中国科学院数学与系统科学研究院期刊网

Acta Mathematicae Applicatae Sinica(English Series) 2016 Vol.32

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Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations
Quan-sen JIU, Huan YU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 1-16.   DOI: 10.1007/s10255-016-0539-z
Abstract128)      PDF(pc) (197KB)(411)       Save

In this paper, we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion:

With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate, we prove the global well-posedness for this system with α≥ 5/4. Moreover, the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique. Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.

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Near-Optimal Controls of Differential Systems with Switching and Random Jumps Subject to Fast Switching and Wideband Noise Perturbation
G. YIN, Xian-ping GUO, Yousef TALAFHA, Nicholas A. BARAN
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 17-34.   DOI: 10.1007/s10255-016-0550-4
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This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching. The random switching is modeled by a continuous-time, time-inhomogeneous Markov chain. Under broad conditions, it is shown that there is an associated limit problem, which is a switching jump diffusion. Using near-optimal controls of the limit system, we then build controls for the original systems. It is shown that such constructed controls are nearly optimal.

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Existence and Multiplicity of Solutions for Nonlocal Systems with Kirchhoff Type
Zhi-tao ZHANG, Yi-min SUN,
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 35-54.   DOI: 10.1007/s10255-016-0545-1
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Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz. We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.

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Convergence Rates to Asymptotic Profile for Solutions of Quasilinear Hyperbolic Equations with Nonlinear Damping
Shi-feng GENG, Zhen WANG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 55-66.   DOI: 10.1007/s10255-015-0535-8
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The quasilinear hyperbolic equation with nonlinear damping is considered in this paper, a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation, the convergence rates of the new profile are better than that obtained by Nishihara (1997, J. Differential Equations 137, 384–395) and H.-J. Zhao (2000, J. Differential Equations 167, 467–494).

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Improved Bounds on the Generalized Acyclic Chromatic Number
Yu-wen WU, Kan-ran TAN, Gui-ying YAN
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 67-72.   DOI: 10.1007/s10255-016-0541-5
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An r-acyclic edge chromatic number of a graph G, denoted by ar'(G), is the minimum number of colors used to produce an edge coloring of the graph such that adjacent edges receive different colors and every cycle C has at least min {|C|, r} colors. We prove that ar'(G)≤(4r+ 1) Δ(G), when the girth of the graph G equals to max{50, Δ(G)} and 4 ≤ r ≤7. If we relax the restriction of the girth to max {220, Δ(G)}, the upper bound of ar'(G) is not larger than (2r + 5) (G) with 4 ≤ r ≤ 10.

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Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems
Qin-long WANG, Wen-tao HUANG, Yi-rong LIU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 73-80.   DOI: 10.1007/s10255-015-0510-4
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In this paper, bifurcation of small amplitude limit cycles from the degenerate equilibrium of a three-dimensional system is investigated. Firstly, the method to calculate the focal values at nilpotent critical point on center manifold is discussed. Then an example is studied, by computing the quasi-Lyapunov constants, the existence of at least 4 limit cycles on the center manifold is proved. In terms of degenerate singularity in high-dimensional systems, our work is new.

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Multiplicity and Uniqueness of Positive Solutions for Nonhomogeneous Semilinear Elliptic Equation with Critical Exponent
Na BA, Yan-yan WANG, Lie ZHENG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 81-94.   DOI: 10.1007/s10255-015-0537-6
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In this paper, we consider the following problem

where λ> 0 is a parameter, p = (N+2)/(N-2). We will prove that there exists a positive constant 0 < λ* < +∞ such that (*) has a minimal positive solution for λ ∈ (0, λ*), no solution for λ> λ*, a unique solution for λ= λ*. Furthermore, (*) possesses at least two positive solutions when λ ∈ (0, λ*) and 3 ≤N ≤5. For N ≥6, under some monotonicity conditions of h we show that there exists a constant 0 < λ** < λ* such that problem (*) possesses a unique solution for λ ∈ (0, λ**).

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On Frankl and Füredi's Conjecture for 3-uniform Hypergraphs
Qing-song TANG, Hao PENG, Cai-ling WANG, Yue-jian PENG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 95-112.   DOI: 10.1007/s10255-015-0513-1
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Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N(r) has the largest Lagrangian of all r-graphs with m edges. Denote this r-graph by Cr,m and the Lagrangian of a hypergraph by λ(G). In this paper, we first show that if m, G is a left-compressed 3-graph with m edges and on vertex set [t], the triple with minimum colex ordering in Gc is (t-2-i)(t-2)t, then λ(G) ≤ (C3,m). As an implication, the conjecture of Frankl and Füredi is true for -6≤m.

