From triangulated categories to abelian categories: cluster tilting in a general framework

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (i.e., a maximal 1-orthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.      

6α,7α-epoxy-5α,17α,dihydroxy-1-oxo-22R-witha-2,24-dienolide in leaves of Withania somnifera: Isolation and its crystal structure

6α,7α-epoxy-5α,17α,dihydroxy-1-oxo-22R-witha-2,24-dienolide (C₂₈H₃₈O₆) was isolated from Withania somnifera leaves. The structure of the withanolide was established by spectral analysis and X-ray diffraction studies as withanone. The compound crystallizes in the orthorhombic space group P2₁2₁2₁ with unit cell parameters: a = 9.191(10) Å, b = 12.858(6) Å, c = 21.400(16) Å, Z = 4. The crystal structure was solved by direct methods and refined to R = 0.0603 for 1742 observed reflections. There is positional disorder of the H atom in a hydroxy group (O5), resulting in two possible hydrogen-bond linkages. All the rings of the steroid skeleton are trans connected. Ring A exists in a half-chair conformation, ring B is intermediate between a half-chair and a sofa, ring C a distorted chair, and five-membered ring D is intermediate between a half-chair and an envelope. The δ-lactone ring E adopts a sofa conformation. The twist along the length of the steroid nucleus is negligible [C19–C10…C13–C18=1.8°]. Both the hydroxy groups are involved in hydrogen bonding.     

Cohomology theories based on Gorenstein injective modules

In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing.

     

Generalization performance of graph-based semi-supervised classification

Semi-supervised learning has been of growing interest over the past few years and many methods have been proposed. Although various algorithms are provided to implement semi-supervised learning,there are still gaps in our understanding of the dependence of generalization error on the numbers of labeled and unlabeled data. In this paper,we consider a graph-based semi-supervised classification algorithm and establish its generalization error bounds. Our results show the close relations between the generalizat...     

多脉冲强流真空电子二极管研究

研究了猝发脉冲串条件下真空强流电子二极管状态和输出电子束参数的变化规律, 建立了阴极等离子体膨胀效应的强流电子二极管参量的方程组, 并提出了阴极等离子体柱状膨胀模型. 实验研究了猝发多脉冲电子二极管输出多脉冲强流电子束的能力和束品质的变化, 给出了以天鹅绒为阴极发射体, 阴极等离子体膨胀速度小于1cm/μs时二极管输出的双脉冲电子束包络的变化和电子束的发射度及亮度.     

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R² and their distance functions. The L² norm of the difference of characteristic functions, the L and the W^1,2 norms of the difference of distance functions define interesting topologies, in particular the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ² of positive reach in the sense of Federer [16], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem.We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational definitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples.     

Finite Order Rank-One Convex Envelopes and Computation of Microstructures with Laminates in Laminates

Finite order rank-one convex envelopes are introduced and it is shown that the i-th order laminated microstructures, or laminates in laminates, can be solved by any of the k-th order rank-one convex envelopes with k i. It is also shown that in finite element approximations of microstructures, replacing the non-quasiconvex potential energy density by its k-th order rank-one convex envelope, one can generally obtain sharper numerical results. Especially, for crystalline microstructures with laminates in laminates of order no greater than k + 1, numerical results with up to the computer precision can be obtained. Numerical examples on the first and second order rank-one convex envelopes for the Ericksen-James two-dimensional model for elastic crystals are given. A numerical example on finite element approximations of a crystalline microstructure by using the first order rank-one convex envelope and the periodic relaxation method is also presented. The methods turn out to be very successful for microstructures with laminates in laminates.     

一类广义遗传环

称环R为左亚遗传环，如果内射左R－模的商模是FG－内射的，给出了左亚遗传环的一些刻划，给出了左亚遗传环的半单环的条件，并研究了左亚遗传环的一些性质。     

丙型肝炎病毒包膜蛋白E1在小鼠和家兔中免疫应答研究

探讨丙型肝炎病毒包膜蛋白E1作为丙肝候选疫苗的可行性．用大肠杆菌表达的非糖基化HCV(丙型肝炎病毒)E1包涵体蛋白免疫小鼠和家兔，分析该包涵体蛋白在小鼠和家兔中所引起的免疫应答及其安全性．该E1蛋白具有良好的免疫原性，能诱导小鼠和家兔产生针对E1的特异性体液免疫应答．小鼠CD8^ T细胞数量在免疫后有明显升高．免疫小鼠未见明显的毒副作用．推测HCV E1这种包涵体结构可能有利于E1抗原的呈递．而HCV E1蛋白的糖基化并不是其免疫原性所必须的．     

Modulational instability and envelope solutions of nonlinear dispersive wave equations

The nonlinear Schrödinger equation describing the evolution of the plane wave solutions of the Hirota equation and of the Boussinesq equation are obtained. The conditions for modulational instability and the localised stationary solutions are derived.