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25 February 2009, Volume 29 Issue 1 Previous Issue    Next Issue

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Approximating Nonlinear Models of Interest Rates with Branching Processes Li Yuqiang Acta mathematica scientia,Series A. 2009, 29 (1):  1-9.  Abstract ( 1672 )   RICH HTML PDF (314KB) ( 1355 )   Save This paper proves a limit theorem of sequences of the state-dependent branching processes, which shows the nonlinear models of the term structure of interest rates can be approximated by the state-dependent branching processes. Related Articles | Metrics

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The Existence of Almost Periodic Solutions of Second Order Nonlinear Systems Lin Muren;Wei Zhen Acta mathematica scientia,Series A. 2009, 29 (1):  10-19.  Abstract ( 1873 )   RICH HTML PDF (274KB) ( 1203 )   Save This paper discusses some second order nonlinear systems. By the method of average, some sufficient conditions for the existence of almost periodic solutions of nonlinear systems are given, which generalize the known ones. Two particular systems are presented to illustrate that our results are feasible and more general. Related Articles | Metrics

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Injective Ideals of Regular Rings Chen Huanyin; Liu Dayong Acta mathematica scientia,Series A. 2009, 29 (1):  20-24.  Abstract ( 1280 )   RICH HTML PDF (248KB) ( 1186 )   Save Let R be regular, A∈ Mn(R). If Mn(R)AMn(R) is injective as a right Mn(R)-module, we prove that there exist U, V∈ GLn(R) such that UAV is a diaogonal matrix. Related Articles | Metrics

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The Euler Genera of Two Classes of Generalized Petersen Graphs Ma Dengju; Ren Han; Lu Junjie Acta mathematica scientia,Series A. 2009, 29 (1):  25-31.  Abstract ( 1801 )   RICH HTML PDF (316KB) ( 1177 )   Save The generalized Petersen graph P(n, m) is such a graph that its vertex set is {ui, vi |i=0,1, …, n-1} and edge set is {uiui+1, vivi+m, uivi | i=0,1, …, n-1}, where m, n are positive integers satisfying m< |n/2| and indices is read modulo n. It is proved that the Euler genus of P(2m+1, m)(m≥2) is 1 and that the Euler genus of P(2m+2, m)(m≥5) is 2. Related Articles | Metrics

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General Radiation via Tunneling in a Charged BTZ Black Hole Liu Wenbiao Acta mathematica scientia,Series A. 2009, 29 (1):  32-37.  Abstract ( 1494 )   RICH HTML PDF (344KB) ( 1161 )   Save Charged massive radiation from a charged BTZ black hole is investigated. The conservation of energy and charge implies the effect of self-gravitation and self-electromagnetism. Viewed as a tunneling process, the emission spectrum derivates from the purely thermal spectrum, but it is consistent with an underlying unitary theory. The result is the same as that of uncharged massless particles. Related Articles | Metrics

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Ladder Height and Supremum of a Random Walk with Applications in Risk Theory Yin Chuancun; Zhao Xianghua; Hu Feng Acta mathematica scientia,Series A. 2009, 29 (1):  38-47.  Abstract ( 1706 )   RICH HTML PDF (340KB) ( 1293 )   Save For a random walk on the real line with negative mean, we obtain a local asymptotic estimate and a tail asymptotic estimate for the distributions of ladder height and supremum for the random walk when the conditions for the exponential estimate are not satisfied. The results are applied to the Sparre Andersen model and some new results on the probability of ruin are presented. Related Articles | Metrics

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Positive Radial Solution to a Class of Nonlinear Dirichlet Boundary Value Problems Yao Qingliu Acta mathematica scientia,Series A. 2009, 29 (1):  48-56.  Abstract ( 1860 )   RICH HTML PDF (340KB) ( 1192 )   Save By constructing a suitable cone and applying the fixed point theorem of cone expansion and compression type, the existence of positive radial solution is studied for a class of singular elliptic Dirichlet boundary value problems, where the nonlinear term may be singular. Main results show that the existence of positive radial solution depends only upon the properties of nonlinear term on a bounded subset of its domain, and the existence is independent of the properties of nonlinear term outside this set. Related Articles | Metrics