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Analysis of a Nutrient-phytoplankton Model in the Presence of Viral Infection
Jian-jun LI, Wen-jie GAO
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 113-128.   DOI: 10.1007/s10255-016-0540-6
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In this paper, a system of reaction-diffusion equations arising in a nutrient-phytoplankton popula-tions is investigated. The equations model a situation in which phytoplankton population is divided into two groups, namely susceptible phytoplankton and infected phytoplankton. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.

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Causality Analysis of Futures Sugar Prices in Zhengzhou Based on Graphical Models for Multivariate Time Series
Jing XU, Xing-wei TONG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 129-136.   DOI: 10.1007/s10255-016-0543-3
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This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series. We construct a partial correlation graph at first which is an undirected graph. For every undirected edge in the partial correlation graph, the measures of linear feedback between two time series can help us decide its direction, then we obtain the mixed graph. Using this method, we construct a mixed graph for futures sugar prices in Zhengzhou (ZF), spot sugar prices in Zhengzhou (ZS) and futures sugar prices in New York (NF). The result shows that there is a bi-directional causality between ZF and ZS, an unidirectional causality from NF to ZF, but no causality between NF and ZS.

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Divergent Solutions to the L2-Supercritical NLS Equations
Qing GUO
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 137-162.   DOI: 10.1007/s10255-016-0544-2
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We investigate the nonlinear Schrödinger equation iut+ u+|u|p-1u = 0 with 1+ 4/N < p < 1+ 4/(N-2) (when N = 1, 2, 1 + 4/N< p < ∞) in energy space H1 and study the divergent property of infinite-variance and nonradial solutions. If M(u)(1-sc)/sc)E(u) < M(Q)(1-sc)/sc)E(Q) and ||u0||(1-sc)/sc)2||∇u0||2 > ||Q||(1-sc)/sc)2||∇Q||2, then either u(t) blows up in finite forward time or u(t exists globally for positive time and there exists a time sequence tn → +∞ such that ||∇u(tn)||2 → +∞. Here Q is the ground state solution of -(1-sc)QQ+|Q|p-1Q = 0. A similar result holds for negative time. This extend the result of the 3D cubic Schrödinger equation obtained by Holmer to the general mass-supercritical and energy-subcritical case.

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A Markov Copula Model with Regime Switching and Its Application
Xue LIANG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 163-174.   DOI: 10.1007/s10255-016-0542-4
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Regime switching, which is described by a Markov chain, is introduced in a Markov copula model. We prove that the marginals (X,Hi), i = 1, 2, 3 of the Markov copula model (X,H) are still Markov processes and have martingale property. In this proposed model, a pricing formula of credit default swap (CDS) with bilateral counterparty risk is derived.

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Stability of Rarefaction Wave for Compressible Navier-Stokes Equations on the Half Line
Li-hua MIN, Xiao-hong QIN
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 175-186.   DOI: 10.1007/s10255-016-0546-0
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This paper is concerned with the large-time behavior of solutions to an initial-boundary-value problem for full compressible Navier-Stokes equations on the half line (0,∞), which is named impermeable wall problem. It is shown that the 3-rarefaction wave is stable under partially large initial perturbation if the adiabatic exponent γ is close to 1. Here partially large initial perturbation means that the perturbation of absolute temperature is small, while the perturbations of specific volume and velocity can be large. The proof is given by the elementary energy method.

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Vertex-Fault-Tolerant Cycles Embedding on Enhanced Hypercube Networks
Min LIU, Hong-mei LIU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 187-198.   DOI: 10.1007/s10255-016-0547-z
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In this paper, we focus on the vertex-fault-tolerant cycles embedding on enhanced hypercube, which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube. Let Fv be the set of faulty vertices in the n-dimensional enhanced hypercube Qn,k (1 ≤ kn-1). When |Fv| = 2, we showed that Qn,k-Fv contains a fault-free cycle of every even length from 4 to 2n-4 where n (n ≤ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2n-4, simultaneously, contains a cycle of every odd length from n-k + 2 to 2n-3 where n (n ≥3) and k have the different parity. Furthermore, when |Fv| = fvn-2, we proof that there exists the longest fault-free cycle, which is of even length 2n-2fv whether n (n ≥3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2n-2fv-1 in Qn,k-Fv where n (n ≥3) and k have the different parity.

