n-Dimensional filiform Leibniz algebras of length (n-1) and their derivations

In this work $n$-dimensional filiform Leibniz algebras admitting a gradation of length $(n-1)$ are classified. Derivations of such algebras are also described.Comment: 15 page

Local and 2-local derivations on filiform associativ algebras

This paper is devoted to the study of local and 2-local derivations of nullfiliform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local derivations which are not derivations. We show that filiform and naturally graded quasi-filiform associative algebras admit 2-local derivations which are not derivations and any 2-local derivation of null-filiform associative algebras is a derivation

Local Derivations on Algebras of Measurable Operators

The paper is devoted to local derivations on the algebra $S(\mathcal{M},\tau)$ of $\tau$-measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ and a faithful normal semi-finite trace $\tau.$ We prove that every local derivation on $S(\mathcal{M},\tau)$ which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras they all are inner derivations. It is proved that for type I finite von Neumann algebras without an abelian direct summand, and also for von Neumann algebras with the atomic lattice of projections, the condition of continuity of the local derivation is redundant. Finally we give necessary and sufficient conditions on a commutative von Neumann algebra $\mathcal{M}$ for the existence of local derivations which are not derivations on algebras of measurable operators affiliated with $\mathcal{M}.$Comment: 20 page

Leibniz algebras constructed by Witt algebras

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself

Accurate Ellipsometric Measurement of Refractive Index and Thickness of Ultrathin Oxide Film

This work presents some suggestions to improve the accuracy of ellipsometry for determining the refractive indices and thicknesses of ultrathin thermal SiO 2 films on silicon. The effects of substrate optical parameter variations on the ellipsometric measurement were ruled out by conducting the ellipsometric measurements in several different media instead of air. An improved ellipsometer adjustment procedure was developed to minimize the error for ⌿ and ⌬ angle measurement and to check the anisotropy of the sample. To extract the thickness and refractive index of ultrathin dielectric film from the light polarization parameters, an optimization technique with fluctuation of substrate parameter taken into account was proposed. Our results show that the refractive indices of ultrathin ͑2.1-8 nm͒ thermal oxide films prepared by several different methods fall in the range of 1.475 ± 0.003

Modular mobility investigation of polymer binder bitumen

© Published under licence by IOP Publishing Ltd. This paper is aimed to obtain polymer binder bitumen for the road applications with improved properties. Objectives included studying the degradation of crumb rubber during devulcanization in melted petroleum bitumen for its modification and resulted structural properties of bitumen. Using equilibrium swelling technique reduced density of the polymer chains was observed and analysis of sol-gel fractions showed a significant decrease in gel fraction. Under selected method of devulcanization 64% of the backbone rubber remained. With The H1 NMR relaxation method the reduction of bitumen molecular mobility was observed due to thickening of its light fractions. The effectiveness of devulcanization was optimized using a new agent in a powder form and vacuum application. The developed binder has an improved spectrum of physical and technical properties such as softening point temperature, hardness, elasticity, frost resistance, low temperature characteristics