Physical Sciences and Mathematics Commons^™

Gaussian Quantum Markov Semigroups In The Fock-Anti-Fock Representation Of Weyl Algebra, A Dhahri, Franco Fagnola, D Poletti, Hyun Jae Yoo

Journal of Stochastic Analysis

No abstract provided.

Approximations Of Koopman Operator Semigroups, Ibrahem Al Jabea

LSU Doctoral Dissertations

The main purpose of this dissertation is to study approximation methods for nonlinear systems using Bernhard Koopman's Global Linearization Method or Sophus Lie's method of continuous transformation groups. This approach enables the application of linear semigroup methods to a nonlinear system by focusing on the dynamics of the observables of the states, rather than directly studying the dynamics of the states. In this dissertation, we studied the pointwise semigroup and introduce the modified space $C_m(\Omega)$ and the modified Koopman-Lie semigroups. We use a splitting operator and outline a systematic approach for approximating the pointwise Koopman-Lie semigroup flows \begin{equation*} t\to T(t)g(x) …

19ne Excited States In Explosive Nucleosynthesis, Khang Pham

LSU Doctoral Dissertations

Classical novae and Type I X-ray bursts are stellar explosions that occur in binary systems, where nuclear reactions involving ¹⁹Ne play a crucial role in nucleosynthesis. In novae, the destruction of ¹⁸F via the ¹⁸F(p,alpha)¹⁵O reaction significantly affects the amount of ¹⁸F remaining in the ejecta, directly influencing the detectability of predicted 511-keV gamma rays. However, discrepancies between observed and predicted ¹⁸F abundances highlight uncertainties in the reaction rates, primarily due to unknown properties of resonances in the compound nucleus ¹⁹Ne. In Type I X-ray bursts, the ¹⁵O(alpha,gamma)¹⁹Ne reaction …

Unavoidable Immersions And Topological Minors Of K-Edge-Connected Graphs, Brittian Qualls

LSU Doctoral Dissertations

In this work, we present results concerning the unavoidable structures in large and infinite k-edge-connected graphs. These results are inspired by the classical result of Ramsey, who proved that for every positive integer r, every sufficiently large graph contains as an induced subgraph either K_r or $\overline{K_r}$. We consider different graph containment relations, focusing primarily on the immersion relation. In the case of finite graphs, we provide the unavoidable immersions of 4-edge-connected graphs and prove that linear edge-connectivity suffices to immerse the graph C_t,r.

This dissertation also considers infinite graphs. We present the …

Optical Spring Tracking For Enhancing Quantum-Limited Interferometers, Scott M. Aronson

LSU Doctoral Dissertations

Gravitational waves were first predicted by Albert Einstein in 1916. Calculations in the 1970s by Rainer Weiss showed an interferometer of sufficient size could realistically detect gravitational waves, which led to a grant by the National Science Foundation (NSF). With steady progress and over decades of funding by the NSF, the construction of two full scale 4km interferometers was approved and began construction in 1994. This project, coined LIGO the Laser Interferometer Gravitational-wave Observatory, came to be a worldwide collaboration of scientists dedicated to the discovery and study of gravitational waves. In 2015, both LIGO detectors detected a coincident inspiral …

Assessing Groundwater Availability And Land Subsidence Risk Associated With Anthropogenic Activities In A Complex Aquifer System, Aya Bakr Attya Mohamed

LSU Doctoral Dissertations

The Southern Hills aquifer system (SHAS) is the primary source of water in the Capital area of Louisiana. However, the overexploitation of freshwater-bearing aquifers and the presence of two active faults, the BR fault and the DSS fault, have resulted in groundwater depletion, saltwater intrusion, and increased the risk of land surface subsidence. Such critical issues pose substantial threats to groundwater availability and exert detrimental effects on the environment and urban infrastructures. This dissertation presents a comprehensive investigation of the SHAS for recognizing the consequences of groundwater depletion and its potential long-term impacts on groundwater availability and land stability. A …

On Unavoidable Infinite Hypergraphs, Samuel Weiner

LSU Doctoral Dissertations

Ramsey's Theorem states that every infinite graph contains either K_∞ or $\overline{K_∞}$ as an induced subgraph. For this reason, K_∞ and $\overline{K_∞}$ are often referred to as the unavoidable infinite graphs. Many similar results have characterized the unavoidable members for various classes of infinite graphs; perhaps the most notable of these is König's Infinity Lemma, which states that every infinite, connected, locally finite graph contains a ray as an induced subgraph. From these findings, one can easily deduce that every infinite, connected graph contains an infinite clique, star, or ray as an induced subgraph; …

