Οι κατασκευές εδαφικής αντιστήριξης εξακολουθούν να βρίσκονται σε ευρύτατη χρήση, με διαρκώς αυξανόμενο ενδιαφέρον λόγω των απαιτήσεων των σύγχρονων έργων υποδομής αλλά και των αναγκών δόμησης σε πυκνό αστικό περιβάλλον. Το ενδιαφέρον εστιάζεται σε κατασκευαστικές λύσεις και μεθόδους σχεδιασμού που συνδυάζουν ασφάλεια και οικονομία. Η ανάλυση των συγκεκριμένων κατασκευών αντιμετωπίζει πλήθος δυσεπίλυτων προβλημάτων στο αντικείμενο της αλληλεπίδρασης εδάφους-κατασκευής που συχνά καθορίζουν τη συμπεριφορά του έργου. Η κατανόηση αυτών των μηχανισμών επιτρέπει το σχεδιασμό με μικρότερα περιθώρια αβεβαιότητας που οδηγούν σε οικονομικότερες και ορθολογικότερες λύσεις. Στην κατεύθυνση αυτή συμβάλει η παρούσα Διατριβή, με την ανάπτυξη αναλυτικών εργαλείων και θεωρητικών ευρημάτων που βοηθούν στην κατανόηση των μηχανισμών της αλληλεπίδρασης και στην εκτίμηση της συμπεριφοράς των τοίχων αντιστήριξης υπό συνδυασμένη βαρυτική και σεισμική φόρτιση. Έμφαση δίνεται στην παραγωγή απλών κλειστών λύσεων και μεθοδολογιών για τον υπολογισμό των εδαφικών ωθήσεων και τη στατική ανάλυση του συστήματος τοίχου εδάφους. Συγκεκριμένα, παράγονται λύσεις άνω και κάτω ορίου για ενδόσιμους τοίχους, οι οποίες, παρότι προσεγγιστικές, πλεονεκτούν έναντι των κλασικών εξισώσεων Coulomb και Mononobe-Okabe τις οποίες μπορούν να αντικαταστήσουν. Σε ειδικές περιπτώσεις, όπως η περίπτωση τοίχων προβόλων με πεπλατυσμένο πέλμα, οι προτεινόμενες λύσεις οδηγούν σε ακριβή αποτελέσματα που βασίζονται σε ένα γενικευμένο πεδίο τάσεων Rankine. Επίσης παρουσιάζονται επεκτάσεις τους οι οποίες επιτρέπουν τον υπολογισμό μη-υδροστατικών κατανομών ωθήσεων γαιών λαμβάνοντας υπόψη την κυματική διάδοση της σεισμικής διέγερσης στο επίχωμα, σύμφωνα με μια ορθότερη παραλλαγή της ιδέας των Steedman & Zeng και τις διαφορετικές κινηματικές συνθήκες που προέρχονται από την απόκριση του τοίχου με περιστροφή περί την κορυφή ή τη βάση σύμφωνα με την τεχνική της Dubrova. Για την περίπτωση ανένδοτων τοίχων παρουσιάζεται μεθοδολογία για τη δραστική απλοποίηση των διαθέσιμων ελαστοδυναμικών, κυματικών λύσεων, όπως αυτή των Veletsos & Younan, η οποία καταλήγει σε κλειστές μαθηματικές εκφράσεις για τον υπολογισμό των ωθήσεων. Τέλος, παρουσιάζονται νέα ευρήματα στην κατεύθυνση της μαθηματικής αντιμετώπισης του δυσεπίλυτου προβλήματος της οριακής ισορροπίας ριπιδίου τάσεων σε εδαφικό μέσο στο οποίο ενεργούν βαρυτικές και αδρανειακές δυνάμεις πεδίου. Η παρούσα εργασία συμβάλλει στην περαιτέρω διερεύνηση του προβλήματος το οποίο θεμελίωσαν θεωρητικά οι Levy, Boussinesq, von Karman και Caquot, μέσω της δραστικής (αλλά ακριβούς) απλοποίησης του σε μία μη-γραμμική συνήθη διαφορική εξίσωση, η οποία επιτρέπει την επίλυση με απλές αριθμητικές και ημιαναλυτικές τεχνικές. Πέρα από τα ακριβή αριθμητικά αποτελέσματα, η προτεινόμενη ανάλυση προσφέρει μια βαθύτερη εποπτεία στο πρόβλημα και ανοίγει το δρόμο για περαιτέρω διερεύνηση ή και επέκταση της μεθόδου πέρα από τα όρια της κλασικής οριακής ανάλυσης. Η αξιοπιστία των προτεινόμενων λύσεων ελέγχεται μέσω συγκρίσεων με καθιερωμένες λύσεις και πειραματικά δεδομένα από τη βιβλιογραφία, αλλά και πρόσφατα πειραματικά αποτελέσματα που παρήχθησαν από τον συγγραφέα και ερευνητές στη σεισμική τράπεζα του Πανεπιστημίου του Bristol του Ηνωμένου Βασιλείου. / Earth retaining structures are still in widespread use, with growing interest due to the demands of modern infrastructure and building needs in a dense urban environment. Building solutions and design methodologies that combine safety and economy are the objectives of modern research. Significant difficulties in the analysis of retaining structures arise from the soil-structure interaction nature of the problem that often prescribes its behavior. Understanding these mechanisms allows design under smaller uncertainties, leading to economical and rational solutions. The contribution of the present thesis consists of the development of analytical tools and theoretical findings, helpful in understanding the mechanisms of interaction and the behavior of walls under combined gravity and seismic loading. Emphasis is given to the derivation of simple closed-form solutions and methodologies for the calculation of earth pressures and the static analysis of wall-soil system. Specifically, approximate Lower and Upper Bound solutions are produced for the case of yielding walls, which are advantageous compared to the classical equations Coulomb and Mononobe-Okabe. In special cases, such as the L-shaped cantilever walls, these solutions lead to exact results, pertaining to a generalized Rankine stress field. Extensions of the above solutions are presented allowing the calculation of non-hydrostatic earth pressure