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The Eigenvalue Problems of Biharmonic Equations Liu Xiangqing; Huang Yisheng; Deng Zhiying Acta mathematica scientia,Series A. 2009, 29 (1):  57-69.  Abstract ( 2174 )   RICH HTML PDF (383KB) ( 1315 )   Save In this paper, we consider the existence of the solution for the biharmonic eigenvalue problem under Navier boundary condition Δ2u=λa(x)u+f(x, u), x∈ Ω, u=Δu=0, x∈ Ω, where Ω is a bounded domain in RN(N ≥ 5), Δ2 is the biharmonic operator, and the weight function a(x) ∈Lr(Ω)(r ≥ N/4) with a(x)> 0 a.e. in Ω. By variational method, we obtain the second eigenvalue of this problem when f(x, u)=0 and study the structure of it, and discuss the existence of the nonzero solutions under resonance and nonresonance conditions. Related Articles | Metrics

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Weak Hopf Superalgebras wsldq(m|n) Liu Junli; Yang Shilin Acta mathematica scientia,Series A. 2009, 29 (1):  70-86.  Abstract ( 1205 )   RICH HTML PDF (342KB) ( 1070 )   Save Along the idea of definition of a weak Hopf algebra in the sense of a bialgebra attached with a weak antipode, we give a definition of weak Hopf uperalgebra. As an example, a class of weak Hopf superalgebras but not Hopf uperalgebras wsldq(m|n) is constructed. The PBW basis of wsldq(m|n) is described. Related Articles | Metrics

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The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rn Xu Xingye Acta mathematica scientia,Series A. 2009, 29 (1):  87-93.  Abstract ( 1803 )   RICH HTML PDF (284KB) ( 1044 )   Save In this paper, author’s aim is to establish the theorems of existence of positive radially symmetric entire solutions for a class of singular nonlinear biharmonic equation Δ2u=f(|x|, u,| u|)u-β (x ∈ Rn, n ≥ 3, β > 0) on Rn with the Schauder-tychonoff fixed point theorem as the principal tool, and presents the properties of the solutions. They enrich and develop the theory and application of papes [1--5]. Related Articles | Metrics

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Duality Principles of Frames in Banach Spaces Xiao Xuemei; Zhu Yucan Acta mathematica scientia,Series A. 2009, 29 (1):  94-102.  Abstract ( 1587 )   RICH HTML PDF (288KB) ( 1159 )   Save Duality principles in Gabor theory such as the Ron-Shen duality principle and the Wexler-Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. For each sequence in a Banach space X, we define a corresponding sequence dependent only on two $p$-Riesz bases in the Banach space X. Then we characterize exactly properties of the first sequence in terms of the associated one. We generate some results that were obtained by P. G. Casazza, G. Kutyniok and M. C. Lammers about duality principles of frames in a separable Hilbert space H. Related Articles | Metrics

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High Accuracy Combination Algorithms for Solving Singular Integral Equations with Hilbert Kernel by Quadrature Methods Huang Jin; Lü Tao; Zhu Rui Acta mathematica scientia,Series A. 2009, 29 (1):  103-113.  Abstract ( 1809 )   RICH HTML PDF (349KB) ( 1335 )   Save This paper presents high accuracy combination algorithms for solving singular integral equations with Hilbert kernel by quadrature methods. A given fine grid set is divided into some subsets with different grid points. After these discrete equations dependent on the subsets are solved in parallel, the global fine grid approximations can be computed by the combination algorithms. It shows that the accuracy of quadrature methods is very high with O(e-nδ) if the coefficients of equations belong to Bδ, Besides, using the combination algorithms can not only obtain a higher order of the accuracy, but also a posterior error estimate is deduced. These excellent numerical results display the significance of these algorithms made in the paper. Related Articles | Metrics

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The Solution Sets and Connectedness for Weak Vector Variational Inequalities Huang Longguang Acta mathematica scientia,Series A. 2009, 29 (1):  114-120.  Abstract ( 1755 )   RICH HTML PDF (291KB) ( 1100 )   Save The existence and connectedness of solutions for weak vector variational inequalities and their scalarization with a C-monotone mapping from a topological vector space to continuous linear mapping space L(X, Y) are shown. With the C-weak hemicontinuity and C-monotonicity for a mapping, and setvalued mapping fixed point theorems, the connectedness are derived by discussing the properties of set-valued mapping induced by solution sets of a scalarization variational inequality related to the weak vector variational inequalities. Related Articles | Metrics

