Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Higher order operations yield wider factorization and representation possibilities which correspond to reductions in the set of primes as well as tiered notions of primality. This comes at the expense of familiar algebraic properties such as associativity, and unique factorization. Criteria for primality and a naive testing algorithm are given for the ternary arithmetic, drawing heavily upon modular arithmetic. Finally, connections with the theory of partitions of integers and quadratic forms are discussed in relation to questions about cardinality of primes.

La «chimie verte » comprend le développement de procédés de synthèse respectueux de l'environnement, en réduisant notamment l'usage de solvants organiques. Dans ce but, nous avons montré qu'il était possible de synthétiser, à partir de microémulsions, des matériaux conducteurs protoniques, de structure prédéfinie, sans l'usage d'un autre solvant que l'eau.La première partie de cette étude a permis de démontrer la faisabilité de ce procédé. Le système ternaire choisi est composé d'une solution aqueuse d'acide 2-acrylamido-2-méthylpropane sulfonique (AMPS), de méthacrylate d'hexyle (HMA) comme phase hydrophobe et du tensioactif, le Brij® 35. Les structures des microémulsions ont été identifiées, selon leur composition, à partir de mesures de conductivité, de viscosité et d'imagerie par microscopies optique et confocale. Ces structures peuvent être inverse, lamellaire, bicontinue et directe. La polymérisation/réticulation par voie radicalaire des monomères présents dans les différentes phases conduit à des matériaux présentant ces mêmes structures. Les polymères étant réticulés, ces matériaux sont des réseaux interpénétrés de polymères (RIP).La seconde partie de cette étude a été consacrée à l'optimisation de la formulation des microémulsions pour obtenir des matériaux aux propriétés souhaitées. Ainsi, la fraction soluble et le taux de gonflement dans l'eau ont été considérablement réduits, tout en conservant une conductivité protonique de l'ordre de 10-3 S.cm-1. Les meilleurs résultats ont été obtenus en synthétisant un « double RIP », c'est-à-dire un RIP dans chacune des phases, matériau tout à fait original à ce jour. / "Green chemistry" includes the development of synthetic methods respectful of the environment, including reducing the use of organic solvents. For this purpose, we have shown that it is possible to synthesize, from microemulsions, proton conductive materials, predefined structure, without the use of a solvent other than water. The first part of this study demonstrates the feasibility of this method. The ternary system is selected from an aqueous solution consisting of 2-acrylamido-2-methylpropane sulphonic acid (AMPS), hexyl methacrylate (HMA) as hydrophobic phase and the surfactant, Brij® 35. The structures of microemulsions have been identified, depending on their composition from measurements of conductivity, viscosity and imaging optical and confocal microscopies. These structures can be inverse, lamellar, bicontinuous and direct. The polymerization/crosslinking of the monomers by free radical present in the various phases leads to materials having the same structures. Being crosslinked polymers, these materials are interpenetrating polymers networks (IPN). The second part of this study has been devoted to the optimization of the formulation of microemulsions to obtain materials with desired properties. Thus, the soluble fraction and the degree of swelling in water were significantly reduced, while maintaining proton conductivity of the order of 10-3 S.cm-1. The best results were obtained by synthesizing a "double IPN", that is to say, an IPN in each phase, entirely original material.

We present a novel modelling approach for the morphology formation from ternary mixtures upon evaporation, which takes into consideration two different length scales of the interaction, and further allows for these length scales to be altered. A quantitative study of the interfacial energy hints towards the existence of a mesoscopic regime - further research is needed to verify the validity of this claim however. We also demonstrate that the solvent initially follows a Fickian law of diffusion, then deviates from this behaviour, presumably due to the phase separated regions produced by the two remaining (active) components. We also attempt to bridge the gap between this work and a hypothetical three-dimensional model by considering a top-down view of the system. Here, we observe domain growth dominated by Ostwald ripening, with some coalescence. The domain growth was further characterised using Fourier image analysis. / Vi presenterar en ny modellansats för morfologiformation från trekomponentsblandningar under avdunstning, som tar hänsyn till två olika längdskalor hos interaktionen, samt möjliggör förändring av dessa längdskalor. En kvantitativ studie av energin vid domängränserna tyder på att det finns en mesoskopisk regim - ytterligare forskning är dock nödvändig för att verifiera giltigheten av detta påstående. Vi visar också att lösningsmedlet ursprungligen följer en Fickiansk diffusionslag, för att senare avvika från detta beteende, förmodligen på grund av de tydliga domänerna som produceras av de två återstående (aktiva) komponenterna. Vi försöker också minska klyftan mellan det här arbetet och en hypotetisk tredimensionell modell genom att behandla systemet uppifrån. Här observerar vi domäntillväxt dominerad av 'Ostwald ripening', med viss koalescens. Domäntillväxten karakteriserades vidare med hjälp av Fourier-bildanalys.

