No description available.

In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish this task, the non-classical method is utilized to find the infinitesimal generator and the invariant surface condition for the subgroup where the solutions for the desired PDE exist. Using the infinitesimal generator and the invariant surface condition, we reduce the PDE to a mildly nonlinear ordinary differential equation that could be explored numerically or perhaps solved in closed form.

The purpose of this paper is to present a study of different methods of solving certain boundary value problems. In particular it will be concerned with solutions by classical methods and by operational methods. Of the various operational methods that may be considered, the Laplace transformation appears to be the best be used in this paper. In the 1951 Encyclopedia Americana Annual is this report on the activities in applied mathematics for the previous year: Progress was made on the general problem of finding the eigenvalues of matrices and systems of differential equations. Considerable effort was also expended in seeking methods of solution for the partial differential equations of physics. This gives an indication of the importance of this type of work at the present time. With the development of atomic energy, Jet air­planes, and guided missiles, have come many new and different boundary value problems. The solution of these problems is an important factor in the development. The paper will include a general description of what is meant by boundary value problem, followed by some examples. These examples will be solved by classical methods and then by operational method (Laplace transformation). Then where possible, comparisons between the two methods will be made. From the study of the solutions of these examples conclusions will be drawn.

This thesis analyses the Eastern enlargement of the EU in comparison with the past four enlargement rounds, as a result of which it proves that Central and Eastern enlargement (CEE) is a unique experience for the EU. After the fourth enlargement, the EU turned its face to the CEECs, which witnessed unexpected events of a historic nature, with the fall of the Berlin Wall in 1989. This date symbolises a great change for the CEECs, such as the end of communism, transition to open market economy, democratisation and stability. A special focus is given to the inclusion of the CEECs into the EU necessitating to make adjustments both in the EU and in the CEECs. The specifity of the fifth enlargement derives from all the changes and challenges that it poses to the applicant countries and the Union but also to its neighbours. It concludes that the factors of uniqueness of the Eastern enlargement will strengthen the probability of the inclusion of the future applicants in the Eastern part of the continent. This enlargement is a positive development for the old and the new member states, it is one of the most important &lsquo / political necessities&rsquo / and &lsquo / historical opportunities&rsquo / that the EU is facing since its establishment, because it will not only ensure the unification, stabilisation, security, economic growth and general well-being of the continent but also because it has opened the way of membership to the future possible applicants in the Eastern part of the continent.

The goal of this diploma thesis is to observe, characterize ale reflect two well-known methods of teaching mathematics - so-called classical method and method according to professor Hejný, on the example of two second grade class teachers of elementary school with a focus on geometry. In the theoretical part I list several research works concerning class room observation. I use these to set up methodology of my own research. Moreover, the methods are characterized according to the literature and the analysis of the textbooks. Also the outputs of the Framework Education Programme (in Czech "Rámcový vzdělávací program") are presented in this theoretical part. I use these outputs to evaluate whether the method leads students to what they should know. The practical part consists of observing lessons of two teachers, my own teaching experience in the given classes and final questionnaire for students. Data collected from these observations are analysed with the help of qualitative and quantitative methods. The representative of the so-called classical method put emphasis on repetition and system. He usually asks students questions that require a shorter response. Students do not enjoy the school and geometry that much, but the knowledge results are quite good. The representative of the method according...

Le présent travail de thèse a porté sur l’étude expérimentale et théorique de signatures spectroscopiques de molécules atmosphériques clés: CO2 et CH3D. 11 a été divise en partie expérimentale, consacrée aux mesures a haute pression des spectres IR CO2, et a la partie théorique, a. savoir le calcul des largeurs de ligne de collision pour CH3D perturbé par divers gaz. Dans la première partie, j'ai présenté des mesures &absorption de CO2 a haute pression a température ambiance dans l'intervalle spectral 600-9650 cm (sondes dans des études d’atmosphère planétaire) pour deux raisons principales: fournit des données exactes et étendues et suivre l’évolution de effets de "line-mixing" avec des variations graduelles de pression. Dans la deuxième partie, j'ai présenté des calculs semi-classiques des coefficients d'élargissement de CH3D -N2 (-H2) en utilisant le modèle de trajectoire exacte dans les bandes v3 parallèles et perpendiculaires vs, v6 de CH3D ---N2 ainsi que dans la bande v3 parallèle de CH3D -142 pour de grands intervalles les de nombres quantiques de rotation requis pour les bases de données spectroscopiques. / Present Ph.D work has focused on experimental and theoretical studying of spectroscopic signatures of key atmospheric molecules: CO2 and CH3D. It was divided into experimental part, devoted to high-pressure measurements of IR CO2 spectra, and theoretical part, namely calculation of collisional line-widths for CH3D perturbed by various gases. In the first part, I reported room-temperature high-pressure CO2 absorption measurements in the spectral interval 600-9650 cm-1 (probed in planetary atmosphere studies) with the double goals: to provide accurate and extensive data and to trace evolution of the line-mixing effects with gradual pressure variations. In the second part, I presented semi-classical calculations of CH3D-N2 and -142 line-broadening coefficients using exact trajectory model in the parallel v3 and perpendicular vs, v6 bands of CH3D-N2 as well as in the parallel v3 band of CH3D-112 for large intervals of rotational quantum numbers required for spectroscopic databases.

