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2025

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Full-Text Articles in Probability

Solvability Of Stochastic Linear-Quadratic Optimal Control Problems Under Partial Stabilizability Conditions, Al-Sadh Rahman Imadh Jan 2025

Solvability Of Stochastic Linear-Quadratic Optimal Control Problems Under Partial Stabilizability Conditions, Al-Sadh Rahman Imadh

Honors Undergraduate Theses

Optimal Control Theory, a branch of Control Theory, is applicable in fields such as engineering, operations research, and economics. Stochastic Optimal Control deals with noisy systems and data using Ito’s formulation. Given a noisy system and a cost functional, the goal is to find a control that will minimize the cost. This thesis focuses on linear quadratic stochastic optimal control, and we explore state equations that are not stabilizable. We first address measurability concerns arising from the semigroup property of the state trajectory. The notions of partial stability and partial stabilizability are introduced, and we formulate their corresponding Lyapunov and …


Developing Consensus-Based Methods For The Examination And Interpretation Of Contemporary Vehicle, Architectural, And Portable Electronic Device Glasses By Micro-X-Ray Fluorescence Spectrometry, Zachary Bailey Andrews Jan 2025

Developing Consensus-Based Methods For The Examination And Interpretation Of Contemporary Vehicle, Architectural, And Portable Electronic Device Glasses By Micro-X-Ray Fluorescence Spectrometry, Zachary Bailey Andrews

Graduate Theses, Dissertations, and Problem Reports (ETD)

Glass is a trace material that is commonly encountered during investigations of violent crimes. When glass is recovered at crime scenes, it can be used to establish links between suspects, victims, and the scene itself. The most discriminatory form of analysis for glass evidence is elemental analysis, and micro-X-ray fluorescence spectrometry (µXRF) is becoming an increasingly common technique used for this purpose. Recent advances in µXRF technology, such as the introduction of silicon drift detectors (SDD) and improved polycapillary optics are promising in enhancing the capabilities for the examination of glass evidence in forensic investigations. However, along with these advances …