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Amendments to the Russian Constitution take effect on 4 July2020. In Chapter 3, "Federal Structure," of the Constitution of the Russian Federation there is a provision for a set of amendments specifying the status of constitutional law in the Russian Federation regarding domestic and international/interstate relations as well as relating to questions of Russian national/state identity and guarantees of its preservation and protection. On 15 January 2020 in the Presidential Address to the Federal Assembly a number of constitutional amendments were proposed for discussion, including the introduction of certain changes to the Constitution of the Russian Federation. These changes will be guaranteed priority in Russia's legal framework. President Vladimir Putin noted that, "requirements of international law and treaties as well as decisions of international bodies can be valid on Russian territory only to the point that they do not restrict the rights and freedoms of our people and citizens and do not contradict our Constitution"" The topicality of considering the relationship between national and international court jurisdictions is predetermined by the fact that Russia has ratified Protocol No. 15. On 1 May 2017 a federal law-ratifying protocol establishing a subsidiary role of the European Court of Human Rights was signed. Such a role, in addition to the national mechanism of the judicial protection of human rights, is necessary to implement judicial protection, primarily in Russian courts including the Supreme Court (which is the highest court for civil, economic, criminal and administrative cases and which also protects human rights and freedoms by considering cassation and supervisory complaints against final and binding court rulings) and the Constitutional Court (which, as the highest court body of constitutional control, considers cases of citizens' complaints about the violation of constitutional rights and freedoms by a law applied by state bodies). At the current level of legal development, there are both a necessity and practical possibility of altering approaches to the implementation of international rules. This paper considers the correlation of national and international law. On the basis of decisions of the Constitutional Court of the Russian Federation on the so-called request for the applicability of decisions of the European Court of Human Righ ts, legal views are given on the applicability of international rules by Russian courts, including their interpretation by international court institutions. The revised version of Article 101 of the Federal Constitutional Law on the Constitutional Court, which makes it possible to apply to the Constitutional Court contrary to an official ECHR decision, has been in effect since 2014.

Agile software development and Formal Methods are traditionally seen as being in conflict. From an Agile perspective, there is pressure to deliver quickly, building vertical prototypes and doing many iterations/sprints, refining the requirements; from a Formal Methods perspective, there is pressure to deliver correctly and any change in requirements often necessitates changes in the formal specification and might even impact all arguments of correctness.

The concept of computable functions (as developed by Godel, Church, Turing, and Kleene in the 1930's) has been extensively studied, leading to the modern subject of recursive function theory. However recent work by category theorists has led to a more conceptual and abstract foundation of computability theory—Turing categories. A Turing category models the notion of partial map as well as recursive computation, using methods of categorical algebra to formalize these concepts. The goal of this work is to provide a formal framework for analyzing this categorical model of computation. We use the Coq Proof Assistant, which implements the Calculus of (co)Inductive Constructions (CIC), and we build on an existing Coq library for general category theory. We focus on both formalizing Turing categories and on building a general framework in the form of a well-structured Coq library that can be further extended. We begin by formalizing definitions, propositions, and proofs pertaining to Turing categories, and then instantiate the more general Turing category formalism with a CIC description of the category which explicitly models the language of partial recursive functions.

The paper investigates the Galerkin method for an initial boundary value problem for heat convection equations. New error estimates for the approximate solutions and their derivatives in strong norm are obtained.

This article investigates the projection-difference method for a Cauchy problem for a linear operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in Hilbert space. This method leads to the solution of a system of linear algebraic equations on each time level; moreover, the projection subspaces are linear spans of eigenvectors of an operator similar to A(t). The convergence estimates are obtained. The application of the developed method for solving the initial boundary value problem is given.