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Multiple Solutions for a Quasilinear Second Order Differential Equation Depending on a Parameter
SHAPOUR HEIDARKHANI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 199-208.   DOI: 10.1007/s10255-016-0548-y
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The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval [a, b] ⊂R

under appropriate hypotheses. We exhibit the existence of at least three (weak) solutions and, and the results are illustrated by examples.

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Further Results on Mutually Nearly Orthogonal Latin Squares
Ke-jun CHEN, Yong ZHANG, Guang-zhou CHEN, Wen LI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 209-220.   DOI: 10.1007/s10255-016-0549-x
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Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level. In this paper, some constructions of mutually nearly orthogonal Latin squares are provided. It is proved that there exist 3 MNOLS(2m) if and only if m≥ 3 and there exist 4 MNOLS(2m) if and only if m≥ 4 with some possible exceptions.

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The Proportional Hazards Model for Multiple Type Recurrent Gap Times
Ji-cai LIU, Huan-bin LIU, Ri-quan ZHANG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 221-230.   DOI: 10.1007/s10255-016-0551-3
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Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies, and often more than one type of recurrent events is of interest. In this paper, we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covariates on the censored event processes of interest. An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions. We examine asymptotic properties of the proposed estimators. Finite sample properties of these estimators are demonstrated by simulations.

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Infinitely Many Periodic Solutions for a Class of Second-order Hamiltonian Systems
Ming-hai YANG, Yue-fen CHEN, Yan-fang XUE
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (1): 231-238.   DOI: 10.1007/s10255-016-0552-2
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In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems

where F(t, u) is even in u, and ∇F(t, u) is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition.

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Convergence to the Rarefaction Wave for a Model of Radiating Gas in One-dimension
Fei-min HUANG, Xing LI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 239-256.   DOI: 10.1007/s10255-016-0576-7
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In this paper, a sequence of solutions to the one-dimensional motion of a radiating gas are constructed. Furthermore, when the absorption coefficient α tends to ∞, the above solutions converge to the rarefaction wave, which is an elementary wave pattern of gas dynamics, with a convergence rate α1/3|lnα|2.

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A New Direct Search Method Based on Separable Fractional Interpolation Model
QIN NI, CUI JIANG, HAO LIU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 257-268.   DOI: 10.1007/s10255-016-0574-9
Abstract159)      PDF(pc) (160KB)(213)       Save

In this paper, we propose a new separable fractional interpolation model which can be established by 2n interpolation points where n is the number of variables. Based on this model, a new direct search method is presented. In this method, a new iterate is determined by solving the fractional interpolation model in trust region. Under mild assumptions, the convergence results of this method are given and proved. Numerical experiments show that the new method is promising.

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Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable
Wei LIANG, Jun-shan SHEN, Shu-yuan HE
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 269-282.   DOI: 10.1007/s10255-016-0562-0
Abstract158)      PDF(pc) (179KB)(194)       Save

In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d. observations of the true distribution, empirical likelihood (EL) procedure is proposed for the inference on mean residual life (MRL) of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio (LR) directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.

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A Note on Homoclinic or Heteroclinic Orbits for the Generalized Hénon Map
Yong-guo SHI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 283-288.   DOI: 10.1007/s10255-016-0580-y
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An important problem in a given dynamical system is to determine the existence of a homoclinic orbit. We improve the results of Qin and Xiao [Nonlinearity, 20 (2007), 2305-2317], who present some sufficient conditions for the existence of a homoclinic/heteroclinic orbit for the generalized Hénon map. Moreover, an algorithm is presented to locate these homoclinic orbits.

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Applications of a Few Lie Algebras
Yu-feng ZHANG, Zhong HAN, Zhong-long ZHAO
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 289-304.   DOI: 10.1007/s10255-016-0553-1
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Two isomorphic groups R2 and M are firstly constructed. Then we extend them into the differential manifold R2n and n products of the group M for which four kinds of Lie algebras are obtained. By using these Lie algebras and the Tu scheme, integrable hierarchies of evolution equations along with multi-component potential functions can be generated, whose Hamiltonian structures can be worked out by the variational identity. As application illustrations, two integrable Hamiltonian hierarchies with 4 component potential functions are obtained, respectively, some new reduced equations are followed to present. Specially remark that the integrable hierarchies obtained by taking use of the approach presented in the paper are not integrable couplings. Finally, we generalize an equation obtained in the paper to introduce a general nonlinear integrable equation with variable coefficients whose bilinear form, Bäcklund transformation, Lax pair and infinite conserved laws are worked out, respectively, by taking use of the Bell polynomials.

