Mathematics Commons^™

On The Generators Of Quantum Dynamical Semigroups, Alexander Wiedemann

Theses and Dissertations

In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. We define the class of pair block diagonal generators, which allows for additional interaction coefficients but preserves the main structural properties. Namely, when the basis of the underlying Hilbert space is given by the eigenbasis of the Hamiltonian (for example the generic semigroups), then the action of the semigroup leaves invariant the diagonal and off-diagonal matrix spaces. In this case, we explicitly compute all invariant states of the semigroup.

In order to define this class we …

A New Characterization Of V-Posets, Peter Gartland

Theses and Dissertations

In 2016, Hasebe and Tsujie gave a recursive characterization of the set of induced N -free and bowtie-free posets; Misanantenaina and Wagner studied these orders fur- ther, naming them “V-posets”. Here we offer a new characterization of V-posets by introducing a property we refer to as autonomy. A poset P is said to be autonomous if there exists a directed acyclic graph D (with adjacency matrix U ) whose transitive closure is P, with the property that any total ordering of the vertices of D so that Gaussian elimination of UT U proceeds without row swaps is a …

A Development Of Transfer Entropy In Continuous-Time, Christopher David Edgar

Theses and Dissertations

The quantification of causal relationships between time series data is a fundamen- tal problem in fields including neuroscience, social networking, finance, and machine learning. Amongst the various means of measuring such relationships, information- theoretic approaches are a rapidly developing area in concert with other methods. One such approach is to make use of the notion of transfer entropy (TE). Broadly speaking, TE is an information-theoretic measure of information transfer between two stochastic processes. Schreiber’s 2001 definition of TE characterizes information transfer as an informational divergence between conditional probability mass func- tions. The original definition is native to discrete-time stochastic processes …

Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell

Undergraduate Honors Thesis Projects

This research will study the effect teaching the history of mathematics in a high school classroom has on student understanding. To accomplish this, lessons both including and excluding historical background on different topics were taught in an Honors Algebra 2 class in the high school setting. This research aims to engage student learning and investigation of topics that normally do not draw a lot of student focus and spark a new or revived interest in mathematics for students by broadening lessons to include material of which students would not otherwise be exposed. The lessons themselves aim to engage other current …

Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions, Nicholas Torello

Senior Theses

Let p_r(n) denote the difference between the number of r-colored partitions of n into an even number of distinct parts and into an odd number of distinct parts. Inspired by proofs involving modular forms of the Hirschhorn-Sellers Conjecture, we prove a similar congruence for p_r(n). Using the Jacobi Triple Product identity, we discover a much stricter congruence for p_3(n).

Exponential Stability Of Intrinsically Stable Dynamical Networks And Switched Networks With Time-Varying Time Delays, David Patrick Reber

Theses and Dissertations

Dynamic processes on real-world networks are time-delayed due to finite processing speeds and the need to transmit data over nonzero distances. These time-delays often destabilize the network's dynamics, but are difficult to analyze because they increase the dimension of the network.We present results outlining an alternative means of analyzing these networks, by focusing analysis on the Lipschitz matrix of the relatively low-dimensional undelayed network. The key criteria, intrinsic stability, is computationally efficient to verify by use of the power method. We demonstrate applications from control theory and neural networks.

Regular Fibrations Over The Hawaiian Earring, Stewart Mason Mcginnis

Theses and Dissertations

We present a family of fibrations over the Hawaiian earring that are inverse limits of regular covering spaces over the Hawaiian earring. These fibrations satisfy unique path lifting, and as such serve as a good extension of covering space theory in the case of nonsemi-locally simply connected spaces. We give a condition for when these fibrations are path-connected.

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

Atmospheric Propagation Of High Energy Lasers: Thermal Blooming Simulation, Jonathan Gustafsson, Benjamin F. Akers, Jonah A. Reeger, Sivaguru S. Sritharan

Faculty Publications

High Energy Laser (HEL) propagation through turbulent atmosphere is examined via numerical simulation. The beam propagation is modeled with the paraxial equation, which in turn is written as a system of equations for a quantum fluid, via the Madelung transform. A finite volume solver is applied to the quantum fluid equations, which supports sharp gradients in beam intensity. The atmosphere is modeled via a coupled advection-diffusion equation whose initial data have Kolmogorov spectrum. In this model the combined effects of thermal blooming, beam slewing, and deep turbulence are simulated.

“Diabesity” Among Latinos: A Culturally Relevant Mathematics Activity By A Mathematics Teacher Candidate, Olga Ramirez, Cherie Mccollough

School of Mathematical & Statistical Sciences Faculty Publications

This paper summarizes a culturally relevant mathematics project conducted by a mentored secondary-level Latino teacher candidate (TC) as a requirement for an undergraduate mathematics project course at a south Texas university. The culturally relevant math project involved four secondary Latino students and their parents. The topic was “diabesity”; that is, diabetes and obesity among Latinos southern region in the United States of America with an emphasis on body mass index, proper diet, and exercise. Remarks by the faculty mentor and a faculty consultant about the TC work and reflections regarding this project are also included and provide perspectives on how …

Non-Finitely Based Finite Involution Semigroups With Finitely Based Semigroup Reducts, Edmond W. H. Lee

Mathematics Faculty Articles

Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.

