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

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

Elaboration of mathematical model of flight trajectory of material point in atmosphere

In the article, the flight trajectory of a material point in the atmosphere is considered. For its calculation the Runge-Kutta method and the system of the equations of external ballistics are used. Moreover, the approximation of the resistance function according to the 1943-year law for subsonic and supersonic speeds is made. The expansion of dependences of the excess above the line of aiming and flight time from the distance in Taylor’s series is implemented. The results of researches are used in solving the direct problem of external ballistics for the definition of trajectory parameters with an increased accuracy

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

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.

State of the Kozmin and Wrangel Bays (Peter the Great Bay, Japan Sea): dynamics of pollution with heavy metals

Pollution with heavy metals, as iron, manganese, zinc, copper, lead, nickel, and cadmium is considered for the coastal waters in two bights of Peter the Great Bay on the data of the metals content in tissues of the algae Sargassum miyabei and Saccharina japonica . The Fe and Mn indicate terrigenous runoff, the Zn and Cu - anthropogenic impact, and the Pb, Ni, and Cd are the tracers of industrial pollution. The content of Fe is the highest among heavy metals; its maximum concentrations are found in the top of the Kozmin Bay and at Cape Petrovsky in the Wrangel Bay. The Pb and Cd contents are higher at the small boats berthing in the Kozmin Bay. The Ni content is the highest (up to 4 mg/g) on reefs in front of the oil terminal in the Wrangel Bay and in the top of the Kozmin Bay that is possibly reasoned by shipping activity because Ni is included in all oils. The Zn concentration is the highest at the pier in the Wrangel Bay constructed of stone blocks. The contents of heavy metals in algae from these bights are compared with similar data from the Avachinsky Bay (Kamchatka), Nha-Trang Bay (Vietnam) and port Santos (Brazil); relatively high pollution of the Kozmin and Wrangel Bays by Pb is revealed. Pollution in these bights has mostly industrial and anthropogenic nature. The pollution with Ni and Cd decreased between 1995 and 2008, but became higher again in 2012-2013, the pollution with Mn, Zn and Fe also increased in 2012-2013

Determination of ππ\pi\pi scattering lengths from measurement of π+π−\pi^+\pi^- atom lifetime

The DIRAC experiment at CERN has achieved a sizeable production of $\pi^+\pi^-$ atoms and has significantly improved the precision on its lifetime determination. From a sample of 21227 atomic pairs, a 4% measurement of the S-wave $\pi\pi$ scattering length difference $|a_0-a_2| = (.0.2533^{+0.0080}_{-0.0078}|_\mathrm{stat}.{}^{+0.0078}_{-0.0073}|_\mathrm{syst})M_{\pi^+}^{-1}$ has been attained, providing an important test of Chiral Perturbation Theory.Comment: 6 pages, 6 figure

Coronal Shock Waves, EUV Waves, and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (2010, ApJL 716, 57) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave including correspondence to the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.Comment: 18 pages, 10 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co