distributions, due to the wave propagation of the seismic excitation in the backfill, according to a better variant of the Steedman & Zeng approach and different kinematic conditions of the wall rotating around the top or bottom, according to the technique of Dubrova. For the case of non-yielding walls, a new methodology for the drastic simplification of available wave solutions, such as the Veletsos & Younan, is presented which leads to closed-form expressions for the dynamic pressure calculation. Finally, new theoretical findings are presented for the mathematical treatment of the intractable problem of plastic limit equilibrium in soil medium subjected to gravitational and inertial forces field. This work contributes to the further investigation of the problem which is founded theoretically by Levy, Boussinesq, von Karman and Caquot, through the significant (but accurate) simplification to a single, non-linear ordinary differential equation, easier to handle by simple numerical and semi-analytical techniques. Apart from the exact numerical results, the proposed analysis provides a deeper physical insight, leading the way to further investigation or extension of the method beyond the classical limit analysis assumptions. The reliability of the proposed solutions is checked through comparisons with established solutions and experimental data from the literature and recent experimental results obtained by the author and researchers in the shake table laboratory of the University of Bristol, UK.

Les premières recherches en détection, localisation et séparation de signaux remontent au début du 20ème siècle. Ces recherches sont d’actualité encore aujourd’hui, notamment du fait de la croissance rapide des systèmes de communications constatée ces deux dernières décennies. Par ailleurs, la littérature du domaine consacre très peu d’études relatives à certains contextes jugés difficiles dont certains sont traités dans cette thèse. Ce travail porte sur la localisation de signaux par détection des temps d’arrivée ou estimation des directions d’arrivée et sur la séparation de sources dépendantes ou à module constant. L’idée principale est de tirer profit de certaines informations a priori disponibles sur les signaux sources telles que la parcimonie, la cyclostationarité, la non-circularité, le module constant, la structure autoregressive et les séquences pilote dans un contexte coopératif. Une première partie détaille trois contributions : (i) un nouveau détecteur pour l’estimation des temps d’arrivée basé sur la minimisation de la probabilité d’erreur ; (ii) une estimation améliorée de la puissance du bruit, basée sur les statistiques d’ordre ; (iii) une quantification de la précision et de la résolution de l’estimation des directions d’arrivée au regard de certains a priori considérés sur les sources. Une deuxième partie est consacrée à la séparation de sources exploitant différentes informations sur celles-ci : (i) la séparation de signaux de communication à module constant ; (ii) la séparation de sources dépendantes connaissant la nature de la dépendance et (iii) la séparation de sources autorégressives dépendantes connaissant la structure autorégressive. / Signal detection, localization, and separation problems date back to the beginning of the twentieth century. Nowadays, this subject is still a hot topic receiving more and more attention, notably with the rapid growth of wireless communication systems that arose in the last two decades and it turns out that many challenging aspects remain poorly addressed by the available literature relative to this subject. This thesis deals with signal detection, localization using temporal or directional measurements, and separation of dependent source signals. The main objective is to make use of some available priors about the source signals such as sparsity, cyclo-stationarity, non-circularity, constant modulus, autoregressive structure or training sequences in a cooperative framework. The first part is devoted to the analysis of (i) signal’s time-of-arrival estimation using a new minimum error rate based detector, (ii) noise power estimation using an improved order-statistics estimator and (iii) side information impact on direction-of-arrival estimation accuracy and resolution. In the second part, the source separation problem is investigated at the light of different priors about the original sources. Three kinds of prior have been considered : (i) separation of constant modulus communication signals, (ii) separation of dependent source signals knowing their dependency structure and (iii) separation of dependent autoregressive sources knowing their autoregressive structure.

