Для трехчастотного квантового резонансного осциллятора исследован приводимый случай, когда его частоты целые, и хотя бы одна пара частот имеет нетривиальный общий делитель. Показано, как описание алгебры симметрий такого осциллятора сводится к неприводимому случаю попарно взаимно простых целых частот. Выписаны полиномиальные алгебраические соотношения, построены неприводимые представления и когерентные состояния.
In 2001 Ivanov and Kerov associated with the infinite permutation group S∞ certain commutative associative algebra A∞ called the algebra of conjugacy classes of partial elements. A standard basis of A∞ islabeled by Yang diagrams of all orders. Mironov, Morozov, Natanzon, 2012, have proved that the completion of A∞ is isomorphic to the direct product of centers of group algebras of groups Sn. This isomorphism was explored in a construction of infinite dimensional Cardy-Frobenius algebra corresponding to asymptotic Hurwitz numbers. In this work algebras of conjugacy classes of partial elements are defined for a wider class of infinite groups. It is proven that completion of any such algebra is isomorphic to the direct product of centers of group algebras of relevant subgroups.
Cohen et al. developed an O(log n)-approximation algorithm for minimizing the total hub label size (l1 norm). We give O(log n)- approximation algorithms for the problems of minimizing the maximum label (l∞ norm) and minimizing lp and lq norms simultaneously.
In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs 1‖maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT j is polynomially solvable. For several special cases of problem 1‖maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.
Changes of professional environment, caused by introduction of new technologies and techniques, create a necessity in continuous education and development of professional competences. In these conditions, managers and other company employees face the choice of methods and tools of personnel training. A business game is one of the most productive tools of business-education This paper elaborates the ideas embodied previously, which considered the conceptual approach to a toolkit creation for active training techniques in a form of competence-based business game studio. Competence-based business game studio is an ergatic system for development of professional competences, which are required to ensure organization’s business processes. Business game control is performed with the help of automate module, which executes the interpretation of expressions in algorithm logical scheme language. Unified business process is the input data for automate model construction. Unified business process is acquired from the information about company’s real business processes, represented in poorly formalized ways. Unified business process transforms into unified training business process, which includes possible business game trainee actions and information about input, output, administrative data and business process operation execution mechanism. The next step to automate model is the construction of scenario graph, which represents a more formalized description of unified training business process. Next, the administrating algorithm of the business game in algorithm logical scheme language is built. The paper considers the algorithms of transition between models that allow to automate the process of acquiring algorithm logical scheme in order to implement the business games scenario.