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) 2017年 33卷

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1. Qualitative Analysis and Approximate Damped Oscillatory Solutions for a Kind of Nonlinear Dispersive-dissipative Equation
Shao-wei LI, Wei-guo ZHANG, Yan ZHAO, Zheng-ming LI, Xiang LI
应用数学学报(英文版)    2017, 33 (1): 1-24.   DOI: 10.1007/s10255-017-0632-y
摘要140)      PDF(pc) (464KB)(143)    收藏

This paper makes qualitative analysis to the bounded traveling wave solutions for a kind of nonlinear dispersive-dissipative equation, and considers its solving problem. The relation is investigated between behavior of its solution and the dissipation coefficient. Further, all approximate damped oscillatory solutions when dissipation coefficient is small are presented by utilizing the method of undetermined coefficients according to the theory of rotated vector field in planar dynamical systems. Finally, error estimate is given by establishing the integral equation which reflects the relation between approximate and exact damped oscillatory solutions applying the idea of homogenization principle.

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2. Global Strong Solutions of the Cauchy Problem for 1D Compressible Navier-Stokes Equations with Density-dependent Viscosity
Sheng-quan LIU, Jun-ning ZHAO
应用数学学报(英文版)    2017, 33 (1): 25-34.   DOI: 10.1007/s10255-016-0631-4
摘要163)      PDF(pc) (231KB)(128)    收藏

We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ(ρ)=α, where α > 0 and A > 0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.

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3. Innovation Governs Everything Eventually: Extensions of the DeGroot Model
Ming-min YANG, Xing-long QU, Zhi-gang CAO, Xiao-guang YANG
应用数学学报(英文版)    2017, 33 (1): 35-42.   DOI: 10.1007/s10255-016-0621-6
摘要145)      PDF(pc) (697KB)(135)    收藏

We study the DeGroot model for continuous opinion dynamics under the influence of innovations. In the original model, individuals' opinions, after given their initial values, evolve merely according to the given learning topology. The main contribution of this paper is that external innovation effects are introduced:each individual is given the opportunity to change her opinion to a randomly selected opinion according to a given distribution on the opinion space and then the external opinion is either adapted by the individual, or combined into her learning process. It turns out that all the classical results of the DeGroot model are violated in this new model. We prove that convergence can still be guaranteed in the expectation sense, regardless of the learning topology. We also study the steady distributions of opinions among the society and the time spent to reach a steady state by means of Monte-Carlo simulations.

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4. A Study on Monotone Self-Dual Boolean Functions
Mustafa ALTUN, Marc D. RIEDEL
应用数学学报(英文版)    2017, 33 (1): 43-52.   DOI: 10.1007/s10255-017-0633-x
摘要120)      PDF(pc) (265KB)(131)    收藏

This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form(IDNF) do not have more variables than disjuncts. Monotone self-dual Boolean functions in IDNF with the same number of variables and disjuncts are examined. An algorithm is proposed to test whether a monotone Boolean function in IDNF with n variables and n disjuncts is self-dual. The runtime of the algorithm is O(n3).

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5. On Optimal Proportional Reinsurance and Investment in a Hidden Markov Financial Market
Qing-bin MENG, Xin ZHANG, Jun-na BI
应用数学学报(英文版)    2017, 33 (1): 53-62.   DOI: 10.1007/s10255-017-0634-9
摘要177)      PDF(pc) (232KB)(140)    收藏

This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky(bond) and risky(stock) asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.