Dans un ordinateur multiprocesseur, lors de l'accès à la mémoire partagée, il faut synchroniser les entités de calcul (processus). Cela peut se faire à l'aide de verrous, mais des problèmes se posent (par exemple interblocages, mauvaise tolérance aux pannes). On s'est intéressé à l'implémentation d'abstractions (consensus et construction universelle) qui peuvent faciliter la programmation concurrente sans attente, sans utiliser de verrous mais basés sur des lectures/écritures atomiques (LEA). L'usage exclusive des LEA ne permet pas de réaliser un consensus sans attente. Néanmoins, autoriser l'usage de primitives offrant une puissance de synchronisation plus forte que des LEA, mais coûteuse en temps de calcul, le permet. Nous nous sommes donc intéressés dans cette thèse à des programmes qui limitent l'usage de ces primitives aux seules situations où les processus sont en concurrence, ces programmes sont dit solo-rapides. Une autre piste étudiée est de permettre à l'objet, lorsqu'il y a de la concurrence, de retourner une réponse spéciale "abandon" qui signifie l'abandon des calculs en cours. Ces objets sont dit abandonnables. D'une part, nous donnons des implémentations d'objets concurrents sans attente, abandonnables et/ou solo-rapides. Pour cela, nous proposons une construction universelle qui assure à l'objet implémenté d'être abandonnable et solo-rapide ; nous avons réalisés des algorithmes de consensus solo-rapides et des algorithmes de consensus abandonnable. D'autre part nous étudions la complexité en espace de ces implémentations en proposant des bornes inférieures sur l'implémentation des objets abandonnables et sur le consensus. / In multiprocessor computer, synchronizations between processes are needed for the access to the shared memory. Usually this is done by using locks, but there are some issues as deadlocks or lack of fault-tolerance. We are interested in implementing abstractions (as consensus or universal construction) which ease the programming of wait-free concurrent objects, without using lock but based on atomic Read/Write operations (ARW). Only using the ARW does not permit to implement wait-free consensus. The use of primitives which offer a higher power of synchronization than the ARW is needed. But these primitives are more expensive in computing time. Therefore, we are interested in this thesis in the design of algorithms which restrict the use of these primitives only to the cases where processes are in contention. These algorithms are said solo-fast. Another direction is to allow the object to abort the computation in progress - and to return a special response "abort" - when there is contention. These objects are named abortable. On the one hand we give wait-free, abortable and/or solo-fast concurrent object implementations. Indeed we proposed a universal construction which ensure to the implemented object to be abortable and solo-fast. We have also realized solo-fast consensus algorithms and abortable consensus algorithms. On the other hand, we study the space complexity of these implementations : we prove space lower bound on the implementation of abortable object and consensus.

