15 January 2013, Volume 29 Issue 1
    

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  • Construction and Regularity of Transition Functions on Polish Spaces under Measurability Conditions
    Liu-er Ye, Xian-ping Guo
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 1-14.
    DOI:10.1007/s10255-013-0208-4
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    This paper concerns the construction and regularity of a transition (probability) function of a non-homogeneous continuous-time Markov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous (in t≥0) and conservative transition rates q(t, x, Λ), we consider the case that q(t, x, Λ) are only required to satisfy a mild measurability (in t≥0) condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.
  • A Batch Arrival Retrial Queue with Two Phases of Service and Bernoulli Vacation Schedule
    Gautam Choudhury, Kandarpa Deka
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 15-34.
    DOI:10.1007/s10255-007-7083-9
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    We consider an MX=G=1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under a linear retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalizes both the classical M=G=1 retrial queue with arrivals in batches and a two phase batch arrival queue with a single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system , including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moment.
  • Chromaticity of Complete 6-Partite Graphs with Certain Star or Matching Deleted II
    Roslan Hasni, Ameen Shaman Ameen, Yee-Hock Peng, Hai-xing Zhao
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 35-42.
    DOI:10.1007/s10255-013-0206-6
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    Let P(G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ~ H, if P(G,λ)=P(H, λ). We write [G] = {H|H ~ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6n+1 vertices according to the number of 7-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, many new families of chromatically unique complete 6-partite graphs with certain star or matching deleted are obtained.
  • Kernel Estimators of the ROC Curve with Censored Data
    Fang-fang Bai, Yong Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 43-54.
    DOI:10.1007/s10255-013-0199-1
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    Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed.
  • A Semiparametric Additive Rates Model for Clustered Recurrent Event Data
    Sui He, Fen Wang, Liu-quan Sun
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 55-62.
    DOI:10.1007/s10255-011-0093-7
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    Recurrent event data often arises in biomedical studies, and individuals within a cluster might not be independent. We propose a semiparametric additive rates model for clustered recurrent event data, wherein the covariates are assumed to add to the unspecified baseline rate. For the inference on the model parameters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established.
  • Global Parametric Sufficient Efficiency Conditions for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized (α, η, ρ)-V-Invex Functions
    G.J. Zalmai, Qing-hong Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 63-78.
    DOI:10.1007/s10255-013-0204-8
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    In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized (α, η, ρ)-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.
  • An Almost Sure Central Limit Theorem for Self-normalized Weighted Sums
    Yong ZHANG, Xiao-yun YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 79-92.
    DOI:10.1007/s10255-010-8247-6
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    Let X, X1, X2,… be a sequence of nondegenerate i.i.d. random variables with zero means, which is in the domain of attraction of the normal law. Let {ani, 1≤i≤n, n≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums.
  • Analysis of φ-divergence for Loglinear Models with Constraints under Product-multinomial Sampling
    Ying-hua JIN, Yao-hua Wu
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 93-104.
    DOI:10.1007/s10255-013-0203-9
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    The loglinear model under product-multinomial sampling with constraints is considered. The asymptotic expansion and normality of the restricted minimum φ-divergence estimator (RMφDE) which is a generalization of the maximum likelihood estimator is presented. Then various statistics based on φ-divergence and RMφDE are used to test various hypothesis test problems under the model considered. These statistics contain the classical loglikelihood ratio test statistics and Pearson chi-squared test statistics. In the last section, a simulation study is implemented.
  • Some Properties for the Estimators in Linear Mixed Models
    Zai-xing Li, Yan Cui, Wang-li Xu
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 105-116.
    DOI:10.1007/s10255-011-0067-9
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    Linear mixed models (LMMs) have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.
  • Hausdorff Measures for a Class of Homogeneous Cantor Sets
    Cheng-qin QU
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 117-122.
    DOI:10.1007/s10255-013-0198-2
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    We consider the homogeneous Cantor sets which are generalization of symmetric perfect sets, and give a formula of the exact Hausdorff measures for a class of such sets.
  • Chromatic Sums of Biloopless Nonseparable Near-Triangulations on the Projective Plane
    Zhao-xiang Li, Yan-pei Liu, Bing-feng Si
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 123-134.
    DOI:10.1007/s10255-013-0197-3
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    In this paper, the chromatic sum functions of rooted biloopless nonseparable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.
  • Managing Procurement and Production Outsourcing under Dynamic Prices
    Xiao-gang CAO, Chao YANG, Hui WEN, Huo-song XIA, Ji-zi LI
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 135-142.
    DOI:10.1007/s10255-013-0196-4
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    This paper proposes a procurement and production outsourcing model subject to a dynamic prices environment. Using the optimal control theory we obtain the necessary conditions of the optimal procurement and production policy. From the study of optimal control conditions, we derive qualitative properties of the optimal procurement and production decisions for a few exemplifying cases. Through these results we are able to provide some managerial implications for managers to make real decisions.
  • Dynamics in a Discrete-time Predator-prey System with Allee Effect
    Xian-wei Chen, Xiang-ling Fu, Zhu-jun Jing
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 143-164.
    DOI:10.1007/s10255-013-0207-5
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    In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases (within a limited value). Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given.
  • Reflected BSDEs with Random Default Time and Related Mixed Optimal Stopping-control Problems
    Dong-mei Guo, Xiao-ming Xu
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 165-178.
    DOI:10.1007/s10255-013-0202-x
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    In this paper we study the one-dimensional reflected backward stochastic differential equations which are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. Using a penalization method, we prove the existence and uniqueness of the solutions to these equations. As an application, we show that under proper assumptions the solution of the reflected equation is the value of the related mixed optimal stopping-control problem.
  • ARTICLES
    Asymptotic Property for Some Series of Probability
    Jian-jun HE, Ting-fan XIE
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 179-186.
    DOI:10.1007/s10255-012-0138-6
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    Let {X, Xn, n≥1} be a sequence of i.i.d.random variables with zero mean, and set Sn=Xk, EX2=σ2>0, λ(ε)=P(|Sn|≥nε). In this paper, we discuss the rate of the approximation of σ2 by ε2λ(ε) under suitable conditions, and improve the corresponding results of Klesov (1994).
  • Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost
    Da-cheng YAO
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 187-200.
    DOI:10.1007/s10255-013-0201-y
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    We study an inventory system in which products are ordered from outside to meet demands, and the cumulative demand is governed by a Brownian motion. Excessive demand is backlogged. We suppose that the shortage and holding costs associated with the inventory are given by a general convex function. The product ordering from outside incurs a linear ordering cost and a setup fee. There is a constant leadtime when placing an order. The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.
  • EQ1rot Nonconforming Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations
    Yan-min Zhao, Fen-ling Wang, Dong-yang Shi
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 201-214.
    DOI:10.1007/s10255-013-0205-7
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    EQ1rot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2) one order higher than its interpolation error O(h), the superclose results of order O(h2) in broken H1-norm are obtained. At the same time, the global superconvergence in broken H1-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ1rot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.
  • The Phase-type Risk Model Perturbed by Diffusion under a Threshold Dividend Strategy
    Wu-yuan Jiang, Zhou-jun Yang
    Acta Mathematicae Applicatae Sinica(English Series). 2013, 29(1): 215-224.
    DOI:10.1007/s10255-013-0200-z
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    This paper considers a perturbed renewal risk process in which the inter-claim times have a phase-type distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the mth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.
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