Analysis of computer communication systems by use of digital signal processing methods

Queueing theory is an effective tool in the analysis of canputer camrunication systems. Many results in queueing analysis have teen derived in the form of Laplace and z-transform expressions. Accurate inversion of these transforms is very important in the study of computer systems, but the inversion is very often difficult. In this thesis, methods for solving some of these queueing problems, by use of digital signal processing techniques, are presented. The z-transform of the queue length distribution for the Mj GY jl system is derived. Two numerical methods for the inversion of the transfom, together with the standard numerical technique for solving transforms with multiple queue-state dependence, are presented. Bilinear and Poisson transform sequences are presented as useful ways of representing continuous-time functions in numerical computations.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

Combination of altimetry data from different satellite missions

Substantial altimetry datasets collected by different satellites have only become available during the past five years, but the future will bring a variety of new altimetry missions, both parallel and consecutive in time. The characteristics of each produced dataset vary with the different orbital heights and inclinations of the spacecraft, as well as with the technical properties of the radar instrument. An integral analysis of datasets with different properties offers advantages both in terms of data quantity and data quality. This thesis is concerned with the development of the means for such integral analysis, in particular for dynamic solutions in which precise orbits for the satellites are computed simultaneously. The first half of the thesis discusses the theory and numerical implementation of dynamic multi-satellite altimetry analysis. The most important aspect of this analysis is the application of dual satellite altimetry crossover points as a bi-directional tracking data type in simultaneous orbit solutions. The central problem is that the spatial and temporal distributions of the crossovers are in conflict with the time-organised nature of traditional solution methods. Their application to the adjustment of the orbits of both satellites involved in a dual crossover therefore requires several fundamental changes of the classical least-squares prediction/correction methods. The second part of the thesis applies the developed numerical techniques to the problems of precise orbit computation and gravity field adjustment, using the altimetry datasets of ERS-1 and TOPEX/Poseidon. Although the two datasets can be considered less compatible that those of planned future satellite missions, the obtained results adequately illustrate the merits of a simultaneous solution technique. In particular, the geographically correlated orbit error is partially observable from a dataset consisting of crossover differences between two sufficiently different altimetry datasets, while being unobservable from the analysis of altimetry data of both satellites individually. This error signal, which has a substantial gravity-induced component, can be employed advantageously in simultaneous solutions for the two satellites in which also the harmonic coefficients of the gravity field model are estimated.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

The single-phase induction motor:a critical appraisal of the rotating-field and cross-field theories with particular reference to skin effect

The purpose of this thesis is twofold: to examine the validity of the rotating-field and cross-field theories of the single-phase induction motor when applied to a cage rotor machine; and to examine the extent to which skin effect is likely to modify the characteristics of a cage rotor machine. A mathematical analysis is presented for a single-phase induction motor in which the rotor parameters are modified by skin effect. Although this is based on the usual type of ideal machine, a new form of model rotor allows approximations for skin effect phenomena to be included as an integral part of the analysis. Performance equations appropriate to the rotating-field and cross-field theories are deduced, and the corresponding explanations for the steady-state mode of operation are critically examined. The evaluation of the winding currents and developed torque is simplified by the introduction of new dimensionless factors which are functions of the resistance/reactance ratios of the rotor and the speed. Tables of the factors are included for selected numerical values of the parameter ratios, and these are used to deduce typical operating characteristics for both cage and wound rotor machines. It is shown that a qualitative explanation of the mode of operation of a cage rotor machine is obtained from either theory; but the operating characteristics must be deduced from the performance equations of the rotating-field theory, because of the restrictions on the values of the rotor parameters imposed by skin effect.

Image Quotient Set Transforms in Segmentation Problems

Image content interpretation is much dependent on segmentations efficiency. Requirements for the image recognition applications lead to a nessesity to create models of new type, which will provide some adaptation between law-level image processing, when images are segmented into disjoint regions and features are extracted from each region, and high-level analysis, using obtained set of all features for making decisions. Such analysis requires some a priori information, measurable region properties, heuristics, and plausibility of computational inference. Sometimes to produce reliable true conclusion simultaneous processing of several partitions is desired. In this paper a set of operations with obtained image segmentation and a nested partitions metric are introduced.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Renewal Processes of Mittag-Leffler and Wright Type

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Mathematics Subject Classification: 33D60, 33E12, 26A33

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

An Application of Convolution Integral

MSC 2010: 30C45