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

Electronic and transport properties of rectangular graphene macromolecules and zigzag carbon nanotubes of finite length

We study one dimensional (1D) carbon ribbons with the armchair edges and the zigzag carbon nanotubes and their counterparts with finite length (0D) in the framework of the H\"{u}ckel model. We prove that a 1D carbon ribbon is metallic if its width (the number of carbon rings) is equal to $2+3n$. We show that the dispersion law (electron band energy) of a 1D metallic ribbon or a 1D metallic carbon nanotube has a universal {\it sin-}like dependence at the Fermi energy which is independent of its width. We find that in case of metallic graphene ribbons of finite length (rectangular graphene macromolecules) or nanotubes of finite length the discrete energy spectrum in the vicinity of $\varepsilon=0$ (Fermi energy) can be obtained exactly by selecting levels from the same dispersion law. In case of a semiconducting graphene macromolecule or a semiconducting nanotube of finite length the positions of energy levels around the energy gap can be approximated with a good accuracy. The electron spectrum of 0D carbon structures often include additional states at energy $\varepsilon=0$, which are localized on zigzag edges and do not contribute to the volume conductivity.Comment: 6 pages, 5 figure

An improved adsorption method for the characterization of water-based supercapacitor electrodes

The specific surface area is a key characteristic of carbon materials used in supercapacitor electrodes. In this paper, the use of a methylene blue technique for specific surface area determination is presented. Values for the specific surface area, determined by a new method, provide better correlation with theoretical values for the specific electrical capacity of highly-porous carbon electrodes than the values measured by the common BET method. Additionally, the methylene blue adsorption method is thought to characterize carbon adsorption activity in relation to a supercapacitor electrolyte

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.

Experimental Substantiation of New Presentation Form of Cholera Diagnostic Sera

Objective of the study is experimental substantiation of possibility to produce new presentation form of cholera diagnostic sera – lyophilizate in bottles. Materials and methods. Cholera diagnostic sera. Liophylization was performed in Martin Christ Epsilon 2-6D. Residual moisture of dry sera was determined using humidity meter Sartorius MA 150. Solubility of experimental samples was assessed visually. pH was evaluated by potentiometry with the help of PK SevenExcellence-475 Mettler Toledo device, measuring pH/ORP/Ion content/conductivity/concentration. Specific activity and specificity was analyzed through expanded agglutination reaction, using relevant control strains of cholera vibrio. Results and conclusions. Experimentally justified is the possibility to lyophilize cholera diagnostic sera in flasks. Specified are the optimum parameters of lyophilization. It is determined that lyophilization does not result in deterioration of properties, as judging by the quality indicators they meet the requirements of regulatory documentation. Using accelerated aging test, it is demonstrated that the new presentation form of cholera diagnostic sera – lyophilizate in flasks – maintains their specific activity within five years term (the set out shelf life), which fully conform to normative standards