In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-prey models with variable time of impulses, ratio-dependent predator-prey systems and logistic equation with piecewise constant argument of generalized type. For the first time, by means of Lyapunov functions coupled with the Razumikhin method, sufficient conditions are established for stability of the trivial solution of differential equations with piecewise constant argument of generalized type. Appropriate examples are worked out to illustrate the applicability of the method. Moreover, stability analysis is performed for the logistic equation, which is one of the most widely used population dynamics models. The behaviour of solutions for a 2-dimensional system of differential equations with discontinuous right-hand side, also called a Filippov system, is studied. Discontinuity sets intersect at a vertex, and are of the quasilinear nature. Through the B&amp / #8722 / equivalence of that system to an impulsive differential equation, Hopf bifurcation is investigated. Finally, the obtained results are extended to a 3-dimensional discontinuous system of Filippov type. After the existence of a center manifold is proved for the 3-dimensional system, a theorem on the bifurcation of periodic solutions is provided in the critical case. Illustrative examples and numerical simulations are presented to verify the theoretical results.

Récemment, la convergence des techniques radio à 60 GHz sur fibre optique (radio over fiber - RoF) et des réseaux d'accès optiques passifs à multiplexage en longueurs d'ondes (wavelength division multiplexing-WDM) a suscité un très grand intérêt dans la communauté scientifique. L'objectif de cette thèse est d'étudier les solutions pour faire converger les systèmes RoF à 60 GHZ et les réseaux passifs optiques (passive optical network - PON) utilisant le WDM, appelés dans la suite PON-WDM. Les résultats principaux de cette thèse axée sur la technologie des systèmes RoF et l'intégration des systèmes RoF avec les réseaux d'accès PON-WDM sont les suivants : Un système RoF utilisant un démultiplexeur WDM, compatible avec les réseaux d'accès PON-WDM, est proposé dans cette thèse. Nous avons mené une étude théorique complète du bruit de phase. Elle inclut la contribution des bruits de phase des générateurs de signaux électriques et celle de la conversion de bruit de phase optique en bruit d'intensité. Cette dernière conversion est due à la détection de deux signaux cohérents, retardés l'un par rapport à l'autre si les longueurs optiques entre les deux canaux optiques se recombinant sont différentes. La densité spectrale de puissance du signal millimétrique généré optiquement est analysée théoriquement et démontrée expérimentalement. Son étude donne une méthode pour compenser un éventuel délai optique │τd│. L'amplitude du vecteur d'erreur (error vector magnitude -EVM) est théoriquement calculée et expérimentalement démontrée, en fonction du rapport │τd│/τcOP où τcOP est la durée de cohérence de la source optique utilisée. Cela donne une règle de conception pour insérer le démultiplexeur optique dans le système d'hétérodynage optique.  Nous avons validé expérimentalement la technique d'hétérodynage optique qui utilise un démultiplexeur pour générer un signal millimétrique respectant le standard ECMA 387. Nous avons proposé un système combinant une partie RoF et un réseau PON-WDM, permettant la génération simultanée d'un signal millimétrique respectant le standard ECMA 387 et la transmission d'un signal en bande de base à plusieurs gigabits par seconde. Nous avons réalisé expérimentalement avec succès la transmission simultanée d'un signal à 60 GHZ, modulé avec une modulation BPSK par un signal à 1588 Mbit/s et celle d'un signal en bande de base à 10 Gbit/s.  Nous avons proposé une nouvelle technique de modulation multi-bandes : la modulation de phase parallèle utilisant un unique modulateur de Mach-Zehnder. Cette technique présente des avantages significatifs comparée à n'importe quelle autre technique de modulation multi-bandes. Il n'y a aucun impact de la modulation en bande de base sur la génération millimétrique. L'impact de la modulation RF sur la transmission en bande de base (impact dû à la non-linéarité de la modulation de phase) est limité. Le taux d'erreurs binaires du signal en bande de base intégrant l'effet du signal RF a été théoriquement calculé et expérimentalement validé. Cela donne des règles de conception pour la technique de modulation de phase parallèle avec un unique modulateur de Mach-Zehnder. Nous avons proposé une architecture et réalisé un démonstrateur d'un système bas-coût bidirectionnel pour la transmission RoF. Ce système utilise le mélange optoélectronique et la technique d'hétérodynage optique. Nous avons prouvé que :  Des signaux à 60 GHz modulés à 397 Mbit/s et 794 Mbit/s avec une modulation BPSK sont convertis vers la bande basse de fréquence en utilisant la technique de mélange optoélectronique : les contraintes du standard ECMA 387 sont respectées.  Pour la liaison descendante utilisant la technique d'hétérodynage optique, aucune pénalité sur l'EVM n'est causée par le choix du régime non linéaire de la photodiode.

