15 July 2010, Volume 26 Issue 3

    

• Select all
  |

• Select
  论文

  Analysis of the M^[X]/G/1 Queues with Second Multi-optional Service and Unreliable Server

  Jin-ting Wang, Jiang-hua Li

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 353-368.

  DOI:10.1007/s10255-010-0001-6

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.

• Select
  论文

  New Model for Image Restoration with Different Boundary Conditions

  Yu-ying Shi, Qian-shun Chang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 369-380.

  DOI:10.1007/s10255-010-0002-5

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper, we propose a new time-dependent model for solving total variation (TV) minimization problems in image restoration. The main idea is applying a priori smoothness on the solution image. Five di?erent BCs are introduced and analyzed. 2D numerical experimental results by explicit numerical schemes are discussed.

• Select
  论文

  Regularity Condition of Solutions to the Quasi-geostrophic Equations in Besov Spaces with Negative Indices

  Bao-quan Yuan

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 381-386.

  DOI:10.1007/s10255-010-0003-4

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  With a Hölder type inequality in Besov spaces, we show that every strong solution θ(t, x) on

• Select
  论文

  Multiplicity of Solutions for a Class of Kirchhoff Type Problems

  Xiao-ming He, Wen-ming Zou

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 387-394.

  DOI:10.1007/s10255-010-0005-2

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper we apply the (variant) fountain theorems to study the symmetric nonlinear Kirchhoff nonlocal problems. Under the Ambrosetti-Rabinowitz’s 4-superlinearity condition, or no Ambrosetti- Rabinowitz’s 4-superlinearity condition, we present two results of existence of infinitely many large energy solutions, respectively.

• Select
  论文

  Bifurcation Problems for a Class of Degenerate Quasilinear Elliptic Equations

  Yun-xiang Li, Yu Ye, Fang-li Xia

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 395-411.

  DOI:10.1007/s10255-010-0006-1

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper we consider the bifurcation problem -divA(x,▽u) = λa(x)|u|^p-2u + f(x, u, λ) in Ω with p > 1.Under some proper assumptions on A(x, ξ),a(x) and f(x, u, λ), we show that the existence of an unbounded branch of positive solutions bifurcating from the principal eigenvalue of the problem -divA(x,▽u) =λa(x)|u|^p-2u.

• Select
  论文

  A Class Hermite Pseudospectral Approximate with ω(x) ≡ 1 and Application to Reaction-diffusion Equation

  Xin-min Xiang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 405-414.

  DOI:10.1007/s10255-010-0004-3

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper, we continue the discussion of [12] to establish the Hermite pseudospectral method with weight ω(x) ≡ 1. As an application, we consider the pseudospectral approximation of the reaction-diffusion equation on the whole line, we prove the existence of the approximate attractor and give the error estimate for the approximate solution.

• Select
  论文

  Qualitative Analysis and Solutions of Bounded Traveling Wave for B-BBM Equation

  Yan Zhao, Wei-guo Zhang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 415-426.

  DOI:10.1007/s10255-010-0007-0

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coefficient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.

• Select
  论文

  Stability of the Standing Waves for a Class of Coupled Nonlinear Klein-Gordon Equations

  Jian Zhang, Zai-hui Gan, Bo-ling Guo

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 427-442.

  DOI:10.1007/s10255-010-0008-z

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  This paper deals with the standing waves for a class of coupled nonlinear Klein-Gordon equations with space dimension By using the variational calculus and scaling argument, we establish the existence of standing waves with ground state, discuss the behavior of standing waves as a function of the frequency ω and give the sufficient conditions of the stability of the standing waves with the least energy for the equations under study.

• Select
  论文

  Unified Characteristic Numbers and Solutions of Equations for Birth and Death Processes with Barriers

  Xiang-qun Yang, He-song Wang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 443-451.

  DOI:10.1007/s10255-010-0009-y

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  The state 0 of a birth and death process with state space E = {0, 1, 2, · · ·} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.

• Select
  论文

  Coincidence Theorem for Admissible Set-valuedMappings and Its Applications in FC-spaces

  Ming-ge Yang, Lei Deng

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 455-462.

