Theses and Dissertations

Any subsequent statements pertaining to modules also apply to abelian groups and general rings when interpreted.

Gauss's theory of congruences, Wilson's theorem, and Fermat's theorem are discussed, followed by Euler's phi function and Euler's theorem.

Of fundamental importance in the theory and study of finite groups are the theorems of Lagrange and Sylow, two theorems very closely related.

A linear programming problem, of minimizing a linear combination of variables subject to a linear set of inequalities, is presented.

The electromagnetic properties of a live biological system are extremely important to many medical applications. While information about electromagnetic properties of tissues are available in the literature, little or no data are available for a single cell or subcellular structures. Microwave biological/cell detection has been demonstrated to be useful and promising in many medical applications due to its internal properties such as non-invasive, fast and label-free.

This report describes the construction of an interval arithmetic implementation package for WIZARD and its use with a general linear equation solver.

For the first time, the impedance spectrum of live Jurkat T-lymphocytes human cells was characterized in a single sweep spanning six decades of frequency from 9 kHz to 9 GHz. The ultrawide bandwidth bridged the traditional impedance spectroscopy at kilohertz to megahertz frequencies with the recently developed microwave dielectric spectroscopy, which can probe the cell interior without being hindered by the cell membrane.

A closed-loop capacitance sensing and control mix-mode circuit with a dedicated sensor electrode and a proportional-integral controller was designed for MEMS varactors. The control was based on tuning the bias magnitude of the MEMS varactor according to t

The attempt to simplify A.M. Turing's theoretical approach to computable functions has lead to the advancement of many theories, some of which seem inequivalent to the original Turing idea. This thesis approaches the problem of equivalence by establishing the existence of translation tables between machines.

This paper deals with The Law of Quadratic Reciprocity which is considered to be the major theorem of the theory of numbers.

For the first time, wafer-scale fabrication of PtSe2 MOSFETs was demonstrated by photolithography. The on PtSe2 is grown by thermally assisted conversion (TAC) of Pt films under Se vapor at 400 °C. Taking advantage of the unique property of PtSe2 to transition from semiconductor to semimetal as its thickness increases beyond a few monolayers, channel recess was adapted for improving gate control while keeping the contact resistance as low as 0.008 Ω∙cm. The wafer-scale fabrication resulted in uniform device characteristics so that average vs. best results were reported, as well as RF vs.