A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.  

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.  

In this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.  

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.  

When the role of network topology is taken into consideration, one of the objectives is to understand the possible implications of topological structure on epidemic models. As most real networks can be viewed as complex networks, we propose a new delayed SE^τIR^ωS epidemic disease model with vertical transmission in complex networks. By using a delayed ODE system, in a small-world (SW) network we prove that, under the condition R₀ ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R₀ > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R₀ > 1. In a scale-free (SF) network we obtain the condition R₁ > 1 under which the system will be of non-zero stationary prevalence.  

The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.  

Based on the modified homotopy perturbation method (MHPM), exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact solutions. Under suitable initial conditions, the PDE is transformed into an ODE. Some illustrative examples reveal the efficiency of the proposed method.  

In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem: a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n^-r, 0 ≤ r < (1/2). Simulation results show that both tests perform satisfactorily.  

This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by s_j the speed of each machine, j = 1, 2, 3. Assume 0 < s₁ = s₂ = r ≤ t = s₃, and let s = t/r be the speed ratio. An algorithm with competitive ratio max{2, (3s+6)/(s+6)} is presented. We also show the lower bound is at least max{2, (3s)/(s+6)}. For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun.  

Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis.  

For k = (k₁, … , k_n) ∈ Nⁿ, 1 ≤ k₁ ≤ … ≤ k_n, let L_k^r be the family of labeled r-sets on k given by L_k^r := {{(a₁, l_a1), … , (a_r, l_ar)} : {a₁, … , a_r} ⊆ [n], l_ai ∈ [k_ai], i = 1, … , r}. A family A of labeled r-sets is intersecting if any two sets in A intersect. In this paper we give the sizes and structures of intersecting families of labeled r-sets.  

In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.  

This paper is concerned with the aging and dependence properties in the additive hazard mixing models including some stochastic comparisons. Further, some useful bounds of reliability functions in additive hazard mixing models are obtained.  

This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σ_p(H) = σ_p(A)∪σ_p¹(-A*). Using the characteristic of the set σ_p¹(-A*), we divide the point spectrum σ_p(A) of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σ_p¹(-A*) and one part of σ_p(A) are symmetric with respect to the real axis each other. Based on this result, the symmetry of σ_p(H) is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.  

The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in R^N, is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone’s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.  

The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors Λ_H(ω) in H; Secondly, we prove the existence of random attractors Λ_V (ω) in V. Then we verify regularity of the random attractors by showing that Λ_H(ω) = Λ_V (ω), which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.  

In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.  

Let G_n^k denote a set of graphs with n vertices and k cut edges. In this paper, we obtain an order of the first four graphs in G_n^k in terms of their spectral radii for 6 ≤ k ≤ (n-2)/3 .  

The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n-partite digraphs with n ≥ 3 is still open. Based on the definition of componentwise complementary cycles, we get the following result. Let D be a 2-strong n-partite (n ≥ 6) tournament that is not a tournament. Let C be a 3-cycle of D and D \ V (C) be nonstrong. For the unique acyclic sequence D₁,D₂, … ,D_α of D\V (C), where α ≥ 2, let D_c = {D_i|D_i contains cycles, i = 1, 2, … , α}, D_c = {D₁,D₂, … ,D_α} \ D_c. If D_c ≠ Ø, then D contains a pair of componentwise complementary cycles.  

In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in B_∞,∞⁰. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole space R³ breaks down if and only if certain norm of the vorticity blows up at the same time.

In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.

This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k, l)- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finitedimensional and infinite-dimensional dissipativity results of (k, l)-algebraically stable Runge-Kutta methods are obtained.

Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components: model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.

Image denoising is still a challenge of image processing. Buades et al. proposed a nonlocal means (NL-means) approach. This method had a remarkable denoising results at high expense of computational cost. In this paper, We compared several fast non-local means methods, and proposed a new fast algorithm. Numerical experiments showed that our algorithm considerably reduced the computational cost, and obtained visually pleasant images.

In this paper, we prove that the generator g of a class of backward stochastic differential equations (BSDEs) can be represented by the solutions of the corresponding BSDEs at point (t, y, z), when the terminal data is in L^p spaces, for 1 < p ≤ 2.

Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data. It eliminates the need to solve nonlinear equations, and it is easy to apply. We also consider exponential empirical likelihood as an alternative method. Numerical results are presented to compare our method with others.

This work studies a proportional hazards model for survival data with “long-term survivors”, in which covariates are subject to linear measurement error. It is well known that the naive estimators from both partial and full likelihood methods are inconsistent under this measurement error model. For measurement error models, methods of unbiased estimating function and corrected likelihood have been proposed in the literature. In this paper, we apply the corrected partial and full likelihood approaches to estimate the model and obtain statistical inference from survival data with long-term survivors. The asymptotic properties of the estimators are established. Simulation results illustrate that the proposed approaches provide useful tools for the models considered.

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained, which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs), neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.

In this paper, we focus on studying approximate solutions of damped oscillatory solutions of the compound KdV-Burgers equation and their error estimates. We employ the theory of planar dynamical systems to study traveling wave solutions of the compound KdV-Burgers equation. We obtain some global phase portraits under different parameter conditions as well as the existence of bounded traveling wave solutions. Furthermore, we investigate the relations between the behavior of bounded traveling wave solutions and the dissipation coefficient r of the equation. We obtain two critical values of r, and find that a bounded traveling wave appears as a kink profile solitary wave if |r| is greater than or equal to some critical value, while it appears as a damped oscillatory wave if |r| is less than some critical value. By means of analysis and the undetermined coefficients method, we find that the compound KdV-Burgers equation only has three kinds of bell profile solitary wave solutions without dissipation. Based on the above discussions and according to the evolution relations of orbits in the global phase portraits, we obtain all approximate damped oscillatory solutions by using the undetermined coefficients method. Finally, using the homogenization principle, we establish the integral equations reflecting the relations between exact solutions and approximate solutions of damped oscillatory solutions. Moreover, we also give the error estimates for these approximate solutions.

In this paper, a new conservative finite difference scheme with a parameter θ is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov (KGZ) equations. Convergence of the numerical solutions are proved with order O(h² + τ²) in the energy norm. Numerical results show that the scheme is accurate and efficient.

In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-φ-non-expansive mappings and the set of solutions of an equilibrium problem. We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).

In this paper we study the existence of nontrivial solutions for the periodic discrete nonlinear equation
Lu_n - ωu_n = f_n(u_n),
where
Lu_n = a_n+1u_n+1 + a_n-1u_n-1 + b_nu_n
is the discrete Laplacian in one spatial dimension. The given real-valued sequences a_n, b_n are assumed to be N-periodic in n, i.e., a_n+N = a_n, b_n+N = b_n. The nonlinearity f_n(t) is N-periodic in n and asymptotically linear at infinity. We show that, if ω is in the spectrum gap of L, there is a nontrivial solution. The proof is based on the strongly indefinite functional critical points theorem developed recently.

In this paper, we obtain the Painlevé-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.

By employing the empirical likelihood method, confidence regions for the stationary AR(p)-ARCH(q) models are constructed. A self-weighted LAD estimator is proposed under weak moment conditions. An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained. Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy, especially for relative small size of observation.

In this article, the Bayes linear unbiased estimator (BALUE) of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Bayesian Pitman closeness (PC) criterion.

An L(2, 1)-labelling of a graph G is a function from the vertex set V (G) to the set of all nonnegative integers such that |f(u) - f(v)| ≥ 2 if d_G(u, v) = 1 and |f(u) - f(v)| ≥ 1 if d_G(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by λ(G), such that there exists an L(2, 1)-labelling function with no label greater than it. In this paper, we study this problem for trees. Our results improve the result of Wang [The L(2, 1)-labelling of trees, Discrete Appl. Math. 154 (2006) 598-603].

In this paper, we prove some results concerning blow-up of viscous compressible reactive (selfgravitating) flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.

Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other (1+1)-dimensional and higher dimensional systems.

In this paper, we propose a dimensional splitting method for the three dimensional (3D) rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces Im and is decomposed by a series of surfaces Im_i into several sub-domains, which are called the layers of the flow. Every interface Im_i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate (S-coordinate) system based on Im_i, Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on Im_i, another one is called the bending operator taking value in the normal space on Im_i. Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface Im_i is obtained, which is called the two-dimensional three-component (2D-3C) Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stokes equations are presented.