The paper describes modelling and control techniques studied and applied to selected pantograph-catenary (PAC) systems. The work has been co-funded by the European Union under the ERDF project: PAntograph-Catenary Interaction Framework for Intelligent Control (PACIFIC). Mechanical models of PAC systems are implemented in MATLAB using novel techniques, where applicable. Next, important physical ...

1.1. We will define a D-module of differential operators on a smooth stack and construct a symbol map when the stack is good, but first we need to give definition of a D-module on a stack. D-modules are local for the smooth topology, so one’s naive guess for the definition of a D-module on a smooth Artin stack is correct. That is, a (left or right) D-module M on X is the assignment for each U π...

Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let g I be the corresponding semi-simple subalgebra of g. Denote by W I the Weyl group of g I and let w • and w I • be the longest elements of W and W I , respectively. In this paper we show that the answer to Kostant's problem, i.e. whether the universal enveloping algebra surjec...

The element $q$ of a ring $R$ is called quasi-idempotent if $q^2=uq$ for some central unit $u$ $R$, or equivalently $q=ue$, where and $e$ an idempotent $R$. In this paper, we define that the almost quasi-clean each sum regular element. Several properties almost-quasi clean rings are investigated. We prove every quasi-continuous nonsingular quasi-clean. Finally, it determined conditions under wh...

Defective droppers pose a significant threat to the performance of contact between train pantograph and railway catenary. In this paper, impact damaged on pantograph–catenary interaction behaviour is analysed, varying degrees damage each dropper labelled. To improve classification accuracy when both degree position are considered, model integrating multiple 1D CNNs proposed. Approaches includin...

With the increasing speed of urban rail trains, vibration between pantograph collector strip and contact wire intensifies, pantograph-catenary arc occurs frequently, which severely wear surface materials pantograph-catenary. The burning strength extinguishing characteristics are affected by temperature parameters. Based on theory magnetohydrodynamics, this paper establishes a mathematical model...

Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring,  named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists  such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...

A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...