Introduction to numerical analysis.

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Methods of mathematical analysis and computation.

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Survey of numerical analysis.

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Advanced numerical analysis /

Mode of access: Internet.

Numerical analysis of capacities for two-qubit unitary operations

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

Analysis and optimisation of the performance of nonlinear optical communication systems

We investigate the feasibility of simultaneous suppressing of the amplification noise and nonlinearity, representing the most fundamental limiting factors in modern optical communication. To accomplish this task we developed a general design optimisation technique, based on concepts of noise and nonlinearity management. We demonstrate the immense efficiency of the novel approach by applying it to a design optimisation of transmission lines with periodic dispersion compensation using Raman and hybrid Raman-EDFA amplification. Moreover, we showed, using nonlinearity management considerations, that the optimal performance in high bit-rate dispersion managed fibre systems with hybrid amplification is achieved for a certain amplifier spacing – which is different from commonly known optimal noise performance corresponding to fully distributed amplification. Required for an accurate estimation of the bit error rate, the complete knowledge of signal statistics is crucial for modern transmission links with strong inherent nonlinearity. Therefore, we implemented the advanced multicanonical Monte Carlo (MMC) method, acknowledged for its efficiency in estimating distribution tails. We have accurately computed acknowledged for its efficiency in estimating distribution tails. We have accurately computed marginal probability density functions for soliton parameters, by numerical modelling of Fokker-Plank equation applying the MMC simulation technique. Moreover, applying a powerful MMC method we have studied the BER penalty caused by deviations from the optimal decision level in systems employing in-line 2R optical regeneration. We have demonstrated that in such systems the analytical linear approximation that makes a better fit in the central part of the regenerator nonlinear transfer function produces more accurate approximation of the BER and BER penalty. We present a statistical analysis of RZ-DPSK optical signal at direct detection receiver with Mach-Zehnder interferometer demodulation

Social and scientific issues in the acceptibility of radiation risks

Ionising radiation hazards are perhaps the most documented and regulated occupational and environmental hazard. In the radiological protection field a single expert advisory organisation has had an unusually large influence on the international standard setting process. This is the International Commission on Radiological Protection (ICRP). Two common, and opposing views, exist over the formulation of protection recommendations by the ICRP. The first, and most widely accepted, is that its recommendations are scientifically determined. The second view, is that its recommendations are politically or socially determined. Neither of these analyses adequately accounts for the complex process in which protection recommendations are formulated. A third view, provided by studies of the origins of scientific controversy, suggests that both science and social factors are important in the assessment and limitation of risk. The aim of this thesis is not simply to examine the origin of controversy. Issues of equal, if not more, importance are the resolution of controversy, the formation of consensus and the maintenance of expert authority and influence. These issues form the central focus of this thesis. The aim is to assess the process through which the ICRP formulates its radiological protection recommendations and comment on the extent that these are influenced by the affiliations of its members. This thesis concludes that the ICRP's recommendations have been shaped by a complex relationship of scientific and social considerations, in which a socio-technical commitment to nuclear energy has played a key role. The Commission has responded to new scientific data by making complex changes to its philosophy and methods of describing risk. Where reductions in numerical limits have been applied they have been accompanied by practical measures designed to limit the impact of the change and provide continuity with the old limits and flexibility in the application of the new recommendations.

The analysis and prediction of the quantity and composition of household refuse

This thesis describes the development of a simple and accurate method for estimating the quantity and composition of household waste arisings. The method is based on the fundamental tenet that waste arisings can be predicted from information on the demographic and socio-economic characteristics of households, thus reducing the need for the direct measurement of waste arisings to that necessary for the calibration of a prediction model. The aim of the research is twofold: firstly to investigate the generation of waste arisings at the household level, and secondly to devise a method for supplying information on waste arisings to meet the needs of waste collection and disposal authorities, policy makers at both national and European level and the manufacturers of plant and equipment for waste sorting and treatment. The research was carried out in three phases: theoretical, empirical and analytical. In the theoretical phase specific testable hypotheses were formulated concerning the process of waste generation at the household level. The empirical phase of the research involved an initial questionnaire survey of 1277 households to obtain data on their socio-economic characteristics, and the subsequent sorting of waste arisings from each of the households surveyed. The analytical phase was divided between (a) the testing of the research hypotheses by matching each household's waste against its demographic/socioeconomic characteristics (b) the development of statistical models capable of predicting the waste arisings from an individual household and (c) the development of a practical method for obtaining area-based estimates of waste arisings using readily available data from the national census. The latter method was found to represent a substantial improvement over conventional methods of waste estimation in terms of both accuracy and spatial flexibility. The research therefore represents a substantial contribution both to scientific knowledge of the process of household waste generation, and to the practical management of waste arisings.

Analysis and Optimization of Synthetic Aperture Ultrasound Imaging Using the Effective Aperture Approach

An effective aperture approach is used as a tool for analysis and parameter optimization of mostly known ultrasound imaging systems - phased array systems, compounding systems and synthetic aperture imaging systems. Both characteristics of an imaging system, the effective aperture function and the corresponding two-way radiation pattern, provide information about two of the most important parameters of images produced by an ultrasound system - lateral resolution and contrast. Therefore, in the design, optimization of the effective aperture function leads to optimal choice of such parameters of an imaging systems that influence on lateral resolution and contrast of images produced by this imaging system. It is shown that the effective aperture approach can be used for optimization of a sparse synthetic transmit aperture (STA) imaging system. A new two-stage algorithm is proposed for optimization of both the positions of the transmitted elements and the weights of the receive elements. The proposed system employs a 64-element array with only four active elements used during transmit. The numerical results show that Hamming apodization gives the best compromise between the contrast of images and the lateral resolution.

Digital Preservation and Access to Cultural and Scientific Heritage: Presentation of the KT-DigiCult-BG Project

The fast development and wide application of digital methods, combined with broadened access to the Internet and falling computing costs, have created intense interest in electronic presentation and access to cultural and scientific heritage resources. Information technologies have offered cultural institutions new opportunities for the presentation of their holdings, which are now made accessible not only to the specialists, but also to the citizens and interested parties worldwide. The paper presents an overview of the Bulgarian experience in the field of digital preservation and access and on-going work on the project “Knowledge Transfer for the Digitisation of Scientific and Cultural Heritage to Bulgaria” (MTKD-CT-2004-509754) supported by the Marie Curie programme of the FP6 of the EC.

An Analysis and Forecast of Software and Services Research in Bulgaria

In the last 40 years much has been achieved in Software Engineering research and still more is to be done. Although significant progress is being made on several fronts in Service-Oriented Architecture (SOA), there is still no set of clear, central themes to focus research activity on. A task within the EU FP7 Sister project aimed at defining research priorities for the Faculty of Mathematics and Informatics (Sofia University) in the area of Software and Services. A dedicated methodology was proposed and developed, based on various sources of information. The information accumulated was systematised and processed according to this methodology. The final results obtained are described and discussed here.

Numerical Analysis of Chemical Reactions by Monte Carlo Simulation

Добри Данков, Владимир Русинов, Мария Велинова, Жасмина Петрова - Изследвана е химическа реакция чрез два начина за моделиране на вероятността за химическа реакция използвайки Direct Simulation Monte Carlo метод. Изследван е порядъка на разликите при температурите и концентрациите чрез тези начини. Когато активността на химическата реакция намалява, намаляват и разликите между концентрациите и температурите получени по двата начина. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC