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) 2013年 29卷

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1. Construction and Regularity of Transition Functions on Polish Spaces under Measurability Conditions
Liu-er Ye, Xian-ping Guo
应用数学学报(英文版)    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.
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2. A Batch Arrival Retrial Queue with Two Phases of Service and Bernoulli Vacation Schedule
Gautam Choudhury, Kandarpa Deka
应用数学学报(英文版)    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.
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3. Chromaticity of Complete 6-Partite Graphs with Certain Star or Matching Deleted II
Roslan Hasni, Ameen Shaman Ameen, Yee-Hock Peng, Hai-xing Zhao
应用数学学报(英文版)    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.
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4. Kernel Estimators of the ROC Curve with Censored Data
Fang-fang Bai, Yong Zhou
应用数学学报(英文版)    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.
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5. A Semiparametric Additive Rates Model for Clustered Recurrent Event Data
Sui He, Fen Wang, Liu-quan Sun
应用数学学报(英文版)    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.
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6. 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
应用数学学报(英文版)    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.
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7. An Almost Sure Central Limit Theorem for Self-normalized Weighted Sums
Yong ZHANG, Xiao-yun YANG
应用数学学报(英文版)    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≤in, 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.
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8. Analysis of φ-divergence for Loglinear Models with Constraints under Product-multinomial Sampling
Ying-hua JIN, Yao-hua Wu
应用数学学报(英文版)    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.
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9. Some Properties for the Estimators in Linear Mixed Models
Zai-xing Li, Yan Cui, Wang-li Xu
应用数学学报(英文版)    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.
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10. Hausdorff Measures for a Class of Homogeneous Cantor Sets
Cheng-qin QU
应用数学学报(英文版)    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.
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11. Chromatic Sums of Biloopless Nonseparable Near-Triangulations on the Projective Plane
Zhao-xiang Li, Yan-pei Liu, Bing-feng Si
应用数学学报(英文版)    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.
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12. Managing Procurement and Production Outsourcing under Dynamic Prices
Xiao-gang CAO, Chao YANG, Hui WEN, Huo-song XIA, Ji-zi LI
应用数学学报(英文版)    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.
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13. Dynamics in a Discrete-time Predator-prey System with Allee Effect
Xian-wei Chen, Xiang-ling Fu, Zhu-jun Jing
应用数学学报(英文版)    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.
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14. Reflected BSDEs with Random Default Time and Related Mixed Optimal Stopping-control Problems
Dong-mei Guo, Xiao-ming Xu
应用数学学报(英文版)    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.
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15. Asymptotic Property for Some Series of Probability
Jian-jun HE, Ting-fan XIE
应用数学学报(英文版)    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, EX22>0, λ(ε)=P(|Sn|≥). 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).
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16. Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost
Da-cheng YAO
应用数学学报(英文版)    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.
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17. EQ1rot Nonconforming Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations
Yan-min Zhao, Fen-ling Wang, Dong-yang Shi
应用数学学报(英文版)    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.
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18. The Phase-type Risk Model Perturbed by Diffusion under a Threshold Dividend Strategy
Wu-yuan Jiang, Zhou-jun Yang
应用数学学报(英文版)    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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19. Parametric Duality Models for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized (α,η,ρ)-V-Invex Functions
G. J. ZALMAI, Qing-hong ZHANG
应用数学学报(英文版)    2013, 29 (2): 225-240.   DOI: 10.1007/s10255-013-0213-7
摘要1676)      收藏
In this paper, we present several parametric duality results under various generalized (α,η,ρ)-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.
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20. Analyzing Left-truncated and Right-censored Data under Cox Models with Long-term Survivors
Fei-peng ZHANG, Yong ZHOU
应用数学学报(英文版)    2013, 29 (2): 241-252.   DOI: 10.1007/s10255-013-0215-5
摘要1875)      收藏
We analyze left-truncated and right-censored data using Cox proportional hazard models with long-term survivors. The estimators of covariate coefficients and the long-term survivor proportion are obtained by the partial likelihood method, and their asymptotic properties are also established. Simulation studies demonstrate the performance of the proposed estimators, and an application to a real dataset is provided.