Neste trabalho foi realizado um estudo sistemático, das interações hiperfinas (campo hiperfino magnético e campo hiperfino elétrico), nos compostos do tipo RMn2Si2 e RMn2Ge2 (onde R = La, Nd, Pr), sendo que, para a amostra de La foi estudada a série LaMn2(Si(1-x)Gex)2 (onde x = 0, 0.2, 0.4, 0.6, 0.8, 1), por meio da técnica de correlação angular gama-gama perturbada (CAP), utilizando os núcleos de prova 111In(111Cd) e 140La(140Ce). Além disso, foram realizadas medições para a caracterização estrutural utilizando a técnica de difração de raios X, para a caracterização magnética, a nível macroscópico, através de medições de magnetização, caracterização nuclear utilizando a técnica de espectrometria da radiação gama e um estudo complementar por cálculos de primeiros princípios somente para as amostras de LaMn2Ge2 e LaMn2Si2. A maior contribuição para o comportamento magnético nesses compostos tem origem no ordenamento magnético da sub rede do Mn, que aparece em temperaturas relativamente altas, da ordem de 480 K, sendo que, esses compostos possuem um ordenamento antiferromagnético e próximo a temperatura ambiente passam a possuir um ordenamento ferromagnético. Além disso, para o caso especifico dos compostos PrMn2Ge2 e NdMn2Ge2, abaixo de 40K é observado, também, o ordenamento ferromagnético dos spins da sub rede da terra rara. O núcleo de prova 111In(111Cd) foi utilizado para medir, tanto as interações de quadrupolo elétrico, como de dipolo magnético na rede do Mn (interação matrizmatriz). Esses resultados evidenciaram a transição de fase magnética (antiferromagnética para ferromagnética), sendo que, o campo hiperfino magnético, para as duas fases magnéticas, segue o comportamento da função de Brillouin. Já o núcleo de prova 140La(140Ce) permitiu medir a interação de dipolo magnético, tanto originada pela rede do Mn, como pela rede da terra rara. Mas, nesse caso, pode ser verificado somente o campo hiperfino magnético da fase ferromagnética da rede do Mn. Para a análise dos resultados PAC levou-se em conta uma interação matriz-impureza, pois o íon Ce3+ possui um elétron 4f desemparelhado, que pode contribuir para o campo hiperfino total. O composto LaMn2Si2 apresentou o comportamento do campo hiperfino magnético com a temperatura que segue o comportamento da função de Brillouin. Já os compostos LaMn2Ge2, PrMn2Ge2 e NdMn2Ge2 apresentaram um comportamento anômalo ao da função de Brillouin. Esse comportamento pode ser associado a uma forte hibridização da banda 4f do Ce com a banda 3d do Mn, tal conclusão foi reforçada pelos resultados do DOS (densidade de estados), resultados dos cálculos de primeiros princípios, dos compostos LaMn2Si2 e LaMn2Ge2. / This thesis reports a systematic study of the hyperfine interactions (magnetic hyperfine field and electric field gradient) in the RMn2Si2 and RMn2Ge2 ( R = La, Nd, Pr) compounds as well as in LaMn2(Si(1-x)Gex)2 (where x = 0, 0.2, 0.4, 0.6, 0.8, 1) mixed compounds. The hyperfine interactions were measured through Perturbed Angular Correlation Gamma-Gamma Spectroscopy technique using 111In(111Cd) and 140La(140Ce) as probe nuclei. Structural, magnetic and chemical analysis characterization were carried out by X-ray diffraction, magnetization measurements and gamma radiation spectrometry, respectively. An additional study by first-principles calculations for LaMn2Ge2 e LaMn2Si2 samples were also performed. The magnetic behavior in these compounds is mainly associated with the ordering of the magnetic moments of Mn sublattice, which appears at high temperature around 480 K. All studied compounds undergo a transition from antiferromagnetic to ferromagnetic ordering around room temperature. Specifically for PrMn2Ge2 and NdMn2Ge2 compounds, an additional ferromagnetic ordering due to the polarization of Pr or Nd magnetic moments is also observed below 40 K. 111In(111Cd) probe nuclei were used to measure the temperature dependence of the electric quadrupole and the dipole magnetic interactions at the Mn sublattice (matrix-matrix interaction). The results show the magnetic transition (antiferromagnetic to ferromagnetic phase), where the magnetic hyperfine field associated to both magnetic phases follows the Brillouin function. For the 140La(140Ce) probe nuclei, only dipole magnetic interaction measurements in the ferromagnetic phase were possible, also caused by the Mn sublattice and, for R = Pr, Nd, by the rare earth sublattice. The analysis of results considers a matrix-impurity interaction because the Ce3+ has an unpaired 4f electron, which can contribute to the total hyperfine field. The compound LaMn2Si2 presents a behavior for the temperature dependence of the magnetic hyperfine field that could be fitted by a Brillouin function. On the other hand, LaMn2Ge2, PrMn2Ge2 and NdMn2Ge2 compounds showed an anomalous Brillouin function behavior. This behavior can be associated with a strong hybridization Ce 4f band with the Mn 3d band. Such conclusion was reinforced by the DOS (density of stats), first-principles calculations, results to LaMn2Si2 and LaMn2Ge2.

