Semigroups containing proximal linear maps

Abels H, Margulis GA, Soifer GA. Semigroups containing proximal linear maps. Israel Journal of Mathematics. 1995;91(1-3):1-30.A linear automorphism of a finite dimensional red vector space V is called proximal if it has a unique eigenvalue-counting multiplicities-of maximal modulus. Goldsheid and Margulis have shown that if a subgroup G of GL(V) contains a proximal element then so does every Zariski dense subsemigroup H of G, provided V considered as a G-module is strongly irreducible. We here show that H contains a finite subset M such that for every g is an element of GL(V) at least one of the elements gamma g, gamma is an element of M, is proximal. We also give extensions and refinements of this result in the following directions: a quantitative version of proximality, reducible representations, several eigenvalues of maximal modulus

Properly discontinuous groups of affine transformations with orthogonal linear part

Abels H, Margulis GA, Soifer GA. Groupes proprement discontinus de transformations affines avec parties linéaires orthogonales. Comptes rendus de l'Académie des sciences. Série 1, Mathématique . 1997;324(3):253-258.Let Gamma be a subgroup of the group of all affine transformations of a real affine space A of finite dimension. Suppose that Gamma acts properly discontinuously on A. We determine which orthogonal groups can occur as Zariski closures of the linear part of Gamma. Our methods yield a proof of Auslander's conjecture for affine spaces of dimension at most 6

Ca doped YBCO on the Ba site

The effect of partial, nominal replacement of Ba with Ca on the properties of the YBa2Cu3O6+gd superconductor varies with the concentration of Ca. For nominal concentrations in Ca up to 50% a two phase system is formed: the known superconducting phase Y1-yCayBa2Cu3O6+δ and a new, non superconducting phase of composition Y1.14Ca1.58Cu3.27O6.45. The x-ray diffraction pattern of this new phase matches the Bragg peaks, as well as the commensurate and incommensurate peaks of a partially indexed pattern of the phase Y2-xCa2+xCu5O10. For nominal Ca concentrations 40 and 50%, microprobe analysis shows that the superconducting phase becomes a mixture of Y1-yCayBa2Cu3O6+° and YBa1.8Ca0.2Cu3O6.5, where Ca enters the structure in the Ba site. The microraman spectra indicate a small substitution of Ba by Ca, while the new phase shows novel characteristics. © 1995 Plenum Publishing Corporation

Effect of Ca substitutions on the properties of YBa2Cu3O6+d

We study the effect of Ca substitutions on the structural and superconducting properties of the system of nominal composition YCaxBa2-xCu3O6+d. The system remains superconducting up to x=1.00 and the critical temperatures vary between 92 and 80K. A new, non superconducting phase of stoichiometry Y1.14Ca1.58Cu3.27O6.45 appears with concentrations that increase with the nominal concentration of Ca. For x=0.80 and x=1.00 we observe a substitution of the Ba with Ca in crystallites of the form YBa1.8Ca0.2Cu3O6.5. © 1994

Is there epidemiology in Russia?

OBJECTIVE—To examine the current state of epidemiology in Russia.
DESIGN—The structure of clinical research and statistical methods was used to shed light on the epidemiology in Russia. The frequencies of specific study designs were evaluated using Medline data for 1970-1997. To determine the proportion of advanced design clinical studies the frequency of cohort, prospective, follow up, or longitudinal studies, and controlled trials was evaluated. All diagnosis related studies were found to determine the usage of advanced statistical technique (ROC analysis). The adequacy of Medline information was checked by hand search of journals. All dissertations in epidemiology defended in Russia in 1995 and 1996 were evaluated for their methodology. The curriculum recommended by Ministry of Health to Medical Universities was evaluated. Available literature and library indexing of epidemiological terms examined.
MAIN RESULTS—Russian medical research uses less frequently advanced study designs and methods of data analysis. Medical students are taught epidemiology as a science of spread of infectious diseases. There is no department of epidemiology in Russian universities where epidemiology is taught in the modern sense and no epidemiological and biostatistical periodicals available in Russia.
CONCLUSION—Epidemiology in Russia remains in an archaic state of science of the spread of infectious diseases and it is detrimental to methodology of medical research in Russia.


Keywords: Soviet Union; Russia; study design; comparative studie