Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Анализ метрологического обеспечения системы измерений количества и показателей качества нефти СИКН-25-РК-А002 на нефтеперекачивающей станции "Кропоткинская"

Объектом исследования является метрологическое обеспечение системы измерений количества и показателей качества нефти СИКН-25-РК-А002 на нефтеперекачивающей станции "Кропоткинская". Цель работы – проведение анализа обеспечения единства измерений на нефтеперекачивающей станции “Кропоткинская”. Для достижения цели работы были поставлены следующие задачи: рассмотреть обеспечение единства измерений системы измерений на НПС “Кропоткинская” и определить её погрешность в зависимости от условий эксплуатации и транспортируемой среды; рассчитать погрешность измерений массы нетто товарной нефти с помощью СИКН № 59462 НПС “Кропоткинская” и проанализировать её составляющие; рассмотреть безопасные условия эксплуатации НПС “Кропоткинская”.Object of research is metrological providing an oil quantity and quality measuring system of SIKN-25-RK-A002 at oil pumping station "Kropotkinskaya". The work purpose – carrying out the analysis of ensuring unity of measurements at oil pumping station "Kropotkinskaya". For goal achievement of work the following tasks have been set: to consider ensuring unity of measurements of measuring system on NPS "Kropotkinskaya" and to determine its error depending on service conditions and the transported environment; to calculate an error of measurements of net weight of commodity oil by means of SIKN No. 59462 NPS "Kropotkinskaya" and to analyse its components; to consider safe service conditions of NPS "Kropotkinskaya"

Расчеты с персоналом по оплате труда в бюджетных организациях

В работе анализируются положения современного трудового законодательства, с чётом специфики бюджетных организаций. Рассмотрены основные вопросы начисления оплаты труда, удержания из заработной платы, предложены рекомендации по совершенствованию учета расчетов с работниками.The paper analyzes the situation of the modern labor legislation, with chёtom specifics of budgetary organizations. The main questions accrual of wages, deductions from wages, provide recommendations for the improvement of payments to employees

Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit

We study a generic but simple non-integrable quantum {\em many-body} system of {\em locally} interacting particles, namely a kicked $t-V$ model of spinless fermions on 1-dim lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). Statistical properties of dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in {\em thermodynamic limit} are considered as the kick parameters (which control the degree of non-integrability) are varied. We find and demonstrate {\em ballistic} transport and non-ergodic, non-mixing dynamics (implying infinite conductivity at all temperatures) in the {\em integrable} regime of zero or very small kick parameters, and more generally and important, also in {\em non-integrable} regime of {\em intermediate} values of kicked parameters, whereas only for sufficiently large kick parameters we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness $D$) which controls the phase transition from non-mixing/non-ergodic dynamics (ordered phase, $D>0$) to mixing/ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find {\em exponential decay of time-correlation function} in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time averaged observables.Comment: 18 pages in REVTeX with 14 eps figures included, Submitted to Physical Review

Modeling Connectivity in Terms of Network Activity

A new complex network model is proposed which is founded on growth with new connections being established proportionally to the current dynamical activity of each node, which can be understood as a generalization of the Barabasi-Albert static model. By using several topological measurements, as well as optimal multivariate methods (canonical analysis and maximum likelihood decision), we show that this new model provides, among several other theoretical types of networks including Watts-Strogatz small-world networks, the greatest compatibility with three real-world cortical networks.Comment: A working manuscript, 5 pages, 3 figures, 1 tabl

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure