This paper presents the theory of Secondary Representation of modules over a commutative ring and their Attached Primes; introduced in 1973 by I. MacDonald as a dual to the important theory of associated primes and primary decomposition in commutative algebra. The paper explores many of the basic aspects of the theory of primary decomposition and associated primes of modules in the hopes to delineate and motivate the construction of a secondary representation, when possible. The thesis discusses the results of the uniqueness of representable modules and their attached primes, and, in particular, the existence of a secondary representation for Artinian modules. It concludes with some interesting examples of both secondary and representable modules, highlighting the consequences of the results thus established.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-10-23T12:34:52Z No. of bitstreams: 2 Dissertação - Glauber Cristo Alves de Carvalho - 2013.pdf: 2320575 bytes, checksum: 5671a75a3a3b2b110d7431a79726479c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-10-23T12:38:41Z (GMT) No. of bitstreams: 2 Dissertação - Glauber Cristo Alves de Carvalho - 2013.pdf: 2320575 bytes, checksum: 5671a75a3a3b2b110d7431a79726479c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-10-23T12:38:41Z (GMT). No. of bitstreams: 2 Dissertação - Glauber Cristo Alves de Carvalho - 2013.pdf: 2320575 bytes, checksum: 5671a75a3a3b2b110d7431a79726479c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper presents a brief history about the numbers. After some important definitions to understand the texts. Following, we encounter the world of prime numbers. This part is presented some important properties, findings and open problems. The study of these figures have managed to find some formulas to generate them, which are presented throughout the text. It presents some numbers especias such as Fermat primes, Mersene, Shopie German and others. Finally, we have an application that uses many properties presented. / Neste trabalho é apresentado um breve histórico sobre os números. Após, algumas definições importantes para compreensão dos textos. Seguindo, nos deparamos com o universo dos números primos. Nesta parte é apresentado algumas propriedades importantes, descobertas e problemas em aberto. O estudo sobre estes números já conseguiu encontrar algumas fórmulas para gerá-los, que são apresentadas no decorrer do texto. Apresenta-se alguns números especias, como os primos de Fermat, Mersene, Shopie German e outros. Por fim, temos uma aplicação que utiliza muitas propriedades apresentadas.

