A link surgery spectral sequence in monopole Floer homology

To a link L⊂S³, we associate a spectral sequence whose E² page is the reduced Khovanov homology of L and which converges to a version of the monopole Floer homology of the branched double cover. The pages Ek for k?2 depend only on the mutation equivalence class of L. We define a mod 2 grading on the spectral sequence which interpolates between the δ-grading on Khovanov homology and the mod 2 grading on Floer homology. We also derive a new formula for link signature that is well adapted to Khovanov homology.More generally, we construct new bigraded invariants of a framed link in a 3-manifold as the pages of a spectral sequence modeled on the surgery exact triangle. The differentials count monopoles over families of metrics parameterized by permutohedra. We utilize a connection between the topology of link surgeries and the combinatorics of graph-associahedra. This also yields simple realizations of permutohedra and associahedra, as refinements of hypercubes.     

Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms

Using ideas and results from polynomial time approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular two paradigmatic problems, max independent set and min vertex cover.     

涟漪效应还是空间互动——基于空间面板联立方程模型的房价与地价关系研究

本文通过构建包含房价和地价在内的空间面板联立方程模型,利用2009～2016年中国286个地市的数据,构建空间面板联立方程模型,以研究房价和地价的空间自相关性和空间溢出效应。实证结果表明：房价与地价之间的空间互动作用明显,房价不但受到当地地价的影响还会受到周边城市房价的影响;而城市地价也会受到当地房价引起的引致需求影响,并且受到周边城市地价的影响。分区域来看,地价对房价的作用强度在东、中、西部地区依次下降,房价对地价作用强度呈现出相反的趋势。而从价格的溢出效应来看,无论是房价还是地价,西部地区的价格溢出效应都最为明显,表明相对于东、中部地区,西部地区城市在房价和地价上都更会受到周围城市的影响。     

Coarse Baum-Connes conjecture

In this paper, we shall prove the coarse Baum-Connes conjecture for metric spaces with Lipschitz good covers. This class of metric spaces includes trees and simply connected nonpositively curved manifolds.Supported by DMS8505550 through a MSRI Postdoctoral Fellowship.     

A note on the edge cover chromatic index of multigraphs

Let G be a multigraph with vertex set V(G). An edge coloring C of G is called an edge-cover-coloring if each color appears at least once at each vertex v∈V(G). The maximum positive integer k such that G has a k-edge-cover-coloring is called the edge cover chromatic index of G and is denoted by . It is well known that , where μ(v) is the multiplicity of v and δ(G) is the minimum degree of G. We improve this lower bound to δ(G)−1 when 2≤δ(G)≤5. Furthermore we show that this lower bound is best possible.     

点删除下的图的$A_\alpha$特征值的交错性

设$G$为具有顶点集$V$, 边集$E$的简单图, 本文给出了图$G$与其子图$G-U$的$A_\alpha$特征值的交错不等式, 其中$U\subset V$. 作为应用, 我们利用该交错不等式导出了一些关于图的独立数, 点覆盖数, 哈密尔顿性及支撑数的$A_\alpha$ 谱条件.     

Finiteness conditions and PD<Subscript><Emphasis Type="Italic">r</Emphasis></Subscript>-group covers of PD<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-complexes

We show that an infinite cyclic covering space M′ of a PD _n -complex M is a PD _n-1-complex if and only if χ(M) = 0, M′ is homotopy equivalent to a complex with finite [(n−1)/2]-skeleton and π₁(M′) is finitely presentable. This is best possible in terms of minimal finiteness assumptions on the covering space. We give also a corresponding result for covering spaces M _ν with covering group a PD _r -group under a slightly stricter finiteness condition.      

Boundary case of equality in optimal Loewner-type inequalities

We prove certain optimal systolic inequalities for a closed Riemannian manifold , depending on a pair of parameters, and . Here  is the dimension of , while is its first Betti number. The proof of the inequalities involves constructing Abel-Jacobi maps from to its Jacobi torus  , which are area-decreasing (on -dimensional areas), with respect to suitable norms. These norms are the stable norm of , the conformally invariant norm, as well as other -norms. Here we exploit -minimizing differential 1-forms in cohomology classes. We characterize the case of equality in our optimal inequalities, in terms of the criticality of the lattice of deck transformations of  , while the Abel-Jacobi map is a harmonic Riemannian submersion. That the resulting inequalities are actually nonvacuous follows from an isoperimetric inequality of Federer and Fleming, under the assumption of the nonvanishing of the homology class of the lift of the typical fiber of the Abel-Jacobi map to the maximal free abelian cover.

     

电解电容器负极引出部位发生跳火的理论研究

研究了在特大纹波电流下电解电容器发生负极跳火的现象。通过对电容器的充放电过程模型进行分析,指出跳火的根本原因在于电容器负极铆接或冷压焊接的引出部位容量很小,会产生反向的电压并逐渐对引出部位进行电压化成,因此产生负极跳火现象。采用负极引出贴箔或增容处理工艺,可有效避免负极跳火,135℃,2000h试验后电容器的失效率为0。