On Perturbation Stability of Metric Regularity

We introduce a measure of closeness for set-valued mappings from a metric space to a Banach space which allows to quantatively estimate the effect of perturbation of a set-valued mapping on its metric regularity and covering characteristics.     

On Directional Metric Regularity, Subregularity and Optimality Conditions for Nonsmooth Mathematical Programs

This paper mainly deals with the study of directional versions of metric regularity and metric subregularity for general set-valued mappings between infinite-dimensional spaces. Using advanced techniques of variational analysis and generalized differentiation, we derive necessary and sufficient conditions, which extend even the known results for the conventional metric regularity. Finally, these results are applied to non-smooth optimization problems. We show that that at a locally optimal solution M-stationarity conditions are fulfilled if the constraint mapping is subregular with respect to one critical direction and that for every critical direction a M-stationarity condition, possibly with different multipliers, is fulfilled.     

On the Image Regularity Condition

In this paper, we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved that IRC implies the existence of generalized Lagrange-John multipliers with first component equal to 1. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can be also nonlinear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that 0 is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives.     

环的弱正则性

本文给出了环的弱正则性的一个充要条件，还讨论了Ｍｕｎｎ环的弱正则性．最后对环的半格和及补半格和，给出了弱正则性的刻画．     

关于右SF-环的正则性

研究了每一个极大的右理想是拟理想的右SF-环的正则性,得到了右SF-环是正则环的一些新的刻画,推广了一些已知的结论.     

On the Regularity of Crossed Products

We study some generalizations of the notion of regular crossed products K * G. For the case when K is an algebraically closed field, we give necessary and sufficient conditions for the twisted group ring K * G to be an n-weakly regular ring, a ξ^* N-ring or a ring without nilpotent elements.     

Directional and Anisotropic Regularity and Irregularity Criteria in Triebel Wavelet Bases

Many natural mathematical objects, as well as many multi-dimensional signals and images from real physical problems, need to distinguish local directional behaviors (for tracking contours in image processing for example). Using some results of Jaffard and Triebel, we obtain criteria of directional and anisotropic regularities by decay conditions on Triebel anisotropic wavelet coefficients (resp. wavelet leaders).     

On the Regularity of Operations of Ideals

Let I be a homogeneous ideal of a polynomial ring K[x₁,…, x_n] over a field K, and denote the Castelnuovo–Mumford regularity of I by reg(I). When I is a monomial complete intersection, it is proved that reg(I^m) ≤ mreg(I) holds for any m ≥ 1. When n = 3, for any homogeneous ideals I and J of K[x₁, x₂, x₃], one has that reg(I ? J), reg(IJ) and reg(I ∩ J) are all upper bounded by reg(I) +reg(J), while reg(I + J) ≤reg(I) +reg(J) ?1.     

关于凝聚局部环的正则性

本文证明了极大理想m是有限生成的交换凝聚局部环（R,M）是正则的充分必要条件是m可以由一个正则R-序列生成,推广了文献[1]中相应的结论并给出了一个由正则凝聚局部环构造大量的非正则凝聚局部环的方法．     

Regularity and Stability for a Convex Feasibility Problem

Set-Valued and Variational Analysis - Let us consider two sequences of closed convex sets {An} and {Bn} converging with respect to the Attouch-Wets convergence to A and B, respectively. Given a...     

On Besov Regularity of Temperatures

We prove space-time parabolic Besov regularity in terms of integrability of Besov norms in the space variable for solutions of the heat equation on cylindrical regions based on Lipschitz domains.     

On Closability of Directional Gradients

Let be a centred Gaussian measure on a separable real Banach space E, and let H be a Hilbert subspace of E. We provide necessary and sufficient conditions for closability in L ^p (E,) of the gradient D _H in the direction of H. These conditions are further elaborated in case when the gradient D _H corresponds to a bilinear form associated with a certain nonsymmetric Ornstein–Uhlenbeck operator. Some natural examples of closability and nonclosability are presented.     

On the Regularity of Powers of Ideal Sheaves

We use the geometry of the secant variety to an embedded smooth curve to prove some vanishing and regularity theorems for powers of ideal sheaves.     

论方向导数与梯度

讨论了几种不同的方向导数和梯度的定义.     

最优值函数的方向导数

本文详细介绍了参数非线性规划问题最优值函数的方向导数的存在性、表示形式和有关的发展历史,本文不仅讨论了这一问题的经典结论,还叙述了最近二十年来的新结果。本文最后指出进一步研究的方向。     

Stability and Clifford Regularity with Respect to Star Operations

In the last few years, the concepts of stability and Clifford regularity have been fruitfully extended by using star operations. In this article we deepen the study of star stable and star regular domains and relate these two classes of domains to each other.     

On the Regularity of Shear Thickening Viscous Fluids

The aim of this note is to improve the regularity results obtained by H. Beirao da Veiga in 2008 for a class of p-fluid flows in a cubic domain. The key idea is exploiting the better regularity of solutions in the tangential directions with respect to the normal one, by appealing to anisotropic Sobolev embeddings.     

桩侧摩阻力对打入桩定向稳定性的影响

在本文中,把打桩时桩顶的锤击力作为一种周期荷载而导得Mathieu方程.从该方程的稳定界限,我们可求得桩的临界长度,也讨论了桩侧摩阻力对定向稳定性的影响.     

On the Regularity Condition for Vector Programming Problems

In this work, we use a notion of approximation derived from Jourani and Thibault [13] to ascertain optimality conditions analogous to those that established but applicable to larger class of vector valued objective mappings and constraint set-valued mappings. To this end, we introduce an appropriate regularity condition to help us discern the Karush-Kuhn-Tucker multipliers.