Reduction method for solving Boundary Value Problem on Graph to it's internal edge: طريقة التخفيض لحل مسألة قيم حدية على البيان إلى ضلع داخلي منه

The main aim to this research is to reduce the boundary value problem for fourth differential equation on geometric graph with cycles to a problem on a internal edge provided that the right hand side of the differential equation is identically zero on some subgraph of the original graph, and in this research we find the sign of some coefficients in the boundary conditions of the reduced problem and relationship between these coefficients. That's helping us to prove existence and uniqueness for a boundary value problem resulting from this reduction. In order to reach our desired goal, we study the reduction method of boundary value problem for fourth differential equation on tree geometric graph(no cycles), finally we can say that our research help us to study green function on edge(interval) instead of complex sty ding on geometric graph(with cycles).

Shock fronts in the long GRB031203 host galaxy

ABSTRACT The detailed modelling of the spectra observed from the long GRB031203 host galaxy at different epochs during the 2003–2009 yr is presented. The line profiles show FWHM of ∼100 $\rm km\, s^{-1}$. A broad-line profile with FWHM ≤ 400 $\rm km\, s^{-1}$ appears in the line sockets from the 2009 observations. We suggest that the narrow lines show the velocity of starburst (SB) debris, while the broad ones are due to the wind from SB stars. The spectra are emitted from the gas downstream of different shock fronts which are at work on the edges of the emitting clouds. A head-on-back shock appears when the wind from the SB stars reaches the internal edge of the SB debris moving outwards. A head-on shock is created by collision of the debris with the ISM clouds. Line ratios in both cases are calculated by the coupled effect of shock and photoionization from the SB. The models selected by fitting the calculated to the observed line ratios show that the ionization parameters, the shock velocities and the gas pre-shock densities slowly decrease with time. Oxygen metallicities (12+log(O/H) = 8.3–8.48) are lower than solar (8.82) by a factor <3 and nitrogen metallicities are lower than solar (12 + log(N/H) = 8.0, Grevesse & Sauval) by factors of 3–5.

The ratio of the Neolithic and Eneolithic complexes of the forest-steppe Volga region according to radiocarbon dating

The following paper provides a database of radiocarbon dating, which was obtained from the Srednevolzhskaya archaeological culture of the developed and late Neolithic, as well as on the Eneolithic materials of the forest-steppe Volga region. The key issue is the chronological ratio of the melon complexes, which is considered through the construction of graphs of the sums of calibrated radiocarbon dates. Verification of previously obtained definitions was carried out with the ratio of the absolute chronology of adjacent regions. As a result of definitions study for C14, the range of the Srednevolzhskaya Neolithic culture and the Eneolithic complexes coexistence was revealed, which begins with 5050 BC with a probability of 68,2% or 5250 BC with a probability of 95,4% and ends with 3900 BC (68,2%) or 4000 BC (95,4%). The results of radiocarbon dating confirm the genetic continuity between the Neolithic and Eneolithic complexes of the forest-steppe Volga region. In the light of data on the absolute chronology, the assumption of continuity between the Neolithic and Eneolithic can be extended to the basin of the Sok River, where there is a closure of a chronological range of comb Neolithic complexes and aneolithic materials of the Chekalinskiy type. The chronological interval of the late Neolithic ceramics partially coincides with the time of the existence of Tokskiy materials, as well as with the Gundorovskiy type and with an internal edge ceramics.

First report of a blue hue Schendylops (Geophilomorpha, Schendylidae), with a description of a new species from Southeastern Brazil

The first report of a blue colored body in schendylid specimens is presented based on a description of Schendylops turmalina sp. nov. recorded from Southeastern Brazil. The female holotype is described and illustrated, and the variations observed in male paratypes and in a juvenile male from the same locality are given. The new species is characterized by having adults with an uninterrupted series of sternal pore-fields, from the first to the penultimate leg-bearing segments, undivided on the anterior and posterior part of the body and divided into two sub-symmetrical areas in the middle region. This characteristic can also be observed in Schendylops tropicus, S. coscaroni, S. parahyhae, S. inquilinus, S. grismadoi and S. demelloi. However, in addition to the blue hue present between the first and ultimate leg-bearing segments, S. turmalina sp. nov. differs from all the aforementioned species in having the following unique characteristics: antennae less than 2.5 times the length of the cephalic plate in both male and female; posterior margin of mid-part of labrum near-straight; forcipular tarsungulum with the internal edge serrate; tarsus 2 of the ultimate pair of legs with an apical tubercle which has two pore-like sensilla and is surrounded by two larger sensilla.

Decay Length in Pressure Vessels

In theory of shell, decay length is defined as the distance affected by localized external (applied loads) or internal (edge effect, discontinuity) forces and moments, beyond which the effect of these loads becomes negligible. The concept of decay length becomes relevant when assessing the interaction effects caused by adjacent discontinuities. In this paper, the decay lengths for several shells geometries, specifically cylindrical, spherical and conical shells, are reviewed. The available expressions for decay lengths in the literature are listed and are compared with finite element analysis to demonstrate the accuracy of some of the solutions.