17 research outputs found

    On some integrable lattice related by the Miura-type transformation to the Itoh-Narita-Bogoyavlenskii lattice

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    We show that by Miura-type transformation the Itoh-Narita-Bogoyavlenskii lattice, for any n1n\geq 1, is related to some differential-difference (modified) equation. We present corresponding integrable hierarchies in its explicit form. We study the elementary Darboux transformation for modified equations.Comment: Latex, 9 page

    Radiation reaction and quantum damped harmonic oscillator

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    By taking a Klein-Gordon field as the environment of an harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator investigated. Applying perturbation method, some transition probabilities indicating the way energy flows between oscillator, reservoir and quantum vacuum, obtainedComment: 12 pages. Accepted for publication in Mod. Phys. Lett.

    Minimal coupling method and the dissipative scalar field theory

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    Quantum field theory of a damped vibrating string as the simplest dissipative scalar field investigated by its coupling with an infinit number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to velocity obtained for a special choice of coupling function and quantum dynamics for such a dissipative system investigated. Some kinematical relations calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment obtained.Comment: 15 pages, no figur

    Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

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    Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux–Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita–Itoh–Bogoyavlensky, Toda, and Adler–Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new

    Differential-difference equations associated with the fractional Lax operators

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    We study integrable hierarchies associated with spectral problems of the form Pψ=λQψP\psi=\lambda Q\psi where P,QP,Q are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous generalizations of the Bogoyavlensky type lattices. While the latter turn into the Korteweg--de Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the Sawada--Kotera and Kaup--Kupershmidt equations. The rr-matrix formulation and several simplest explicit solutions are presented.Comment: 23 pages, 2 figure

    Non-High Density Lipoprotein Cholesterol: A Modern Benchmark for Assessing Lipid Metabolism Disorders

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    Aim. To perform a population analysis of Non-High Density Lipoprotein Cholesterol level (non-HDL-c) in Russian population and to evaluate its association with cardiovascular events.Material and Methods. The material consisted of results obtained from 11 regions of the ESSE-RF1 Study and from 4 regions of the ESSE-RF2 Study. Study protocols were identical. The studies were performed in 2012-2014 and 2017, respectively. Endpoints were assessed in 19041 people aged 35-64 years. The median follow-up was 6.5 years in ESSE RF (1) and 3.8 years in ESSE RF(2). Analysis was performed for three lipid variables: total cholesterol (TC), low-density lipoprotein cholesterol (LDL-C), and non-HDLC in two samples: the general population sample and the same sample without individuals with coronary heart disease (CHD), myocardial infarction (MI) and/or stroke history and not taking statins (the population sample of "without a history of cardiovascular diseases [CVD]". The analysis of nonlinear associations was performed using the generalized additive Cox model. The combined cardiovascular endpoint was represented by cardiovascular death and nonfatal MI and stroke. Traditional and laboratory FRs, socio-demographic parameters were analyzed. The significance level for all tested hypotheses was set to be 0.05.Results. The prevalence of elevated non-HDL-C level (>3.7 mmol/l) was found to be 74.6%. No gender differences were found: there was 74.6% for men and 74.5% for women. Both mean values and prevalence of elevated non-HDL-C were increased with age in women, and its level was slightly decreased in men after 55 years old. Almost all analyzed RFs were significantly associated with elevated non-HDL-C in these two population samples. In both samples elevated total CH and elevated LDL-C were associated with all-cause mortality after correction for all RFs. On the contrary, the non-HDL-C was associated with CVD combined end pints. It has been shown that the risk of these end points increases uniformly with increase in levels of non HDL cholesterol, no nonlinear associations were found.Conclusion. The results of a population-based analysis of non-HDL-C performed in the Russian population for the first time confirmed that elevated non-HDL-C levels contribute significantly to determining the risk of cardiovascular events in the medium term. It can be assumed that the new risk scales (SCORE2 and SCORE OP) proposed by the European Society of Cardiology and the European Society of Preventive Cardiology, which include non-HDL C instead of TC, will allow adequate assessment of 10-year cardiovascular risk for Russians. However, continued monitoring of endpoints in order to obtain stable associations is required

    Modelling a Crawler Robot Using Wheels as Pseudo-Tracks: Model Complexity vs Performance

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    © 2020 IEEE. Crawler mobile robots have a large variety of applications, including urban search and rescue. Before new algorithms and concepts could be integrated into a real robot control system and tested in field experiments, extensive virtual simulations should be performed in order to verify them carefully. This requires a proper modelling of a robot in a virtual environment, but a specific construction of crawler robot crawlers complicates the modelling. In this paper, in order to provide a high level of physical interaction similarity of a crawler with a supporting surface we model crawlers of mobile robot Servosila Engineer with a set of virtual wheels and study a relationship between a model complexity and a simulation performance. The model complexity is reflected by a number of virtual wheels that approximate each crawler of the robot. Verification experiments were performed in ROS/Gazebo simulator

    Genetic structure, morphological variation, and gametogenic peculiarities in water frogs (Pelophylax) from northeastern European Russia

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    The edible frog, Pelophylax esculentus, is a hybrid form that reproduces via clonal propagation of only one of the parental genomes through generations of hybrids while the genome of other parental species is eliminated during gametogenesis. Such reproductive ability requires hybrids to coexist with one of the parental species or rarely both parental species causing the formation of so-called population systems. Population systems and reproductive biology of water frogs from the east of the range remained partially unexplored. In this study, we investigated the distributions, population systems, genetic structure, types of gametes, and morphological variability of water frogs of the genus Pelophylax from the northeastern parts of their ranges (Mari El Republic and adjacent territories, Russia). We examined 1,337 individuals from 68 localities using morphological traits combined with DNA flow cytometry and a multilocus approach (fragments of a nuclear and two mitochondrial genes). We revealed five types of population systems: “pure” populations of the parental P. ridibundus (R) and P. lessonae (L), mixed populations of parental species (R-L) along and with their hybrids (R-E-L), as well as mixed populations of P. lessonae and P. esculentus (L-E). However, the “pure” hybrid (E) and the mixed P. ridibundus and P. esculentus (R-E) population systems were not found. All hybrids studied by DNA flow cytometry were diploid. Analysis of gametogenesis showed that the majority of hybrid males, as well as hybrid females from the L-E system, produced gametes with the P. ridibundus genome. However, in the R-E-L system, hybrid females were usually sterile. The reproduction of hybrids in such systems is primarily based on crosses of P. esculentus males with P. lessonae females. Molecular analysis showed the presence of mitochondrial and nuclear DNA introgression of the Anatolian marsh frog (P. cf. bedriagae) into both P. ridibundus and P. esculentus. The observations of alleles and haplotypes of P. cf. bedriagae in P. ridibundus and P. esculentus individuals from the same localities suggest de novo formation of local hybrids. However, the presence of the Balkan marsh frog (P. kurtmuelleri) haplotypes in local hybrids supports the hypothesis regarding the migration of old hemiclonal lineages from glacial refugia. Finally, the diagnostic value of various morphological characteristics was discussed
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