The Financial analysis Crystalex a.s. examines a general financial situation of the company. I use classical methods for financial analysis. The significant part of my project is the application of creditworthy and bankruptcy models. The aim of my thesis is to find out if these models were able to predict the current situation for management in the past.

L'utilisation de plasmas froids à base de gaz rares (Rg) dans des applications biomédicales ainsi que dans la propulsion spatiale est en nette évolution. Pour optimiser ces réacteurs plasmas, une compréhension fine des processus ayant lieu dans ces réacteurs est nécessaire. Ce travail de thèse a pour objectif de fournir les données manquantes dans la littérature (coefficients de transport et réaction) en passant par des données mésoscopiques (sections efficaces) obtenues à partir de données microscopiques (potentiels d'interaction) pour le xénon et krypton dans leur gaz parent. Seul des plasmas froids composés d'un seul type d'atome sont considérés. Comme le krypton et le xénon sont des gaz rares, et ont donc, à l'état de neutralité peu/pas d'interaction entre eux. Par conséquent, seules les collisions ion - atome seront considérées. Du fait des faibles énergies des ions dans le plasma froid, seul les 6 premiers états excités du couple Rg2+ seront pris en compte. Ces 6 états seront classés en deux groupes, 2P1/2 et 2P3/2. Lors de ce travail, deux potentiels d'interaction différents disponibles dans la littérature sont utilisés et comparés pour les systèmes collisionnels Kr+/Kr et Xe+/Xe dans le calcul des sections efficaces. Pour les collisions impliquant des dimères ioniques (Kr2+/Kr et Xe2+/Xe), les potentiels d'interaction sont calculés à partir du modèle DIM (Diatomics In Molecules) qui est une combinaison des potentiels atomiques d'interaction neutre - neutre et ion - neutre. Les sections efficaces, requises pour obtenir les données mésoscopiques manquantes, sont calculées à partir de trois méthodes différentes. La première méthode est la méthode quantique qui permet, par une résolution de l'équation de Schrödinger, d'obtenir de manière exacte les sections efficaces à partir des potentiels d'interaction. Cette méthode exacte, étant grande consommatrice de temps de calcul, est utilisée en tant que référence pour valider les deux autres méthodes approchées. La seconde méthode, nommée semi-classique, est basée sur la même expression que la section efficace quantique mais utilise un déphasage approché (approximation JWKB), induit par le potentiel d'interaction, entre l'onde diffusée et l'onde incidente. [...] / The use of cold plasmas based on rare gases (Rg) in biomedical applications as well as in space propulsion is clearly evolving. To optimize these plasma reactors, a fine understanding of the processes taking place in these reactors is necessary. This thesis aims to provide the missing data in the literature (transport coefficients and reaction rates) through mesoscopic data (cross-sections) obtained from microscopic data (interaction potentials) for xenon and krypton in their parent gas. Only cold plasmas composed of a single type of atom are considered. As krypton and xenon are rare gases, and so have, in the neutral state little / no interaction between them. Therefore, only ion - atom collisions will be considered. Due to the low ion energies in the cold plasma, only the first 6 excited states of the Rg2+ pair will be taken into account. These 6 states will be classified in two groups, 2P1/2 and 2P3/2. In this work, two different interaction potentials available in the literature are used and compared for the Kr+/Kr and Xe+/Xe collision systems in the calculation of cross-sections. For collisions involving ionic dimers (Kr2+/Kr and Xe2+/Xe), the interaction potentials are calculated from the DIM model (Diatomics In Molecules) which is a combination of the atomic potentials of neutral - neutral and ionic - neutral interactions. The cross-sections required to obtain the missing mesoscopic data are calculated from three different methods. The first method is the quantum method which allows, by a resolution of the Schrödinger equation, to obtain exactly the cross-sections from the interaction potentials. This exact method, which consumes a lot of computation time, is used as a reference to validate the two other approximate methods. The second method, called semi-classical, is based on the same expression as the quantum cross section but uses an approximate phase shift (JWKB approximation), induced by the interaction potential, between the scattered wave and the incident wave. [...]