let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

The pantograph-overhead contact wire system is investigated by using an infrared camera. As the pantograph has a vertical motion because of the non-uniform elasticity of the catenary, in order to detect the temperature along the strip from a sequence of infrared images, a segment-tracking algorithm, based on the Hough transformation, has been employed. An analysis of the stored images could hel...

Non-diffracting Bessel beams, including zero-order and high-order Bessel Beams which carry orbital angular momentum (OAM), enable a variety of important applications in optical micromanipulation, sub-diffraction imaging, high speed photonics/quantum communication, etc. The commonly used ways to create Bessel beams, including an axicon or a digital hologram written to a spatial light modulator (...

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 ...

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...

We show that group algebras kG of polycyclic-by-finite groups G, where k is a field, are catenary: If P = I0 I1 · · · Im = P ′ and P = J0 J2 · · · Jn = P ′ are both saturated chains of prime ideals of kG, then m = n.