The thesis describes interactions and relationships between selected economic indicators. These indicators are the gross domestic product and the average gross monthly wage. The analysis of these selected indicators, are made for the Czech Republic and Slovakia. The work has four main parts, which are divided into several other sections. The first defines the concept of national accounting, the second part contents gross domestic product, the method of its calculating and the frequency of compilation. In the third section is described the field theory of wages and salaries and the concepts such as minimum wage, the average gross monthly wage and median wage and salary are defined. In this two chapters are compared selected countries on the basis of the tables and graphs of selected indicators. The last chapter analyzes the relationships between selected economic indicators in selected countries based on quarterly data from the years 2001-2013.

Cette thèse est dédiée à l'étude mathématique de l'approximation de champ-moyen des gaz de bosons. En physique quantique une telle approximation est vue comme la première approche permettant d'expliquer le comportement collectif apparaissant dans les systèmes quantiques à grand nombre de particules et illustre des phénomènes fondamentaux comme la condensation de Bose-Einstein et la superfluidité. Dans cette thèse, l'exactitude de l'approximation de champ-moyen est obtenue de manière générale comme seule conséquence de principes de symétries et de renormalisations d'échelles. Nous recouvrons l'essentiel des résultats déjà connus sur le sujet et de nouveaux sont prouvés, particulièrement pour les systèmes quantiques sur réseau, incluant le modèle de Bose-Hubbard. D'autre part, notre étude établit un lien entre les équations aux hiérarchies de Gross-Pitaevskii et de Hartree, issues des méthodes BBGKY de la physique statistique, et certaines équations de transport ou de Liouville dans des espaces de dimension infinie. Résultant de cela, les propriétés d'unicité pour de telles équations aux hiérarchies sont prouvées en toute généralité utilisant seulement les caractéristiques génériques de problèmes aux valeurs initiales liés à de telles équations. Egalement, de nouveaux résultats de caractères bien posés et un contre-exemple à l'unicité d'une hiérarchie de Gross-Pitaevskii sont prouvés. L’originalité de nos travaux réside dans l'utilisation d'équations de Liouville et de puissantes techniques de transport étendues à des espaces fonctionnels de dimension infinie et jointes aux mesures de Wigner, ainsi qu'à une approche utilisant les outils de la seconde quantification. Notre contribution peut être vue comme l'aboutissement d'idées initiées par Z. Ammari, F. Nier et Q. Liard autour de la théorie de champ-moyen. / This thesis is dedicated to the mathematical study of the mean-field approximation of Bose gases. In quantum physics such approximation is regarded as the primary approach explaining the collective behavior appearing in large quantum systems and reflecting fundamental phenomena as the Bose-Einstein condensation and superfluidity. In this thesis, the accuracy of the mean-field approximation is proved in full generality as a consequence only of scaling and symmetry principles. Essentially all the known results in the subject are recovered and new ones are proved specifically for quantum lattice systems including the Bose-Hubbard model. On the other hand, our study sets a bridge between the Gross-Pitaevskii and Hartree hierarchies related to the BBGKY method of statistical physics with certain transport or Liouville's equations in infinite dimensional spaces. As an outcome, the uniqueness property for these hierarchies is proved in full generality using only generic features of some related initial value problems. Again, several new well-posedness results as well as a counterexample to uniqueness for the Gross-Pitaevskii hierarchy equation are proved. The originality in our works lies in the use of Liouville's equations and powerful transport techniques extended to infinite dimensional functional spaces together with Wigner probability measures and a second quantization approach. Our contributions can be regarded as the culmination of the ideas initiated by Z. Ammari, F. Nier and Q. Liard in the mean-field theory.

