by Chiu Chak Lam. / Thesis submitted in: June, 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 67-69). / Abstract also in Chinese. / Chapter 1 --- Basic Knowledge of Elliptic Curve --- p.2 / Chapter 1.1 --- Elliptic Curve Group Law --- p.2 / Chapter 1.2 --- Discriminant and j-invariant --- p.7 / Chapter 1.3 --- Elliptic Curve over C --- p.10 / Chapter 1.4 --- Complex Multiplication --- p.15 / Chapter 2 --- Order of Elliptic Curve Group Over Finite Fields and the Endo- morphism Ring --- p.18 / Chapter 2.1 --- Hasse's Theorem --- p.18 / Chapter 2.2 --- The Torsion Group --- p.23 / Chapter 2.3 --- The Weil Conjectures --- p.33 / Chapter 3 --- Computing the Order of an Elliptic Curve over a Finite Field --- p.35 / Chapter 3.1 --- Schoof's Algorithm --- p.35 / Chapter 3.2 --- Computation Formula --- p.38 / Chapter 3.3 --- Recent Works --- p.42 / Chapter 4 --- Primality Test Using Elliptic Curve --- p.43 / Chapter 4.1 --- Goldwasser-Kilian Test --- p.43 / Chapter 4.2 --- Atkin's Test --- p.44 / Chapter 4.3 --- Binary Quadratic Form --- p.49 / Chapter 4.4 --- Practical Consideration --- p.51 / Chapter 5 --- Elliptic Curve Factorization Method --- p.54 / Chapter 5.1 --- Lenstra's method --- p.54 / Chapter 5.2 --- Worked Example --- p.56 / Chapter 5.3 --- Practical Considerations --- p.56 / Chapter 6 --- Elliptic Curve Public Key Cryptosystem --- p.59 / Chapter 6.1 --- Outline of the Cryptosystem --- p.59 / Chapter 6.2 --- Index Calculus Method --- p.61 / Chapter 6.3 --- Weil Pairing Attack --- p.63

This work is a compilation of structural results for the von Neumann algebras of poly-hyperbolic groups established in a series of works done jointly with I. Chifan and T. Sinclair; and S. Pant. These works provide a wide range of circumstances where the product structure, a discrete structural property, can be recovered from the von Neumann algebra (a continuous object). The primary result of Chifan, Sinclair and myself is as follows: if Γ = Γ1 × · · · × Γn is a product of non-elementary hyperbolic icc groups and Λ is a group such that L(Γ)=L(Λ), then Λ decomposes as an n-fold product of infinite groups. This provides a group-level strengthening of the unique prime decomposition of Ozawa and Popa by eliminating any assumption on the target group Λ. The methods necessary to establish this result provide a malleable procedure which allows one to rebuild the product of a group from the algebra itself. Modifying the techniques found in the previous work, Pant and I are able to demonstrate that the class of poly-groups exhibit a similar phenomenon. Specifically, if Γ is a poly-hyperbolic group whose corresponding algebra is non-prime, then the group must necessarily decompose as a product of infinite groups.

Veteran-owned small businesses that possess ratings as service-disabled companies (i.e., service-disabled, veteran-owned small businesses [SDVOSB] are 1 of 5 socioeconomic small business contracting goals that U.S. government agencies seek to comply with U.S. Small Business Administration (SBA) set-aside goals. Little is known about collaborative strategies for improving training regarding single point of entry into Department of Defense (DOD) subcontracting. The research questions in this study focus on how veteran-owned small businesses pursue acquisition opportunities from training opportunities. Sabatier's advocacy coalition theory was used as the theoretical foundation for this study. This qualitative study was employed using 6 semistructured interviews of small business owners who possessed SDVOSB status and a content analysis of training policies from corporate supplier diversity offices, procurement assistance centers, small business development centers, and DOD Office of Small Business programs from a midwestern city. The emergent themes were (a) availability of training from procurement support assistance agencies is of limited value to mature small businesses; (b) additional support and training are needed for subcontractors desiring to enter the DOD subcontracting market; (c) significant obstacles are present in gaining access to federal subcontracting opportunities, including complex acquisition strategies and selection of contract type; and (d) understanding and enforcement of SDVOSB regulations were perceived as insufficient. SDVOSB entities can use these findings to comprehend what questions to ask about subcontracting training.

The present study was designed to investigate the effects of a stimulus change inserted in the large component of a mixed fixed-ratio 10 fixed-ratio 100 schedule. In mixed fixed-ratio schedules, a run of responses which approximates the response requirement of the smaller fixed ratio occurs at the beginning of the larger fixed ratio. This run of responses and the pause it precedes is called a prime. In Experiment I, priming acquisition was compared in a mixed schedule in which a change in key-color followed completion of the first 10 responses of the fixed-ratio 100 component and a mixed schedule with no stimulus change. Primes were acquired more rapidly in the mixed schedule with the stimulus change and the number of responses in a priming run was less variable than occurred without the stimulus change. In Experiment II, the effect of the stimulus change on primes was further investigated by removal of the smaller fixed-ratio component or by varying the location of the stimulus change. Primes occurred only when the smaller fixed-ratio component was present. Varying the location of the stimulus change resulted in the transfer of control from the external stimulus to response-produced stimuli. Future investigation of this point of transfer should prove useful in the study of the proprioceptive stimulus control of homogeneous behavior sequences. In Experiments Ill through VI, the variables controlling the length of the post-prime and the post-reinforcement pauses were investigated using the mixed FR x chained FR x FR y schedule. In this series of experiments, FR x was varied with FR y held constant at both high and low values. In addition, FR y was varied with FR x held constant at both high and low values. The results indicate that the post-prime pause is primarily a function of FR y, the number of responses required after the priming run. On the other hand, both post-reinforcement pauses were shown to be a function of FR x, the size of the small fixed ratio. An interaction between FR x and FR y and both the post-reinforcement and the post-prime pauses suggested that pausing in mixed schedules is a closed system. Taken as a whole, these results indicate the importance of mixed chained schedules in the investigation of the priming phenomenon.

