerical examples also show that the LG method has a potential to escape the stationary point of optimization problems. Related Articles | Metrics

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Cauchy Problem for the Nonhomogeneous Hyperbolic Conservation Laws with the Degenerate Viscous Term Wang Bing;Xu Xuewen Acta mathematica scientia,Series A. 2008, 28 (1):  109-115.  Abstract ( 1949 )   RICH HTML PDF (323KB) ( 1081 )   Save In this paper, the authors consider Cauchy problem for the nonhomogeneous hyperbolic conservation laws with the degenerate viscous term $$ \left\{\begin{array}{l} u_t+f(u)_x=a^2t^\alpha u_{xx}+g(u),\ \ \ x\in{\bf R},\ \ \ t>0,\\ u(x,0)=u_0(x) \in L^\infty({\bf R}). \end{array}\right. \eqno{({\rm I})} $$ where here $f(u),g(u)$ is a one order continuous and differentiable function defined on ${\bf R}, a>0, 0<\alpha <1$ are both constants. Under these conditions, the authors obtain the local existence of solutions of the Cauchy problem (I). Then, the authors get $L^\infty$ estimate of solution by the maximum principle and make use of the extension theorem to obtain the global existence. Related Articles | Metrics

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Comonotonic Theorems of BSDEs with Stochastic Generators Zhang Hui Acta mathematica scientia,Series A. 2008, 28 (1):  116-127.  Abstract ( 1874 )   RICH HTML PDF (366KB) ( 1150 )   Save In this paper, the authors explore the solution (y,z) of BSDEs via the theory of Malliavin derivative. Some methods of comparing part z have been given. And the authors point out that the comonotonic theorems for part z given by Zengjing Chen et al (see [3]) aren't correct when the generators of BSDEs are stochastic. Thus some special conditions, under which the comonotonic theorems for part z are correct even the generators of BSDEs are stochastic, are studied. Then, applying the comonotonic theorems, the authors study the additivity of a class of conditional g-expectations and Choquet integral represention theorems. Related Articles | Metrics

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The Rigidity of Clifford Torus {\boldmath Sm(\sqrt{\frac{m}{n}})\timesSn-m(\sqrt{\frac{n-m}{n}}) Zhang Yuntao ;Xu Senlin Acta mathematica scientia,Series A. 2008, 28 (1):  128-132.  Abstract ( 2078 )   RICH HTML PDF (228KB) ( 1125 )   Save Let $M$ be an $n$-dimensional closed minimal hypersurface of the unit sphere $S^{n+1}(1)$. If $n \le S \le n+\frac{2}{3}$,then $S=n$ and $M$ is isometric to $S^m(\sqrt{m/n}) \times S^{n-m}(\sqrt{(n-m)/n})$. Related Articles | Metrics

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Distance-Regular Graphs of Type E1 ο Ed and the Q -polynomial Property Gao Suogang;You Hong Acta mathematica scientia,Series A. 2008, 28 (1):  133-143.  Abstract ( 1794 )   RICH HTML PDF (299KB) ( 1142 )   Save Let $\Gamma$ be a nonbipartite distance-regular graph with $d\geq 3$, and eigenvalues $\theta_{0}>\theta_{1}>\cdots >\theta_{d}.$ Let $\theta_{1'}\in\{ \theta_{1},\theta_{d}\}, $ and let $\theta_{d'}$ be the complement of $\theta_{1'}$ in $\{ \theta_{1},\theta_{d}\}$. Assume that $\Gamma$ is of type $E_{1}\circ E_{d}$ with property $ E_{1}\circ E_{d}=|X|^{-1}(q^{d-1}_{1d}E_{d-1}+q^{d}_{1d}E_{d})$ and that $\sigma_{0},\sigma_{1},\cdots,\sigma_{d}$, $\rho_{0},\rho_{1},\cdots,\rho_{d}$ and $\beta_{0},\beta_{1},\cdots,\beta_{d}$ are the cosine sequences associated with $\theta_{1'}$,$\theta_{d'}$ and $\theta_{d-1}$, respectively. Using the above cosine sequences, the authors give some equivalence conditions of $\Gamma$ being $Q$-polynomial with respect to $\theta_{1}$ or $\theta_{d}.$ Related Articles | Metrics

