Assume that X is a normed linear space (not necessarily complete) and Σ(X)=X^N₀. In this paper, it is proved that for weighted shift operator B_w: Σ(X)→Σ(X), (x₀, x₁, …)→(w₀x₁, w₁x₂, …) B_w is distributionally ε-chaotic for any 0<ε X)=2 and the principal measure of B_w is 1. Besides, this property is preserved under iterations.

This paper is focused on classical solutions and regularity of weak solutions on 2D magnetohydrodynamic (MHD) flow with constant suction passing through the porous channel. For this purpose, we apply the parabolic regularization process and Modified Darcy's law for fluid in flow modeling.

A fast projection and contraction method for second-order cone programming is proposed. The second-order cone programming is transformed into an equivalent projection equation, which is solved by a fast projection and contraction method. The projection on the second-order cone is simple and costs less computation time. We also give the analysis of the convergence. Numerical results demonstrate that our method is fast and efficient, especially for the large-scale second-order cone programming problems.

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.

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

In this paper, we study the existence of solutions for the following kind of fractional differential equations with Dirichlet boundary conditions, 

When F is asymptotically quadratic at infinity, by using critical point theory we obtain the new existence results of nontrivial solutions for the above boundary value problem.

Previous option pricing research typically assumes that the stock volatility and expectation return rate are constant during the life of the option. In this study, we release this assumption such that stock volatility and expectation return rate are the function of stock in option valuation model. And then we study the pricing problem of barrier options. First, the partial differential equations for barrier options are transformed into a series of parabolic equations with constant coefficients by perturbation theory. Second, the approximate pricing formulae of the barrier options are given by solving those parabolic equations. Finally, error estimates of these asymptotic solutions are illustrated by using the Feymann-Kac formula in which the results indicate that the asymptotic solutions uniformly converges to its exact solutions.

Using Nevanlinna theory of the value distribution of meromorphic functions, the problem of existence of admissible meromorphic solutions of two types of systems of complex difference equations is investigated. Improvements and extensions of some results in references are presented. Examples show that the results are precise.

In this paper, an improved Fletcher-Reeves conjugate gradient method is proposed for unconstrained optimization. The direction generated by the improved method provides a descent direction for the objective function not depending on any line search. Under the standard Wolfe line search, the global convergence of the proposed method is proved. Some elementary numerical experiments are reported, which show that the proposed method is efficient.

By means of differential forms and Lie derivatives, Harrison B K, Estabrook F B have presented a methodology to find symmetries of differential equations. Recently, the method has been extended to analysis semi-discrete differential equations. In this paper, we use a different discrete differential ideal to obtain the Lie symmetry of the differential-difference equations.

In many fields, such as medicine and finance and insurance, researchers are often interested in the distribution of failure time under competing risks, especially tail behavior of the distribution. In this article, a smoothed nonparametric estimator of quantile residual lifetime under competing risks is proposed, which ensures that the numerical solution does exist. The asymptotic properties of the smoothed estimator are established. Also, simulation studies are conducted and show that the smoothed estimate is more efficient by means of deficiency.

The concept of incidence-adjacent vertex distinguishing equitable total coloring of a graph is proposed. Some properties of the incidence-adjacent vertex distinguishing equitable total coloring of graphs are discussed and the incidence-adjacent vertex distinguishing equitable total chromatic numbers of some graphs, such as path, cycle, fan, wheel, complete graph, complete bipartite graph, and so on are investigated. And a conjecture is given by us which the incidence-adjacent vertex distinguishing equitable total chromatic number of a graph is no more than Δ+2.

In this paper we consider the nonlinear algebra system Bu=f(u), where B is a non-negative matrix, f is subquadratic near ∞ and has some singularity at 0, or f is superquadratic near ∞ and 0. By means of the elementary variational approach, we establish some sufficient conditions which insure the existence of positive solutions and negative solution of this system. Such conditions are "sharp" and our conclusions are new. The Theorem 4 of this paper also relax the restrictions on the the matrix B in the literature. Some examples are given to illustrate our main results.

In this paper, complete convergence for weighted sums of ρ-mixing random variable sequences are discussed. By utilizing the Rosenthal maximal type inequality, the results on NA case are extended to the ρ-mixing setting. Complete convergence theorems for weighted sums of ρ-mixing random variable sequences are obtained, which generalize and extend the well-known results on independent random variables.

