Mathematics Commons^™

Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.

Mode-Sum Prescription For Vacuum Polarization In Black Hole Spacetimes In Even Dimensions, Peter Taylor, Cormac Doran

Articles

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function f(r). As an explicit example of our method, we …

Wavelet Neural Network Model For Yield Spread Forecasting, Firdous Ahmad Shah, Lokenath Debnath

School of Mathematical & Statistical Sciences Faculty Publications

In this study, a hybrid method based on coupling discrete wavelet transforms (DWTs) and artificial neural network (ANN) for yield spread forecasting is proposed. The discrete wavelet transform (DWT) using five different wavelet families is applied to decompose the five different yield spreads constructed at shorter end, longer end, and policy relevant area of the yield curve to eliminate noise from them. The wavelet coefficients are then used as inputs into Levenberg-Marquardt (LM) ANN models to forecast the predictive power of each of these spreads for output growth. We find that the yield spreads constructed at the shorter end and …

Edge Colorings Of Complete Multipartite Graphs Forbidding Rainbow Cycles, Peter Johnson, Andrew Owens

Theory & Applications of Graphs

It is well known that if the edges of a finite simple connected graph on n vertices are colored so that no cycle is rainbow, then no more than n-1 colors can appear on the edges. In previous work it has been shown that the essentially different rainbow-cycle-forbidding edge colorings of K_n with n-1 colors appearing are in 1-1 correspondence with (can be encoded by) the (isomorphism classes of) full binary trees with n leafs. In the encoding, the natural Huffman labeling of each tree arising from the assignment of 1 to each leaf plays a role. Very recently …

Stability Of Equilibria In Quantitative Genetic Models Based On Modified-Gradient Systems, Benjamin J. Ridenhour, Jerry R. Ridenhour

Mathematics and Statistics Faculty Publications

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system x′ = P(t)∇f(x) which arise as critical points of f, under the assumption that P(t) is positive semi-definite. It is shown that the condition ∫^∞λ₁(P(t)) dt = ∞, where λ₁(P(t)) is the smallest eigenvalue of P(t), plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.

Generalized D-Kaup-Newell Integrable Systems And Their Integrable Couplings And Darboux Transformations, Morgan Ashley Mcanally

USF Tampa Graduate Theses and Dissertations

We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries, i.e., they are Liouville integrable.

We use the soliton hierarchies and a non-seimisimple matrix loop Lie algebra in order …

Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward

Mathematics & Statistics ETDs

At The University of New Mexico (UNM), Intermediate Algebra (MATH 120 and MATH 101-102-103) has historically been a so-called “killer course”, with very low pass rates: approximately 40% in Fall 2009 to Spring 2011 and about 50% from Fall 2011 to Spring 2013. Furthermore, many students failed the class multiple times. Since 2013, a computer system called ALEKS has been used to teach the course and, along with some additional interventions, on Albuquerque/Main campus success rates for MATH 101 have increased to roughly 80% and MATH 102 to about 70%. This thesis provides a strategy to identify those 20-30% as-risk …

Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry

LSU Doctoral Dissertations

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …

Estimating Memory Deterioration Rates Following Neurodegeneration And Traumatic Brain Injuries In A Hopfield Network Model, Melanie Weber, Pedro D. Maia, J. Nathan Kutz

Mathematics Faculty Publications - Archive

Neurodegenerative diseases and traumatic brain injuries (TBI) are among the main causes of cognitive dysfunction in humans. At a neuronal network level, they both extensively exhibit focal axonal swellings (FAS), which in turn, compromise the information encoded in spike trains and lead to potentially severe functional deficits. There are currently no satisfactory quantitative predictors of decline in memory-encoding neuronal networks based on the impact and statistics of FAS. Some of the challenges of this translational approach include our inability to access small scale injuries with non-invasive methods, the overall complexity of neuronal pathologies, and our limited knowledge of how networks …

An Answer To A Question Of A. Lubin: The Lifting Problem For Commuting Subnormals, Sang Hoon Lee, Woo Young Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we give an answer to a long-standing open question on the lifting problem for commuting subnormals (due to A. Lubin): The subnormality for the sum of commuting subnormal operators does not guarantee the existence of commuting normal extensions.

A Class Of Transformations Of A Quadratic Integral Generating Dynamical Systems, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A class of transformation is investigated which maps a quadratic integral back to its original form but under a redefinition of free parameters. When this process is iterated, a dynamical system is generated in the form of recursive sequences which involve the parameters of the integrand.

