This paper aims to design and analyze a linearized compact finite difference scheme for solving a dissipative nonlinear Schrödinger equation. By introducing a transform of variable to eliminate the dissipative term, a new system which preserves the total mass and energy is obtained. Then an efficient compact finite difference scheme is proposed for the new system. Corresponding to the fact that the original problem preserves the total mass and energy, the novel scheme is proved to also preserve the two invariant quantities in the discrete sense. The unique solvability of the numerical scheme is proved by using a fixed point theorem together with the standard energy method. Unlike the classical analysis method based on the a priori estimate of the numerical solution, we here introduce an induction argument together with an H¹ technique in building the optimal error bound. The convergence rate is proved to be of fourth-order in space and second-order in time, respectively. Numerical results are reported to support the theoretical analysis and show that the novel scheme is superior to the existing scheme.

Impulsive control has been used extensively in the control of the dynamic systems with random disturbance for their rapid responses, strong robustness and anti-disturbances. This paper investigates global exponential stability problems of a class cellular neural networks with time-varying delays and random disturbance. By means of the Lyapunov stability theory and discrete-time Halanay inequality technique, sufficient conditions for their global exponential stability of cellular neural networks with time-varying delays are derived under impulsive control, including the cases that the parameter is random disturbance and non-disturbance, respectively. Finally, numerical examples are presented to illustrate the obtained results.

A graph is said to be primitive if its automorphism group is primitive on the vertex set. In this paper, we not only classify completely vertex primitive 2-arc transitive graphs admitting a two-dimensional linear group, but also we determine the automorphism groups and the number of non-isomorphic ones of such graphs.

The dynamics of a disease model with general relapse phenomenon and nonlinear incidence rate are investigated, where the model takes the forms of integro-differential equations with infinite-distributed delay. The model can describe a general relapse phenomenon in infectious diseases including herpes. By applying the uniform persistence theory and using the method of Lyapunov functionals, it is shown that that the global dynamics are completely determined by the basic reproduction number R₀: the disease dies out if R₀≤ 1 and that the disease becomes endemic permanently and globally attractively if R₀> 1.

In this paper, we study the estimation of partial functional linear regression models with stationary α-mixing random error sequence. With approximating to the slope function by the Karhunen-Loève expansion, we propose an estimation method for the unknown parameters and the slope function. The asymptotic normality of the proposed parameter estimators and the convergence rate of the slope function estimator are established. Intensive simulation experiments and real data analysis are conducted to show that the proposed method performs well with a finite sample.

Let G be an edge-colored graph. A rainbow subgraph is a subgraph whose edges have distinct colors. A set of disjoint rainbow stars S is a rainbow dominating star set of G if S covers V(G). The {rainbow domination number of G, denoted by γ(G), is the minimum cardinality of a rainbow dominating star set. A polynomial-time algorithm is proposed in this paper for finding a minimum rainbow dominating star set and hence the value γ(T) for an edge-colored tree T.

This paper is concerned with stability of traveling front solutions for an extended forest dynamical system with cross diffusion. Under some assumptions, by applying the detailed spectral analysis and the continuous semi-group theory, linear and nonlinear exponential stability can be proved by spectral stability of solutions.

In this paper we establish a generalized retarded nonlinear integral inequalities with maxima in two variables and more than one distinct nonlinear term. Requiring neither monotonicity nor separability of given functions, we apply monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply our result to prove boundedness of the solutions of certain partial differential equations with the maxima.

Given a graph G=(V, E) and S\subseteq V. If G-S is acyclic, then S is called a decycling set of G. The minimum decycling set of G is called the decycling number, and denoted by ▽(G). A type of plane triangulation G_nK4 containing n copies of K₄ has been considered in this paper. We prove that ▽(G_nK4)=|V(G_nK4)|/2 for n=1, 2, 3, 4, which confirm the induced forest conjecture of Albertson and Berman that the decycling number of any planar graph is at most half of its vertices. The case for n≥5 is unsolved.

This paper considers an M/M/1 retrial queue with a constant retrial rate and Bernoulli vacation, in which arriving customers are only informed about the server's state. If the server is busy upon the arrival instant, a customer either joins the retrial orbit with probability q or balks with complementary probability 1-q. After each service completion, the server either begins a single vacation with probability p or remains idle with probability 1-p. In this paper, the individual optimal joining strategy, the joining strategy for the social net welfare and the joining strategy for the optimal profit are derived under a natural reward-cost structure. We give a rigorous proof regarding the ordering of the optimal joining probabilities. Finally, some numerical examples are given to illustrate the effect of on the joining strategies.