A class of non-nearest-neighbor random walks on half-line in a random environment are introduced and which contain a special case of nearest-neighbor random walks on half-line in a random environment, an application background is given. Several sufficient conditions that recurrence criterions of states for non-nearest-neighbor random walks are obtained by using suitable inequality and recurrence criterions of Markov chains, assuming the environment is a sequences of random variables, the recurrence criterions of states for random walks in a random environment with success-runs are obtained by using limit theory of random variables.

This paper studies mean-variance reinsurance and investment strategies selection problem for compound Poisson-Geometric risk process. Excess of loss reinsurance and investment in financial market are adopted by the insurance company to reduce risk and increase profit. The financial markets composition by a risk-free asset and a risky asset and the risky asset with poisson jump.The aim is to obtain optimal reinsurance and investment strategies and efficient frontier which minimization the variance of final wealth under constraint that the mean of final wealth is given. By using the method of Zhou X Y and Li D in reference, we change the original mean-variance problem into an auxiliary problem. Through stochastic control theory, we solve the corresponding Hamilton Jacobi Bellman (HJB) equation, then solve the auxiliary problem. Finally closed form of optimal reinsurance and investment strategies and efficient frontier are obtained. Through this research can guide insurance company to select the appropriate investment strategy, to gain some wealth meanwhile minimum the risk.

Let K_n denote the complete graph with n vertices. A (k,λ)-cycle packing (resp. covering) of K_n is a pair (V,C), where V is the vertex set of K_n and C is a collection of k-cycles of K_n, such that each edge of K_n is contained in at most (resp. at least) λ k-cycles of C. A (k,λ)-cycle packing (resp. covering) (V,C) is called almost resolvable if C can be partitioned into almost parallel classes, each of which is a collection of [n/k] floor vertex disjoint k-cycles. A maximum(resp. minimum) almost resolvable (k,λ)-cycle packing (resp. covering) of K_n, is an almost resolvable (k,λ)-cycle packing (resp. covering) of K_n (V,C) in which the number of almost parallel classes, denoted by P_λ(n,k) (resp. C_λ(n,k)), is as large (resp. small) as possible. P₁(n,4) and C₁(n,4) have been decided by Billington et al. recently. In this paper, we shall decide P₂(n,4) and C₂(n,4) for any n≥ 4.

A problem in WDM network is to minimize the cost of the network. This paper focuses on minimizing the total number of Add-Drop Multiplexers (ADMs) required in the network. This problem corresponds to a partition of the edges of the complete graph into subgraphs such that the total number of their nodes has to be minimized and each subgraph has at most C edges (where C is the grooming ratio). Using tools of graph and design theory, some methods to obtain the minimal values of ADMs are provided for a given C. Furthermore, the optimal solutions when C=12 and N≡0, 16 (mod 24) are obtained, where N is the size of the WDM ring network.

In this paper, on the basis of NS-equilibrium for non-cooperative games under uncertainty, the notions of strong Berge equilibrium for generalized non-cooperative games under uncertainty and weakly Pareto-strong Berge equilibrium for generalized non-cooperative multi-objective games under uncertainty are defined, and the existence theorem of generalized non-cooperative games under uncertainty and weakly Pareto-strong Berge generalized non-cooperative multi-objective games under uncertainty are also provided by using Fan-Glicksberg fixed point theorem.

In this paper, by establishing appropriate linear auxiliary equations and using exponential dichotomy, fixed-point theorem, some sufficient conditions are derived for the existence and uniqueness of almost periodic solution of a class of neutral BAM-type Cohen-Grossberg neural networks.

In this paper, a new penalty-function type sequential quadratically constrained quadratic programming (SQCQP) algorithm for nonlinear inequality constrained optimization problems is presented. The algorithm solves at each iteration only a quadratically constrained quadratic programming (QCQP) subproblem, and by employing a new active identification set technique, the scale of the QCQP subproblem is greatly decreased, thus the computational cost is also reduced. Without assuming the convexity of the objection function or the constraints, the algorithm possesses global convergence under weaker conditions, and some preliminary numerical results show that the proposed algorithm is stable and promising.

