On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.

Leak identification in saturated unsteady flow via a Cauchy problem

This work is an initial study of a numerical method for identifying multiple leak zones in saturated unsteady flow. Using the conventional saturated groundwater flow equation, the leak identification problem is modelled as a Cauchy problem for the heat equation and the aim is to find the regions on the boundary of the solution domain where the solution vanishes, since leak zones correspond to null pressure values. This problem is ill-posed and to reconstruct the solution in a stable way, we therefore modify and employ an iterative regularizing method proposed in [1] and [2]. In this method, mixed well-posed problems obtained by changing the boundary conditions are solved for the heat operator as well as for its adjoint, to get a sequence of approximations to the original Cauchy problem. The mixed problems are solved using a Finite element method (FEM), and the numerical results indicate that the leak zones can be identified with the proposed method.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

The political economy of inequality and growth: Essays on sovereign debt, democracy and saving

This dissertation addresses three issues in the political economy of growth literature. The first study empirically tests the hypothesis that income inequality influences the size of a country's sovereign debt for a sample of developing countries for the period 1970–1990. The argument examined is that governments tend to yield to popular pressures to engage in redistributive policies, partially financed by foreign borrowing. Facing increased risk of default, international creditors limit the credit they extend, with the result that borrowing countries invest less and grow at a slower pace. The findings do not seem to support the negative relationship between inequality and sovereign debt, as there is evidence of increases in multilateral, countercyclical flows until the mid 1980s in Latin America. The hypothesis would hold for the period 1983–1990. Debt flows and levels seem to be positively correlated with growth as expected. ^ The second study empirically investigates the hypothesis that pronounced levels of inequality lead to unconsolidated democracies. We test the existence of a nonmonotonic relationship between inequality and democracy for a sample of Latin American countries for the period 1970–2000, where democracy appears to consolidate at some intermediate level of inequality. We find that the nonmonotonic relationship holds using instrumental variables methods. Bolivia seems to be a case of unconsolidated democracy. The positive relationship between per capita income and democracy disappears once fixed effects are introduced. ^ The third study explores the nonlinear relationship between per capita income and private saving levels in Latin America. Several estimation methods are presented; however, only the estimation of a dynamic specification through a state-of-the-art general method of moments estimator yields consistent estimates with increased efficiency. Results support the hypothesis that income positively affects private saving, while system GMM reveals nonlinear effects at income levels that exceed the ones included in this sample for the period 1960–1994. We also find that growth, government dissaving, and tightening of credit constraints have a highly significant and positive effect on private saving. ^

Economic Inequality and the Conditions of Freedom- Views from the American Founding

Professor Clement Fatovic, Director of Graduate Studies for Politic Sciences, lectures on the subject of the American Founding. Lecture held at the Green Library, Modesto Maidique Campus, Florida International University, on April 10, 2013.

Three essays on the economics of defense contracting, output and income inequality

This dissertation analyzes both the economics of the defense contracting process and the impact of total dollar obligations on the economies of U.S. states. Using various econometric techniques, I will estimate relationships across individual contracts, state level output, and income inequality. I will achieve this primarily through the use of a dataset on individual contract obligations. ^ The first essay will catalog the distribution of contracts and isolate aspects of the process that contribute to contract dollar obligations. Accordingly, this study describes several characteristics about individual defense contracts, from 1966-2006: (i) the distribution of contract dollar obligations is extremely rightward skewed, (ii) contracts are unevenly distributed in a geographic sense across the United States, (iii) increased duration of a contract by 10 percent is associated with an increase in costs by 4 percent, (iv) competition does not seem to affect dollar obligations in a substantial way, (v) contract pre-payment financing increases the obligation of contracts from anywhere from 62 to 380 percent over non-financed contracts. ^ The second essay will turn to an aggregate focus, and look the impact of defense spending on state economic output. The analysis in chapter two attempts to estimate the state level fiscal multiplier, deploying Difference-in-Differences estimation as an attempt to filter out potential endogeneity bias. Interstate variation in procurement spending facilitates utilization of a natural experiment scenario, focusing on the spike in relative spending in 1982. The state level relative multiplier estimate here is 1.19, and captures the short run, impact effect of the 1982 spending spike. ^ Finally I will look at the relationship between defense contracting and income inequality. Military spending has typically been observed to have a negative relationship with income inequality. The third chapter examines the existence of this relationship, combining data on defense procurement with data on income inequality at the state level, in a longitudinal analysis across the United States. While the estimates do not suggest a significant relationship exists for the income share of the top ten percent of households, there is a significant positive relationship for the income share of top one percent households for an increase in defense procurement.^

The effect of economic inequality on voter turnout in Canadian federal elections, 1979-2011

Since the 1990s, voter turnout in Canadian federal elections has decreased considerably. During the same period, economic inequality significantly increased. Although there is much theoretical work, there have been few empirical studies examining the effect of economic inequality on voter turnout. Using data collected from both national and international sources, I conducted an aggregate level, time series analysis of national turnout and economic inequality for Canadian federal elections between 1979 and 2011. Moreover, this thesis tests Schattschneider's (1960) hypothesis, which argues that increasing rates of voter abstention are a result of economic inequality magnifying differences in relative power between affluent and non-affluent citizens. The findings indicate that economic inequality has a strong negative effect on voter turnout.

The impact of migration on regional wage inequality : a semiparametric approach

Peer reviewed

Estimation of Inequality Indices of the Cumulative Distribution Function

Date of Acceptance: 02/03/2015