On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the Reflection equation algebras

Ignition of wood subjected to the decreasing radiant energy flux

In this paper we analyze the ignition of wood samples subjected to the decreasing heat flow. The experimental setup was created on the base of the optical wave "Uran-1". The intensity of the heat flow was changed during the experiment by moving the test sample along the optical axis of the elliptic reflector in the setup. Pine wood was used as the test samples. We received the delay times for ignition of pine wood during heating by the decreasing heat flow. The received data were compared with the data for a static heat flow

Control-matrix approach to stellarator design and control

The full space Z always equal to {l{underscore}brace}Zj=1,..Nz{r{underscore}brace} of independent variables defining a stellarator configuration is large. To find attractive design points in this space, or to understand operational flexibility about a given design point, one needs insight into the topography in Z-space of the physics figures of merit Pi which characterize the machine performance, and means of determining those directions in Z-space which give one independent control over the Pi, as well as those which affect none of them, and so are available for design flexibility. The control matrix (CM) approach described here provides a mathematical means of obtaining these. In this work, the authors describe the CM approach and use it in studying some candidate Quasi-Axisymmetric (QA) stellarator configurations the NCSX design group has been considering. In the process of the analysis, a first exploration of the topography of the configuration space in the vicinity of these candidate systems has been performed, whose character is discussed

Методи синтезу, будова та біологічна активність 5-нітро-9-N-ариламіноакридинів

With the purpose of search of new biologically active substances the synthesis of nine derivatives of 5-nitro-9-Narylaminoacridinium (2a-i) has been carried out by interaction of the corresponding 5-nitro-9-chloracridines and aromatic amines in two ways: in the phenol medium (method A) and in the dioxane medium in the presence of hydrochloric acid (method B). It has been experimentally proven that method B is more expedient because it is characterized by the absence of toxic phenol in the synthesis, reduction of the experiment time, a high yield of the desired product (87-94%). The structure and individuality of compounds synthesized that are undescribed in the literature have been confirmed by IR-, NMR-spectral and chromatographic analysis. The choice of the pharmacological screening spectrum has been conducted using data of PASS-prognosis, scientific and patent literature. It has been found experimentally that the substances synthesized possess a moderate bacteriostatic and fungistatic, expressed anti-inflammatory and analgesic, high diuretic (compounds 2d-f) and antidiuretic (compounds 2h-i) activities. According to the classification by K.K.Sydorov the compounds synthesized when introduced intragastrically belong to low toxic compounds. Some regularities of the “structure – biological activity – toxicity” dependence have been analyzed, and it is an important element in determining the areas for further research to develop new biologically active substances.С целью поиска новых малотоксичных биологически активных веществ осуществлен синтез девяти метоксизамещенных 5-нитро-9-N-ариламиноакридинив (2а-з) взаимодействием соответствующих 5-нитро-9-хлоракридинов с ароматическими аминами двумя способами: в среде фенола (способ А) и в среде диоксана в присутствии хлористоводородной кислоты (способ Б). Экспериментально доказано, что способ Б является более рациональным, так как для него характерны: легкость проведения синтеза, сокращение времени эксперимента, отсутствие в синтезе токсического фенола, высокий выход целевых продуктов (87-94%). Строение и индивидуальность неописанных в литературе синтезированных соединений подтверждены данными ИК-, ПМР-спектрального и хроматографического анализа. Выбор спектра фармакологического скрининга проводили, опираясь на данные PASS-прогноза, научной и патентной литературы. По результатам экспериментальных биологических исследований выявлено, что для синтезированных соединений (2а-з) характерна умеренная бактерио- и фунгистатическая, выраженная противовоспалительная и анальгетическая, высокая диуретическая (соединения 2г-е) и антидиуретическая (соединения 2ж-з) активность. По классификации К.К.Сидорова синтезированные вещества при внутрижелудочном введении относятся к классу малотоксичных соединений. Проанализированы некоторые закономерности связи «структура – биологическая активность – токсичность», что является важным элементом для определения направлений дальнейшей научной работы по созданию новых биологически активных субстанций.З метою пошуку нових малотоксичних біологічно активних речовин здійснено синтез дев’яти метоксизаміщених 5-нітро-9-N-ариламіноакридинів (2а-з) взаємодією відповідних 5-нітро-9-хлоракридинів з ароматичними амінами двома способами: у середовищі фенолу (спосіб А) та у середовищі діоксану в присутності хлористоводневої кислоти (спосіб Б). Експериментально доведено, що спосіб Б є більш раціональним, так як для нього характерні: легкість проведення синтезу, скорочення часу експерименту, відсутність у синтезі токсичного фенолу, високий вихід цільових продуктів (87-94%). Будову та індивідуальність неописаних у літературі синтезованих сполук підтверджено даними ІЧ-, ПМР-спектрального та хроматографічного аналізу. Вибір спектра фармакологічного скринінгу проводили, опираючись на дані PASS-прогнозу, наукової та патентної літератури. За результатами експериментальних біологічних досліджень виявлено, що для синтезованих сполук (2а-з) характерна помірна бактеріо- і фунгістатична, виражена протизапальна та аналгетична, висока діуретична (сполуки 2г-е) та антидіуретична (сполуки 2ж-з) активність. За класифікацією К.К.Сидорова синтезовані речовини при внутрішньошлунковому введенні належать до класу малотоксичних сполук. Проаналізовано деякі закономірності зв’язку «структура – біологічна активність – токсичність», що є важливим елементом для визначення напрямків подальшої наукової роботи по створенню нових біологічно активних субстанцій

