中国科学院数学与系统科学研究院期刊网

应用数学学报(英文版) 2011年 27卷

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1. Empilrical Likelihood for Non-parametric Regression Models with Missing Responses: Multiple Design Case
Qing-zhu Lei, Yong-song Qin
应用数学学报(英文版)    2011, 27 (1): 1-12.   DOI: 10.1007/s10255-011-0035-4
摘要70)      收藏
Empirical likelihood (EL) ratio statistic on θ = g(x) is constructed based on the inverse probability weighted imputation approach in a nonparametric regression model Y = g(x)+ε (x ∈ [0, 1]p) with fixed designs and missing responses, which asymptotically has χ12 distribution. This result is used to obtain a EL based confidence interval on θ.

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2. Faber-Krahn Inequality for Robin Problems Involving p-Laplacian
Qiu-yi Dai, Yu-xia Fu
应用数学学报(英文版)    2011, 27 (1): 13-28.   DOI: 10.1007/s10255-011-0036-3
摘要83)      收藏
The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.

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3. Semiparametric Analysis of Longitudinal Data with Informative Observation Times
Liu-quan Sun, Xiao-yun Mu, Zhi-hua Sun, Xing-wei Tong
应用数学学报(英文版)    2011, 27 (1): 29-42.   DOI: 10.1007/s10255-011-0037-2
摘要80)      收藏
In many longitudinal studies, observation times as well as censoring times may be correlated with longitudinal responses. This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.

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4. Fluid Approximation and Its Convergence Rate for GI/G/1 Queue with Vacations
Yong-jiang Guo
应用数学学报(英文版)    2011, 27 (1): 43-58.   DOI: 10.1007/s10255-011-0038-1
摘要67)      收藏
A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed (i.i.d.) random variables, that is max-ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.

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5. On the Discovery of the Cycle-axiom of Hypergraphs
Jian-fang Wang
应用数学学报(英文版)    2011, 27 (1): 59-62.   DOI: 10.1007/s10255-011-0039-0
摘要68)      收藏
In this paper, the path through which the cycle axiom of hypergraphs was discovered will be retraced. The long process of discovery will be described, in particular how acyclic hypergraphs originated from the study of relational database schemes and how cycles of hypergraphs originated from the study of acyclic hypergraphs.

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6. Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound PascalModel
Xian-min Geng, Shu-chen Wan
应用数学学报(英文版)    2011, 27 (1): 63-74.   DOI: 10.1007/s10255-011-0040-7
摘要81)      收藏
The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U(T - 1), |U(T)| and U(n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery) and the distributions of some actuarial random vectors.

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7. On Optimality of the Barrier Strategy for the Classical Risk Model with Interest
Ying Fang, Rong Wu
应用数学学报(英文版)    2011, 27 (1): 75-84.   DOI: 10.1007/s10255-011-0041-6
摘要99)      收藏
In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended.

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8. Inverse Coefficient Problems for Nonlinear Elliptic Variational Inequalities
Run-sheng Yang, Yun-hua Ou
应用数学学报(英文版)    2011, 27 (1): 85-92.   DOI: 10.1007/s10255-011-0042-5
摘要60)      收藏
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.

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9. Oscillation of Second-order Quasilinear Neutral Delay Difference Equations
Dong-mei Wang, Zhi-ting Xu
应用数学学报(英文版)    2011, 27 (1): 93-104.   DOI: 10.1007/s10255-011-0043-4
摘要50)      收藏
By using the Riccati transformation and mathematical analytic methods, some sufficient conditions are obtained for oscillation of the second-order quasilinear neutral delay difference equations where

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10. Upper Bounds of the Rates of Decay for Solutions of the Boussinesq Equations
Ying Liu
应用数学学报(英文版)    2011, 27 (1): 105-114.   DOI: 10.1007/s10255-011-0044-3
摘要62)      收藏
In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of L2 decay rate for the smooth solutions and di?erence between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method.