In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schr&uml / odinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.

In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron condition is investigated in chapter 3. In chapter4, we give a result that characterizes the behavior of solutions in the case there is a bounded solution. Moreover, a necessary and sufficient condition for the existence of periodic solutions is obtained. In the last chapter, a series of consequences on the existence of periodic solutions of functionally equivlent impulsive systems with delays is established.

During the last decade, the use of time scales as a means of unifying and extending results about various types of dynamic equations has proven to be both prolific and fruitful. Many classical results from the theories of differential and difference equations have time scale analogues. In this thesis we derive new oscillation criteria for second order dynamic equations on time scales.

ABSTRACT INVERSE PROBLEMS FOR A SEMILINEAR HEAT EQUATIONS WITH MEMORY Kaya, M&uuml / jdat Ph.D, Department of Mathematics Supervisor: Prof. Dr. A. Okay &Ccedil / elebi Co-Supervisor: Prof. Dr. Varga Kalantarov May 2005, 79 pages In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.

Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun&rsquo / s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.

In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincar&eacute / , the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant argument of generalized type in noncritical case, that is, the unperturbed linear ordinary differential equation has not any nontrivial periodic solution, are investigated. The continuous and differential dependence of the solutions on an initial value and a parameter is considered. A new Gronwall-Bellmann type lemma is proved. Next, quasilinear differential equations with alternately advanced-retarded piecewise constant argument of generalized type is addressed. The critical case, when associated linear homogeneous system admits nontrivial periodic solutions, is considered. Using the technique of Poincar&eacute / -Malkin, criteria of existence of periodic solutions of such equations are obtained. One of the main auxiliary results is an analogue of Gronwall-Bellmann Lemma for functions with alternately advanced-retarded piecewise constant argument. Dependence of solutions on an initial value and a parameter is investigated. Finally, a new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations: existence and uniqueness of solutions, the existence of the periodic solutions, the stability of the zero solution are obtained. Appropriate examples are constructed.

A deep and analytical understanding of the human metabolism grabbed attention of scientists from biology, medicine and pharmacy. Mathematical models of metabolic pathways offer several advances for this deep and analytical understanding due to their incompensable potential in predicting metabolic processes and anticipating appropriate interventions when required. This thesis concerns mathematical modeling analysis and simulation of metabolic pathways. These pathways include intracellular and extracellular compounds such as enzymes, metabolites, nucleotides and cofactors. Experimental data and available knowledge on metabolic pathways are used in constituting a mathematical model. The models are either in the form of nonlinear ordinary differential equations (ode&#039 / s) or differential algebraic equations (dae&#039 / s). These equations are composed of kinetic parameters such as kinetic rate constants, initial rates and concentrations of metabolites. The non-linear nature of enzymatic reactions and large number of parameters cause trouble in efficient simulation of those reactions. Metabolic engineering tries to simplify these equations by reducing the number of parameters. In this work, enzymatic system which includes Creatine Kinase, Hexokinase and Glucose 6-Phosphate Dehydrogenase (CK-HK-G6PDH) is modeled in the form of dae&#039 / s, solved numerically and the system parameters are estimated. The numerical results are compared with the results from an existing work in literature. We demonstrated that, our solution method based on direct solution of the CK-HK-G6PDH system significantly from simplified solutions. We also showed that genetic algorithm(GA) for parameter estimation, provides much clear results to the experimental values of the metabolite, especially with NADPH. Keywords: metabolic engineering, kinetic modelling, biochemical reactions, enzymatic reactions, differential algebraic equations, parameter estimation, genetic algorithm.

