Determinant Line Bundles and Topological Invariants of Hyperbolic Geometry - Expository Remarks

We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in topological quantum field theory.Comment: 10 pages. To appear in G@C, special issue devoted to QG, Unified Models and Strings, to mark 100th Anniversary of Tomsk State Pedagogical University. Editor - S.D. Odintso

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

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

Multiple Quantum NMR Dynamics in Dipolar Ordered Spin Systems

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasi-equilibrium state which establishes after the time of order T2 after the MQ NMR experiment. The other method uses an additional resonance 45^0 -pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.Comment: 11 pages, 3 figures. accepted for publication in Physical Review

Oxidative dehydrogenation of 2,3,5-trimethyl-1,4-hydroquinone in the presence of titanium dioxide hydrogel

Liquid-phase oxidative dehydrogenation of 2,3,5-trimethyl-1,4-hydroquinone in the presence of titanium dioxide hydrogel was studied by a kinetic method. Associative interactions between the substrate, oxidant, and gel were detected by voltammetry and ESR and IR spectroscopy.Russian Foundation for Basic Researc