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11. Axisymmetric Stokes Exterior Problem and Its Numerical Computation
Neng-sheng Fang, Cai-xiu Liao
应用数学学报(英文版)    2011, 27 (1): 115-128.   DOI: 10.1007/s10255-011-0045-2
摘要76)      收藏
We establish variational formulation and prove the existence and uniqueness of the three dimensional axisymmetric Stokes exterior problem in weighted spaces. Error estimates and convergence for P2 - P0 elements with infinite element methods are also obtained. Numerical experiments are presented to verify the theoretical analysis.

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12. New Time Dependent Pretreat Models Based on Total Variational Image Restoration
Jing Xu, Qian-shun Chang
应用数学学报(英文版)    2011, 27 (1): 129-140.   DOI: 10.1007/s10255-011-0046-1
摘要60)      收藏
In this paper, we propose new pretreat models for total variation (TV) minimization problems in image deblurring and denoising. Specially, blur operator is considered as useful information in restoration. New models in form is equivalent to pretreat the initial value by image blur operator. We successfully get a new (L. Rudin, S. Osher, and E. Fatemi) ROF model, a new level set motion model and a new anisotropic diffusion model respectively. Numerical experiments demonstrate that, under the same stopping rule, the proposed methods significantly accelerate the convergence of the mothed, save computation time and get the same restored effect.

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13. Notes on Linear Codes over Finite Commutative Chain Rings
Zi-hui Liu
应用数学学报(英文版)    2011, 27 (1): 141-148.   DOI: 10.1007/s10255-011-0047-0
摘要58)      收藏
The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS (AMDS) codes are studied.

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14. Some I-Convergent Sequence Spaces Defined by Orlicz Functions
Binod Chandra Tripathy, Bipan Hazarika
应用数学学报(英文版)    2011, 27 (1): 149-154.   DOI: 10.1007/s10255-011-0048-z
摘要45)      收藏
In this article we introduce the sequence spaces cI (M), c0I(M), mI (M) and m0I(M) using the Orlicz function M. We study some of the properties like solid, symmetric, sequence algebra, etc and prove some inclusion relations.

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15. The Recursive Solution for Geom/G/1(E,SV ) Queue with Feedback and Single Server Vacation
Chuan-yi Luo, Ying-hui Tang
应用数学学报(英文版)    2011, 27 (1): 155-166.   DOI: 10.1007/s10255-011-0049-y
摘要49)      收藏
Using recursive method, this paper studies the queue size properties at any epoch n+ in Geom/G/1(E, SV ) queueing model with feedback under LASDA (late arrival system with delayed access) setup. Some new results about the recursive expressions of queue size distribution at different epoch (n+, n, n-) are obtained. Furthermore the important relations between stationary queue size distribution at different epochs are discovered. The results are different from the relations given in M/G/1 queueing system. The model discussed in this paper can be widely applied in many kinds of communications and computer network.

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16. Distribution Estimation with Smoothed Auxiliary Information
Xu Liu, Ahmad Ishfaq
应用数学学报(英文版)    2011, 27 (1): 167-176.   DOI: 10.1007/s10255-010-9318-4
摘要57)      收藏
Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable. A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.

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17. First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs
Yong-hui Huang, Xian-ping Guo
应用数学学报(英文版)    2011, 27 (2): 177-190.   DOI: 10.1007/s10255-011-0061-2
摘要1726)      收藏
This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal (or ε-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.

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18.
Gang-rong Qu
应用数学学报(英文版)    2011, 27 (2): 191-208.   DOI: 10.1007/s10255-011-0056-z
摘要1667)      收藏
A class of piecewise smooth functions in R2 is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagation law. The examples of singularities and singularities inversion of the Radon transform are given.

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19. Precise Large Deviations for a Customer-based Individual Risk Model
Xue-min Ma
应用数学学报(英文版)    2011, 27 (2): 209-222.   DOI: 10.1007/s10255-011-0050-5
摘要1598)      收藏
In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d. heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospective-loss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV (extended regular variation). Lundberg type limiting results on the finite time ruin probabilities are also investigated.

