This dissertation is a comprehensive study of governmental expenditures and their impact on economic growth of the United States economies; the research will contribute to existing literature with the use of a unique database that collects actual expenditures and is not based on proxies. The first chapter is a review of the various strands of the theoretical literature and analyzes the results of empirical estimations in Europe and in the U.S. where regional development policies are already well established, as well as providing recommendations for future research in this field. The second chapter relies on a Cobb-Douglas production function approach to analyze the role of physical and human capital on the US states economies over 2000-2008. It makes use of recent theoretical developments on the role of inter-state technological spillovers on income. In addition, the chapter adopts a unique set of data on publicly funded investments in physical and human capital that brings new insights into the traditional measurements of the Mankiw-Romer-Weil model of regional income distribution and regional growth dynamics. The third chapter analyzes the impact of the actual amounts of all federally funded development programs on the growth rate of U.S. counties. Relying on a conditional neoclassical beta convergence, it measures the impacts of the U.S. federal government expenditures as overall spending, for each of 15 types of federal spending, and by agency-based classification from 2000-2007. The chapter accounts for the significant difference in the growth dynamics of the metropolitan and non-metropolitan counties and potential heterogeneity of public expenditures. The forth chapter evaluates the hypothesis that federal grants crowd-out state and local government spending using a cross-classification of actual federal and state-local types of expenditures. The literature has not reached an empirical conclusion, with the majority of the empirical research concluding a crowding-in of federal spending. Therefore, this study incorporates recent discussions about potential endogeneity of federal funds and lack of flexibility of state-local budgets due to institutional or political commitments using a dynamic panel of U.S. states over 1997-2009.

In this work we research convergence rates of densities of independent random extreme values. Using [4] and [2] work results, we will get nonuniform estimate of convergence rates in local theorem of extreme values of independent random variables exploring different distribution functions. [4], [2] work results we will generalize exploring nonuniform normalized extreme values convergence.

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The United States has a long history of doing things differently than other countries. Its accounting standards are no different; to date, it continues to use its own Generally Accepted Accounting Principles and have yet to converge to the International Financial Reporting Standards ("IFRS") as set by the International Accounting Standards Board. In 2008, the U.S. Securities and Exchange Commission ("SEC") Chairman Christopher Cox published a press release in which the SEC published for public comment a roadmap towards convergence by 2014. However, in subsequent years, Memorandum of Understandings published by the IASB and the United States' Financial Accounting Standards Boards ("FASB") pushed back the date of implementation at each publication. As a result, the convergence efforts have been stalling greatly. It is very unlikely that the U.S. will ever completely converge to IFRS as the financial costs and obstacles to convergence are not insignificant. Not only will the costs of implication be great, but also the costs of training and education of auditors and accountants. It is not feasible for the U.S. to converge with IFRS in the near future, as the benefits most countries obtain through convergence such as increased quality of financial statements will not be realized. As such, this paper seeks to prove why IFRS convergence will not be realized in the United States.

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The goal of the present work is the development of a numerical method for compressible viscous flows on mixed unstructured grids. The discretisation is based on a vertex-centred finite-volume method. The concept of grid transparency is developed as a framework for the discretisation on mixed unstructured grids. A grid-transparent method does not require information on the cell types. For this reason, the numerical method developed in the present work can be applied to triangular, quadrilateral, and mixed grids without modification. The inviscid fluxes are discretised using the approximate Riemann solver of Roe. A limited linear-reconstruction method leads to monotonic capturing of shock waves and second-order accuracy in smooth regions of the flow. The discretisation of the viscous fluxes on triangular and quadrilateral grids is first studied by reference to Laplace's equation. A variety of schemes are evaluated against several criteria. The chosen discretisation is then extended to the viscous fluxes in the Navier-Stokes equations. A careful study of the various terms allows a form to be developed which may be regarded as a thin-shear-layer approximation. In contrast to previous implementations, however, the present approximation does not require knowledge of normal and tangential coordinate directions near solid surfaces. The effects of turbulence are modelled through the eddy-viscosity hypothesis and the one-equation model of Spalart and Allmaras. The discrete equations are marched to the steady-state solution by an explicit Runge-Kutta method with local time-stepping. The turbulence-model equation is solved by a point-implicit method. To accelerate the convergence rate, an agglomeration multigrid method is employed. In contrast to previous implementations, the governing equations are entirely rediscretised on the coarse grid levels. The solution method is applied to various inviscid, laminar, and turbulent flows. The performance of the multigrid method is compared for triangular and quadrilateral grids. Care is taken to assess numerical errors through grid-refinement studies or comparisons with analytical solutions or experimental data. The main contributions of the present work are the careful development of a solution method for compressible viscous flows on mixed unstructured grids and the comparison of the impact of triangular, quadrilateral, and mixed grids on convergence rates and solution quality.

This thesis is an analysis of convergence results on Fourier series. Convergence of Fourier series is studied in two ways in this thesis. The first way is in the context of Banach spaces, where the set of functions is restricted to a certain Banach space. Then the problem is in determining whether the Fourier series of a function can be represented as an element of that Banach space. The second way is in the context of pointwise convergence. Here, the problem is in determining what conditions need to be placed on an arbitrary function for its Fourier series to converge at a point.

The main aim of this thesis is to study the convergence of Lyapounov functions along the trajectories of nonexpansive semigroups in a Hilbert space. The outline of the thesis is as follows. In Chapter 3, it is shown that a regularly Lyapounov function for a semigroup of contractions on a Hilbert space converges to its minimum along the trajectories of the semigroup. In Chapter 4, we show that while a convex Lyapounov function for a semigroup of contractions on a Hilbert space may not converge to its minimum along the trajectories of the semigroup, it converges generically along the trajectories of the semigroups generated by a class of bounded perturbations of the semigroup generator. In Chapter 5, we show that the regularly Lyapounov function nearly converges to its minimum along the trajectories of the semigroups generated by small bounded perturbations of the semigroup generator. Besides that we study a problem of interest in its own right, about the direction of movement of the element of minimal norm in a moving convex set, in Section 4.9. We show that if C is a nonempty closed convex subset of a real Hilbert space H, e is a non-zero arbitrary vector in H, and for each t Є R, z(t) is the closest point in C + te to the origin, then the angle z(t) makes with e is a decreasing function of t while z(t) ≠ 0.

The main aim of this thesis is to study the convergence of Lyapounov functions along the trajectories of nonexpansive semigroups in a Hilbert space. The outline of the thesis is as follows. In Chapter 3, it is shown that a regularly Lyapounov function for a semigroup of contractions on a Hilbert space converges to its minimum along the trajectories of the semigroup. In Chapter 4, we show that while a convex Lyapounov function for a semigroup of contractions on a Hilbert space may not converge to its minimum along the trajectories of the semigroup, it converges generically along the trajectories of the semigroups generated by a class of bounded perturbations of the semigroup generator. In Chapter 5, we show that the regularly Lyapounov function nearly converges to its minimum along the trajectories of the semigroups generated by small bounded perturbations of the semigroup generator. Besides that we study a problem of interest in its own right, about the direction of movement of the element of minimal norm in a moving convex set, in Section 4.9. We show that if C is a nonempty closed convex subset of a real Hilbert space H, e is a non-zero arbitrary vector in H, and for each t Є R, z(t) is the closest point in C + te to the origin, then the angle z(t) makes with e is a decreasing function of t while z(t) ≠ 0.