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

Philosophical Reflection of the Concept of "Borders" in Modern Culturechinese Performing

Objective: philosophical reflection problems of the frontiers of science, knowledge and creativity in the modern intercultural integration; rationale for new interpretations and understanding of the concept "border" providing an integrative model for science and culture, which, in turn, implies the unacceptability of Orthodox approaches, and rigid demarcation between different spheres of cultural production. This explains the need to develop a "rational-reflexive culture" that meets the new demands of modern society. Research procedure and methods: the theoretical and methodological research of the work is based on the works of classics of Western and domestic philosophical, cultural, historical, and other thought in the field of studying the essence of social and cognitive phenomena; classical and non-classical methodological paradigms of understanding the concept of "borders" in ontological, epistemological grounds and socio-cultural dynamics are used. The main method is the classical method of dialectics, associated with the consideration of things in a broad ontological, epistemological and cultural-historical context; a method of comparative analysis, a combination of historical and logical, concrete-universal, phenomenological and systemic principles, a thesaurus approach. The results of the study: analyzed new meanings of the concept "border", "rational – reflexive culture" in knowledge and creativity; proven illegality model "narrow" technological oriented science and culture to the detriment of the spiritual nature of man; it is proved that as the modern world blurs the lines of demarcation in science, culture, art, insofar exacerbated the task of establishing priorities, implying the transition from a world of "pure rationality" to the life world of man; an optimal model of the conjugacy of all forms of human cognitive and creative activity in culture is proposed, due to the genetic connection of rational and other mental and cognitive forms of world development. Theoretical / practical significance consists in the justification and author's interpretation of the new understanding of the boundaries of science-culture-man; in proving the need to expand the boundaries of science in ontological and epistemological grounds to the "borders of culture"; implemented criticism of the technogenic interpretation of science (science as "sciepse"), with the connection with which the thesis is justified about the inexpediency of excessive rationalization of knowledge and cognition to the detriment of other ways and forms of world development

Limitations of the classical phase-locked loop analysis

Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical engineering phase-locked loop analysis are demonstrated, e.g., hidden oscillations, which can not be found by simulation, are discussed. It is shown that the use of simplified dynamical models and the application of simulation may lead to wrong conclusions concerning the operability of PLL-based circuits

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

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