In this paper, we study the following quasilinear Schrödinger-Poisson system without compactness condition

where κ<0,λ>0,p ≥ 12,f∈ C (R,R), V∈ C (R³,R). We first construct a truncated function and obtain the existence of nontrivial solutions of the truncated system by means of concentrated-compactness principle and the approximation method; then, the existence of nontrivial solutions for the above-mentioned system is discussed by using Moser iterative technique.

The negative correlations between stock returns and their volatility changes are called the leverage effect, which is a core issue in financial research. Because the common simple correlation coefficient isn't consistent any more in the context of high frequency data, some researchers proposed a new characterization of leverage effect: the integrated leverage effect and its estimators as well. As is well-known, high frequency data are too apt to be contaminated by market microstructure noise. Rounding is a crucial source of market microstructure noise and is the common phenomena in stock returns data. Based the rounding-error-contaminated high frequency data, the paper studies the robustness of the estimator of the integrated leverage effect and deduces its consistency and asymptotic normality. Furthermore, simulations illustrate our theoretical results.

The Mostar index of a graph G is defined as Mo(G)=???20210102???|n_u-n_υ|is the number of vertices of G closer to vertex u than to vertex υ, and n_υ is the number of vertices closer to vertex υ than to vertex u. A non-complete graph G has diameter two if the distance of every pair of vertices in G is at most two. It was known that the minimum degree of a maximal planar graph of diameter two and having at least four vertices equals to 3 or 4. Let G be a maximal planar graph having n vertices, minimum degree 4, and diameter two. In this paper, we determine the value of Mo(G) if n ≥ 13,then ???20210102(1)??? ≤ Mo(G) ≤ 2n²+16n+24 and the corresponding extremal graphs attaining upper and lower bounds are given.

This paper is devoted to investigate the optimality conditions for approximate quasi globally proper efficient solutions for a class of nonsmooth Vector Equilibrium Problem (VEP). Firstly, a necessary optimality condition to problem (VEP) for approximate quasi globally proper efficient solutions is established by utilizing the separation theorem with respect to the quasi relative interior of convex sets and the properties of the Clarke subdifferential. Secondly, the concept of approximate pseudoconvex function is introduced, and its existence is verified by a concrete example. Under the assumption of introduced convexity, a sufficient optimality condition for problem (VEP) in sense of approximate quasi globally proper efficiency is also presented. Finally, by using Tammer's function and constructing the nonlinear functional with mild conditions, the scalarization theorems of the approximate quasi globally proper efficient solutions to the problem (VEP) are proposed.

An avian influenza model on a periodically evolution region is studied in this paper. First, by assumping that the growth of the region is isotropic, the model is transformed into a reaction-diffusion problem over a fixed region. Then, the asymptotic behavior of the model is obtained by using the related eigenvalue questions and the up-down solution method. The results show that the impact of periodic evolution regions on the spread and inhibition of disease depends on the integral average value ρ^-2=???20210105??? dt of the periodic evolution rate ρ(t) of the region. If ρ^-2>1, the evolution of periodic regions can inhibit the spread of disease; if ρ^-2<1, the evolution of periodic regions can accelerate the spread of disease; if ρ^-2=1, the evolution of periodic regions has no effect on the spread of disease.

Robust principal component analysis, where a given observation data is separated into a low-rank part and a sparse part, has been widely studied since it is a basic tool in the field of statistics and data science. This paper focuses on a non-convex model for robust principal component analysis problems, where the low-rank matrix is factorized as a product of two small-size matrices such that the low-rank requirement is automatically fulfilled. Based on the non-convex model, we develop an alternating direction method equipped with a non-monotone search technique for solving robust principal component analysis problems. In the new algorithm, the variables are alternately updated, the variables of the low rank part are updated by a gradient descent method with an exact step size, and the variables of the sparse part are updated by a non-monotonic search technique. We established the convergence theory of the new algorithm under certain conditions. The final numerical results show the effectiveness of the proposed algorithm.

The Allen-Cahn model in phase field simulation is studied considering the numerical approximation of the one-dimensional Allen-Cahn equation by the compact difference method. A fully discrete compact difference scheme with a second order accuracy in time and fourth-order accuracy in is space is established, and that the numerical solution satisfies the principle of discrete maximization under the constraints of reasonable step ratio and time step is proved. On this basis,the stability of the fully discrete format Energy stability is studied. Finally, numerical examples are given to illustrate that the results are generalized to the two-dimensional Allen-Cahn, and unlike the one-dimensional Allen-Cahn equation, the accuracy of the fully discrete compact difference scheme is established by the two-dimensional Allen-Cahn equation.

