An integrable discretization of KdV at large times

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.Comment: 12 page

A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

Surgical Treatment of Giant Cavernous Hemangioma Liver

In the past five years, 16 adults (10 females, age 25–61 years, mean 48) with giant cavernous hemangioma of the liver measuring 15–31 cm (mean-19) underwent surgery in a single Institution. Diagnosis was made with the help of multimodal investigations– ultrasound (US), computed tomography (CT), hepatic angiography, hepatic scintigraphy and fine needle biopsy. Ultrasound and CT had sensitivities of 69% and 82% respectively. Fourteen had preoperative selective hepatic artery embolization to study its effect on operative blood loss. Indication for surgery in all cases was a large abdominal mass with varying severity of pain. In addition, 5 had hemetological and/or coagulation abnormalities, hemobilia in and pyrexia in 1. Seven left lobectomies, 3 left lateral segmentectomies, 2 right lobectomies, 2 right trisegmentectomies and 4 non-anatomical resections of to 3 segments were performed. Postoperative complications developed in 25% with no operative mortality. Preoperative selective hepatic artery embolization helped to decrease the operative hemorrhage in 13 (mean blood loss– 1146 ml). In two cases severe bleeding required use of Cell-saver and massive donor blood transfusion. Our results suggest use of preoperative selective hepatic artery embolization and Cell-saver as an adjunct to the liver resection for these vascular tumors

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

Mimicking diffuse supernova antineutrinos with the Sun as a source

Measuring the electron antineutrino component of the cosmic diffuse supernova neutrino background (DSNB) is the next ambitious goal for low-energy neutrino astronomy. The largest flux is expected in the lowest accessible energy bin. However, for E < 15 MeV a possible signal can be mimicked by a solar electron antineutrino flux that originates from the usual 8B neutrinos by spin-flavor oscillations. We show that such an interpretation is possible within the allowed range of neutrino electromagnetic transition moments and solar turbulent field strengths and distributions. Therefore, an unambiguous detection of the DSNB requires a significant number of events at E > 15 MeV.Comment: 4 pages, 1 figur

Models of coherent exciton condensation

That excitons in solids might condense into a phase-coherent ground state was proposed about 40 years ago, and has been attracting experimental and theoretical attention ever since. Although experimental confirmation has been hard to come by, the concepts released by this phenomenon have been widely influential. This tutorial review discusses general aspects of the theory of exciton and polariton condensates, focussing on the reasons for coherence in the ground state wavefunction, the BCS to Bose crossover(s) for excitons and for polaritons, and the relationship of the coherent condensates to standard lasers.Comment: 27 pages, 6 figures. Submitted for a special issue of J. Phys. Cond. Matt. associated with the EU network "Photon-mediated phenomena in semiconductor nanostructures

К решению экологических вопросов энергетических систем

The paper analyses a possibility to minimize damage due to operation of power systems using fossil fuels. Technological schemes of purification processes ensuring efficient  solution of  the ecological problem, particularly, in the case of power station operating on natural gas and fuel oil  are proposed in the paper. The paper contains an analysis of the mechanism in respect of processes occurring in the proposed methods for gas and liquid purification against detrimental impurities. Проанализированы возможности сведения к минимуму ущерба, возникающего в результате работающих на ископаемом топливе энергетических систем. Предложены технологические схемы очистительных процессов, обеспечивающих эффективное решение экологической проблемы, в частности в случае электрической станции, работающей на природном газе и мазуте. Проанализирован механизм процессов, происходящих в предложенных методах очистки газов и жидкостей от вредных примесей

The Relation Between the Surface Brightness and the Diameter for Galactic Supernova Remnants

In this work, we have constructed a relation between the surface brightness ($\Sigma$) and diameter (D) of Galactic C- and S-type supernova remnants (SNRs). In order to calibrate the $\Sigma$-D dependence, we have carefully examined some intrinsic (e.g. explosion energy) and extrinsic (e.g. density of the ambient medium) properties of the remnants and, taking into account also the distance values given in the literature, we have adopted distances for some of the SNRs which have relatively more reliable distance values. These calibrator SNRs are all C- and S-type SNRs, i.e. F-type SNRs (and S-type SNR Cas A which has an exceptionally high surface brightness) are excluded. The Sigma-D relation has 2 slopes with a turning point at D=36.5 pc: $\Sigma$(at 1 GHz)=8.4$^{+19.5}_{-6.3}$$\times10^{-12}$ D$^{{-5.99}^{+0.38}_{-0.33}}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ (for $\Sigma$$\le3.7\times10^{-21}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ and D$\ge$36.5 pc) and $\Sigma$(at 1 GHz)=2.7$^{+2.1}_{-1.4}$$\times$ 10$^{-17}$ D$^{{-2.47}^{+0.20}_{-0.16}}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ (for $\Sigma$$>3.7\times10^{-21}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ and D$<$36.5 pc). We discussed the theoretical basis for the $\Sigma$-D dependence and particularly the reasons for the change in slope of the relation were stated. Added to this, we have shown the dependence between the radio luminosity and the diameter which seems to have a slope close to zero up to about D=36.5 pc. We have also adopted distance and diameter values for all of the observed Galactic SNRs by examining all the available distance values presented in the literature together with the distances found from our $\Sigma$-D relation.Comment: 45 pages, 2 figures, accepted for publication in Astronomical and Astrophysical Transaction