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21. Construction of Supersaturated Design with Large Number of Factors by the Complementary Design Method
Yan LIU, Min-Qian LIU
应用数学学报(英文版)    2013, 29 (2): 253-262.   DOI: 10.1007/s10255-013-0214-6
摘要1693)      收藏
Supersaturated designs (SSDs) have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E(fNOD) criterion. We also propose a new method, called the complementary design method, for constructing E(fNOD) optimal SSDs. The basic principle of this method is that for any existing E(fNOD) optimal SSD whose E(fNOD) value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E(fNOD) optimal. This method applies to both symmetrical and asymmetrical (mixed-level) cases. It provides a convenient and efficient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.
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22. Θ-type Calderón-Zygmund Operators with Non-doubling Measures
Ru-long XIE, Li-sheng SHU
应用数学学报(英文版)    2013, 29 (2): 263-280.   DOI: 10.1007/s10255-013-0217-3
摘要1761)      收藏
Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ(B(x, r))≤Crn for all x∈Rd, r>0 and for some fixed 0<n≤d. In this paper, under this assumption, we prove that θ-type Calderón-Zygmund operator which is bounded on L2(μ) is also bounded from L1(μ) into RBMO(μ) and from Hatb1,∞(μ) into L1(μ). According to the interpolation theorem introduced by Tolsa, the Lp(μ)-boundedness (1<p<1) is established for θ-type Calderón-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type Calderón-Zygmund operator with RBMO(μ) function are bounded on Lp(μ) (1<p<1).
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23. Hölder Continuity for a Class of Strongly Degenerate Schrödinger Operator Formed by Vector Fields
Yong-yang JIN, Jie-lin Lü, Rong-fei LIN
应用数学学报(英文版)    2013, 29 (2): 281-288.   DOI: 10.1007/s10255-011-0098-2
摘要1645)      收藏
In this paper we obtain the Hölder continuity property of the solutions for a class of degenerate Schrödinger equation generated by the vector fields:
 ,
where X={X1, ···,Xm} is a family of C vector fields satisfying the Hörmander condition, and the lower order terms belong to an appropriate Morrey type space.
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24. Regularity Criteria of Axisymmetric Weak Solutions to the 3D Magnetohydrodynamic Equations
Bao-quan YUAN, Feng-ping LI
应用数学学报(英文版)    2013, 29 (2): 289-302.   DOI: 10.1007/s10255-013-0223-5
摘要1796)      收藏
In this paper, we study the regularity criteria for axisymmetric weak solutions to the MHD equa- tions in R3. Let ωθ, Jθ and uθ be the azimuthal component of ω, J and u in the cylindrical coordinates, respectively. Then the axisymmetric weak solution (u, b) is regular on (0, T) if (ωθ, Jθ)∈Lq(0, T;Lq) or (ωθ,∇(uθeθ))∈Lq(0, T;Lq) with 3/p+2/q≤2, 3/2<p<∞. In the endpoint case, one needs conditions (ωθ, Jθ)∈L1(0, T; B∞,∞0) or (ωθ,∇∇(uθeθ))∈L1(0, T; B∞,∞0).
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25. A Separation Theorem for Stochastic Singular Linear Quadratic Control Problem with Partial Information
Hong-ji MA, Ting HOU
应用数学学报(英文版)    2013, 29 (2): 303-314.   DOI: 10.1007/s10255-013-0218-2
摘要1590)      收藏
In this paper, we provide a separation theorem for the singular linear quadratic (LQ) control problem of Itô-type linear systems in the case of the state being partially observable. Above all, the Kalman- Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation (GDRE).
