Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process. First, we create a model of hematopoiesis, the processes of creating new blood cells. We analyze stem cell collection regimens and statistically sample parameter space in order to create a model accounts for the dynamics of multiple patients. Next, we modify an existing model of the wound healing response by introducing a variable for two inflammatory cell types. We analyze the timing of the inflammatory response and introduce the presence of systemic estrogen in the model, as there is evidence that the presence of estrogen leads to a more efficient wound healing response. Last, we mathematically model the gas exchange process in the lungs and body in order to lay the foundation for a model of the inflammatory response in the lung under conditions of mechanical ventilation. We introduce normal and ventilation breathing waveforms and a third state of hemoglobin in a closed loop partial differential equations model. We account for gas exchange in the lung and body compartments in addition to introducing a third discretized well-mixing compartment between the two. We use ordinary and partial differential equations to model these systems over one or more independent variables, as well as classical analysis techniques and computational methods to analyze systems. Statistical sampling is also used to investigate parameter values in order for the mathematical models developed to account for patient-to-patient variability. This alters the traditional mathematical model, which yields a single set of parameter values that represent one instance of the physiology, into a mathematical model that accounts for many different instances of physiology.}

The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W^1,1(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in the absence of a constraint. In the subsequent chapters we study various static continuum theories of liquid crystals. More specifically we look to explain a particular cholesteric fingerprint pattern observed by HP Labs. We begin in Chapter 2 by focusing on a specific cholesteric liquid crystal problem using the theory originally derived by Oseen and Frank. We find the global minimisers for general elastic constants amongst admissible functions which only depend on a single variable. Using the one-constant approximation for the Oseen-Frank free energy, we then show that these states are global minimisers of the three-dimensional problem if the pitch of the cholesteric liquid crystal is sufficiently long. Chapter 3 concerns the application of the results from the first chapter to the situations investigated in the second. The local stability of the one-dimensional states are quantified, analytically and numerically, and in doing so we unearth potential shortcomings of the classical Oseen-Frank theory. In Chapter 4, we ascertain some equivalence results between the continuum theories of Oseen and Frank, Ericksen, and Landau and de Gennes. We do so by proving lifting results, building on the work of Ball and Zarnescu, which relate the regularity of line and vector fields. The results prove to be interesting as they show that for a director theory to respect the head to tail symmetry of the liquid crystal molecules, the appropriate function space for the director field is S BV² (Ω,S<sup>2,/sup>). We take this idea and in the final chapter we propose a mathematical model of liquid crystals based upon the Oseen-Frank free energy but using special functions of bounded variation. We establish the existence of a minimiser, forms of the Euler-Lagrange equation, and find solutions of the Euler-Lagrange equation in some simple cases. Finally we use our proposed model to re-examine the same problems from Chapter 2. By doing so we extend the analysis we were able to achieve using Sobolev spaces and predict the existence of multi-dimensional minimisers consistent with the known experimental properties of high-chirality cholesteric liquid crystals.

