The differential variational inequality composed of differential equation and variational inequality is a very important problem in the field of nonlinear analysis and its application. Recently, differential variational inequality has attracted the great attention and exploration of many scholars. In this paper, we study the existence of solutions to a new class of differential variational inequalities with nonconvex constraint set, but the constraint set of the variational inequality for this kind of problems is star-shaped with respect to a certain ball. This allows one to use a discontinuity property of the generalized Clarke subdifferential of the distance function. Then the existence of solutions to differential variational inequalities are obtained by applying a surjectivity theorem for multivalued pseudomonotone operators, a hemivariational inequality approach and a penalization method in which a small parameter does not have to tend to zero. Finally, as samples of applications, we consider a parabolic initial-boundary value problem with nonconvex constraint and illustrate the application of the main results.

The oscillation for certain third-order dynamic equations with positive and negative coefficients and damping term and nonlinear neutral term on time scales is discussed in this article. By using the generalized Riccati transformation and the inequality techniques, we establish some new oscillation criteria for the equations. Our results extend and improve some known results. Examples are given to illustrate the main results of this article.

The thin-plate spline (TPS) function is a good deformation analysis tool, which is often used for image registration. The traditional TPS function only uses the coordinate information of feature points, but in reality, many feature points have orientation information, such as fingerprint minutiae and sift feature points. In order to use the orientation information, this paper adds a orientation parallel penalty item and a orientation consistency penalty item based on the traditional TPS objective function. According to the conclusion of the variational method, the solution of the objective function is transformed into solving a differential equation, which is solved by the Green function method, so that a new form of the TPS function with orientation information is obtained. The TPS function obtained in this paper is suitable for point sets of any dimension. Experiments on fingerprint image registration and artificial point set interpolation show that the TPS function proposed in this paper is more accurate for image registration and point set interpolation with orientation information.

In this paper we mainly consider quantile regression for stratified data. To fully exploit the group information of the data, we assume that the regression coefficients for each group can be decomposed into the common part and the individual part. We propose a Lasso estimate of the decomposed coefficients and further propose its adaptive version. Furthermore, we transform the observation matrix to simplify the optimization problem involved. We prove the Oracle property of the adaptive Lasso estimates and study the finite sample performance via thorough numerical simulation. Finally, we apply the proposed method to analyze a gene expression dataset related to breast invasive carcinoma.

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.

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.

In this paper, based on the nonlocal boundary conditions, the Robin coefficient of one kind of parabolic equation with variable coefficients is determined, the Robin coefficient is only related to time.Here the first variational formula is given, the uniqueness is proved by using the variational formula, second time discrete model is given, based on linear variational form of discretization, a series of a prior estimate are derived, the existence of weak solutions is proved, and it’s error is analyzed.

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.

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.

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.

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.

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.