A Key Note On Performance Of Smoothing Parameterizations In Kernel Density Estimation, Israel U. Siloko, Osayomore Ikpotokin, Edith A. Siloko

Tanzania Journal of Science

The univariate kernel density estimator requires one smoothing parameter while the bivariate and other higher dimensional kernel density estimatorsdemand more than one smoothing parameter depending on the form of smoothing parameterizations used. The smoothing parameters of the higher dimensional kernels are presented in a matrix form called the smoothing matrix. The two forms of parameterizations frequently used in higher dimensional kernel estimators are diagonal or constrained parameterization and full or unconstrained parameterization. While thefull parameterization has no restrictions, the diagonal hassome form of restrictions.Thestudyinvestigates the performance of smoothing parameterizations of bivariate kernel estimator using asymptotic mean integrated squared error aserror …

A Key Note On Performance Of Smoothing Parameterizations In Kernel Density Estimation, Israel U. Siloko, Osayomore Ikpotokin, Edith A. Siloko

Tanzania Journal of Science

The univariate kernel density estimator requires one smoothing parameter while the bivariate and other higher dimensional kernel density estimatorsdemand more than one smoothing parameter depending on the form of smoothing parameterizations used. The smoothing parameters of the higher dimensional kernels are presented in a matrix form called the smoothing matrix. The two forms of parameterizations frequently used in higher dimensional kernel estimators are diagonal or constrained parameterization and full or unconstrained parameterization. While thefull parameterization has no restrictions, the diagonal hassome form of restrictions.Thestudyinvestigates the performance of smoothing parameterizations of bivariate kernel estimator using asymptotic mean integrated squared error aserror …

Relaxed Strong Colorings Of Hypergraphs, Harrison Piehowski

Undergraduate Research Symposium 2019

No abstract provided.

The Knill Graph Dimension From Clique Cover, Evatt Salinger, Dr. Kassahun Betre

Seaver College Research And Scholarly Achievement Symposium

In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim (G1 + G2) = 1 + dim G1 + dim G2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order KN will have dimension N − 1.

Association Of Rare Coding Mutations With Alzheimer Disease And Other Dementias Among Adults Of European Ancestry, Devanshi Patel, Jesse Mez, Badri N. Vardarajan, Lyndsay Staley, Jaeyoon Chung, Xiaoling Zhang, John J. Farrell, Michael J. Rynkiewicz, Lisa A. Cannon-Albright, Craig C. Teerlink, Jeffery Stevens, Chris Corcoran, Et Al.

Mathematics and Statistics Faculty Publications

IMPORTANCE Some of the unexplained heritability of Alzheimer disease (AD) may be due to rare variants whose effects are not captured in genome-wide association studies because very large samples are needed to observe statistically significant associations.

OBJECTIVE To identify genetic variants associated with AD risk using a nonstatistical approach.

DESIGN, SETTING, AND PARTICIPANTS Genetic association study in which rare variants were identified by whole-exome sequencing in unrelated individuals of European ancestry from the Alzheimer’s Disease Sequencing Project (ADSP). Data were analyzed between March 2017 and September 2018.

MAIN OUTCOMES AND MEASURES Minor alleles genome-wide and in 95 genes previously associated …

Assessing The Likelihood Of Having False Positives Caused By Population Stratification, Renfang Jiang, Jianping Dong

Michigan Tech Publications, Part 1

Population stratification is always a concern in association analysis. There is a debate on the extent of the problem in less extreme situations (Thomas and Witte [1], Wacholder et al. [2]). Wacholder et al.[3] and Ardlie et al. [4] showed that hidden population structure is not a serious threat to case-control designs. We propose a method of assessing the seriousness of the population stratification before designing association studies. If population stratification is not a serious problem, one may consider using case-control study instead of family-based design to get more power. In a case-control design, we compare chi-square …

Linear Operators That Preserve The Genus Of A Graph, Leroy B. Beasley, Jeong Han Kim, Seok-Zun Song

Mathematics and Statistics Faculty Publications

A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k−1. A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k+1 to graphs …

Reflection Positivity: A Quantum Field Theory Connection, Joseph W. Grenier

LSU Doctoral Dissertations

At the heart of constructive quantum field theory lies reflection positivity. Through its use one may extend results for a Euclidean field theory to a relativistic theory. In this dissertation we connect functorial and constructive quantum field theories through reflection positivity. In 2014 Santosh Kandel constructed examples of $d$-dimensional functorial QFTs when $d$ is even. We define functorial reflection positivity and show that this functorial theory is a reflection positive theory. We go on to show that every reflection positive theory produces a reflection positive Hilbert space. Iterated doubles are then introduced and used as a starting point to produce …

University Scholar Series: Tatiana Shubin, Tatiana Shubin

University Scholar Series

Moving in Circles: the Beauty and Joy of Mathematics for Everyone

Tatiana Shubin joined the faculty of San Jose State University in 1985 after earning her Ph.D. in Math­ematics from University of California, Santa Barbara. In 1998, she founded San Jose Math Circle and the Bay Area Math Adventures. In 2006, Shubin became a co-founder of the first Math Teachers' Circle in the US. This circle proved to be a seed which germinated to produce the entire Math Teachers' Circle Network. She launched the Navajo Nation Math Circles project in 2012, became a co-founder and co-director of the Alliance of …

Critical Mathematical Inquiry

Occasional Paper Series

Welcome to Issue 41 of Bank Street’s Occasional Paper Series. The issue features a collection of papers by authors with a shared affinity for the work of critical mathematical inquiry (CMI). In what follows, we present our framing of mathematics education as a participatory venue for CMI and situate it in the context of another, perhaps more familiar approach to teaching mathematics for social justice (TMfSJ).

