Symmetry properties of a charged fluid in the general theory of relativity

The problem of specifying the symmetry properties of a charged fluid in space-time V4, which has a definite group of motions, is considered. It is shown that if nonempty spacetime V4 with an energy-momentum tensor for the charged fluid has symmetry (i.e., admits a group of motions), then the mass density, the pressure, and the four-velocity of the fluid inherits this symmetry, and for an electromagnetic field the relation Lξfij=7.*fij is satisfied. The necessary and sufficient conditions are found so that χ=0 in the case of a one-parameter group. Then additional relationships between κ and the structure constants are obtained in the case of an r-parameter group. It is shown that under certain conditions the symmetry properties obtained for charged matter are necessary and sufficient conditions for the symmetry of space-time V4. © 1979 Plenum Publishing Corporation

Phase transitions for PP-adic Potts model on the Cayley tree of order three

In the present paper, we study a phase transition problem for the $q$-state $p$-adic Potts model over the Cayley tree of order three. We consider a more general notion of $p$-adic Gibbs measure which depends on parameter \rho\in\bq_p. Such a measure is called {\it generalized $p$-adic quasi Gibbs measure}. When $\rho$ equals to $p$-adic exponent, then it coincides with the $p$-adic Gibbs measure. When $\rho=p$, then it coincides with $p$-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of $|\rho|_p$. Namely, in the first regime, one takes $\rho=\exp_p(J)$ for some J\in\bq_p, in the second one $|\rho|_p<1$. In each regime, we first find conditions for the existence of generalized $p$-adic quasi Gibbs measures. Furthermore, in the first regime, we establish the existence of the phase transition under some conditions. In the second regime, when $|\r|_p,|q|_p\leq p^{-2}$ we prove the existence of a quasi phase transition. It turns out that if $|\r|_p<|q-1|_p^2<1$ and \sqrt{-3}\in\bq_p, then one finds the existence of the strong phase transition.Comment: 27 page

On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three

In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two now quasi equivalent QMC for the given family of interaction operators $\{K_{}\}$.Comment: 34 pages, 1 figur

Participation of NKVD and Prosecutor’s Office in Ensuring Construction of Kuibyshev Defensive Line (November 1941 — January 1942)

The article discusses the activities of the NKVD and the prosecutor’s office to ensure the mobilization and suppression of desertions from the construction of the Kuibyshev defensive line. The relevance of the study is due to the fact that the experience of the activities of the NKVD structures and the prosecutor’s office, aimed at ensuring defensive construction in the extreme realities of military operations, is an indispensable source for military engineers of the Russian Federation. Based on the introduction into scientific circulation of previously secret archival documents from the funds of RGASPI, SOGASPI and GANI UO, they paid attention to the process of building a defensive line, the situation of the mobilized and analyzed the problems of the activities of the NKVD and the prosecutor’s office. It was revealed that the employees of the internal affairs bodies and the prosecutor’s office, in order to prevent desertions, first of all sought to normalize the supply of workers with food, clothing and equipment, the establishment of exact production standards, based on the gender and age characteristics of the builders. In the course of the work, it was proved that by mid-December 1941 the repressive policy had been curtailed, and local authorities took measures to improve the food supply for workers

Homelessness of Children as a Social Phenomenon in 1941-1945: Manifestations and Attempts to Overcome in Middle Volga

The article is devoted to the analysis of the main directions and specifics of the activities of state bodies and public organizations of the Middle Volga region in the fight against children homelessness in 1941-1945. At the present stage of Russia’s development, the government and society are paying considerable attention to eliminating crime and preventing deviant behavior among minors, which in turn strengthens the urgency of the problem. The authors introduce into the scientific circulation previously unavailable documents of the State Archive of the Ulyanovsk Region, the State Archive of Recent History of the Ulyanovsk Region, the Samara Regional State Archive of Socio-Political History. The reasons for the development of homelessness, its scope are analyzed in detail in the article, and also the key areas of activity of the internal affairs bodies are considered. It is proved that in the initial period of the Great Patriotic War in the territory of the Middle Volga region a number of factors were recorded that contributed to the criminalization of minors: significant population migration, unstable work of railway and water transport, the termination of educational institutions, an increase in the number of street and street children. It is shown that the answer to the challenge was the development of a method for combating juvenile crime, based on the close interaction of law enforcement, educational bodies and public organizations. It is alleged that the use of new methods has partially reduced the impact of negative trends and, consequently, improved the criminal situation among minors

3-Benzyl-6-(2-chloro­benzo­yl)-1,3-benzoxazol-2(3H)-one

In the title compound, C21H14ClNO3, the benzoxazolone ring system is planar (r.m.s. deviation = 0.022 Å) and forms dihedral angles of 75.38 (10) and 65.92 (13)° with the mean planes of the chloro­benzoyl (r.m.s. deviation = 0.045 Å, excluding O atom) and benzyl (r.m.s. deviation = 0.023 Å) groups. The observed structure is stabilized by weak C—H⋯O hydrogen bonds and weak inter­molecular C—H⋯π inter­actions

Personnel Support of Prosecutor’s Office of Simbirsk (Ulyanovsk) Province in 1922—1928

The article deals with the staffing of the prosecutor’s office in the Simbirsk (Ulyanovsk) province in 1922—1928. The relevance of the study is due to the fact that, from an objective point of view, for the first time on the basis of the introduction into scientific circulation of previously inaccessible due to their secrecy archival materials, seized from the depositories of the State Archive of the Ulyanovsk Region and the State Archive of Recent History of the Ulyanovsk Region, the prosecutor’s office personnel work of the authorities was comprehensively analyzed in the regional context in the Simbirsk (Ulyanovsk) province during the period of the new economic policy. The authors studied the specifics of the selection and placement of personnel specialists in accordance with the approved criteria in the prosecutor’s office, traced changes in the regular staff, determined the level of material support for prosecutors, and also noted positive and negative factors in the implemented personnel policy. In the course of the work, it was found that the ongoing personnel policy made it possible to form such a model of the prosecutor’s office, during the functioning of which the Bolsheviks could control the activities of government bodies, law enforcement agencies, economic institutions, public and private organizations, feel safe, and also regularly influence society

Counterrevolutionary Crimes in Judicial Practice of Simbirsk Governorate Revolutionary Tribunal in 1918-1920

The article is devoted to the analysis of counterrevolutionary crimes in 1918-1920 on the basis of the cases accepted for consideration by Simbirsk Governorate Revolutionary Tribunal. The authors introduce previously unavailable archival documents into scientific circulation. Details are given to such aspects of the topic as the jurisprudence of the emergency justice system in the fight against the counter-revolution, as well as the necessary conditions for the final verdict against the accused. The analysis of the verdicts issued by the emergency justice body is carried out. Attention is paid to examples of acts committed by citizens in 1918-1920 and recognized as counterrevolutionary. Statistical data on the activity of the emergency justice body of Simbirsk governorate are given. The novelty of the research is seen in the fact that for the first time a large layer of previously classified unpublished archival documents was introduced into scientific circulation. The main conclusions of the study are the following key provisions: firstly, Simbirsk Governorate Revolutionary Tribunal was an effective tool of the Bolshevik regime, and secondly, the emergency justice body in 1918-1920 paid close attention to the investigation of counter-revolutionary cases, which amounted to about 29 %, and thirdly, in sentencing Tribunal staff were guided by the class principle

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page