by Kwok-man Lui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 167-172.

The mathematical modelling of a market, and the proof of existence of equilibria have been of central importance in mathematical economics. Since the existence proof is non-constructive in general, a natural question is if computation of equilibria can be done efficiently. Moreover, the emergence of Internet and e-commerce has given rise to new markets that have completely changed the traditional notions. Add to this the pervasiveness of computing resources, and an algorithmic theory of market equilibrium becomes highly desirable. The goal of this thesis is to provide polynomial time algorithms for various market models. Two basic market models are the Fisher model: one in which there is a demarcation between buyers and sellers, buyers are interested in the goods that the sellers possess, and sellers are only interested in the money that the buyers have; and the Arrow-Debreu model: everyone has an endowment of goods, and wants to exchange them for other goods. We give the first polynomial time algorithm for exactly computing an equilibrium in the Fisher model with linear utilities. We also show that the basic ideas in this algorithm can be extended to give a strongly polynomial time approximation scheme in the Arrow-Debreu model. We also give several existential, algorithmic and structural results for new market models: - the *spending constraint* utilities (defined by Vazirani) that captures the "diminishing returns" property while generalizing the algorithm for the linear case. - the capacity allocation market (defined by Kelly), motivated by the study of fairness and stability of the Transmission Control Protocol (TCP) for the Internet, and more generally the class of Eisenberg-Gale (EG) markets (defined by Jain and Vazirani). In addition, we consider the adwords market on search engines and show that some of these models are a natural fit in this setting. Finally, this line of research has given insights into the fundamental techniques in algorithm design. The primal-dual schema has been a great success in combinatorial optimization and approximation algorithms. Our algorithms use this paradigm in the enhanced setting of Karush-Kuhn-Tucker (KKT) conditions and convex programs.

Hybrid waveguides based on antiresonant reflecting optical waveguide (ARROW) structure on Si substrates is investigated. The core layer of the waveguide is separated from the Si substrate by interference cladding which consists of a high index first cladding layer and a low index second cladding layer. The Ta2O5 first cladding layer was grown by rf magnetron sputtering system. The SiON second cladding layer was deposited by plasma-enhanced chemical vapor deposition (PECVD) based on the reaction of SiH4/N2O mixtures. Typical propagation losses of the waveguides using this SiON material system are less than 0.15 dB/cm. The high quality cladding layers are prepared to form the Fabry-Perot cavities to ensure low loss operation of the ARROW device at antiresonant conditions. Two methods were proposed to demonstrate the enormous applications of hybrid ARROW waveguides. First, polyimide/Ta2O5/SiON ARROWs were fabricated to achieve high extinction ratio waveguide polarizers. This is accomplished by tuning the operating point of the TM0 mode from antiresonant condition toward high-order antiresonance of the second cladding layer utilizing birefringence of the waveguide core. The measured extinction ratio and insertion loss of a 2-cm-long ARROW polarizer are 40 dB and 2.2 dB, respectively. In addition, the temperature dependence of refractive index of organic-inorganic sol-gel glasses was measured by Mach-Zehnder interferometry using the ARROW waveguides. The Sol-gel/Ta2O5/SiO2 ARROWs were fabricated to characterize index-to-temperature coefficients (dn/dT) of the sol-gel glasses because the optical confinement factor of the ARROW is very close to 1. The measured index-to-temperature coefficients of the sol-gel glasses with different compositions are negative and are on the order of 10-4.

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Title from PDF of title page (University of Missouri--Columbia, viewed on December 22, 2009). Thesis advisor: Yuyi Lin. Includes bibliographical references.

Thesis (D. Min.)--Columbia International University, Columbia, S.C., December, 1994. / Includes bibliographical references (leaves 108-113).

Bachelor-Arbeit Univ. St. Gallen, 2007.

The controversial topic of which the conditions of transversality are for problems of infinite temporal horizon is presented here within the general context of the theory of Optimal Control. Results are presented for linear and autonomous case, as well as Arrow's theorem.