Ce travail est une contribution à l'étude des équations de Schrödinger non-linéaires (NLS) en dimension un d'espace. De telles équations interviennent notamment comme modèles dans plusieurs domaines de la physique mathématique, tels l'optique non-linéaire, la superfluidité, la supraconductivité et la condensation de Bose-Einstein.Cette thèse contient trois thèmes connexes inclus dans les chapitres 2, 3 et 4. Dans la première partie (chapitre 2), on s'intéresse à la construction des solutions en multi-solitons de l'équation de Gross-Pitaevskii (NLS défocalisante avec non-linéarité cubique), comme une superposition approximative des ondes progressives (solitons). Cette partie contient également une description détaillée des interactions entre les solitons. Ces résultats sont obtenus en exploitant l'intégrabilité de l'équation de Gross-Pitaevskii et son système de Marchenko associé.La deuxième partie (chapitre 4) clarifie les relations entre la formulation classique et la formulation dite hydrodynamique de l'équation de Gross-Pitaevskii. Cette dernière a un sens lorsque la solution ne s'annule jamais dans le domaine spatial. La dernière partie (chapitre 3) est consacrée à l'étude du problème de Cauchy d'une famille d'équations aux dérivées partielles quasi-linéaires qui généralise l'équation du flot par courbure binormal d'une courbe dans l'espace euclidien de dimension trois. Cette dernière est liée formellement à NLS par la transformation de Hasimoto. Dans notre généralisation, la vitesse d'un point de la courbe est toujours dirigée dans la direction du vecteur binormal, mais son amplitude peut dépendre de l'abscisse curviligne ainsi de la position dans l'espace. Notre approche pour prouver l'existence est le suivant: schéma semi-discret (discret en espace et continu en temps), obtention de bornes sur les problèmes discrets et argument par compacité. Un théorème de comparaison entraîne l'unicité. / This work is a contribution to the study of nonlinear Schrödinger equations (NLS) in the one-dimensional space. Such equations arise in many physical fields, including nonlinear optics and Bose-Einstein condensation. The thesis contains three connected themes included in chapters 2, 3 and 4. The first part (chapter 2) constructs multi-soliton solutions of the Gross-Pitaevskii (or defocussing NLS) equation, as an approximate superposition of traveling waves (solitons). This part contains also a detailed description of the interactions between solitons. These results are obtained by exploiting the integrability of the the Gross-Pitaevskii equation and its associated Marchenko system. The second part (chapter 4) clarifies the relations between the classical formulation and the so-called hydrodynamical formulation that only has a meaning when the solution does not vanish anywhere in the spatial domain The last part (chapter 3) of this thesis concerns existence and uniqueness results for a family of quasi-linear partial differential equations that generalize the equation of the binormal curvature flow for a curve in the three-dimensional space. The latter equation is in connection to the focussing cubic NLS by Hasimoto transformation. In our generalization, the velocity of a point on the curve is still directed along the binormal vector (so that in particular the length of the curve is preserved) but the magnitude of the speed is allowed to depend both on the curvilinear parameter and on the position in space. Existence is proven using spatial discretization together with some a priori bounds on the approximate solutions. Uniqueness follows from a comparison theorem.

Le résultat principal de ce texte est une généralisation de la formule de Gross-Zagier p-adique de Perrin-Riou au cas de courbes de Shimura sur les corps totalement réels. Soit F un corps totalement réel. Soit f une forme modulaire de Hilbert sur F de poids parallel 2, qui est une forme nouvelle et est ordinaire en p. Soit E est une extension quadratique totalement imaginaire de F de discriminant premier à p et au conducteur de f. On peut construire une fonction L p-adique qui interpole valeurs spéciales de la fonction L complexe associée à f, E et caractères de Hecke d'ordre fini de E. La formule p-adique de Gross-Zagier relie la dérivée centrale de cette fonction L p-adique à la hauteur d'un divisor de Heegner sur une certaine courbe de Shimura. La stratégie de la preuve est proche de celle du travail original de Perrin-Riou. Dans la partie analytique, on construit le noyau analytique par calculs adéliques; dans la partie géométrique, on décompose le noyau géométrique en deux parties: places hors de p et places divisant p. Pour les places hors de p, les hauteurs p-adiques sont essentiellement des nombres d'intersection et sont calculées dans les travaux de S. Zhang, et il s'avère que cette partie est bien liée au noyau analytique. Pour les places divisant p, on utilise la méthode dans le travail de J. Nekovar pour montrer que la contribution de cette partie est nulle. / The main result of this text is a generalization of Perrin-Riou's p-adic Gross-Zagier formula to the case of Shimura curves over totally real fields. Let F be a totally real field. Let f be a Hilbert modular form over F of parallel weight 2, which is a new form and is ordinary at p. Let E be a totally imaginary quadratic extension of F of discriminant prime to p and to the conductor of f. We may construct a p-adic L function that interpolates special values of the complex L functions associated to f, E and finite order Hecke characters of E. The p-adic Gross-Zagier formula relates the central derivative of this p-adic L function to the p-adic height of a Heegner divisor on a certain Shimura curve. The strategy of the proof is close to that of the original work of Perrin-Riou. In the analytic part, we construct the analytic kernel via adelic computations, in the geometric part, we decompose the geometric kernel into two parts: places outside p and places dividing p. For places outside p, the p-adic heights are essentially intersection numbers and are computed in works of S. Zhang, and it turns out that this part is closely related to the analytic kernel. For places dividing p, we use the method in the work of J. Nekovar to show that the contribution of this part is zero.