This paper is concerned with the initial boundary value problem for one-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data. We prove that there exists a unique global weak solution for piecewise regular initial density with arbitrarily large jump discontinuity. Moreover, we show that the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as time tends to infinity.

The generalized Kuramoto-Sivashinsky equation which describes the fluctuations of the position of a flame front, the motion of a fluid going down a vertical wall, or a spatially uniform oscillating chemical reaction in a homogeneous medium, is discussed by the extended(G'/G)-expansion method. By using the extended(G'/G)-expansion method, new hyperbolic function traveling wave solutions of this equation are presented. The restrictions on the parameters are also identified. It is shown that the extended(G'/G)-expansion method is a competent and influential tool in solving nonlinear partial differential equations in mathematical physics.

Let G=G(n, p) be a binomial random graph with n vertices and edge probability p=p(n), and let k be a positive integer such that k<np-2√nplogn. A spanning subgraph F of G is called a [k, k+1]-factor if k ≤d_F(x) ≤ k+1 for every x∈V(G). In this paper, we proved that for any binomial random graph G(n, p) with p≥n^-(2)/(3) almost surely contains a [k, k+1]-factor.

In this paper, we study the topological properties of approximate Henig efficient solution set for set-valued optimization problem. The relations between approximate Henig efficient solution set and Henig efficient solution set are discussed. Moreover, the closedness of approximate Henig efficient solution set is proved and the connectedness of approximate Henig efficient solution set is obtained under the condition that the objective function be a cone-arcwise connected set-valued mapping. As an application of the result, the connectedness of super efficient solution set is given.

The purpose of this article is to propose and investigate an algorithm for solving the {multiple-set split feasibility problem in infinite-dimensional Hilbert spaces}. The results presented in the paper improve and extend some recent results of Moudafi [Inverse Problem, 26 (2010), 055007], Xu [Inverse Problems, 26 (2010), 105018; 22 (2006), 2021-2034], Censor and Segal [J. Convex Anal., 16 (2009), 587-600], Censor et al. [Inverse Problems 21 (2005), 2071-2084], Masad and Reich [J. Nonlinear Convex Anal. 8 (2007), 367-371], Censor et al [J. Math. Anal. Appl., 327 (2007), 124-1256], Yang [Inverse Problem, 20 (2004), 1261-1266] and others.

In this paper we study a problem on joint decisions of scheduling and outsourcing, in which each job can be processed by a single machine at a manufacturer or outsourced to a subcontractor. The manufacturer needs to determine which jobs should be produced in-house and which jobs should be outsourced. Furthermore, it needs to determine a production schedule for all jobs. The objective is to minimize the weighted sum of scheduling measures, production and outsourcing cost. According to the number of subcontractor's machines, we consider two models. For each model, we show the NP-hardness and propose dynamic programming algorithms.

In this paper, we establish the bounded rationality model M for the equilibrium problems in the setting of compact and noncompact sets. We proof that equilibrium problems in the sense of Baire category are structurally stable and robust to ε-equilibrium. Then, by using the model M, we study the unification of well-posedness for equilibrium problems. Sufficient conditions for the well-posedness for equilibrium problems are given. Finally, we obtain the well-posed characterizations for equilibrium problems.

This paper deals with a class of strongly damped wave equations u_tt+η(-Δ)^θu_t+(-Δ)u=f(u) with critical nonlinearities. The main task is to prove the existence of the global attractor of C₀-semigroup T(t) derived by the wave equation for critical growth indicator ρ=(N+2)/(N-2) under Lipshitz and dissipative conditions. In case 1/2< θ≤ 1, by studying the energy functional attached to T(t), we prove that, every bounded subset of the energy space is absorbed uniformly by a bounded set B₀ independent of the index θ, which combined with the compactness of T(t), leads to the existence of the global attractor. And in case θ=1, the method of modification and approximation are adopted. We show that all the modified semigroups T_ν(t)(ν∈(0,1]) exhibit the same asymptotic behavior as t→∞, and they converge to T(t) in strong topology uniformly on bounded intervals as ν→0. Based on these properties, we prove the existence of the global attractor, which can be represented by the upper limit of attractors of modified semigroups.

A new kind of modified second-order tangent cone is introduced, with which a new kind of modified second-order tangent derivatives for a set-valued function is introduced, those properties are investigated. By using modified second-order tangent derivative, a new kind of second-order weakly efficient subgradients is introduced, whose existence theorem is established, in terms of which the characterizations of the weak minimizer of set-valued optimization problem are presented.

