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Full-Text Articles in Mathematics
A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman
A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman
USF Tampa Graduate Theses and Dissertations
The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …
Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function, Daniel Siebel-Cortopassi
Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function, Daniel Siebel-Cortopassi
USF Tampa Graduate Theses and Dissertations
A coupled delay-feedback system of two cantilevers can yield greater sensitivity than that of asingle cantilever system, with potential applications in atomic force microscopy. The Lambert W-function analysis concept for delay differential equations is used to more accurately model the behavior of specific configurations of these cantilever systems. We also use this analysis concept to find parameters which yield stability for greater parameter ranges, of the delay differential equations. The Q factor, or quality factor, is the ratio of energy stored in the system, to the energy lost per fixed oscillation/movement cycle. Having stability of the cantilevers corresponds to the …