Classical and Quantum Nonultralocal Systems on the Lattice

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix . A nonultralocal quantum algebras on the lattices for these systems are constructed.For some class of such algebras an ultralocalization procedure is proposed.The technique of the modified Bethe-Anzatz for these algebras is developed.This technique is applied to the nonlinear sigma model problem.Comment: 33 pp. Latex. The file is resubmitted since it was spoiled during transmissio

Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case

The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic deformation of the Lie bialgebra structure on the associated loop algebra. The related classical r-matrix is explicitly described in terms of the Coxeter transformation. We also present a cross-section theorem for q-gauge transformations which generalizes a theorem due to R.Steinberg.Comment: 19 pp., AMS-LaTeX. The paper replaces a temporarily withdrawn text; the first part (written by E. Frenkel, N. Reshetikhin, and M. A. Semenov-Tian-Shansky) is available as q-alg/970401

Higgsless Electroweak Theory following from the Spherical Geometry

A new formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The free Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same fields with the same masses as the Standard Electroweak Model. The vector bosons and electron masses are generated automatically, so there is no need in special mechanism.Comment: 6 page

Theory and practice of unit creation for technogenic material compacting

No Abstrac

Multiplicative slices, relativistic Toda and shifted quantum affine algebras

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces. In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.Comment: 125 pages. v2: references updated; in section 11 the third local Lax matrix is introduced. v3: references updated. v4=v5: 131 pages, minor corrections, table of contents added, Conjecture 10.25 is now replaced by Theorem 10.25 (whose proof is based on the shuffle approach and is presented in a new Appendix). v6: Final version as published, references updated, footnote 4 adde

Processing of basalt fiber production waste

The production of mineral rock wool forms a large proportion of off-test waste products. In addition to the cost of their production, there are costs for processing and utilization, such as transportation, disposal and preservation. Besides, wastes have harmful effect on the environment. This necessitates research aimed to study the stress-related characteristics of materials, their recyclability and use in the production of heat-saving product

Schwinger particle production: rapid switch off of the external field versus dynamical assistance

We consider the process of electron-positron pair production in the presence of strong electric backgrounds being rapidly switched on and off and examine the total particle yield. For sufficiently sharp field profiles, the particle number can be substantially enhanced. It is demonstrated that this enhancement is quite similar to the phenomenon of dynamical assistance by a weak high-frequency field superimposed on a strong background. Both these mechanisms are analyzed by means of exact numerical computations and the locally-constant field approximation. We identify the time scale of the switching profile leading to the pair-production enhancement and argue that the particle yield is highly unlikely to be increased by shaping the switch off of realistic laser pulses. On the other hand, we confirm that it is feasible to observe the dynamically assisted Schwinger effect by adding a rapidly oscillating field to a strong electric background.Comment: 9 pages, 5 figures, 1 tabl

Kinetic description of vacuum e+e−e^+ e^- production in strong electric fields of arbitrary polarization

We present a detailed analysis of the self-consistent system of kinetic equations (KEs) describing electron-positron pair production from vacuum under the action of a spatially homogeneous time-dependent electric field of arbitrary polarization. The physical significance of all the basic functions of the kinetic theory is ascertained. It is demonstrated that the total system of the KEs consists of two coupled quasiparticle and spin subsystems with their integrals of motion. A projection method is proposed in order to obtain the KE system in two particular cases: linearly polarized external electric field and (2+1)-dimensional description of quasiparticles in graphene. We also address the energy conservation law taking into account the internal plasma field and describe an alternative rigorous derivation of the KE system.Comment: 15 page

Process organisation modelling for maintaining rail track geometry

Introduction. The increase in freight traffic density and axial loads on the Eastern polygon is affecting the condition of the railway and reducing the time available for maintenance. The increased workload caused by track deformation in difficult operating conditions makes the planning and organisation of railway maintenance work much more difficult. One of the main factors affecting the safety and smooth running of trains is the geometry of the rail track, which is kept in a normal condition by track maintenance. The study examines the problem of increasing the efficiency of maintaining rail track geometry.Materials and methods. Mathematical modelling and statistical methods were used to solve the problem. A process organisation model was created based on formalising the process of incoming and outgoing work. The estimated workload required to rectify the identified deviations was determined on the basis of the results of the track condition assessment using track measuring devices, taking into account the regulatory time standards for their rectification.Results. The mathematical model for the process organisation of rail track geometry maintenance is presented, which allows to determine the necessary level of daily workload on a linear section to perform the full scope of works within the regulated terms, which would reduce the desicion time during the planning of works.Discussion and conclusion. The use of this model makes it possible to simplify the planning and organisation of work on a section of track, which is particularly important at a high level of urgent and high-priority work on particularly heavy-traffic sections. Further research would focus on the development of a mathematical model, the development of a software product and its implementation into a unified enterprise automated infrastructure management system

Constructive and Technological Features of Units for Milling Polymer Material

Constructive and Technological Features of Units for Milling Polymer Material / V. S.Sevostyanov [et al.] // IOP Conf. Series: Journal of Physics. - 2018. - Vol.1066. - 012006.This article presents specific physical and mechanical properties of techno genic poly-mer materials. The features of their processing are revealed. The ways of constructive and techno-logical perfection of grinders are proposed, namely, the creation of units based on needle-milling working parts that ensure selective complex influence on the processed materials with the cantile-vered ends of their rod elements and the creation of energy-efficient mechanisms of destruction