  DOI:10.1007/s10255-010-0010-5

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.

• Select
  论文

  Mixture Normal Models in which the Proportions of Susceptibility are Related to Dose Levels

  Bing He, Min Chen, Li-xin Song, De-huiWang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 463-472.

  DOI:10.1007/s10255-010-0020-3

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use EM-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.

• Select
  论文

  Proof of Ding’s Conjecture on Maximal Stable Sets and Maximal Cliques in Planar Graphs

  Jing Sun, Zhi-quan Hu

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 473-480.

  DOI:10.1007/s10255-006-6185-0

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  X. Deng et al. proved Chvátal’s conjecture on maximal stable sets and maximal cliques in graphs. G. Ding made a conjecture to generalize Chvátal’s conjecture. The purpose of this paper is to prove this conjecture in planar graphs and the complement of planar graphs.

• Select
  论文

  Exponential Convergence in Probability for Empirical Means of Lévy Processes

  Shu-lan Hu, Nian Yao

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 481-488.

  DOI:10.1007/s10255-010-0013-2

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  Let (X_t)_t≥0 be a Lévy process taking values in R^d with absolutely continuous marginal distributions. Given a real measurable function f on R^d in Kato’s class, we show that the empirical mean converges to a constant z in probability with an exponential rate if and only if f has a uniform mean z. This result improves a classical result of Kahane et al. and generalizes a similar result of L. Wu from the Brownian Motion to general Lévy processes.

• Select
  论文

  The Number of Nonseparable Maps on the Projective Plane

  Zhao-xiang Li, Li-ying Mou, Fen Lei, Jie Xu

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 489-494.

  DOI:10.1007/s10255-010-0014-1

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation.

• Select
  论文

  Directional Derivatives of Difference Functions of Nonsmooth Max-functions

  Lu-lin Tan

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 495-502.

  DOI:10.1007/s10255-010-0015-0

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper, we give an upper estimate for the Clarke-Rockafellar directional derivatives of a function of the form f - g, where f, g are max-functions defined by locally Lipschitz but not necessarily differentiable functions on a closed convex set in a Euclidean space. As an application, we give a sufficient condition for f - g to have an error bound.

• Select
  论文

  Equivalent Conditions of Local Asymptotics for the Solutions of Defective Renewal Equations, with Applications

  Kai-yong Wang, Yue-bao Wang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 503-512.

  DOI:10.1007/s10255-010-0019-9

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  The paper obtains some equivalent conditions of local asymptotics for the solutions of defective renewal equations in the heavy-tailed case. As applications, the paper gives a different proof of a classical result about the local distribution of the supremum of a random walk. These results are also applied in examples involving the renewal function for terminating renewal processes and the age-dependent branching processes.

• Select
  论文

  New Explicit Periodic Wave Solutions and their Limits for Modified form of Camassa-holm Equation

  Quan-di Wang, Min-ying Tang

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 513-524.

  DOI:10.1007/s10255-008-8013-1

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper, we consider the following nonlinear equation u_t + 2ku_x - u_xxt + au²u_x = 2u_xu_xx + uu_xxx, which is a modified form of the Camassa-Holm equation. We construct four new explicit periodic wave solutions by bifurcation method of dynamical systems. We also obtain two explicit solitary wave solutions via the limits of the explicit periodic wave solutions. One of the two solitary wave solutions is new.

• Select
  论文

  On the Relations of Graph Parameters and Its Total Parameters

  Jing-wen Li, Zhi-wen Wang, Jaeun Lee, Moo Young Sohn, Zhong-fu Zhang, En-qiang Zhu

  Acta Mathematicae Applicatae Sinica(English Series). 2010, 26(3): 525-528.

  DOI:10.1007/s10255-008-8152-4

  Abstract ( )    Download PDF ( )   Knowledge map   Save

  In this paper we get some relations between α(G), α′(G), β(G), β′(G) and α_T (G), β_T (G). And all bounds in these relations are best possible, where α(G), α′(G), β(G), β′(G), α_T (G) and β_T (G) are the covering number, edge-covering number, independent number, edge-independent number (or matching number), total covering number and total independent number, respectively.