On a q-difference Painlev\'e III equation: II. Rational solutions

Rational solutions for a $q$-difference analogue of the Painlev\'e III equation are considered. A Determinant formula of Jacobi-Trudi type for the solutions is constructed.Comment: Archive version is already official. Published by JNMP at http://www.sm.luth.se/math/JNMP

Модели и методы машинного обучения для решения задач оптимизации и прогнозирования работы морских портов

Machine learning techniques have made significant advances and expanded application sphere over the past decade to include problems of port operations. This happened due to the growing amount of data available cargo ports. We review the literature on models and methods of machine learning and their application to optimization of port operations. A special attention is paid to the port planning and development a wide range of topics in port operations, including port planning and development, their safety and security, water and land port operations.За последнее десятилетие существенно улучшились методы машинного обучения и расширилась сфера их применения, которая дополнилась рядом операционных задач, возникающих в грузовых портах. Это связано с накоплением и возможностью использования имеющихся в грузовых портах больших объемов данных. Статья посвящена обзору литературы по моделям и методам машинного обучения и их применению к оптимизации портовых операций. Основное внимание уделено планированию и развитию портов, их безопасности и охране, водным и сухопутным портовым операциям

Vilna governors (1864-1917): construction of historical myths and reality

The article discusses the mythologization in the Soviet historiography of the image of the pre-revolutionary governor. It is shown that for an objective assessment of this category of officials, it is necessary to reveal their real socio-cultural appearance. A mechanism for such an analysis is proposed using the example of Vilna governors (1864-1917) for key positions (educational level, origin, religion, age, marital status, career).В статье рассматривается мифологизация в советской историографии образа дореволюционного губернатора. Показано, что для объективной оценки этой категории чиновников необходимо раскрыть их реальный социокультурный облик. Предлагается механизм подобного анализа на примере виленских губернаторов (1864-1917 гг.) по ключевым позициям (образовательный уровень, происхождение, вероисповедание, возраст, семейное положение, карьера)

Painleve IV and degenerate Gaussian Unitary Ensembles

We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t, this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diagonal recurrence coefficients satisfy a particular Painleve IV equation for any real multiplicity. If the multiplicity is even they are expressed in terms of the generalized Hermite polynomials, with t as the independent variable.Comment: 17 page

Determinant Structure of the Rational Solutions for the Painlev\'e IV Equation

Rational solutions for the Painlev\'e IV equation are investigated by Hirota bilinear formalism. It is shown that the solutions in one hierarchy are expressed by 3-reduced Schur functions, and those in another two hierarchies by Casorati determinant of the Hermite polynomials, or by special case of the Schur polynomials.Comment: 19 pages, Latex, using theorem.st

Rational Solutions of the Painleve' VI Equation

In this paper, we classify all values of the parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ of the Painlev\'e VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlev\'e VI equation.Comment: 13 pages, 1 Postscript figure Typos fixe

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Internal scheme of the body assessment in an experiment with environmental uncertainty

The aim of the work was to analyze the influence of various environmental factors forming environmental uncertainty on the nature of the transformation of the "internal scheme of the body". Materials and methods. For the study, a group of healthy volunteers (n = 90) was selected. The results in this paper are median, 75 and 25 percentiles (Me [UQ / LQ]). The study was conducted in several stages. At the first stage, the criteria for excluding potential participants from the experiment were formed. At the second stage of the study, a video analysis of the main anatomical orientations of the pelvic region in static and dynamic samples was conducted for all participants. Conclusion. In the course of the study, specific patterns of spatial deviations of biomechanical blocks of the pelvic region were established, triggered by changes in the qualitative and quantitative parameters of the external environment. So, in conditions of static equilibrium, coordination is activated with involvement of the anterior and posterior half-rings of the pelvis (frontal biomechanical blocks); in conditions of dynamic equilibrium, diagonal biomechanical blocks of the pelvic region are activated; in conditions of deprivation of visual afferentation, the compensatory reactions of the lateral semirings of the pelvic region (lateral biomechanical blocks) are formed

Adsorption and two-body recombination of atomic hydrogen on 3^3He-4^4He mixture films

We present the first systematic measurement of the binding energy $E_a$ of hydrogen atoms to the surface of saturated $^3$He-$^4$He mixture films. $E_a$ is found to decrease almost linearly from 1.14(1) K down to 0.39(1) K, when the population of the ground surface state of $^3$He grows from zero to $6\times10^{14}$ cm$^{-2}$, yielding the value $1.2(1)\times 10^{-15}$ K cm$^2$ for the mean-field parameter of H-$^3$He interaction in 2D. The experiments were carried out with overall $^3$He concentrations ranging from 0.1 ppm to 5 % as well as with commercial and isotopically purified $^4$He at temperatures 70...400 mK. Measuring by ESR the rate constants $K_{aa}$ and $K_{ab}$ for second-order recombination of hydrogen atoms in hyperfine states $a$ and $b$ we find the ratio $K_{ab}/K_{aa}$ to be independent of the $^3$He content and to grow with temperature.Comment: 4 pages, 4 figures, all zipped in a sigle file. Submitted to Phys. Rev. Let

Structure and Electron-Transport Properties of Photoresist Implanted by Sb + Ions

Morphology and electron-transport properties in the photoresist-silicon structures implanted by 60 keV antimony in the fluence range 1 × 10 15 ÷ 5 × 10 16 cm −2 with the ion current density 4 µA/cm 2 have been investigated. Microhardness increases with the increasing fluence. Non-monotonous dependence of microhardness on the depth in the implanted structures was observed. Transition from insulating to the metallic regime of conductivity was not observed