Dans cette thèse, nous nous étudions des algorithmes d’optimisation non linéaire. D’une part nous proposons des techniques de détection rapide de la non-réalisabilité d’un problème à résoudre. D’autre part, nous analysons le comportement local des algorithmes pour la résolution de problèmes singuliers. Dans la première partie, nous présentons une modification d’un algorithme de lagrangien augmenté pour l’optimisation avec contraintes d’égalité. La convergence quadratique du nouvel algorithme dans le cas non-réalisable est démontrée théoriquement et numériquement. La seconde partie est dédiée à l’extension du résultat précédent aux problèmes d’optimisation non linéaire généraux avec contraintes d’égalité et d’inégalité. Nous proposons une modification d’un algorithme de pénalisation mixte basé sur un lagrangien augmenté et une barrière logarithmique. Les résultats théoriques de l’analyse de convergence et quelques tests numériques montrent l’avantage du nouvel algorithme dans la détection de la non-réalisabilité. La troisième partie est consacrée à étudier le comportement local d’un algorithme primal-dual de points intérieurs pour l’optimisation sous contraintes de borne. L’analyse locale est effectuée sans l’hypothèse classique des conditions suffisantes d’optimalité de second ordre. Celle-ci est remplacée par une hypothèse plus faible basée sur la notion de borne d’erreur locale. Nous proposons une technique de régularisation de la jacobienne du système d’optimalité à résoudre. Nous démontrons ensuite des propriétés de bornitude de l’inverse de ces matrices régularisées, ce qui nous permet de montrer la convergence superlinéaire de l’algorithme. La dernière partie est consacrée à l’analyse de convergence locale de l’algorithme primal-dual qui est utilisé dans les deux premières parties de la thèse. En pratique, il a été observé que cet algorithme converge rapidement même dans le cas où les contraintes ne vérifient l’hypothèse de qualification de Mangasarian-Fromovitz. Nous démontrons la convergence superlinéaire et quadratique de cet algorithme, sans hypothèse de qualification des contraintes. / This thesis is devoted to the study of numerical algorithms for nonlinear optimization. On the one hand, we propose new strategies for the rapid infeasibility detection. On the other hand, we analyze the local behavior of primal-dual algorithms for the solution of singular problems. In the first part, we present a modification of an augmented Lagrangian algorithm for equality constrained optimization. The quadratic convergence of the new algorithm in the infeasible case is theoretically and numerically demonstrated. The second part is dedicated to extending the previous result to the solution of general nonlinear optimization problems with equality and inequality constraints. We propose a modification of a mixed logarithmic barrier-augmented Lagrangian algorithm. The theoretical convergence results and the numerical experiments show the advantage of the new algorithm for the infeasibility detection. In the third part, we study the local behavior of a primal-dual interior point algorithm for bound constrained optimization. The local analysis is done without the standard assumption of the second-order sufficient optimality conditions. These conditions are replaced by a weaker assumption based on a local error bound condition. We propose a regularization technique of the Jacobian matrix of the optimality system. We then demonstrate some boundedness properties of the inverse of these regularized matrices, which allow us to prove the superlinear convergence of our algorithm. The last part is devoted to the local convergence analysis of the primal-dual algorithm used in the first two parts of this thesis. In practice, it has been observed that this algorithm converges rapidly even in the case where the constraints do not satisfy the Mangasarian-Fromovitz constraint qualification. We demonstrate the superlinear and quadratic convergence of this algorithm without any assumption of constraint qualification.

The majority of black South Africans utilize the services of indigenous healers and the new National Health Plan for South Africa makes provision for cooperation between the healers and formal health practitioners. The purpose of this study was to determine the role played by indigenous African healers in the prevention of diseases and the promotion of health, and to design a model which will provide guidelines for cooperation between indigenous healers and formal health workers. This study was ethno-medical, contextual, exploratory and qualitative. It was designed to look into the health care of a specific cultural group to explore in depth the experiences of indigenous healers in providing health care within their cultural context. Data was collected by individual free-type interviews from indigenous African healers, users of formal health services and by observation. It was found that there is dual utilization of both formal and indigenous health service systems by clients. A specific culbrral terminology relating to health was found to be used. Such terminology could result in communication gaps and breakdowns if not known to or used by formal health workers. The findings show that cultural beliefs are still strongly adhered to. These were found to influence the life-styles and health maintenance behaviour of a cultural group. The fmdings show that divination fonns the core of health assessment and health-problem diagnosis. It was found that no health problem could be attended to without first going through a divination session. The findings also show involvement of indigenous healers in primary health care workers at first contact levels of prevention in the field of paediatric preventive care. Diarrhoea and vomiting in children was found to be the preventable disease in which healers specialize. Infertility and impotence were found to be conditions taken to healers for treatment. Other sexually transmitted diseases as well as culture-bound syndromes treated by indigenous healers were found in this study. The use of rituals and rites of passage and the involvement of ancestors were found to form part ofholistic health care. The fmdings show the willingness of healers to collaborate with formal health workers. A model is designed to guide the process of collaboration. / Health Studies / D. Lit. et Phil. (Advanced Nursing Sciences)

