On a class of integrable systems connected with GL(N,\RR)

In this paper we define a new class of the quantum integrable systems associated with the quantization of the cotangent bundle $T^*(GL(N))$ to the Lie algebra $\frak{gl}_N$. The construction is based on the Gelfand-Zetlin maximal commuting subalgebra in $U(\frak{gl}_N)$. We discuss the connection with the other known integrable systems based on $T^*GL(N)$. The construction of the spectral tower associated with the proposed integrable theory is given. This spectral tower appears as a generalization of the standard spectral curve for integrable system.Comment: LaTeX, 13 page

Giant Keplerate molecule Fe30 - the first octopole magnet

The multipole expansion technique is applied to one of the largest magnetic molecules, Fe30. The molecule's dipole, toroid and quadrupole magnetic moments are equal to zero (in the absence of magnetic field) so the multipole expansion starts from the octopole moment. Probably the Fe30 molecule is the most symmetrical magnetic body synthesized so far. The magnetization process is considered theoretically in different geometries. Some components of the octopole moment experience a jump while the magnetization rises linearly up to its saturation value. An elementary octopole moment consisting of four magnetic dipoles is proposed as a hint for designing of an experiment for measurement of octopole magnetic moment components.Comment: 7 pages, 9 figure

Investigation of Changes of Short-range Ordering and Electron Density in Simulating Alloys Based on Iron

Short-range ordering and electron density in simulation alloys, containing Cr, Mo, W and V as a doping addition, were studied by Mossbauer spectroscopy and positron annihilation methods. A number of peculiarities was observed in alloys with vanadium as a doping

Business cooperation technology between a swimming coach-instructor and parents of infants

The experimental program for the development of swimming skills in infants with the help of our proposed online pedagogical technology of cooperation between an instructor and parents to improve their health-improving competencies has shown greater efficiency compared to the traditional program. And it can be recommended for use in health-improving swimming centers for infants and in children’s clinic

Асиметрії гемостаза як показник фізіологічної адаптації на дію навколишнього зовнішнього середовища

As it is demonstrated in experiments on rats, polarized ligt influence on head right and left hemispheres cause different degreed reactions from blood coagulation and fibrinolysis side. This difference is conected with polarized light action to peroxidative lipid oxidation (PIO) reactions course, antioxidative enzymes aitivity, brain hemispheres procoagulant and fibrinolytic features. They are unegual in different hemispheres and this asymmetry is supported (enforced) by polarized light action. Polarized light is haemostasis asymmetries modulator in brain hemispheres that is, probably, adaptation reaction under physiological conditions directed to normal (asymmetrical) interrelations creation betwen them.У експериментах на щурах показано, що дії поляризованим світлом на праву і ліву половину голови викликають різну ступень реакції з боку згортання крові і фібриноліза. Ця різниця пов’язана з впливом поляризованого світла на перебіг реакцій перекисного окислення ліпідів (ПОЛ), активність антіоксидантних ферментів, прокоагулянтних і фібринолітичних властивостей півкуль мозку. У різних півкулях вони неоднакові і ця їх асиметрія підтримується (посилюється) дією поляризованого світла. Поляризоване світло є модулятором асиметрій гемостаза в півкулях мозку, що, мабуть, є реакцією адаптації у фізіологічних умовах, що спрямована на створення нормальних (асиметричних) взаємостосунків між ними

Experimental and theoretical study of swept-wing boundary-layer instabilities. Three-dimensional Tollmien-Schlichting instability

Extensive combined experimental and theoretical investigations of the linear evolution of three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. The flow under consideration is the boundary layer over an airfoil at 35 degrees sweep and an angle of attack of +1.5 degree. At these conditions, TS instability is found to be the predominant one. Perturbations with different frequencies and spanwise wavenumbers are generated in a controlled way using a row of elastic membranes. All experimental results are deeply processed and compared with results of calculations based on theoretical approaches. Very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved

Quantitative study of localized mechanisms of excitation of cross-flow instability modes in a swept-wing boundary layer

An experimental study of two efficient receptivity mechanisms of excitation of cross-flow (CF) instability modes is carried out in a boundary layer of a real airfoil section of a swept wing due to: (i) action of localized surface vibrations, and (ii) scattering of 2D freestream vortices on them. It is found that the two mechanisms lead to rather efficient excitation of CF-modes both at surface vibration frequency and at combination 'vortex-vibration' frequencies. First estimations of the corresponding localized receptivity coefficients are obtained. Direct comparison of the experimental amplification curves of the excited CF-modes with those calculated based on the linear stability theory (LST) has shown that the experimental data obtained at vibration frequency are in excellent agreement with the LST. At the same time, growth rates of the CF-modes excited at combination frequencies are found to be completely inconsistent with the LST. A possible explanation of this phenomenon via action of a new efficient distributed receptivity mechanism is suggested. This mechanism is associated with scattering of freestream vortices on rather high-amplitude CF-modes excited by surface vibrations

Experimental and theoretical study of swept-wing boundary-layer instabilities: Unsteady crossflow instability

Extensive combined experimental and theoretical investigations of the linear evolution of unsteady (in general) Cross-Flow (CF) and threedimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. CF-instability characteristics are investigated in detail at an angle of attack of −5○ when this kind of instability dominates in the laminarturbulent transition process, while the 3D TS-instability characteristics are studied at an angle of attack of +1.5○ when this kind of instability is predominant in the transition process. All experimental results are deeply processed and compared with results of calculations based on several theoretical approaches. For the first time, very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved both for unsteady CF- and 3D TS-instability modes for the case of a boundary layer developing on a real swept airfoil. The first part of the present study (this paper) is devoted to the description of the case of CF-dominated transition, while the TS-dominated case will be described in detail in a subsequent second part of this investigation