Los materiales objeto de estudio en esta Tesis son óxidos de Mn del tipo La2/3A1/3MnO3 (A=Ca, Sr), que presentan una transición ferro-paramagnética acompañada de una transición metal-aislante a temperaturas del orden de TC=300K. La aplicación de un campo magnético favorece la aparición del orden ferromagnético produciendo un desplazamiento de la transición hacia temperaturas más elevadas. Esto genera una fuerte disminución de la resistividad, dando lugar a un importante efecto magnetoresistivo (magnetoresistencia colosal). Dado el complicado entramado de los diferentes fenómenos físicos concurrentes en las manganitas, estos óxidos tienen un gran interés tanto desde el punto de vista básico como del desarrollo de nuevos dispositivos de electrónica de espín. Dentro de este marco, esta tesis está organizada en tres apartados : 1. Una gran parte del trabajo experimental ha consistido en el desarrollo de un sistema de crecimiento de láminas delgadas mediante pulverización catódica de radiofrecuencia. Los distintos elementos del sistema (calefactores, portasustratos, magnetrones, etc) se controlan por ordenador, lo cual permite crecer muestras de forma automática. 2. La segunda parte del trabajo consiste en controlar el crecimiento de láminas del compuesto La2/3Ca1/3MnO3 a nivel nanoscópico. La influencia de las condiciones de depósito sobre los distintos parámetros claves del material (parámetros de celda, temperaturas de transición, resistividad, rugosidad, etc) ha sido estudiada de exhaustivamente y se ha conseguido la fabricación de muestras de alta calidad de forma reproducible. 3. La parte más importante de la investigación se ha dedicado a determinar el papel de las intercaras sobre las propiedades de capas de manganita. Como es bien sabido, la interacción responsable del ferromagnetismo en este material es muy sensible a las distorsiones estructurales, lo cual, combinado con la alta polarización de los portadores de carga, lleva a una magnetoresistencia de bajo campo muy fuerte en cerámicas nanométricas. Esta alta polarización también da lugar a una fuerte respuesta a campo débil en uniones túnel. Nuestra contribución consiste en la fabricación de intercaras artificiales de varios tipos y en la correlación de la magnetoresistencia obtenida con el análisis estructural. Las propiedades magnetoelectrónicas de las intercaras entre una manganita y un aislante (SrTiO3, LaAlO3 o NdGaO3) también han sido estudiadas. En estas regiones la temperatura de Curie TC y la conductividad eléctrica son más bajas que en el bulk, lo cual se atribuye a la coexistencia de fases con distintas propiedades electrónicas. Por otra parte, fenómenos más fundamentales como la magnetoresistencia anisotrópica y el efecto Hall anómalo también han sido objeto de estudio y se han intentado correlacionar con el acoplamiento espín-órbita y el estado magnético cerca de TC. / This thesis reports on properties of Mn oxides of the type La2/3A1/3MnO3 (A=Ca, Sr) which exhibit a ferromagnetic-to-paramagnetic transition concomitant of a metallic-to-insulator transition around TC=300K. The application of an external magnetic field favours the ferromagnetic ordering of Mn moments which leads to a shift of TC to higher temperatures, which in turn produces a decrease of the resistivity. This gives rise to a strong magnetoresistive effect called colossal magnetoresistance. In these compounds, many interactions have similar energy scales and compete to determine the ground state, making manganites very interesting materials from the basic point of view as well as for the development of new devices for spin electronics. Within this frame, this thesis is focused on the three following points : 1. The biggest effort in the experimental work has been dedicated to the set-up of a radiofrequency sputtering system for the fabrication of thin films of oxides. The different elements of the system (substrate heaters and holders, magnetrons, etc) are computer-controlled, which allows the growth of films and heterostructures in a fully automated fashion. 2. The second part of the work consisted in controlling the growth of thin films of mixed valence manganites, mainly La2/3Ca1/3MnO3, at the nanoscopic scale. The influence of several growth parameters on the key characteristics of the material (cell parameters, transition temperatures, resisitivity, roughness, etc) has been extensively studied and a reproducible fabrication of high-quality films has been achieved. 3. The main part of the work is focused on the role of interfaces on the properties of manganite films. It is well know that the interaction responsible for ferromagnetism in these compounds is very sensitive to structural distortions which, combined with a high polarisation of the charge carriers, leads to a strong low-field magnetoresistance in nanometric ceramic powders. This high polarisation also gives rise to a large low-field response in tunnel junctions. To probe these effects, we have fabricated artificial interfaces of several types and correlated their magnetotransport response with data from structural analysis. We have also studied the magnetoelectronic properties of the interface between a manganite film and an insulator (SrTiO3, LaAlO3, NdGaO3). A marked decrease of TC and of the electrical conductivity compared to bulk material is observed. This correlates with the detection of multiphase separation between regions with different electronic properties at these interfaces. Besides, fundamental transport phenomena such as anisotropic magnetoresistance and anomalous Hall have been investigated. Their magnitude and temperature dependence have been analysed and a semi-quantitative explanation involving the spin-orbit interaction and the electronic texture close to TC has been proposed. / Cette Thèse a été consacrée à l'étude d'oxydes de Mn La2/3A1/3MnO3 (A=Ca, Sr) présentant une transition ferromagnétique-paramagnétique concomitante d'une transition métal-isolant aux environs de TC=300K. L'application d'un champ magnétique externe favorise un ordre ferromagnétique du moment des ions Mn, ce qui déplace TC vers les hautes températures et induit une forte diminution de la résistivité. Ce fort effet magnétorésistif est appelé magnétorésistance colossale. Dans ces composés, de nombreux interactions sont en compétition ce qui les rend très intéressants du point de vue fondamental comme pour le développement de nouveaux dispositifs en électronique de spin.Dans ce cadre, cette thèse est structurée autour des trois points suivants :1. Un grand effort expérimental a été fourni pour développer un bâti de pulvérisation cathodique radiofréquence destiné à l'élaboration de couches minces d'oxydes. Les différents éléments du système (chaufferettes, porte-substrats, magnétrons) sont pilotés par ordinateur ce qui permet de fabriquer des couches minces de façon totalement automatique.2. La seconde partie du travail a consisté à contrôler la croissance de couches minces de La2/3Ca1/3MnO3 à l'échelle nanoscopique. L'influence des paramètres de croissance sur certaines caractéristiques du matériau (paramètres de maille, températures de transition, résistivité, rugosité de surface, etc) a été étudiée de façon extensive de sorte que des couches de très bonne qualité ont pu être obtenues de façon reproductible.3. Le rôle des interfaces sur les propriétés physiques de couches de manganite a fait l'objet de la majeure partie de cette thèse. En effet, l'interaction responsable du ferromagnétisme de ces composés est très sensible aux distorsions structurales, ce qui, du fait de la forte polarisation de spin des porteurs, donne lieu à une forte magnétorésistance à faible champ dans des céramiques nanométriques. Cette forte polarisation conduit également à une forte réponse magnétorésistive dans des jonctions tunnel. Nous nous sommes donc intéressés aux propriétés d'interfaces et avons fabriqué des interfaces artificielles de plusieurs types, et relié leur propriétés de magnétotransport aux résultats des analyses structurales. Par ailleurs, nous avons étudié les interfaces entre une manganite et un isolant (SrTiO3, LaAlO3, NdGaO3). Celles-ci possèdent une Tc et une conductivité beaucoup plus faibles que le matériau massif, ce qui est lié à la coexistence de régions présentant des propriétés électroniques différentes (séparation de phase). Par ailleurs, nous nous sommes également intéressés à des phénomènes de transport intrinsèques comme la magnétorésistance anisotrope et l'effet Hall extraordinaire dont nous avons essayé de comprendre la dépendance en température en la reliant au couplage spin-orbite et à la texture électronique près de TC.

