Dirac operator on κ\kappa-Minkowski space bicovariant differential calculus and deformed U(1) gauge theory

Derivation of $\kappa$-Poincare bicovariant commutation relations between coordinates and 1-forms on $\kappa$-Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U(1) gauge theory and appearance of an additional spin 0 gauge field is discussed

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

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

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.

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

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

Root polytopes and abelian ideals

We study the root polytope $\mathcal P_\Phi$ of a finite irreducible crystallographic root system $\Phi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\Phi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal P_\Phi$ and analyze its relation with the facets of $\mathcal P_\Phi$. For $\Phi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal P_\Phi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal P_\Phi^+$.Comment: 41 pages, revised version, accepted for publication in Journal of Algebraic Combinatoric

О РОЛИ ВЛИЯНИЯ ЛЕГИРУЮЩИХ ДОБАВОК НА СТРУКТУРУ И СВОЙСТВА МАГНИЙ–ЦИНКОВЫХ ФЕРРИТОВ

Promising absorbing materials along with Ni−Zn−ferrites are Mg—Zn−ferrites, as they are also intensively absorb electromagnetic waves in the frequency range from 50 MHz to 1000 MHz. The main advantage of the Mg−Zn−ferrite is that it is an inexpensive raw material magnesium oxide. The aim of this work was to study the effect of alloying elements — TiO2 and Bi2O3, — as well as impurities on the microstructure and properties of radar Mg—Zn−ferrite. The influence of alloying elements and impurities on the magnetic and dielectric constant of Mg—Zn−ferrite absorbing materials has been revealed. The addition of bismuth oxide causes a reduction of the permittivity and permeability Mg—Zn−ferrite in the range of up to 1000 MHz. Addition of titanium oxide increases the dielectric constant in the range of up to 1000 MHz, which is important to reduce the wavelength of radar ferrite materials. Addition of titanium oxide leads to a frequency shift of the absorption Mg—Zn−polycrystalline ferrite material towards lower frequencies, and bismuth — towards high frequencies.Thus, the dopant can be regarded as a tool to regulate the wavelength range of the absorption of radar and ferrite materials.К перспективным радиопоглощающим материалам, наряду с Ni—Zn−ферритами, относятся Mg—Zn− ферриты. Эти материалы интенсивно поглощают электромагнитные волны в интервале частот от 50 до 1000 МГц. Основным преимуществом Mg—Zn− ферритов является использование в качестве сырья недорогого оксида магния. Изучено влияние легирующих добавок ТiO2 и Bi2O3, а также примесей на микроструктуру и свойства радиопоглощающих Mg—Zn−ферритов.Установлено влияние легирующих добавок и примесей на магнитную и диэлектрическую проницаемость Mg— Zn−ферритовых радиопоглощающих материалов. Добавка оксидов висмута приводит к некоторому снижению диэлектрической и магнитной проницаемостей Mg—Zn−феррита в диапазоне до 1000 МГц. Добавка оксида титана увеличивает диэлектрическую проницаемость в диапазоне до 1000 МГц, что важно для уменьшения длины электромагнитной волны радиопоглощающих ферритовых материалов. Добавка оксида титана приводит к сдвигу частоты поглощения поликристалличе- ского Mg—Zn−ферритового материала в сторону нижних частот, а висмута — в сторону верхних частот.Показано, что легирующие добавки можно рассматривать как инструмент, регулирующий длину волны и диапазон поглощения радиопоглощающих ферритовых материалов