The creation of this dynamical system and some of its convergence properties are investigated.

MR3724632

On Extending Hansel's Theorem To Hypergraphs, Gregory Sutton Churchill

USF Tampa Graduate Theses and Dissertations

For integers $n \geq k \geq 2$, let $V$ be an $n$-element set, and let $\binom{V}{k}$ denote the family of all $k$-element subsets of $V$. For disjoint subsets $A, B \subseteq V$, we say that $\{A, B\}$ {\it covers} an element $K \in \binom{V}{k}$ if $K \subseteq A \dot\cup B$ and $K \cap A \neq \emptyset \neq K \cap B$. We say that a collection $\cC$ of such pairs {\it covers} $\binom{V}{k}$ if every $K \in \binom{V}{k}$ is covered by at least one $\{A, B\} \in \cC$. When $k=2$, covers $\cC$ of $\binom{V}{2}$ were introduced in~1961 by R\'enyi~\cite{Renyi}, where they …

Apathy And Concern Over The Future Habitability Of Earth: An Introductory College Assignment Of Forecasting Co2 In The Earth’S Atmosphere, Benjamin J. Burger

Journal on Empowering Teaching Excellence

Non-science, first year regional undergraduate students from rural Utah communities participated in an online introductory geology course and were asked to forecast the rise of CO₂ in the Earth’s atmosphere. The majority of students predicted catastrophic rise to 5,000-ppm sometime over the next 3,100 years, resulting in an atmosphere nearly uninhabitable to human life. However, the level of concern the students exhibited in their answers was not directly proportional with their timing in their forecasted rise of CO₂. This study showcases the importance of presenting students with actual data and using data to develop student forecasted models. …

A Geometric Formulation Of Lax Integrability For Nonlinear Equationsin Two Independent Variables, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A geometric formulation of Lax integrability is introduced which makes use of a Pfaffan formulation of Lax integrability. The Frobenius theorem gives a necessary and suffcient condition for the complete integrability of a distribution, and provides a powerful way to study nonlinear evolution equations. This permits an examination of the relation between complete integrability and Lax integrability. The prolongation method is formulated in this context and gauge transformations can be examined in terms of differential forms as well as the Frobenius theorem.

Borges And The Subjective-Idealism In Relativity Theory And Quantum Mechanics, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is intended to be a follow-up to our previous paper with title: "Reinterpreting Tlon, Uqbar, Orbis Tertius: On the antirealism tendency in modern physics." We will give more background for our propositions in the previous paper. Our message here is quite simple: allow us to remind fellow physicists and cosmologists to become more aware of Berkeley-idealism tendency, which can lead us to so many distractions instead of bringing us closer to the truth. We observe that much of the progress of modern physics in the last few decades only makes us as confused as before, but at a …

The Classification Of Infinite Abelian Groups With Partial Decomposition Bases In L∞Ω, Carol Jacoby, Peter Loth

Mathematics Faculty Publications

We consider the class of abelian groups with partial decomposition bases, which includes groups classified by Ulm, Warfield, Stanton and others. We define an invariant and classify these groups in the language L∞ω, or equivalently, up to partial isomorphism. This generalizes a result of Barwise and Eklof and builds on Jacoby's classification of local groups with partial decomposition bases in L∞ω.

Relativity From Mathematics Or Why Newton Could Have Beaten Einstein To The Punch, Diego Castano

Mathematics Colloquium Series

Special Relativity was developed by Albert Einstein and relied crucially on Electromagnetism, a theory not fully developed until 1873. Yet there is nothing in the basic theory's development that requires physics beyond what Newton knew. A derivation of the theory based on Newton's laws and mathematical consistency is presented.

Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn–Hilliard–Navier–Stokes equations with matched densities. the scheme combines a standard second order Crank–Nicolson method for the Navier–Stokes equations and a modification to the Crank–Nicolson method for the Cahn–Hilliard equation. in particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn–Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown …

Combustion-Derived Nanoparticles, The Neuroenteric System, Cervical Vagus, Hyperphosphorylated Alpha Synuclein And Tau In Young Mexico City Residents, Lilian Calderón-Garcidueñas, Rafael Reynoso-Robles, Beatriz Pérez-Guillé, Partha S. Mukherjee, Angélica Gónzalez-Maciel

