Configuration controllability for non-zero potential mechanical control systems with dissipation

Introduction Mechanicalcontrolsystemspresentachallengingandpromisingresearchareabetweenthe studyofclassicalmechanicsandmodernnonlineargeometriccontroltheory.Forthestudyof mechanicalcontrolsystems,therichresultshavebeenproducedwithintheHamiltonian frameworkandLagrangianframework,respectively[1,2].FromtheLagrangianperspective,itis worthwhiletomentiontheconfigurationcontrollabilitynotions,recentlyintroducedbyLewisandMurray[3,4]forsimplemechanicalcontrolsystemswhoseLagrangianiskineticenergy minu…     

钢结构框架中组合梁等效刚度的确定方法

刚接或半刚性连接的组合梁在荷载作用下,在梁的长度范围内既有正弯矩作用段,又有负弯矩作用段,由于组合梁截面在正弯矩作用和负弯矩作用下截面抗弯刚度不一致,因而在弯矩为零的点处梁的截面抗弯刚度发生突变,而组合梁框架分析的关键是确定组合梁刚度突变分界点的位置及确定在整体分析中所采用的等效梁的刚度。本文根据应变能相等的原理对钢结构框架中组合梁的等效抗弯刚度进行了研究,推导了其等效刚度的表达式,并给出不同荷载作用形式下刚接框架组合梁等效刚度简化计算公式,为组合梁钢框架的整体分析提供了便利。最后分析了水平荷载以及梁柱连接特性对组合梁等效刚度的影响,分析结果表明,采用本文提出的组合梁等效刚度进行半刚性连接框架整体分析偏于安全。     

局部网格生成中初始探索圆半径的搜索算法

无网格不一致性的基于节点的局部网格生成(NLMG)算法是基于节点的局部有限元方法(NLFEM)实现无缝连接的核心算法之一,而快速合理的确定中心节点的初始探索圆半径是降低NLMG算法计算量和确保其可靠性的关键一步。本文提出了基于均匀桶的快速局部搜索算法(UBFLSM),并将其成功应用于NLMG算法,解决了初始探索圆半径和探索圆半径优化后候选卫星点集的确定这两个难点,确保NLMG算法无网格不一致性。并/串行数值试验(实现从网格生成到总刚度矩阵生成之间的无缝连接)均表明,该算法是快速及可靠的。     

基于网络的主动跟踪框架

在分析现有入侵检测系统跟踪方法的基础上，提出了一种基于网络的主动跟踪模型及体系结构，并对其工作机制进行了描述。     

简单图的一种计数方法

对某一类图的邻接矩阵进行分类 ,从而给出这类图的一种计数方法 ,并且这种方法比较原来的Polya方法更为可行 .     

Influence of the vacuum on the separation efficiency in coupled (GC)2-MS

Summary The van Deemter polts for the same glass capillary column one coupled to an FID detector and once to an MS instrument are compared. With full vacuum at the capillary end the column still produces 75% of the maximum attinable separation efficiency.     

Diffeomorphisms preserving R‐circles in three dimensional CR manifolds

R ‐circles in (non‐degenerate) three dimensional CR manifolds are the analogues to traces of Lagrangian totally geodesic planes on S³ viewed as the boundary of two dimensional complex hyperbolic space. They form a family of certain Legendrian curves on the manifold. We prove that a diffeomorphism between three dimensional CR manifolds which preserve circles is either a CR diffeomorphism or a conjugate CR diffeomorphism.     

The coupling constant averaged exchange–correlation energy density

ABSTRACT

The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy.     

Connections and Higgs fields on a principal bundle

Let M be a compact connected Kähler manifold and G a connected linear algebraic group defined over \({\mathbb{C}}\) . A Higgs field on a holomorphic principal G-bundle ε _G over M is a holomorphic section θ of \(\text{ad}(\epsilon_{G})\otimes {\Omega}^{1}_{M}\) such that θ∧ θ = 0. Let L(G) be the Levi quotient of G and (ε _G (L(G)), θ _l ) the Higgs L(G)-bundle associated with (ε _G , θ). The Higgs bundle (ε _G , θ) will be called semistable (respectively, stable) if (ε _G (L(G)), θ _l ) is semistable (respectively, stable). A semistable Higgs G-bundle (ε _G , θ) will be called pseudostable if the adjoint vector bundle ad(ε _G (L(G))) admits a filtration by subbundles, compatible with θ, such that the associated graded object is a polystable Higgs vector bundle. We construct an equivalence of categories between the category of flat G-bundles over M and the category of pseudostable Higgs G-bundles over M with vanishing characteristic classes of degree one and degree two. This equivalence is actually constructed in the more general equivariant set-up where a finite group acts on the Kähler manifold. As an application, we give various equivalent conditions for a holomorphic G-bundle over a complex torus to admit a flat holomorphic connection.