Decomposition of enzyme kinetics equations

The problem of singularly perturbed di erential systems decomposition by the method of integral manifolds is studied and the application of the method to the problems of kinetics is considered.This work was funded by RFBR and Samara Region (project 16-41-630529-p) and the Ministry of Education and Science of the Russian Federation under the Competitiveness Enhancement Program of Samara University (2013-2020)

Decomposition of travelling wave existence problem for singularly perturbed semilinear parabolic equations

The travelling waves problem for the singularly perturbed semilinear parabolic equations is considered in the paper.It is shown that the corresponding problem for a singularly perturbed ODE system can be reduced to a certain problem of lower dimension using a splitting transformation based on the technique of slow and fast integral manifolds.The authors are supported by the Russian Foundation for Basic Research and Samara Region (project 16-41-630529-p) and the Ministry of Education and Science of the Russian Federation under the Competitiveness Enhancement Program of Samara University (2013-2020)

Decomposition of PD-regulators design problem for systems with slow and fast modes

The PD-regulators design problem for the singularly perturbed control system is considered in the paper. It is shown that this problem can be reduced to the P-regulators design problems for two subsystems of lower dimension.The authors are supported by the Russian Foundation for Basic Research and Samara Region (project 16-41-630524-p) and the Ministry of Education and Science of the Russian Federation under the Competitiveness Enhancement Program of Samara University (2013-2020)

Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Long- and short-term earthquake prediction in Kamchatka

This paper presents the results of long- and short-term earthquake prediction obtained during 1971–1974. They can be summarized as follows: The map of long-term prediction for the Kurile—Kamchatka zone compiled in 1965 and supplemented in 1972 by S.A. Fedotov is in good agreement (in four of four possible cases) with recorded seismicity. The results obtained allow us to suppose that the areas for which the log (Ep/Es) of small earthquakes is low may be the areas of future large earthquakes. Prediction of active periods for the Kamchatka earthquakes with M > 7 has been made on the basis of studying the correlation of seismicity with the lunar tide with a 18.6-year period. A possibility has been found for using the phenomenon of “induced foreshocks” for earthquake prediction, i.e., when a large remote earthquake induces small preceding events in the zone of preparation of a large earthquake. The following three methods were used for operative short-term prediction of the time and place of future earthquakes with M > 5.5. 1.(1) Use of specific electrotelluric field anomalies, from 5 to 20 days in duration, which are recorded by a specially designed network of stations. 2.(2) Method of Vp/Vs anomalies. The anomalously high and low Vp/Vs values for a seismic station point to the possibility of large earthquakes near the latter. 3.(3) The earthquake statistics method described by Fedotov et al. in 1972. Short-term seismic prediction is being made twice a week in two versions: Forecast I (for the whole of Kamchatka) and Forecast II (for each of six overlapping segments of the Kamchatka seismic zone). This paper discusses the results of successful testing of short-term earthquake prediction during two years. During the “alarm” periods the probability of large earthquakes is double the average. Paper presented at the Symposium on Earthquake Forerunners Searching, Tashkent, May 26–June 1, 1974

The ^4He trimer as an Efimov system

We review the results obtained in the last four decades which demonstrate the Efimov nature of the $^4$He three-atomic system.Comment: Review article for a special issue of the Few-Body Systems journal devoted to Efimov physic

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362