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25 May 2010, Volume 30 Issue 3 Previous Issue    Next Issue

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Solutions of Finite Order to a Completely Indeterminate Hamburger Matrix Moment Problem CHEN Gong-Ning, QIN Jian-Guo Acta mathematica scientia,Series A. 2010, 30 (3):  577-583.  Abstract ( 1582 )   RICH HTML PDF (363KB) ( 1223 )   Save In this paper we describe solutions ρ of finite order to a completely indeterminate Hamburger matrix moment problem with moments {νm}0∞( Cq×q: νm=∫-∞∞xmdρ(x), m=0,1, …, i.e., those solutions ρ for which the linear space P of Cq ×q -valued polynomials is dense in the corresponding L2(R, dρ / E(x) for some scalar polynomial E(x) positive on the real line R. As preliminaries we consider a certain connection of a matrix version of the so-called generalized Akhiezer interpolation with its related matrix moment problem. References | Related Articles | Metrics

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A Class of New Solutions to the Einstein's Field Equations SHEN Ming, SUN Qing-You Acta mathematica scientia,Series A. 2010, 30 (3):  584-592.  Abstract ( 1461 )   RICH HTML PDF (336KB) ( 1086 )   Save In this paper the authors construct a new class of solutions to the vacuum Einstein's field equations, and give two interesting examples including a time-periodic solution which is related to the loop cosmology. The authors show that this class of soultions are not Minkowski, and essentially differnt from other space-times. One can expect that these solutions can be applied to   modern cosmology and general relativity. References | Related Articles | Metrics

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Regularity Criteria for the Compressible Magneto-hydrodynamic Equations WU Hong-Wei Acta mathematica scientia,Series A. 2010, 30 (3):  593-602.  Abstract ( 1619 )   RICH HTML PDF (294KB) ( 1154 )   Save We study the magneto-hydrodynamic (MHD) equations of 3D compressible isentropic and 2$D$ heat-conducting flows with positive density respectively. We prove some blow-up criteria for the local strong solutions. References | Related Articles | Metrics

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Two Schemes for Lifting Frames LU Da-Yong, FAN Qi-Bin Acta mathematica scientia,Series A. 2010, 30 (3):  603-612.  Abstract ( 2004 )   RICH HTML PDF (360KB) ( 1158 )   Save This paper presents two methods for lifting frames that allow people to modify existing dyadic wavelet frames or filters to construct new ones. In particular, these methods enable people to design nonseparable frames from tensor products of a piecewise linear spline tight frame, which can play the roles of the weighted average operator, the Sobel operator and the Laplacian operator in directions that are integer multiples of π/4. References | Related Articles | Metrics

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Uniqueness of Solutions of Martingale Problems with Degenerate Coefficients LI Yu-Qiang Acta mathematica scientia,Series A. 2010, 30 (3):  613-622.  Abstract ( 1620 )   RICH HTML PDF (335KB) ( 1056 )   Save In this paper, we first prove the uniqueness of solutions of a kind of martingale problems with degenerate diffusion coefficients in Skorokhod space D[0,+∞)[0,+∞) under some bounded condtions. Then, it is proved that these bounded conditions can be weakened via a transformation. References | Related Articles | Metrics

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On Perturbation of Generalized Dirichlet Forms by Singed Smooth Measures and the Associated Nice Markov Processes HAN Xin-Fang, MA Li, YANG Xue Acta mathematica scientia,Series A. 2010, 30 (3):  623-629.  Abstract ( 1950 )   RICH HTML PDF (377KB) ( 1177 )   Save This paper studies the perturbations εμ  of the generalized Dirichlet form ε by some signed smooth measures and the associated Markov processes.  It proves that the perturbations are also generalized Dirichlet forms and associated with ``nice'' Markov processes under some conditions. References | Related Articles | Metrics