<p>In this thesis it is investigated if representing a field <i>Z</i><i>p</i><i>, p</i> = 1 (mod 4) prime, by another field <i>Z[i]</i>/ < <i>a + bi </i>> over the gaussian integers, with <i>p</i> = <i>a</i><i>2</i><i> + b</i><i>2</i>, results in arithmetic architectures using a smaller number of logic gates. Only bit parallell architectures are considered and the programs Espresso and SIS are used for boolean minimization of the architectures. When counting gates only NAND, NOR and inverters are used.</p><p>Two arithmetic operations are investigated, addition and multiplication. For addition the architecture over<i> Z[i]/ < a+bi ></i> uses a significantly greater number of gates compared with an architecture over<i> Z</i><i>p</i>. For multiplication the architecture using gaussian integers uses a few less gates than the architecture over <i>Z</i><i>p</i> for <i>p</i> = 5 and for<i> p</i> = 17 and only a few more gates when <i>p</i> = 13. Only the values 5, 13, 17 have been compared for multiplication. For addition 12 values, ranging from 5 to 525313, have been compared.</p><p>It is also shown that using a blif model as input architecture to SIS yields much better performance, compared to a truth table architecture, when minimizing.</p>

We consider complete subgraphs of the graph induced by the noncommutativity of a ring, and prove that the graph induced by an infinite noncommutative prime ring contains an infinite complete subgraph. We also compute the clique number and the chromatic number of the graphs induced by some concrete graphs.

Le marché financier américain et canadien présentent beaucoup de similitudes. La question qu'on se pose est que les incohérences détectées chez le premier vont-elles se généraliser partout. En effet une évaluation des données boursières américaines a montré que les primes de risque constatées sont trop excessives par rapport aux prévisions du modèle de CAPM de consommation. Ce modèle qui fait partie des plus parfaits dont disposent les économistes et financiers, va nous permettre de faire des prévisions de primes de risque avec les données canadiennes. Pour la période retenue, les résultats obtenus ont confirmé la tendance constatée dans les précédentes études. C'est à dire des primes de risques anormalement élevées. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : CAPM, CAPM de consommation, MEDAF, MEDAF de consommation, CCAPM, Énigme de la prime de risque, Prime de risque excédentaire.

Les accidents de la route représentent un coût social important dans les sociétés industrialisées. C'est vrai aussi sur le plan individuel et il n'est donc pas étonnant que la souscription d'assurance soit devenue une dépense incontournable. Cependant, la mise en oeuvre des protections fournies par l'assurance se traduit par des iniquités importantes entre catégories de conducteurs. L'objectif de ce mémoire est d'illustrer empiriquement la question de l'interfinancement entre catégories de conducteurs. Dans cette étude, nous utilisons des données statistiques sur la population conductrice québécoise afin de calculer une nouvelle forme de prime d'assurance automobile. Notre prime d'assurance selon le coût social marginal impute aux conducteurs une prime représentative du risque de dommage qu'ils imposent à la société. Nos résultats montrent que les formules couramment utilisées pour le calcul de la prime d'assurance ne facturent pas un "juste prix" aux conducteurs: les mauvais conducteurs et les conducteurs à dommages élevés en bénéficient au détriment d'autres catégories de conducteurs. Notre analyse fournit une estimation de l'écart entre les formules utilisées actuellement et une prime au coût social marginal. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Assurance automobile, Tarification, Interfinancement, Coût social marginal.

In this thesis it is investigated if representing a field Zp, p = 1 (mod 4) prime, by another field Z[i]/ &lt; a + bi &gt; over the gaussian integers, with p = a2 + b2, results in arithmetic architectures using a smaller number of logic gates. Only bit parallell architectures are considered and the programs Espresso and SIS are used for boolean minimization of the architectures. When counting gates only NAND, NOR and inverters are used. Two arithmetic operations are investigated, addition and multiplication. For addition the architecture over Z[i]/ &lt; a+bi &gt; uses a significantly greater number of gates compared with an architecture over Zp. For multiplication the architecture using gaussian integers uses a few less gates than the architecture over Zp for p = 5 and for p = 17 and only a few more gates when p = 13. Only the values 5, 13, 17 have been compared for multiplication. For addition 12 values, ranging from 5 to 525313, have been compared. It is also shown that using a blif model as input architecture to SIS yields much better performance, compared to a truth table architecture, when minimizing.

In this thesis, we describe the Jordan isomorphisms and Jordan derivations on prime rings of characteristic 2. We prove that every Jordan isomorphism of M_{n}(F),n >= 3 is either an isomorphism or an antiisomorphism if n is odd, and it is not true if n is even. We also describe the Jordan isomorphisms and Jordan derivations on M_{2}(GF(2)).