Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum

Possibility of the treatment effects on the dynamics of apoptosis processes in tissues of kidneys in acute pyleonephritis and comparative diabetes mellitus in the experiment

Programmed cell death under conditions of an infectious-inflammatory process plays a biologically exclusively positive role in the elimination of cells. Acute inflammatory process is a phenomenon capable of excessive concentration of aggressive effectors of inflammation. The aim of the work was to assess the dynamics of ultrastructural changes and early signs of apoptosis in the kidney tissues in experimental modeling of acute pyelonephritis (AP) and concomitant diabetes mellitus (DM) of type II and II when conducting complex drug correction. The work was performed on 300 adult Wistar rats, divided into 6 groups. Fragments of the kidneys were studied and photographed in the electron microscope PEM-100-01. In the kidneys of animals of the group, where traditional medical correction was used after the friendly modeling of pyelonephritis and type I diabetes, it was found that the glomerular ultrastructure was more preserved, but part of the capillaries of the glomerulus remained deformed with a narrowed lumen, there are signs of insufficient restoration of the glomerular capillary network. In the group of animals using the proposed complex drug correction, the renal structure was preserved, the capillaries of the glomerular network with unchanged architectonics. It has been established that the traditional medical correction did not sufficiently contribute to the restoration of damaged kidney tissue ultrastructure. After carrying out the complex medical correction proposed by us after a friendly simulation of an OP of DM type II, the ultrastructure of the kidney tissue in form and structure approached that of control animals, signs of a compensatory-restorative process appeared: most of the podocytes were hyperplastic and hypertrophied. The podocytes of the outer leaflet were in the active phase of activity, as evidenced by an increase in contractile function and, possibly, the release of urine from the cavity into the lumen of the proximal tubules. The structure of the tubules and interstitial tissue is close to the structure of the group of control animals, only in the cytoplasm of the podocytes of the proximal tubules there is an increased content of lysosomes. The ultrastructure of the glomeruli was normalized; the number of hypertrophic podocytes of the inner leaflet with signs of enhanced protein synthesis increased. Changes in the structures of the cortical and medulla are similar except for the state of cytotrabeculae, where their size decreased in the medulla and signs of deformation of the plasmolemma appeared. In experimental modeling of PD and DM of types I and II, pronounced ultrastructural changes in the kidney tissues were established, and manifestations of early apoptosis processes are significantly limited. The use of the complex drug correction proposed by us stimulates the development of the reparative processes of the kidney and moderately activates apoptosis. The addition of multi-vector preparations (Armadin and Nuklex) to the complex of treatment intensifies compensatory-restorative changes in the kidneys and apoptosis, which contributes to the elimination from the renal microstructures of excess damaged cells and aggressive effectors of inflammation

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $b$ located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any $a,b>0$. When $a$ and $b$ tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure

CPT and Lorentz violation effects in hydrogen-like atoms

Within the framework of Lorentz-violating extended electrodynamics, the Dirac equation for a bound electron in an external electromagnetic field is considered assuming the interaction with a CPT-odd axial vector background $b_\mu$. The quasi-relativistic Hamiltonian is obtained using a $1/c$-series expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential are found accurate up to the second order in $b_0$. $b_0$-induced CPT-odd corrections to the electromagnetic dipole moment operators of a bound electron are calculated that contribute to the anapole moment of the atomic orbital and may cause a specific asymmetry of the angular distribution of the radiation of a hydrogen atom.Comment: 13 pages, 1 figure; (5.14) is corrected to conform to the normalization convention for Laguerre polynomials adopted at present; minor grammatical change

Integrable quadratic Hamiltonians on so(4) and so(3,1)

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.Comment: 16 page

Integrable Euler top and nonholonomic Chaplygin ball

We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio

Neutron diffraction, magnetization and ESR studies of pseudocubic Nd(0.75)Ba(0.25)MnO3 and its unusual critical behavior above Tc

Results of structural neutron diffraction study, magnetization and ESR measure-ments are presented for insulating Nd0.75Ba0.25MnO3, Tc = 129 K. The crystal structure is refined in the range 4.2-300 K. The compound is found to exhibit the Jahn-Teller (JT) transition at 250 K. The field cooled (FC) magnetization data are in a reasonable agreement with the predictions for a 3D isotropic ferromagnet above Tc. However, these measurements reveal a difference between the FC and zero FC data in the paramagnetic region. ESR results are also in a correspondence with behavior of a cubic ferromagnet above T* = 143 K. It is shown that an anisotropic exchange coupling of the Mn and Nd magnetic moments can give a substantial contribution in ESR linewidth masking its critical enhan-cement. The different temperature treatments of the sample reveal a temperature hysteresis of the ESR spectra below T* indicating an anomalous response in the paramagnetic region. The study of phase transition in this manganite suggests change in its character from the second to first order at T*. The conventional free energy including the magnetization and magnetic field is not found to describe the first order transition. This suggests that the charge, orbital and JT phonon degrees of freedom, in addition to magnetization, may be the critical variables, the unusual character of the transition being determined by their coupling. Unconventional critical behavior is attributed to orbital liquid metallic phase that coexists with the initial orbital ordered phase below T*.Comment: 18 pages, 5 figures, submitted to Phys. Rev.

Exponential bounds for the probability deviations of sums of random fields

Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field