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Diagnostic Checking for Multivariate GARCH-type Models in Time Series WU Jian-Hong, ZHU Li-XIng Acta mathematica scientia,Series A. 2010, 30 (3):  630-638.  Abstract ( 1672 )   RICH HTML PDF (627KB) ( 1121 )   Save Multiple time series with time-varying conditional variance are verified to be useful in both theory and real applications. In this article, a battery of score-type diagnostic tests are suggested for checking the adequacy of multivariate GARCH-type models fitting multiple time series. The resulting tests are asymptotically chi-squared under the null hypothesis, and critical values can  be obtained easily. Moreover, they are sensitive to alternatives and  can detect the alternatives approaching the null at the rate arbitrarily close to 1/√n,  the fastest possible rate in goodness-of-fit test. For a large number of alternatives, an asymptotically distribution-free maximin test is constructed. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. Furthermore, it is worthwhile to show that the battery of tests can detect separate aspects of possible departures from the null and then provide us more specifical information about the likely source of misspecification. Simulation results indicate that the tests perform well. References | Related Articles | Metrics

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A Liouville-type Theorem for a Doubly Degenerate Parabolic Inequality JIANG Chao-Xin, ZHENG Si-Ning Acta mathematica scientia,Series A. 2010, 30 (3):  639-643.  Abstract ( 2061 )   RICH HTML PDF (259KB) ( 1187 )   Save This paper deals with the nonexistence of nontrivial nonnegative global solutions to a doubly degenerate parabolic inequality ut ≥ div(|\nabla u| β\nabla u m)+u p on the half space S=Rn×(0, ∞), where the parameters m≥1, p>1, β≥0. By using a test function method, we establish a Liouville-type theorem tha the inequality has no nontrivial nonnegative solution on S if m+β< p <m+β+β+2/n. References | Related Articles | Metrics

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The Smooth Point in C(Ω) WANG Rui-Dong Acta mathematica scientia,Series A. 2010, 30 (3):  644-648.  Abstract ( 1264 )   RICH HTML PDF (266KB) ( 1232 )   Save In this paper, we study the smooth point (peak function) in space of C(Ω), where Ω is compact Hausdorff space. We give an example to show that there exists compact Hausdorff space Ω1 such that the smooth point of C(Ω1) is dense in the whole space. And we give an counter example to show that there exists compact Hausdorff space Ω2 such that the smooth point of C(Ω2) is empty. Finally we give an intrinsic character of the smooth point of space C(Ω) is dense in the whole space. References | Related Articles | Metrics

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Characterizations of Pairwise Stratifiable Spaces LI Ke-Dian Acta mathematica scientia,Series A. 2010, 30 (3):  649-655.  Abstract ( 1380 )   RICH HTML PDF (268KB) ( 1191 )   Save In this paper, we give some characterizations of pairwise stratifiable spaces by means of pairwise g-functions and semi-continuous functions. It is established that: a space  (X, τ1, τ2)  is pairwise stratifiable  if and only if for each f  ∈ τi - LSC(X),  one assigns an  h(f) ∈τi -LSC(X)∩τj - USC(X) such that. (1)   0≤ h(f)≤ f and 0<h(f)(x)<f(x) whenever f(x)>0 . (2)    h(f)≤ h(f') whenever f≤ f' . References | Related Articles | Metrics

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The Erlang (2) Risk Model with Interclaim-dependent Claim Sizes and Constant Dividend Barrier DONG Ying-Hui, WANG Guo-Jing Acta mathematica scientia,Series A. 2010, 30 (3):  656-665.  Abstract ( 1709 )   RICH HTML PDF (312KB) ( 1079 )   Save This paper considers Erlang(2) risk process with a constant dividend barrier. The Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments associated with the proposed model are investigated. Integral equations, integro-differential equations are derived. And  the Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments are analyzed. References | Related Articles | Metrics

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Mixed Finite Element Approximation for the Plate Contact Problem AN Rong, LI Kai-Tai Acta mathematica scientia,Series A. 2010, 30 (3):  666-676.  Abstract ( 1742 )   RICH HTML PDF (395KB) ( 1057 )   Save The finite element approximation for the fourth order elliptic variational inequality of the second kind modeling of the plate contact problem is investigated in this paper. By the regularized method, the variational inequality is reduced to the variational equation. By using the refined Ciarlet-Raviart's mixed finite element method via the technique of mesh dependent norm, some error estimates are obtained. References | Related Articles | Metrics