L’incorporation de nanoplaquettes d’argile dans une matrice ou un mélange de thermoplastiques s’avère prometteur pour en améliorer les propriétés d’usage. Récemment, un procédé de synthèse hydrothermale a permis d’obtenir un hydrogel chargé de nanoplaquettes de talc, ouvrant des perspectives d’élaboration de nanomatériaux à base de talc, potentiellement concurrents de ceux à base d’argile modifié. La grande quantité d’eau, introduite dans les appareils de mise en œuvre à l’état fondu, conduit à une perte de matière minérale importante et à l’agrégation partielle du talc. Ces contraintes rendent obligatoire l’utilisation de la mini-extrudeuse, de faible capacité, pour élaborer ces systèmes multiphasiques innovants, comme les nanocomposites polyamide/talc synthétique ou les mélanges polypropylène/polyamide (PP/PA) chargés de talc synthétique. Dans une phase polaire, le talc synthétique présente une structure constituée majoritairement de nanoparticules, mais aussi d’agrégats formés lors du malaxage. Il a été montré qu’une polarité accrue de la phase polyamide facilitait la nanodispersion du talc synthétique. Dans le cas des mélanges chargés, le talc synthétique est préférentiellement localisé dans les nodules de PA. Pour un polyamide peu polaire, l’effet émulsifiant est amplifié, ce qui s’explique par la rupture des nodules au niveau de zones peu cohésives PA/talc synthétique. D’autre part, l’augmentation de la viscosité de la matrice PP entraîne une localisation partielle du talc synthétique à l’interface matrice/nodules.Les relations structure-rhéologie des systèmes binaires et ternaires ont été discutées. / Addition of clay nanoplatelets within a thermoplastic matrix or immiscible thermoplastic blend usually improves final properties of materials. Recently, a hydrogel containing talc nanoplatelets has been obtained from hydrothermal synthesis, opening possibilities of development of talc based nanomaterials, which could rival the nanocomposites based on organically modified clay.The presence of large amount of water in the mixing chamber leads to significant losses of inorganic matter and to the presence of a few synthetic talc aggregates. These observations require the use of a twin screw mini-extruder which is appropriate to the elaboration of innovative multiphase materials, such as the synthetic talc/polyamide nanocomposites or the synthetic talc/polyamide/polypropylene blends.The structure of nanocomposites based on synthetic talc is mainly composed of nanometric entities, but also of a few micrometric aggregates. It has been shown that an increase of the polarity of the polyamide favours the dispersion of synthetic talc at nanometric scale.In the case of filled blends, the synthetic talc particles are preferentially located within PA nodules. The reduction of nodule size is explained by the breakup of nodules, due to numerous cohesion defects between synthetic talc nanoparticles and polyamide dispersed phase. Moreover, increasing polypropylene matrix viscosity leads to a selective localization of the synthetic talc at the nodule/matrix interface.Relationships between structure and rheology of binary and ternary systems have been discussed.

