What Are The Characteristics Of A Problem Statement

Research Methodology

How to Design, Write, and Present a Successful Dissertation Proposal

How to Design, Write, and Present a Successful Dissertation Proposal, by Elizabeth A. Wentz, is essential reading for any graduate student entering the dissertation process in the social or behavioral sciences. The book addresses the importance of ethical scientific research, developing your curriculum vitae, effective reading and writing, completing a literature review, conceptualizing your research idea, and translating that idea into a realistic research proposal using research methods. The author also offers insight into oral presentations of the completed proposal, and the final chapter presents ideas for next steps after the proposal has been presented. Taking the view that we “learn by doing,” the author provides Quick Tasks, Action Items, and To Do List activities throughout the text that, when combined, develop each piece of your research proposal. Designed primarily for quantitative or mixed methods research dissertations, this book is a valuable start-to-finish resource.

Generalized Characteristics of First Order PDEs

In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs. A well-known classical result states a sufficiency condition for local existence and uniqueness of twice differentiable solution. This result is based on the method of characteristics (MC). Very often, and as a rule in control theory, the continuous nonsmooth (non-differentiable) functions have to be treated as a solutions to the PDE. At the points of smoothness such solutions satisfy the equation in classical sense. But if a function satisfies this condition only, with no requirements at the points of nonsmoothness, the PDE may have nonunique solutions. The uniqueness takes place if an appropriate matching principle for smooth solution branches defined in neighboring domains is applied or, in other words, the notion of generalized solution is considered. In each field an appropriate matching principle are used. In Optimal Control and Differential Games this principle is the optimality of the cost function. In physics and mechanics certain laws must be fulfilled for correct matching. A purely mathematical approach also can be used, when the generalized solution is introduced to obtain the existence and uniqueness of the solution, without being aimed to describe (to model) some particular physical phenomenon. Some formulations of the generalized solution may meet the modelling of a given phenomenon, the others may not.