<p>LAG ELLER VÄRDEGRUND. VAD STYR I PRAKTIKEN?Öberg, MariaÖstberg, YlvaÖrebro UniversitetAkademin för juridik, psykologi och socialt arbeteSocionomprogrammetSocialt arbete, 61-90 poängC-uppsats, 15 poängHt 2009</p><p> </p><p>Sammanfattning</p><p>Studien syftar till att belysa den problematik som finns gällande tillämpningen av lagstiftningen i brottsbalken (BrB, 1962:700) och offentlighet – och sekretesslagen (OSL, 2009:400) då brukare inom 9:9 lagen om stöd och service till vissa funktionshindrade (LSS, 1993:387) begår brott. Dessutom vill vi undersöka chefers tillämpning av ovan nämnda lagstiftning utifrån fiktiva fall. Vidare syftar studien till att undersöka hur de etiska grundprinciperna inom LSS påverkar enhetschefernas beslut om åtgärder gällande situationer då brukare begått brott. Vi vill också undersöka om det finns en problematik med att brukare inom LSS begår brott.</p><p>Vi har använt oss av en kvalitativ metod där fyra semistrukturerade intervjuer genomförts med chefer inom verksamhetsområdet. Intervjuerna utgick delvis ifrån två fiktiva fall. Vi ville med det ge alla respondenter samma utgångs punkt. Vi har transkriberat vårt material för att tematisera och tolka det.</p><p>Studien visar på att det finns en problematik med tillämpningen av lagstiftningen. Samtliga respondenter visste i teorin hur lagstiftningen såg ut, men ingen av respondenterna visste hur lagstiftningen tillämpades. Resultatet visar också att det finns en skillnad i synen på värdegrunderna beroende på hur nära brukaren respondenten arbetar. De respondenter som arbetat närmast brukarna vill skydda brukarna från allt ont, vilket ibland kan påverka brukarnas möjligheter att uppleva de värdegrunder som finns inom LSS. Respondenterna som inte arbetade nära brukarna uppfattade brukarna som vilka medborgare som helst.</p><p>Nyckelord: Lagen om stöd och service till vissa funktionshindrade (LSS 1993:387), Offentlighet och sekretesslagen (OSL 2009:400), Brottsbalken (BrB 1962:700), värdegrunder inom LSS, chef.</p><p> </p> / <p>LAW OR VALUES? WHAT RUNS IN PRACTICE? Öberg, MariaÖstberg, YlvaÖrebro UniversityDepartment for Behavioral, Social and Legal SciencesSocial Work programSocial work, 61-90 pointsC-essay, 15 pointsAutumn term 2009</p><p> </p><p>Abstract</p><p>The study aims to highlight the problems that are related to enforcement of the law for criminal code (BrB, 1962:700) and law of publicity and confidentiality ( OSL, 2009:400) when patient in the 9:9 § in law of support and service for some functional disability peoples (LSS, 1993:387) commit crimes. We also want to investigate managers' implementation of the said law on the basis of fictitious cases. Furthermore, the study aims to examine how the basic ethical principles of LSS affects of Unit Decision on measures concerning situations where patient have committed crimes. We also want to investigate if there is a problem with users, within LSS, committing crimes.</p><p>We have used a qualitative approach in which four semi-structured interviews conducted with managers in the business field. The interviews were based in part from two fictional cases. We wanted to give it all respondents the same starting point. We have transcribed our material for themed and interpret it.</p><p>The study shows that there is a problem in law enforcement. All respondents knew in theory how the legislation looked like, but none of the respondents knew what the law was applied. The results also show that there is a difference of opinion on the value basis depending on how close to the patient the respondent works. Respondents who worked closest to the patient want to protect patient from all trouble, this sometimes can affect patient' ability to experience the values that exist in the LSS. Respondents who did not work close to patient, perceived the patient´s as any other citizens.</p><p>Keywords: patient, functional disability, ethnical values, crime, manager.</p><p> </p>