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Condition of Reliable D Stability for a Class of Dynamic Systems-an LMI Approach Zhou Wuneng ;Su Hongye;Chu Jian Acta mathematica scientia,Series A. 2008, 28 (1):  144-154.  Abstract ( 1953 )   RICH HTML PDF (285KB) ( 1171 )   Save The synthesis problem of reliable robust control for a class of dynamic systems is considered. A practical and general faults model with sensor, actuator is addressed. A necessary and sufficient condition of D -stability is presented, based on which a sufficient condition of existence of the reliable H∞ controller is given for the case of sensor, actuator failures. The reliable H∞ controller is designed in terms of linear matrix inequalities (LMIs), which guarantees the closed-loop to be D -stable and possesses H∞ performance when all control components are operational as well as some control components experience failures. Finally, a numerical example is given to illustrate the design procedures and the effectiveness. Related Articles | Metrics

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Second-order Optimality Conditions for C1,1 Semidefinite Programming Zhao Wenhui;Gao Yan Acta mathematica scientia,Series A. 2008, 28 (1):  155-163.  Abstract ( 1800 )   RICH HTML PDF (285KB) ( 1022 )   Save In this paper the authors study a class of nonsmooth semidefinite programming problems, where the objective function is of class C1,1 and the constrain is semidefinite. By using Peano generalized derivatives necessary and sufficient second-order optimality conditions are derived. Related Articles | Metrics

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Focal Quantities Algorithms and Center Conditions Deduction Sang Bo ;Zhu Siming Acta mathematica scientia,Series A. 2008, 28 (1):  164-173.  Abstract ( 1719 )   RICH HTML PDF (347KB) ( 1533 )   Save For general cases, this paper gives recursive formulas for computing focal quantities by return map method, and brings in an algorithm for computing and simplication of focal quantities by formal series method. For a class of polynomial systems, an algorithm for deriving time-reversible conditions is given, and the time-reversible conditions for a quintic polynomial system are obtained. Related Articles | Metrics

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Positive Solutions of Some Singular Sub-linear Three-point Boundary Value Problems Wei Zhongli Acta mathematica scientia,Series A. 2008, 28 (1):  174-182.  Abstract ( 2120 )   RICH HTML PDF (255KB) ( 1105 )   Save This paper investigates the existence of positive solutions for second-order singular sub-linear three-point boundary value problems. A necessary and sufficient condition for the existence of C [0,1] as well as C1[0,1] positive solutions is given by constructing lower and upper solutions and with the comparison theorem. The nonlinearity f(t,x) may be singular at , \ t=0 and /or t=1 . Related Articles | Metrics

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Quasiconformal Mappings and Hausdorff Dimension Liao Maoxin; Chu Yuming Acta mathematica scientia,Series A. 2008, 28 (1):  183-187.  Abstract ( 2048 )   RICH HTML PDF (225KB) ( 1376 )   Save The authors discuss change of Hausdorff dimensiondimH(F) for standard Cantor set F under quasiconformal mapping f ,and obtain sharp superior and inferior bounds of dimH(f(F)). Related Articles | Metrics

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Oscillation of Higher Order Nonlinear Functional Differential Equation with Impulses Zhang Chaolong; Yang Fengjian; Yang Jianfu Acta mathematica scientia,Series A. 2008, 28 (1):  188-200.  Abstract ( 2071 )   RICH HTML PDF (296KB) ( 1223 )   Save A kind of extensively higher order nonlinear FDE with impulses is studied in this paper. Several criteria on the oscillations of solutions are given. Related Articles | Metrics