Quantum matrix algebra for the SU(n) WZNW model

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.Comment: 48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys.

Covariant differential complexes on quantum linear groups

We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all monomials of these forms possess the unique ordering. For the obtained external algebras we define the exterior derivative possessing the usual nilpotence condition, and the generally deformed version of Leibniz rules. The status of the known examples of GL_q(N)-differential calculi in the proposed classification scheme, and the problems of SL_q(N)-reduction are discussed.Comment: 23 page

Diffusion algebras

We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional stochastic processes with exclusion. One considers processes in which one has N species, the number of particles of each species being conserved. All diffusion algebras are obtained. The known examples already used in applications are special cases in our classification. To help the reader interested in physical problems, the cases N=3 and 4 are listed separately.Comment: 29 pages; minor misprints corrected, few references adde

All bicovariant differential calculi on Glq(3,C) and SLq(3,C)

All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with the help of the R-matrix of GLq(3,C). Some calculi induce bicovariant differential calculi on SLq(3,C) and on real forms of GLq(3,C). For generic deformation parameter q there are six calculi on SLq(3,C), on SUq(3) there are only two. The classical limit q-->1 of bicovariant calculi on SLq(3,C) is not the ordinary calculus on SL(3,C). One obtains a deformation of it which involves the Cartan-Killing metric.Comment: 24 pages, LaTe

First principle study of intrinsic defects in hexagonal tungsten carbide

The characteristics of intrinsic defects are important for the understanding of self-diffusion processes, mechanical strength, brittleness, and plasticity of tungsten carbide, which present in the divertor of fusion reactors. Here, we use first-principles calculations to investigate the stability of point defects and their complexes in WC. Our calculation results confirm that the formation energies of carbon defects are much lower than that of tungsten defects. The outward relaxations around vacancy are found. Both interstitial carbon and interstitial tungsten atom prefer to occupy the carbon basal plane projection of octahedral interstitial site. The results of isolated carbon defect diffusion show that the carbon vacancy stay for a wide range of temperature because of extremely high diffusion barriers, while carbon interstitial migration is activated at lower temperatures for its considerable lower activation energy. These results provide evidence for the presumption that the 800K stage is attributed by the annealing out of carbon vacancies by long-range migration.Comment: Submitted to Journal of Nuclear Material