456 research outputs found
Quasi-exactly solvable quartic: elementary integrals and asymptotics
We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where
p, h and P are polynomials in one variable. For the case when h is an odd cubic
polynomial, we found an interesting identity which is used to describe the
spectral locus. We also establish some asymptotic properties of the QES
spectral locus.Comment: 20 pages, 1 figure. Added Introduction and several references,
corrected misprint
Two-parametric PT-symmetric quartic family
We describe a parametrization of the real spectral locus of the
two-parametric family of PT-symmetric quartic oscillators. For this family, we
find a parameter region where all eigenvalues are real, extending the results
of Dorey, Dunning, Tateo and Shin.Comment: 23 pages, 15 figure
HIV INFECTION AS A RISK FACTOR OF TUBERCULOSIS IN CHILDREN
The article presents the results of three year follow-up over 96 HIV positive children registered in the AIDS Center. During 3 year follow up the infection with tuberculous mycobacteria was diagnosed in 27.3% (n = 23) of HIV positive children from the followed up group. The leading risk factor of tuberculosis is family exposure to a tuberculosis patient – 22.6% (n = 19). Compliance to follow-up and treatment, timely prescribed preventive anti-tuberculosis chemotherapy and highly active antiretroviral therapy enhanced prevention of development of local forms of tuberculosis in the followed up group of children
Convergence Radii for Eigenvalues of Tri--diagonal Matrices
Consider a family of infinite tri--diagonal matrices of the form
where the matrix is diagonal with entries and the matrix
is off--diagonal, with nonzero entries The spectrum of is discrete. For small the
-th eigenvalue is a well--defined analytic
function. Let be the convergence radius of its Taylor's series about It is proved that R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq
\alpha <11/6.$
THE CURRENT SITUATION ON ANTHRAX IN RUSSIA AND IN THE WORLD. MAIN TRENDS AND FEATURES
The current situation on anthrax is characterized as unstable. Instability is associated with recurring epizootic outbreaks complicated by human anthrax cases, as people contract infection mainly through contact with sick animals, their carcasses or animal products. Mentioned are new aerosol and parenteral ways of anthrax contracting. Parenteral use of contaminated heroin led to emergence of new clinical form of anthrax – injectional. Conception on anthrax agent evolution is replenished by data on pathogenic bacilli strains, that occupy an intermediate position between B. anthracis and B. cereus. Ecology of anthrax microbe is considered in view of its interaction with bacteriophages, rhizosphere and soil microflora. Research related to the environmental characteristics of habitat niches and genotypes of B. anthracis, explaining the geographical distribution of areas with a high risk of disease, may allow to optimize the program of animals immunization, which is the most effective measure for the prevention of anthrax
Y-System and Deformed Thermodynamic Bethe Ansatz
We introduce a new tool, the Deformed TBA (Deformed Thermodynamic Bethe
Ansatz), to analyze the monodromy problem of the cubic oscillator. The Deformed
TBA is a system of five coupled nonlinear integral equations, which in a
particular case reduces to the Zamolodchikov TBA equation for the 3-state Potts
model. Our method generalizes the Dorey-Tateo analysis of the (monomial) cubic
oscillator. We introduce a Y-system corresponding to the Deformed TBA and give
it an elegant geometric interpretation.Comment: 12 pages. Minor corrections in Section
Photoproduction of Long-Lived Holes and Electronic Processes in Intrinsic Electric Fields Seen through Photoinduced Absorption and Dichroism in Ca_3Ga_{2-x}Mn_xGe_3O_{12} Garnets
Long-lived photoinduced absorption and dichroism in the
Ca_3Ga_{2-x}Mn_xGe_3O_{12} garnets with x < 0.06 were examined versus
temperature and pumping intensity. Unusual features of the kinetics of
photoinduced phenomena are indicative of the underlying electronic processes.
The comparison with the case of Ca_3Mn_2Ge_3O_{12}, explored earlier by the
authors, permits one to finally establish the main common mechanisms of
photoinduced absorption and dichroism caused by random electric fields of
photoproduced charges (hole polarons). The rate of their diffusion and
relaxation through recombination is strongly influenced by the same fields,
whose large statistical straggling is responsible for a broad continuous set of
relaxation components (observed in the relaxation time range from 1 to about
1000 min). For Ca_3Ga_{2-x}Mn_xGe_3O_{12}, the time and temperature dependences
of photoinduced absorption and dichroism bear a strong imprint of structure
imperfection increasing with x.Comment: 20 pages, 10 figure
Beyond the periodic orbit theory
The global constraints on chaotic dynamics induced by the analyticity of
smooth flows are used to dispense with individual periodic orbits and derive
infinite families of exact sum rules for several simple dynamical systems. The
associated Fredholm determinants are of particularly simple polynomial form.
The theory developed suggests an alternative to the conventional periodic orbit
theory approach to determining eigenspectra of transfer operators.Comment: 29 pages Latex2
The Julia sets and complex singularities in hierarchical Ising models
We study the analytical continuation in the complex plane of free energy of
the Ising model on diamond-like hierarchical lattices. It is known that the
singularities of free energy of this model lie on the Julia set of some
rational endomorphism related to the action of the Migdal-Kadanoff
renorm-group. We study the asymptotics of free energy when temperature goes
along hyperbolic geodesics to the boundary of an attractive basin of . We
prove that for almost all (with respect to the harmonic measure) geodesics the
complex critical exponent is common, and compute it
Spectral dependence of photoinduced spin precession in DyFeO3
Spin precession was nonthermally induced by an ultrashort laser pulse in
orthoferrite DyFeO3 with a pump-probe technique. Both circularly and linearly
polarized pulses led to spin precessions; these phenomena are interpreted as
the inverse Faraday effect and the inverse Cotton-Mouton effect, respectively.
For both cases, the same mode of spin precession was excited; the precession
frequencies and polarization were the same, but the phases of oscillations were
different. We have shown theoretically and experimentally that the analysis of
phases can distinguish between these two mechanisms. We have demonstrated
experimentally that in the visible region, the inverse Faraday effect was
dominant, whereas the inverse Cotton-Mouton effect became relatively prominent
in the near-infrared region.Comment: 27 pages, 8 figure
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