De quelle notion de sujet avons-nous besoin rendre compte de nos pratiques et notamment de notre pratique du langage ? Cette question du sujet et de la subjectivité se pose à nouveaux frais dans le cadre de la philosophie du langage ordinaire et tout particulièrement à partir de la théorie des actes de parole de J.L. Austin. En effet, si le langage n’a de signification qu’en tant que parole, et même qu’en tant qu’acte d’un sujet qui prend la parole, le langage ne saurait être un processus sans sujet. Un acte nécessite un agent et si cet acte est un acte de parole, il faut un agent capable de comprendre la signification de ce qui est dit, en d'autres termes, il semble bien qu’il faille un sujet pensant, un sujet psychologique. C’est dans cette voie que s’engagèrent les premières interprétations d’Austin. Les actes de parole donnèrent naissance d’une nouvelle discipline : la pragmatique, où le rôle de l’intention dans la signification est primordial. Or, la philosophie du langage ordinaire se situe dans le projet initial de la philosophie analytique, tel que mené par Frege, Russell et le premier Wittgenstein, qui détachaient la signification de la subjectivité des représentations en la liant à la référence ou dénotation. Le sujet psychologique se trouve alors hors du champ de la pensée et de la vérité. Austin poursuit et radicalise ce projet : dans la théorie des actes de parole, la vérité devient la dimension d’évaluation de certains énoncés à l’intérieur de la catégorie plus générale de la félicité, évaluation qui n’est possible qu’en situant l’énonciation dans son contexte. C’est donc le contexte, et non l’intériorité du sujet parlant qui permet la compréhension. Ainsi, Le sujet des actes de paroles n’est pas le sujet intentionnel du mentalisme. C’est en fait un sujet pensant dont la pensée se lit dans le comportement, un sujet dont la pensée publique se fonde et s’exprime dans des conventions sociales qui le rendent responsables de ses paroles. Le sujet parlant est un sujet social pour qui l’enjeu est de parvenir à trouver et faire entendre sa voix alors même qu’il parle dans les mots des autres, un sujet responsable et mis en position de fragilité car il doit répondre de plus qu’il ne le voudrait. / What kind of a notion of subject do we need in order to account for our practices, and especially our practice of language? The issue of subject and subjectivity is raised anew within the ordinary language philosophy, more particularly within J.L. Austin's speech acts theory. As a matter of fact, if language has a meaning only inasmuch as it is a speech—the speech act of a subject—language cannot be a process devoid of subject. There must be an agent to perform an act, and if the act is a speech act, the agent must be able to understand what is meant, in other words, what seems to be needed is a thinking, psychological subject. Austin's first interpretations actually went down that path. Speech acts gave birth to a new theory: pragmatics, in which intention plays a key role in meaning. Nevertheless, ordinary language philosophy is in continuity with the original project of analytical philosophy as conducted by Frege, Russell and the first Wittgenstein, who separated the meaning from the subjectivity of representations and linked it instead to the reference or denotation. The psychological subject is then excluded from the field of thought and truth. Austin continues and toughens that project. Within the speech acts theory, truth becomes the assessment dimension of some utterances within the more general category of felicity—such an assessment being possible only when the issuing of the utterance is inserted in its whole context. Therefore, what enables comprehension is context, not inwardness. So, the subject of speech acts isn't the intentional subject of mentalism. In fact, it's a subject whose thought is to be read in their behaviour, a subject whose public thought is based on and expressed in social conventions which make them responsible for what they say. The speaking subject is a social subject whose issue is to find their voice and make themselves heard, although they speak in other people's words, a responsible subject in a vulnerable position as they must answer for more than they care for.

