On a new compactification of moduli of vector bundles on a surface, IV: Nonreduced moduli

The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced moduli scheme contains an open subscheme which is isomorphic to moduli scheme of semistable vector bundles.Comment: 20 pages, additions and removal

Synthesis and characterization of ZnBTC-based MOFs: effect of solvents and salt

In this work, we studied the optimization of synthetic approaches to creating structurally modified metal-organic frameworks under various synthesis conditions. We investigated the influence of the various solvents and zinc salts on the structural characteristics of the metal-organic framework based on benzene-1,3,5-tricarboxylic acid (H3BTC). The results indicate that the variation of the types of both solvent and salt is a parameter affecting the crystallinity, phase purity, and morphology of the metal-organic framework. This was confirmed by comprehensive structural characterization (SEM, EDX, PXRD)

Об одном изоморфизме компактификаций схемы модулей векторных расслоений

A morphism of the reduced Gieseker - Maruyama moduli functor (of semistable coherent torsion-free sheaves) on the surface to the reduced moduli functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. It is shown that main components of reduced moduli scheme for semistable admissible pairs ((eS; eL); eE) are isomorphic to main components of the reduced Gieseker - Maruyama moduli scheme.Построен морфизм приведенного функтора модулей Гизекера – Маруямы (полустабильных когерентных пучков без кручения) на приведенный функтор модулей допустимых полустабильных пар c тем же полиномом Гильберта. Показано, что основные компоненты приведенной схемы модулей полустабильных допустимых пар ((S; L); E) изоморфны основным компонентам приведенной схемы Гизекера – Маруямы

Изоморфизм компактификаций модулей векторных расслоений: неприведенные схемы модулей

We continue the study of the compactification of the moduli scheme for Gieseker-semistable vector bundles on a nonsingular irreducible projective algebraic surface S with polarization L, by locally free sheaves. The relation of main components of the moduli functor or admissible semistable pairs and main components of the Gieseker – Maruyama moduli functor (for semistable torsion-free coherent sheaves) with the same Hilbert polynomial on the surface S is investigated. The compactification of interest arises when families of Gieseker-semistable vector bundles E on the nonsingular polarized projective surface (S, L) are completed by vector bundles E on projective polarized schemes (S, L) of special form. The form of the scheme S, of its polarization L and of the vector bundle E is described in the text. The collection ((S, L), E) is called a semistable admissible pair. Vector bundles E on the surface (S, L) and E on schemes (S, L) are supposed to have equal ranks and Hilbert polynomials which are compute with respect to polarizations L and L, respectively. Pairs of the form ((S, L), E) named as S-pairs are also included into the class under the scope. Since the purpose is to study the compactification of moduli space for vector bundles, only families which contain S-pairs are considered. We build up the natural transformation of the moduli functor for admissible semistable pairs to the Gieseker – Maruyama moduli functor for semistable torsion-free coherent sheaves on the surface (S, L), with same rank and Hilbert polynomial. It is demonstrated that this natural transformation is inverse to the natural transformation built in the preceding paper and defined by the standard resolution of a family of torsion-free coherent sheaves with a possibly nonreduced base scheme. The functorial isomorphism constructed determines the scheme isomorphism of compactifications of moduli space for semistable vector bundles on the surface (S, L).В работе продолжено изучение компактификации схемы модулей полустабильных по Гизекеру векторных расслоений на неособой неприводимой проективной алгебраической поверхности S с поляризацией L, локально свободными пучками. Исследуется связь основных компонент функтора модулей допустимых полустабильных пар и основных компонент функтора модулей Гизекера –Маруямы (полустабильных когерентных пучков без кручения) с тем же полиномом Гильберта на поверхности S. Рассматриваемая компактификация получается, если семейства полустабильных по Гизекеру векторных расслоений E на поляризованной неособой проективной поверхности (S,L) пополняются векторными расслоениями E на проективных поляризованных схемах (S,L) специального вида. Вид схемы S, поляризации L и расслоения E описан в тексте работы. Набор ((S,L),E) назван полустабильной допустимой парой. Векторные расслоения E на поверхности (S,L) и E на схемах (S,L) предполагаются имеющими равные ранги и полиномы Гильберта, вычисляемые относительно поляризаций L и L соответственно. Пары вида ((S,L),E), называемые S-парами, также входят в рассматриваемый класс. Поскольку целью исследования является изучение компактификации пространства модулей векторных расслоений, рассматриваются только семейства, содержащие S-пары. Построено естественное преобразование функтора модулей допустимых полустабильных пар в функтор модулей Гизекера – Маруямы полустабильных когерентных пучков без кручения на поверхности (S,L), имеющих те же ранг и полином Гильберта. Показано, что это естественное преобразование является двусторонним обратным к естественному преобразованию, построенному в предшествующей работе и определяемому стандартным разрешением семейства когерентных пучков без кручения, имеющего возможно неприведенную базисную схему. Построенный изоморфизм функторов модулей определяет изоморфизм компактификаций пространства модулей полустабильных векторных расслоений на поверхности (S,L) как алгебраических схем

