Criticality for branching processes in random environment

We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching processes are developed under a general assumption, known as Spitzer's condition in fluctuation theory of random walks, and some additional moment condition. We determine the exact asymptotic behavior of the survival probability and prove conditional functional limit theorems for the generation size process and the associated random walk. The results rely on a stimulating interplay between branching process theory and fluctuation theory of random walks.Comment: Published at http://dx.doi.org/10.1214/009117904000000928 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit theorems for weakly subcritical branching processes in random environment

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, 'supercritical'. This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on non-extinction. Also a functional limit theorem is proven, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.Comment: 35 page

Modern approaches to the treatment of genital prolapse in obese women

Introduction. The problem of female genital prolapse (GP) remains in the sportlight of gynecologists, because despite the variety of surgical methods, there are still recurrences of the disease, which are associated not only with the failure of the restored ligaments, fascia, muscles, damaged pelvic floor and perineum, but with the imperfection of the operation. The solution of this problem is especially important in the treatment of patients with extragenital pathology, in particular obesity. The purpose: to optimize the treatment of genital prolapse in obese patients by determining an individual approach to planning surgical treatment taking into account the degree of obesity and concomitant pathology. Materials and methods. We examined 65 patients of which 20 had genital prolapse and obesity (main group), 25 had genital prolapse and normal weight (comparison group), 20 women did not have gynecological diseases and extragenital pathology made up control group. To diagnose obesity and determine its degree we calculated body mass index (BMI). To determine the degree of GP its quantitative assessment was used (POP-Q; 1996). Surgical intervention included transvaginal extirpation of the uterus without appendages, anterior colporrhaphy, colpoperineoraphy with levatoplasty, sacrospinal colpopexy. Transabdominal and laparoscopic colposacropexy in obese women were not used due to the presence of relative contraindications for laparoscopy (cardiovascular disease, respiratory pathology, adhesions, the condition after hernias’ surgery). Therefore, all operations on women with GP and obesity were performed transvaginally due to the inability to perform abdominal access. In comparison group transvaginal surgery was performed. All the groups under study were representative. Before the use of polypropylene mesh "Polymesh" to minimize purulent-septic complications associated with the use of synthetic prostheses aquadissection was performed with 0.9% saline with the addition of 1 g of ceftriaxone per 200 ml. After the operation, the women used suppositories with hyaluronic acid (revitax). Results. The results of surgical treatment have been analyzed and the following data were obtained: recurrences in the main and in the comparison group were 4% (2 women in whom operations were performed with the use of their own tissues without  mesh prosthesis). Infectious complications, dyspareunia and pelvic pain were not observed. Conclusions. Surgical treatment of GP in obese women by using polypropylene mesh "Polymesh" for colposacropexy after transvaginal uterine extirpation increases the effectiveness of treatment  and redduces the number of recurrences. Hydropreparation of the mesh with an antibacterial agent and postoperative use of hyaluronidase intravaginally helps to reduce purulent-septic complications of surgery and improves the patients’quality of life

The multilevel trigger system of the DIRAC experiment

The multilevel trigger system of the DIRAC experiment at CERN is presented. It includes a fast first level trigger as well as various trigger processors to select events with a pair of pions having a low relative momentum typical of the physical process under study. One of these processors employs the drift chamber data, another one is based on a neural network algorithm and the others use various hit-map detector correlations. Two versions of the trigger system used at different stages of the experiment are described. The complete system reduces the event rate by a factor of 1000, with efficiency $\geq$95% of detecting the events in the relative momentum range of interest.Comment: 21 pages, 11 figure

Density Matrix Kinetic Equation Describing a Passage of Fast Atomic Systems Through Matter

The quantum-mechanical consideration of a passage of fast dimesoatoms through matter is given. A set of quantum-kinetic equations for the density matrix elements describing their internal state evolution is derived. It is shown that probabilistic description of internal dynamics of hydrogen-like atoms is impossible even at sufficiently low energies because of the ``accidental'' degeneracy of their energy levels.Comment: 12 pages, LATEX, submitted to J. Phys.

Dependence of optical properties and hardness on carbon content in silicon carbonitride films deposited by plasma ion immersion processing technique

Materials with Si-C-N composition are of great interest due to their remarkable properties such as high hardness and oxidation resistance. In this study amorphous silicon nitride and silicon carbonitride films were deposited on glass, fised silica, and carbon substrates by the plasma immersion ion processing technique. Gas pressure during the deposition was kept around 0.13 Pa (1 mTorr) and S a, N2, Ar, and C2H2 gas mixtures were used. Film hardness, composition, and UV-visible optical absorption were characterized using nanoindentati on, ion beam analysis techniques, and UV-visible spectroscopy, respectively. The films exhibit high transparency in the visible and near UV regions. Addition of the carbon to the films causes decrease in the density of the films, as well as decrease in hardness and transparency. These results suggest that in the low energy regime of PTIP the deposition of hard carbon composites with nitrogen and silicon does not take place