Classification of edges using compactly supported shearlets

We analyze the detection and classification of singularities of functions $f={\chi }_S$, where $S?{\mathbb{R}}^d$ and $d=2,3$. It will be shown how the set ?S can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ?S is a $d?1$ dimensional piecewise smooth manifold with $d=2$ or 3, we will classify smooth and non-smooth components of ?S. This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in 3 dimensions by compactly supported shearlets. Finally, geometric properties of ?S such as curvature are described in terms of the continuous shearlet transform of f.     

感应熔炼高锰硅的结构和形貌特性

采用场发射扫描电镜(FESEM)和X射线能谱仪(EDXS)对感应熔炼高锰硅(HMS)中的第二相条纹的形貌和成份进行了研究,发现第二相条纹平行贯穿整个高锰硅晶粒,其条纹宽度约30nm,间距在5-30μm内,成份为MnSi.通过高分辨透射电镜(HRTEM)观察到MnSi条纹为短程有序而长程无序的非晶形态.采用选区电子衍射(SAED)确定了高锰硅的晶体结构,结果表明所获得的高锰硅为单一的Mn4Si7相,未观察到高锰硅其它的非公度结构.透射电镜(TEM)结果表明,熔炼的高锰硅经过球磨和热压后产生了大量缺陷和应力畴,与热压之前的熔锭材料相比有明显差异.     

A universal differentiability set in Banach spaces with separable dual

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fréchet differentiable somewhere in S.     

Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.     

Global decaying solution to dissipative nonlinear evolution equations with ellipticity

We establish the global existence and decaying results for the Cauchy problem of nonlinear evolution equations:

(E)     

Failure of n‐uniqueness: a family of examples

In this paper, the connections between model theory and the theory of infinite permutation groups (see 11 ) are used to study the n‐existence and the n‐uniqueness for n‐amalgamation problems of stable theories. We show that, for any n ? 2, there exists a stable theory having (k + 1)‐existence and k‐uniqueness, for every k ? n, but has neither (n + 2)‐existence nor (n + 1)‐uniqueness. In particular, this generalizes the example, for n = 2, due to Hrushovski given in 3 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Cluster tilting for higher Auslander algebras

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten translation functor τn plays an important role in the study of n-cluster tilting subcategories. We study the category Mn of preinjective-like modules obtained by applying τn to injective modules repeatedly. We call a finite-dimensional algebra Λ n-complete if for an n-cluster tilting object M. Our main result asserts that the endomorphism algebra EndΛ(M) is (n+1)-complete. This gives an inductive construction of n-complete algebras. For example, any representation-finite hereditary algebra Λ(1) is 1-complete. Hence the Auslander algebra Λ(2) of Λ(1) is 2-complete. Moreover, for any n?1, we have an n-complete algebra Λ(n) which has an n-cluster tilting object M(n) such that Λ(n+1)=EndΛ(n)(M(n)). We give the presentation of Λ(n) by a quiver with relations. We apply our results to construct n-cluster tilting subcategories of derived categories of n-complete algebras.     

Quasi-hereditary covers of higher zigzag algebras of type A

In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Δ, according to the definition given in [24]. This last property gives rise to a well defined duality and we compute the Δ-Koszul dual as the path algebra of a quiver with relations.     

函数两种凸性定义等价性的今惑前世之初探

通过研究中点凸函数和一般凸函数这两种凸性定义的早期发展历史和凸性性质来探索两种凸性定义的等价性.结果表明,两种凸性定义不等价;但是,当函数满足连续、可微、半连续和有界这四个条件中的任何一个条件时,两种凸性定义等价.     

新超复结构和Clifford分析

本文在Ｈ．Ｍａｌｏｎｅｋ［１］新的超复结构的意义下，研究Ｃｌｉｆｆｏｒｄ分析中Ａ值函数超复可微性及其一种新的锁链规则和微分法则．