Constructions of regular algebras Lpw(G)L_p^w(G)

Criterion of (Shilov) regularity for weighted algebras $L_1^w(G)$ on a locally compact abelian group $G$ is known by works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation invariant weighted algebras $L_p^w(G)$ with $p>1$. Regular algebras $L_p^w(G)$ are constructed on any sigma-compact abelian group $G$. It was proved earlier by the author that sigma-compactness is necessary (in the abelian case) for the existence of weighted algebras $L_p^w(G)$ with $p>1$.Comment: Submitted to Mat. Sborni

A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis

Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop physical model.Comment: Accepted to American Control Conference (ACC) 2015 (Chicago, USA

On the Benefits of Rational Simplicity: How to Teach Humanities in Technical Universities?

The article continues the discussion of teaching humanities disciplines in technical universities, which has been going on for several years on the pages of our journal. First of all, the authors object to raising the question of teaching humanities knowledge in technical universities “in general” and reject the unambiguous recommendations and prescriptions addressed to teachers “for all occasions”. The authors’ position can be formulated as a search and selection of cases that are most appropriate for promoting the overlapping cultures of science/engineering/technical and humanities. They share their approaches to the problem outlined against the background of critical reflection on A.A. Polonnikov’s article published in the same issue. Contradicting their colleague in the teaching profession, the authors emphasize the importance of the humanities teacher’s creativity and at the same time defend the principle of recursive continuity (“rational simplicity”) once proclaimed by Michel Foucault: “Not all discursive strategies are equally possible, but only those that are allowed by the preceding levels”

Formation of human capital as a key factor in ensuring the national security of agriculture in the digital economy

Over the past few years in many literary sources and the media an issue of the digital economy is rapidly gaining popularity due to the qualitative technological changes in society. In current circumstances the qualitative component of labor resources called “human capital” is a priority value. The authors have identified the main realities of the development of agribusiness, studied the main directions of information support on the example of the agricultural sector of the economy and identified the root causes of the slowdown in the innovation development of agriculture in Russia, the features of using information technologies in agribusiness have been considered in detail.peer-reviewe