On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis

LSU Doctoral Dissertations

The Boltzmann equation describes the time evolution of the density function in position-velocity space for a classical particle subjected to possible collisions by other particles in a diluted gas that expands in vacuum for a given initial distribution. While many authors have studied the probabilistic interpretation of the spatially homogeneous Boltzmann equation, there is a dearth of articles on the stochastic framework of the full (that is, spatially inhomogeneous) Boltzmann equation. In this thesis, we examine a stochastic process, developed by S. Albevario, B. Ruediger, and P. Sundar, whose law is a weak solution to a mollified Boltzmann equation. This …

Quaternary Subsurface Characterization Of The Mississippi River Valley Alluvial Aquifer: Insights From Interval Kriging And Airborne Em-Borehole Data Integration, Yuqi Song

LSU Doctoral Dissertations

The Pleistocene period significantly contributed to the formation of alluvial aquifer worldwide. These productive aquifers are crucial for domestic, industrial, and agricultural water supplies. The Mississippi River Valley alluvial aquifer (MRVA), a principal aquifer in the U.S., is crucial for national food security and global agricultural supply. This study aims to characterize the subsurface architecture of the MRVA, thereby enhancing fundamental understanding of sedimentological processes involved in the genesis of glacio-fluvial aquifers worldwide. The research objectives are threefold: (1) to provide a detailed characterization of the MRVA; (2) to develop 3D geostatistical methods for geological modeling; and (3) to develop …

Explicit Modularity And Moments For Certain Hypergeometric Character Sums, Brian Grove

LSU Doctoral Dissertations

A great deal of progress in number theory throughout history has been motivated by trying to solve equations. One of the most famous challenges is to show there are no positive integer solutions to $x^{n}+y^{n} = z^{n}$ for $n > 2$, posed by Fermat around 1637. Special cases, such as the $n = 3$ and $n = 4$ cases, can be established using various algebraic manipulations. However, a general solution was elusive until the late 1990s when the combined work of Wiles \cite{Wiles} and Taylor--Wiles \cite{TaylorWiles} give a full proof.

One of the key insights used in proving Fermat's conjecture involves …

Evaluating Biotic Effecrs Associated With The Paleocene-Eocene Thermal Maximum In Mississippi And Alabama: A Palynological And Biostratigraphic Study Of Amoco's Legacy Samples, Sarah Fortin Bancroft

LSU Master's Theses

The Paleocene-Eocene Thermal Maximum (PETM) was a ~200 ka period of rapid global warming in the earliest Eocene (~56 Ma) involving a roughly 7 °C rise in atmospheric and sea-surface temperatures. The Gulf of Mexico Wilcox Group contains very well-preserved terrestrial and deltaic sediments that contain exploitable hydrocarbons . The Wilcox Group’s Paleocene Tuscahoma and Eocene Hatchetigbee Formations have been roughly dated with calcareous and planktonic foraminiferal assemblages by AMOCO; however, the precise ages of these formations, their palynological assemblages, and their paleo-depositional geosystems are an area of active research.

Through a high-resolution palynological analysis, this study assesses the depositional …

Stochastic Analysis And White Noise Calculus Of Nonlinear Wave Equations With Application To Laser Generation And Propagation, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.

The Boltzmann-Enskog Equation With Brownian Forcing, Aurora Wallace

LSU Doctoral Dissertations

Interacting particle systems (IPS) are used to rigorously derive partial differential equations modeling macroscopic behavior given by systems of stochastic differential equa- tions in physics, biology, and other sciences. These systems model the time evolution of n interacting particles with desired dynamics. In the n-system studied here, only two parti- cles may interact at a time (binary collisions). The particles are exchangeable; that is, the ordering of the particles does not play a role, and the interaction between the ith particle and the jth particle models an elastic collision. In this thesis, we use the method of inter- acting particle …

An Operator Information Quantity Of A Semigroup And Associated Differential Equations, Kimiaki Saito, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.

The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih

Journal of Stochastic Analysis

No abstract provided.

American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah

Journal of Stochastic Analysis

No abstract provided.

About Fixed Points Of Quantum Channels, Raffaella Carbone

Journal of Stochastic Analysis

No abstract provided.

