A local proof for the characterization of Young measures generated by sequences in BV

This work presents a new proof of the recent characterization theorem for generalized Young measures generated by sequences in BV by Kristensen and Rindler (2010) [14]. The present argument is based on a localization technique together with a local Hahn–Banach argument in novel function spaces combined with an application of Alberti's Rank-One Theorem. This strategy avoids employing a relaxation theorem as in the previously known proof, and the new tools introduced in its course should prove useful in other contexts as well. In particular, we introduce “homogeneous” Young measures, separately at regular and singular points, which exhibit rather different behavior than the classical homogeneous Young measures. As an application, we show how for BV-Young measures with an “atomic” part one can find a generating sequence respecting this structure.     

CMOS工艺中NPN bipolar的开发

由于技术的迅速发展与突破,使集成电路的制造得以在短短的60年间,单一晶粒已经可以容纳数千万个电晶体的超大型集成电路。其主要工艺为CMOS工艺,原因是它有功耗低、集成度高、噪声低、抗辐射能力强等优点,但是传统bipolar工艺有频率高、功率大的优点,因此提出在CMOS中集成三极管、二极管。论述了在0.5μm CMOS工艺中集成NPN bipolar的方法以及各个关键技术指标的确定。     

DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHEODORY SPACES

The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the     

4H-SiC基超结器件各向异性的TCAD建模分析

基于文献报道的4H-SiC材料的各向异性物理特性,首次提出4H-SiC基超结器件的各向异性物理模型,并对不同晶向的碰撞电离分别进行考虑。基于该模型,我们对 和 两种晶向晶圆的4H-SiC超结器件的电学特性进行了研究。与 晶圆相比, 晶圆的碰撞电离系数较小,可以实现更高的击穿电压。由于碰撞电离各向异性,与传统4H-SiC基器件相比,超结器件的二维电场分布可以将 晶圆器件的击穿电压从 晶圆器件的60%提高到72%。     

Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems

We provide some lower semicontinuity results in the space of special functions of bounded deformation for energies of the type and give some examples and applications to minimum problems, arising in Fracture Mechanics for linearly elastic materials. Copyright © 2011 John Wiley & Sons, Ltd.     

临界增长的1-Laplace 方程的非负解

在BV 空间中研究如下一类含临界指数的1-Laplace 方程非负解的存在性:
-Div(Du/|Du|)=g(x, u)+|u|^1*-2u, x∈Ω,
其中Ω⊂R^N 为有界光滑开区域, 1^*=N/(N-1),g(x, u) 为Carathéodory 函数.     

Knot invariants and new weight systems from general 3D TFTs

We introduce and study the Wilson loops in general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in the Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the Ward identities of these theories imply that the expectation value of the Wilson loop is a pairing of two dual constructions of (co)cycles of certain extended graph complex (extended from Kontsevich’s graph complex to accommodate the Wilson loop). We also prove that there is an isomorphism between the same complex and certain extended Chevalley-Eilenberg complex of Hamiltonian vector fields. This isomorphism allows us to generalize the Lie algebra weight system for knots to weight systems associated with any homological vector field and its representations. As an example we construct knot invariants using holomorphic vector bundle over hyperKähler manifolds.     

Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions

The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions （2000）. The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form
δtfi＋（fi^mi）=Qi（f1,f2...,fn）,（mi〉1,i-1,...n）
with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.     

DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHÉODORY SPACES

The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Carathéodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L¹ functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = ∇u · Lⁿ + X^sи is proved, where и ∈ BVx(Ω) and ∇u denotes the approximate differential of u.     

Identification of Potential Anti-Neuroinflammatory Inhibitors from Antarctic Fungal Strain Aspergillus sp. SF-7402 via Regulating the NF-κB Signaling Pathway in Microglia

Microglia play a significant role in immune defense and tissue repair in the central nervous system (CNS). Microglial activation and the resulting neuroinflammation play a key role in the pathogenesis of neurodegenerative disorders. Recently, inflammation reduction strategies in neurodegenerative diseases have attracted increasing attention. Herein, we discovered and evaluated the anti-neuroinflammatory potential of compounds from the Antarctic fungi strain Aspergillus sp. SF-7402 in lipopolysaccharide (LPS)-stimulated BV2 cells. Four metabolites were isolated from the fungi through chemical investigations, namely, 5-methoxysterigmatocystin (1), sterigmatocystin (2), aversin (3), and 6,8-O-dimethylversicolorin A (4). Their chemical structures were elucidated by extensive spectroscopic analysis and HR-ESI-MS, as well as by comparison with those reported in literature. Anti-neuroinflammatory effects of the isolated metabolites were evaluated by measuring the production of nitric oxide (NO), tumor necrosis factor (TNF)-α, and interleukin (IL)-6 in LPS-activated microglia at non-cytotoxic concentrations. Sterigmatocystins (1 and 2) displayed significant effects on NO production and mild effects on TNF-α and IL-6 expression inhibition. The molecular mechanisms underlying this activity were investigated using Western blot analysis. Sterigmatocystin treatment inhibited NO production via downregulation of inducible nitric oxide synthase (iNOS) expression in LPS-stimulated BV2 cells. Additionally, sterigmatocystins reduced nuclear translocation of NF-κB. These results suggest that sterigmatocystins present in the fungal strain Aspergillus sp. are promising candidates for the treatment of neuroinflammatory diseases.