4,365 research outputs found
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 are investigated. We impose the Neumann
boundary condition on the two concentric windows of the radii and
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 .
When and 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
. The quasi-relativistic Hamiltonian is obtained using a -series
expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential
are found accurate up to the second order in . -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, -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
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