Induced-Minor-Closed Classes Of Matroids, James Dylan Douthitt

LSU Doctoral Dissertations

A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple GF(q)-representable matroids that can be built from projective geometries over GF(q) by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when q=2 is distinctive. Additionally, we show that the class of GF(2)-chordal matroids coincides …

Infrared Laser Ablation Of Biomolecules From Formalin-Fixed Tissue, Blessing Chisom Egbejiogu

LSU Doctoral Dissertations

In the research described in this dissertation, a high-precision infrared laser ablation microsampling method was utilized for spatially resolved proteomic and lipidomic analyses of formalin fixed paraffin embedded (FFPE) tissue, a widely used archival sample in biomedical research. Despite its extensive use, FFPE tissue presents challenges for proteomic analysis due to protein cross-linking and modifications introduced during fixation, which can hinder extraction and identification. Developing a streamlined high-resolution method to recover biomolecules from FFPE samples is critical for advancing biomarker discovery, retrospective studies, and multi-omics research. To address these challenges, this study employs an infrared (IR) laser ablation microdissection system …

Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu

Journal of Stochastic Analysis

No abstract provided.

Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Non-Orientable Surfaces Bounded By Knots, Megan K. Fairchild

LSU Doctoral Dissertations

The non-orientable 4-genus of a knot $K$ in $S^{3}$ is defined to be the minimum first Betti number of a non-orientable surface $F$ in $B^{4}$ so that $K$ bounds $F$. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots, torus knots, and Whitehead doubles. We also will view obstructions to a knot bounding a M\"{o}bius band given by the double branched cover of $S^{3}$ branched over $K$. Additionally, we discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used …

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley

Journal of Stochastic Analysis

No abstract provided.

On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.

Temporal Scales Of Sediment Accumulation, Mass Wasting, And Stratigraphy Across The Mississippi River Delta Front, Jeffrey E. Duxbury

LSU Doctoral Dissertations

The Mississippi River Delta Front (MRDF) is a subaqueous apron of rapidly deposited, weakly

consolidated sediment extending from the subaerial portions of the Mississippi River’s Birdsfoot Delta, historically known for sediment transport via mass wasting. To better understand the spatial and temporal dynamics of processes influencing the MRDF, 29 cores ranging from 5.8 to 8.71 meters in length were collected from the South Pass (SP) and Southwest Passes (SWP). These cores targeted specific depositional environments, including the undisturbed topset apron, medial mudflow gully, mudflow lobe, and prodelta. The cores were analyzed along their full lengths for gamma density, grain size, …

Thermal Noise Measurement Below The Standard Quantum Limit, Ronald Pagano

LSU Doctoral Dissertations

Quantum mechanics places sensitivity restrictions on physical measurements. These limitations manifest themselves in interferometric force and displacement measurements as uncertainty both in the photon number measured at a photodetector (shot noise), and in the quantum radiation pressure applied to the interferometer (quantum back action noise manifested as quantum radiation pressure noise). The balance between shot noise and quantum radiation pressure noise imposes the Standard Quantum Limit (SQL). A large body of work has been dedicated to measuring these quantum effects and mitigating them. Owing to the inherently small scale at which quantum effects are visible, classical effects must be subverted …

Studying The Low-Lying Structure Of 9b Via The 10b(3he,A)9b Reaction, Rachel M. Shaffer

LSU Doctoral Dissertations

The unstable nature of ⁹B makes it a challenging isotope to study. The first-excited state of ⁹B has been particularly difficult to characterize. Since the first experimental observation of this state in 1955, many experimental and theoretical nuclear structure studies have sought to classify it, but with large discrepancies in the energy and width values from these results, the properties of the state remain inconclusive.

An experiment using the ¹⁰B(³He,α)⁹B reaction was performed at the John D. Fox Superconducting Linear Accelerator Laboratory at Florida State University in an effort to populate and characterize …

Baryon Number Violation Search, Tyler D. Stokes

LSU Doctoral Dissertations

Understanding the fundamental forces and symmetries of nature has long been a central goal of particle physics. While the Standard Model (SM) provides a successful framework, it does not guarantee the conservation of baryon number B or lepton number L, thus motivating searches for their violation. Proton decay, a fundamental process violating B, has been at the forefront of experimental searches for decades.

The discovery of the weak neutral current in 1973 unified the electromagnetic and weak forces and inspired the creation of Grand Unified Theories (GUTs) that also unify the strong force. In 1974, the first-ever GUT, …