This is a diploma thesis on Buchdahl's equations for the description of massive particles of arbitrary spin s/2. On 4-dimensional, globally hyperbolic Lorentzian spacetime manifolds, existence of advanced and retarded Green's operators is proved, the Cauchy problem for Buchdahl's equations is solved globally and two possible constructions for quantizing Buchdahl fields using CAR algebras in the fashion of [Dimock 1982] are given.

Title: Hierarchical Problems with Evolutionary Equilibrium Constraints Author: Lukáš Adam Supervisor: Prof. Jiří Outrata Abstract: In the presented thesis, we are interested in hierarchical models with evolutionary equilibrium constraints. Such models arise naturally when a time-dependent problem is to be controlled or if parameters in such a model are to be identified. We intend to discretize the problem and solve it on the basis of the so-called implicit programming approach. This technique requires knowledge of a generalized derivative of the solution mapping which assigns the state variable to the control variable/parameter. The computation of this generalized derivative amounts equivalently to the computation of (limiting) normal cone to the graph of the solution mapping. In the first part we summarize known techniques for computation of the normal cone to the set which can be represented as a finite union of convex polyhedra. Then we propose a new approach based on the so-called normally admissible stratification and simplify the obtained formulas for the case of time-dependent problems. The theoretical results are then applied first to deriving a criterion for the sensitivity analysis of the solution mapping and then to the solution of two practically motivated problems. The first one concerns optimal...

在許多實際情形下，傳統的統計檢定方法是不足以應付的。故本論文提出模糊檢定方法，我們定義出模糊樣本期望值與模糊樣本變異數的計算方法，再針對不同的模糊資料，分別提出不同的檢定方法，去解決最實際需要解決的問題，其中包括推廣古典的統計檢定方法與自創的檢定方法。 關鍵字：隸屬度函數，模糊樣本取樣，模糊樣本期望值，模糊樣本變異數，人性思考，t檢定，F檢定，模糊常態分配。 / In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this paper, we present a class of fuzzy statistical decision process in which testing hypothesis can be naturally reformulated in terms of interval-valued statistics. We provide the definitions of fuzzy mean, fuzzy distance as well as investigation of their related properties. We also give some empirical examples to illustrate the techniques and to analyze fuzzy data. Empirical studies show that fuzzy hypothesis testing with soft computing for interval data are more realistic and reasonable in the social science research. Finally certain comments are suggested for the further studies. We hope that this reformation will make the corresponding fuzzy techniques more acceptable to researchers whose only experience is in using traditional statistical methods. Key words: Membership function, fuzzy sampling survey, fuzzy mean, human thought, t-test, F-test, normally distributed.

Two and three-phase flow processes involving gas, liquid and solid, are common in nature and industry, and include some of the most complex and poorly-understood transport problems. In this research hydrodynamics, heat and mass transfer processes in complex two and three-phase flows were investigated. The interfacial surface area concentration in a short vertical column subject to the through flow of fiber-liquid-gas slurry was experimentally measured using the gas absorption technique. The experimental data were statistically analyzed for parametric effects, and were empirically correlated. The absorption of a gaseous species by a slurry droplet with internal circulation and containing reactive micro-particles was simulated, and parametrically studied. The micro-particles were found to enhance the absorption rate. The absorption rate was sensitive to droplet recirculation, and shrinkage of particles with time resulted in declining absorption rates. The transport of soot particles, suspended in laminar hot gas flowing in a tube, was modeled and parametrically studied. Due to coupled thermal radiation and thermophoresis, a radially-nonuniform temperature profile develops, leading to sharp, non-uniform radial soot-concentration profiles. The assumption of monodisperse particles leads to over-prediction of thermophoresis. The transport and removal of particles suspended in bubbles rising in a stagnant liquid pool were modeled based on a Eulerian – Monte Carlo method. The bubble hydrodynamics were treated in Eulerian frame, using the Volume-of-Fluid (VOF) technique, while particle equations of motion were numerically solved in Lagrangian frame. The bubbles undergo shape change, and have complex internal circulation, all of which influence the particle removal. Model predictions were also compared with experimental data. Using a resemblance between two-phase flow in microchannels, and in large channels at microgravity, a simple Weber number-based two-phase flow regime map was developed for microchannels. Based on the available air-water experimental data, a criterion for the prediction of conditions that lead to flow regime transition out of the stratified-wavy flow pattern in horizontal annular channels was proposed. The thermocapillary effects on liquid-vapor interface shape during heterogeneous bubble ebullition in microchannels were analytically studied.