La procédure pénale est le théâtre de réformes législatives incessantes qui aboutissent à une multiplication sans précédent des régimes spécifiques à certaines catégories de délinquants ou d'infractions. Il en résulte un éclatement du système procédural pénal qui accroît la complexité de la matière et fait perdre de vue le sens même de l'adaptation des règles. L'analyse de la procédure pénale sous l'angle de la dialectique du droit commun et du droit spécial permet de prendre conscience de l'importance qu'il convient d'attacher, d'une part, à la distinction entre un régime applicable à toutes les affaires pénales et des régimes applicables à certaines d'entre elles, d'autre part, à la gestion des rapports entre ces différents types de régimes. Mise à l'épreuve de la procédure pénale, la distinction entre droit commun et droit spécial souffre d'une méconnaissance profonde en l'état actuel du droit. Celle-ci est traduite par la difficulté à situer les frontières du droit commun et du droit spécial, mais surtout attestée par la marginalisation progressive du droit commun face à l'expansion continue du droit spécial. La reconnaissance de la distinction entre droit commun et droit spécial n'en apparaît que plus nécessaire tant elle est, en réalité, consubstantielle à l'organisation de la procédure pénale. Mise à l'épreuve des rapports entre droit commun et droit spécial, la procédure pénale souffre, quant à elle, du désordre qui règne en ce domaine. Le désintérêt du législateur pour les rapports entre procédure pénale de droit commun et procédures pénales spéciales impose, dès lors, de chercher les moyens propres à assurer la maîtrise des relations entre ces ensembles. / Incessant legislative reforms in criminal procedural law produce an astonishing multiplication of specific procedures for certain categories of offenders or offences. Criminal procedural system is torn apart, increasing the complexity of law and clouding the very meaning of rules' adaptation. The dialectic of ordinary and special rules of law casts a new light on the evolution of criminal procedural law. On the one hand it is important to make a distinction between a common procedural framework that is applicable to every criminal case and specific procedures only applicable to some of them. On the other hand it becomes vital to manage the connections between these two types of law. Regarding the first point, there is a profound misunderstanding of the distinction in contemporary law. Indeed, it is difficult to determinate the frontiers of ordinary and special rules of criminal procedural law. Moreover, it is obviously attested by a progressive marginalization of ordinary criminal procedure facing an ever-expansion of special criminal procedures. A new understanding of the distinction appears even more necessary because the distinction between ordinary and special rules of law is essential to organize the criminal procedural system. Regarding the second point, criminal procedural law suffers from the resulting disorder from the mismanagement of the connections between ordinary and special rules. While the lawmakers seem not to pay much attention, the actual disorder cries out for appropriate means to control the connections between ordinary criminal procedure and special criminal procedures.

The diploma thesis deals with eating habits in Benešov Region in 50's and 60's of 20th Century. The thesis analyses results of a field research, which was realized by using kvalitative methods. The Results were compared with theoretical basis of contemporary and earlier literature and sources. The aim of this thesis was to illustrate situation in a small town and compare it with the countryside. Ordinary food was compared with festive food and its changes in consequence of migration. The root of the thesis was description of staple food, its gaining (shopping, self-suppling, …), processing and frequency of its consumption.

This thesis uses a simple deterministic model represented by an ordinary di- fferential equation with two equilibrium points - depending on the initial state the illness either vanishes or persists forever. This model is expanded by adding some diffusion coefficients leading to different stochastic differential equations. They are analyzed to show how the choice of diffusion coefficients changes be- havior of the model in proximity of its equilibria and near the boundary of area with biological meaning. The theoretical results are than illustrated by computer simulations. 1

The main purpose of this study is to empirically assess the relationship between inflation and economic growth in Ethiopia using quarterly dataset from 1992Q1 to 2010Q4. In doing so, an interesting policy issue arises. What is the threshold level of inflation for the Ethiopian economy? Based on the Engle-Granger and Johansen co-integration tests it is found out that there is a positive long-run relationship between inflation and economic growth. The error correction models show that in cases of short-run disequilibrium, the inflation model adjusts itself to its long-run path correcting roughly 40% of the imbalance in each quarter. In addition, based on the conditional least square technique, the estimated threshold model suggests 10% as the optimal level of inflation that facilitates growth. An inflation level higher or lower than the threshold level of inflation affects the economic growth negatively and hence fiscal and monetary policy coordination is vital to keep inflation at the threshold. / Economics / M. Com. (Economics)

