It's quite an concerned question about how to extract the true features among ultrahigh-dimensional data, especially in today's era of big data, this question plays a key role in many related industries. The core idea of feature screening is excluding those features that significantly unrelated to response variably to solve this question. The Sure Explained Variability and Independence Screening method has obvious advantages in handling the asymmetry and nonlinearity situations compare to the methods before. But it's kernel estimation still has space for improvement. From this point, we change the kernel estimation to local estimation which been known as more accurate and effective. Some simulations about the feature screening in special situations also proof our view and show that our new algorithm is more efficient than the kernel-based one.

This paper deals with a class of nonsmooth semi-infinite multiobjective optimization problem and discusses its saddle point criteria. Firstly, Lagrange function and saddle point are defined in two ways, i.e. scalar case and vector case. Secondly, necessary conditions for saddle point criteria are established in scalar case and vector case respectively. And lastly, sufficient conditions for saddle point criteria are obtained in both cases under the assumptions of nonsmooth (Φ, ρ)-invexity.

In this paper, two kinds of fractional stage-structured predator-prey systems with delay are provided and the stability of the systems is investigated. Simple and reasonable sufficient conditions are derived for the asymptotic stability of the equilibria. Moreover, two numerical simulations are presented to demonstrate the validity and feasibility of the proposed theoretical results.

In this paper, we mainly study an optimization problem constrained by cartesian product of unit balls. Many efforts have been devoted to obtain efficient gradient descent schemes for this problem such as Chambolle algorithm or iterative shrinkage thresholding algorithm. The detail analysis of the optimal conditions of this problem are presented. Meanwhile, we extend some classic projected gradient algorithms to a general shrinking form. The new algorithm depends on two parameters, which are step length and shrinking factor. We give two types of shrinking algorithms based on different choices of step length and shrinking factor. What is more, the global convergence of the proposed algorithm is given in this paper. We conduct numerical experiments for solving rand test problems and total variation denoised model. Numerical results demonstrate that the proposed algorithm is competitive to some classic algorithms, especially when high accuracy is required.

GARCH model is widely used in modeling of financial time series datas, the estimation precision of the parameters and diagnostic test of the model has been two major problems people focused on. This paper aims at the smooth GARCH model, we hope to construct an integrated estimation and test system for stationary GARCH series under heavy-tailed distribution situations. By extending Fan (2014)'s NGQMLE, we build a new two-step NGQMELE through changing the estimator within the first step from QMLE to QMELE. This will lower the moment requirements for time series data. Then we established it's consistency and asymptotic normality under the condition of limited secondary moment of the residuals. Numerical results show that our new two-step NGQMELE could greatly improve the estimation precision of scale parameter σ, while in NGQMLE it's not consistent. In addition, for the new two-step NGQMELE we proposed two goodness-of-fit test statistics Q(M), Q²(M) based on the autocorrelation function of the residuals' absolute value and square value, and proved their asymptotic properties in limited secondary moment and fourth-order moment cases respectively. The results of numerical simulation and real-data analysis both show that Q²(M) will lose power in thick tail situations, and Q(M) is always a better test through thick and thin. Thus, we have finished the estimation and test construction for stationary GARCH models under heavy-tailed distribution situations. Using NGQMELE and Q(M) we can derive an appropriate GARCH model to fit any stationary time series data.

The main purpose of this paper is to establish the existence of multiple solutions for a quasilinear elliptic system involving sign-changing weight functions. It is shown, by variational methods, that under certain conditions, the system has at least two nontrivial nonnegative solutions.

Based on game theory and Principal-agent theory, this article studies dynamic moral hazard models between corporate system and limited partnership, and analyzes principal and agent's optimal choice between mechanisms. The results indicate that moral hazard occurs in both mechanisms while there are improvements in limited partnership. Comparing the two mechanisms under certain conditions, the corporate system can be the best choice to principal and agent. However, limited partnership can't be principal and agent's common choice when they are of equal status.

This paper is concerned with a non-autonomous delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term and continuously distributed delays, which is defined on the nonnegative function space. Some criteria are established for the existence, uniqueness, and global exponential stability of positive periodic solutions for this model. Moreover, an example and its numerical simulation are employed to illustrate the main results.