The problem addressed in this study is the difference in patterns of verbal and non-verbal communication across gender and generational groups, specifically between members of traditional and urban communities. These differences, it is argued, are linked to differences in values, attitudes, beliefs, views, etc., i.e. cultural differences, between the groups. Misunderstanding in such communicative interaction arises because people are unaware of the role of cultural differences in the construction and interpretation of texts/cases of language use, for example, the gender differences in the way men and women from different age groups and different habitats (rural vs. urban) can generate misunderstanding. In the Ndebele community, there is a marked diversity in communication patterns and practices by gender. These differences in communication patterns between men and women are socially constructed and are related to power. For example, women are not expected to maintain eye contact with their male counterparts in mutual conversation. Where they disregard these communicative norms, it would be regarded as socially unacceptable and such behaviour would be regarded as disrespectful by the traditional members of the society. Non-verbal behaviour may also impede effective communication because there are different systems of using and understanding gesture, posture, silence, touch and physical appearance in different gender, age and rural/urban communities. Copyright / Dissertation (MA)--University of Pretoria, 2007. / Afrikaans / unrestricted

The Gross-Neveu model is a quantum field theory of interacting N-flavor fermions in 1+1dimensions, with interaction term $(\bar{\psi}_f\psi_f )^2$. This model is studied using the property offactorized scattering. The spectrum of bound states including the kinks are discussed andthe thermodynamic state equations are derived using the thermodynamic Bethe ansatz.The full particle-particle integral kernel and corresponding S-matrix is derived startingfrom the Gross-Neveu version of the Y -system introduced by Zamolodchikov. / Gross-Neveu-modellen är en kvantfältteori som beskriver N identiska versioner av fundamentala fermioner i 1 + 1 dimensioner, växelverkande med potentialen $(\bar{\psi}_f\psi_f )^2$. Modellen studeras med utgångspunkt i partiklarnas så kallade faktoriserade spridning. Samtligafysikaliska bundna tillstånd inklusive solitonerna diskuteras och de termodynamiska tillståndsekvationerna härleds med hjälp av Bethe-ansatsen. Alla integralkärnor och motsvarande S-matriselement beräknas på sluten form utifrån Y-systemet som först beskrevs av Zamolodchikov.

The South African Income Tax Act (58 of 1962) does not specifically deal with the tax treatment of receipts resulting from illegal activities. Expenditure resulting from illegal activities is also only partly dealt with in terms of Section 23(o) of the Income Tax Act. This has resulted in uncertainty pertaining to the normal income tax treatment of illegal activities within a South African context. In response to this, the South African Revenue Service has issued a draft interpretation note dealing with the tax consequences of embezzlement and theft of money for both the victim as well as the offender during 2013. This draft interpretation note also deals with the normal tax consequences of illegal receipt in the hands of the thief. In an attempt to evaluate this draft interpretation note to clarify the tax consequences of illegal activities in South Africa, the meaning of illegal receipts is firstly determined. Subsequently the concept of „illegal receipts‟ is measured against the definition of „gross income‟ contained in Section 1 of the Income Tax Act. Expenditure relating to illegal activities is also analysed and measured against the general deduction formula contained in Section 11(a) of the Income Tax Act. Relevant principles established from general case law applicable to the definition of gross income as well as the general deduction formula is analysed to determine its applicability within the context of illegal receipts and expenditure. Also, principles established through case law, both nationally and internationally, specifically applicable to the taxation of illegal activities were analysed to establish guidelines that could be applied to clarify the taxability of illegal activities within a South African context. / MCom (South African and International Tax), North-West University, Potchefstroom Campus, 2015

