Parity and the spin—statistics connection

A simple demonstration of the spin—statistics connection for general causal fields is obtained by using the parity operation to exchange spatial coordinates in the scalar product of a locally commuting field operator, evaluated at position x, with the same field operator evaluated at − x, at equal times.     

串—并联系统的可靠性分析

本利用侯振挺等提出的马尔可夫骨架过程理论讨论了串一并联系统的可靠性．     

CP^n中法联络平坦的全实子流形

获得了ＣＰ＾ｎ中法联络平坦的全实子流形成为全脐点子流形的若干特征。     

Solutions of Euler-Lagrange equations for self-interacting field of linear frames on product manifold of group space

We investigate a model of self-interacting field of linear frames on the product manifold M × G, where G is a semisimple Lie group acting freely and transitively on a manifold M. We find two families of solutions of the Euler-Lagrange equations for the field of frames.     

Constructive Solvability Conditions for the Riemann-Hilbert Problem

Sufficient and necessary conditions for the solvability of the Riemann-Hilbert problem are studied. These conditions consist in the possibility of constructing stable and semistable pairs (of bundles and connections) for a given monodromy. The obtained results make it possible to develop algorithms for testing the solvability conditions for the Riemann-Hilbert problem.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 643–655.Original Russian Text Copyright ©2005 by I. V. V’yugin.I dedicate this work to the blessed memory of my teacher Andrei Andreevich Bolibrukh     

基于联系数的预先危险性分析技术与应用

工程施工中的预先危险性分析受到随机、模糊、不确知等多种不确定性的干扰 ,采用集对分析联系数对客观存在的不确定性作系统描述 ,形成一种计及不确定性的预先危险性分析新技术 ,为工程施工预防安全事故、安全检查与评估提供了一种新的科学分析方法 .     

The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids

This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either ℝ or sl(2, ℝ) or so(3) are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to n + 1, where n is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For ℝ-Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf theorem for flat connections) saying that the index sum is independent of the choice of a connection. Multiplying this index sum by the orientation class of M, we get the Euler class of this Lie algebroid. Some integral formulae for indices are given.     

On the existence of prolongation of connections

We classify all bundle functors G admitting natural operators transforming connections on a fibered manifold Y → M into connections on GY → M. Then we solve a similar problem for natural operators transforming connections on Y → M into connections on GY → Y. Dedicated to Professor Ivan Kolář on the occasion of his 70th birthday     

Irreducible Fuchsian system with reducible monodromy representation

We present an example of the reducible representation χ = χ₁ ? χ₂, which, on the one hand, is the monodromy representation of a Fuchsian system. On the other hand, the representation χ₂ is a counterexample to the Riemann-Hilbert problem. Using a meromorphic gauge transformation, one cannot reduce this system to the direct sum of Fuchsian systems corresponding to the subrepresentations.     

A Link Between Two Connectedness Notions

The composition of two previously introduced Galois connections is used to provide a wider perspective on the Clementino–Tholen connectedness versus separation Galois connection. Moreover, a link between this and Castellini's connectedness–disconnectednes Galois connection is also presented.