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20. A Comparison Theorem and Uniqueness Theorem of Backward Doubly Stochastic Differential Equations
Qian Lin, Zhen Wu
应用数学学报(英文版)    2011, 27 (2): 223-232.   DOI: 10.1007/s10255-011-0057-y
摘要1730)      收藏
In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs). We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.

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21. Three Symmetric Positive Solutions for Second-order Nonlocal Boundary Value Problems
Yong-ping Sun
应用数学学报(英文版)    2011, 27 (2): 233-242.   DOI: 10.1007/s10255-011-0058-x
摘要1616)      收藏
Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u″(t) + g(t)f(t, u(t)) = 0, 0 < t < 1, u(0) = u(1) = ∫01 m(s)u(s)ds, where mL1[0, 1], g : (0, 1) → [0,∞) is continuous, symmetric on (0, 1) and maybe singular at t = 0 and t = 1, f : [0, 1] × [0,∞) → [0,∞) is continuous and f(·, x) is symmetric on [0, 1] for all x ∈ [0,∞).

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22. Least Absolute Deviation Estimation of Autoregressive Conditional Duration Model
Wei Liu, Hui-min Wang, Min Chen
应用数学学报(英文版)    2011, 27 (2): 243-254.   DOI: 10.1007/s10255-011-0059-9
摘要1688)      收藏
This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration (ACD) model. The asymptotic properties of the estimator are studied given mild regularity conditions. Furthermore, we develop a Wald test statistic for the linear restriction on the parameters. A simulation study is conducted for the finite sample properties of our estimator. Finally, we give an empirical study of financial duration.

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23. New Approach to Differential Equations with Countable Impulses
Hong-Kun Zhang, Jin-Guo Lian, Jiong Sun
应用数学学报(英文版)    2011, 27 (2): 255-262.   DOI: 10.1007/s10255-011-0060-3
摘要1682)      收藏
This paper provides a new approach to study the solutions of a class of generalized Jacobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n + 1. A new class of generalized differential operators is defined. We investigate the kernel of the corresponding maximal operators by applying operator theory. It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic, in which there are n dimension solutions with exponential-decaying amplitude.

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24. Existence and Uniqueness of Solutions of Surface Reconstruction Problem
Zhu-cui Jing, Guo-liang Xu
应用数学学报(英文版)    2011, 27 (2): 263-276.   DOI: 10.1007/s10255-011-0054-1
摘要1636)      收藏
Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design. In solving partial differential equations derived from surface reconstruction problems, level-set method has been successfully used. We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface reconstruction using the level-set approach. We give the uniqueness analysis of the classical solution. Results on the existence and uniqueness of the viscosity solution are also established.

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25. Asymptotic Tail Probability of RandomlyWeighted Sums of Dependent Random Variables with Dominated Variation
Hai-zhong Yang
应用数学学报(英文版)    2011, 27 (2): 277-280.   DOI: 10.1007/s10255-009-8155-9
摘要1743)      收藏
This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result we obtain extends the corresponding result of Wang and Tang[7] .

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26. Backward Perturbation Analysis for the Matrix Equation ATXA + BTY B = D
Xing-dong Yang, Xiu-hong Feng, Qing-quan He
应用数学学报(英文版)    2011, 27 (2): 281-288.   DOI: 10.1007/s10255-011-0055-0
摘要1611)      收藏
Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples.

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27. Regularity of the Attractor for 3-D Complex Ginzburg-Landau Equation
Dong-long Li, Bo-ling Guo, Xu-hong Liu
应用数学学报(英文版)    2011, 27 (2): 289-302.   DOI: 10.1007/s10255-011-0062-1
摘要1773)      收藏
In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor Ai in Hi(Ω) is actually equal to a global attractor Ai in Hi(Ω) (ij, i, j = 1, 2, · · ·m).

