On a nonlocal elliptic problem arising in the confinement of a plasma in a current carrying stellarator

This paper deals with a nonlocal free boundary problem arising in the study of the dynamics of the confinement of a plasma in a Stellarator device. The free boundary represents the separation between the plasma and vacuum regions, and the nonlocal term involves the notions of relative rearrangement and monotone rearrangement. We establish some new properties on the decreasing rearrangement that can be used to prove the convergence of the approximate problem, and then prove the existence of solutions by Galerkin method. Copyright © 2013 John Wiley & Sons, Ltd.     

On Groups with a CC(n)-Subgroup

A subgroup H of G is a CC(n)-subgroup of G if |G: H| >n and |C_G(x): C_H(x)| ≤n for each element x ∈ H ? {1}. In this article, we study the finite p-groups with a nontrivial CC(p)-subgroup, and the locally nilpotent groups with a nontrivial CC(n)-subgroup.     

Sharp learning rates of coefficient-based l q -regularized regression with indefinite kernels

Learning with coefficient-based regularization has attracted a considerable amount of attention in recent years, on both theoretical analysis and applications. In this paper, we study coefficient-based learning scheme (CBLS) for regression problem with l ^q -regularizer (1 < q ? 2). Our analysis is conducted under more general conditions, and particularly the kernel function is not necessarily positive definite. This paper applies concentration inequality with l ²-empirical covering numbers to present an elaborate capacity dependence analysis for CBLS, which yields sharper estimates than existing bounds. Moreover, we estimate the regularization error to support our assumptions in error analysis, also provide an illustrative example to further verify the theoretical results.     

局部质量守恒的高阶Taylor-Hood元

本文推广了R．W．Thatcher[4]的结果，给出局部质量守恒的P3－P2元，并对矩形网格的高阶Qn－Qn-1进行了讨论．     

On <Emphasis Type="Italic">c</Emphasis><Superscript>#</Superscript>-normal subgroups infinite groups

A subgroup H of a finite group G is called a c^#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G: In this paper, we investigate the influence of fewer c^#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.     

A penalty function method based on bilevel programming for solving inverse optimal value problems

In this work, we reformulate the inverse optimal value problem equivalently as a corresponding nonlinear bilevel programming (BLP) problem. For the nonlinear BLP problem, the duality gap of the lower level problem is appended to the upper level objective with a penalty, and then a penalized problem is obtained. On the basis of the concept of partial calmness, we prove that the penalty function is exact. Then, an algorithm is proposed and an inverse optimal value problem is resolved to illustrate the algorithm.     

Existence,uniqueness and asymptotic behavior of traveling wave fronts for a vector disease model

This paper is concerned with the existence, uniqueness and asymptotic behavior of traveling wave fronts for a vector disease model. We first establish the existence of traveling wave fronts by using geometric singular perturbation theory. Then the asymptotic behavior and uniqueness of traveling wave fronts are obtained by using the standard asymptotic theory and sliding method. In addition, our method is also suitable to establish the uniqueness and asymptotic behavior of traveling wave fronts for a cooperative system.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.