In this paper, we investigate a class of real quartic polynomial differential systems with four finite critical points, where, in particular, three of which are symmetric. We search for effective conditions for the critical points in order to be isochronous centers (or linearizable centers). We stress that few results are available concerning with several finite isochronous centers in a polynomial differential system of degree n, and our work is new and interesting.

In this paper, we study the existence of solutions of the following nonlinear fractional integro-differential equations boundary value problem

where D₀₊^α+I₀₊^α are the standard Riemann-Liouville fractional derivative and fractional integral respectively. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.

In this paper we consider the Markov-modulated risk model in which the rate for the Poisson claim arrivals, the distribution for the claim amounts and the rate of tax vary in time depending on the state of an external Markov chain. The model also assumes that the insurer earns interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment the surplus first drops below a critical negative constant level. Analytical expressions of the non-absolute-ruin probability, the expected discounted tax payments as well as the probability of recovery are obtained. When the claims are exponentially distributed and there is only one state in the state space of the underlying Markov chain, explicit expression of the probability of recovery is also derived. Finally, for exponential claims, numerical comparison of the resulting non-absolute-ruin probabilities and discounted expected tax payments with Markov modulation, interest and debit interest to the case without are given.

We study the strong Feller property and the exponential ergodicity for stochastic differential equations with additive pure jump Lévy process, by assuming that the driving Lévy process has subordinated Brownian motion as a component.

This paper mainly investigates the closure properties about the subexponential class for the minimum and maximum of two subexponential random variables according to a wide type of dependence structure. It is proven that the minimum of two subexponential random variables under such a dependence structure is still subexponential. It also gives a sufficient and necessary condition which ensures that the maximum of two subexponential random variables under this dependence structure is subexponential. The obtained results generalize some existing ones in the literature, which imply that the dependence structure is insensitive to the subexponentiality for two subexponential random variables under the operations of minimum and maximum.

This paper studies a non-autonomous non-Newtonian fluid with delayed external force on two-dimensional unbounded channel-like domains. The authors first prove the global well-posedness of the problem associated to the motion equations of the fluid. Then they establish the existence of the pullback attractors for the generated process, for the universe of fixed bounded sets and for another universe given by a tempered condition.

In this letter, a general form of enlarged AKNS spectral problem is discussed, the corresponding hierarchies of AKNS integrable couplings are derived, including positive non-isospectral hierarchy and negative non-isospectral hierarchy. The Hamiltonian structure is presented also.

In cooperative game theory,normalizing a value means making it to be efficient.Hamiache obtains a normalization of the Myerson value for transferable utility cooperative games with a graph structure via the matrix approach.By giving a new collection of sets satisfying unique minimal partition property,this paper proposes another normalization of the Myerson value also with the matrix approach.Particularly,if the restriction of the graph on every component is complete,then a normalization of the Aumann-Drèze value for transferable utility cooperative games with a coalition structure is proposed.Comparative analysis with other normalization of the Myerson value shows that the one proposed in the paper is equivalent to the one of van den Brink et al.Thus both the normalization of van den Brink et al and of Hamiache can be represented by the matrix approach,and the difference between them is pinpointed to the collection of sets satisfying unique minimal partition property.

The generalized Logistic distribution is an important distribution,and widely used in biology,medicine,financial management,meteorology,hydrology,geology and other fields.So far,many statistical scholars have proposed many theories and methods of statistical inference,and a wide range of applications for the Logistic distribution.Unfortunately,the Logistic distribution,especially the type I generalized Logistic distribution with locationscale-shape parameter,needs further research,the application of this distribution needs more exploration and exploitation.We discussed the parameter estimations for 3-parameter type I generalized Logistic distribution using methods of moments and L moments,provided two parameter estimate equations,proved the existence,uniqueness and asymptotically normal consistency of the solution of the estimate equations under some conditions in this paper.We compared the estimated results about the two parameter estimations,in cases of different parameters,different sample size by simulation.

Determining the crossing number of an arbitrary graph is NP-complete problem.The crossing numbers of join product of path with 5-vertex graphs mostly are known,but there is still a few join product of path with 5-vertex graphs which have complex structure are not determined.In this paper,we will extent those result.According to the structure of graph,we proved the crossing numbers of the join product of K_1,1,1,2+P_n is Z(5,n)+2n+2.Our proof depends on Kleitman's results for the complete bipartite graph cr(K5,n)=Z(5,n),as well as Ho's results for the complete multipartite graph cr(K_1,1,1,2,n)=Z(5,n)+2n.