The South African Income Tax Act (58 of 1962) does not specifically deal with the tax treatment of receipts resulting from illegal activities. Expenditure resulting from illegal activities is also only partly dealt with in terms of Section 23(o) of the Income Tax Act. This has resulted in uncertainty pertaining to the normal income tax treatment of illegal activities within a South African context. In response to this, the South African Revenue Service has issued a draft interpretation note dealing with the tax consequences of embezzlement and theft of money for both the victim as well as the offender during 2013. This draft interpretation note also deals with the normal tax consequences of illegal receipt in the hands of the thief. In an attempt to evaluate this draft interpretation note to clarify the tax consequences of illegal activities in South Africa, the meaning of illegal receipts is firstly determined. Subsequently the concept of „illegal receipts‟ is measured against the definition of „gross income‟ contained in Section 1 of the Income Tax Act. Expenditure relating to illegal activities is also analysed and measured against the general deduction formula contained in Section 11(a) of the Income Tax Act. Relevant principles established from general case law applicable to the definition of gross income as well as the general deduction formula is analysed to determine its applicability within the context of illegal receipts and expenditure. Also, principles established through case law, both nationally and internationally, specifically applicable to the taxation of illegal activities were analysed to establish guidelines that could be applied to clarify the taxability of illegal activities within a South African context. / MCom (South African and International Tax), North-West University, Potchefstroom Campus, 2015

Leaf traits have long been used to classify and characterise species in natural ecosystems. In addition, leaf traits provide important information about plants’ strategies for the use of resources and can be used to improve our understanding of ecosystem level processes such as nutrient cycling and carbon allocation. To explore the linkages between leaf traits and productivity, we worked in two resource-limited ecosystems (a grassland and a forest), and used leaf traits to understand how species respond to changes in available resources and their relationship to ecosystem processes. We worked in a species rich limestone-grassland located in central England, which has been subjected to long-term climatic manipulation (winter warming, summer drought and extra summer rainfall). We characterised species composition in terms of their identity, abundance and leaf structural properties (nitrogen content and leaf mass per area (LMA)) in the main treatments and the control. We found that change in species abundance was the most important factor to understand the differences in productivity (above ground biomass and total foliar nitrogen). We then measured CO2 exchange at ecosystem level, using a chamber technique, and assessed the treatments’ effect on the gross primary productivity (GPP) and ecosystem respiration (Reco). GPP and Reco were controlled by soil moisture and above ground biomass but also influenced by the conditions experienced during the growing season prior to the measuring period. Our second location was a post-disturbance chronosequence in a seasonally dry tropical forest in Costa Rica and we used leaf level gas exchange measurements to explore the role of nitrogen (N) and phosphorus (P) on the temporal-spatial variation of photosynthesis of dominant species. We found that photosynthetic efficiency was strongly linked to leaf N and P content, but that there was an important seasonal pattern on this relationship likely associated to P remobilization. Additionally we found seasonal changes in resources (water, nutrients) had a larger impact on the photosynthetic parameters than changes along the chronosequence. The two ecosystems studied for this thesis are contrasting in their physiognomy, species composition and climate, but are also characterised by species whose structural traits (high LMA and high C:N ratio) are likely to have a significant impact on the nutrient cycling processes. We learned that leaf traits provide important information about species strategies and their usage of resources and they can also aid to address questions at ecosystem level in time and space, either through simple aggregation or as emergent properties. Additionally, the traits explored are important input information to up-scale processes from leaf to the ecosystem level, a step needed to address the effect changes in resources will have on the seasonally dry tropical forest and grasslands, which represent a significant fraction of the total global carbon storage.

The purpose of my study was to investigate the child's gross motor movement activities as well as study of the educators planning of gross motor movement activities, and if so, how they are implemented. Methods used in the study is observational and interview. I observed children aged 3-6 years and interviewed two preschool teachers in two different kindergartens in a small municipality in northern Småland. The results showed that the teachers see positively movement in kindergarten and they work daily on children's gross motor skills most unplanned but even with a few planned activities during the week. In kindergarden there are many opportunities for children to exercise gross motor movement activities .