Elliptic equations, manifolds with non-smooth boundaries, and boundary value problems

We discuss basic principles for constructing the theory of boundary value problems on manifolds with non-smooth boundaries. It includes studying local situations related to model pseudo-differential equations in canonical domains. The technique consists of Fourier transform, multi-dimensional Riemann boundary value problem, wave factorization, and multi-variable complex analysi

On some approximate calculations for certain pseudo-differential equations

We consider discrete pseudo - differential operatots and equations as approximate operators and equations for their continuous analogues. For this purpose we study a solvability for such equations in appropriate discrete spaces and give some error estimates for discrete and continuous solutions. This approach is based on the discrete Fourier transform and factorization tecnique which is used for special canonical domains in Euclidean space

On Discrete Solutions for Elliptic Pseudo-Differential Equations

We consider discrete analogue for simplest boundary value problem for elliptic pseudo-differential equation in a half-space with Dirichlet boundary condition in Sobolev-Slobodetskii spaces. Based on the theory of discrete boundary value problems for elliptic pseudo-differential equations we give a comparison between discrete and continuous solutions for certain model boundary value problem

Discrete singular integrals in a half-space

We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf Z}^m_{+}$) iff such is its continual analogue. The key point for this consideration takes solvability theory of so-called periodic Riemann boundary problem, which is constructed by authors.Comment: 9 pages, 1 figur

Difference equations and boundary value problems

We study multidimensional difference equations with a continual variable in the Sobolev-Slobodetskii spaces. Using ideas and methods of the theory of boundary value problems for elliptic pseudo-differential equations, we suggest to consider certain boundary value problems for such difference equation

Discreteness, periodicity, holomorphy, and factorization

The main topic of the paper is to establish some relations between the solvability of a special kind of discrete equations in certain canonical domains and holomorphy properties of their Fourier analogue

The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model

We present a new way of probing the universality class of the site-diluted two-dimensional Ising model. We analyse Monte Carlo data for the magnetic susceptibility, introducing a new fitting procedure in the critical region applicable even for a single sample with quenched disorder. This gives us the possibility to fit simultaneously the critical exponent, the critical amplitude and the sample dependent pseudo-critical temperature. The critical amplitude ratio of the magnetic susceptibility is seen to be independent of the concentration $q$ of the empty sites for all investigated values of $q\le 0.25$. At the same time the average effective exponent $\gamma_{eff}$ is found to vary with the concentration $q$, which may be argued to be due to logarithmic corrections to the power law of the pure system. This corrections are canceled in the susceptibility amplitude ratio as predicted by theory. The central charge of the corresponding field theory was computed and compared well with the theoretical predictions.Comment: 6 pages, 4 figure

The process e+e−→π+π−π0e^+e^-\to\pi^+\pi^-\pi^0 in the energy range 2E_0=1.04 - 1.38 GeV

In the experiment with the SND detector at VEPP-2M e^+e^- collider the process $e^+e^-\to\pi^+\pi^-\pi^0$ was studied in the energy range 2E_0 from 1.04 to 1.38 GeV. A broad peak was observed with the visible mass $M_{vis}=1220\pm 20$ MeV and cross section in the maximum $\sigma_0\simeq 4$ nb. The peak can be interpreted as a $\omega$-like resonance $\omega (1200)$.Comment: 10 pages LATEX and 5 figure

Results of the BiPo-1 prototype for radiopurity measurements for the SuperNEMO double beta decay source foils

The development of BiPo detectors is dedicated to the measurement of extremely high radiopurity in $^{208}$Tl and $^{214}$Bi for the SuperNEMO double beta decay source foils. A modular prototype, called BiPo-1, with 0.8 $m^2$ of sensitive surface area, has been running in the Modane Underground Laboratory since February, 2008. The goal of BiPo-1 is to measure the different components of the background and in particular the surface radiopurity of the plastic scintillators that make up the detector. The first phase of data collection has been dedicated to the measurement of the radiopurity in $^{208}$Tl. After more than one year of background measurement, a surface activity of the scintillators of $\mathcal{A}$($^{208}$Tl) $=$ 1.5 $\mu$Bq/m$^2$ is reported here. Given this level of background, a larger BiPo detector having 12 m$^2$ of active surface area, is able to qualify the radiopurity of the SuperNEMO selenium double beta decay foils with the required sensitivity of $\mathcal{A}$($^{208}$Tl) $<$ 2 $\mu$Bq/kg (90% C.L.) with a six month measurement.Comment: 24 pages, submitted to N.I.M.