In this paper we consider the existence of nonoscillatory solutions of variable coefficient higher-order nonlinear neutral differential equations with distributed deviating arguments. We use the Banach contraction principle to obtain new sufficient condition for the existence of nonoscillatory solutions.

In this paper, the characterization of self-adjoint domains for the product of differential expressions which have an interval singular point are investigated, where the differential expressions are n-th order symmetric differential expressions with complex value coefficients as following . For the purpose we constructed a direct sum space, by the theory of direct sum space and under the assumption that the power l² is partially separated in the direct sum space, and (-r,r)⊆Π(T₀(l))∩R, where 0<r≤q1 and Π(T₀(l)) is the regularity domain of the corresponding minimal operator T₀(l) generated by l on the direct sum space. We give the complete and analytic characterization for self-adjoint domains of the l² by means of the solutions of equations l_y=±λ_y with λ∈(-r,r), λ≠0. And the matrix defined the boundary conditions is only determined by the initial values of the regular points of the solutions.

In this paper a predator-prey model with cross diffusion under homogeneous Neumann boundary condition is studied. Firstly,by using Harnack inequality and the regular theory of elliptic equation,the asymptotic behavior of non-constant positive steady-state solution is discussed when at least one of the diffusion coefficients taking limit.Then, we establish an existence result of non-constant steady-state positive solutions by using the asymptotic limit and a singular perturbation method.

By constructing convergent sequences on quasi-metric spaces, we obtiam the existence theorem of unique fixed point for a map with Lipschitz contractive condition and the coincidence point theorems and common fixed point theorems for two maps and unique fixed point theorems for a map satisfying contractive conditions determined by contractive functions.

The paper shows the existence and uniqueness of the solution for backward doubly stochastic differential equation with jumps under non-Lipschitz coefficients, where the nonlinear noise term is given by Itô-Kunita's stochastic integral. Furthermore, we obtain the comparison theorem for this kind of equations.

This article mainly has two parts: the first part finds a model which has a better ability to capture the behavior of the vix than others. The second part discusses the vix option pricing under the better model In the first part, using a nonparametric method, this paper estimates the draft and diffusion items of stochastic volatility models. Then this paper estimates and compares seven continuous time volatility models. In the second part, the optimum model we get in the first part will be turned into a jump-diffusion model and then the partial differential equation and analytical solution of the option pricing are discussed under the optimum jump-diffusion model.

The method of transition probability flow graphs is an important tool for studying the overall characteristics of discrete stochastic processes. It is especially effective for obtaining the probability generating functions of random variables and the transition probability functions of transition routes. In this paper, by applying transition probability flow graphs methods, we discuss the Pascal distribution, derive 2 combinatorial identities; study the means、variances and probability distributions of the I-type and II-type generalized Pascal distributions. And we obtain some new results in the research.

In this paper, we introduce a class of affine equivariant multivariate medians based on depth functions. We show that the influence function of the proposed medians is bounded, and the asymptotic addition breakdown point can achieve 0.5. Consistency and asymptotic normality of the Geman-McClure medians are established. Simulation studies are conducted to examine the performance of the proposed medians, and illustrate that the Geman-McClure medians can achieve high efficiency and robustness simultaneously. Finally, we apply the proposed methodology to analyze a real dataset.

In this paper, we consider a branching random walk in an independent and identically random environment which controls the probability distribution and the positions of offspring. In this model, the positions of each generation particles is given by a point process. The Laplace transform of all these point processes normalized by their own conditional expectations is a martingale. Here it is shown that under certain conditions, the martingale converges uniformly in some appropriate region, almost surely and in mean.

Esscher measure is an important risk measure which is widely used in financial risk management, statistics and actuarial science. However, most of the literature on Esscher risk measure are considered only in individual risk models. In this paper, the estimate models of Esscher measure under the collective risk are built and corresponding non-parametric estimation of Esscher measure are derived. In addition, the strong consistency and asymptotic normality are proved. Finally, the numerical simulation methods are given to verify the large sample properties of the estimator.