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28. Uzawa Iteration Method for Stokes Type Variational Inequality of the Second Kind
Yuan Li, Kai-tai Li
应用数学学报(英文版)    2011, 27 (2): 303-316.   DOI: 10.1007/s10255-011-0063-0
摘要1930)      收藏
In this paper, the Uzawa iteration algorithm is applied to the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind. Firstly, the multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity. Moreover, the solution of the variational identity satisfies the saddle-point problem of the Lagrangian functional L. Subsequently, the Uzawa algorithm is proposed to solve the solution of the saddle-point problem. We show the convergence of the algorithm and obtain the convergence rate. Finally, we give the numerical results to verify the feasibility of the Uzawa algorithm.

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29. A New Method of Moving Asymptotes for Large-scale Linearly Equality-constrained Minimization
Hai-jun Wang, Qin Ni, Hao Liu
应用数学学报(英文版)    2011, 27 (2): 317-328.   DOI: 10.1007/s10255-011-0065-y
摘要1762)      收藏
A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved. The numerical results show that the new method may be capable of processing some large scale problems.

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30. Asymptotic Ruin Probabilities of the RenewalModel with Constant Interest Force and Dependent Heavy-tailed Claims
Jin-zhu Li, Rong Wu
应用数学学报(英文版)    2011, 27 (2): 329-338.   DOI: 10.1007/s10255-011-0064-z
摘要1759)      收藏
In this paper, we investigate the asymptotic behavior for the finite- and infinite-time ruin probabilities of a nonstandard renewal model in which the claims are identically distributed but not necessarily independent. Under the assumptions that the identical distribution of the claims belongs to the class of extended regular variation (ERV) and that the tails of joint distributions of every two claims are negligible compared to the tails of their margins, we obtain the precise approximations for the finite- and infinite-time ruin probabilities.

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31. Robust Solutions to Uncertain Linear Complementarity Problems
Dan Wu, Ji-ye Han, Jing-hao Zhu
应用数学学报(英文版)    2011, 27 (2): 339-352.   DOI: 10.1007/s10255-010-0033-y
摘要1723)      收藏
In this paper, we adopt the robust optimization method to consider linear complementarity problems in which the data is not specified exactly or is uncertain, and it is only known to belong to a prescribed uncertainty set. We propose the notion of the ρ - robust counterpart and the ρ - robust solution of uncertain linear complementarity problems. We discuss uncertain linear complementarity problems with three different uncertainty sets, respectively, including an unknown-but-bounded uncertainty set, an ellipsoidal uncertainty set and an intersection-of-ellipsoids uncertainty set, and present some sufficient and necessary (or sufficient) conditions which ρ - robust solutions satisfy. Some special cases are investigated in this paper.