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Joint Distributions of Some Actuarial Random Vectors in the Continuous-time Compound Binomial Model ZHAO Jin-Yan, LIU Guo-Xin Acta mathematica scientia,Series A. 2010, 30 (3):  677-693.  Abstract ( 2086 )   RICH HTML PDF (408KB) ( 1224 )   Save The continuous-time compound binomial model, firstly proposed by[1], is the continuous-time version of the compound binomial model. In this paper, a renewal mass function of a defective renewal sequence constituted by the up-crossing zero points is introduced in the continuous-time compound binomial model. By the mass function together with the strong Markov property of the surplus process X(t), the explicit expressions of the ruin probability and the joint distributions of some actuarial random vectors such as (T, X(T-), |X(T)|), (T, X(T-), |X(T)|, inf0≤t<L X(t)) and (T, X(T-), |X(T)|, sup0≤t<T X(t)) are obtained, where T represents the time of ruin and L the time of the surplus process leaving deficit ultimately. The corresponding joint distributions are directly obtained for the compound binomial model, {X(n)}, as the 1-skeleton chain of the continuous-time compound binomial model. Finally, a special case with the claim amount being geometrically distributed in the compound binomial model is considered. References | Related Articles | Metrics

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Stability of |Impulsive Coupled |Delay Differential and Continuous Time Difference Systems ZHANG Yu, SUN Ji-Tao Acta mathematica scientia,Series A. 2010, 30 (3):  694-702.  Abstract ( 1846 )   RICH HTML PDF (352KB) ( 1290 )   Save The purpose of this paper is to investigate the stability of impulsive coupled delay differential and continuous time difference systems. First, some new concepts of L2 stability, attraction and L2 asymptotic stability for this kind of systems are introduced, then some criteria of L2 stability and L2 asymptotic stability are obtained. An example is also presented to illustrate the efficiency of the obtained results. It should be noticed that this kind of impulsive systems is considered for the first time. References | Related Articles | Metrics

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Existence of Local Solutions of a Class of Integral Equations FAN Jin-Jun Acta mathematica scientia,Series A. 2010, 30 (3):  703-707.  Abstract ( 1563 )   RICH HTML PDF (222KB) ( 1288 )   Save In this paper,  using the Daher fixed point theorem, we prove the existence of local solutions of integral equations of Volterra type, which improves or extends the results in [1]. References | Related Articles | Metrics

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The Weighted Generalized Inverses of Matrices over Rings LIAO Zu-Hua, HUANG Yu, YI Li-Hua Acta mathematica scientia,Series A. 2010, 30 (3):  708-717.  Abstract ( 1587 )   RICH HTML PDF (341KB) ( 1232 )   Save In this paper, we give a new kind of answer from another aspect to an open problem posed by   Hartwig R E[27]. Let R be an arbitrary ring with involution *. We define a new type of the weighted generalized inverse of matrices over R, denoted by A+P, Q, and give the necessary and sufficient conditions for the existence of A+P, Q. And several expressions of A+P, Q are also given. Meanwhile, some important properties are obtained. References | Related Articles | Metrics

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Solutions of Some m-point Boundary Value Problems for Second-order Differential Equations LI Xing-Chang, ZHAO Zeng-Qin Acta mathematica scientia,Series A. 2010, 30 (3):  718-729.  Abstract ( 1791 )   RICH HTML PDF (312KB) ( 1205 )   Save In this paper, we consider some m-point boundary value problems of second-order differential equations. We give the uniqueness and the  exact expressions of the solutions for the linear differential equations with some m-point boundary conditions. As applications, we study the solution by iteration method for some nonlinear singular boundary value problems. References | Related Articles | Metrics

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Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales LI Yong-Kun, ZHANG Hong-Tao Acta mathematica scientia,Series A. 2010, 30 (3):  730-742.  Abstract ( 1865 )   RICH HTML PDF (328KB) ( 1122 )   Save By using a fixed point theorem on strict-set-contraction, some sufficient conditions  are obtained for the existence of positive periodic solutions for a periodic neutral functional differential equation on time scales of the form xΔ(t)=x(t)[r(t)-a(t)x(t)-∑nj=1aj(t) x(t-τj(t, x(t)))-∑nj=1cj(t) xΔ(t-σj(t, x(t)))g ], where r, a, aj, cj ∈C( T, R+)(j =1, 2, … , n) are ω -periodic functions, and τj, σj ∈C( T×R, T)(j =1, 2, … , n) are ω -periodic functions with respect to their first arguments, respectively. References | Related Articles | Metrics