In this article, we propose a general class of semiparametric rates models for recurrent event data, which includes the proportional rates model and a semiparametric additive rates model as special cases. For the inference on the model parameters, estimating equation approaches are developed. The consistency and asymptotic normality properties of the proposed estimators are established.

The spectral analysis of a kind of Sturm-Liouville problems with boundary conditions polynomially dependent on the eigenparameter is investigated. By construction we prove that this kind of problem has finite spectrum and all the spectrum are consist of eigenvalues.

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed to make G rainbow connected. Following the ideas of Caro and Chakrabortyet al., in this paper we also investigate the rainbow connection number of dense graphs, and get some generalized results. We show that for k ≥ 2, if G is a non-complete graph of order n with minimum degree δ(G) ≥ (n)/2 -1 + log_k n, or minimum degree-sum σ²(G) ≥ n -2 + 2 log_k n, then rc(G) ≤ k. We also consider the condition of minimum degree with rc(G) ≤ k in the graph of diameter 2 and bipartite graph.

Uniform experiment design is one of main methods for fractional factorial designs, which has been widely applied in manufacturing, system engineering, pharmaceutics and natural sciences. Many kinds of discrepancies have been used in measure uniformity of fractional factorial designs. No matter using which discrepancy, the key issue is to provide a accurate discrepancy lower bound, because it may be as a criterion to measure uniformity of designs. In this paper, a lower bound of symmetric L₂-discrepancy on three-level U-type designs is provided by applying for conditional extremum. It may be as a benchmark to look for uniform designs.

In this article, we define a new labelling, called (k,d)-edge magic graceful labelling. A connection between (k,d)-edge magic graceful labelling and (k,d)-graceful labelling has been built up. We provide some methods for constructing large scale of trees having our labellings, and our methods can be easily transformed into algorithms.

In this paper, the problem of how to control the high-order multi-agent systems is considered by iterative learning method. During the process of tracking, the consistency tracking is realized after rectifying the initial state errors. In the process of rectifying, the systems only rectify a type of the state errors within a certain interval. When this type of state errors rectifying operation is completed, the systems begin to rectify another type of state errors, and so on. All the initial state errors can be completely rectified, and all the rectifying operations are completed within a specified time. Finally, the simulation results verify the effectiveness of the proposed algorithm.

In this paper, we study the singular elliptic equation
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Here Ω⊂ R^N is a smooth bounded domain, 0∈ Ω, N ≥ 3, p=p(a,b)≜(2N/(N-2(1+a-b))), 1 < q < p-1 and h(x)∈ L²(Ω). Applying the perturbation method,we show that there exists q_N > 1 such that for any q∈ (1,q_N), the above equation possesses infinitely many distinct solutions.

Discrete inequalities involving two independent variables with more than one nonlinear term are discussed. The upper bound of the unknown function is given with the aid of the mathematical induction. The results obtained generalize some existed results. An application example to show the explicit bound of solutions of a difference equation is also given.

In this paper, we consider the exact travelling wave solutions of the Gardner-Kadomtsev-Petviashvili equation, which has widespread applications in physics. With the bifurcation theory of dynamical systems, we first get all bifurcations and phrase portraits of the equation and then by discussing the range of the parameter exact parametric representations of all wave solutions are given, including solitary wave solution, periodic wave solution, kink (anti-kink) wave solution and breaking wave solution.

In this paper, a Bernstein inequality, a Kolmogorov inequality and a Rademacher inequality are established under sublinear expectations introduced by Peng. Then, as applications of those inequalities, the quasi sure convergence of random variables under sublinear expectations is investigated and several strong limit theorems are obtained.

In this paper, we study the minimal inequalities for (non-negative) conditional demimartingales, and extend the minimal inequality (like _εP^F(???20180208???c_iS_i ≤ ε)) for non-negative conditional demimartingale in corresponding reference to the case of _εP^F(???20180208???c_ig (S_i) ≤ ε). In addition, we give some other forms of minimal inequalities for conditional demimartingales, such as _εP^F(???20180208??? g (S_i) ≤ ε) and _εP^F(???20180208???g (S_i) ≤ -ε).

