Первая краевая задача для уравнения теплопроводности с нагрузкой дробного порядка. II

В статье рассмотрена первая краевая задача для нагруженного уравнения теплопроводности в четверти плоскости. Нагруженное слагаемое - след производной дробного порядка на многообразии x=t. Решение задачи сводится к исследованию особого интегрального уравнения Вольтерра второго рода с несжимаемым ядром. Решение характеристического уравнения методом регуляризации показало, что особое интегральное уравнение Вольтерра имеет непустой спектр при 1/2≤β<1. Доказана теорема осуществовании нетривиального решения однородной краевой задачи в неограниченной области

The VMC Survey - XIII : Type II Cepheids in the Large Magellanic Cloud

Date of Acceptance: 27/10/2014The VISTA (Visible and Infrared Survey Telescope for Astronomy) survey of the Magellanic Clouds System (VMC) is collecting deep Ks-band time-series photometry of the pulsating variable stars hosted in the system formed by the two Magellanic Clouds and the Bridge connecting them. In this paper, we have analysed a sample of 130 Large Magellanic Cloud (LMC) Type II Cepheids (T2CEPs) found in tiles with complete or near-complete VMC observations for which identification and optical magnitudes were obtained from the OGLE III (Optical Gravitational Lensing Experiment) survey. We present J and Ks light curves for all 130 pulsators, including 41 BL Her, 62 W Vir (12 pW Vir) and 27 RV Tau variables. We complement our near-infrared photometry with the V magnitudes from the OGLE III survey, allowing us to build a variety of period-luminosity (PL), period-luminosity-colour (PLC) and period-Wesenheit (PW) relationships, including any combination of the V, J, Ks filters and valid for BL Her and W Vir classes. These relationships were calibrated in terms of the LMC distance modulus, while an independent absolute calibration of the PL(Ks) and the PW(Ks, V) was derived on the basis of distances obtained from Hubble Space Telescope parallaxes and Baade-Wesselink technique. When applied to the LMC and to the Galactic globular clusters hosting T2CEPs, these relations seem to show that (1) the two Population II standard candles RR Lyrae and T2CEPs give results in excellent agreement with each other; (2) there is a discrepancy of ~0.1 mag between Population II standard candles and classical Cepheids when the distances are gauged in a similar way for all the quoted pulsators. However, given the uncertainties, this discrepancy is within the formal 1σ uncertainties.Peer reviewedFinal Accepted Versio

Experimental Study of Coherent Summation of Radiation from Two Widely Aperture Pulsed

Emission of two high-power pulsed CO2-lasers with a transverse discharge at atmospheric pressure in the active medium and the output beam aperture 100х100 mm, united by a joint unstable telescopic reso-nator, was coherently summarized under conditions of real ground-level trackon the screen surface, which was remote from output mirror of the laser at a distance of 263 m. Output Brewster windows of laser cu-vettes were manufactured from single-crystal plates of sodium chloride which had a diameter of 300 mm. Mirrors for resonator and optical circuit were manufactured from oxygen-free copper. Active medium - a mixture of gases: CO2: N2: He in the ratio 1 : 2 : 3. Laser pulse duration is 5 microseconds. During the ex-periment, when summing on the screen 2-laser beams at the lowest possible convergence angle of rays, the interference pattern was registered. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3610

On the solution of boundary value problems by the spectral element method

In spectral element method approximate solution of the original differential operator is found in the form of a combination of the linearly independent system of orthogonal functions on the unit interval. Using the spectral decomposition for sufficiently smooth functions, one can obtain an exponential rate of convergence of the approximate solution to the exact solution and the approximation error will decrease exponentially as n grows. In the article the application of spectral element method to the solution of the boundary value problem for the Poisson equation is presented

Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $AdS_5\times S^5$. We argue that the moduli space of the null-surfaces is the space of contours in the super-Grassmanian parametrizing the complex $(2|2)$-dimensional subspaces of the complex $(4|4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.Comment: v4: added a reference to the earlier work; corrected the formula for the stabilizer of the BMN vacuum; added the discussion of the complex structure of the odd coordinates in Section 3.

