On Additive Combinatorics of Permutations of Z(n)

Let Z(n) denote the ring of integers modulo n. A permutation of Z(n) is a sequence of n distinct elements of Z(n). Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Z(n), namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s (n) and t (n) respectively. The case when n is even is trivial in both the cases, with s (n) = 1 and t (n) = n!. For n odd, we prove (n phi(n))/2(k) <= s(n) <= n!.2(-)(n-1)/2/((n-1)/2)! and 2 (n-1)/2 . (n-1/2)! <= t (n) <= 2(k) . (n-1)!/phi(n), where k is the number of distinct prime divisors of n and phi is the Euler's totient function.

Distribution asymptotique du nombre de diviseurs premiers distincts inférieurs ou égaux à m

Le sujet principal de ce mémoire est l'étude de la distribution asymptotique de la fonction f_m qui compte le nombre de diviseurs premiers distincts parmi les nombres premiers $p_1,...,p_m$. Au premier chapitre, nous présentons les sept résultats qui seront démontrés au chapitre 4. Parmi ceux-ci figurent l'analogue du théorème d'Erdos-Kac et un résultat sur les grandes déviations. Au second chapitre, nous définissons les espaces de probabilités qui serviront à calculer les probabilités asymptotiques des événements considérés, et éventuellement à calculer les densités qui leur correspondent. Le troisième chapitre est la partie centrale du mémoire. On y définit la promenade aléatoire qui, une fois normalisée, convergera vers le mouvement brownien. De là, découleront les résultats qui formeront la base des démonstrations de ceux chapitre 1.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

Computational aspects of modular parametrizations of elliptic curves

Thesis (Ph.D.)--University of Washington, 2016-06

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

Engineering a financial bloodbath: how sub-prime securitization destroyed the legitimacy of financial capitalism

"This book investigates the origins and implications of the securitization crisis, described by the chief executive of ANZ as a "financial services bloodbath". Based on extensive interviews it offers an integrated series of case studies drawn from the United States, the United Kingdom and Australia. A central purpose is to not only chart what went wrong with the investment houses and why the regulatory systems failed, but also provide policy guidance. The book therefore combines the empirical with the normative. In so doing, it provides a route map to navigate one of the most significant financial and regulatory failures in modern times."

Poverty in perception : a study of the twentieth-century prime ministers of Australia and New Zealand

Australia and New Zealand, as English-speaking nations with dominant white populations, present an ethnic anomaly not only in South East Asia, but also in the Southern Hemisphere. Colonised by predominantly workingclass British immigrants from the late eighteenth century, an ethnic and cultural connection grew between these two countries even though their indigenous populations and ecological environments were otherwise very different. Building a new life in Australia and New Zealand, the colonists shared similar historic perceptions of poverty – perceptions from their homelands that they did not want to see replicated in their new adopted countries. Dreams of a better life shaped their aspirations, self-identity and nationalistic outlook. By the twentieth century, national independence and self-government had replaced British colonial rule. The inveterate occurrence of poverty in Australia and New Zealand had created new local perspectives and different perceptions of, and about, poverty. This study analyses what relationship existed between the political directions adopted by the twentieth-century prime ministers of Australia and New Zealand and their perceptions of poverty. Using the existential phenomenological theory and methodology of Maurice Merleau-Ponty, the study adds to the body of knowledge about poverty in Australia and New Zealand by revealing the structure and origin of the poverty perceptions of the twentieth-century prime ministers.

Grown-Up Government: Bindi for Prime Minister! (Or President!).

Last week I called the Australian federal campaign the Inception election. As we lurch toward voting day on August 21, reality has tried to kick in, but to little avail. The two leaders, Prime Minister Julia Gillard (Labor) and challenger Tony Abbott (Liberal), both of whom recently toppled their predecessors in party-room coups, are now frantically searching for their own identity. And that’s what the election itself is increasingly about. Even though both have substantial track records as ministers, they are untried as national leaders. The real conundrum of the campaign – for them, if not for voters – is: Who the heck are these people?

A prime-boost immunisation regimen using recombinant BCG and Pr55 gag virus-like particle vaccines based on HIV type 1 subtype C successfully elicits Gag-specific responses in baboons

Mycobacterium bovis BCG is considered an attractive live bacterial vaccine vector. In this study, we investigated the immune response of baboons to a primary vaccination with recombinant BCG (rBCG) constructs expressing the gag gene from a South African HIV-1 subtype C isolate, and a boost with HIV-1 subtype C Pr55 gag virus-like particles (Gag VLPs). Using an interferon enzyme-linked immunospot assay, we show that although these rBCG induced only a weak or an undetectable HIV-1 Gag-specific response on their own, they efficiently primed for a Gag VLP boost, which strengthened and broadened the immune responses. These responses were predominantly CD8+ T cell-mediated and recognised similar epitopes as those targeted by humans with early HIV-1 subtype C infection. In addition, a Gag-specific humoral response was elicited. These data support the development of HIV-1 vaccines based on rBCG and Pr55 gag VLPs. © 2009 Elsevier Ltd. All rights reserved.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Synthesis of biodegradable polymer-mesoporous silica composite microspheres for DNA prime-protein boost vaccination

DNA vaccines or proteins are capable of inducing specific immunity; however, the translation to the clinic has generally been problematic, primarily due to the reduced magnitude of immune response and poor pharmacokinetics. Herein we demonstrate a composite microsphere formulation, composed of mesoporous silica spheres (MPS) and poly(d,l-lactide-co-glycolide) (PLGA), enables the controlled delivery of a prime-boost vaccine via the encapsulation of plasmid DNA (pDNA) and protein in different compartments. Method with modified dual-concentric-feeding needles attached to a 40 kHz ultrasonic atomizer was studied. These needles focus the flow of two different solutions, which passed through the ultrasonic atomizer. The process synthesis parameters, which are important to the scale-up of composite microspheres, were also studied. These parameters include polymer concentration, feed flowrate, and volumetric ratio of polymer and pDNA-PEI/MPS-BSA. This fabrication technique produced composite microspheres with mean D[4,3] ranging from 6 to 34 μm, depending upon the microsphere preparation. The resultant physical morphology of composite microspheres was largely influenced by the volumetric ratio of pDNA-PEI/MPS-BSA to polymer, and this was due to the precipitation of MPS at the surface of the microspheres. The encapsulation efficiencies were predominantly in the range of 93-98% for pDNA and 46-68% for MPS. In the in vitro studies, the pDNA and protein showed different release kinetics in a 40 day time frame. The dual-concentric-feeding in ultrasonic atomization was shown to have excellent reproducibility. It was concluded that this fabrication technique is an effective method to prepare formulations containing a heterologous prime-boost vaccine in a single delivery system.