### Article

## On a higher structure on operadic deformation complexes

In this paper, we prove that there is a canonical homotopy (n+1)-algebra structure on the shifted operadic deformation complex Def(e_n → P)[−n] for any operadP and a map of operads f : e_n → P. This result generalizes a result of Tamarkin, who considered the case P = End_{O_p}(X). Another more computational proof of the same result was recently sketched by Calaque and Willwacher.

Our method combines the one of Tamarkin, with the categorical algebra on the category of symmetric sequences, introduced by Rezk and further developed by Kapranov-Manin and Fresse. We define suitable deformation functors on n-coalgebras, which are consid- ered as the “non-commutative” base of deformation, prove their representability, and translate properties of the functors to the corresponding properties of the representing objects. A new point, which makes the method more powerful, is to consider the argu- ment of our deformation theory as an object of the category of symmetric sequences of dg vector spaces, not as just a single dg vector space .

The model of a growing medium consisting of two phases, liquid and solid, is developed. Growth is treated as a combination of the irreversible deformation of the solid phase and its mass increment due to mass exchange with the liquid phase. The inelastic strain rate of the solid phase depends on the stresses in it, which are determined by the forces both external with respect to the medium and exerted by the liquid phase. In the liquid phase the pressure develops due to the presence of a chemical component whose displacement is hampered by its interaction with the solid phase. The approach developed makes it possible to waive many problems discussed in the theory of growing continua. Possible generalizations are considered.

The model of a growing medium consisting of two phases, liquid and solid, is developed. Growth is treated as a combination of the irreversible deformation of the solid phase and its mass increment due to mass exchange with the liquid phase. The inelastic strain rate of the solid phase depends on the stresses in it, which are determined by the forces both external with respect to the medium and exerted by the liquid phase. In the liquid phase the pressure develops due to the presence of a chemical component whose displacement is hampered by its interaction with the solid phase. The approach developed makes it possible to waive many problems discussed in the theory of growing continua. Possible generalizations are considered.

We give a simple construction of the correspondence between square-zero extensions R of a ring R by an R-bimodule M and second MacLane cohomology classes of R with coefficients in M (the simplest non-trivial case of the construction is R = M = Z/p, R = Z/p^2, thus the Bokstein homomorphism of the title). Following Jibladze and Pirashvili, we treat MacLane cohomology as cohomology of non-additive endofunctors of the category of projective R-modules. We explain how to describe liftings of R-modules and complexes of R-modules to R in terms of data purely over R. We show that if R is commutative, then commutative square-zero extensions R correspond to multiplicative extensions of endofunctors.

We then explore in detail one particular multiplicative non- additive endofunctor constructed from cyclic powers of a

module V over a commutative ring R annihilated by a prime p. In this case, R is the second Witt vectors ring W_2(R) considered as a square-zero extension of R by the Frobenius twist R(1).

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

The article is devoted to the study of the authoritarianism prevalent in the mass consciousness of Russians. The article describes a new approach to the consideration of the authoritarian syndrome as the effects of the cultural trauma as a result of political and socio-cultural transformation of society. The article shows the dynamics of the symptoms of the authoritarianism, which appear in the mass consciousness of Russians from 1993 to 2011. This paper proposes a package of measures aimed at reducing the level of the authoritarianism in Russian society.

This work looks at a model of spatial election competition with two candidates who can spend effort in order to increase their popularity through advertisement. It is shown that under certain condition the political programs of the candidates will be different. The work derives the comparative statics of equilibrium policy platform and campaign spending with respect the distribution of voter policy preferences and the proportionality of the electoral system. In particular, it is whown that the equilibrium does not exist if the policy preferences are distributed over too narrow an interval.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

The article examines "regulatory requirements" as a subject of state control over business in Russia. The author deliberately does not use the term "the rule of law". The article states that a set of requirements for business is wider than the legislative regulation.

First, the article analyzes the regulatory nature of the requirements, especially in the technical field. The requirements are considered in relation to the rule of law. The article explores approaches to the definition of regulatory requirements in Russian legal science. The author analyzes legislation definitions for a set of requirements for business. The author concludes that regulatory requirements are not always identical to the rule of law. Regulatory requirements are a set of obligatory requirements for entrepreneurs’ economic activity. Validation failure leads to negative consequences.

Second, the article analyzes the problems of the regulatory requirements in practice. Lack of information about the requirements, their irrelevance and inconsistency are problems of the regulatory requirements in Russia.

Many requirements regulating economic activity are not compatible with the current development level of science and technology. The problems are analyzed on the basis of the Russian judicial practice and annual monitoring reports by Higher School of Economics.

Finally, the author provides an approach to the possible solution of the regulatory requirements’ problem. The author proposes to create a nationwide Internet portal about regulatory requirements. The portal should contain full information about all regulatory requirements. The author recommends extending moratorium on the use of the requirements adopted by the bodies and organizations of the former USSR government.