Interior estimates for the n-dimensional Abreuʼs equation

We study the Abreu?s equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.     

Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds

In this paper we consider the problem of finding closed hypersurfaces with prescribed Weingarten curvature in a large class of Riemannian manifolds. Under some sufficient conditions, we obtain an existence result by establishing a priori estimates and standard degree theory for the admissible solutions to the prescribed curvature equation. We mainly show that the primary technique developed in Urbas, Wang and the second author’s work in 2004 is flexible enough to be used in more general ambient geometry.     

Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

具有交易成本的证券投资组合选择：一种求解方法

本研究一类带交易成本证券投资组合选择的求解,在风险不超过某个阈值的假设下,我们给出一种求解方法,最后本通过实例计算表明该方法是有效的。     

New extragradient-type methods for solving variational inequalities

In this paper, we propose new methods for solving variational inequalities. The proposed methods can be viewed as a refinement and improvement of the method of He et al. [B.S. He, X.M. Yuan, J.J. Zhang, Comparison of two kinds of prediction–correction methods for monotone variational inequalities, Comp. Opt. Appl. 27 (2004) 247–267] by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. Under certain conditions, the global convergence of the both methods is proved. Preliminary numerical experiments are included to illustrate the efficiency of the proposed methods.     

Learning from regularized regression algorithms with <Emphasis Type=Italic>p</Emphasis>-order Markov chain sampling

Evaluation for the performance of learning algorithm has been the main thread of theoretical research of machine learning. The performance of the regularized regression algorithm based on independent and identically distributed(i.i.d.) samples has been researched by a large number of references. In the present paper we provide the convergence rates for the performance of regularized regression based on the inputs of p-order Markov chains.     

Well-Posedness and Asymptotic Behaviors for a Predator-Prey System with Lévy Noise

In this paper, well-posedness and asymptotic behaviors for a predator-prey system with Lévy noise are studied by using stochastic analytical techniques. Firstly, the existence and uniqueness of positive global solution with positive initial value is proved. Then, stochastic permanence for the system is investigated. Finally, persistence in mean and extinction for the system are discussed and some numerical simulations are provided to support our results.