ВИКОРИСТАННЯ СПЕЦІАЛІЗОВАНОГО ПРИКЛАДНОГО ІНСТРУМЕНТАРІЮ ДЛЯ АНАЛІЗУ ПРОЦЕСІВ ЕМІСІЇ ПАРНИКОВИХ ГАЗІВ В ЕЛЕКТРОЕНЕРГЕТИЧНІЙ ГАЛУЗІ УКРАЇНИ

This article analyzes the electricity sector of Ukraine in terms of greenhouse gas emissions and the basic algorithms of software tools to automate the process of spatial analysis of greenhouse gas emissions in this branch have been presented. The main advantages of the developed software include the ability of automatic database forming of input data, spatial modeling of greenhouse gas emissions from electricity production at level of point sources and also generate appropriate results in the form of digital thematic maps.Здійснено аналіз електроенергетичної галузі України в сенсі емісії парникових газів та представлено основні алгоритми програмного інструментарію для автоматизації просторового аналізу процесів емісії основних парникових газів в цій галузі. Основні переваги розробленого програмного забезпечення включають можливість автоматично формувати бази вхідних даних, здійснювати просторове моделювання процесів емісії парникових газів при виробництві електроенергії на рівні точкових джерел, а також формувати відповідні результати у вигляді цифрових тематичних карт

The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

Theory of random matrices with strong level confinement: orthogonal polynomial approach

Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal with respect to exponential weights we calculate with asymptotic accuracy the two-point kernel over all distance scale, and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the endpoints of spectrum. We also obtain exact expressions for density of levels, one- and two-point Green's functions, and prove that new universal local relationship exists for suitably normalized and rescaled connected two-point Green's function. Connection between structure of Szeg\"o function entering strong polynomial asymptotics and mean-field equation is traced.Comment: 12 pages (latex), to appear in Physical Review

Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extende

A pedestrian's view on interacting particle systems, KPZ universality, and random matrices

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo

Introduction to Random Matrices

These notes provide an introduction to the theory of random matrices. The central quantity studied is $\tau(a)= det(1-K)$ where $K$ is the integral operator with kernel 1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y). Here $I=\bigcup_j(a_{2j-1},a_{2j})$ and $\chi_I(y)$ is the characteristic function of the set $I$. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in $I$ is equal to $\tau(a)$. Also $\tau(a)$ is a tau-function and we present a new simplified derivation of the system of nonlinear completely integrable equations (the $a_j$'s are the independent variables) that were first derived by Jimbo, Miwa, M{\^o}ri, and Sato in 1980. In the case of a single interval these equations are reducible to a Painlev{\'e} V equation. For large $s$ we give an asymptotic formula for $E_2(n;s)$, which is the probability in the GUE that exactly $n$ eigenvalues lie in an interval of length $s$.Comment: 44 page

Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering

We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060 (stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Design, Performance, and Calibration of CMS Hadron-Barrel Calorimeter Wedges

Extensive measurements have been made with pions, electrons and muons on four production wedges of the Compact Muon Solenoid (CMS) hadron barrel (HB) calorimeter in the H2 beam line at CERN with particle momenta varying from 20 to 300 GeV/c. Data were taken both with and without a prototype electromagnetic lead tungstate crystal calorimeter (EB) in front of the hadron calorimeter. The time structure of the events was measured with the full chain of preproduction front-end electronics running at 34 MHz. Moving-wire radioactive source data were also collected for all scintillator layers in the HB. These measurements set the absolute calibration of the HB prior to first pp collisions to approximately 4%