>Magister Scientiae - MSc / With the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.

In this dissertation, I examine the changes to the nature of the accounting paradigms of U.S. GAAP and International Financial Reporting Standards (IFRS) over the course of the U.S. GAAP and IFRS convergence project. I further examine whether the changes to the nature of IFRS following convergence impacts the financial reporting quality. The motivation for this study is to provide an initial review of the progress of the convergence process between U.S. GAAP and IFRS that aims to converge both sets of standards towards more principles-based paradigms. The ultimate goal of the convergence process was the development of globally recognized high quality financial reporting standards (FASB, 2002) and the development of principles-based accounting standards was identified as an essential component of such a goal. Extant literature and professional practice agree that U.S. GAAP is more rules-based whereas IFRS is more principles-based. Thus, both the International Accounting Standards Board (IASB) and the U.S. Financial Accounting Standards Board (FASB) agreed that the convergence process would be an ideal vehicle to converge both sets of standards towards more principles-based paradigm. I document that over the course of the convergence project, the underlying accounting paradigm of U.S. GAAP has remained consistent whereas the accounting paradigm of IFRS has become more rules-based. Amendments to existing International Standards and newer standards added over the course of the convergence have moved IFRS towards a more rules-based nature which was not the intended outcome of the convergence process. I further examine if the changes in rules vs. principles-based nature of IFRS has impacted the accounting quality. Using a firm level instrument developed in Folsom et al. (2016) that measures the extent to which firms rely on principles-vs –rules-based accounting, standards I find a relation between firm reliance on principles-based standards and earnings persistence. I also find an association between firm reliance on principles-based standards and earnings ability to predict future cash flows as well as concurrent returns. More, importantly the results of my study provide initial evidence that these associations are significantly manifested in the post-convergence period.

As traffic congestion continues to worsen in large urban areas, solutions are urgently sought. However, transportation planning models, which estimate traffic volumes on transportation network links, are often unable to realistically consider travel time delays at intersections. Introducing signal controls in models often result in significant and unstable changes in network attributes, which, in turn, leads to instability of models. Ignoring the effect of delays at intersections makes the model output inaccurate and unable to predict travel time. To represent traffic conditions in a network more accurately, planning models should be capable of arriving at a network solution based on travel costs that are consistent with the intersection delays due to signal controls. This research attempts to achieve this goal by optimizing signal controls and estimating intersection delays accordingly, which are then used in traffic assignment. Simultaneous optimization of traffic routing and signal controls has not been accomplished in real-world applications of traffic assignment. To this end, a delay model dealing with five major types of intersections has been developed using artificial neural networks (ANNs). An ANN architecture consists of interconnecting artificial neurons. The architecture may either be used to gain an understanding of biological neural networks, or for solving artificial intelligence problems without necessarily creating a model of a real biological system. The ANN delay model has been trained using extensive simulations based on TRANSYT-7F signal optimizations. The delay estimates by the ANN delay model have percentage root-mean-squared errors (%RMSE) that are less than 25.6%, which is satisfactory for planning purposes. Larger prediction errors are typically associated with severely oversaturated conditions. A combined system has also been developed that includes the artificial neural network (ANN) delay estimating model and a user-equilibrium (UE) traffic assignment model. The combined system employs the Frank-Wolfe method to achieve a convergent solution. Because the ANN delay model provides no derivatives of the delay function, a Mesh Adaptive Direct Search (MADS) method is applied to assist in and expedite the iterative process of the Frank-Wolfe method. The performance of the combined system confirms that the convergence of the solution is achieved, although the global optimum may not be guaranteed.

Simulation of rare events can be costly with respect to time and computational resources. For certain processes it may be more efficient to begin at the rare event and simulate a kind of reversal of the process. This approach is particularly well suited to reversible Markov processes, but holds much more generally. This more general result is formulated precisely in the language of stationary point processes, proven, and applied to some examples. An interesting question is whether this technique can be applied to Markov processes which are substochastic, i.e. processes which may die if a graveyard state is ever reached. First, some of the theory of substochastic processes is developed; in particular a slightly surprising result about the rate of convergence of the distribution pi(n) at time n of the process conditioned to stay alive to the quasi-stationary distribution, or Yaglom limit, is proved. This result is then verified with some illustrative examples. Next, it is demonstrated with an explicit example that on infinite state spaces the reversal approach to analyzing both the rate of convergence to the Yaglom limit and the likely path of rare events can fail due to transience.

This thesis deals with mutual socio-economic relations core and hinterland on the example of Prague and Central Bohemia. In the introduction relevant theoretical approaches which deal with this topic are presented. Furthermore most important relations between Prague and Central Bohemia are identified and analyzed. These are migration of population from core to hinterland known as suburbanization, commercial suburbanization, commuting to work and changes in land use. The last chapter is a comparative analysis of relation between core and periphery on examples of Vienna and Budapest. In all three regions there are similarities consisting of faster growth of hinterland in terms of population and the spatial differentiation of suburbanization, which depends on the attractiveness of location and traffic accessibility.

Creating a stabile economic environment that is able to resist the competitive pressure at the European market was one of the main conditions for candidate countries in the integration process. In present all new member countries of the European Union are getting ready to enter the European Area, which will represent the round-off of their integration efforts. The countries of the Visegrad group, that are former centrally planned economies of the Soviet block, form quite homogeneous unit and their positions in the integration process were very similar. The main objective of my work is to provide a complex illustration of the progress made in economies of V4 group both during the integration process and over last few years after their accession to the European Union.

The diploma thesis is focused on evaluating the state of convergence process of the Czech Republic to the European Union with major accent on areas governed by the Czech National Bank. In the theoretical part a brief description of past and present monetary cooperation in Europe is presented, as well as a description of the Czech National Bank. Next part deals with the achieved level of convergence, from the perspective of both the Maastricht criteria and real convergence. The main contribution of the thesis is an evaluation of the prospects of adopting euro under conditions of the expected economic development.

This thesis deals with the convergence process in the European Union. It focuses primarily on processes associated with the member states from Central and Eastern Europe which joined the EU in 2004 and 2007. The work is divided into two main parts which are dealing with real and nominal convergence.

This thesis focuses on two integration blocks in Latin America -- the Pacific Alliance and MERCOSUR. The analysis should confirm the hypothesis that the integrated countries converge faster than non-integrated. With use of beta-convergence and sigma-convergence approaches, this hypothesis was rejected for the two Latin American integration groups. It is also supposed that market-led policies should diverge from the protectionist countries in terms of per capita income. However, this hypothesis was not neither confirmed, nor rejected for the observed region and time period. The income growth analysis showed that the Pacific Alliance countries are less dependent on their initial incomes than MERCOSUR members. However, the macroeconomic data exhibit multicollinearity, autocorrelation and unit root generated process. The explanatory coefficients likely lose their statistical significance, when this is controlled for. Therefore, the lower growth dependence in the Pacific Alliance integration on initial income cannot be fully confirmed.

The main target of this thesis is to investigate and compare influence of changing nominal interest rates of ECB on GDP and its main components: investments and consumption and find out how the mometary policy influences real convergence of Slovakia and Estonia comparing to eurozone countries.