On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms $\rho: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism $\mathcal{N}_r(G) \cong |G|$ to arbitrary infinitesimal unipotent supergroup schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and 3.3. Simplified the proof of Proposition 3.3.

Galois cohomology of certain field extensions and the divisible case of Milnor-Kato conjecture

We prove the "divisible case" of the Milnor-Bloch-Kato conjecture (which is the first step of Voevodsky's proof of this conjecture for arbitrary prime l) in a rather clear and elementary way. Assuming this conjecture, we construct a 6-term exact sequence of Galois cohomology with cyclotomic coefficients for any finite extension of fields whose Galois group has an exact quadruple of permutational representations over it. Examples include cyclic groups, dihedral groups, the biquadratic group Z/2\times Z/2, and the symmetric group S_4. Several exact sequences conjectured by Bloch-Kato, Merkurjev-Tignol, and Kahn are proven in this way. In addition, we introduce a more sophisticated version of the classical argument known as "Bass-Tate lemma". Some results about annihilator ideals in Milnor rings are deduced as corollaries.Comment: LaTeX 2e, 17 pages. V5: Updated to the published version + small mistake corrected in Section 5. Submitted also to K-theory electronic preprint archives at http://www.math.uiuc.edu/K-theory/0589

Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravit

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

The quotient Unimodular Vector group is nilpotent

Jose-Rao introduced and studied the Special Unimodular Vector group $SUm_r(R)$ and $EUm_r(R)$, its Elementary Unimodular Vector subgroup. They proved that for $r \geq 2$, $EUm_r(R)$ is a normal subgroup of $SUm_r(R)$. The Jose-Rao theorem says that the quotient Unimodular Vector group, $SUm_r(R)/EUm_r(R)$, for $r \geq 2$, is a subgroup of the orthogonal quotient group $SO_{2(r+1)}(R)/EO_{2(r + 1)}(R)$. The latter group is known to be nilpotent by the work of Hazrat-Vavilov, following methods of A. Bak; and so is the former. In this article we give a direct proof, following ideas of A. Bak, to show that the quotient Unimodular Vector group is nilpotent of class $\leq d = \dim(R)$. We also use the Quillen-Suslin theory, inspired by A. Bak's method, to prove that if $R = A[X]$, with $A$ a local ring, then the quotient Unimodular Vector group is abelian

IMPROVING THE QUALITY OF THE ORGANIZATION OF TEMPORARY DISABILITY EXAMINATION IN A CITY HOSPITAL

Aim - improving the quality of the organization of temporary disability examination (TDE) in a city hospital. Materials and methods. The research focuses on the organization of temporary disability examination in Samara City Hospital No. 10 providing services to the population of Kuibyshevsky district of Samara, which amounts to more than 87 thousand people. The study involved the following research methods: statistical, analytical, expert assessment, organizational modeling. Results. We implemented an organizational model of TDE improvement, which is based on organizational and methodological aspects of TDE development, methodological approaches to the quality control of TDE, indices of efficiency of TDE organization system. Conclusion. Development of an organizational model for the improvement of TDE based at the City general hospital contributes to the timely acceptance of instructive and methodological documents, raising the level of personnel qualification, developing information support for TDE, and providing quality control of TDE. The following results of the implementation of the organizational model for improving the organization of TDE from 2010 to 2015 were obtained: an increase in the quality of TDE; a reduction in the number of all defects per 100 cases of temporary disability - from 257.2 to 111.1; a reduction in the proportion of unreasonably issued sick-leaves from 4.8% to 1.9%; an increase in the integrated assessment of the quality of care in the model of the final results of the TDE service performance in the City general hospital from 0.75 in 2010 to 0.85 in 2015

Framed transfers and motivic fundamental classes

We relate the recognition principle for infinite P1-loop spaces to the theory of motivic fundamental classes of Deglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with An/(An-0), and the Gysin transfers defined via Verdier's deformation to the normal cone. We then introduce the category of finite R-correspondences for R a motivic ring spectrum, generalizing Voevodsky's category of finite correspondences and Calmes and Fasel's category of finite Milnor-Witt correspondences. Using the formalism of fundamental classes, we show that the natural functor from the category of framed correspondences to the category of R-module spectra factors through the category of finite R-correspondences

Algebraic K-theory of endomorphism rings

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let Y\ra X be a covariant morphism of objects in ${\mathcal C}$. Then $K_n\big(_{\mathcal C}(X\oplus Y)\big)\simeq K_n\big(_{{\mathcal C},Y}(X)\big)\oplus K_n\big(_{\mathcal C}(Y)\big)$ for all $1\le n\in \mathbb{N}$, where $_{{\mathcal C},Y}(X)$ is the quotient ring of the endomorphism ring $_{\mathcal C}(X)$ of $X$ modulo the ideal generated by all those endomorphisms of $X$ which factorize through $Y$. Moreover, let $R$ be a ring with identity, and let $e$ be an idempotent element in $R$. If $J:=ReR$ is homological and $_RJ$ has a finite projective resolution by finitely generated projective $R$-modules, then $K_n(R)\simeq K_n(R/J)\oplus K_n(eRe)$ for all $n\in \mathbb{N}$. This reduces calculations of the higher algebraic $K$-groups of $R$ to those of the quotient ring $R/J$ and the corner ring $eRe$, and can be applied to a large variety of rings: Standardly stratified rings, hereditary orders, affine cellular algebras and extended affine Hecke algebras of type $\tilde{A}$.Comment: 21 pages. Representation-theoretic methods are used to study the algebraic K-theory of ring

PECULIARITIES OF MORBIDITY WITH TEMPORARY DISABILITY AMONG POPULATION OF THE SAMARA REGION

Aim - to study morbidity with temporary disability among the population of the Samara region in order to characterize the health status of the working population. Materials and methods. The form of statistical reporting No. 16-VN "Information on the causes of temporary incapacity for work" for 2013-2015 for the Samara region was analyzed. Analytical, statistical and epidemiological methods of research were used. Results. The characteristic of morbidity among the working population of the Samara region in dynamics for 2013-2015 is presented. The structure of temporary incapacity for work (TIW) in cases and in days, the average duration of one case of TIW, the number of cases and days of TIW per 100 workers were calculated. Conclusion. For the period 2013-2015 there was a decrease in the number of working population by 6.4% to 1366.4 thousand people in the Samara region. There was a slight increase (3.7% in cases and 3.4% in days) in the incidence of temporary disability for all reasons, as well as due to illness (4.0% in cases and 3.8% in days), mainly for account of the urban population. The incidence with temporary disability is almost half as high in rural areas of the region compared with cities. In the structure of morbidity due to diseases, cases of respiratory diseases, musculoskeletal system and connective tissue, as well as trauma and poisoning account for more than 70% of the total pathology. The duration of one case of temporary incapacity for work in the Samara region did not change and amounted to 12.3 days for all reasons and 13.2 days due to illness

FORMATION AND DEVELOPMENT OF TEMPORARY DISABILITY EXAMINATION SERVICE IN RUSSIA

Aim - characterization of the formation, organization, development and prospects of temporary disability examination (TDE) services in Russia. Materials and methods. A review of the data from the scientific publications and legal documents was conducted. Results. The characteristics of the organization and development of temporary disability examination service in Russia since the establishment of the service to date are described. The problems and prospects of TDE service were examined. Conclusion. The organization and development of temporary disability examination in Russia is determined by the formation of the whole healthcare system and by legal acts. The implementation of modern requirements to the temporary disability examination is determined by the challenges faced by healthcare providers, as well as the solution of the problems faced by the subjects of the internal control of activities of healthcare organizations