On meromorphically harmonic starlike functions with respect to symmetric conjugate points

In a previous paper M.P. Chen, Z.-R. Wu and Z.-Z. Zou [M.P. Chen, Z.-R. Wu, Z.-Z. Zou, On functions α-starlike with respect to symmetric conjugate points, J. Math. Anal. Appl. 201 (1996) 25-34] developed a method, using some operators, to deal with functions analytic and starlike with respect to symmetric conjugate points in the unit disc. Then, the same method is employed to functions meromorphic by Z.Z. Zou and Z.-R. Wu [Zhong Zhu Zou, Zhuo-Ren Wu, On meromorphically starlike functions and functions meromorphically starlike with respect to symmetric conjugate points, J. Math. Anal. Appl. 261 (2001) 17-27]. Now, the method can be employed to functions meromorphic harmonic in the punctured disc 0<|z|<1. Especially, a sharp coefficient estimate and a structural representation of such functions are obtained.     

Infinitely many solutions for a class of sublinear Schrödinger–Maxwell equations

In this paper we study the existence of infinitely many solutions for a class of sublinear Schrödinger–Maxwell equations. The proof is based on the variant fountain theorem established by Zou. Recent results from the literature are extended.     

A priori estimates for nonlinear differential inequalities and applications

The aim of the paper is to derive a priori estimates and obtain the Harnack-type inequalities of positive weak solutions for the nonlinear differential inequalities in an exterior domain or interior domain. By using the test function method developed by Mitidieri and Pohozaev, we extend and improve some known results proved by Serrin and Zou, Bidaut-Véron and Pohozaev.     

Infinitely many solutions for resonant cooperative elliptic systems with sublinear or superlinear terms

In this paper, we study a class of resonant cooperative elliptic systems with sublinear or superlinear terms and obtain infinitely many nontrivial solutions by two variant fountain theorems developed by Zou.     

一类超线性椭圆方程的无穷多解

本文研究了一类超线性椭圆方程,这里的非线性项是奇的.我们不需要假设Ambrosetti-Rabinowitz条件,得到了无穷多个大能量解的存在性.我们的结论推广了邹文明最近的结果。     

Elastic-net regularization in learning theory

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie [H. Zou, T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B, 67(2) (2005) 301–320] for the selection of groups of correlated variables. To investigate the statistical properties of this scheme and in particular its consistency properties, we set up a suitable mathematical framework. Our setting is random-design regression where we allow the response variable to be vector-valued and we consider prediction functions which are linear combinations of elements (features) in an infinite-dimensional dictionary. Under the assumption that the regression function admits a sparse representation on the dictionary, we prove that there exists a particular “elastic-net representation” of the regression function such that, if the number of data increases, the elastic-net estimator is consistent not only for prediction but also for variable/feature selection. Our results include finite-sample bounds and an adaptive scheme to select the regularization parameter. Moreover, using convex analysis tools, we derive an iterative thresholding algorithm for computing the elastic-net solution which is different from the optimization procedure originally proposed in the above-cited work.     

Resonant functional problems of fractional order

We study a resonant functional boundary value problem of fractional order. Our results are based on the coincidence degree theory of Mawhin and improve those in a recent paper of Y. Zou and Y. Cui [Adv. Difference Equ. 2013 (2013), 1–25].     

Comments on “Elasto-plastic solution for shallow tunnel in semi-infinite space”

This paper considers the approach proposed by Zou et al. for determining the plastic zone around a shallow circular tunnel in an elasto-plastic semi-infinite space that incorporates the gravitational effect based on the bipolar coordinate system. The paper aims to analyze the correctness of the analytic expressions for elastic and plastic stress, as well as the reasonableness of the procedure building for solving the elasto-plastic interface. Finally, a promising way of solving this problem more exactly is presented.     

The newton filtration and d-determination of bifurcation problems related to C 0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

Traveling wave solutions in delayed lattice differential equations with partial monotonicity

In this paper, we investigate a system of delayed lattice differential equations with partial monotonicity. By using Schauder's fixed point theorem, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. Our main results can deal with the existence of traveling wave solution for a class of delayed reaction diffusion system with partial monotonicity and generalize the results of Wu and Zou (J. Differential Equations 135 (1997) 315–357).     

Superlinear problems without Ambrosetti and Rabinowitz growth condition

Superlinear elliptic boundary value problems without Ambrosetti and Rabinowitz growth condition are considered. Existence of nontrivial solution result is established by combining some arguments used by Struwe and Tarantello and Schechter and Zou (also by Wang and Wei). Firstly, by using the mountain pass theorem due to Ambrosetti and Rabinowitz is constructed a solution for almost every parameter λ by varying the parameter λ. Then, it is considered the continuation of the solutions.     

比估计的两个常用的方差估计量的小样本比较

本文利用冯士雍和邹国华［１］或Ｓｕｎｄｂｅｒｇ［２］提出的比较方差估计量的新准则对比估计的两个常用的方差估计量进行了小样本比较．这是Ｃｏｃｈｒａｎ［３］提出的一个公开问题．我们的结果在一定的意义下回答了该问题．     

Infinitely many homoclinic solutions for some second order Hamiltonian systems

In this paper, we investigate the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems. By using fountain theorem due to Zou, we obtain two new criteria for guaranteeing that second order Hamiltonian systems have infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved.     

一类时滞格种群模型波前解的存在性

This paper considers the travelling wave fronts to a delayed lattice differential equation.The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions developed by J Wu and X Zou in[6].This work extends that of [4]in a general class of nonlinear terms.     

The newton filtration and d-determination of bifurcation problems related to C0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

准正交基与准正交变换

利用内积给出了准正交基,准正交变换与准对合变换的概念,研究了它们的性质及其之间的联系,获得了许多新的结果,推广了正交基,正交变换,对合变换的概念,性质以及张禾瑞,郝新,邹本强等先生的相关结果。     

Traveling wavefronts in diffusive and cooperative Lotka-Volterra system with delays

Existence of traveling wave front solutions is established for diffusive and cooperative Lotka-Volterra system with delays. The result is an extension of an existing result for delayed logistic scaler equation to systems, and is somewhat parallel to the existing result for diffusive and competitive Lotka-Volterra systems without delay. The approach used in this paper is the upper-lower solution technique and the monotone iteration recently developed by Wu and Zou (J. Dynam. Differential Equations 13 (2001) 651-687) for delayed reaction-diffusion systems without the so-called quasimonotonicity.     

The Newton filtration and d-determination of bifurcation problems related to C~0 contact equivalence

In this paper, from the Newton filtration's point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C0 contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

Asymptotically or super linear cooperative elliptic systems in the whole space

Under the assumption that F is asymptotically or super linear as |U| → ∞ with U = (u, v) ∈ ?², we obtain the existence of ground state solutions of a class of cooperative elliptic systems in ? ^N by using a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. To the best of our knowledge, there is no result published concerning the systems in the whole space ? ^N .     

随机脉冲干扰对B—CKdV方程扭状孤波解的影响

本文利用侯振挺等^[1]提出的马尔可夫骨架过程理论求出了在随机随冲干扰下,B－CKdV方程ut auux bu^2ux ruxx uxxx=0的行波解及其一维分布,并研究了行波解的渐近性质。