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6. Fujita Type Conditions to Heat Equation with Variable Source
Yun-xia LIU, Yun-hua WANG, Si-ning ZHENG
应用数学学报(英文版)    2017, 33 (1): 63-68.   DOI: 10.1007/s10255-017-0635-8
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This paper studies heat equation with variable exponent utu+up(x)+uq in RN×(0, T), where p(x) is a nonnegative continuous, bounded function, 0 < p-=inf p(x) ≤ p(x) ≤ sup p(x)=p+. It is easy to understand for the problem that all nontrivial nonnegative solutions must be global if and only if max{p+, q} ≤ 1. Based on the interaction between the two sources with fixed and variable exponents in the model, some Fujita type conditions are determined that that all nontrivial nonnegative solutions blow up in finite time if 0 < q ≤ 1 with p+> 1, or 1 < q < 1+(N)/(2). In addition, if q > 1+(N)/(2), then(i) all solutions blow up in finite time with 0 < p-≤ p+≤ 1+(N)/(2);(ii) there are both global and nonglobal solutions for p-> 1+(N)/(2);and(iii) there are functions p(x) such that all solutions blow up in finite time, and also functions p(x) such that the problem possesses global solutions when p-< 1+(N)/(2) < p+.

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7. Upper Minus Total Domination Number of Regular Graphs
Zhen-lin LI, Xin-zhong LÜ
应用数学学报(英文版)    2017, 33 (1): 69-74.   DOI: 10.1007/s10255-017-0637-6
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Let Γt-(G) be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the bound. Thus, we answer an open problem by Yan, Yang and Shan

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8. Entire Solution of the Degenerate Fisher Equation
Li-na WANG
应用数学学报(英文版)    2017, 33 (1): 75-82.   DOI: 10.1007/s10255-017-0638-5
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This paper deals with the solutions defined for all time of the degenerate Fisher equation. Some solutions are obtained by considering two traveling fronts with critical speed that come from both sides of the X-axis and mix. Unfortunately, the entire solutions which behave as two opposite wave fronts with non-critical speed approaching each other from both sides of the X-axis can not be obtained, because the essential difficulty originates from the algebraic decay rate of the fronts with non-critical speed.

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9. Oscillation Criteria of Second Order Half Linear Delay Dynamic Equations on Time Scales
H. A. AGWO, A. M. M. KHODIER, HEBA A. HASSAN
应用数学学报(英文版)    2017, 33 (1): 83-92.   DOI: 10.1007/s10255-017-0639-4
摘要164)      PDF(pc) (235KB)(104)    收藏

In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation
(r(t)g(xΔ(t)))Δ+p(t)f(x(τ(t)))=0,
on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=R, difference equations when T=N but can be applied on different types of time scales such as when T=qN for q > 1 and also improve most previous results. Finally, we give some examples to illustrate our main results.

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10. A Short Note on the Derivation of the Elastic Von Kármán Shell Theory
Hui LI
应用数学学报(英文版)    2017, 33 (1): 93-106.   DOI: 10.1007/s10255-017-0640-y
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We derive the Γ-limit of scaled elastic energies h-4Eh(uh) associated with deformations uh of a family of thin shells Sh={z=x+t(x);xS, -gh1(x)< t < gh2(x)}. The obtained von Kármán theory is valid for a general sequence of boundaries gh1, gh2 converging to 0 in an appropriate manner as h vanishes. Our analysis relies on the techniques and extends the results in[10]and[11].

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11. Nonparametric Estimation of Interval-censored Failure Time Data in the Presence of Informative Censoring
Chun-jie WANG, Jian-guo SUN, De-hui WANG, Ning-zhong SHI
应用数学学报(英文版)    2017, 33 (1): 107-114.   DOI: 10.1007/s10255-017-0641-x
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Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures(Kalbfleisch and Prentice, 2002). In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism(Sun, 2006; Turnbull, 1976). In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.

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12. Pentavalent Symmetric Graphs of Order 16p
Song-tao GUO, Hai-long HOU, Jiang-tao SHI
应用数学学报(英文版)    2017, 33 (1): 115-124.   DOI: 10.1007/s10255-017-0642-9
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A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p=2 or 31, and that up to isomorphism, there are three such graphs.

