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01 January 2010, Volume 30 Issue 1 Previous Issue    Next Issue

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Duration of Negative Surplus for Compound Poisson Risk Model with Constant Interest Force XU Jin-You, HU Yi-Jun, WEI Xiao Acta mathematica scientia,Series A. 2010, 30 (1):  1-17.  Abstract ( 1769 )   RICH HTML PDF (453KB) ( 1395 )   Save In this paper, the authors discuss the duration of negative surplus of the classical compound Poisson risk model with constant interest force. By presenting a new approach different from the martingale method proposed by Gerber (1990), the moment generating functions and the moments of both the single and total duration of negative surplus are formulated. Explicit expressions are given when the claim is exponentially distributed. Finally, the influence of interest force on the duration of negative surplus is illustrated by numerical results. References | Related Articles | Metrics

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On Absolute Continuity of Periodic Elliptic Operators with Singularity ZHAO Pei-Hao, LIU Wu-Long Acta mathematica scientia,Series A. 2010, 30 (1):  18-30.  Abstract ( 2541 )   RICH HTML PDF (389KB) ( 1362 )   Save In this paper we consider the spectral properties of periodic elliptic operator ∑dj,l=1Djw(x)ajlDl+V(x) in Rd, d ≥  3, where A=(ajl) is a d×d positive definite matrix with real constant entries, V(x)  and w(x) are periodic scalar function with respect to the same lattice, and w({x) is positive. Using a new uniform Sobolev inequalities on the d-torus   established in [22], we prove that the spectrum of the operator is purely absolutely continuous if Lloc2pd/d+2p(Rd) and w ∈ ∧1+αp, ∞(Td)∩L∞(Td) for some α>0, p≥ d, or V ∈ L loc2d/3(Rd), w ∈ C1(Td), or V ∈ Llocd/2(Rd), w ∈ L2, locd/2(Td). References | Related Articles | Metrics

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On the Perturbed Compound Poisson Risk Model under Absolute Ruin with Debit Interest and a Constant Dividend Barrier WANG Chun-Wei, YIN Chuan-Cun Acta mathematica scientia,Series A. 2010, 30 (1):  31-41.  Abstract ( 2127 )   RICH HTML PDF (371KB) ( 1318 )   Save In this paper, we consider the perturbed compound Poisson risk model under absolute ruin  with debit interest and a constant dividend barrier.  Integro-differential equations satisfied by the expectation of discounted dividend payments, the moment generating function and the expected discounted penalty function (Gerber-Shiu function) with certain boundary conditions are obtained. For some special cases, explicit  expressions are obtained. References | Related Articles | Metrics

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Exponential Stability for Stochastic Neural Networks with Multiple Delays: an LMI Approach WANG Hong-Chu, HU Shi-Geng Acta mathematica scientia,Series A. 2010, 30 (1):  42-53.  Abstract ( 1691 )   RICH HTML PDF (382KB) ( 1195 )   Save This paper studies mean square exponential stability for a class of stochastic neural networks with multiple constant or time-varying delays. Based on the Lyapunov-Krasovskii stability theory, new stability criterion is derived in terms of the linear matrix inequalities (LMIs) for these networks.  Some examples are also presented as illustration. References | Related Articles | Metrics

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BV Solutions for the Quasilinear Hyperbolic Equation with Nonlinear Source and Finite Radon Measure as Initial Conditions YUAN Hong-Jun, TONG Li-Ning Acta mathematica scientia,Series A. 2010, 30 (1):  54-70.  Abstract ( 1498 )   RICH HTML PDF (331KB) ( 1195 )   Save The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the form ut+(um)x=up with nonnegative finite Radon measures as initial conditions, where m>1,1<p<m are some given real numbers. In particular, the existence and uniqueness of BV solutions for the above problem is obtained. References | Related Articles | Metrics

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Varying-Coefficient Partially Linear Models with Censored Data LUO Xian-Hua, LI Yuan, MA Yun-Bei, ZHOU Yong Acta mathematica scientia,Series A. 2010, 30 (1):  71-85.  Abstract ( 2465 )   RICH HTML PDF (605KB) ( 1172 )   Save This paper considers varying-coefficient partially linear model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of censored data. It is very important and useful  to fit statistical models by linear construction for response and covariates. For censored data, the usual statistical techniques are not directly applicable to this model. In this paper, we propose a class of  transformations of the data so that a unbiased conditional expectation is established. Then the profile least-squares estimators for the parametric and nonparametric components are proposed by profile least-squares technique. The asymptotic normality of the proposed estimators are established. Some numerical examples are given to illustrate the effectiveness of the proposed procedures. References | Related Articles | Metrics

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Classifications of Low Dimensional 3-Lie Algebras BAI Rui-Pu, WANG Xiao-Ling Acta mathematica scientia,Series A. 2010, 30 (1):  86-96.  Abstract ( 1462 )   RICH HTML PDF (280KB) ( 1155 )   Save This paper concerns the classification of m-dimensional 3-Lie algebras with m≤5 over a complete field of characteristic 2, and shows the concrete multiplication table in a basis of 3-Lie algebras for each classes. References | Related Articles | Metrics

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A Proof of the Complete Convergence Theorem for Contact Processes on Some Product Graphs YAO Qiang Acta mathematica scientia,Series A. 2010, 30 (1):  97-102.  Abstract ( 1615 )   RICH HTML PDF (310KB) ( 1007 )   Save In this article a proof of the complete convergence theorem for the basic contact process on the product graph G1×G2×Z is given, provided that the infection parameter is large enough, where G1and G2 are arbitrary infinite locally finite transitive graphs. It extends the result of Schonmann [1] in some content. References | Related Articles | Metrics

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Representation of the Exact Solution for Singular Boundary-value Problems of Eighth-order MO Huan-Min, LIN Ying-Zhen Acta mathematica scientia,Series A. 2010, 30 (1):  103-113.  Abstract ( 1964 )   RICH HTML PDF (347KB) ( 1322 )   Save In this paper, a new algorithm for solving singular boundary-value problems of eighth-order is presented based on the reproducing kernel space W29[0,1]. The representation of the exact solution is given in the series form. Some examples are mentioned for the usefulness of the method. The numerical results demonstrate that our method is more effective. References | Related Articles | Metrics

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On Sonnier-Christov's Difference Scheme for the Nonlinear Coupled Schrodinger System  WANG Ting-Chun, ZHANG Lu-Ming, CHEN Fang-Qi Acta mathematica scientia,Series A. 2010, 30 (1):  114-125.  Abstract ( 1833 )   RICH HTML PDF (472KB) ( 1250 )   Save In this paper, numerical analysis of the Sonnier-Christov's difference scheme for the coupled nonlinear Schrodinger system is given. we prove that the difference scheme is unconditional stable and the second-order convergent in discrete L2-norm. Unique existence of the numerical solution and a iterative algorithm are also discussed in detail. Collision of two solitary waves is also simulated. References | Related Articles | Metrics

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p-Moment Boundedness of Functional Differential Equations with Random Impulses WU Shu-Jin, SONG Qiong, GUO Xiao-Lin Acta mathematica scientia,Series A. 2010, 30 (1):  126-141.  Abstract ( 2806 )   RICH HTML PDF (396KB) ( 1320 )   Save Random impulsive functional differential equation is a mathematical model with extensive applications. By means of Liapunov's direct method coupled with Razumikhin technique and comparison principle, some sufficient conditions for uniformly (uniformly and ultimately, uniformly and uniformly ultimately) p-moment boundedness of such systems are presented, where dV(t, x(t))/dt is imposed only on a little restriction even to obtain uniform boundedness and uniformly ultimate boundedness. Thus the obtained results are very convenient to apply. References | Related Articles | Metrics

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The Errors of Simultaneous Approximation by Bernstein Type |Operators DING Chun-Mei Acta mathematica scientia,Series A. 2010, 30 (1):  142-153.  Abstract ( 1372 )   RICH HTML PDF (288KB) ( 1073 )   Save In this paper,  we show that the functions in space C[0,1] and their derivatives can be simultaneously approximated by the combinations of the Bernstein operators. Both direct and inverse theorems are proved.   An equivalence relation between the derivatives of  the Bernstein operators and the smoothness of function is obtained as well.  These results bridge the gap between the classical  pointwise conclusions and the  global conclusions for simultaneous approximation by the Bernstein operators. References | Related Articles | Metrics

