Resonances and O-curves in Hamiltonian systems

We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.Comment: 12 page

Современные клинико-морфологические аспекты изучения расстройств микроциркуляции крови

Modern data about microcirculation disorders are presented. The methodical base of carrying out clinical-morphological and functional researches of microcirculation is discussed. The individual typological features of microcirculation caused by active and passive mechanisms of modulation of a tissue blood flow are revealed. The characteristics of different forms of microcirculation disorders (hyperemic, spastic, spastic-atonic, stagnat and stasic forms) are given. Classification of microcirculation disorders, including four degree of insufficiency of tissue blood flow is offered.Представлены современные сведения о диагностике расстройствах микроциркуляции крови. Выявлены индивидуально-типологические особенности микроциркуляции, обусловленные различным уровнем тканевого кровотока и разными механизмами его модуляции. Дана характеристика различных форм расстройств микроциркуляции: гиперемической, спастической, спастико-атонической, застойной и стазической. Предложена классификация расстройств микроциркуляции, основанная на степенях декомпенсации тканевого кровотока

Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

Особенности микроциркуляции крови в коже у детей

The characteristics of a skin blood microcirculation by method of laser Doppler flowmetry (LDF) in 70 children at the age from 4 till 7 years are studied. During this period of life, gradual decrease in intensity of blood microcirculation in the skin is observed. For surveyed children three types of microcirculation are characteristic: mesohaemic, hypohaemic and hiperhaemic. Mesohaemic type of microcirculation (51,4% of children) prevails with balanced sympathetic and parasympathetic regulatory influences.Методом лазерной доплеровской флоуметрии (ЛДФ) изучено состояние кожного кровотока у 70 детей в возрасте от 4 до 7 лет. В этот период наблюдается постепенное снижение интенсивности кровотока в коже. Для обследованных детей характерны три типа микроциркуляции: мезоемический, гипоемический и гиперемический. Преобладает мезоемический тип микроциркуляции (51,4% детей), при котором регуляторные влияния сбалансированы

Experimental limits on the proton life-time from the neutrino experiments with heavy water

Experimental data on the number of neutrons born in the heavy water targets of the large neutrino detectors are used to set the limit on the proton life-time independently on decay mode through the reaction d -> n+?. The best up-to-date limit tau_p > 4 10^23 yr with 95% C.L. is derived from the measurements with D_2O target (mass 267 kg) installed near the Bugey reactor. This value can be improved by six orders of magnitude with future data accumulated with the SNO detector containing 1000 t of D_2O.Comment: LaTeX, 7 pages, 1 table; small typo is correcte

Complex assessment of parameters of central hemodynamics and microcirculation in children of 6-7 years old

The paper presents the results of a comprehensive assessment of central hemodynamic and microcirculation indices in the skin of upper and lower limbs in 6–7-year-old children. 14 girls and 7 boys were examined using laser Doppler flowmetry methods (the LASMA-PF device, allowing simultaneous recording by four sensors) and the analysis of heart rate variability ("Varicard"). The parameters characterizing microcirculation in the limbs were determined and the signs of the appearing functional asymmetry of the upper limbs, as well as the differences in the mechanisms of modulation of cutaneous blood flow in boys and girls were revealed. The estimation of heart rate variability reveals the signs of girls' inclination to sympathotony and boys' inclination to vagotony at the given age. It was marked that central regulation mechanisms have the greater contribution to cardiac rhythm formation in girls. The data obtained testify to the fact that age-related changes at different levels of the cardiovascular system and regulation mechanisms occur somewhat earlier in girls than in boys

The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.Comment: 13 page

The Dynamics of a Rigid Body in Potential Flow with Circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte

Contact complete integrability

Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two foliations, Legendrian and co-Legendrian, and a holonomy-invariant transverse measure of the former in the latter. This turns out to be equivalent to the existence of a canonical $\R\ltimes \R^{n-1}$ structure on the leaves of the co-Legendrian foliation. Further, the above structure implies the existence of $n$ contact fields preserving a special contact 1-form, thus providing the geometric framework and establishing equivalence with previously known definitions of contact integrability. We also show that contact completely integrable systems are solvable in quadratures. We present an example of contact complete integrability: the billiard system inside an ellipsoid in pseudo-Euclidean space, restricted to the space of oriented null geodesics. We describe a surprising acceleration mechanism for closed light-like billiard trajectories