Cyclotomic shuffles

Analogues of 1-shuffle elements for complex reflection groups of type $G(m,1,n)$ are introduced. A geometric interpretation for $G(m,1,n)$ in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group $G(m,1,n)$. Considering shuffling as a random walk on the group $G(m,1,n)$, we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum of the 1-shuffle analogue in the cyclotomic Hecke algebra $H(m,1,n)$ for $m=2$ and small $n$

Innovations in foreign (chinese) students’ grammar competence formation while training them russian as a foreign language: network technology and the module approach

The article deals with the researches in the field of finding new methods of teaching Russian to foreign (Chinese) students and its Grammar aspect, in particular. In this connection the authors share the results of the investigation dealt with the development of one of the most future-oriented approaches in methods of training the Russian Grammar standards which may be called the Module Approach realized by means of Network Technologie

Місце судової товарознавчої експертизи у запобіганні правопорушенням на роздрібному ринку електричної енергії

 The article emphasizes that the threatening dynamics of the annual increase in the facts of damage and theft of energy equipment, theft of electrical energy, spontaneous connection to electrical grids can lead to imbalance anddestruction of the electrical industry not only in a separate region, but also in the country as a whole. Attention is drawn to the fact that regulatory legal acts are aimed at curbing this dangerous dynamic, that carry out state regulation in the energy sector which, unfortunately, do not ensure stable security in this area.  It is stated that specialists from different suppliers of electric energy prepare all the necessary materials to open criminal proceedings under Article 1881 of the Criminal Code of Ukraine, submit petitions to the investigating authorities about the need to carry out certain investigative actions, however, violators are not prosecuted. It was found that the main obstacle in bringing the perpetrators of these violations to criminal responsibility is the lack of methodological materials and skills in the police units in the investigation of criminal proceedings on the facts of theft of electrical energy and the practice of their consideration by courts. It has been proved that the lack of methodological materials with a complete list of initial data that are necessary to determine the market price of products of the energy complex leads to discrepancies in conclusions of experts. New methods for determining the market price of energy products during forensic commodity examinations will help to resolve the issue of assessing the products of the energy complex in expert practice. It is proposed to determine the subject, tasks, object of research of this forensic examination; outline possible approaches and methods for assessing their value; establish the assortment of goods that has formed in this market in the world and in Ukraine; clearly identify the boundaries of competence of commodity experts. It is emphasized that the determination of the market price for electricity and the cost of services for its provision goes beyond the competence of commodity experts, since the mechanism for setting prices (tariffs) for this type of product is controlled by the state and approved by the Regulator – National Energy and Utilities Regulatory Commission. Зауважено, що притягненню до кримінальної відповідальності винних у пошкодженні й викраденні енергообладнання, розкраданні електроенергії заважає відсутність у підрозділів поліції методичних матеріалів і навичок розслідування таких правопорушень і практики їх розгляду судами. Акцентовано, що визначення ринкової вартості електроенергії та послуг з її надання перебуває за межами компетенції експертів-товарознавців, оскільки механізм формування цін (тарифів) на цей вид продукції затверджує Національна комісія, що здійснює державне регулювання у сферах енергетики та комунальних послуг, а контролює держава. Мета статті — окреслити місце судової товарознавчої експертизи у запобіганні правопорушенням на роздрібному ринку електроенергії

MSSM-inspired multifield inflation

Despite the fact that experimentally with a high degree of statistical significance only a single Standard Model--like Higgs boson is discovered at the LHC, extended Higgs sectors with multiple scalar fields not excluded by combined fits of the data are more preferable theoretically for internally consistent realistic models of particle physics. We analyze the inflationary scenarios which could be induced by the two-Higgs doublet potential of the Minimal Supersymmetric Standard Model (MSSM) where five scalar fields have nonminimal couplings to gravity. Observables following from such MSSM-inspired multifield inflation are calculated and a number of consistent inflationary scenarios are constructed. Cosmological evolution with different initial conditions for the multifield system leads to consequences fully compatible with observational data on the spectral index and the tensor-to-scalar ratio. It is demonstrated that the strong coupling approximation is precise enough to describe such inflationary scenarios.Comment: 27 pages, 4 figures, 5 tables. Version to appear in JHEP. Additions made to the text of the Introduction dealing with the issues of conformity of this multifield model and models of N=1 supergravity (pages 2-3). Added new inflationary scenarios, which are an artifact of such analysis (pages 11-12, Tables 1-4). Additional comments on page 9 and page 13. New references adde

The Peculiarities of Obtaining a Parents Consent (Legal Representative’s) to the Departure of a Minorfrom the Russian Federation

The analysis of the current legislation regulating the procedure for the entry and exit of minors outside the Russian Federation has been carried out, the features of obtaining consent for the departure of a minor outside the Russian Federation have been noted. The necessity of notarization of such consent has been investigated, judicial decisions on this issue have been considered, and the legal norms governing the form of withdrawal of consent to a minor’s departure have been examined. The author has formulated proposals to improve the current legislation governing the entry and exit of minors outside the Russian Federation, including legislatively stating the obligation of the person who has withdrawn consent to leave the minor, to inform the interested person and the minor himself about such actions within a reasonable time

The Speifics of Obtaining a Spouse's Consent to Improve Deals, Involving the Improvement of Property

In this article the importance of the spouse's consent to engage in civil law deals is considered. The specifics of obtaining consent of the spouse for the deal under the disposal of jointly acquired property are analyzed. In addition, proposals have been made to improve the legislation in the sphere of obtaining the consent of the spouse to dispose of movable property, as well as to dispose of the property by the spouse whose marriage is terminated by the time the transaction is concluded

The Legal Assessment of Alcohol-Intoxicated Persons’ Appearance in Public Places According to the Laws of Foreign Countries

The article deals with foreign legislation regarding alcohol-intoxicated persons seen in public places. The author analyzed the interpretation of the concepts of "intoxicated condition", "public place" under the laws of foreign countries. The emphasis is given to the problems of bringing intoxicated persons seen in public places to administrative and criminal liability. Much attention is paid to the US laws containing rules of responsibility for public intoxication