Three-magnon problem for exactly rung-dimerized spin ladders: from general outlook to Bethe Ansatze

Three-magnon problem for exactly rung-dimerized spin ladder is brought up separately at all total spin sectors. At first a special duality transformation of the $\rm Schr\ddot odinger$ equation is found within general outlook. Then the problem is treated within Coordinate Bethe Ansatze. A straightforward approach is developed to obtain pure scattering states. At values S=0 and S=3 of total spin the $\rm Schr\ddot odinger$ equation has the form inherent in the $XXZ$ chain. For $S=1,2$ solvability holds only in five previously found {\it completely integrable} cases. Nevertheless a partial S=1 Bethe solution always exists even for general non integrable model. Pure scattering states for all total spin sectors are presented explicitly.Comment: 38 page

On a systematic approach to defects in classical integrable field theories

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Backlund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical $r$-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.Comment: 27 pages, no figures. Final version accepted for publication. References added and section 5 amende

Integrable boundary conditions for classical sine-Gordon theory

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line $x\leq 0$ with local boundary condition at the origin is considered. The most general form of this boundary condition is found such that the problem be integrable. For the resulting system an infinite number of involutive integrals of motion exist. These integrals are calculated and one is identified as the Hamiltonian. The results found agree with some recent work of Ghoshal and Zamolodchikov.Comment: 10 pages, DTP/94-3

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.

Enhancement of the Technology for Live Tularemia Vaccine Production

Objective of the study was to develop and test new biotechnological approaches for live tularemia vaccine production.Materials and methods: Francisella tularensis 15 NIIEG strain was used as producer-strain; Francisella tularensis 503 strain – as test infecting one. Producer strain was cultivated on solid and liquid nutrient media. Tangential ultrafiltration was performed with the help of microfiltration module “Viva-flow”. Lyophilization was conducted using drying installation – Free Zone 2.5 L.Results and discussion: Application of the designed liquid nutrient medium on the basis of enzymatic fibrin hydrolysate and submerged cultivation of the producer-strain has allowed for a significant biomass yield increment. At the stage of tularemia microbe culture concentration via microfiltration through filtering membranes with pore size of 0.2 μm, in the mode of tangential liquid flow, increased has been the content of microbe cells; the nutrient media residues – removed. Comparative analysis of the obtained in accordance with experimental technique laboratory series of the vaccine and commercial preparation of live tularemia vaccine has demonstrated their conformity with the specific normative properties. It is established that application of modified liquid nutrient medium, submerged cultivation conditions, methods of biomass concentration and separation has no negative influence on the main properties of live tularemia vaccine and will provide for considerable produce-ability increase in the future