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26. Existence of Solutions for the Critical Elliptic System with Inverse Square Potentials
Zhao-xia LIU, Zhao-hui LIU
应用数学学报(英文版)    2013, 29 (2): 315-328.   DOI: 10.1007/s10255-013-0225-3
摘要1903)      收藏
Let Ω∋0 be an open bounded domain in RN (N≥3) and 2*(s)=2(N-s)/N-2 , 0<s<2. We consider the following elliptic system of two equations in H01(Ω)×H01(Ω):
,
where λ, μ>0 and α,β> 1 satisfy α+β=2*(s). Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions.
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27. Solutions to BSDEs Driven by Both Standard and Fractional Brownian Motions
Wei-yin FEI, Deng-Feng XIA, Shu-guang ZHANG
应用数学学报(英文版)    2013, 29 (2): 329-354.   DOI: 10.1007/s10255-013-0219-1
摘要1706)      收藏
The backward stochastic differential equations driven by both standard and fractional Brownian motions (or, in short, SFBSDE) are studied. A Wick-Itô stochastic integral for a fractional Brownian motion is adopted. The fractional Itô formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.
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28. Complex Dynamics in a Discrete-time Predator-prey System without Allee Effect
Xian-wei CHEN, Xiang-ling FU, ZHU-JUN JING
应用数学学报(英文版)    2013, 29 (2): 355-376.   DOI: 10.1007/s10255-013-0221-7
摘要1885)      收藏
In this paper, complex dynamics of the discrete-time predator-prey system without Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. Chaos, in the sense of Marotto, is also proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and richer dynamics behaviors. More specifically, this paper presents the finding of period-one orbit, period-three orbits, and chaos in the sense of Marotto, complete period-doubling bifurcation and invariant circle leading to chaos with a great abundance period-windows, simultaneous occurrance of two different routes (invariant circle and inverse period- doubling bifurcation, and period-doubling bifurcation and inverse period-doubling bifurcation) to chaos for a given bifurcation parameter, period doubling bifurcation with period-three orbits to chaos, suddenly appearing or disappearing chaos, different kind of interior crisis, nice chaotic attractors, coexisting (2,3,4) chaotic sets, non-attracting chaotic set, and so on, in the discrete-time predator-prey system. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding is given of the discrete-time predator-prey systems with Allee effect and without Allee effect.
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29. Weak Centers and Local Bifurcations of Critical Periods at Infinity for a Class of Rational Systems
Wen-tao HUANG, Valery G. ROMANOVSKI, Wei-nian ZHANG
应用数学学报(英文版)    2013, 29 (2): 377-390.   DOI: 10.1007/s10255-013-0220-8
摘要1474)      收藏
We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.
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30. Bayesian Estimation for Generalized Exponential Distribution Based on Progressive Type-Ⅰ Interval Censoring
Xiu-yun PENG, Zai-zai YAN
应用数学学报(英文版)    2013, 29 (2): 391-402.   DOI: 10.1007/s10255-013-0222-6
摘要1745)      收藏
In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive Type-Ⅰ interval censoring. The Bayesian estimates of parameters and reliability function cannot be obtained as explicit forms by applying squared error loss and Linex loss functions, respectively; thus, we present the Lindley's approximation to discuss these estimations. Then, the Bayesian estimates are compared with the maximum likelihood estimates by using the Monte Carlo simulations.
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31. Superconvergence Analysis and Extrapolation of Quasi-Wilson Nonconforming Finite Element Method for Nonlinear Sobolev Equations
Dong-yang SHI, Fen-ling WANG, Yan-min ZHAO
应用数学学报(英文版)    2013, 29 (2): 403-414.   DOI: 10.1007/s10255-013-0216-4
摘要1807)      收藏
Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equations is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that (∇h(u-Ihu),∇hvh)h may be estimated as order O(h2) when uh3(Ω), where Ihu denotes the bilinear interpolation of u, vh is a polynomial belongs to quasi-Wilson finite element space and ∇h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O(h2)/O(h3) in broken H1-norm, which is one/two order higher than its interpolation error when uH3(Ω)/H4(Ω). Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapolation result of order O(H3), two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.