Mathematics Faculty Publications and Presentations

Mexico City (MC) young residents are exposed to high levels of fine particulate matter (PM_2.5), have high frontal concentrations of combustion-derived nanoparticles (CDNPs), accumulation of hyperphosphorylated aggregated α-synuclein (α-Syn) and early Parkinson's disease (PD). Swallowed CDNPs have easy access to epithelium and submucosa, damaging gastrointestinal (GI) barrier integrity and accessing the enteric nervous system (ENS). This study is focused on the ENS, vagus nerves and GI barrier in young MC v clean air controls. Electron microscopy of epithelial, endothelial and neural cells and immunoreactivity of stomach and vagus to phosphorylated ɑ-synuclein Ser129 and Hyperphosphorylated-Tau (Htau) …

Biomarkers Of Cardiovascular Disease, Ying Huang, Kailash Gulshan, Truc Nguyen, Yuping Wu

Mathematics and Statistics Faculty Publications

No abstract provided.

2017: "Lighting Up The Night", Shyam Sai, Istvan Kovach, Abhay Gupta, James Wei

Distinguished Student Work

Drone technology is beginning to permeate many aspects of life in the modern world, and for good reason. Delivery drones can efficiently deliver packages better than any existing methods. Medical drones can reach emergency patients faster than any ambulance. Security drones can surveil areas more quickly and more thoroughly than a team of human guards. The advent of commercial and industrial uses for drones, however, begets the vital question of how can drones be used outside the workplace. Intel's answer? Entertainment.

Thus, the Intel Shooting Star^TM drone was born, a quadcopter explicitly built for producing breathtaking aerial light shows …

2017: "The Wasatch Range Ski-Matic", Andy Liu, Bert Cao, Joshua Eberhardt, Allen Chen

Distinguished Student Work

Ski resorts are very popular among both avid skiers and families who are looking to have fun. In fact, winter resorts account for over 3 billion dollars in revenue, with an annual growth of 2.6% [IBI]. In addition to their use as recreational areas, ski resorts are also used for various winter competitions, most famously the Olympics. Our job was to design and create a suitable ski resort for both the Olympics and for recreational use in the Wasatch Peaks Range property. In addition, we were advised to create over 160km of trails and maintain a 20%- 40%-40% balance between …

2017: Himcm International Mathematics Modeling Contest: Finalist Rating, Aryan Walia, Katie Lu, Mia Ye, Kevin Mikos

Distinguished Student Work

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken into account including the …

2017: Himcm International Mathematics Modeling Contest: Meritorious Rating, Spoorthi Jakka, Claire Wang, Amy Wang, Claudia Zhu '18

Distinguished Student Work

Restatement of the Problem:

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken …

A High Quality, Eulerian 3d Fluid Solver In C++, Lejon Anthony Mcgowan

Computer Science and Software Engineering

Fluids are a part of everyday life, yet are one of the hardest elements to properly render in computer graphics. Water is the most obvious entity when thinking of what a fluid simulation can achieve (and it is indeed the focus of this project), but many other aspects of nature, like fog, clouds, and particle effects. Real-time graphics like video games employ many heuristics to approximate these effects, but large-scale renderers aim to simulate these effects as closely as possible.

In this project, I wish to achieve effects of the latter nature. Using the Eulerian technique of discrete grids, I …

Cardinal Characteristics And Countable Borel Equivalence Relations, Samuel Coskey, Scott Schneider

Mathematics Faculty Publications and Presentations

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number ��. We analyze some of the basic behavior of these properties, showing, e.g., that the property corresponding to the splitting number �� coincides with smoothness. We then settle many of the implication relationships between the properties; …

On The Finite W-Algebra For The Lie Superalgebra Q(N) In The Non-Regular Case, Elena Poletaeva, Vera Serganova

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the finite W-algebra for the queer Lie superalgebra Q(N) associated with the non-regular even nilpotent coadjoint orbits in the case when N = nl, and the corresponding nilpotent element has Jordan blocks each of size l. We prove that this finite W-algebra is isomorphic to a quotient of the super-Yangian of Q(n).

Perpetual Integral Functionals Of Brownian Motion And Blowup Of Semilinear Systems Of Spdes, Eugenio Guerrero, José Alfredo López-Mindela

Communications on Stochastic Analysis

No abstract provided.

The Moments Of Lévy's Area Using A Sticky Shuffle Hopf Algebra, Robin Hudson, Uwe Schauz, Yue Wu

Communications on Stochastic Analysis

No abstract provided.

Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara

Branch Mathematics and Statistics Faculty and Staff Publications

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.