The effectiveness of language requires that users of a language be provided with the right knowledge to cope with its complexity and demanding nature especially in the area of writing. In this sense, this thesis sought to draw attention to some of the important features of writing and speaking skills in the English language at two higher learning institutions in Namibia. English is a second language for students at these institutions. Articles 3 and 20 of the Namibian Constitution stipulate that the language policy must promote the use of English in schools (The Constitution of Namibia (1990). It is now 24 years since English as medium of instruction was introduced in schools and tertiary institutions, but some students’ English proficiency is still relatively poor, especially in writing and speaking communication skills. This study investigated the barriers that prevent students to write and speak English well at University A and University B. The writing and speaking skills were investigated through the lens of syllabi/study guides, and lack of practical teaching of oral communication and writing skills inter alia morphology and syntax. Fifty-seven respondents took part in the research, comprising Heads of Departments (Language, Communication and Language Centre), Course Coordinators, lecturers and students in the English field at the two institutions investigated. Students were deliberately selected for the questionnaire to illustrate the difficulties they face when writing and speaking English as a second language. The lecturers were also deliberately selected because they were the ones who were with the students in classrooms. This study used qualitative research to gather information through methods such as observation, interviews, open-response questionnaire items, document analysis and verbal reports. The following were the main findings. There was a lack of specific teaching objectives in oral communication and written skills in the syllabi, while the inability of students to write correct sentences, and the limited time allocated to these courses also played a role. The conclusion drawn from this study is that students’ communicative competency is very poor. Therefore, it is the opinion of this researcher that improvement is much needed regarding syllabi content, teaching approaches of speaking and writing skills, students’ admission criteria and the time frame allocated for the different courses. To answer the research question: firstly the time allocated to some of the English courses is short, there is lack of teaching and learning of oral and writing skills approaches and, the syllabi were planned and design in a way that do not enhance much the teaching and learning of the second language. There are not many activities in the study guides that could be used to enhance students’ communicative competency. Such activities should include subject and verb agreement, passive and active form, sentence construction, word-building using prefixes and suffixes, auxiliaries or activities which give the students a chance to practice a certain aspect of language. Also, since English is a second language for students in Namibia, the institutions must seriously look at the time allocated to the courses they offer so that lecturers can appropriately apply proper approaches to teach writing and speaking skills. / Curriculum and Instructional Studies / D. Ed. (Curriculum Studies)

L'un des enjeux majeurs pour les systèmes d'imagerie par diffraction acoustique et micro-onde, est l'amélioration des performances obtenues au moment de la reconstruction des objets étudiés. Cette amélioration peut s'effectuer par la recherche d'algorithmes d'imagerie plus performants d'une part et par la recherche d'une meilleure configuration de mesures d'autre part. La première approche (recherche d'algorithmes) permet d'améliorer le processus d'extraction de l'information présente dans un échantillon de mesures donné. Néanmoins, la qualité des résultats d'imagerie reste limitée par la quantité d'information initialement disponible. La seconde approche consiste à choisir la configuration de mesures de manière à augmenter la quantité d'information disponible dans les données. Pour cette approche, il est nécessaire de quantifier la quantité d'information dans les données. En théorie de l'estimation, ceci équivaut à quantifier la performance du système. Dans cette thèse, nous utilisons la Borne de Cramer Rao comme mesure de performance, car elle permet d'analyser la performance des systèmes de mesures sans être influencé par le choix de la méthode d'inversion utilisée. Deux analyses sont proposées dans ce manuscrit. La première consiste en l'évaluation de l'influence des facteurs expérimentaux sur la performance d'inversion. Cette analyse a été effectuée pour différents objets le tout sous une hypothèse de configuration bidimensionnelle. La seconde analyse consiste à comparer les performances de l'estimateur obtenu avec l'approximation de Born aux valeurs de la borne de Cramer Rao (BCR); l'objectif étant d'illustrer d'autres applications possibles de la BCR. / Improving the performance of diffraction based imaging systems constitutes a major issue in both acoustic and electromagnetic scattering. To solve this problem, two main approaches can be explored. The first one consists in improving the inversion algorithms used in diffraction based imaging. However, while this approach generally leads to a significant improvement of the performance of the imaging system, it remains limited by the initial amount of information available within the measurements. The second one consists in improving the measurement system in order to maximize the amount of information within the experimental data. This approach does require a quantitative mean of measuring the amount of information available. In estimation problems, the {appraisal of the} performance of the system is often used for that purpose. In this Ph.D. thesis, we use the Cramer Rao bound to assess the performance of the imaging system. In fact, this quantity has the advantage of providing an assessment which is independent from the inversion algorithm used. Two main analysis are discussed in this thesis. The first analysis explores the influence on the system's performance, of several experimental conditions such as the antennas positions, the radiation pattern of the source, the properties of the background medium, etc. Two classes of objects are considered: 2D homogeneous circular cylindrical objects and 2D cylindrical objects with defect. The second analysis studies the performance of an estimator based on Born approximation with the Cramer Rao Bound as reference. The aim of this second analysis is to showcase other possible applications for the Cramer Rao Bound.

