Deformations of algebroid stacks

In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.     

Adsorption and photo-catalytic properties of layered lepidocrocite-like quasi-amorphous compounds based on modified potassium polytitanates

TiO2 compounds possess relatively high adsorption abilities and exhibit high photocatalytic activities that exhibit potential for the destruction of organic pollutants in natural and waste waters.Nanostructured potassium polytitanates modified using transition metals and their oxides/hydroxides generate new nanomaterials that operate in the visible spectral range.This study presents the synthesis and investigation of the structure,composition and photocatalytic activity of powdered nanoscale quasi-amorphous potassium polytitanates particles modified with iron,zinc,copper,cobalt and nickel sulfate in aqueous solutions.All of the powders investigated in this work exhibit a high adsorption capacity for methylene blue dye（15-20mg/g） related to the welldeveloped surface of the layered potassium polytitanate particles.Introducing transition metals and their oxides/hydroxides influences the electronic structure of the obtained systems.A high photocatalytic activity was observed for systems containing iron,zinc,nickel and their oxides/hydroxides in the ultraviolet and visible ranges.     

Deformation quantization of gerbes

This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We also classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.     

Chern Classes in Alexander–Spanier Cohomology

In this article we construct explicit cocycles in the AlexanderSpanier cohomological complex, representing the Chern character of an element in Ktheory     

Formality theorem for gerbes

The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an _L∞$L_{\infty }$ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe.     

Effect of chemical composition on the photocatalytic activity of potassium polytitanates intercalated with nickel ions

Results of a synthesis and study of the photocatalytic properties of nanosize powder compounds based on amorphous potassium polytitanate, modified with nickel ions are reported. The effect of protonation is noted, resulting in an increase in the specific surface area and adsorption capacity of the substances obtained. It is shown that the increase in the photoactivity of potassium polytitanates modified in aqueous solutions of nickel salts is due to the formation of multiple potassium polytitanate-NiO _x semiconductor heterojunctions on the surface and to the doping of potassium polytitanate with nickel ions.     

The complexity of Dehn's algorithm for word problems in groups

Given the presentation for a group of Dehn's algorithm, a multitape Turing machine is shown to exist that solves the word problem for that presentation in linear time. Key to this solution is the pattern matching methodology from complexity theory as well as a recent result for confluent Thue systems.     

Synthesis and electric properties of the high-k ceramic composites based on potassium polytitanate modified by manganese

Research on Chemical Intermediates - Potassium polytitanates powders were modified by treatment in aqueous solutions of manganese sulfate at different pH, the obtained intermediates (PPT/Mn) were...