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Rough Parametric Marcinkiewicz Integrals on Generalized Campanato Spaces ZHANG Song-Yan, TAO Xiang-Xing Acta mathematica scientia,Series A. 2010, 30 (1):  154-166.  Abstract ( 1933 )   RICH HTML PDF (376KB) ( 1106 )   Save As a Littlewood-Paley function, let μρΩ, b(f) be the parametric Marcinkiewicz integral with the rough kernel Ω∈Lq(Sn-1) satisfing the cancellation condition and integral Dini continuity, and the radial kernal b ∈?s(R+)∩Θs(Rn),  1<q, s<∞, and the parameter ρ ∈C with Re(ρ)>0. Under the only assumption of one point finiteness, the existence and boundedness of μρΩ, b(f) on the generalized Campanato space Lp, φ(Rn) are obtained. The theorems in this paper substantially extend early results. References | Related Articles | Metrics

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Boundedness Properties for Multilinear Singular Integral Operators with Non-Smooth Kernels LIU Lan-Zhe Acta mathematica scientia,Series A. 2010, 30 (1):  167-178.  Abstract ( 1534 )   RICH HTML PDF (280KB) ( 1083 )   Save In this paper, we establish a sharp function estimate for some multilinear singular integral operators with non-smooth kernels. As an application, we obtain the Lp(1<p<∞) norm inequality for the multilinear operators. References | Related Articles | Metrics

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Cohomology for Coalgebras with Twisted Coactions of Commutative Hopf Algebras JU Teng-Xia Acta mathematica scientia,Series A. 2010, 30 (1):  179-196.  Abstract ( 1286 )   RICH HTML PDF (352KB) ( 1057 )   Save In this paper, we show that the twisted coactions of commutative Hopf algebras H on coalgebras C are invertible if the corresponding coassociators are convolution invertible. In this case, we define the regular cohomology and show that every invertible twisted coaction gives rise to a regular cohomology class of H with coefficients in C of degree three. We also show that the obstruction for $\rho$ vanishes if and only if the the twisted coaction ρ is corresponding to a cleft coextension. References | Related Articles | Metrics

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Energy Decay Estimates for the Nonhomogeneous Timoshenko Beam with a Local Nonlinear Feedback ZHANG Chun-Guo, QIU Zhe-Yong Acta mathematica scientia,Series A. 2010, 30 (1):  197-206.  Abstract ( 1720 )   RICH HTML PDF (309KB) ( 1147 )   Save In this paper, it is considered that the energy decay estimates of the nonhomogeneous Timoshenko beam with a local nonlinear feedback. The well-posedness of the system is proved via the nonlinear operator semigroup theory. By virtue of multiplier method, the energy decay estimates of the system is given. References | Related Articles | Metrics

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Alternating Oppenheim Expansions over the Field of Formal Laurent Series SHEN Lu-Ming, ZHANG Ji-Hong, ZHEN Zhi-Yong Acta mathematica scientia,Series A. 2010, 30 (1):  207-216.  Abstract ( 1905 )   RICH HTML PDF (331KB) ( 1151 )   Save In this paper, we introduce a new algorithm, alternating Oppenheim expansion over the field of formal Laurent series. Metric properties, such as strong and weak number laws, central limit theorem, and iterated logarithm law, of the digits occurring in this expansion are considered. At the same time, we investigate the approximation orders by rational fractions which are the partial sums of these series. References | Related Articles | Metrics

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Coexistence States of a Prey-predator Model with Diffusion LI Bo, WANG Lu-Xin Acta mathematica scientia,Series A. 2010, 30 (1):  217-226.  Abstract ( 1620 )   RICH HTML PDF (306KB) ( 1395 )   Save This paper deals with a prey-predator model with diffusion. The coexistence states of the elliptic system are given by using upper and lower solutions method and bifurcation theory. And the stability of coexistence states is also considered.  References | Related Articles | Metrics