This master thesis aims to describe problematics of the effects of unconventional monetary policy, also known as quantitative easing, on economics of USA, Japan, Eurozone and Great Britain, by using empirical analysis of events related to quantitative easing and large BVAR model. In theoretical part of the thesis there are described transmission mechanisms of conventional monetary policy still effective in conditions of interest rates close to zero, as well as channels of unconventional monetary policy. Practical part of the thesis demonstrates analysis of impact of events related to quantitative easing in all the in-scope economics by applying a method of empirical observation of interest rates reactions on every event. Further, based on the received results of the empirical analysis, broader economic effects of quantitative easing are examined by using large BVAR model and afterwards the conclusion is made.

Les Systèmes à Evénements Discrets (SED) peuvent être définis comme des systèmes dans lesquels les variables d'état changent sous l'occurrence d'évènements au fil du temps. Les SED mettant en jeu des phénomènes de synchronisation peuvent être modélisés par des équations linéaires dans les algèbres de type (max,+). L'analyse d'atteignabilité est une problématique majeure pour les systèmes dynamiques. L'objectif est de calculer l'ensemble des états atteignables d'un système dynamique pour toutes les valeurs admissibles d'un ensemble d'états initiaux. Le problème de l'analyse d'atteignabilité pour les systèmes Max-Plus Linéaire (MPL) a été, proprement, résolu en décomposant le système MPL en une combinaison de systèmes affines par morceaux où les composantes affines du système sont représentées par des matrices de différences bornées (Difference Bound Matrix, DBM). La contribution principale de cette thèse est de présenter une procédure similaire pour résoudre le problème de l'atteignabilité pour des systèmes MPL incertains (uMPL), c'est-à-dire des systèmes MPL soumis à des bruits bornés, des perturbations et/ou des erreurs de modélisation. Tout d'abord, nous présentons une procédure permettant de partionner l'espace d'état d'un système uMPL en parties représentables par des DBM. Ensuite, nous étendons l'analyse d'atteignabilité des systèmes MPL aux systèmes uMPL. Enfin, les résultats sur l'analyse d'atteignabilité sont mis en oeuvre pour résoudre le problème d'atteignabilité conditionnelle, qui est étroitement lié au calcul du support de la densité de probabilité impliquée dans le problème de filtage stochastique / Discrete Event Dynamic Systems (DEDS) are discrete-state systems whose dynamics areentirely driven by the occurrence of asynchronous events over time. Linear equations in themax-plus algebra can be used to describe DEDS subjected to synchronization and time delayphenomena. The reachability analysis concerns the computation of all states that can bereached by a dynamical system from an initial set of states. The reachability analysis problemof Max Plus Linear (MPL) systems has been properly solved by characterizing the MPLsystems as a combination of Piece-Wise Affine (PWA) systems and then representing eachcomponent of the PWA system as Difference-Bound Matrices (DBM). The main contributionof this thesis is to present a similar procedure to solve the reachability analysis problemof MPL systems subjected to bounded noise, disturbances and/or modeling errors, calleduncertain MPL (uMPL) systems. First, we present a procedure to partition the state spaceof an uMPL system into components that can be completely represented by DBM. Then weextend the reachability analysis of MPL systems to uMPL systems. Moreover, the results onreachability analysis of uMPL systems are used to solve the conditional reachability problem,which is closely related to the support calculation of the probability density function involvedin the stochastic filtering problem. / Os Sistemas a Eventos Discretos (SEDs) constituem uma classe de sistemas caracterizada por apresentar espaço de estados discreto e dinâmica dirigida única e exclusivamente pela ocorrência de eventos. SEDs sujeitos aos problemas de sincronização e de temporização podem ser descritos em termos de equações lineares usando a álgebra max-plus. A análise de alcançabilidade visa o cálculo do conjunto de todos os estados que podem ser alcançados a partir de um conjunto de estados iniciais através do modelo do sistema. A análise de alcançabilidade de sistemas Max Plus Lineares (MPL) pode ser tratada por meio da decomposição do sistema MPL em sistemas PWA (Piece-Wise Affine) e de sua correspondente representação por DBM (Difference-Bound Matrices). A principal contribuição desta tese é a proposta de uma metodologia similar para resolver o problema de análise de alcançabilidade em sistemas MPL sujeitos a ruídos limitados, chamados de sistemas MPL incertos ou sistemas uMPL (uncertain Max Plus Linear Systems). Primeiramente, apresentamos uma metodologia para particionar o espaço de estados de um sistema uMPL em componentes que podem ser completamente representados por DBM. Em seguida, estendemos a análise de alcançabilidade de sistemas MPL para sistemas uMPL. Além disso, a metodologia desenvolvida é usada para resolver o problema de análise de alcançabilidade condicional, o qual esta estritamente relacionado ao cálculo do suporte da função de probabilidade de densidade envolvida o problema de filtragem estocástica.