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13. Additive Rate Model With Auxiliary Covariates
Zhi-bin XU, Lu-qin LIU, Yan-yan LIU
应用数学学报(英文版)    2017, 33 (1): 125-140.   DOI: 10.1007/s10255-017-0643-8
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In this paper, we consider an inference method for recurrent event data in which the primary exposure covariate is assessed only in a validation set, while as an auxiliary covariate for the main exposure is available for the full cohort. Additive rate model is considered. The existing estimating equations in the absence of primary exposure are corrected by taking use of the validation data and auxiliary information, which yield consistent and asymptotically normal estimators of the regression parameters. The estimated baseline mean process is shown to converge weakly to a zero-mean Gaussian process. Extensive simulations are conducted to evaluate finite sample performance.

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14. A Trace Formula for Integro-differential Operators on the Finite Interval
Yu-ping WANG, Hikmet Koyunbakan, Chuan-fu YANG
应用数学学报(英文版)    2017, 33 (1): 141-146.   DOI: 10.1007/s10255-017-0644-7
摘要122)      PDF(pc) (197KB)(152)    收藏

In this paper, we consider the eigenvalue problem for integro-differential operators with separated boundary conditions on the finite interval and find a trace formula for the integro-differential operator.

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15. Analysis of Panel Count Data with Time-dependent Covariates and Informative Observation Process
Sha FANG, Hai-xiang ZHANG, Liu-quan SUN, De-hui WANG
应用数学学报(英文版)    2017, 33 (1): 147-156.   DOI: 10.1007/s10255-017-0645-6
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Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.

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16. Verification of Compressible Closure Models for Turbulent Multifluid Mixing
Hyeonseong JIN
应用数学学报(英文版)    2017, 33 (1): 157-168.   DOI: 10.1007/s10255-017-0646-5
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For compressible multiphase flow models the proper definition of averages of nonlinear terms is an essential problem which is called the closure problem. The purpose of the present work is to verify the spatial homogeneity closure, based on analysis of the simulation data. Various proposed closures are compared in a verification study to spatial averages of numerical simulations.

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17. Up-embeddability of Graphs with New Degree-sum
Sheng-xiang Lv, Meng-da FU, Yan-pei LIU
应用数学学报(英文版)    2017, 33 (1): 169-174.   DOI: 10.1007/s10255-017-0647-4
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Let G be a k(k ≤ 2)-edge connected simple graph with minimal degree ≥ 3 and girth g, r=「(g-1)/(2)」. For any edge uvE(G), if
dG(u)+dG(v)>(2ν(G)-2(k+1)(g-2r))/((k+1)(2r-1)(g-2r))+2(g-2r-1),
then G is up-embeddable. Furthermore, similar results for 3-edge connected simple graphs are also obtained.

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18. Acceleration of the EM Algorithm Using the Vector Aitken Method and Its Steffensen Form
Xu GUO, Qiu-yue LI, Wang-li XU
应用数学学报(英文版)    2017, 33 (1): 175-182.   DOI: 10.1007/s10255-017-0648-3
摘要139)      PDF(pc) (272KB)(302)    收藏

Based on Vector Aitken(VA) method, we propose an acceleration Expectation-Maximization(EM) algorithm, VA-accelerated EM algorithm, whose convergence speed is faster than that of EM algorithm. The VA-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm, thus it keeps the flexibility and simplicity of the EM algorithm. Considering Steffensen iterative process, we have also given the Steffensen form of the VA-accelerated EM algorithm. It can be proved that the reform process is quadratic convergence. Numerical analysis illustrate the proposed methods are efficient and faster than EM algorithm.

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19. Additive-multiplicative Hazards Model for Case-Cohort Studies with Multiple Disease Outcomes
Jun-e LIU, Jie ZHOU
应用数学学报(英文版)    2017, 33 (1): 183-192.   DOI: 10.1007/s10255-016-0581-x
摘要153)      PDF(pc) (241KB)(117)    收藏

Case-cohort design is an efficient and economical design to study risk factors for diseases with expensive measurements, especially when the disease rate is low. When several diseases are of interest, multiple case-cohort design studies may be conducted using the same subcohort. To study the association between risk factors and each disease occurrence or death, we consider a general additive-multiplicative hazards model for case-cohort designs with multiple disease outcomes. We present an estimation procedure for the regression parameters of the additive-multiplicative hazards model, and show that the proposed estimator is consistent and asymptotically normal. Large sample approximation works well in finite sample studies in simulation. Finally, we apply the proposed method to a real data example for illustration.