To improve convergence rate and computing time of modulus-based multigrid method for solving large sparse linear complementarity problems, we employ the accelerated modulus-based successive overrelaxation (AMSOR) iteration method as smoother in this paper. The local Fourier analysis and numerical results indicate that this smoother can improve the performance of modulus-based multigrid method in terms of the convergence factor, the iteration number and the computing time.

In this paper, we consider the contrast structure for a class of linear singularly perturbed optimal control problem with fixed initial and free terminal states. Firstly, the variational method is used to obtain the optimality condition. Secondly, we prove the existence of heteroclinic orbit by the solution of reduced problem, then, the existence of contrast structure solution for the original problem is obtained by the singularly perturbed theory. Moreover, based on the structure of the solution, we construct the uniformly valid formal asymptotic solution for the singularly perturbed optimal control problem by the boundary layer function method. Finally, an example is given to show the main result.

Single-index panel models have been widely used in a variety of research fields. They have many different estimation methods. However, few methods consider the case of correlation in subjects. Therefore, this paper studies a partially linear single-index panel model with fixed effect which has correlation in subjects. We estimate the model using combination of penalized quadratic inference function and LSDV. The consistency and asymptotic normality of the estimators are derived. Meantime, Monte Carlo simulation shows that the finite sample performances of the proposed estimation method are still very good. Furthermore, the proposed estimation technique is illustrated in the analysis of a real data set.

In this paper, we study the optimality conditions of weakly efficient element for nonconvex set-valued optimization problems based on quasi-relative interior. Firstly, the relationship between weakly efficient element and linear subspace is discussed, by using separation theorem involving the quasi-relative interior, optimality conditions of weakly efficient element is obtained. Then, Lagrange multiplier theorem of weakly efficient element based on quasi-relative interior is presented.

Based on the parameter estimation problem of partial linear variable-coefficient models, a novel composite quantile regression estimation method is proposed. The parameter part is estimated by using the composite quantile regression method, the variable coefficient function part is estimated by the local nonlinear composite quantile regression method. And under some regular conditions, it is proved that the estimators of constant coefficient and variable coefficient functions have better asymptotic normal properties. Through stochastic simulation and a real data analysis, the good performance of the proposed estimation method under limited samples is verified, which effectively proves the superiority of the proposed method.

First, the two current graphs of the complete graph K₁₉ satisfies the Kirchhoff’s Global Current Law. We can establish a system of linear equations and use the computer to find all the solutions of the equations. A set of solution corresponds to a current assignment method of the K₁₉ current graph. The number of different current assignment methods of the two current graphs are 34 and 6; Then, the basic graph of K₁₉ two current graphs are obtained with 16 different single face embeddings on the orientable surface. From the above conclusions, we obtain that the complete graph K₁₉ has at least 640 different triangulation embeddings on the orientable surface. Finally, finding out the number of non-strong isomorphism in two current graphs, and there is not non-trivial strong automorphism in any current assignment method. As a result K₁₉ has 24 non-isomorphic triangulation embeddings on the orientable surface.

A Ross more risk averse individual does not always invest more in precautionary effort in the intertemporal investment model of decision-making. This paper uses the characterization of restricted Ross more risk aversion to resolve this inconsistency, and obtains some comparative static results consistent with individual’s risk preferences: if the present value of the increment in the future average wealth is less than 1 unit which additional precautionary effort the individual invests in now, then a linearly-restricted Ross more risk averse individual always invests more in precautionary effort; Besides, under the conditions that the initial probability of loss is less than 1/2 and the individual’s current consumption level is not at least less than the minimal average wealth in the future, then a quadratically-restricted Ross more risk averse individual always invests more in precautionary effort.

Let Sm∪K1 be a discrete graph, which consists of a star Sm and with one isolated vertex K₁. In this paper, we first obtain the crossing numbers of (Sm∪K1)+Dn for m = 1, 2, 3. Moreover, assume that the conjecture cr(K_6,n+1\e)=Z(6,n+1)-2[n/2] is true, the crossing number of (S₄∪K₁)+D_n are determined.

