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Full-Text Articles in Analysis
Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi
Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi
Electronic Theses and Dissertations
Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes nonsmooth versions …
Predictive Diagnostic Analysis Of Mammographic Breast Tissue Microenvironment, Dexter G. Canning
Predictive Diagnostic Analysis Of Mammographic Breast Tissue Microenvironment, Dexter G. Canning
Honors College
Improving computer-aided early detection techniques for breast cancer is paramount because current technology has high false positive rates. Existing methods have led to a substantial number of false diagnostics, which lead to stress, unnecessary biopsies, and an added financial burden to the health care system. In order to augment early detection methodology, one must understand the breast microenvironment. The CompuMAINE Lab has researched computational metrics on mammograms based on an image analysis technique called the Wavelet Transform Modulus Maxima (WTMM) method to identify the fractal and roughness signature from mammograms. The WTMM method was used to color code the mammograms …
Understanding Volume Transport In The Jordan River: An Application Of The Navier-Stokes Equations, Gwyneth E. Roberts
Understanding Volume Transport In The Jordan River: An Application Of The Navier-Stokes Equations, Gwyneth E. Roberts
Honors College
This study aims to characterize the circulation patterns in short and narrow estuarine systems on various temporal scales to identify the controls of material transport. In order to achieve this goal, a combination of in situ collected data and analytical modeling was used. The model is based on the horizontal Reynolds Averaged Navier-Stokes equations in the shallow water limit with scaling parameters defined from the characteristics of the estuary. The in situ measurements were used to inform a case study, seeking to understand water level variations and tidal current velocity patterns in the Jordan River and to improve understanding of …