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20. Some Minimax Problems in Lexicographic Order
Yu ZHANG, Sheng-jie LI
应用数学学报(英文版)    2017, 33 (1): 193-200.   DOI: 10.1007/s10255-017-0650-9
摘要120)      PDF(pc) (198KB)(243)    收藏

In this paper, minimax theorems and saddle points for a class of vector-valued mappings f(x, y)=u(x)+β(x) v(y) are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.

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21. A Mathematical Approach to the Property of One -dimensional Steady Solution of Reverse Smolder Waves
Qiu-shu LI, Lan-xi XU
应用数学学报(英文版)    2017, 33 (1): 201-206.   DOI: 10.1007/s10255-017-0651-8
摘要105)      PDF(pc) (191KB)(227)    收藏

The mathematical property of one-dimensional steady solution for reverse smolder waves in the context of a model that permits both fuel-rich and fuel-lean has been studied using the method of analysis. Based on the equations and the boundary conditions some asymptotic properties of the solution at infinity are proved. It is shown that the value of oxygen or the mass of fuel(corresponding to the fuel-rich case and the fuel-lean case, respectively) tends to zero, and the temperature approaches to a fixed value. This is confirmed by other authors using large activation energy asymptotic methods.

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22. Global Cauchy Problem for a Leray-α Model
Hua QIU, Yi DU, Zheng-an YAO
应用数学学报(英文版)    2017, 33 (1): 207-220.   DOI: 10.1007/s10255-017-0652-7
摘要145)      PDF(pc) (287KB)(98)    收藏

In this paper, we consider the Cauchy problem for the 3D Leray-α model, introduced by Cheskidov et al. [11]. We obtain the global solution for the 3D Leray-α model in the fractional index Sobolev space, and prove that the 3D Leray-α model reduces to the homogeneous incompressible Navier-Stokes equations as α↘0+, and the solution of the 3D Leray-α model will converge to the weak solution of the corresponding Navier-Stokes equations.

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23. A Numerical Approach to Optimal Dividend Policies with Capital Injections and Transaction Costs
Zhuo JIN, Hai-liang YANG, G. YIN
应用数学学报(英文版)    2017, 33 (1): 221-238.   DOI: 10.1007/s10255-017-0653-6
摘要173)      PDF(pc) (567KB)(143)    收藏

This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. Using dynamic programming principle, the value function obeys a quasi-variational inequality(QVI). The state constraint of the impulsive control gives rise to a capital injection region with free boundary. Since the closed-form solutions are virtually impossible to obtain, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved.

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24. Testing for Serial Correlation in Three-dimensional Panel Data Models
Jian-hong WU, Qing DING, Jin-xu QIN
应用数学学报(英文版)    2017, 33 (1): 239-250.   DOI: 10.1007/s10255-017-0654-5
摘要208)      PDF(pc) (238KB)(118)    收藏

This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial autoregression modeled by centering and differencing residuals. The test can be shown to asymptotically chisquare distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects. Monte Carlo simulations are carried out for illustration.

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25. Global Existence and Blow up for Damped Generalized Boussinesq Equation
Run-zhang XU, Yong-bing LUO, Ji-hong SHEN, Shao-bin HUANG
应用数学学报(英文版)    2017, 33 (1): 251-262.   DOI: 10.1007/s10255-017-0655-4
摘要159)      PDF(pc) (258KB)(105)    收藏

We study the Cauchy problem of damped generalized Boussinesq equation utt-uxx+(uxx+f(u))xx-αuxxt=0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.

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26. Existence of Positive Solutions of Second-order Periodic Boundary Value Problems with Sign-Changing Green's Function
Cheng-hua GAO, Fei ZHANG, Ru-yun MA
应用数学学报(英文版)    2017, 33 (2): 263-268.   DOI: 10.1007/s10255-017-0657-2
摘要288)      PDF(pc) (193KB)(476)    收藏

In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem
u"+((1)/(2)+ε)2u=λg(t)f(u), t∈[0, 2π], u(0)=u(2π), u'(0)=u'(2π), where 0 < ε < (1)/(2), g:[0, 2π]→R is continuous, f:[0, ∞)→R is continuous and λ > 0 is a parameter.

