On classical description of radiation from neutral fermion with anomalous magnetic moment

Electromagnetic radiation from an uncharged spin 1/2 particle with an anomalous magnetic moment moving in the classical electromagnetic external field originates from quantum spin-flip transitions. Although this process has a purely quantum nature, it was observed for certain particular external field configurations that, when quantum recoil is neglected, the radiation power corresponds to the classical radiation from an evolving magnetic dipole. We argue that this correspondence has a more general validity in the case of an unpolarized particle and derive a general formula for radiation in terms of the external field strength and its derivatives. A classical dynamics of the spin is described by the Bargmann-Michel-Telegdi equation.Comment: 6 pages,latex, v2, typos correcte

On systems of polynomial equations over finite rings

Finding and storing the set of solutions for systems of polynomial equations with parameters over finite associative (not necessarily, commutative) rings is one of basic problems in various applications connected with exploring algebraic models over these rings. In this paper, it developed unifi ed approach for presenting in implicit form the set of solutions for systems of polynomial equations with parameters over any finite associative (not necessarily, commutative) ring with unit. Proposed approach is based on notions of classes of l-associated or r-associated elements of the ring developed in the paper.Пошук та зберігання множини розв’язків систем поліноміальних рівнянь із параметрами над скінченними асоціативними (не обов’язково комутативними) кільцями є однією з основних проблем для різних прикладень, у яких використовуються алгебраїчні моделі над такими кільцями. У цій статті розвинемо уніфікований підхід для представлення у неявному вигляді множини розв’язків систем поліноміальних рівнянь із параметрами над довільним скінченним асоціативним (не обов’язково комутативним) кільцем з одиницею. Запропонований підхід засновано на поняттях класів l-асоційованих або r-асоційованих елементів кільця, які розвинемо у статті

Finite automata over algebraic structures: models and some methods of analysis

In this paper some results of research in two new trends of finite automata theory are presented. For understanding the value and the aim of these researches some short retrospective analysis of development of finite automata theory is given. The first trend deals with families of finite automata defined via recurrence relations on algebraic structures over finite rings. The problem of design of some algorithm that simulates with some accuracy any element of given family of automata is investigated. Some general scheme for design of families of hash functions defined by outputless automata is elaborated. Computational security of these families of hash functions is analyzed. Automata defined on varieties with some algebra are presented and their homomorphisms are characterized. Special case of these automata, namely automata on elliptic curves, are investigated in detail. The second trend deals with quantum automata. Languages accepted by some basic models of quantum automata under supposition that unitary operators associated with input alphabet commute each with the others are characterized

Recommended Data on Electron-ion Collision Strengths and Effective Collision Strengths for Fe X. Fe XI and Fe XIII Ions

Data obtained for electron-induced excitation transitions between levels with principal quantum numbers n=3 in Cl-like Fe X, S-like Fe XI, and Si-like Fe XIII ions by different theoretical methods were compared, and recommended data for electron collision strengths and effective collision strengths have been chosen. Simple analytical formulas with 7 free parameters were used to describe electron temperature dependence of effective collision strengths in a wide temperature range. The values of free parameters have been determined by fitting the recommended numerical data. The obtained results can be used for plasma kinetics calculations and for spectroscopic methods of plasma diagnostics

A new type of the quasi-TEM eigenmodes in a rectangular waveguide with one corrugated hard wall

The problem of determining the eigenmodes of a rectangular waveguide with one hard wall formed by longitudinal corrugations with grooves filled with dielectric is considered. The characteristic equation is derived by using the asymptotic boundary conditions for corrugated surfaces. It is shown analytically that if the groove depth is equal to the value 0.25 lambda/(epsilon - 1)(1/2) corresponding to the hard wall condition, the TE eigenmode spectrum of the waveguide contains an infinite set of new non-uniform quasi-TEM modes with different transverse propagation constants in the empty part and identical longitudinal propagation constants equal to the wavenumber k. Analytical solution for the case of excitation of the waveguide by a specified source is given, and an example of forming local quasi-TEM waves is considered and discussed