In the last twenty years, algebraic techniques have been applied with great success to several areas in theoretical computer science. However, for many problems involving modular counting, there is a huge gap in our understanding depending on whether the modulus is prime or composite. A prime example is the problem of showing lower bounds for circuits with Mod gates in circuit complexity. Proof techniques that work well for primes break down over composites. Moreover, in some cases, the problem for composites turns out to be very different from the prime case. Making progress on these problems seems to require a better understanding of polynomials over composites. In this thesis, we address some such "prime vs. composite" problems from algorithms, complexity and combinatorics, and the surprising connections between them. We consider the complexity-theoretic problem of computing Boolean functions using polynomials modulo composites. We show that symmetric polynomials can viewed as simultaneous communication protocols. This equivalence allows us to use techniques from communication complexity and number theory to prove degree bounds. We use these to give the first tight degree bounds for a number of Boolean functions. We consider the combinatorial problem of explicit construction of Ramsey graphs. We present a simple construction of such graphs using polynomials modulo composites. This approach gives a unifying view of many known constructions,and explains why they all achieve the same bound.We show that certain approaches to this problem cannot give better bounds. Finally, we consider the algorithmic problem of interpolation for polynomials modulo composites. We present the first query-efficient algorithms for interpolation and learning under a distribution. These results rely on some new structural results about such polynomials.

A considerable body of research supports the application of behavioral economic principles to study the relative reinforcing efficacy of drug and alcohol use. One self-report measure, the Alcohol Purchase Task, is thought to account for individual differences in the subjective valuation of alcohol consumption. To date, however, behavioral economic approaches have not evaluated the possible influence of memory-based expectations regarding the cognitive and behavioral effects of substance use on their measures. Alcohol expectancy research has found that more positive expectancies about the effects alcohol directly mediate drinking behavior and are associated with a number of alcohol-related outcomes. Given the importance of alcohol expectancies, the current study incorporated cognitive priming techniques into the Alcohol Purchase Task instruction set to test whether the activation of alcohol expectancy primes influenced patterns of alcohol consumption. Although previous research has primarily used the Alcohol Purchase Task in samples of heavy drinkers, we also examined differences between heavier and lighter drinkers to test whether expectancy primes would differentially influence alcohol demand. As expected, both heavier and lighter drinkers in the expectancy priming conditions purchased more alcohol overall relative to those in a non-primed condition. Results also suggest the positive-social expectancy content in the Alcohol Purchase Task increased the overall demand for alcohol relative to a modified Alcohol Purchase Task with no contextual primes, even after controlling for alcohol consumption. Although previous behavioral economic research has examined alcohol expectancies as a secondary outcome, the current study is the first to directly examine the influence of expectancies on alcohol demand using the Alcohol Purchase Task.