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The Generalized (Anti)reflexive Solutions to a System of Quaternion Matrix Equations ZHANG Qin, WANG Qing-Wen, CHANG Hai-Xia Acta mathematica scientia,Series A. 2010, 30 (3):  743-752.  Abstract ( 2078 )   RICH HTML PDF (308KB) ( 1120 )   Save We give necessary and sufficient conditions for the existence of the general solution to the system of quaternion matrix equations  X1B1=C1, X2B2=C2, A1X1B3+A2X2B4=Cb . When the solvability conditions are met, we present an expression of the general solution to this system. Using the results on this system, we investigate necessary and sufficient conditions for the existence of generalized reflexive and generalized antireflexive solutions to the system of quaternion matrix equations XBa=Ca, AbXBb=Cb . We present expressions of the generalized reflexive and generalized antireflexive solutions to the system mentioned above when the solvability condtions are satisfied. References | Related Articles | Metrics

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Asymptotic Behavior for a Class of Nonlinear Impulsive Neutral Delay Differential Equations WEI Geng-Ping, SHEN Jian-Hua Acta mathematica scientia,Series A. 2010, 30 (3):  753-763.  Abstract ( 1589 )   RICH HTML PDF (312KB) ( 1048 )   Save This paper is concerned with the nonlinear impulsive neutral delay differential equation with positive and negative coefficients, $$\left\{ \begin{array}{ll} [x(t)-c(t)x(t-\tau)]'+p(t)f(x(t-\delta))-q(t)f(x(t-\sigma))=0,\quad t\geq t_0,~ t\not= t_k, \\ x(t_k)= b_kx(t_k^-)\\ \disp\qquad \quad\ \ +(1-b_k)\left(\int^{t_k}_{t_k-\delta}p(s+\delta)f(x(s)){\rm d}s- \int^{t_k}_{t_k-\sigma}q(s+\sigma)f(x(s)){\rm d}s\right),\\ \hskip 9.7cm k=1,2,3,\cdots. \end{array} \right.$$ Sufficient conditions are obtained for every solution of the above equation tending to a constant as $t\to \infty$. References | Related Articles | Metrics

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Nonconforming Finite Element Method for Integro-Differential Equation of Parabolic Type with Weakly Singular Kernel SHI Dong-Yang, GUO Cheng, WANG Hai-Hong Acta mathematica scientia,Series A. 2010, 30 (3):  764-775.  Abstract ( 1683 )   RICH HTML PDF (337KB) ( 1197 )   Save The nonconforming finite element methods for integro-differential equation with a weakly singular kernel are studied. The same optimal error estimates as the traditional methods both in semi-discrete scheme and full discretization are obtained without using Ritz-Volterra projection. References | Related Articles | Metrics

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An Iterative Method for the Least Squares Centrosymmetric Solution of the Matrix Equation AXB+CXD=F SHANG Li-Na, ZHANG Kai-Yuan Acta mathematica scientia,Series A. 2010, 30 (3):  776-783.  Abstract ( 2018 )   RICH HTML PDF (317KB) ( 1120 )   Save An iterative method is presented to solve the minimum Frobenius norm residual problem: min AXB+CXD-F with unknown centrosymmetric matrix X. By this iterative method, for any initial centrosymmetric matrix X0, a solution X* can be obtained automatically within finite iteration steps in the absence of roundoff errors, and the solution X* with least Frobenius norm can be obtained by choosing a special initial centrosymmetric matrix. In addition, its optimal approximation matrix to a given matrix can be obtained. Numerical examples are given to show that the intertive method is quite efficient. References | Related Articles | Metrics

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The Existence of Symmetric Positive |Solutions for a Three-point Singular Boundary Value Problem with a p-Laplace Operator TIAN Yuan-Sheng, LIU Chun-Gen Acta mathematica scientia,Series A. 2010, 30 (3):  784-792.  Abstract ( 1763 )   RICH HTML PDF (293KB) ( 1150 )   Save In this paper, we consider the three-point singular boundary value problem with a p-Laplace operator by using the fixed point index theory, the existence and multiplicity results of symmetric positive solutions are obtained. References | Related Articles | Metrics

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Uniqueness Theorems of Meromorphic Functions in an Angular Domain WU Zhao-Jun Acta mathematica scientia,Series A. 2010, 30 (3):  793-799.  Abstract ( 2181 )   RICH HTML PDF (316KB) ( 1131 )   Save In this paper, we first investigate the uniqueness of meromorphic functions dealing with two shared sets in an angular domain and obtain several uniqueness theorems, which extend the recent results by Yi H X and Lin W C who investigated the uniqueness of meromorphic functions dealing with two shared sets in the whole complex plane. References | Related Articles | Metrics