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27. Solving the 2-D Elliptic Monge-Ampère Equation by a Kansa's Method
Qin LI, Zhi-yong LIU
应用数学学报(英文版)    2017, 33 (2): 269-276.   DOI: 10.1007/s10255-017-0656-3
摘要340)      PDF(pc) (805KB)(411)    收藏
In this paper, a Kansa's method is designed to solve numerically the Monge-Ampère equation. The primitive Kansa's method is a meshfree method which applying the combination of some radial basis functions (such as Hardy's MQ) to approximate the solution of the linear parabolic, hyperbolic and elliptic problems. But this method is deteriorated when is used to solve nonlinear partial differential equations. We approximate the solution in some local triangular subdomains by using the combination of some cubic polynomials. Then the given problems can be computed in each subdomains independently. We prove the stability and convergence of the new method for the elliptic Monge-Ampère equation. Finally, some numerical experiments are presented to demonstrate the theoretical results.
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28. Face Labelings of Klein-bottle Fullerenes
Martin BAČA, Maria NASEEM, Ayesha SHABBIR
应用数学学报(英文版)    2017, 33 (2): 277-286.   DOI: 10.1007/s10255-017-0658-1
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The Klein-bottle fullerene is a finite trivalent graph embedded on the Klein-bottle such that each face is a hexagon. The paper deals with the problem of labeling the vertices, edges and faces of the Klein-bottle fullerene in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face and the weights of all 6-sided faces constitute an arithmetic progression of difference d. In this paper we study the existence of such labelings for several differences d.
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29. Existence of Three Solutions for Quasilinear Elliptic Equations: an Orlicz-Sobolev Space Setting
Fei FANG, Zhong TAN
应用数学学报(英文版)    2017, 33 (2): 287-296.   DOI: 10.1007/s10255-017-0659-0
摘要257)      PDF(pc) (160KB)(400)    收藏
In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in[13].
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30. Numerical Algorithm for Solving Multi-Pantograph Delay Equations on the Half-line Using Jacobi Rational Functions with Convergence Analysis
Eid H. DOHA, Ali H. BHRAWY, Ramy M. HAFEZ
应用数学学报(英文版)    2017, 33 (2): 297-310.   DOI: 10.1007/s10255-017-0660-7
摘要313)      PDF(pc) (213KB)(297)    收藏
A new spectral Jacobi rational-Gauss collocation (JRC) method is proposed for solving the multipantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods.
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31. Green Function of Fourth-order Differential Operator with Eigenparameter-dependent Boundary and Transmission Conditions
Xin-yan ZHANG, Jiong SUN
应用数学学报(英文版)    2017, 33 (2): 311-326.   DOI: 10.1007/s10255-017-0661-6
摘要226)      PDF(pc) (176KB)(315)    收藏
We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.
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32. Partial Penalized Empirical Likelihood Ratio Test Under Sparse Case
Shan-shan WANG, Heng-jian CUI
应用数学学报(英文版)    2017, 33 (2): 327-344.   DOI: 10.1007/s10255-017-0663-4
摘要394)      PDF(pc) (383KB)(320)    收藏
A consistent test via the partial penalized empirical likelihood approach for the parametric hypothesis testing under the sparse case, called the partial penalized empirical likelihood ratio (PPELR) test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypothesis and the local alternatives of order n-1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical likelihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.
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33. Group Classification of Differential-difference Equations: Low-dimensional Lie Algebras
Shou-feng SHEN, Yong-yang JIN
应用数学学报(英文版)    2017, 33 (2): 345-362.   DOI: 10.1007/s10255-017-0664-3
摘要244)      PDF(pc) (211KB)(311)    收藏

Differential-difference equations of the form =Fn(t, un-1, un, un+1-1, +1) are classified according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry algebras. Here Fn is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t.

