This thesis is concerned with the properties of 1 + 1 dimensional massive field theories in both infinite and semi-infinite geometries. Chapters 1, 2 and 3 develop the necessary theoretical framework and review existing work by Chim and Zamolodchikov [1] on integrable perturbations of the (bulk) q-state Potts model, the particular model under consideration in this thesis. Chapter 4 consists of a detailed analysis of the bootstrap for this model, during the course of which unexpected behaviour arises. The treatment of 1] has consequently been revised, but further investigation will be necessary before complete understanding of this behaviour can be reached. In the final chapter, attention turns to the imposition of boundary conditions on two dimensional systems. After looking at this from a statistical mechanical point of view, a brief review of boundary conformal held theory and its integrable perturbations is given. This leads once more to a consideration of the q-state Potts model. After summarising [2], where fixed and free boundary conditions are considered, a third and previously untreated boundary condition is discussed.

<p> Two isotopes of platinum, Pt192 and Pt194, have been investigated using Ge(Li) vs. NaI coincidence techniques. The following corrected angular distributions and mixing ratios in Pt192 were obtained: 468-316 keV A22 = 0.100(8) A44 = 0.011(8) 604-316 keV A22 = -0.410(15) A44 = -0.070(22) 308-612 keV A22 = -0.120(20) A44 = -0.027(20) 417-468 keV A22 = -0.120(26) A44 = -0.110(30) δ308 = -9.4(15) δ604 = + 3(1) |δ417|> 11 g factors for the following five levels of these nuclei were obtained using the method of perturbed angular correlations where the perturbing agent was the hyperfine field on platinum in an iron alloy: Pt192 316 keV g = 0.30(3) Pt192 612 keV g = 0.28(7) Pt192 785 keV g = 0.14(10) Pt194 329 keV g = 0.28(3) Pt194 622 keV g = 0.22(4) A comparison with the predictions of a microscopic collective model, the pairing-plus-quadrupole model, is made. / Thesis / Master of Science (MSc)

<p> The (α,n) reaction on natural chromium has been used to study levels in 55Fe up to 2.5 MeV excitation. Intensities and angular distributions of the decay gamma rays were measured, yielding branching and E2/M1 mixing ratios. In a magnetized target of the alloy Cr20Fe80, the rotation of the angular distributions was observed. Using recently determined lifetimes and the average internal field of 277 kOe measured in the target material by Mössbauer absorption, the following g-factors are obtained: - 931 keV, 5/2- -: +1.2 ±0.5 1316 keV, 7/2- -: +0.5 ± 0.5 1408 keV, 7/2- -: -0.77 ± 0.16 </p> / Thesis / Master of Science (MSc)

A form of detectability, known as the input-output-to-state stability property, for singularly perturbed systems is examined in this work. This work extends the result of a paper by Christofides & Teel wherein they presented a notion of total stability for input-to-state stability with respect to singular perturbations. Analyzing singularly perturbed systems with outputs we show that if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input-output-to-state stable with respect to disturbances, then these properties continue to hold, up to an arbitrarily small offset, for initial conditions in an arbitrarily large compact set and sufficiently small singular perturbation parameter over the time interval for which disturbances, their derivatives, and outputs remain in an arbitrarily large compact set. An application of the result is presented where we analyze the stability of a circuit with a nonlinear element through the measurement of only one of the variables of interest.

For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.

A form of detectability, known as the input-output-to-state stability property, for singularly perturbed systems is examined in this work. This work extends the result of a paper by Christofides & Teel wherein they presented a notion of total stability for input-to-state stability with respect to singular perturbations. Analyzing singularly perturbed systems with outputs we show that if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input-output-to-state stable with respect to disturbances, then these properties continue to hold, up to an arbitrarily small offset, for initial conditions in an arbitrarily large compact set and sufficiently small singular perturbation parameter over the time interval for which disturbances, their derivatives, and outputs remain in an arbitrarily large compact set. An application of the result is presented where we analyze the stability of a circuit with a nonlinear element through the measurement of only one of the variables of interest.

Power system dynamics are commonly modeled by parameter dependent nonlinear differential-algebraic equations (DAE) x &#61478;&#61501;&#61472;p y x f ) and 0 = p y x g ) . Due to (,, (,, the algebraic constraints, we cannot directly perform integration based on the DAE. Traditionally, we use implicit function theorem to solve for fast variables y to get a reduced model in terms of slow dynamics locally around x or we compute y numerically at each x . However, it is well known that solving nonlinear algebraic equations analytically is quite difficult and numerical solution methods also face many uncertainties since nonlinear algebraic equations may have many solutions, especially around bifurcation points. In this thesis, we apply the singular perturbation method to model power system dynamics in a singularly perturbed ODE (ordinary-differential equation) form, which makes it easier to observe time responses and trace bifurcations without reduction process. The requirements of introducing the fast dynamics are investigated and the complexities in the procedures are explored. Finally, we propose PTE (Perturb and Taylor’s expansion) technique to carry out our goal to convert a DAE to an explicit state space form of ODE. A simplified unreduced Jacobian matrix is also introduced. A dynamic voltage stability case shows that the proposed method works well without complicating the applications.

Small aerial vehicles such as quad-rotors have been widely used commercially, for research and for hobby for the last decade with use still growing. The high interest is mainly due to the vehicles being small, simple, cheap and versatile. Among rigid body dynamics fast dynamics exist cohering to motors and other fast actuators. A linear quadratic control design technique is here investigated. The design technique suggests that the linear quadratic controller can be designed with penalties on the slow states only. The fast dynamics are modeled but the states are not penalised in the linear quadratic design. The design technique is here applied and evaluated. The results show that this in several cases is a suitable design technique for linear quadratic control design. MATLAB and Simulink have been widely used for design and implementation of control systems. With additional toolboxes these control systems can be compiled to and run on remote computers. Small, lightweight computers with high computational capacity are now easily accessible. In this thesis an avionics solution based on a small, powerful computer is presented. Simulink models can be compiled and transferred to the computer from the Simulink environment. The result is a user friendly way of rapid prototyping and evaluation of control systems.

In this thesis we investigate a model of nonlinearly perturbed continuous-time renewal equation. Some characteristics of the renewal equation are assumed to have non-polynomial perturbations, more specifically they can be expanded with respect to a non-polynomial asymptotic scale. The main result of the present study is exponential asymptotic expansions for the solution of the perturbed renewal equation. These asymptotic results are also applied to various applied probability models like perturbed risk processes, perturbed M/G/1 queues and perturbed dam/storage processes. The thesis is based on five papers where the model described above is successively studied.

The restrictions of micro-scale systems are approaching rapidly. In anticipation of this development, nano-scale electronics has become the focus of many researchers and engineers in academia and industry since early 1990s. The basic building blocks of modern integrated circuits have been diodes and transistors with their current-voltage I-V characteristics being of prime significance for the design of complex signal processing and shaping devices and systems. Classical and semi-classical physical principles are no longer powerful enough or even valid to describe the phenomena involved. The application of rich and powerful concepts in quantum theory has become indispensable. These facts have been influential in undertaking this research project. This research is built upon the determination of the Eigenpairs of one and two dimensional positive differential operators with periodic boundary conditions. The Schrödinger equation was solved for positive operators in both one and two dimensions. Fourier series were used to express the derivatives as the summation of Fourier terms. This led to a novel approach for the calculation of the eigenmodels of a perturbed potential well. The perturbation can be done via an electric field applied to the potential well. The research in this thesis includes a thorough understanding of quantum mechanics fundamentals, mastering of different approximation techniques such as the variational technique and results that have been generated and published using the novel techniques.