Initiated with the purpose of assigning the Fraunhofer lines in the solar spectrum to atomic transitions in the 18th century, the collaboration between spectroscopists and astrophysicists has remained fruitful, successful and ever fascinating. This collaboration has resulted in the unique detection of over 200 different molecular species in the interstellar medium (ISM). These interstellar molecular species play significant roles in diverse fields such as atmospheric chemistry, astrochemistry, prebiotic chemistry, astrophysics, astronomy, astrobiology, etc, and in our understanding of the solar system ''the world around us''. This Thesis work focuses on understanding of the different aspects of the chemistry of the various classes of these molecular species. Chapter one starts with an historical perspective of what is now regarded as Molecular Astrophysics or Astrochemistry and discusses the interstellar medium and its properties; interstellar molecular species and their importance; molecular spectroscopy as an indispensible tool in interstellar chemistry and the different formation routes of these molecular species. It also discusses hydrogen bonding which is one of the most important of all the intermolecular interactions. The chapter ends by setting the stage for the present investigations. The chapter two of the Thesis saddled with the task of describing the methodology employed in this Thesis begins by setting the stage on the importance of computational chemistry in interstellar chemistry. It discusses the Gaussian 09 suite of programs and the various theoretical methods used in all the quantum chemical calculations reported in this Thesis. The chapter ends with a brief summary on the homebuilt Pulsed Nozzle Fourier Transform Microwave (PN-FTMW) spectrometer used for the preliminary studies on Isoprene...Argon weakly bound complex reported in the appendix. After the introductory chapters, chapter three begins with what is unarguably one of the most important classes of interstellar molecular species - 'interstellar isomers'. In this chapter, the Energy, Stability and Abundance (ESA) relationship existing among interstellar molecular species has been firmly established using accurate thermochemical parameters obtained with the composite models and reported observational data. From the relationship, “Interstellar abundances of related species are directly proportional to their stabilities in the absence of the effect of interstellar hydrogen bonding”. The immediate consequences of the relationship in addressing some of the questions in interstellar chemistry such as: Where are Cyclic Interstellar Molecules? What are the possible candidates for astronomical observation? Why are more Interstellar Cyanides than isocyanides? among others are briefly discussed. Following the ESA relationship, other studies addressing some of the whys and wherefores in interstellar chemistry are discussed in details. From ESA relationship, though there has not been any successful astronomical observation of any heterocycle, the ones so far searched remain the best candidates for astronomical observation in their respective isomeric groups. The observation of the first branched chain molecule in ISM is in agreement with the ESA relationship and the C5H9N isomers have been shown to contain potential branched chain interstellar molecules. That molecules with the C-C-O backbone have less potential of formation in ISM as compared to their counterparts with the C-O-C backbone has been demonstrated not to be true following the ESA relationship. A detailed investigation on the relationship between molecular partition function and astronomical detection of isomeric species (or related molecules) shows that there is no direct correlation between the two rather there is a direct link between the thermodynamic stability of the isomeric species (or related molecules) and their interstellar abundances which influences the astronomical observation of some isomers at the expense of others. Chapter four presents an interesting and a fascinating phenomenon among the interstellar molecular species as it discusses for the first time, the existence and effects of Interstellar Hydrogen Bonding. This interstellar hydrogen bonding is shown to be responsible for the deviations from thermodynamically controlled processes, delayed observation of the most stable isomers, unsuccessful observations of amino acids among other happenings in interstellar chemistry and related areas. On the prediction that ketenes are the right candidates for astronomical searches among their respective isomers, a ketenyl radical; HCCO has recently been detected in line with this prediction. The deviation from the rule that the ratio of an interstellar sulphur molecule to its oxygen analogue is close to the cosmic S/O ratio is well accounted for on the basis of hydrogen bonding on the surface of