Neste trabalho foi realizado um estudo sistemático, das interações hiperfinas (campo hiperfino magnético e campo hiperfino elétrico), nos compostos do tipo RMn2Si2 e RMn2Ge2 (onde R = La, Nd, Pr), sendo que, para a amostra de La foi estudada a série LaMn2(Si(1-x)Gex)2 (onde x = 0, 0.2, 0.4, 0.6, 0.8, 1), por meio da técnica de correlação angular gama-gama perturbada (CAP), utilizando os núcleos de prova 111In(111Cd) e 140La(140Ce). Além disso, foram realizadas medições para a caracterização estrutural utilizando a técnica de difração de raios X, para a caracterização magnética, a nível macroscópico, através de medições de magnetização, caracterização nuclear utilizando a técnica de espectrometria da radiação gama e um estudo complementar por cálculos de primeiros princípios somente para as amostras de LaMn2Ge2 e LaMn2Si2. A maior contribuição para o comportamento magnético nesses compostos tem origem no ordenamento magnético da sub rede do Mn, que aparece em temperaturas relativamente altas, da ordem de 480 K, sendo que, esses compostos possuem um ordenamento antiferromagnético e próximo a temperatura ambiente passam a possuir um ordenamento ferromagnético. Além disso, para o caso especifico dos compostos PrMn2Ge2 e NdMn2Ge2, abaixo de 40K é observado, também, o ordenamento ferromagnético dos spins da sub rede da terra rara. O núcleo de prova 111In(111Cd) foi utilizado para medir, tanto as interações de quadrupolo elétrico, como de dipolo magnético na rede do Mn (interação matrizmatriz). Esses resultados evidenciaram a transição de fase magnética (antiferromagnética para ferromagnética), sendo que, o campo hiperfino magnético, para as duas fases magnéticas, segue o comportamento da função de Brillouin. Já o núcleo de prova 140La(140Ce) permitiu medir a interação de dipolo magnético, tanto originada pela rede do Mn, como pela rede da terra rara. Mas, nesse caso, pode ser verificado somente o campo hiperfino magnético da fase ferromagnética da rede do Mn. Para a análise dos resultados PAC levou-se em conta uma interação matriz-impureza, pois o íon Ce3+ possui um elétron 4f desemparelhado, que pode contribuir para o campo hiperfino total. O composto LaMn2Si2 apresentou o comportamento do campo hiperfino magnético com a temperatura que segue o comportamento da função de Brillouin. Já os compostos LaMn2Ge2, PrMn2Ge2 e NdMn2Ge2 apresentaram um comportamento anômalo ao da função de Brillouin. Esse comportamento pode ser associado a uma forte hibridização da banda 4f do Ce com a banda 3d do Mn, tal conclusão foi reforçada pelos resultados do DOS (densidade de estados), resultados dos cálculos de primeiros princípios, dos compostos LaMn2Si2 e LaMn2Ge2. / This thesis reports a systematic study of the hyperfine interactions (magnetic hyperfine field and electric field gradient) in the RMn2Si2 and RMn2Ge2 ( R = La, Nd, Pr) compounds as well as in LaMn2(Si(1-x)Gex)2 (where x = 0, 0.2, 0.4, 0.6, 0.8, 1) mixed compounds. The hyperfine interactions were measured through Perturbed Angular Correlation Gamma-Gamma Spectroscopy technique using 111In(111Cd) and 140La(140Ce) as probe nuclei. Structural, magnetic and chemical analysis characterization were carried out by X-ray diffraction, magnetization measurements and gamma radiation spectrometry, respectively. An additional study by first-principles calculations for LaMn2Ge2 e LaMn2Si2 samples were also performed. The magnetic behavior in these compounds is mainly associated with the ordering of the magnetic moments of Mn sublattice, which appears at high temperature around 480 K. All studied compounds undergo a transition from antiferromagnetic to ferromagnetic ordering around room temperature. Specifically for PrMn2Ge2 and NdMn2Ge2 compounds, an additional ferromagnetic ordering due to the polarization of Pr or Nd magnetic moments is also observed below 40 K. 111In(111Cd) probe nuclei were used to measure the temperature dependence of the electric quadrupole and the dipole magnetic interactions at the Mn sublattice (matrix-matrix interaction). The results show the magnetic transition (antiferromagnetic to ferromagnetic phase), where the magnetic hyperfine field associated to both magnetic phases follows the Brillouin function. For the 140La(140Ce) probe nuclei, only dipole magnetic interaction measurements in the ferromagnetic phase were possible, also caused by the Mn sublattice and, for R = Pr, Nd, by the rare earth sublattice. The analysis of results considers a matrix-impurity interaction because the Ce3+ has an unpaired 4f electron, which can contribute to the total hyperfine field. The compound LaMn2Si2 presents a behavior for the temperature dependence of the magnetic hyperfine field that could be fitted by a Brillouin function. On the other hand, LaMn2Ge2, PrMn2Ge2 and NdMn2Ge2 compounds showed an anomalous Brillouin function behavior. This behavior can be associated with a strong hybridization Ce 4f band with the Mn 3d band. Such conclusion was reinforced by the DOS (density of stats), first-principles calculations, results to LaMn2Si2 and LaMn2Ge2.

