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"Actual models for fixed-bed reactor modeling make this assumption that temperature is uniform, or at least symmetric, within the catalytic pellets. However, if this holds true for large beds (tube-to-particle diameter ratio N greater than 10), it appears that for small N tubes (N = 3-10) that wall effects cannot be neglected anymore. A large temperature gradient appears in the near wall region. Hence for a particle at the wall a variation in temperature of up to 50¢ªC was noticed. This temperature change was investigated, and it has been noticed that the proximity to the wall, but also to a low velocity region could explain a maximum in temperature. Furthermore, species concentration discrepancies were also notice. An adiabatic run was made to show that these were not due to heated wall effects. Instead it appeared that these concentration variations are due to both their proximity to a low flow region and to a confined area. Hence incoming diffusion in these zones appeared to be lower than for the rest of the surface. We also could notice a strong impact of the flow on the temperature patterns in the near wall regions. Hence in our case, it appeared that the 4 holes geometries allowed a better flow in front the particle at the flow, and therefore better transport phenomena. On the contrary, the full cylinder geometry tend to block the flow, consequently temperature on the wall particles were hotter than what they were with the 4 holes cylinder geometry. A study of the diffusion within the catalytic particles was also conducted. Hence, the Maxwell-Stefan, the dusty gas and the binary friction models were implemented in Fluent. The goal here is to refine step by step the diffusion model used. First products and reactants molar fluxes were assumed to be proportional. The next step was to compute the actual molar fluxes; however this added one more parameter to converge; that is the diffusion coefficient. Finally the assumption of negligible pressure variation within the pellets was dropped. Unfortunately, the implementation into Fluent was not successful, and few possible reasons were given. "

by Ip Che-ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaf 136). / Covering Page --- p.i / Acknowledgement --- p.ii / Abstract --- p.iii / Table of Content --- p.v / Chapter 1. --- Fundamentals of Complex Analys --- p.is / Chapter 1.1 --- The extended complex plane --- p.1 / Chapter 1.2 --- Stereographic projection --- p.2 / Chapter 1.3 --- Analytic functions --- p.3 / Chapter 1.4 --- Rational functions --- p.5 / Chapter 1.5 --- Mobius transformation --- p.6 / Chapter 2. --- The Topology of the Extended Plane / Chapter 2.1 --- The topology of S2 and C ∞ --- p.9 / Chapter 2.2 --- Smooth map and manifolds --- p.10 / Chapter 2.3 --- Regular points --- p.11 / Chapter 2.4 --- Degree of maps --- p.13 / Chapter 2.5 --- Euler characteristics --- p.14 / Chapter 2.6 --- Covering space --- p.16 / Chapter 2.7 --- Riemann-Hurwritz formula --- p.17 / Chapter 3 --- The Montel Theorem / Chapter 3.1 --- Introduction --- p.21 / Chapter 3.2 --- Normality and Equicontinuous --- p.21 / Chapter 3.3 --- Local boundedness --- p.23 / Chapter 3.4 --- Covering and uniformization --- p.26 / Chapter 3.5 --- Montel's theorem --- p.28 / Chapter 4 --- Fatou Set and Julia Set / Chapter 4.1 --- Iteration of functions --- p.31 / Chapter 4.2 --- Fatou set and Julia set --- p.35 / Chapter 4.3 --- Iteration of Mobius transformtion --- p.39 / Chapter 4.4 --- Fixed points and their classification --- p.44 / Chapter 4.5 --- Periodic points and cycles --- p.45 / Chapter 4.6 --- Critical points --- p.47 / Chapter 4.7 --- Dlustractions of local behaviour of map near periodic points --- p.48 / Chapter 5 --- More about Julia Set / Chapter 5.1 --- Some examples of Julia set --- p.57 / Chapter 5.2 --- Completely invariant set --- p.58 / Chapter 5.3 --- Exceptional set --- p.61 / Chapter 5.4 --- Properties of Julia set --- p.63 / Chapter 5.5 --- Forward and backward convergence of sets --- p.66 / Chapter 6 --- More about Fatou Set / Chapter 6.1 --- Components of Fatou set --- p.97 / Chapter 6.2 --- Simply connected Fatou components --- p.98 / Chapter 6.3 --- Number of components in Fatou set --- p.100 / Chapter 6.4 --- Classification of forward invariant components of the Fatou set --- p.102 / Chapter 6.5 --- Examples illustrating the five possible forward invariant components --- p.104 / Chapter 7 --- Critical Points / Chapter 7.1 --- Introduction --- p.108 / Chapter 7.2 --- Some interesting results --- p.110 / Chapter 7.3 --- The Fatou set of polynomials --- p.114 / Chapter 7.4 --- Quadratic polynomial and Mandelbrot set --- p.116 / Appendix --- p.125 / Reference --- p.136

In this thesis, we consider the properties of diffeomorphisms of R3 called trace maps. We begin by introducing the definition of the trace map. The group B3 acts by trace maps on R3. The first two chapters deal with the action of a specific element of B3,called αn. In particular, we study the fixed points of αn lying on a topological subspace contained in R3, called T . We investigate the duality of the fixed points of the action ofαn, which will be defined later in the thesis.Chapter 3 involves the study of the fixed points of an element called γnm, and it generalizes the results of chapter 2. Chapter 4 involves a study of the period two points of γnm. Chapters 5-8 deal with surfaces and curves induced by trace maps, in a manner described in chapter 5. Trace maps define surfaces, and we study the intersection of those surfaces. In particular, we classify each such possible intersection.