In the fields of economy, biomedical and environmental science, there is a kind of mixed data which is asymmetric, nonlinear and contains outliers or strong influence points. If the data is diagnosed roughly, the results may not be accurate. Therefore, the statistical diagnosis of the mixture nonlinear location regression model with the skew-normal data is studied. In this paper, by comparing the diagnosis of mixed data with the diagnosis after classification, we find that the diagnosis after classification is more accurate. Secondly, Pena distance was extended to the skew-normal nonlinear regression model, and the Likelihood distance, Cook distance and Pena distance are given to distinguish outliers or strong influence points. The results presents that Pena distance is more sensitive to outliers, and the diagnostic effect is slightly better than Likelihood distance and Cook distance. Finally, the model and method proposed in this paper are proved to be reasonable through the Monte-Carlo simulation and real data analysis.

The paper study the structural stability of two different kinds of fluids in a bounded smooth region. Assuming their governing equations are the temperature-dependent Brinkman-Forchheimer equation and Darcy equation and there is a heat source or sink in the interior of Brinkman-Forchheimer type fluid. By using the energy analysis method and the differential inequality technique, the continuous dependence of the solution of the equations on the heat source and the viscosity coefficient is obtained.

In this paper, we study the Allen-Cahn model of the phase-field simulation. Considering the two-dimensional nonlinear Allen-Cahn equation, we establish Crank-Nicolson difference scheme, and give truncation errors. The existence of the difference solution is proved with the help of Browder fixed point theorem. At the same time, the difference scheme is demonstrated to be unconditionally convergent in L_∞ norm by introducing an auxiliary smooth function. In the end, the study of maximum principle is given. The numerical experiments also verify the reliability of the method.

This paper is concerned with nonlinear stability of traveling wave fronts for competitive-cooperative Lotka-Volterra systems of three species. The existence and comparison principle of solutions to initial value problems are established by sing the theory of analytic semigroups and differential equations. The system is established by using the theory of weighted energy method and comparison principle, with the exception of exponential attenuation of traveling wave solutions in initial perturbations. The results show that the traveling wave solution, as the steady-state solution of the system, usually determines the long-term asymptotic behavior of the solution of the initial value problem. The stability of the traveling wave solution reveals that the phenomena and the results of competition and cooperation among populations can be clearly observed.

An upwind difference approximation is proposed on a mesh constructed by equidistributing the arc-length monitor function for a singularly perturbed boundary value problem. Uniformly first-order convergent solutions in the maximum norm are obtained independent of the perturbation parameter based on the priori truncation error estimates, the discrete comparison principle and the barrier function technique. The convergence analysis is carried out in the whole domain instead of dividing the domain into subregions. Numerical results are presented to verify the theoretical analysis.

In this paper, the dynamic behavior of a class of gene regulatory network model with two delays is studied. Firstly, the existence of the positive equilibrium point of the system is discussed, and the conditions for the occurrence of B-T bifurcation at the positive equilibrium point are given. Secondly, based on the theories of universal unfolding, normal form and central manifold, the dynamic behavior near the positive equilibrium point is transformed into the dynamic characteristics of normal form confined to the central manifold. Finally, the results are simulated numerically, the bifurcation curves near the B-T bifurcation point are given, and the corresponding bifurcation diagrams are obtained, and the conclusions are summarized.

In this article, we investigate the concentration-compactness principle associate with the Trudinger-Moser-Lorentz type inequalities on the whole space. By using the method of level sets of truncation, we extend the concentration-compactness principle on finite domains associate with the Trudinger-Moser-Lorentz type inequalities to the whole space. Moreover, we construct a function sequence to show the sharpness of our result.

This paper aims to study the estimation and inference of a semiparametric varying-coefficient additive model for panel data. The model assumes the relationship between a response variable and predictors as unknown functions and allows the relationship is time-varying, which can simultaneously capture time-variant and non-linear structure. We develop an estimation procedure to estimate unknown parameters and functions. We first average the response variable over cross-sections and, then our model becomes a varyingcoefficient additive model. We then provide initial estimates of functions by a spline smoothing method and those of parameters by a least square method. Once these initial estimates are obtained, we upgrade these estimates using the spline method and least square method based on our original model. Asymptotic properties of the resulting estimators are also derived under a setting of (N, T) → ∞. Simulation studies are reported to evaluate the performance of our estimation procedure. We apply our model to investigate time-variant behaviours of Fama–French three factors and find that the size and value factors are significantly time-variant.