Abstract not available

Abstract not available

Previous research indicates that many important changes in executive functions, or higher cognitive capacities, occur between the ages of three and five years. Additionally, a distinction can be made between the cognitive functions associated with two different cortical regions. The functions of the dorsolateral prefrontal cortex (DL-PFC) are assessed using 'cool' tasks that are abstract and decontextualised. In contrast, the functions of the orbitofrontal cortex (OFC) are assessed using 'hot' tasks that require flexible appraisal of the affective significance of stimuli (Zelazo & Müller, 2002). Different clinical populations have been hypothesized to differ in terms of their impairment on tasks associated with each area of functioning. Current research conclusions regarding the primacy of hot versus cool executive function impairments are limited, however, as they have not taken complexity into account. That is, tasks currently used in investigations of hot and cool executive functions might differ in terms of the complexity of the cognitive processes that the tasks require. Therefore, comparisons across tasks may be misleading because these tasks vary in terms of the demands they place on participants as well as their hot versus cool status. While complexity theories have been applied to a number of cool tasks, only one hot task, those measuring theory-of-mind abilities, have been analysed in terms of complexity. One aim of the current research was to modify several tasks presumed to measure OFC performance to include a complexity manipulation. Tasks from three hot domains (conditional discrimination, the Children's Gambling Task, and future-oriented decision-making) were analysed in terms of their relational complexity, that is, the number of related entities or arguments inherent in a task or concept (Halford, 1993). Based on these complexity analyses, binary-relational and ternary-relational items of each of these tasks were developed or existing tasks were selected and/or modified. The binary-relational items were closely matched to the ternary-relational items in terms of stimuli and procedure, however, they were lower in complexity. After pilot testing, the three new measures of hot executive functioning were included in a larger test battery that was administered to a sample of 120 normally developing 3-, 4-, 5- and 6-year-old children. Existing binary- and ternary-relational items assessing theory-of-mind (a hot task) and three cool measures (transitivity, class inclusion and the Dimensional Change Card Sort test) were also included. The inclusion of measures of both hot and cool executive functions, each with complexity manipulated, allowed for the examination of a possible differential age of emergence of executive abilities associated with the DL-PFC versus the OFC. In support of the relational complexity approach, significant complexity effects were found across all seven tasks. Items at a higher level of complexity were experienced as relatively more difficult by children of all ages. Significant effects of age were also observed, with performance across all tasks increasing with age. The age effects were strongest on the ternary-relational items. The pass-fail data indicated that the majority of children in all age groups succeeded on the binary-relational items. However, it was not until a median of five years of age that children were able to process ternary relations. Consequently, the ternary-relational items produce the greatest differences in performance between the four age groups. The overall pattern of the results also suggested that a distinction can be made between the ages of emergence of abilities associated with the OFC versus the DL-PFC. The results of the pass-fail percentages, patterns of age-related change and age effects on domain factor scores all suggested that while hot executive functions may begin to develop around four years of age, similar levels of improvement are not seen in cool executive functions until five years of age. Thus, the ability to succeed on ternary-relational items of hot executive function tasks appeared to emerge slightly earlier than the cool executive function tasks. Complexity appears to be a critical factor underlying children's performance on executive function tasks, and future assessment regarding the development of executive abilities will benefit from keeping this in mind. While some refinement of new task items may be beneficial, the current test battery may have utility in further examinations of the executive profiles underlying clinical groups, such as children with autism and ADHD.

Recently short word-length (normally 1 bit or bits) processing has become a promising technique. However, there are unresolved issues in sigma-delta modulation, which is the basis for 1b/2b systems. These issues hindered the full adoption of single-bit techniues in industry. Among these problems is the stability of high-order modulators and the limit cycle behaviour. More importantly, there is no adaptive LMS structure of any kind in 1b/2b domain. The challenge in this problem is the harsh quantization that prevents straightforward LMS application. In this thesis, the focus has been made on three axes: designing new single-bit DSP applications, proposing novel approaches for stability analysis, and tacking the unresolved problems of 1b/2b adaptive filtering. Two structures for 1b digital comb filtering are proposed. A ternary DC blocker structure is also presented and performance is tested. We also proposed a single-bit multiplierless DC-blocking structure. The s tability of a single-bit high-order signma-delta modulator is studied under dc inputs. A new approach for stability analysis is proposed based on analogy with PLL analysis. Finally we succeeded in designing 1b/2b Wiener-like filtering and introduced (for the first time) three 1b/2b adaptive schemes.