A class of integrable lattices and KP hierarchy

We introduce a class of integrable $l$-field first-order lattices together with corresponding Lax equations. These lattices may be represented as consistency condition for auxiliary linear systems defined on sequences of formal dressing operators. This construction provides simple way to build lattice Miura transformations between one-field lattice and $l$-field ($l\ge 2$) ones. We show that the lattices pertained to above class is in some sense compatible with KP flows and define the chains of constrained KP Lax operators.Comment: LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge

Radiation reaction and quantum damped harmonic oscillator

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.

Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice

It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is constructed.Comment: LaTeX, uses IOP styl

Optimality Principles and Motion Planning of Human-Like Reaching Movements

The paper deals with modeling of human-like reaching movements. Several issues are under study. First, we consider a model of unconstrained reaching movements that corresponds to the minimization of control effort. It is shown that this model can be represented by the wellknown Beta function. The representation can be used for the construction of fractional order models and also for modeling of asymmetric velocity proï¬les. Next, we address the formation of boundary conditions in a natural way. From the mathematical point of view, the structure of the optimal solution is deï¬ned not only by the form of the optimality criterion but also by the boundary conditions of the optimization task. The natural boundary conditions, deï¬ned in this part of the paper, can also be used in modeling asymmetric velocity proï¬les. Finally, addressing the modeling of reaching movements with bounded control actions, we consider the minimum time formulation of the optimization problem and (for the n-th order integrator) ï¬nd its analytical solution

Reductions of the Volterra and Toda chains

The Volterra and Toda chains equations are considered. A class of special reductions for these equations are derived.Comment: LaTeX, 6 page

Minimal coupling method and the dissipative scalar field theory

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

Inverse dynamics-based motion control of a fluid-actuated rolling robot

In this paper, the rest-to-rest motion planning problem of a fluid-actuated spherical robot is studied. The robot is driven by moving a spherical mass within a circular fluid-filled pipe fixed internally to the spherical shell. A mathematical model of the robot is established and two inverse dynamics-based feed-forward control methods are proposed. They parameterize the motion of the outer shell or the internal moving mass as weighted Beta functions. The feasibility of the proposed feed-forward control schemes is verified under simulations

Some integrable maps and their Hirota bilinear forms

We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the Laurent property, and the tropical (or ultradiscrete) analogue of this homogeneous recurrence confirms the quadratic degree growth found empirically by Demskoi et al. We prove that the tau function also satisfies two different bilinear equations, each of which is a reduction of the Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence). Furthermore, these bilinear equations are related to reductions of particular two-dimensional integrable lattice equations, of discrete KdV or discrete Toda type. These connections, as well as the cluster algebra structure of the bilinear equations, allow a direct construction of Poisson brackets, Lax pairs and first integrals for the birational maps. As a consequence of the latter results, we show how each member of the family can be lifted to a system that is integrable in the Liouville sense, clarifying observations made previously in the original DTKQ case

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

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