Based on the risk compensation of higher-order risk changes,we propose a comparative characterization for higher-order Ross more risk aversion.Our result indicates that any increases in the nth degree risk incur the changes from F to G,u is nth degree Ross more risk averse than v if and only if the risk compensation is not less for u than for v.More generally,when any risk increases in the nth degree first l(l ≥ 2) moments preserving stochastic dominance incur the changes from F to G,u is kth degree Ross more risk averse than v for k=l+1,…,n,if and only if the risk compensation is not less for u than for v.

In this paper,the notions of augmented dual cones are extended from normed linear spaces to locally convex spaces.The extended augmented dual cones are defined respectively in two cases.Then we discuss their main properties,and also establish existence conditions of nontriviality of the extended augmented dual cones under suitable hypothesis.

This paper deals with an unstirred chemostat with external toxin.The introduction of the external toxin makes the conservation law invalid,which leads to the usual reduction of the system to a competitive system of one order lower is lost.Thus the system with predation and competition is non-monotone.First,the uniqueness and asymptotic behaviors of the semi-trivial solutions are established by the degree theory and linearized stability analysis.Second,the existence and structure of positive solutions are given by the degree theory and bifurcation theory.Finally,we present some numerical simulations to verify and complement our theoretical analysis.It turns out that two species can coexist in the presence of an external toxin in the form of equilibria or limit cycles.

This paper deals with homogeneous Dirichlet boundary value problem to a class of porous medium equations with variable reaction
u_t=△u^m+u^p(x).
.A blow-up result is established for certain solution with positive initial energy.A Lower bound for blow-up time is given.

A class of nonlinear disturbed generalized NNV differential system was considered.Firstly,leading a travelling wave transformation,we take the NNV system change a set of nonlinear system of ordinary differential equations.Next,a solitary solution of correspond typical system is obtained using the method of the undetermined coefficients hyperbolic function.Then a generalized functional mapping iteration was constructed.And the solitary asymptotic travelling wave solution of the NNV differential system were solved successively.Finally,from the example for this method,obtained approximate solution possess simple and valid strong point.

A new projection-type stabilized formulation for the parabolic problem is proposed.The method is based on the same equal-order mixed finite element space for both regions.Compared with usual local projection stabilization methods,we add a new projectiontype stabilization term and a pressure jump term,which can effectively bypass the inf-sup condition.It also ensures that our technique can be applied to not only continuous pressure space but also discontinuous pressure space.The stability of the proposed scheme is proved.Error estimates are obtained.At last,some numerical experiments are given to verify our theoretical results and the efficiency.

Utilizing the Rademacher-Menshov's inequality of the partial sums of END random variables,the complete moment convergence of the maximal partial sums of weighted sums of sequences of END random variables is obtained,the corresponding results in series of previous papers are enriched and extended.

The conjugate gradient method is a very effective iterative method for solving large-scale optimal problems.In this paper,consider the poor convergent properties and the nice numerical performance of the Polak-Ribière-Polyak (PRP) method,and the good convergent properties of the Fletcher-Reeves (FR) method,we further study the PRP method.In order to obtain the same convergent properties as the FR method and preserves the good properties of the PRP method,we introduced an adjusting factor to the PRP formula and follows propose an self-adjusting conjugate gradient method for general unconstrained optimizations.The proposed method is proved to share the common property of the PRP method which so-called property (*),and we show that the proposed method not only satisfies sufficient descent condition but also converges globally under the usual assumptions and the strong wolfe line search.Finally,some elementary numerical experiments and their performance profiles are reported,which show that our proposed method is promising.

We use Fan-Browder type fixed point theorem on generalized convex spaces to obtain some new fixed point theorems for weak φ-maps on ω-connected spaces without any convex and linear structure and compact framework.As applications,using the obtained Fan-Browder type fixed point theorem on ω-connected spaces,we discuss the existence problems of coincidence points for two weak φ-mappings and collectively fixed points for a family of weak φ-mappings.The obtained results generalize and improve the corresponding conclusions in references.

By utilizing a fixed theorem in cones,we study the existence of the unique positive almost periodic solution for a generalized Lasota-Wazewska model with a nolinear harvesting terms.Some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived and it cannot be obtained by the contraction mapping principle.Furthermore,under proper conditions,we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution.An example is provided to illustrate the effectiveness of the proposed result.

In this paper, the uniqueness of solutions for monotone variational inequalities is studied. By employing the method of set-valued analysis, we prove that, in the sense of Baire category, most of the monotone variational inequalities have unique solution and that each monotone variational inequality which possesses more than one solution can be approximated arbitrarily closely by a sequence of monotone variational inequalities each of which has a unique solution. Our discussion is under two different settings. One setting considers the perturbation of objective functions, the other one considers not only the perturbation of objective functions but also the perturbation of feasible sets.