稀土单分子磁体

单分子磁体因其磁性双稳态和慢弛豫机制而在超高密度存储材料、自旋电子器件等领域具有潜在的应用. 稀土单分子磁体因为具有较大的磁矩和磁各向异性而成为近年来研究的热点话题. 目前有关稀土单分子磁体的综述都主要集中在它们的合成、结构及磁性能, 而在其它性质方面缺少深入而系统的研究. 因此, 本论文结合现有的研究成果, 围绕稀土单分子磁体的高翻转能垒、复杂的多弛豫机制、可调控的磁性以及多功能材料的四个特点进行了综述, 旨在更好的理解稀土单分子磁体的物理、化学本质, 为稀土单分子磁体的设计与调控提供思路.     

C~3中一类拟凸超曲面的局部全纯自同构

给出了C~3中一类拟凸超曲面定义在原点邻域内的实解析无穷小CR自同构,并得到了这类超曲面在原点处稳定群的单位连通分支.     

Determination of a Homogeneous Strictly Pseudoconvex Surface from the Coefficients of Its Normal Equation

Mathematical Notes -     

Variational composition of a monotone operator and a linear mapping with applications to elliptic PDEs with singular coefficients

This paper proposes a regularized notion of a composition of a monotone operator with a linear mapping. This new concept, called variational composition, can be shown to be maximal monotone in many cases where the usual composition is not. The two notions coincide, however, whenever the latter is maximal monotone. The utility of the variational composition is demonstrated by applications to subdifferential calculus, theory of measurable multifunctions, and elliptic PDEs with singular coefficients.     

On Set-Valued Differentiation and Integration

Both the notion of differential of a set-valued mapping and the concept of a set-valued integral are introduced in such a way that, on the one hand, the class of differentiable mappings is rather extensive, while on the other hand, the concept of integral includes as special cases Dinghas' approach and Pontryagin's alternated integral. At the same time, the differential of an integral with respect to the upper limit of integration equals in some sense the integrant. Thus the differentiation of a set-valued mapping can be interpreted as an operation inverse to set-valued integration. Both the differential and the integral are defined via approximation by quasi-affine mappings introduced below. The class of quasi-affine mappings is compared with the classes of affine, semi-affine, eclipsing and multi-affine mappings.     

集值映射空间上的Tightness和Fan Tightness

本文讨论了连续集值映射空间在赋予点态收敛拓扑和紧开拓扑下的tightness和fan tightness, 将关于连续单值映射空间的某些结果推广到连续集值映射空间.     

Representations of Affine Multifunctions by Affine Selections

The paper deals with affine selections of affine (both convex and concave) multifunctions acting between finite-dimensional real normed spaces. It is proved that each affine multifunction with compact values possesses an exhaustive family of affine selections and, consequently, can be represented by its affine selections. Moreover, a convex multifunction with compact values possesses an exhaustive family of affine selections if and only if it is affine. Thus the existence of an exhaustive family of affine selections is the characteristic feature of affine multifunctions which differs them from other convex multifunctions with compact values. Besides a necessary and sufficient condition for a concave multifunction to be affine on a given convex subset is also proved. Finally it is shown that each affine multifunction with compact values can be represented as the closed convex hull of its exposed affine selections and as the convex hull of its extreme affine selections. These statements extend the Straszewicz theorem and the Krein–Milman theorem to affine multifunctions. Dedicated to Boris Mordukhovich in honour of his 60th birthday.     

Metric regularity of composition set-valued mappings: Metric setting and coderivative conditions

The paper concerns a new method to obtain a proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years in the literature. In turn, these techniques are based on several important concepts (like error bounds, lower semicontinuous envelope of a set-valued map, local composition stability of multifunctions) and allow us to obtain two new proofs of a recent result having deep roots in the topic of regularity of mappings. Moreover, we make clear the idea that it is possible to use (co)derivative conditions as tools of proof for openness results in very general situations.     

Levi problem and semistable quotients

A complex space X is in class 𝒬 _G if it is a semistable quotient of the complement to an analytic subset of a Stein manifold by a holomorphic action of a reductive complex Lie group G. It is shown that every pseudoconvex unramified domain over X is also in 𝒬 _G .