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Empirical Likelihood Inference for a Partially Linear Errors-in-variables Model with Covariate Data Missing at Random
Shan-shan WANG, Heng-jian CUI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 305-318.   DOI: 10.1007/s10255-016-0586-5
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The authors study the empirical likelihood method for partially linear errors-in-variables model with covariate data missing at random. Empirical likelihood ratios for the regression coefficients and the baseline function are investigated, and the corresponding empirical log-likelihood ratios are proved to be asymptotically standard chi-squared, which can be used to construct confidence regions. The finite sample behavior of the proposed methods is evaluated by a simulation study which indicates that the proposed methods are comparable in terms of coverage probabilities and average length of confidence intervals. Finally, the Earthquake Magnitude dataset is used to illustrate our proposed method.

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Epidemic Spreading with Time Delay on Complex Networks
Rui-xia ZHANG, Zhen JIN, Shu-ping LI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 319-326.   DOI: 10.1007/s10255-016-0553-1
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In this paper, we propose a susceptible-infected-susceptible (SIS) model on complex networks, small-world (WS) networks and scale-free (SF) networks, to study the epidemic spreading behavior with time delay which is added into the infected phase. Considering the uniform delay, the basic reproduction number R0 on WS networks and R0 on SF networks are obtained respectively. On WS networks, if R0≤1, there is a disease-free equilibrium and it is locally asymptotically stable; if R0>1, there is an epidemic equilibrium and it is locally asymptotically stable. On SF networks, if R0≤1, there is a disease-free equilibrium; if R0>1, there is an epidemic equilibrium. Finally, we carry out simulations to verify the conclusions and analyze the effect of the time delay τ, the effective rate λ, average connectivity <k> and the minimum connectivity m on the epidemic spreading.

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Nonexistence and Longtime Behaviors of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form
Yu-dong SUN, Yi-min SHI, MIN WU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 327-332.   DOI: 10.1007/s10255-016-0556-y
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In this paper, we study the nonexistence and longtime behavior of weak solution for the degenerate parabolic equation tun=umdiv(|∇um|p-2um)+γ|∇um|p+βun with zero boundary condition. Blow-up time is derived when the blow-up does occur.

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The Impulsive Solution for a Semi-linear Singularly Perturbed Differential-difference Equation
Ai-feng WANG, Mei XU, Ming-kang NI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 333-342.   DOI: 10.1007/s10255-016-0557-x
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The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.

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A General Comparison Theorem for 1-dimensional Anticipated BSDEs
Xiao-ming XU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 343-348.   DOI: 10.1007/s10255-016-0558-9
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Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for ABSDEs.

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Viability Property of Jump Diffusion Processes on Manifolds
Xue-hong ZHU, Guang-zu LIU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 349-354.   DOI: 10.1007/s10255-016-0559-8
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In this note, we give a necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of Rm. Our result is the system is viable in a closed submanifold K iff the coefficients are tangent to K along K if the equation is in the sense of stratonovich integral and the solution jumps from K to K.

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A Class of Parameter-free Filled Functions for Box-constrained System of Nonlinear Equations
Liu-yang YUAN, Zhong-ping WAN, Qiu-hua TANG, Yue ZHENG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 355-364.   DOI: 10.1007/s10255-016-0560-2
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In this paper, a class of parameter-free filled functions is proposed for solving box-constrained system of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a class of parameter-free filled functions is proposed for solving the problem. Some properties of the new class of filled functions are studied and discussed. Finally, an algorithm which neither computes nor explicitly approximates gradients during minimizing the filled functions is presented. The global convergence of the algorithm is also established. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.

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An Implicit Degree Condition for Relative Length of Long Paths and Cycles in Graphs
Jun-qing CAI, Hao LI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 365-372.   DOI: 10.1007/s10255-016-0561-1
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For a graph G, we denote by p(G) and c(G) the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id(v) denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n+1, then either G contains a hamiltonian path, or c(G)≥p(G)-1.

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Hierarchical Mixture Models for Zero-inflated Correlated Count Data
Xue-dong CHEN, Hong-xing SHI, Xue-ren WANG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 373-384.   DOI: 10.1007/s10255-016-0564-y
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Count data with excess zeros are often encountered in many medical, biomedical and public health applications. In this paper, an extension of zero-inflated Poisson mixed regression models is presented for dealing with multilevel data set, referred as hierarchical mixture zero-inflated Poisson mixed regression models. A stochastic EM algorithm is developed for obtaining the ML estimates of interested parameters and a model comparison is also considered for comparing models with different latent classes through BIC criterion. An application to the analysis of count data from a Shanghai Adolescence Fitness Survey and a simulation study illustrate the usefulness and effectiveness of our methodologies.