In this thesis I describe a toxic protein, diamphotoxin, that is present in the pupae of the beetle Diamphidia nigro-ornata. This insect is used as an arrow poison by the !Kung Bushmen inhabiting the savannah of eastern Namibia and western Botswana. Preliminary investigations showed that the pupae contained a 3,7 S cationic protein which caused haemolysis and, after intramuscular injection, local paralysis followed by death. By intravenous lethality assay, one 200 mg pupa contained 20 000 mouse lethal doses. Assays for the toxin were developed based upon haemolysis in vitro and lethality in vivo. These assays were used to monitor purification of the toxin. Diamphotoxin was purified by acid extraction in 0,1M glycine-HCl pH 3,0 followed by ammonium sulphate fractionation, chromatography on hydroxyl apatite, phosphocellulose and, finally, on DEAE cellulose. A consistent increase in activity after the hydroxyl apatite chromatography pointed to the removal of an inhibitor during this step. A subsequent severe loss of activity after chromatography on phosphocellulose could neither be explained nor overcome. The phosphocellulose chromatography step yielded three peaks of toxic activity. Immunological studies revealed cross-reactivity but not identity between these three toxin species. The toxin in the first peak to elute from the phosphocellulose column was purified to electrophoretic homogeneity by chromatography on DEAE cellulose. Attempts to purify the toxin in the other two phosphocellulose peaks were not successful. The isolated molecule was confirmed to be the toxin by haemolysis in a blood-agarose underlay after SDS-gel electrophoresis. The molecular weight estimate for the toxin by SDS-gel electrophoresis was 60 700 daltons and by analytical ultracentrifugation 62 100 daltons. The molecule appeared to exist as a single polypeptide chain. The amino acid composition showed a high proportion of hydrophobic amino acids. Isoelectric focussing showed an isoelectric point of pH 9,45. Toxin mediated haemolysis was studied in detail. The haemolytic event could be broken down into two stages. In the first stage toxin bound irreversibly to the cell but, provided no divalent cations were present, no damage to the cell could be detected. The second stage required the presence of free calcium (or certain other divalent cations), with an optimum concentration at 1 mM. The interaction of calcium with the cell-bound toxin resulted in the cell membrane becoming highly permeable to Na⁺ and K⁺ ions. Experiments designed to detect phospholipase or protease activity in toxin solutions gave negative results. Erythrocytes incubated with ¹²⁵I-labelled pure toxin in calcium-free medium retained a quantity of bound toxin which could not be removed by repeated washing. Incubation of erythrocytes with calcium-free toxin resulted in depletion of the activity of the toxin solution. The kinetics of the haemolytic action of the toxin were shown to be stoichiometric rather than catalytic. It was estimated that haemolysis by the toxin required a minimum of approximately 100 molecules per cell. Studies using circular dichroism measurements and the fluorescent probe 8-anilino-1-naphthalene sulphonic acid (ANS) indicated that a conformational change occurred in the toxin upon exposure to calcium. The ANS studies indicated that upon the addition of calcium the toxin molecule became more hydrophobic. It was concluded that the toxin functions as a calcium regulated Na⁺ and K⁺ ionophore in that it binds to the cell membrane and, in the presence of calcium or certain other divalent cations, assumes a conformation which mediates the free passage of Na⁺ and K⁺ ions. The resultant disruption of normal transmembranous ionic concentration gradients leads to cell lysis by loss of osmoregulation and, in the case of excitable membranes, disruption of electrophysiological activity.

Racionalidade é um importante tema para a economia e qualquer outra área que se dedica à tomada de decisão. Ao longo do século XX, economistas deram diferentes definições do que seria um comportamento racional. Tais definições foram formalizadas matematicamente e, mediante uma hipótese plausível, mostradas equivalentes no teorema de Arrow- Sen. Após o surgimento da teoria de conjuntos fuzzy, diferentes autores se debruçaram na expansão através da matemática fuzzy de tais definições e equivalências. Este trabalho retoma o histórico dessas definições e a passagem da formalização clássica para a fuzzy. Também expõe resultados obtidos com provas alternativas e exemplos que mostram as limitações das equivalências numa abordagem sob a ótica da teoria de conjuntos fuzzy. / Rationality is among the most important subjects in economics and the study of decisionmaking process. Different definitions of what is a rational behavior were given in the 20th century. The Arrow-Sen theorem shows that such definitions are equivalent under a plausible hypothesis. With the development of fuzzy theory, a fuzzy approach to this problem was given by different authors. This work shows this historical development of the definitions and the transition from the classical to the fuzzy view. It also presents the results obtained with alternative proofs and examples that show the limitations of the equivalences in the fuzzy setup.

Racionalidade é um importante tema para a economia e qualquer outra área que se dedica à tomada de decisão. Ao longo do século XX, economistas deram diferentes definições do que seria um comportamento racional. Tais definições foram formalizadas matematicamente e, mediante uma hipótese plausível, mostradas equivalentes no teorema de Arrow- Sen. Após o surgimento da teoria de conjuntos fuzzy, diferentes autores se debruçaram na expansão através da matemática fuzzy de tais definições e equivalências. Este trabalho retoma o histórico dessas definições e a passagem da formalização clássica para a fuzzy. Também expõe resultados obtidos com provas alternativas e exemplos que mostram as limitações das equivalências numa abordagem sob a ótica da teoria de conjuntos fuzzy. / Rationality is among the most important subjects in economics and the study of decisionmaking process. Different definitions of what is a rational behavior were given in the 20th century. The Arrow-Sen theorem shows that such definitions are equivalent under a plausible hypothesis. With the development of fuzzy theory, a fuzzy approach to this problem was given by different authors. This work shows this historical development of the definitions and the transition from the classical to the fuzzy view. It also presents the results obtained with alternative proofs and examples that show the limitations of the equivalences in the fuzzy setup.