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34. Asymptotic Results for Random Processes
HEE-JIN MOON, CHANG-HO HAN, YONG-KAB CHOI
应用数学学报(英文版)    2017, 33 (2): 363-372.   DOI: 10.1007/s10255-017-0665-2
摘要270)      PDF(pc) (165KB)(300)    收藏
In this paper we establish asymptotic results and a generalized uniform law of the iterated logarithm (LIL) for the increments of a strictly stationary random process, whose results are proved by separating linearly positive quadrant dependent (LPQD) random process and linearly negative quadrant dependent (LNQD) one, respectively.
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35. Variable Selection for the Partial Linear Single-Index Model
Wu WANG, Zhong-yi ZHU
应用数学学报(英文版)    2017, 33 (2): 373-388.   DOI: 10.1007/s10255-017-0666-1
摘要435)      PDF(pc) (202KB)(335)    收藏
In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.
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36. On Global Existence for Mass-supercritical Nonlinear Fractional Hartree Equations
Dan WU
应用数学学报(英文版)    2017, 33 (2): 389-400.   DOI: 10.1007/s10255-017-0668-z
摘要346)      PDF(pc) (180KB)(312)    收藏
In this paper, we consider the nonlinear fractional Schrödinger equations with Hartree type nonlinearity in mass-supercritical and energy-subcritical case. By sharp Hardy-Littlewood-Sobolev inequality and the Pohozaev identity, we established a threshold condition, which leads to a global existence of solutions in energy space.
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37. General Energy Decay of Solutions for a Weakly Dissipative Kirchhoff Equation with Nonlinear Boundary Damping
Amir Peyravi
应用数学学报(英文版)    2017, 33 (2): 401-408.   DOI: 10.1007/s10255-017-0669-y
摘要224)      PDF(pc) (144KB)(305)    收藏

In this article, we study the weak dissipative Kirchhoff equation
utt-M(||∂u||22)△u+b(x)ut+f(u)=0,
under nonlinear damping on the boundary
(∂u)/(∂ν)+α(t)g(ut)=0. We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao (2010) in which only exponential energy decay is considered and the work by Zhang and Huang (2014) where the energy decay has been not considered.

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38. A Stabilized Crank-Nicolson Mixed Finite Element Method for Non-stationary Parabolized Navier-Stokes Equations
Yan-jie ZHOU, Fei TENG, Zhen-dong LUO
应用数学学报(英文版)    2017, 33 (2): 409-416.   DOI: 10.1007/s10255-017-0670-5
摘要205)      PDF(pc) (151KB)(360)    收藏
In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element (SCNMFE) formulation based on two local Gauss integrals and parameterfree with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.
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39. The Existence of Semiclassical States for Some P-Laplacian Equation with Critical Exponent
Ji-xiu WANG
应用数学学报(英文版)    2017, 33 (2): 417-434.   DOI: 10.1007/s10255-017-0671-4
摘要271)      PDF(pc) (220KB)(325)    收藏
In this paper, we study the existence of semiclassical states for some p-Laplacian equation. Under given conditions and minimax methods, we show that this problem has at least one positive solution provided that εΕ; for any m∈N, it has m pairs solutions if εΕm, where Ε, Εm are sufficiently small positive numbers. Moreover, these solutions are closed to zero in W1,p(RN) as ε→0.
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40. Numerical Approximation of Solution for the Coupled Nonlinear Schrödinger Equations
Juan CHEN, Lu-ming ZHANG
应用数学学报(英文版)    2017, 33 (2): 435-450.   DOI: 10.1007/s10255-017-0672-3
摘要260)      PDF(pc) (1741KB)(384)    收藏
In this article, a compact finite difference scheme for the coupled nonlinear Schrödinger equations is studied. The scheme is proved to conserve the original conservative properties. Unconditional stability and convergence in maximum norm with order O(τ2+h4) are also proved by the discrete energy method. Finally, numerical results are provided to verify the theoretical analysis.
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