Extreme Value Theory nds application in problems concerning low probability but high consequence events. In hydrology the study of heavy rainfall is important in regional ood risk assessment. In particular, the N-year return level is a key output of an extreme value analysis, hence care needs to be taken to ensure that the model is accurate and that the level of imprecision in the parameter estimates is made explicit. Rainfall is a process that evolves over time and space. Therefore, it is anticipated that at extreme levels the process would continue to show temporal and spatial correlation. In this study interest is in whether any trends in heavy rainfall can be detected for the Western Cape. The focus is on obtaining the 50-year daily winter rainfall return level and investigating whether this quantity is homogenous over the study area. The study is carried out in two stages. In the rst stage, the point process approach to extreme value theory is applied to arrive at the return level estimates at each of the fteen sites. Stationarity is assumed for the series at each station, thus an issue to deal with is that of short-range temporal correlation of threshold exceedances. The proportion of exceedances is found to be smaller (approximately 0.01) for stations towards the east such as Jonkersberg, Plettenbergbay and Tygerhoek. This can be attributed to rainfall values being mostly low, with few instances where large amounts of rainfall were observed. Looking at the parameters of the point process extreme value model, the location parameter estimate appears stable over the region in contrast to the scale parameter estimate which shows an increase towards in a south easterly direction. While the model is shown to t exceedances at each station adequately, the degree of uncertainty is large for stations such as Tygerhoek, where the maximum observed rainfall value is approximately twice as large as the high rainfall values. This situation was also observed at other stations and in such cases removal of these high rainfall values was avoided to minimize the risk of obtaining inaccurate return level estimates. The key result is an N-year rainfall return level estimate at each site. Interest is in mapping an estimate of the 50-year daily winter rainfall return level, however to evaluate the adequacy of the model at each site the 25-year return level is considered since a 25 year return period is well within the range of the observed data. The 25-year daily winter rainfall return level estimate for Ladismith is the smallest at 22:42 mm. This can be attributed to the station's generally low observed winter rainfall values. In contrast, the return level estimate for Tygerhoek is high, almost six times larger than that of Ladismith at 119:16 mm. Visually design values show di erences between sites, therefore it is of interest to investigate whether these di erences can be modelled. The second stage is the geostatistical analysis of the 50-year 24-hour rainfall return level The aim here is to quantify the degree of spatial variation in the 50-year 24-hour rainfall return level estimates and to use that association to predict values at unobserved sites within the study region. A tool for quantifying spatial variation is the variogram model. Estimation of the parameters of this model require a su ciently large sample, which is a challenge in this study since there is only fteen stations and therefore only fteen observations for the geostatistical analysis. To address this challenge, observations are expanded in space and time and then standardized and to create a larger pool of data from which the variogram is estimated. The obtained estimates are used in ordinary and universal kriging to derive the 50-year 24-hour winter rainfall return level maps. It is shown that 50-year daily winter design rainfall over most of the Western Cape lies between 40 mm and 80 mm, but rises sharply as one moves towards the east coast of the region. This is largely due to the in uence of large design values obtained for Tygerhoek. In ordinary kriging prediction uncertainty is lowest around observed values and is large if the distance from these points increases. Overall, prediction uncertainty maps show that ordinary kriging performs better than universal kriging where a linear regional trend in design values is included.

La thèse analyse le recours, en droit pénal, à la technique énumérative, particulièrement aux listes d'infractions. Cette figure légistique, jadis utilisée dans les conventions bilatérales d'extradition, est aujourd'hui fortement répandue pour délimiter le champ d'application de règles exceptionnelles. Le droit pénal international, le droit pénal français et le droit pénal italien sont simultanément interrogés sur leurs recours à la technique énumérative. L'intérêt de ce rapprochement est de fournir un corpus d'étude riche et varié mettant en jeu différents systèmes et ordres juridiques. La liste n'est pas considérée sous le seul aspect légistique ; sa fonction politique est également analysée. Opérant une sélection d'infractions soumises à un régime différencié, elle est au service d'une répression aggravée ou innovante.L'utilisation de cette technique législative est évaluée à l'aune des résultats escomptés d'une part et avérés d'autre part. On découvre que l'extension, qui est naturelle à toute énumération, appelle une appréciation tantôt critique, tantôt positive. On regrette la dénaturation des listes d'infractions par des rédacteurs qui en détournent la vocation première. L'évaluation se fonde sur les grands principes du droit pénal, à savoir les principes de légalité et de proportionnalité, dont le respect effectif constitue in fine le remède proposé à la dénaturation des listes d'infractions. / The thesis analyses the utilization of enumeration through the "listing of crimes" as a legislative technique in criminal law. Such a method of legislative drafting was used historically in bilateral conventions, specifically in the area of extradition, but nowadays it is heavily employed in criminal law to delimit the scope of application of exceptional rules. Aiming at providing a rich and solid base of knowledge in a domain that is rarely studied, this work reviews various systems and legal orders. As such, the resort to "listing of crimes" will be examined in international criminal law as well as in French and Italian criminal law. Being a tool to select a group of crimes in order to treat them differently than the common crimes, the listing technique serves the needs of aggravated or innovative repression. In that regard, the "listing" technique is not only considered as a means of legislative drafting, but its political function is also analyzed. The utilization of this technique is assessed in the light of the expected as well as the verified results. The extension of an existing "list of crimes", a normal consequence of resorting to enumeration, is found to be positive in some cases but more or less criticized in other cases where legislatures deviate from the original reason for which this drafting technique has been elaborated. Examined from the perspective of the fundamental principles of criminal law, namely the principle of legality and the principle of proportionality, the usage of this technique is appraised. The respect of these two primordial principles constitutes the ultimate solution proposed for any deviated resort to "listing of crimes" as a legislative tool.

A busca por novos materiais estruturais visa a melhoria da qualidade e desempenho das estruturas, impulsionando o desenvolvimento científico e tecnológico. O concreto auto-adensável surgiu da necessidade de se dispensar o difícil e oneroso trabalho de vibração do concreto, sendo definido como um material capaz de fluir dentro de uma fôrma, passando pelas armaduras e preenchendo a mesma, sem o uso de equipamentos de vibração. Esta pesquisa caracteriza-se como um estudo teórico-experimental da aderência aço-concreto, utilizando concreto do tipo auto-adensável, mediante ensaios monotônicos de flexão em vigas e de arrancamento seguindo o modelo padrão do Rilem-Ceb-Fip (1973). O estudo considerou como parâmetros fundamentais o tipo de concreto (auto-adensável e convencional), a resistência à compressão do concreto e os diâmetros das barras. Ainda, realizou-se um estudo com relação à variabilidade do concreto auto-adensável nos estados fresco e endurecido, constatando que este possui pequena variação. De posse dos resultados, buscou-se verificar a previsão das formulações empregadas na literatura e pelos principais códigos internacionais. De acordo com os resultados, o comportamento dos modelos de viga e de arrancamento para ambos os concretos foi similar, mostrando que o concreto auto-adensável possui características semelhantes ao concreto convencional, com as vantagens da trabalhabilidade no estado fresco. Quanto à análise numérica, os modelos desenvolvidos representaram de forma satisfatória o comportamento dos ensaios, e forneceram uma idéia do comportamento da tensão de aderência na sua interface. Com relação às formulações teóricas, verificou-se que tanto para o concreto convencional quanto para o auto-adensável, ocorre uma superestimativa da resistência de aderência. / The search for new structural materials aims the improvement of the structures performance, pushing the scientific and technological development. Self-compacting concrete (SCC) origin was due to the need to avoid the difficult and expensive process of concrete vibration. It has been defined as a material capable to flow inside a formwork, passing through the reinforcement and filling it completely, without using of any special equipment. This research is characterized as a theoretical and experimental study of steel-concrete bond, using SCC, through pull-out tests and beam tests standardized by Rilem-Ceb-Fip model. The study considered as main parameters the concrete type (ordinary concrete and SCC), its compressive strength and the steel bars diameters. Yet, a study of the variability of the properties of SCC, both in fresh and hardened state was also performed, showing that SCC is a very reliable material. The obtained results were compared with the ones established by the related bibliography and by the main international codes. According to the results, the behavior of the beams and pull-out tests were very similar for both concretes (SCC and OC), with the well know advantages for the SCC in fresh state. About the numerical approach, the developed models represented satisfactory the test behavior (beam and pull-out) and gave an idea of the bond stress behavior on the steel-concrete interface. About the theoretical formulations, it was verified the they usually overestimate the bond strength, for both types of concrete.