the dust grains. Detecting weakly bound complexes in ISM has not been a major interest in the field so far but the detectability of weakly bound complexes in ISM is very possible as discussed in this chapter. Following the conditions in which these complexes are observed in the terrestrial laboratory as compared to the ISM conditions; it suffices to say that weakly bound complexes are present and are detectable in ISM. They could even account for some of the 'U' lines. Chapter five of the Thesis discusses the Linear Interstellar Carbon Chains which are the dominant theme in interstellar chemistry accounting for over 20% of all the known interstellar and circumstellar molecular species. Accurate spectroscopic parameters within experimental accuracy of few kHz which are the indispensable tools for the astronomical observation of these molecular species; are obtained for over 200 different species from the various chains using an inexpensive combined experimental and theoretical approach. With the availability of the spectroscopic parameters; thermodynamics is utilized in accounting for the known systems and in examining the right candidates for astronomical searches. These molecular species are shown to also obey the ESA relationship observed for the isomeric species discussed in chapter three of this work. The effect of kinetics on the formation processes of these molecular species is well controlled by thermodynamics as discussed in this chapter. Finally, the application of these studies in reducing the 'U' lines and probing new molecular species has been briefly summarized. Chapter six discusses Interstellar Ions and Isotopologues which are two unique classes of interstellar molecular species. Different studies on interstellar ions and isotopologues are presented. From the studies on interstellar protonated species with over 100 molecular species; protonated species resulting from a high proton affinity prefers to remain protonated rather than transferring a proton and returning to its neutral form as compared to its analogue that gives rise to a lower proton affinity from the same neutral species. The studies on detectable interstellar anions account for the known interstellar anions and predict members of the C2nO-, C2nS-, C2n-1Si-, HC2nN-, CnP-, and C2n chains as outstanding candidates for astronomical observation including the higher members of the C2nH- and C2n-1N- groups whose lower members have been observed. From high level ab initio quantum chemical calculations; ZPE and Boltzmann factor have been used to explain the observed deuterium enhancement and the possibility of detecting more deuterated species in ISM. Though all the heterocycles that have so far been searched for in ISM have been shown to be the right candidates for astronomical observation as discussed in the ESA relationship, they have also been shown to be strongly bonded to the surface of the interstellar dust grains thereby reducing their abundances, thus, contributing to their unsuccessful detection except for furan which is less affected by hydrogen bonding. The D-analogues of the heterocycles are shown from the computed Boltzmann factor to be formed under the dense molecular cloud conditions where major deuterium fractionation dominates implying very high D/H ratio above the cosmic D/H ratio which suggests the detectability of these deuterated species. Chapter seven examines the isomerization of the most stable isomer (which is probably the most abundant) to the less stable isomer(s) as one of the plausible formation routes for interstellar molecular species. An extensive investigation on the isomerization enthalpies of 243 molecular species from 64 isomeric groups is reported. From the results, the high abundances of the most stable isomers coupled with the energy sources in interstellar medium drive the isomerization process even for relative enthalpy difference as high as 67.4 kcal/mol. Specifically, the cyanides and their corresponding isocyanides pairs appear to be effectively synthesized via this process. The following potential interstellar molecules; CNC, NCCP, c-C5H, methylene ketene, methyl Ketene, CH3SCH3, C5O, 1,1-ethanediol, propanoic acid, propan-2-ol and propanol are identified and discussed. In all the isomeric groups, isomerization appears to be an effective route for the formation of the less stable isomers (which are probably less abundant) from the most stable ones. Chapter eight summarizes the conclusions drawn from the different studies presented in this Thesis and also highlights some of the future directions of these studies. The first appendix presents the preliminary study on Isoprene...Ar weakly bound complex while the second appendix contains a study on interstellar C3S describing the importance of accurate dipole moment in calculating interstellar abundances of molecular species and in astrophysical and astronomical models.