Effect of nitric acid modification of montmorillonite clay on synthesis of solketal from glycerol and acetone

[EN]The effect of acid modification of a natural montmorillonite clay (MM) by HNO3 on the catalytic properties of MM from Dash-Salakhlinsk (Kazakhstan) has been investigated in the synthesis of solketal from glycerol and acetone in solvent free and acetonitrile media. HNO3 concentration allowed to control the chemical composition, the surface acidity, the porous structure of the acid-activated MMs and their catalytic performance. The main reaction product was solketal with 86.6–98% selectivity. Conversion of glycerol depended on the Brønsted acidity. The most active sample, namely, MM activated with 0.5 mol/dm3 HNO3, showed good reusability for 3 catalyst cycle

Methods of probe microscopy in the study of topography and elastic properties of cold-resistant elastomers

The work was carried out under the financial support of the Russian Science Fund, grant 14-29-00198-П(sample preparation and scanning electron microscopy) and the Federal Agency of Scientific Organizations - Agreement No 007-ГЗ/Ч3363/26 (scanning probe microscopy)

About some economic applications of cohort analysis

Nowadays, there is the problem of evaluating the return on advertising costs for industries with a delayed conversion. Cohort analysis is a series of studies which are conducted at certain time intervals. Using cohort analysis we can better assess the effectiveness of advertising channels for industries with a delayed conversion. Cohort analysis can be used to analyze following items: efficiency in the context of "traffic sources", usefulness of changes on the web site; assessment of effectiveness of marketing campaigns; assessment of impact of seasonality on the behavior of the user; the decision-making period. The article presents an overview of tools we can use to collect data for analysis. The article also describes the method of selection and the variants of the cohorts to construct the analysis. For demonstration of the proposed method and calculation variant, there is considered the practical example of building a cohort analysis. Using these method and the example of calculating, the companies with delayed conversion can analyze the effectiveness of Internet advertising for different advertising channels. © 2018 Author(s)

STRA13 Interacts with STAT3 and Modulates Transcription of STAT3-dependent Targets

STRA13 is a pVHL-dependent bHLH transcription factor up-regulated on the mRNA level in multiple cancer cell lines and implicated recently in the regulation of immune cell homeostasis and autoimmunity. In searching for STRA13-interacting proteins with oncogenic potential by the yeast two-hybrid screening, we identified STAT3β as a STRA13-binding partner. We showed that STRA13 binds predominantly to phosphorylated (active) STAT3 α and β isoforms via its HLH and C-terminal regions. We also found that STRA13 was able to activate transcription from STAT-dependent cis-elements. Expression of endogenous STRA13 was shown to be cytokine-inducible, consistent with STRA13 involvement in STAT-dependent transcription regulation. We demonstrated that the STAT3-regulated promoter of the pro-apoptotic Fas gene was activated upon STRA13 over-expression and that co-expression of STRA13 with STAT3β or STAT3α modulated the transcriptional outcome. Forced expression of STRA13 induced apoptosis, in agreement with the STRA13 activation effect on the Fas promoter. Simultaneous expression of STRA13 and STAT3β resulted in alleviation of the STRA13 pro-apoptotic effect. Thus, for the first time, we identify STRA13 as a STAT3 partner and provide a consistent line of evidence for STRA13 involvement into regulation of apoptosis via the STAT pathways