In this paper, we study primary decomposition of any proper submodule N of a module M over a noetherian ring R. We start by briefly discussing basic facts about the very well known case where M is a finitely generated module over a Noetherian ring R, then we proceed to discuss the general case where M is any module over a Noetherian ring R. We put a lot of focus on the associated primes that occur with the primary decomposition, essentially studying their uniqueness and their relation to the associated primes of M/N.

Inaug. _ Diss.: Rechtsund staatswissenschaftliche Fakultät: Zürich: 1976. Résumé p. 226-235. _ Bibliogr. p. 236-244.

This research provides a thorough review of the research on priming and marketing (essay 1) as well as empirically explores several unintended consequences of priming (essay 2) and the antecedents to priming effects (essay 3). In essay 1, priming research is reviewed using a classification system based on priming outcome using the ABC model of attitudes (i.e., affective, behavioral, and cognitive priming). The priming process is discussed, and types of priming in each category are reviewed before challenges in the priming process are discussed. In essay 2, non-product-centric (i.e., collateral) primes (e.g., co-branding, sponsorship, cause marketing) are explored. This research explores how collateral information works as a prime to influence product evaluations, specifically with application to cause marketing. Study 1 of essay 2 explores the consumer outcomes of collateral communication primes by showing that adding a health cause to a cookie package (i.e., the prime) significantly increases product health perceptions. Study 2 explores limits on collateral communication priming and finds that health charities on product packaging increase brand attitude and purchase intentions, while disclaimers increase processing and reduce prime effects. Study 3 explores person specific antecedents to collateral communication primes revealing that an individual's theory of mind leads to ad skepticism that, in turn, influences reaction to primes. Essay 3 specifically examines the theoretical framework underlying priming effects by examining priming from two bodies of competing theory rooted in individual and social antecedents to behavior. Study 1 of essay 3 confirms past findings and develops materials to be used in studies 2 and 3 by showing that spokesfigures are marketer-supplied cues that vary in manipulativeness, and these cues interact with other cues, such as complexity and persuasion. Study 2 provides support for individual antecedents to cue-based primes (cognitive abilities, as measured by working memory capacity, and advertising skepticism). Study 3 builds on study 2 by adding in social antecedents (theory of mind and psychological reactance) to develop a comprehensive model of consumer information processing. All together, these three essays explore the literature on priming and marketing and provide a more holistic understanding of the antecedents to priming effects. / 2016-09-29

Orientador: Ricardo Miranda Martins / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T03:12:47Z (GMT). No. of bitstreams: 1 Spina_AndreVinicius_M.pdf: 1532380 bytes, checksum: 1525ba4a0d466a2c148b8b1a485ccec2 (MD5) Previous issue date: 2014 / Resumo: A pesquisa apresentará uma introdução a Teoria dos Números através de uma abordagem sobre os métodos criptográficos RSA e Diffie-Hellman, onde pode-se constatar situações onde eles são eficientes. A teoria matemática presente nesse trabalho envolve conhecimentos em números primos, aritmética modular, testes de primalidade, grupos e outras questões envolvendo teoria dos números / Abstract: The paper presents a Number Theory introduction, trough a RSA and Diffie-Hellman cryptographic methods approach, where one can observe situations where they are effective. The mathematical theory introduced in this paper encompass prime numbers, Modular arithmetic,Primality test, groups and other Number Theory related branches / Mestrado / Matemática em Rede Nacional - PROFMAT / Mestre em Matemática em Rede Nacional - PROFMAT

Thesis (PhD)–Stellenbosch University, 2014. / ENGLISH ABSTRACT: See pdf for abstract / AFRIKAANSE OPSOMMING: Sien PDF vir die opsomming