Piezoelectric Sensor Crack Detection On Airframe Systems, Kevin J. Lin

Theses and Dissertations

In 2008, the Department of Defense published a guidebook for a methodology named Condition-Based Maintenance Plus (CBM+) which capabilities include improving productivity, shortening maintenance cycles, lowering costs, and increasing availability and reliability. This push replaces existing inspection criteria, often conducted as non-destructive testing (NDT), with structural health monitoring (SHM) systems. The SHM system addressed utilizes guided Lamb waves generated by piezoelectric wafer active sensors (PWAS) to detect the existence, size, and location of damage from through-thickness cracks around a rivet hole. The SHM field lacks an experiment testing how small changes in receiver sensor distances affect damage detection. In addition, …

Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas

Theses and Dissertations

Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in …

Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt

Theses and Dissertations

An equiangular tight frame (ETF) is a sequence of equal-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs, which are formed by restricting the characters of a finite abelian group to a difference set. Recently, it was shown that some harmonic ETFs are themselves comprised of regular simplices. In this thesis, we continue the …

The Systems Of Post And Post Algebras: A Demonstration Of An Obvious Fact, Daviel Leyva

USF Tampa Graduate Theses and Dissertations

In 1942, Paul C. Rosenbloom put out a definition of a Post algebra after Emil L. Post published a collection of systems of many–valued logic. Post algebras became easier to handle following George Epstein’s alternative definition. As conceived by Rosenbloom, Post algebras were meant to capture the algebraic properties of Post’s systems; this fact was not verified by Rosenbloom nor Epstein and has been assumed by others in the field. In this thesis, the long–awaited demonstration of this oft–asserted assertion is given.

After an elemental history of many–valued logic and a review of basic Classical Propositional Logic, the systems given …

Analyses Of Unorthodox Overlapping Gene Segments In Oxytricha Trifallax, Shannon Stich

USF Tampa Graduate Theses and Dissertations

A ciliate is a phylum of protozoa that has two types of nuclei, macronuclei and micronuclei. There may be more than one of each type of nucleus in the organism [1]. The macronucleus is the structure where protein synthesis and cell metabolism occur [1]. The micronucleus stores genetic information and is mobilized during a sexual reproduction process called conjugation [1]. The somatic macronucleus (MAC) is developed from the germ-line micronucleus (MIC) through genome rearrangement during a sexual reproduction process called conjugation [6, 8]. Segments of the MIC that form the MAC during conjugation are called macronuclear destined sequences (MDSs) [8]. …

Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda

Theses and Dissertations

High-speed Schlieren photography was utilized to visualize flow in the Air Force Research Laboratory Mach 6 Ludwieg tube facility. A 7° half-angle cone/flare model with variable nosetip radius and flare angle options was used in the study. Testing was performed at two driver tube pressures, generating freestream Reynolds numbers of 10.0x10⁶ and 19.8x10⁶ per meter. The variable-angle flare portion of the model provided a method for adjusting the intensity of the adverse pressure gradient at the cone/flare junction. As expected from existing literature, boundary layer separation along the cone frustum occurred further upstream as the magnitude of the …

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

Theses and Dissertations

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research …

Solving The Traveling Salesman Problem Using Ordered-Lists, Petar D. Jackovich

Theses and Dissertations

The arc-greedy heuristic is a constructive heuristic utilized to build an initial, quality tour for the Traveling Salesman Problem (TSP). There are two known sub-tour elimination methodologies utilized to ensure the resulting tours are viable. This thesis introduces a third novel methodology, the Greedy Tracker (GT), and compares it to both known methodologies. Computational results are generated across multiple TSP instances. The results demonstrate the GT is the fastest method for instances below 400 nodes while Bentley's Multi-Fragment maintains a computational advantage for larger instances. A novel concept called Ordered-Lists is also introduced which enables TSP instances to be explored …

Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, Brendon T. Sands

Theses and Dissertations

While modern day weather forecasting is not perfect, there are many benefits given by the multitude and variety of predictive models. In the interest of routing airplanes, this paper uses time series analysis on successive weather forecasts to predict the optimal path and fuel burn of wind-based, fuel-burn networks with stochastic correlated arcs. Networks are populated with either deterministic or ensemble-based weather data, and the two data sources with and without time series analysis are compared. Methods were compared by fuel burn prediction accuracy and ability to predict a future optimal path. Of the four options, the ensemble-based methods were …