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32. A Note on Moments of Dividends
Hansjörg Albrecher, Hans U. Gerber
应用数学学报(英文版)    2011, 27 (3): 353-354.   DOI: 10.1007/s10255-011-0074-x
摘要1867)      PDF(pc) (1KB)(898)    收藏
We reconsider a formula for arbitrary moments of expected discounted dividend payments in a spectrally negative Lévy risk model that was obtained in Renaud and Zhou (2007, [4]) and in Kyprianou and Palmowski (2007, [3]) and extend the result to stationary Markov processes that are skip-free upwards.  
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33. Dynamic Concept of Returns to Scales and Its Characteristics on Production Frontier in Intersection Form
Quan-ling Wei, Hong Yan
应用数学学报(英文版)    2011, 27 (3): 355-366.   DOI: 10.1007/s10255-011-0075-9
摘要2058)      收藏
This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale (RTS) of economic units with multiple inputs and outputs. It is frequently noticed that when we increase the input of a decision making unit (DMU) with a certain status of RTS, different status of RTS is observed. For example, when we increase the input of a DMU with constant RTS under the traditional method, a decreasing RTS is often observed instead of the expected constant RTS. We thus define the RTS of each DMU in both input expansion and contraction regions respectively. The research starts from transferring the production possibility set into the intersection form, by giving the explicit linear inequality representation of production frontiers. The RTS structural characteristics of DMUs' on the production frontier are described. Status of RTS of those DMUs on the production frontier include increasing RTS, constant RTS, decreasing RTS, saturated RTS and evidence of congestion. Necessary and sufficient conditions for RTS evaluation are provided. The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.  
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34. Existence of Positive Solutions for a General Nonlinear Eigenvalue Problem
Xi-you Cheng, Zhi-tao Zhang
应用数学学报(英文版)    2011, 27 (3): 367-372.   DOI: 10.1007/s10255-011-0076-8
摘要1831)      收藏
Let Ω ⊂ Rn be a bounded domain, H = L2(Ω), L : D(L) ⊂ HH be an unbounded linear operator, fC(Ω × R, R) and λ ∈ R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem Lu = λf(x, u), uD(L), which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a secondorder ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.  
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35. Cooperative Hedging in the Complete Market under g-expectation Constraint
Qing Zhou
应用数学学报(英文版)    2011, 27 (3): 373-380.   DOI: 10.1007/s10255-011-0077-7
摘要1851)      PDF(pc) (1KB)(672)    收藏
The paper studies the muiti-agent cooperative hedging problem of contingent claims in the complete market when the g-expected shortfall risks are bounded. We give the optimal cooperative hedging strategy explicitly by the Neyman-Pearson lemma under g-probability.    
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36. Estimates for Correlations in Billiards with Large Arcs
Hong-Kun Zhang
应用数学学报(英文版)    2011, 27 (3): 381-392.   DOI: 10.1007/s10255-011-0078-6
摘要1872)      PDF(pc) (1KB)(705)    收藏
Bunimovich billiards are ergodic and mixing. However, if the billiard table contains very large arcs on its boundary then if there exist trajectories experience infinitely many collisions in the vicinity of periodic trajectories on the large arc. The hyperbolicity is nonuniform and the mixing rate is very slow. The corresponding dynamics are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. The study of mixing rates in intermittent chaotic systems is more difficult than that of truly chaotic ones, and the resulting estimates may depend on delicate details of the dynamics in the traps. We present a rigorous analysis of the corresponding singularities and correlations to certain class of billiards and show the mixing rate is of order 1/n.  
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37. Existence of Nontrivial Solutions for p-Laplacian-Like Equations
Zhou-xin Li, Yao-tian Shen
应用数学学报(英文版)    2011, 27 (3): 393-406.   DOI: 10.1007/s10255-011-0079-5
摘要1703)      收藏
In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations discussed can be applied to a variety of different fields in applied mechanics.  
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38. Incomplete Group Divisible Designs with Block Size Four and General Index
Li-dong Wang, Hai-rong Kong, Hong-juan Liu
应用数学学报(英文版)    2011, 27 (3): 407-418.   DOI: 10.1007/s10255-011-0080-z
摘要1845)      PDF(pc) (1KB)(812)    收藏
In this paper, we investigate the existence of incomplete group divisible designs (IGDDs) with block size four, group-type (g, h)u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg(u-1) ≡ 0 (mod 3), λ(g-h)(u-1) ≡ 0 (mod 3), and λu(u-1)(g2-h2) ≡ 0 (mod 12). These necessary conditions are shown to be sufficient for all λ ≥ 2. The known existence result for λ = 1 is also improved.  
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39. Multiple Positive Solutions for Semi-positone m-point Boundary Value Problems
Cheng-bo Zhai, Cheng Yang
应用数学学报(英文版)    2011, 27 (3): 419-426.   DOI: 10.1007/s10255-009-6180-3
摘要2085)      PDF(pc) (1KB)(1218)    收藏
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter
 
where λ > 0 is a parameter, 0 < ξ1 < ξ2 < · · · < ξm-2 < 1 with 0 < and f(t, u) ≥ -M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.  
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40. Periodic Solution to BAM-type Cohen-Grossberg Neural Network with Time-varying Delays
An-ping Chen, Qun-hua Gu
应用数学学报(英文版)    2011, 27 (3): 427-442.   DOI: 10.1007/s10255-011-0082-x
摘要1901)      PDF(pc) (1KB)(883)    收藏
By using the continuation theorem of Mawhin's coincidence degree theory and the Liapunov functional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.  
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