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Inequalities for Residuals of Power Series for Hyperbolic Sine and Hyperbolic Cosine Functions SONG Ying-Qing, JIA Wei-Feng, CHU Yu-Ming Acta mathematica scientia,Series A. 2010, 30 (3):  800-807.  Abstract ( 1762 )   RICH HTML PDF (279KB) ( 1398 )   Save In this paper, the authors obtain some inequalities for residuals of power series for the hyperbolic sine and hyperbolic consine functions. References | Related Articles | Metrics

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Generalized Projection Methods for Noor Variational Inequalities in Banach Spaces XU Yong-Chun, HE Xin-Feng, HOU Zhi-Bin, HE Zhen Acta mathematica scientia,Series A. 2010, 30 (3):  808-817.  Abstract ( 1559 )   RICH HTML PDF (356KB) ( 1227 )   Save In this paper, we suggest and analyze generalized projection methods for finding the  elements of the set of solutions of the generalized  variational inequalities. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Since the generalized variational inequalities include variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results. References | Related Articles | Metrics

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Some Distributions for the Classical |Risk Process Perturbed by Brownian Motion HE Jing-Min, WU Rong Acta mathematica scientia,Series A. 2010, 30 (3):  818-827.  Abstract ( 1897 )   RICH HTML PDF (294KB) ( 1066 )   Save In this paper, we consider the classical risk process perturbed by Brownian motion. Using the results of the modified ladder heights of this process, we obtain the marginal and joint distributions of the surplus prior to ruin and the deficit at ruin. The explicit solutions for them are derived when the claims are exponentially distributed. References | Related Articles | Metrics

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On S-Armendariz Modules and Quasi S-Armendariz Modules OU Yang-Lun-Qun Acta mathematica scientia,Series A. 2010, 30 (3):  828-834.  Abstract ( 1488 )   RICH HTML PDF (248KB) ( 1134 )   Save In this paper, the author introduce the notion of S-Armendariz  modules, which is a natural generalization of Armendariz rings. It is shown that S-Armendariz  modules have some properties similar to those of  Armendariz rings. Consequently, several known results in  [8], [10] and [11] are extended to a general setting. References | Related Articles | Metrics

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Robust Nonparametric Regression with Simultaneous Scale Curve Estimation Based on Dependent Observations WANG Hong-Ning, YU Huan-Ran Acta mathematica scientia,Series A. 2010, 30 (3):  835-847.  Abstract ( 1745 )   RICH HTML PDF (379KB) ( 1055 )   Save Härdle and Tsybakov's results ([6, p120--135]) is extended to the case where samples are drawn from the strictly stationary sequence with α-mixing. The consistency and asymptotic normality of the estimators are obtained. Simulation studies are conducted to examine the small-sample properties of the proposed estimates. References | Related Articles | Metrics

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The Geometric Rate of Approximation of Neural Network in Lp-Space YU Guo-Hua Acta mathematica scientia,Series A. 2010, 30 (3):  848-856.  Abstract ( 1638 )   RICH HTML PDF (327KB) ( 996 )   Save This paper is devoted to the investigation of approximation of neural network in Lp-space. The convex greedy iteration method is applied to a class of functions that satisfy the so-called "δ-angular condition'' in Lp-space. We show that the rate of approximation is of order o(qn) for some 0<q<1, which extends the result of [1] to Lp-space. References | Related Articles | Metrics

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Thermal Radiation of Weyl Neutrino in Arbitrarily Accelerating Charged Axially Symmetries Dynamic Black Hole CAO Jiang-Ling, YANG Bo Acta mathematica scientia,Series A. 2010, 30 (3):  857-863.  Abstract ( 1385 )   RICH HTML PDF (345KB) ( 1142 )   Save In arbitrarily accelerating charged axial symmetric dynamic space time with new Tortoise coordinate transformation to research the quantum thermal effect of Weyl neutrino the event vision position and thermal radiation temperature of the Weyl neutrino near the vision interface area are gotten and Hawking thermal spectrum equation is deduced. It shows that event vision interface area's location and thermal radiation temperature depend on not only time but also angle. References | Related Articles | Metrics