In this paper, we consider the blow-up phenomena and global existence of the solution to a more general nonlinear parabolic problem under Robin boundary condition. By giving some suitable restrictive conditions on the known functions and applying a differential inequality technique, a lower bound for blow-up time of solution is derived when the blow-up occurs. This type of lower bound is widely used in physics, biology, astronomy and other many fields. The global existence of the solution is also proved.

In this paper, the stabilization of a one-dimensional wave equation with non-collocated observation at its unstable free end and controller at another end is considered. A novel output feedback control law with a constant time-delay only based on boundary displacement observation is proposed. The well-posedness of the close-loop system is proved by using operator semigroup theory and Riesz basis theory. The condition which guarantees the exponential stability of the closed-loop system can be determined. The result's relevance is illustrated with a numerical simulation.

By constructing an appropriate payoff function, quasi-variational inequality, generalized variational inequality, Von Neumann Lemma and the extension of Gale-Nikaido-Debreu Lemma, can be derived from Nash equilibrium theorem, with the aid of the inverse of the Berge maximum theorem. Moreover, an important method is provided that an upper semicontinuous and convex compact set-valued mapping problem is converted into a binary function. Our results and proofs are all new.

In this paper, we study the existence and uniqueness of solutions to the following kind of variational inequalities


where L is a degenerate parabolic operators with variable exponent. The existence and uniqueness results for the above variational inequalities are obtained by some new penalty function and differential inequality technique.

In this paper, the model of birth and death process is applied to the invasion model of multi-patches poisonous weeds to study the invasive relationship between poisonous weeds and the surrounding limited number of patches of edible pasture. With the theory of birth death process, the differential equation is constructed by using the total expectation formula,and the expectation of poisonous weeds is calculated. By calculating the limit expectation analysis,we got the conditions for successful invasion of poisonous weeds into surrounding patches. Using the cellular automata theory, the competition model is extended to the space lattice to simulate and study the spatial distribution patterns of poisonous weeds, which will provide data supporting their control. The results showed that:(1) If the intrinsic growth rate of poisonous weeds is greater than the mortality rate, and the difference between the intrinsic growth rate and mortality rate is greater than the invasion rate of poisonous weeds,the probability of successful invasion of poisonous weeds into edible pasture increases, which increases the risk of the extinction of edible pasture and is harmful to the continued existence of edible pastu; (2) If the intrinsic growth rate of poisonous weeds is less than the mortality rate or the difference between the intrinsic growth rate and mortality rate is less than the invasion rate of poisonous weeds, the poisonous weeds do not have enough biomass to invade the edible pasture, and the probability of successful invasion of poisonous weeds to edible pasture becomes smaller; (3) The invasion of poisonous weeds affected the spatial distribution of poisonous weed populations, and accelerated the aggregation degree of spatial distribution.

In communications, the sender sends a message to a group of the receivers. However, the sender or part of the receiving party may sometimes jointly cheat a member of the group. Multi-receive authentication codes can effectively prevent this kind of deception attack. The purpose of this paper is to study the construction of multi-receive authentication codes. Based on the symplectic geometry over finite field, a class of multi-receive authentication codes with arbitration is constructed and proved to be reasonable. Then, the structure and counting principle of the subspaces of symplectic spaces are fully applied, and the relevant parameters and the maximum probability of success of various attacks are calculated. In the end, a simulation is made about the impersonation attacks from the sender in the multi-receiver authentication codes.

Zero-crossing rate (ZCR) is an important research content in time series analysis, and it is widely used in speech recognition, signal detection and other scientific research field. So far, many statistical scholars have proposed a series of research achievements, such as the relationship between asymptotic zero-crossing rate of 2th-oraer autoregressive process and 1th-oraer asymptotic correlative function, and the relationship between the mean square asymptotic zero-crossing rate and the characteristic roots of Pth-oraer autoregressive processes, etc. In this paper the concept of asymptotic band-crossing rate (BCR) of Pth-oraer autoregressive processes is introduced and the relationship between the asymptotic BCR of 2 consecutive points and the 1th-oraer asymptotic correlative function is investigated. In most cases, it brings about little error for taking the asymptotic BCR of 2 consecutive points as the asymptotic BCR as long as the band is chosen narrow enough. Further the links between the asymptotic BCR and the 1th-oraer asymptotic correlative function and the variance are set up.

