Showing papers in "Acta Mathematicae Applicatae Sinica in 2015"

Optimal control of a frictional contact problem

Abstract: We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca’s friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.

A central limit theorem for m-dependent random variables under sublinear expectations

Abstract: In this paper, we prove a central limit theorem for m-dependent random variables under sublinear expectations. This theorem can be regarded as a generalization of Peng’s central limit theorem.

The Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims

Abstract: A recursive formula of the Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims is obtained. In the discount-free case, an explicit formula is given. Utilizing such an explicit expression, we derive some useful insurance quantities, including the ruin probability, the density of the deficit at ruin, the joint density of the surplus immediately before ruin and the deficit at ruin, and the density of the claim causing ruin.

Rotating-symmetric solutions for nonlinear systems with symmetry

Abstract: It is proved that if a nonlinear system possesses some group-symmetry, then under certain transversality it admits solutions with the corresponding symmetry. The method is due to Mawhin’s guiding function one.

The applications of vague soft sets and generalized vague soft sets

Abstract: The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definitions, some novel methods of object recognition from an imprecise multiobserver data has been presented. Moreover, we introduce the notion of generalized vague soft sets and study some of its properties. The similarity measure of generalized vague soft sets is also presented and an application of this measure in decision making problems has been shown.

Bound states of (1+1)-dimensional Dirac equation with kink-like vector potential and delta interaction

Abstract: The relativistic problem of spin-1/2 fermions subject to vector hyperbolic (kink-like) potential (∼ tanh kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials in two cases.

Exact Tail Asymptotics for a Discrete-time Preemptive Priority Queue

Abstract: In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous-time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.

Local discontinuous Galerkin method for parabolic interface problems

Abstract: In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves. The proposed method is proved to be L 2 stable and the order of error estimates in the given norm is O(h|logh|1/2). Numerical experiments show the efficiency and accuracy of the method.

Global optimization method for linear multiplicative programming

Abstract: In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming (LMP). The problem (LMP) is firstly converted into an equivalent programming problem (LMP (H)) by introducing p auxiliary variables. Then by exploiting structure of (LMP(H)), a linear relaxation programming (LP (H)) of (LMP (H)) is obtained with a problem (LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems (LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

The Asymptotic Relation Between the Maxima and Sums of Discrete and Continuous Time Strongly Dependent Gaussian Processes

Abstract: In this paper,the asymptotic relation between the maximum and the sum of a continuous strongly dependent stationary Gaussian process,and the maximum and the sum of this process sampled at discrete time points is studied.It is shown that these two extreme values and sums are asymptotically totally dependent no matter what the grid of the discrete time points is.

New abundant exact solutions for Kundu equation

Abstract: In this paper, the higher order NLS equation with cubic-quintic nonlinear terms is studied, new abundant solitary solutions with traveling-wave envelope of this equation are obtained with the aid of a generalized auxiliary equation method and complex envelope non-traveling transform approach.

Periodic Solution for a Modified Leslie-Gower Model with Feedback Control

Abstract: Based on the theory of economic threshold,we consider a modified Leslie-Gower model with impulsive state feedback control in this paperWe obtain sufficient conditions for existence and stability of periodic solution of order one of the given systemIn some cases,it is possible that the system exists periodic solution of order two or order threeOur results show that the control measure is effective and reliable

The Stable Farkas Lemma for composite convex functions in infinite dimensional spaces

Abstract: In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.