The VMC survey - XIV : First results on the look-back time star formation rate tomography of the Small Magellanic Cloud

Date of Acceptance: 20/01/2015We analyse deep images from the VISTA survey of the Magellanic Clouds in the YJKs filters, covering 14 deg2 (10 tiles), split into 120 subregions, and comprising the main body and Wing of the Small Magellanic Cloud (SMC). We apply a colour-magnitude diagram reconstruction method that returns their best-fitting star formation rate SFR(t), age-metallicity relation (AMR), distance and mean reddening, together with 68 per cent confidence intervals. The distance data can be approximated by a plane tilted in the East-West direction with a mean inclination of 39°, although deviations of up to ±3 kpc suggest a distorted and warped disc. After assigning to every observed star a probability of belonging to a given age-metallicity interval, we build high-resolution population maps. These dramatically reveal the flocculent nature of the young star-forming regions and the nearly smooth features traced by older stellar generations. They document the formation of the SMC Wing at ages <0.2 Gyr and the peak of star formation in the SMC Bar at ~40 Myr. We clearly detect periods of enhanced star formation at 1.5 and 5 Gyr. The former is possibly related to a new feature found in the AMR, which suggests ingestion of metal-poor gas at ages slightly larger than 1 Gyr. The latter constitutes a major period of stellar mass formation. We confirm that the SFR(t) was moderately low at even older ages.Peer reviewe

The spectrum features of UHECRs below and surrounding GZK

The energy spectrum of UHECRs is discussed on the basis of the Yakutsk array database analysis. In the region E=0.1 to 30 EeV the showers are detected under trigger-500, while at energies above 30 EeV the whole acceptance area for trigger-1000 is used in order to utilize all the data available in the region of GZK cutoff.Comment: Invited talk at CRIS2004: GZK and surroundings, Catania, Italy, 31.05.04. To appear in Nucl. Phys. B Proc. Supp

On the Calculation of the NLO Virtual Photon Impact Factor

The definition of the virtual photon impact factor involves the integration of the s-channel discontinuity of the photon-Reggeon scattering amplitude over the right cut. It permits to formulate a new approach for the calculation of the impact factor based on analytical properties of the amplitude in question. In the next-to-leading order it may give a possibility for considerable simplification of the calculation. We have shown that a part of the diagrams contributing to the impact factor can be treated without their real calculation.Comment: 18 pages, latex, axodraw.sty for figures, version to appear in Nucl. Phys.

Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift

Self-energy corrections involving logarithms of the parameter Zalpha can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by alpha the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy ``potentials'' that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B_62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B_62 based on nonrelativistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.Comment: 14 pages, 1 figure; references added and typographical errors corrected; to appear in Phys. Rev.

A molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids

We investigate in detail the initial susceptibility, magnetization curves, and microstructure of ferrofluids in various concentration and particle dipole moment ranges by means of molecular dynamics simulations. We use the Ewald summation for the long-range dipolar interactions, take explicitly into account the translational and rotational degrees of freedom, coupled to a Langevin thermostat. When the dipolar interaction energy is comparable with the thermal energy, the simulation results on the magnetization properties agree with the theoretical predictions very well. For stronger dipolar couplings, however, we find systematic deviations from the theoretical curves. We analyze in detail the observed microstructure of the fluids under different conditions. The formation of clusters is found to enhance the magnetization at weak fields and thus leads to a larger initial susceptibility. The influence of the particle aggregation is isolated by studying ferro-solids, which consist of magnetic dipoles frozen in at random locations but which are free to rotate. Due to the artificial suppression of clusters in ferro-solids the observed susceptibility is considerably lowered when compared to ferrofluids.Comment: 33 pages including 12 figures, requires RevTex