With the assistance of geometric lattices, up to isomorphism, we find the corresponding relationships between simple matroids and some contexts. Meanwhile, we construct matroids from some contexts and build up contexts from simple matroids. Finally, two examples show the applications of these relationships found above.

A perturbation result on the ranges of m-accretive mappings is proved and used to show that a family of nonlinear elliptic boundary value problems with the generalized p-Laplacian operator have solutions in L²(Ω). The relationship between the solution and the zero point of a suitably defined nonlinear maccretive mapping is investigated. Moreover, some iterative schemes are constructed to be weakly or strongly convergent to the solution. Some new techniques of constructing appropriate operators and decomposing the equations are employed, which extend and complement some of the previous work.

In this paper, we study dynamical behaviors of bidirectional associative memory (BAM) neural networks with distributed delays. By the continuation theorem of coincidence degree theory, Krasnosel' skii's fixed point theorem on cones, and analysis technique, we deduce some new sufficient conditions ensuring existence as well as the global exponential stability of periodic solution. Some existing results are improved and extended. Even corresponding to discrete delays system, our results that these conditions are milder and less restrictive than previous known criteria since the hypothesis of boundedness and differentiability on the activation function are dropped. The theoretical analysis are verified by numerical simulations.

The oscillation for certain second-order nonlinear delay Emden-Fowler dynamic equations on time scales is discussed. Using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the equations under the condition ∫_t0^+∞[A^-1(s)e_-b/A(s, t₀)]^1/λ△s < +∞, the results obtained extend and improve some related results reported in the literature. Finally, examples are provided to illustrate assumptions in our theorem are less restrictive.

In this paper, we consider the method for solving linear complementarity problems. By a kind of generalized complementarity function, we transform the linear complementarity problems into the nonlinear equations and use the Levenberg-Marquardt type methods to solve it. Under mild conditions, we give the convergence analysis of the given methods. Finally, the numerical results indicate the efficiency of the given methods.

In this paper we consider a two-stage flow-shop scheduling model which combines flexible flow shop with parallel scheduling. There is only one machine at the first stage and m identical parallel executing machines at the other. Each task needs size_i parallel machines execute simultaneously at the second stage. The objective is to minimize the makespan. This model has been proved to be NP-hard and an approximation algorithm has been proposed as well. In this paper we describe the process of the previous algorithm and point out the limitations of algorithm approximate ratio analysis. Then we propose a 3-approximation algorithm based on parallel scheduling results. Our algorithm discards the constraints of previous 3-approximation algorithm analysis. Lastly we study the two special cases with two parallel machines and three parallel machines in the second stage respectively. We propose two approximation algorithms with 2.5 and 2.67 approximate ratio correspondingly according to list scheduling rules.

To save resources, many researchers have combined the biological statistics with sampling design methods together in the biomedical statistics. A large number of the multivariate failure time data from case-cohort designs then have been generated. In this paper, we will use a general additive-multiplicative hazards model to study case-cohort designs with multiple type event data. We first present an effective weighted estimating equation, and the parameter estimations are obtained, and then the resulting estimators are shown to be consistent and asymptotically normal. Simulation studies demonstrate that the proposed method performs well, and is more effective. Finally, the proposed method is applied to a real example.

In this paper, a new method of the analytical solutions for solving the equation with the Dirichlet boundary and Neumann boundary conditions is proposed based on the functional extreme value theory of variational principle for a class of diffusion equations with diffusion coefficient is nonlinear exponential function and power function respectively. And It is proved that the new method is the necessary and sufficient of the extreme solution of functional problems. Taking the unsaturated soil water movement problem as the background, the analytical solution of horizontal absorption problem under the condition of water accumulation and constant flux is given by the new method in this paper. Numerical examples are given to compare the analytical solution with the numerical solution. The results show that the analytical solution obtained by this method can predict the distribution of soil water content in unsaturated soil water level absorption problem accurately, which is an effective method. Therefore, this paper provides an effective new method for solving the nonlinear diffusion equation with the exponential term and the power function. It has certain superiority and applicability.