Let D be a digraph. An undirected graph G denoted by C^m(D) is called the m-step competition graph of D if it satisfies the following two conditions: (1) G has the same vertices set as D; (2) There is an edge between two vertices x and y in G if and only if there exists a vertex z in D, such that there are two directed walks of length m both from x to z and from y to z for any vertices x,y in D. In 2004, the notation of competition index was defined firstly by Cho and Kim. For some positive integer r and all non-negative integer i, if there is a smallest positive integer q such that C^q+i(D) = C^q+i+r(D), then the integer q is called the competition index of D, which is denoted by cindex (D). In 2008, Kim gave the upper bound of the competition index of tournaments. In 2009, Akelbek and Kirkland gave the competition index of the primitive digraph. In this paper, the competition index of regular multipartite tournaments is studied and calculated.

In this paper, Bäcklund transformations for two generalized short pulse equations are considered. With the help of reciprocal transformation and the associated generalized short pulse equations, the Bäcklund transformations, which involves both independent and dependent variables, are constructed for the generalized short pulse equations. Based on the Bäcklund transformations, the corresponding nonlinear superposition formulas are also worked out and some solutions to the generalized short pulse equations are presented.

Under the framework of the calculus of Peng’s G-nonlinear expectation, by using G-Brownian motion on a sublinear expectation space (Ω, H, E Ê), we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Finally, the two-fund separation theorem is explicitly obtained, and an illustrative example is provided.

A bipartite multigraph is called a standard bipartite multigraph if each edge in it contains at least two edges. Let D be a standard bipartite multigraph with|V₁|=|V₂|= n ≥ 2, where n is a positive integer. We prove that if the minimum degree of D is at least 3n/2, then D contains 「n/2」 vertex-disjoint quadrilatearls. Moreover, if n is odd, then n-2/3 of 「n/2」 disjoint quadrilaterals has four multiedges and the rest one of them has at least three multiedges; if n is even, then n-2/4 of 「n 2」 disjoint quadrilaterals has four multiedges and each of the rest of two has at least three multiedges, with only one exception.

The initial boundary value problem for some nonlinear higher-order wave equation with damping and source terms in a bounded domain is studied. The local existence and uniqueness of solution is discussed under appropriate assumptions. Meanwhile, we show that this solution blows up in finite time as the initial energy is negative, and give the lifespan estimation of solution.

In this paper, we employ the MiniMax martingale measure to study the optimal management problem for a general insurance company which holds shares of an insurance company and a reinsurance company.The insurer can purchase proportional reinsurance, and both the insurer and the reinsurer can invest in a risk-free asset and a risky asset. The objective of the general insurance company is to maximize the expected exponential utility of the weighted sum of the insurance company’s and reinsurance company’s terminal wealth. We obtain the explicit solutions of optimal strategies for exponential utility function.

By the nonuniform estimates of the remainder term in the central limit theorem, the authors obtain the generalized Davis-Gut law for the weighted sums of independent and identically distributed random variables, which extends the well-known result

In Kaleva-Seikkala type fuzzy metric spaces, fixed point theorems for BoydWong’s type and Alber-Guerre Delabriere’s type nonlinear contractions are established. These results enrich some recent results of Xiao et al. As applications of our results, fixed point theorems for nonlinear contractions in ordinary metric spaces and Menger probabilistic metric spaces are obtained.

In this paper, we study a nonlocal dispersal cholera model. The existence of traveling wave solutions is obtained by applying Schauder’s fixed point theorem with upperlower solutions in the case of R₀ > 1 with c > c^*. Moreover, we construct suitable Lyapunov function to analyze the boundary asymptotic behavior of traveling wave solutions at +∞. Finally, we show the existence of the traveling wave solutions in the case of R₀ > 1 with c = c^*.

Based on the principal-agent theory, this paper studies the sequential game equilibria of the limited partnership system and the company system under intertemporal consumption decision-making. By comparing and analyzing the game equilibria of these two mechanisms, this paper concludes that under the influence of the agent’s intertemporal consumption decision, only the limited partnership system reinforces incentives, thus relieving the moral hazard problem. In particular, when the game interval tends to zero, the Pareto optimal is achieved. Moreover, the company system is not a dominant mechanism comparing with the limited partnership system, and both sides of the game would not agree to adopt the company system at the same time. However, under certain conditions, the limited partnership system could be a dominant mechanism, and therefore being accepted by both sides. To sum up, the limited partnership system has incentive advantages over the company system.