Multi-peak nodal solutions for a two-dimensional elliptic problem with large exponent in weighted nonlinearity

Abstract: We consider the boundary value problem \(\Delta u + \left| x \right|^{2\alpha } \left| u \right|^{p - 1} u = 0, - 1 < \alpha e 0\), in the unit ball B with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, we prove that for any positive integer m, there exists a multi-peak nodal solution up whose maxima and minima are located alternately near the origin and the other m points \(\widetilde{q_l } = (\lambda \cos \frac{{2\pi (l - 1)}} {m},\lambda \sin \frac{{2\pi (l - 1)}} {m}),l = 2, \cdots ,m + 1 \), such that as p goes to +∞, $$p\left| x \right|^{2\alpha } \left| {u_p } \right|^{p - 1} u_p \rightharpoonup 8\pi e(1 + \alpha )\delta _0 + \sum\limits_{l = 2}^{m + 1} {8\pi e( - 1)^{l - 1} \delta _{\widetilde{q_l }} } $$ , where λ ∈ (0, 1), m is an odd number with (1+α)(m+2)−1 > 0, or m is an even number. The same techniques lead also to a more general result on general domains.

Random attractors for partly dissipative stochastic lattice dynamical systems with multiplicative white noises

Abstract: The present paper is devoted to the existence of the random attractor for partly dissipative stochastic lattice dynamical systems with multiplicative white noises

A numerical algorithm for determination of a control parameter in two-dimensional parabolic inverse problems

Abstract: Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspecialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations (ODEs). Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature. Also we will investigate the effect of noise in data on the approximate solutions.

Robust M -estimate of GJR model with high frequency data

Abstract: In this paper, we study the GJR scaling model which embeds the intraday return processes into the daily GJR model and propose a class of robust M-estimates for it. The estimation procedures would be more efficient when high-frequency data is taken into the model. However, high-frequency data brings noises and outliers which may lead to big bias of the estimators. Therefore, robust estimates should be taken into consideration. Asymptotic results are derived from the robust M-estimates without the finite fourth moment of the innovations. A simulation study is carried out to assess the performance of the model and its estimates. Robust M-estimate of GJR model is also applied in predicting VaR for real financial time series.

Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation

Abstract: We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed. Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit.

Stochastic Liénard equations with state-dependent switching

Abstract: This work focuses on stochastic Lienard equations with state-dependent switching. First, the existence and uniqueness of a strong solution are obtained by successive construction method. Next, strong Feller property is proved by introducing certain auxiliary processes and using the Radon-Nikodym derivatives and truncation arguments. Based on these results, positive Harris recurrence and exponential ergodicity are obtained under the Foster-Lyapunov drift conditions. Finally, examples using van der Pol equations are presented for illustrations, and the corresponding Foster-Lyapunov functions for the examples are constructed explicitly.

Statistical inference of partially specified spatial autoregressive model

Abstract: This paper studies estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, the unknown parameter is estimated by applying the instrumental variable estimation. Under certain sufficient conditions, the proposed estimator for the finite dimensional parameters is shown to be root-n consistent and asymptotically normally distributed; The proposed estimator for the unknown function is shown to be consistent and asymptotically distributed as well, though at a rate slower than root-n. Consistent estimators for the asymptotic variance-covariance matrices of both estimators are provided. Monte Carlo simulations suggest that the proposed procedure has some practical value.

On estimating regression coefficients in seemingly unrelated regression system

Abstract: In the system of m (m ≥ 2) seemingly unrelated regressions, we show that the Gauss-Markov estimator (GME) of any regression coefficients has unique simplified form, which exactly equals to the one-step covariance-adjusted estimator of the regression coefficients, and hence we conclude that for any finite k ≥ 2 the k-step covariance-adjusted estimator degenerates to the one-step covariance-adjusted estimator and the corresponding two-stage Aitken estimator has exactly one simplified form. Also, the unique simplified expression of the GME is just the estimator presented in the Theorem 1 of Wang’ work [1988]. A new estimate of regression coefficients in seemingly unrelated regression system, Science in China, Series A 10, 1033-1040].

Regularity of solutions to the Navier-Stokes equations with a nonstandard boundary condition

Abstract: In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to Lq-theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore, for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions, which is similar to J.M.Bernard’s results[6] for the time-dependent 2-D Stokes equations.

