On the geometry of the Batalin–Vilkovisky formalism

In this work it is proved that the geometry of the well-known quantization scheme of general gauge theories, the so-called Batalin–Vilkovisky formalism, is the odd Riemannian geometry. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 28–31, November, 2008.     

Flow prolongation of some tangent valued forms

We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.     

Manifold of nondegenerate affinor fields

We consider the quotient set of the set of nondegenerate affinor fields with respect to the action of the group of nowhere vanishing functions. This set is endowed with a structure of infinite-dimensional Lie group. On this Lie group, we construct an object of linear connection with respect to which all left-invariant vector fields are covariantly constant (the Cartan connection).     

并联电感线圈的电流分配

用复频域分析法精确计算了并联电感线圈的暂态过程解，讨论了并联电感线圈的电流比等于其电阻反比的条件。     

部分剪力连接钢—砼组合梁的滑移及曲率分析

对受均布荷载作用的简支部分剪力连接钢－砼组合梁的滑移应变和滑移的分布规律进行了理论分析,得出部分剪力连接钢－砼组合梁的剪力连接程度系数与滑移应变和滑移的关系。分析了考虑滑移效应的梁的曲率及其与剪力连接程度系数之间的关系。结果与结构在弹性阶段的实验相当吻合,对组合梁挠度的精确计算有指导意义。     

射影半对称联络的一个不变量

本文研究与Levi-Civita联络▽射影等价地射影半对称联络D。获得了一个射影不变量,并给出其成立的一个充分必要条件。进而给出其保持相应共变导数不变的另一充分条件。     

利用变压器研究两个互感线圈的串并联

利用变压器研究了两个互感线圈串并联的等效电感。     

Distinguished Connections on Finsler Algebroids

Considering the prolongation of a Lie algebroid,the authors introduce Finsler algebroids and present important geometric objects on these spaces.Important endomorphisms like conservative and Barthel,Cartan tensor and some distinguished connections like Berwald,Cartan,Chern-Rund and Hashiguchi are introduced and studied.     

On holonomy of Weyl connections in Lorentzian signature

Holonomy algebras of Weyl connections in Lorentzian signature are classified. In particular, examples of Weyl connections with all possible holonomy algebras are constructed.