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32. On the Existence of Solutions for an Elliptic System of Equations with Arbitrary Order Growth
Zhong-yuan LIU
应用数学学报(英文版)    2013, 29 (2): 415-424.   DOI: 10.1007/s10255-013-0224-4
摘要1909)      收藏
Let BR be the ball centered at the origin with radius R in RN (N≥2). In this paper we study the existence of solution for the following elliptic system
 
where λ>0, μ>0 p≥2, q≥2, υ is the unit outward normal at the boundary ∂BR. Under certain assumptions on κ(|x|), using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity.
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33. Stability and Bifurcation Analysis in a System of Four Coupled Neurons with Multiple Delays
Xiu-ling LI, Jun-jie WEI
应用数学学报(英文版)    2013, 29 (2): 425-448.   DOI: 10.1007/s10255-013-0212-8
摘要1641)      收藏
A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.
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34. Improvement of Convergence to Steady State Solutions of Euler Equations with Weighted Compact Nonlinear Schemes
Shu-hai ZHANG, Xiao-gang DENG, Mei-liang MAO, Chi-Wang SHU
应用数学学报(英文版)    2013, 29 (3): 449-464.   DOI: 10.1007/s10255-013-0230-6
摘要1263)      收藏
The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X. and Zhang H. (2000), J. Comput. Phys. 165, 22-44 and Zhang S., Jiang S. and Shu C.-W. (2008), J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. (2007), J. Sci. Comput. 31, 273-305 and Zhang S., Jiang S and Shu. C.-W. (2011), J. Sci. Comput. 47, 216-238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.
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35. Asymptotic Analysis of Quantum Dynamics in Crystals:the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase
Weinan E, Jian-feng LU, Xu YANG
应用数学学报(英文版)    2013, 29 (3): 465-476.   DOI: 10.1007/s10255-011-0095-5
摘要1123)      收藏
We study the semi-classical limit of the Schrödinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.
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36. Generalized Profile LSE in Varying-Coefficient Partially Linear Models with Measurement Errors
Yun-bei MA, Jin-hong YOU, Yong ZHOU
应用数学学报(英文版)    2013, 29 (3): 477-490.   DOI: 10.1007/s10255-013-0229-z
摘要1314)      收藏
This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi = Xiτ +Ziτ (Ui)+εi, Wi = Xi+ ξi, i = 1,…, n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.
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37. A Trust Region Algorithm for Solving Bilevel Programming Problems
Guo-shan LIU, Shi-qin XU, Ji-ye HAN
应用数学学报(英文版)    2013, 29 (3): 491-498.   DOI: 10.1007/s10255-013-0231-5
摘要1444)      收藏
In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.
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38. Flows Associated to Cameron-martin Type Vector Fields on Path Spaces Over a Riemannian Manifold
Jing-xiao ZHANG
应用数学学报(英文版)    2013, 29 (3): 499-508.   DOI: 10.1007/s10255-013-0245-z
摘要948)      收藏
The flow on theWiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.
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39. Large Time Behavior of Entropy Solutions to Some Hyperbolic System with Dissipative Structure
Hui-min YU
应用数学学报(英文版)    2013, 29 (3): 509-516.   DOI: 10.1007/s10255-011-0097-3
摘要1116)      收藏
In this paper the large time behavior of the global L entropy solutions to the hyperbolic system with dissipative structure is investigated. It is proved that as t→∞ the entropy solutions tend to a constant equilibrium state in L2 norm with exponential decay even when the initial values are arbitrarily large. As an illustration, a class of 2×2 system is studied.
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40. On the Spectral Spread of Bicyclic Graphs with Given Girth
Bing WANG, Ming-qing ZHAI, Jin-long SHU
应用数学学报(英文版)    2013, 29 (3): 517-528.   DOI: 10.1007/s10255-013-0228-0
摘要1101)      收藏
The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and |E(G)| = |V(G)| + 1. Let B(n, g) be the set of bicyclic graphs on n vertices with girth g. In this paper some properties about the least eigenvalues of graphs are given, by which the unique graph with maximal spectral spread in B(n, g) is determined.
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