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Uniform Domain and Max-min Inequality Property Liao Maoxin; Chu Yuming; Li Xianyi Acta mathematica scientia,Series A. 2009, 29 (1):  121-126.  Abstract ( 2301 )   RICH HTML PDF (259KB) ( 1007 )   Save Introducing the max-min inequality property of domain,we investigate the relation between uniform domain and max-min inequality property, and obtain the following results: (1) if D is uniform domain, then D has max-min inequality property; (2) if D R2 and D*=R2\D have max-min inequality poperty, respectively, then D is uniform domain. Related Articles | Metrics

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The Existence of Positive Solutions of a Class of Fourth-order Singular Boundary Value Problems Zhang Kemei; Wang Chunmei Acta mathematica scientia,Series A. 2009, 29 (1):  127-135.  Abstract ( 1907 )   RICH HTML PDF (304KB) ( 1217 )   Save By using the fixed point index theorem and the properties of Green function, the author presents the existence of positive solutions for singular boundary value problems of fourth-order differential equations. The conditions used in this paper are weaker. Related Articles | Metrics

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Parameterization of 4-Band Orthogonal Scaling Filters with Linear Phase Feng Xiaoxia;Guo Xiaoyong;Cheng Zhengxing Acta mathematica scientia,Series A. 2009, 29 (1):  136-144.  Abstract ( 1707 )   RICH HTML PDF (392KB) ( 1108 )   Save In this paper, the authors give parameterization of 4-band orthogonal scaling filters with linear phase, and propose a simple method to construct the corresponding wavelet filters. Applying this parameterization form, the authors can derive symmetric orthogonal scaling functions with compact support. Furthermore, the corresponding wavelets can be obtained by the method. Related Articles | Metrics

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Independence Number in Claw-free Cubic Graphs Wang Chunxiang Acta mathematica scientia,Series A. 2009, 29 (1):  145-150.  Abstract ( 1533 )   RICH HTML PDF (287KB) ( 1007 )   Save A set X is independent if no two vertices of X are adjacent. A set X is dominating if N[X]=V(G). A dominating set X is minimal if no set X\{x} with x∈ X is dominating. The independence number i(G)(\beta(G)) is the minimum (maximum) cardinality of a maximal independent set of G. The domination number γ(G) (the upper domination number Γ(G)) is the minimum (maximum) cardinality of a minimal dominating set of G. In this paper, we prove that: (1) if G ∈ R and G is a cubic graph of order n, then γ(G)=i(G), β(G)=n/3; (2) for every connected claw-free cubic graph G of order n, if G(G≠ K4) contains no K4-e as induced subgraph, then β(G)=n/3. Related Articles | Metrics

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The Embedded Subbundles over Module Bundles Zhang Feijun; Li Kaitai Acta mathematica scientia,Series A. 2009, 29 (1):  151-157.  Abstract ( 1508 )   RICH HTML PDF (339KB) ( 1097 )   Save To construct the embedded subbundles of free bundles and the embedded free subbundles of any module bundles, by using embedded relation of module bundles. It is indicated that any module bundles can becomes a embedded subbundles of free bundles,and that there is a free bundles (or projective bundles) is a embedded subbundles of any module bundles also. In particular, the condition which projective bundles change into free bundles is given. Related Articles | Metrics

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Recoupling Matrix of Action on Rescaled Basis in Loop Gravity Shao Dan; Shao Liang; Shao Changgui; Xiao Ming Acta mathematica scientia,Series A. 2009, 29 (1):  158-164.  Abstract ( 1864 )   RICH HTML PDF (326KB) ( 1118 )   Save Using the basis change for four-valent vertices which are connected with the recoupling theorem two four-valent rescaled bases are obtained in the spin networks representation, and it is proved that the basis change is a unitary transformation. The graph and the symbol expressions of the recoupling matrix used in action of volume operator on rescaled basis are obtained with the graph calculation method. Finally the eigenvalues of the volume operator and the space quantization are discussed. Related Articles | Metrics

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Modified Stefan-Boltzmann’s law near the Black Hole Zhang Jia; Li Zhongheng Acta mathematica scientia,Series A. 2009, 29 (1):  165-169.  Abstract ( 1435 )   RICH HTML PDF (307KB) ( 975 )   Save The modified Stefan-Boltzmann’s law near the general static spherically symmetric black holes is obtained by using WKB approximation. We find that there exists an additive term which is proportional to the square power of the local temperature beyond the leading term in flat spacetime due to spin fields. It hints that the radiation from the black hole may be not exactly thermal. Related Articles | Metrics