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Laws of the Iterated Logarithm for ρ-mixing Random Variables with Normal Distribution
Qun-ying WU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 385-394.   DOI: 10.1007/s10255-016-0565-x
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Consider a ρ-mixing sequence of identically distributed random variables with the underlying distribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng (1996) from the i.i.d. case to ρ-mixing sequences.

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Reliable Control for Nonlinear Systems with Stochastic Actuators Fault and Random Delays Through a T-S Fuzzy Model Approach
Jin-liang LIU, Zhou GU, Shu-min FEI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 395-406.   DOI: 10.1007/s10255-016-0566-9
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This paper considers the reliable control design for T-S fuzzy systems with probabilistic actuators faults and random time-varying delays. The faults of each actuator occurs randomly and its failure rates are governed by a set of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of each actuator and time-varying random delays, new fault model is proposed. Based on the new fuzzy model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of T-S fuzzy systems are derived by using Lyapunov functional method and linear matrix inequality (LMI) technique. It should be noted that the obtained criteria depend on not only the size of the delay, but also the probability distribution of it. Finally, a numerical example is given to show the effectiveness of the proposed method.

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Infinite Horizon Backward Doubly Stochastic Differential Equations with Non-degenerate Terminal Functions and Their Stationary Property
Hui-nan LENG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 407-422.   DOI: 10.1007/s10255-016-0567-8
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In this paper we consider infinite horizon backward doubly stochastic differential equations (BDSDEs for short) coupled with forward stochastic differential equations, whose terminal functions are non-degenerate. For such kind of BDSDEs, we study the existence and uniqueness of their solutions taking values in weighted Lp(dx)⊗L2(dx) space (p≥2), and obtain the stationary property for the solutions.

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Unsteady Flow of Shear-Thinning non-Newtonian Incompressible Fluid Through a Twin-Screw Extruder
Ya-zhou CHEN, Qiao-lin HE, Xiao-ding SHI, Teng WANG, Bing ZHANG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 423-436.   DOI: 10.1007/s10255-016-0568-7
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The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed boundary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it contains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

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A Class of New Special Solution of Nonlinear Diffusion Equation
Yan TANG
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 437-446.   DOI: 10.1007/s10255-016-0569-6
Abstract164)      PDF(pc) (131KB)(298)       Save

One of the most interesting problems of nonlinear differential equations is the construction of partial solutions. A new method is presented in this paper to seek special solutions of nonlinear diffusion equations. This method is based on seeking suitable function to satisfy Bernolli equation. Many new special solutions are obtained.

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Improved Sampling and Reconstruction in Spline Subspaces
Jun XIAN, Song LI
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 447-460.   DOI: 10.1007/s10255-016-0570-0
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As a special shift-invariant spaces, spline subspaces yield many advantages so that there are many practical applications for signal or image processing. In this paper, we pay attention to the sampling and reconstruction problem in spline subspaces. We improve lower bound of sampling set conditions in spline subspaces. Based on the improved explicit lower bound, a improved explicit convergence ratio of reconstruction algorithm is obtained. The improved convergence ratio occupies faster convergence rate than old one. At the end, some numerical examples are shown to validate our results.

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Double Exp-Function Method for Multisoliton Solutions of The Tzitzeica-Dodd-Bullough Equation
Alaattin ESEN, N. Murat YAGMURLU, Orkun TASBOZAN
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 461-468.   DOI: 10.1007/s10255-016-0572-y
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In this work, it is aimed to find one-and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough (TDB) equation. Since the double exp-function method has been widely used to solve several nonlinear evolution equations in mathematical physics, we have also used it with the help of symbolic computation for solving the present equation. The method seems to be easier and more accurate thanks to the recent developments in the field of symbolic computation.

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Four Forbidden Subgraph Pairs for Hamiltonicity of 3-connected Graphs
Hou-yuan LIN, Zhi-quan HU
Acta Mathematicae Applicatae Sinica(English Series)    2016, 32 (2): 469-476.   DOI: 10.1007/s10255-016-0573-x
Abstract212)      PDF(pc) (156KB)(181)       Save

For non-negative integers i, j and k, we denote the generalized net as Ni, j, k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that every 3-connected {K1, 3, N8-i, i, 1}-free graph is hamiltonian, where 1≤i≤4.

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