Kakutani’s fixed point theorem has many applications in economics and game theory. One of its most well known applications is in John Nash’s paper [8], where the theorem is used to prove the existence of an equilibrium strategy in n-person games. Sperner’s lemma, on the other hand, is a combinatorial result concerning the labelling of the vertices of simplices and their triangulations. It is known that Sperner’s lemma is equivalent to a result called Brouwer’s fixed point theorem, of which Kakutani’s theorem is a generalization. A natural question that arises is whether we can prove Kakutani’s fixed point theorem directly using Sperner’s lemma without going through Brouwer’s theorem. The objective of this thesis to understand Kakutani’s theorem, Sperner’s lemma, and how they are related. In particular, I explore ways in which Sperner’s lemma can be used to prove Kakutani’s theorem and related results.

Results from combinatorial topology have shown that certain combinatorial lemmas are equivalent to certain topologocal fixed point theorems. For example, Sperner’s lemma about labelings of triangulated simplices is equivalent to the fixed point theorem of Brouwer. Moreover, since Sperner’s lemma has a constructive proof, its equivalence to the Brouwer fixed point theorem provides a constructive method for actually finding the fixed points rather than just stating their existence. The goal of this research project is to develop a combinatorial analogue for the Poincare ́-Birkhoff fixed point theorem.

Animals performing on simple fixed-ratio (FR) schedules vi typically pause after reinforcement delivery. The present study demonstrated systematic control of pause length in multiple fixed ratio schedules by manipulating FR size and reinforcement magnitude. In Experiment I, two adult male rabbits were stabilized on an alternating, two component, multiple FR 10 FR 10 schedule. Different colored lights were correlated with both FR components. Stability was determined and mean pause lengths were calculated as one FR component was increased in size until the schedule was FR 10 FR 50. Pausing was longer before the large FR component and was positively correlated with increases in FR size. Schedule and stimulus control were demonstrated by randomizing the order of FR presentations and by reversing the colored lights previously correlated with either the small or large FR components. Existing pause differentials were not disrupted under the light reversal or random conditions. In Experiment II, the same rabbits were stabilized at mult FR 10 FR 30 with 1/2 cc of water delivered after each component. In subsequent conditions the magnitude of reinforcement (cc's of water) delivered at the completion of the large FR component, was systematically shifted from 4 cc, to 3 cc, 2 cc, 1 cc and finally back to 1/2 cc. Pausing before the large FR was found to be inversely related to the magnitude of reinforcement delivered in that component. Clearly the animals in this experiment discriminated upcoming schedule conditions and paused relative to FR size and reinforcement magnitude. Hence, it is proper to point out that the term "post-reinforcement pause" is a misnomer since it incorrectly implies a functional relation between pause length and prior schedule conditions.

This thesis presents the nonlinear in-plane behaviour of circular fixed arches subjected to thermal loading only. Due to the nonlinear prebuckling behaviour of arches and its effects, classical buckling theory which is founded on geometric prebuckling linearity can not predict the in-plane buckling of arches accurately. Based on a nonlinear formulation of the strain and displacement relationship and considering constant thermal distributions only, virtual work formulations are used to establish the differential equations of in-plane equilibrium and the statical boundary conditions, from which the nonlinear equilibrium equations are derived in closed form and which are suitable to use in design. By considering the adjacent buckled configurations, the differential buckling equilibrium equations are formulated from the principle of virtual work as well, and the analytical solutions for the nonlinear buckling of fixed arches are obtained. It is shown that nonlinear elastic buckling of a fixed in the plane of it curvature can not occur when it is subjected to thermal loading only, except if the arch is as a straight column. By using the algebraic representation of nonlinear in-plane equilibrium derived in this thesis, the elastic response of fixed arches at elevated temperatures and the attainment of first yield are examined in detail. The arch deflects transversely without bound in the elastic range at elevated temperatures, whereas it will yield first at the top extreme fibre of the cross section at the supports when a critical temperature is reached. The influence of several parameters such as the included angle is also considered. Based on the models of stress distributions at cross sections, the spread of yield both through the cross section and along the length of the arch is studied. It is indicated that the progress of yielding causes the first two hinges to form at the supports of the fixed arches, and then moment redistribution leads to the generation of the third hinge at the crown with an increase of temperature. Thus nonlinear plastic hinge analysis can be applied to the arch analysis under thermal loading.

The study examines the development of telecommunications and its impacts on Chinese economic growth since telecommunications has been undergoing dramatic reforms in the 1980s. On November 2001, China was officially the WTO member to open the market for foreign investors. It is obvious that the telecommunications infrastructure development can play a key role in economic growth in China. Furthermore, China has become the world’s single largest telecommunications market since 2002. In this research, I present evidence that it empirically not only investigates the telecommunications development and its impacts on economic growth, but also tests their relationship with initial economic condition, fixed investment, population growth, foreign direct investment as well as telecommunications infrastructure development using the panel data approach with a dynamic fixed effect model for the span of time from 2003 to 2008. I find that that mobile phone user density to be the new proxy for telecommunications infrastructure in China contributes in a major way to the economic growth. It means that mobile communication systems do have positive impact and effect on the regional economy of China. It is a crucial determinant as findings indicate a significant and positive correlation between telecommunications development and regional growth in China, after controlling for a number of other factors. Results also show that investment in telecommunications is subject to diminishing returns.