This paper investigates the global stability of an HIV dynamics model with discrete delays incorporating Crowley-Martin functional response infection rate. An eclipse stage of infected cells (i.e. latently infected cells), not yet producing virus, is included in our model. We consider nonnegativity, boundedness of solutions and global asymptotic stability of the uninfected and infected equilibria (steady states) by constructing suitable Lyapunov functionals. We have proved that if the basic reproduction number R₀ is less than unite, then the disease-free equilibrium is globally asymptotically stable, and if R₀ is greater than unite, then the infected equilibrium is globally asymptotically stable. Numerical simulations have been presented to illustrate the asymptotical stability of equilibrium points by using Matlab.

Guo and Tan in[Ji-Ming Guo, Shang-Wang Tan, A conjecture on the second largest eigenvalue of a tree with perfect matchings, Linear Algebra and its Applications 347 (1-3) (2002) 9-15] and[Ji-Ming Guo, Shang-Wang Tan, A note on the second largest eigenvalue of a tree with perfect matchings, Linear Algebra and its Applications 380 (2004) 125-134] presented the upper bounds for the second largest eigenvalue of a tree on 2k vertices with perfect matchings in terms of the number of vertices and characterized the trees whose second largest eigenvalues attain the upper bounds. In this paper, we present the upper bounds for the second largest eigenvalue of a tree on 2k vertices in terms of the number of vertices and the size of maximum matchings and characterize the trees whose second largest eigenvalues attain the upper bounds.

One-sided test is an important part of hypothesis test theory. Some kind of one-sided test for log-linear models under product-multinomial sampling is studied in this paper. Based on φ-divergence and the restricted minimum φ-divergence estimator (RMφDE), three families of statistic are proposed. All the three proposed statistics have identical asymptotic distribution as Chi-bar-square distribution, and include the likelihood ratio statistic and the Pearson statistic as special cases. These proposed statistics can be treated as a generalization of the results in existing literature with three improvements:the model in this paper is much wider than the saturated log-linear model they considered; the form of one-sided test is much more general than the likelihood ratio ordering test they constructed; and RMφDE used to construct these statistic is more general than the maximum likelihood estimator (MLE) they used. Real data analysis demonstrates the effect of these statistic. A simulation study shows that some members of the power-divergence family could act as superior alternatives to the likelihood ratio statistic and the Pearson statistic under finite sample sizes.

In this paper,a new type of option is proposed,which is called generalized European option with random expiration time. The new option is a generalization of European option and American option.When the market is frictionless and complete continuous market without arbitrage, we construct two theoretical models and derive the martingale pricing formulas of generalized European option. Under appropriate conditions, the results of the two models are consistent.When the random expiration time is not independent of the underlying asset value, the generalized European option pricing formulas are given in several cases.For the stochastic factors such as interest rate, asset price,expiration time, etc., two specific market models are defined,and the generalized European option pricing formulas are derived under the Vasicek short-term interest rate model,or when the random expiration time indicates a certain market state, the interest rate is not random, in which the underlying asset value is based on the general itô process.The results of the model can be applied to the valuation of the company, the newly opened project, the stock option,etc.In this paper,a new way of pricing is given.

In this paper, we consider the multiplicity of positive solution for boundary value problem of fractional differential equations with p-Laplacian operator. By using the fixed-point theorem on a convex cone, the existence and the multiplicity results of positive solution are obtained.

In this paper, the regularized long wave-KdV equation is studied. First, using the classical Lie symmetry method, all vector fields and symmetry reduction of the equation with nonlinearity are constructed. Then, the exact traveling wave solutions is provided by using traveling wave transformation, the homogeneous balance principle and e^-φ(ξ)-expansion method, include the trigonometric function solution, the hyperbolic function solution and the rational function solution. In addition, the new exact solution are obtained the lambertW function method. Finally, adjoint equation, Lagiangian and conservation laws of the regularized long wave-KdV equation are derived.