On dominant contractions and a generalization of the zero-two law

Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m) be two positive contractions such that $T\leq S$. If $\|S-T\|<1$ then $\|S^n-T^n\|<1$ for all n\in\bn. In the present paper we generalize this result to multi-parameter contractions acting on $L^1$. As an application of that result we prove a generalization of the "zero-two" law.Comment: 10 page

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

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

2-n-Butyl-6-chloro-1-(2,4-dimethyl­phenyl­sulfon­yl)-1H-benzimidazole–2-n-butyl-5-chloro-1-(2,4-dimethyl­phenyl­sulfon­yl)-1H-benzimidazole (0.759/0.241)

The title compound, 0.759C19H21ClN2O2S·0.241C19H21ClN2O2S, was synthesized by aryl­sulfonyl­ation of 2-n-butyl-5-chloro-1H-benzimidazole in the presence of triethyl­amine. The crystal structure is composed of two mol­ecules, 2-n-butyl-6-chloro-1-(2,4-dimethylphenyl­sulfon­yl)-1H-benzimidazole and 1-(2,4-dimethylphenyl­sulfon­yl)-2-n-butyl-5-chloro-1H-benz­imidazole, in the refined ratio of 0.759 (4):0.241 (4) disordered at the same position in the unit cell. The mol­ecule has three essentially planar fragments viz. benzimidazole, dimethyl­benzene and n-butyl (r.m.s. deviations of 0.009, 0.024 and 0.003 Å, respectively). The angle between the benzimidazole and dimethyl­benzene fragments is 86.0 (1)°. In the crystal, pairs of inter­molecular C—H⋯π inter­actions form centrosymmetrical dimers, which are linked by weak inter­molecular C—H⋯O hydrogen bonds

Ising spin glass models versus Ising models: an effective mapping at high temperature III. Rigorous formulation and detailed proof for general graphs

Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over such a graph, can be exactly mapped on the critical surface and behavior of a non random Ising model. A graph can be infinite dimensional in a strict sense, like the fully connected graph, or in a broad sense, as happens on a Bethe lattice and in many random graphs. In this paper, we firstly introduce our definition of dimensionality which is compared to the standard definition and readily applied to test the infinite dimensionality of a large class of graphs which, remarkably enough, includes even graphs where the tree-like approximation (or, in other words, the Bethe-Peierls approach), in general, may be wrong. Then, we derive a detailed proof of the mapping for all the graphs satisfying this condition. As a byproduct, the mapping provides immediately a very general Nishimori law.Comment: 25 pages, 5 figures, made statements in Sec. 10 cleare

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

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

Implementation of Party-State Social Programme in 1960ies-1980ies: Housing Construction in Ulyanovsk and Dimitrovgrad

The article analyzes the features of the formation and development of the construction industry in the Ulyanovsk region in the 1960-80ies, as well as the state of the material and technical base of construction. The relevance of the study is due to both the historiographical lacuna on this topic and the degree of high social significance of the housing construction sector. A detailed analysis of the housing policy of local authorities in Ulyanovsk and Dimitrovgrad is necessary to recreate the historical reality that has developed in the region during this period. The main difficulties of implementing the programme of mass housing construction are revealed. Archival data from the funds of the State archive of the Ulyanovsk region and the State archive of the modern history of the Ulyanovsk region are introduced into scientific circulation, materials of the periodical press are involved. It is noted that the construction was characterized by construction monotony, questionable architectural value of buildings, allowed irrational layout of housing: small apartments with low ceilings, small kitchens, walk-through rooms. The authors claim that the campaign initiated by the local party bodies in the 1960ies-1980ies to build residential quarters in Ulyanovsk and Dimitrovgrad helped to significantly relieve tensions in the housing sector: the population was provided with comfortable housing, resettlement from communal apartments, barracks, dilapidated housing was carried out

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

1-[(4-tert-Butyl­phen­yl)sulfon­yl]-1H-benzimidazole

The title compound, C17H18N2O2S, was synthesized by aryl­sulfonyl­ation of 1-hy­droxy­methyl-1H-benzimidazole in the presence of triethyl­amine. The benzimidazole and benzene rings form a dihedral angle of 84.1 (1)°. The tert-butyl group was treated as rotationally disordered over two orientations in a 0.51 (2):0.49 (2) ratio. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds link the mol­ecules into chains propagating in [010]