Thesis (M. A.)--University of Notre Dame, 2005. / Thesis directed by Ke-Hai Yuan for the Department of Psychology. "October 2005." Includes bibliographical references (leaves 60-63).

In this study, we consider the generalized function solutions to nonlinear wave equation with distribution initial data. J. F. Colombeau shows that the initial value problem u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 then inspect the generalized function representatives for the initial value problem solution to see if the generalized function solution is a distribution or is more singular. Using the numerical technics, we show for specific F and specific distribution initial data u_0, u_1, there is no distribution solution.

Alcohol is the most widely used psychoactive drug on earth and continues to be responsible for a substantial burden of death and disability. Mitigating these harms is an important focus of any healthful society. Population-level alcohol policy strategies may be employed to decrease these harms and improve population health. To assist towards these goals, this dissertation has two research objectives relating to the estimation and mitigation of alcohol harms: (1) to complete a series of studies regarding the Alcohol Total Consumption Model (TCM) and (2) to specify and test a novel alcohol health harms estimator and alcohol policy scenario modeler, the International Model of Alcohol Harms and Policies (InterMAHP). The TCM is an important theory in alcohol studies and connects alcohol policies, per capita alcohol consumption and alcohol-attributable (AA) harms in a unified social theory. In brief, policies are expected to reflect on population-level consumption, which in turn is the most important predictor of alcohol harms. The TCM theorizes that change should flow directionally through the model – a policy expected to decrease consumption would be predicted to decrease alcohol harms. This theory has been critical towards informing alcohol control policies in the past five decades. In this dissertation, a series of studies were conducted to test the assumptions of the TCM, to test their continued viability. Study A is a comprehensive systematic review and series of meta-analyses that established the link between alcohol policies influencing day/hours of sale and outlet density and per capita consumption. Study B is a primary research study that examined the direct effect of a changed alcohol policy on alcohol-related ED visits, in the context of Saskatchewan. Studies C and D establish the link between alcohol consumption and AA mortality and morbidity through mathematical specification of InterMAHP. Next, the model was applied to the exemplar of AA mortality in Canada in 2016. Last, Study E extended InterMAHP functionalities to include modeling changes in AA harms expected from potential or realized per capita consumption changes resulting from policy change. An application was provided in the context of Québec. The results of this dissertation research provide some support, in a modern context, to the relationships defined in the TCM. The findings suggest that the TCM continues to be a largely appropriate conceptual model in consideration of alcohol policy-making. InterMAHP provides global alcohol researchers with a novel model towards estimating the health harms of alcohol. / Graduate / 2020-04-09

Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica. / Department of Mathematical Sciences

Please read the abstract in the section 00front of this document / Dissertation (MSc (Industrial Systems))--University of Pretoria, 2006. / Industrial and Systems Engineering / unrestricted

Thesis (MSc (Mathematics))--Stellenbosch University, 2008. / LULU smoothers is a class of nonlinear smoothers and they are compositions of the maximum and minimum operators. By analogy to the discrete Fourier transform and the discrete wavelet transform, one can use LULU smoothers to create a nonlinear multiresolution analysis of a sequence with pulses. This tool is known as the Discrete Pulse Transform (DPT). Some research have been done into the distributional properties of the LULU smoothers. There exist results on the distribution transfers of the basic LULU smoothers, which are the building blocks of the discrete pulse transform. The output distributions of further smoothers used in the DPT, in terms of input distributions, has been a challenging problem. We motivate the use of these smoothers by first considering linear filters as well as the median smoother, which has been very popular in signal and image processing. We give an overview of the attractive properties of the LULU smoothers after which we tackle their output distributions. The main result is the proof of a recursive formula for the output distribution of compositions of LULU smoothers in terms of a given input distribution.