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Branches of |Solutions to Semilinear Polyharmonic Equations JIN Ling-Yu, WANG Xia, FANG Shao-Mei Acta mathematica scientia,Series A. 2010, 30 (1):  227-238.  Abstract ( 1410 )   RICH HTML PDF (327KB) ( 1063 )   Save This paper considers a class of nonlinear polyharmonic eigenvalue problem, describes the behavior of the branches of solutions emanating from an eigenvalue of odd multiplicity below the essential spectrum of the linearized problem. The discussion is based on the degree theory for C2 proper Fredholm maps developed by P. M. Fitzpatrick, J. Pejsachowicz and P. J. Rabier[7]. References | Related Articles | Metrics

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Two-Parameter Nonresonance Condition Described by Ellipse for Fourth-order Boundary Value Problems LI Yong-Xiang, YANG He Acta mathematica scientia,Series A. 2010, 30 (1):  239-244.  Abstract ( 1841 )   RICH HTML PDF (279KB) ( 1241 )   Save This paper deals with the existence of solutions for the fourth-order boundary value problem u(4)=f(t, u, ,u''),  0≤ t ≤ 1,  u(0)=u(1)=u''(0)=u''(1)=0 where f: [0,1]]×R×R→R is continuous. We present a two-parameter nonresonance condition described by ellipse for the existence of the problem. References | Related Articles | Metrics

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Solving the Semilinear Heat Equation with Integral Boundary Conditions in the Reproducing Kernel Space DU Juan, CUI Ming-Gen Acta mathematica scientia,Series A. 2010, 30 (1):  245-257.  Abstract ( 1647 )   RICH HTML PDF (333KB) ( 1270 )   Save In this paper, we give a new method to solve the semilinear heat equation with integral boundary conditions. Its exact solution is represented in the form of series in the reproducing kernel space. The n-term approximation un(x, t) of the exact solution u(x, t) is proved to converge to the exact solution. Some numerical examples are displayed to demonstrate the accuracy of the present method. References | Related Articles | Metrics

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Positive Solutions of Multiple-point Boundary Value Problems for Systems of Nonlinear Second Order Differential Equations XIE Sheng-Li Acta mathematica scientia,Series A. 2010, 30 (1):  258-266.  Abstract ( 2761 )   RICH HTML PDF (301KB) ( 1182 )   Save In this paper, by means of fixed point index theory, the existence of positive solutions and multiple positive solutions of m-point boundary value problems for the system of nonlinear second order singular differential equations are studied. Some limit type conditions for ensuring the existence of the solutions are given, which are applicable for more general functions. References | Related Articles | Metrics

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Asymptotic Analysis to Parabolic Equations with Absorptions and Coupled Localized Sources KONG Ling-Hua, ZHAO Li-Zhong, ZHENG Shi-Ning Acta mathematica scientia,Series A. 2010, 30 (1):  267-277.  Abstract ( 1758 )   RICH HTML PDF (350KB) ( 1262 )   Save This paper deals with asymptotic analysis to a parabolic model with absorptions and coupled localized sources, for which it is shown that any blow-up occurs everywhere in the domain with one of three possible simultaneous blow-up rates under different dominations of nonlinearities. All the three blow-up rates are simply represented in a characteristic algebraic system introduced for the problem. In particular, uniform blow-up profiles are established for the case of weak absorptions. While for the two cases of unbalanced absorptions, we establish uniform  blow-up rates (instead of blow-up profiles) which are absorption-related. This is substantially different from scalar parabolic problems with absorptions in  current literatures, where all the blow-up rates are known as absorption-independent. The results of the paper mainly rely on the scaling method with a complete classification for the nonlinear parameters in the model. References | Related Articles | Metrics

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Positive Solutions of a Class of Operator Equations Lx=Nx WANG Feng, SUN Jing-Xian, CUI Yu-Jun Acta mathematica scientia,Series A. 2010, 30 (1):  278-288.  Abstract ( 1706 )   RICH HTML PDF (344KB) ( 1324 )   Save In this paper, the concept about coincidence degree is generalized to the zero point index of L-N operators in cones. Some methods of computation of the zero point index and the existence theorems of operator equations are given by making use of the theory of cones and applied to investigate the existence of nonnegative solutions for the second order ordinary differential equation of m-point nonlocal boundary value problems at resonance. References | Related Articles | Metrics