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Global Exponential Stability of Neural Networks’ Periodic Solution Involving Finite Distributed Delays with Periodic Inputs Xia Wenhua;Deng Feiqi;Luo Yiping Acta mathematica scientia,Series A. 2009, 29 (1):  170-178.  Abstract ( 2143 )   RICH HTML PDF (363KB) ( 1221 )   Save Without assuming the boundedness, continuous, derivation of the active functions and the boundedness of the mean time-delay, the existence of a class of neural networks’ periodic solution involving distributed delays with periodic inputs is obtained by using the theory of coincidence degree and the knowledge of Dini derivative, when the active functions satisfy the Lipchitz condition and the relations of the interconnection matrix is an M-matrix. Meanwhile, under the same conditions, the global exponential stability of neural networks’ periodic solution is obtained by employing Dini derivative and the analysis technique of inequality. Some existing conclusions are improved, extended and complemented. An example is also worked out to demonstrate the advantages of these results. Related Articles | Metrics

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On the Distribution of Zeros of Solutions of Second Order Differential Equations Wu Zhaojun; Tian Honggen; Wu Jia Acta mathematica scientia,Series A. 2009, 29 (1):  179-185.  Abstract ( 1825 )   RICH HTML PDF (302KB) ( 1159 )   Save In this paper, we investigate the distribution of zeros of solutions of second order differential equations f’’+A(z)f=0, where A(z) is an entire function of finite order. By using the Nevanlinna’s characteristic function and Ahlfors-Shimizu’s characteristic function on an angular domain, we established the existence of some ray which has the property that near which the exponent of convergence of the zero-sequence is infinite. Furthermore, by using a new method, we give a different proof of the Theorem 2 which has been given by Wu Shengjian in [5]. Related Articles | Metrics

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Strong Convergence of Implicit Iterative Sequence with Errors for a Finite Family of Strictly Pseudocontractive Mappings Yang Liping Acta mathematica scientia,Series A. 2009, 29 (1):  186-192.  Abstract ( 1780 )   RICH HTML PDF (263KB) ( 1153 )   Save The purpose of this paper is to study the strong convergence of a process of implicit iteration with errors to a common fixed point for a finite family of strictly pseudocontractive mappings under suitable conditions. The results in this paper improve the corresponding results of Osilike and Xu, Ori. Related Articles | Metrics

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The Centrosymmetric Solutions of Matrix Equation A1X1B1+A2X2B2+…+AlXlBl=C and its Optimal Approximation Peng Zhuohua;Hu Xiyan;Zhang Lei Acta mathematica scientia,Series A. 2009, 29 (1):  193-207.  Abstract ( 2046 )   RICH HTML PDF (361KB) ( 1279 )   Save A matrix X=(xij)∈Rn×n is said to be centrosymmetric if xij=xn+1-i, n+1-j(i, j=1,2, …, n). In this paper, an iterative method is constructed for finding the centrosymmetric solutions of matrix equation A1X1B1+A2X2B2+…+AlXlBl=C, where [X1, X2,…, Xl] is a real matrix group. By this iterative method, the solvability of the matrix equation can be judged automatically. When the matrix equation is consistent, for any initial centrosymmetric matrix group [X1(0), X2(0),…, Xl(0), a centrosymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm centrosymmetric solution group can be obtained by choosing a special kind of initial centrosymmetric matrix group . In addition, the optimal approximation centrosymmetric solution group to a given centrosymmetric matrix group [X1, X2, …, Xl] in Frobenius norm can be obtained by finding the least norm centrosymmetric solution group of new matrix equation A1X1B1+A2X2B2+…+AlXlBl=C, where C=C-A1X1B1-A2X2B2-…-AlXlBl. Given numerical examples show that the iterative method is efficient. Related Articles | Metrics

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The Spike-type Contrast Structures for a Nonlinear Singularly Perturbed Second Order Equation Wang Aifeng;Ni Mingkang Acta mathematica scientia,Series A. 2009, 29 (1):  208-216.  Abstract ( 1966 )   RICH HTML PDF (323KB) ( 1185 )   Save In this paper, a kind of nonlinear singulary perturbed second order equation is considered. Under suitable conditions, a contrast structure solution of this problem is obtained. Using the method of boundary function the formula asymptotic expansions of the solution is constructed. At the same time, the existence of the solution is proved and the error estimate of this asymptotic solution is obtained. Related Articles | Metrics