Optimal generalized case-cohort analysis with Cox’s proportional hazards model

Abstract: Generalized case-cohort design has been proved to be a cost-effective way to enhance the efficiency of large epidemiological cohort. In this article, we propose an inference procedure for estimating the unknown parameters in Cox’s proportional hazards model in generalized case-cohort design and establish an optimal sample size allocation to achieve the maximum power at a given budget. The finite sample performance of the proposed method is evaluated through simulation studies. The proposed method is applied to a real data set from the National Wilm’s Tumor Study Group.

Stability and Hopf bifurcation analysis of a predator-prey model with time delayed incomplete trophic transfer

Abstract: A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.

Dynamic asset allocation with loss aversion in a jump-diffusion model

Abstract: This paper investigates a dynamic asset allocation problem for loss-averse investors in a jump-diffusion model where there are a riskless asset and N risky assets. Specifically, the prices of risky assets are governed by jump-diffusion processes driven by an m-dimensional Brownian motion and a (N − m)-dimensional Poisson process. After converting the dynamic optimal portfolio problem to a static optimization problem in the terminal wealth, the optimal terminal wealth is first solved. Then the optimal wealth process and investment strategy are derived by using the martingale representation approach. The closed-form solutions for them are finally given in a special example.

Existence and uniqueness of positive solutions to three coupled nonlinear Schrödinger equations

Abstract: In this paper, we consider existence and uniqueness of positive solutions to three coupled nonlinear Schrodinger equations which appear in nonlinear optics. We use the behaviors of minimizing sequences for a bound to obtain the existence of positive solutions for three coupled system. To prove the uniqueness of positive solutions, we use the radial symmetry of positive solutions to transform the system into an ordinary differential system, and then integrate the system. In particular, for N = 1, we prove the uniqueness of positive solutions when 0 ≤ β = μ1 = μ2 = μ3 or β > max{μ1, μ2, μ3}.

Empirical entropy for right censored data

Abstract: The maximum entropy method has been widely used in many fields, such as statistical mechanics, economics, etc. Its crucial idea is that when we make inference based on partial information, we must use the distribution with maximum entropy subject to whatever is known. In this paper, we investigate the empirical entropy method for right censored data and use simulation to compare the empirical entropy method with the empirical likelihood method. Simulations indicate that the empirical entropy method gives better coverage probability than that of the empirical likelihood method for contaminated and censored lifetime data.

Streamline-diffusion method of a lowest order nonconforming rectangular finite element for convection-diffusion problem

Abstract: The streamline-diffusion method of the lowest order nonconforming rectangular finite element is proposed for convection-diffusion problem. By making full use of the element’s special property, the same convergence order as the previous literature is obtained. In which, the jump terms on the boundary are added to bilinear form with simple user-chosen parameter δK which has nothing to do with perturbation parameter e appeared in the problem under considered, the subdivision mesh size hK and the inverse estimate coefficient μ in finite element space.

A characterization of PM-compact Hamiltonian bipartite graphs

Abstract: The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. A graph is called perfect matching compact (shortly, PM-compact), if its perfect matching polytope has diameter one. This paper gives a complete characterization of simple PM-compact Hamiltonian bipartite graphs. We first define two families of graphs, called the H2C-bipartite graphs and the H23-bipartite graphs, respectively. Then we show that, for a simple Hamiltonian bipartite graph G with |V(G)| ≥ 6, G is PM-compact if and only if G is K3,3, or G is a spanning Hamiltonian subgraph of either an H2C-bipartite graph or an H23-bipartite graph.

A general additive-multiplicative rates model for recurrent and terminal events

Abstract: Recurrent events data with a terminal event (e.g. death) often arise in clinical and observational studies. Most of existing models assume multiplicative covariate effects and model the conditional recurrent event rate given survival. In this article, we propose a general additive-multiplicative rates model for recurrent event data in the presence of a terminal event, where the terminal event stop the further occurrence of recurrent events. Based on the estimating equation approach and the inverse probability weighting technique, we propose two procedures for estimating the regression parameters and the baseline mean function. The asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The finite-sample behavior of the proposed methods is examined through simulation studies, and an application to a bladder cancer study is also illustrated.