Statistical inference theory and methods of the population quantiles have always been an important topic in statistical research, mainly because the application of quantile involves many fields, and it plays a decisive role in the research of various fields. This review paper summarizes the current progresses of quantile estimation. We discuss the theory and methods of non-parametric statistical inference systematically based on the population quantile of sample order statistics. The interval estimation of the population quantile and the difference between the population quantile, the tolerance interval of the population, and sign test are given in this paper. These will help readers in scientific research and application.

With the increasing risk of asymptomatically infected and imported cases of COVID-19, it brought tremendous pressure to the prevention and control strategy of “both imported cases and spread within the city should be prevented” in China. In this study, we propose a discrete stochastic model to describe and analyze the impact of imported cases and asymptomatic infected popualtion on the evolution of the COVID-19 dynamics in China. Defining a risk-index, we evaluate the risk of a secondary COVID-19 wave under different import patterns and different levels of control interventions. Using the epidemic data of Beijing, Shanghai, and Shenzhen, we first calibrated the proposed model. The main results show that the risk of a secondary peak in Shenzhen is much smaller than those in Beijing and Shanghai, while the risk in Shanghai is slightly lower than it in Beijing. Particularly, considering three levels of control interventions, we find that 1) the probability of a secondary epidemics in Beijing is always 0 if the control intervention keeps strict (with a minimum contact rate 1.07) no matter what the quarantine ratio of the imported cases; 2) the higher the quarantine ratio, the lower the probability of a secondary wave when the contact rate increases to 3.1 in three weeks; 3) the probability of a secondary wave becomes 58.3% even the quarantine ratio of the imported cases is 100%. Considering the situation in Shanghai or the impact of the imported asymptomatic cases, we obtained similar results. Therefore, in addition to continuing the strict control intervention, strengthening the management of immigration personnel and screening of asymptomatically infected is the key to preventing the occurrence of secondary epidemics. The main results provide the critical qualitative and quantitative decision-making basis for the prediction, early-warning and risk assessment of a secondary COVID-19 peak.

The objective of this paper is to study oscillatory and asymptotic behaviors of solutions of a class of third-order nonlinear neutral differential equations with continuously distributed delay （r（t）[（x（t）+∫_a^bp（t，ξ）x（τ（t，ξ）） dξ）'']^α）'+∫_c^dq（t，ξ）f（x（σ（t，ξ））） dξ=0, where f（x）/x^β≥δ>0，x≠0，α>0 and β>0 are the quotient of positive odd number. By using generalized Riccati transformations and integral averaging technique, we establish a set of new sufficient conditions for α≠β which ensure that every solution of the equations oscillates or converges to zero. Our results improve and extend related criteria in the literature, recently. Examples are provided to illustrate new results.

This paper introduces partial information into the Tobin’s q model, and utilizes the managers’ belief to depict the learning process of the uncertainty of expected returns on the productivity shocks. We also use the homogeneity of the company’s value to solve the ordinary differential equation that is about the company’s Tobin’s q on the manager beliefs, and then discuss about the manager beliefs and the impact of adjusting cost of investment on the company’s Tobin’s q, investment decisions, sensitivity of company’s value as a result of manager beliefs, as well as the company’s assets in place value and growth opportunity value. The model and conclusions extended in this paper have certain reference value for valuation of company and investment decisions.

In this paper, the existence and multiplicity of solutions for boundary value problem of a class of second-order impulsive differential equations with p-Laplacian operator are considered. Under the assumption that the impulsive functions satisfy the super-linear growth conditions, the impulsive problem has at least one classical solution and infinitely many classical solutions by using variational methods.

This paper studies the existence and uniqueness of mild solutions for a class of semi-linear integro-differential evolution equations with memory non-instantaneous impulses and nonlocal conditions in a Banach space, the mainly results are provided by the operator semigroup theory, Banach contraction principle and Krasnoselskii’s fixed point theorem, and then the sufficient conditions for the existence of strong solutions are obtained. Compared with previous evolution equation models with non-instantaneous impulses, the two parameter evolution system problems discussed in this paper is more complex, the conclusions obtained promote and develop the existing related results. Finally, an application of the main results is given by an example.

To detect state changes in extreme events, the generalized Pareto distribution (GPD) change point detection model was studied based on likelihood ratio method. This paper considered the testing problem of the GPD change point with three parameters, and proposed maximization likelihood ratio test statistics. The asymptotic distribution of test statistic was obtained by proving a series of limit properties of the log-likelihood of GPD after parameter transformation and the test statistic. We evaluated the finite sample properties of the proposed method through simulation studies. The case study also verified the feasibility of the proposed method.