On the geometry of the domain of the solution of nonlinear Cauchy problem

We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study also a variant of the inverse problem of the Cauchy problem and prove that the considered inverse problem has a solution under certain regularity condition. We illustrate the Cauchy and the inverse problems in some interesting examples such that the families of the characteristic curves have either common envelopes or singular points. In these cases the definition domain of the solution of the differential equation contains a gap.Comment: accepted for publication in the book Lie groups, differential equations and geometry in Springer Unip

A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).Comment: 20 pages, 13 figure

Screening of Georgian grapevine germplasm for susceptibility to downy mildew (Plasmopara viticola)

Downy mildew, caused by the obligate biotrophic parasite Plasmopara viticola, is one of the most serious grapevine diseases with worldwide distribution. Resistant grapevines can be used to reduce damages caused by the pathogen, recently different levels of susceptibility to P. viticola were detected in some Georgian autochthonous varieties.  The aim of the present work was to classify additional Georgian autochthonous varieties into different groups according to their susceptibility to the downy mildew agent in the framework of COST Action FA1003 "East-West Collaboration for Grapevine Diversity Exploration and Mobilization of Adaptive Traits for Breeding". The leaf disk assay defined by the OIV 452-1 protocol was used for screening 61 native varieties of Georgia. Screened varieties showed different degree of resistance: very high – 7 accessions, high - 13, medium - 15, low – 23, and very low - 3 accessions. The results suggest that further resistant genotypes are likely to be found within more than 500 Georgian grapevine cultivars

Design, Commissioning and Performance of the PIBETA Detector at PSI

We describe the design, construction and performance of the PIBETA detector built for the precise measurement of the branching ratio of pion beta decay, pi+ -> pi0 e+ nu, at the Paul Scherrer Institute. The central part of the detector is a 240-module spherical pure CsI calorimeter covering 3*pi sr solid angle. The calorimeter is supplemented with an active collimator/beam degrader system, an active segmented plastic target, a pair of low-mass cylindrical wire chambers and a 20-element cylindrical plastic scintillator hodoscope. The whole detector system is housed inside a temperature-controlled lead brick enclosure which in turn is lined with cosmic muon plastic veto counters. Commissioning and calibration data were taken during two three-month beam periods in 1999/2000 with pi+ stopping rates between 1.3*E3 pi+/s and 1.3*E6 pi+/s. We examine the timing, energy and angular detector resolution for photons, positrons and protons in the energy range of 5-150 MeV, as well as the response of the detector to cosmic muons. We illustrate the detector signatures for the assorted rare pion and muon decays and their associated backgrounds.Comment: 117 pages, 48 Postscript figures, 5 tables, Elsevier LaTeX, submitted to Nucl. Instrum. Meth.

A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background

A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under su(1,1) algebra can be brought back to the general Natanzon hypergeometric potentials

Eigenvalue problems associated with Korn's inequalities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46189/1/205_2004_Article_BF00251798.pd

HIBISCUS: Hydroxychloroquine for the secondary prevention of thrombotic and obstetrical events in primary antiphospholipid syndrome

The relapse rate in antiphospholipid syndrome (APS) remains high, i.e. around 20%-21% at 5 years in thrombotic APS and 20-28% in obstetrical APS [2, 3]. Hydroxychloroquine (HCQ) appears as an additional therapy, as it possesses immunomodulatory and anti-thrombotic various effects [4-16]. Our group recently obtained the orphan designation of HCQ in antiphospholipid syndrome by the European Medicine Agency. Furthermore, the leaders of the project made the proposal of an international project, HIBISCUS, about the use of Hydroxychloroquine in secondary prevention of obstetrical and thrombotic events in primary APS. This study has been launched in several countries and at now, 53 centers from 16 countries participate to this international trial. This trial consists in two parts: a retrospective and a prospective study. The French part of the trial in thrombosis has been granted by the French Minister of Health in December 2015 (the academic trial independent of the pharmaceutical industry PHRC N PAPIRUS) and is coordinated by one of the members of the leading consortium of HIBISCUS