In this paper, we discuss a stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response and driven by Lévy noise. By the construction of Lyapunov functions and stopping time technique, we show that there is a unique positive solution to the system with a positive initial value. We show that the moments of the solution to the stochastic system is asymptotic bounded. Furthermore, by the exponential martingale inequality with jumps, the upper growth rate of the solution is obtained. Finally, some sufficient conditions of extinction are established.

In this paper, some properties of Weyl-Titchmarsh m-function of Sturm-Liouville problems and an application of them were discussed. Firstly, we give the derivatives of Weyl-Titchmarsh m-function of Sturm-Liouville problems for the spectral parameter and end-points, and have that m-function is a piecewise monotone increasing function for the spectral parameter on the real axis. Then we defined the generalized characteristic function of Sturm-Liouville Problems by using the Weyl-Titchmarsh m-function, and provide a short proof for the eigenvalues of Sturm-Liouville problems depend continuously on the the end-points and the boundary conditions by using generalized characteristic function.

In this work, some problems in logistics management will be modeled by graph partitioning, and we will solve the corresponging model, which involve matrix rank constraints, by a new method. Finally, some preliminary numerical results are shown.

Non-respondents are often happened in sampling surveys. Resampling from non-respondents subpopulation is an important methods often used. For unknown population mean of the auxiliary variable, triple-sampling procedure for ratio estimation with double-sampling the non-respondents is provided. Hierarchical Hansen-Hurwitz estimator and ratio estimator are separately introduced to analyze survey data from triple-sampling procedure. For ratio estimator of triple-sampling, the variance and its estimator are proved. For Hierarchical Hansen-Hurwitz estimator of triple-sampling, the variance and its estimator is also given. Given total survey cost constraint for triple-sampling procedure, optimal design parameters are calculated. For the same total survey cost for triple-sampling procedure, Hierarchical Hansen-Hurwitz estimator and ratio estimator are simulated for illustration.

The embedding model of joint tree is an efficient method to graph embedding. It is specially convenient to graph embedding on sphere, torus, projective plane and Klein bottle. By selecting an appropriate spanning tree, the joint tree and associated surface is gotten. Then the graph embedding number is gotten by calculating the number of the associated surfaces. This paper calculates the number of embeddings of circular graph C(2n+1,2) (n >2) on projective planes.

In this paper, the underlying is the company's asset, and assumed that it is a Markov skeleton process (abbreviated MSP): this process can be better reflecting the instability of the financial market. Using the properties of Markov skeleton process, the characteristic function of the price process is given, combined with the option properties of convertible bonds, and Fast Fourier Transform (FFT) method, the pricing formula of convertible bonds under the Markov skeleton process convertible bonds is given. The results of this paper can be applied to price other financial derivatives, and it enriching the pricing theory of financial derivatives.

Let G be a simple graph. A general edge-coloring of a graph G is an assignment of a number of colors to the edges. It is not necessary to assign two distinct colors to two adjacent edges. A general edge-coloring f of a graph G is called vertex distinguishing by multisets, if, for any two distinct vertices u, v of a graph G, the multisets of the colors used to color the edges incident with u is different from the multisets of the colors used to color the edges incident with v. The minimum number of colors required for a general edge-coloring of G which is vertex distinguishing by multisets, denoted by c(G), is called the vertex distinguishing general edge chromatic number of G by multisets. Suppose mC₄ denotes the vertex-disjoint union of m cycles of lengths 4. We will determine c(mC₄) in this paper.

A two strain model with nonlinear incidence and diffusion is investigated. The basic reproduction number and invasion reproduction numbers are obtained. If the basic reproduction number R₀ <1, then the disease equilibrium is globally asymptotically stable; if R₁ >1, R₂¹ <1 and β_i(x)=β_i, i=1,2, the strain 1 dominated equilibrium is locally asymptotically stable; while if R₂ >1, R₁² <1 and β_i(x)=β_i, i=1,2,, the strain 2 dominated equilibrium is locally asymptotically stable. When R₁ >1, R₂ >1, R₁² >1, R₂¹ >1, there exists a coexistence equilibrium by using sub-sup solution method.

In this paper, we consider a class of fractional boundary value problems with integral boundary conditions. Using the properties of Green's function and Krasnoselskii fixed point theorem, some sufficient conditions for nonexistence and existence of at least one or two positive solutions are obtained.