Physical Sciences and Mathematics Commons^™

Estimation Of The Kelvin–Helmholtz Unstable Boundary, Xuanye Ma

Publications

The Kelvin–Helmholtz (KH) instability is one of the most important mechanisms of the viscous like interaction between the solar wind and the magnetosphere (MSP), which transport the mass, energy, momentum, and magnetic flux. Thus, it is important to examine whether the magnetopause boundary is KH unstable or not. Based on the KH onset conditions, this report proposes to use a matrix to identify the most KH unstable direction based on the in-situ measurements of the density, velocity, and magnetic field in the MSP and magneto sheath. The range of the KH unstable direction can be easily estimated based on the …

Modeling Exciton Migration In Two-Dimensional Space, Christian D. Etnyre

DePaul Discoveries

Computational analysis through density matrix quantum mechanics was performed to model exciton migration in two-dimensional space for a zinc-substituted tetraazaphthalocyanine. The model produced resembles a two-dimensional sheet of molecules. Energy transport mechanisms, controlled by point dipole couplings, were evaluated while altering the size of the crystal lattice. It was determined that energy transport was much more significant with a decreasing size of the crystal lattice. Likewise, the result of increasing the size of the crystal lattice had the effect of dampening the rate of energy transport. It was of interest to determine, with varying crystal lattice dimensions, the time that …

The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall

Honors Theses

One can see that this matrix is unitary and has eigenvalues {1,−i,−1, I}, each of infinite multiplicity. Throughout the remainder of this thesis, we will convince the reader that the above linear transformation is actually the Fourier transform. We will compute the commutant, as well as its invariant subspaces. The key to do this relies on the Hermite polynomials. Why do we recast the Fourier transform from its well-known and well studied integral form to the matrix form shown above? As we will see, the matrix form allows us to efficiently discover the operator theory of the Fourier transform obfuscated …

Carbon Dioxide Capture Potential Of Chitosan-Nanocrystalline Cellulose Aerogel Composite Materials: Synthesis, Functionalization, And Characterization, Victor Oghenekohwo

Theses and Dissertations

The carbon dioxide capture technology has been established as an invaluable player in the current global efforts to allay the warming of the planet and climate change. In this connection, the study centers on the valorization of waste organic materials for the application described herein. The sorbents, sourced from a combination of by-products of food processing and agricultural residue waste products, viz. seafood waste and sugarcane bagasse, showed prospects for selective carbon dioxide capture, adsorbing up to 5.78 mg/g of the gas at 273 K and 2.82 mg/g at 298 K, as observed on the Micromeritic ASAP 2020 surface area …

The Matrix Sortability Problem, Seth Cleaver

Boise State University Theses and Dissertations

Sorting is such a fundamental component of achieving efficiency that a significant body of mathematics is dedicated to the investigation of sorting. Any modern textbook on algorithms contains chapters on sorting.

One approach to arranging a disorganized list of items into an organized list is to successively identify two blocks of contiguous items, and swap the two blocks. In a fundamental paper D.A. Christie showed that a special version of block swapping, in recent times called context directed swapping and abbreviated cds, is the most efficient among block swapping strategies to achieve an organized list of items. The cds …

An Application Of Matrices To The Spread Of The Covid 19, Selena Suarez

Theses and Dissertations

We represented a restaurant seating arrangement using matrices by using 0 entry for someone without covid and 1 entry for someone with covid. Using the matrices we found the best seating arrangements to lessen the spread of covid. We also investigated if there was a factor needed to create a formula that could calculate the matrix that shows who would be affected with covid with each seating arrangement. However, there did not seem to be a clear pattern within the factors. Aside from covid applications, we also investigated the symmetries in seating arrangements and the possible combinations with these arrangements …

The Ion Pair Thermal Model Of Maldi Ms, Shiyue Fang

Michigan Tech Publications

The ion pair thermal model for MALDI MS is described. Key elements of the model include thermal desorption and ionization, strong tendency to neutralization via ion pair formation and proton transfer in the gas phase, thermal equilibrium, overall charge neutral plume, and thermal energy assisted free ion generation via ion pair separation by ion extraction potential. The quantities of ions in the solid sample and in the gaseous plume are estimated. Ion yields of different classes of molecules including peptides, nucleic acids, permanent salts and neutral molecules are estimated at the macroscale and single ion pair levels. The estimated ion …

Lecture 11: The Road To Exascale And Legacy Software For Dense Linear Algebra, Jack Dongarra

Mathematical Sciences Spring Lecture Series

In this talk, we will look at the current state of high performance computing and look at the next stage of extreme computing. With extreme computing, there will be fundamental changes in the character of floating point arithmetic and data movement. In this talk, we will look at how extreme-scale computing has caused algorithm and software developers to change their way of thinking on implementing and program-specific applications.

The Effects Of Increasing Positively Charged Metal Ions Within Synovial Fluid, Kandisi Anyabwile

Williams Honors College, Honors Research Projects

Osteoarthritis is a degenerative joint disease that affects 10% of men and 13% of women over age of 60. It is the degradation of the cartilage between two bones; obesity, age, overuse, or injury are major contributors to the development of this disease. The joint is incapsulated by the synovial sac filled with a viscous solution that aids in lubrication referred to as synovial fluid. If the synovial sac is ruptured due to injury, positive ions (K⁺, Na⁺, Ca²⁺, and Fe³⁺) may affect viscoelastic properties within the sac. The purpose of this …

Modified Hermite Operational Matrix Method For Nonlinear Lane-Emden Problem, Bushra Esaa Kashem

Al-Qadisiyah Journal of Pure Science

Nonlinear Lane –Emden equations are significant in astrophysics and mathematical physics. The aim of this paper is submitted a new approximate method for finding solution to nonlinear Lane-Emden type equations appearing in astrophysics based on modified Hermite integration operational matrix. The suggest technique is based on taking the truncated modified Hermite series of the solution function in the nonlinear Lane-Emden equation and then changed into a matrix equation with the given conditions. Nonlinear system of algebraic equation using collection points is obtained. The present method is applied on some relevant physical problems as nonlinear Lane-Emden type equations.

Demonstrating And Testing The Deutsch-Jozsa Quantum Algorithm Towards The Realization Of Quantum Computing At Bsu, John J. Gilmore Jr.

Honors Program Theses and Projects

The world is changing, and fast. Quantum computing and photonic engineering are revolutionary new technologies that could change the way humans interact with information; though the eld hasn't always been that way. As with most new elds, proof of concept is needed to show that this new technology isn't just hear to stay, but it's hear to take the lead. In this, nothing is more important the the Deutsch-Jozsa Quantum algorithm; as it did just that . The majority of this research paper revolves around understanding the very essence of quantum computing. As the eld of quantum computing is in …

Boundary Theorem Of Morera In The Space Of Rectangular Matrices, B. T. Kurbanov

Karakalpak Scientific Journal

In the theory of functions of one complex variable, Morer's theorem is known, which is inverse in some sense to the classical Cauchy theorem. On the complex plane, results on functions with the one-dimensional property of holomorphic continuation are trivial, and Morer's boundary theorems are absent. We note that the ordinary (non-boundary) Morera theorems in domains of space are well known. The first result related to our topic was obtained by Agranovsky M.L. and Valsky R.E. [1], who studied functions with the one-dimensional property of holomorphic continuation in a ball. The proof was based on the properties of the automorphism …

Deepcon-Pre: Improved Protein Contact Map Prediction Using Inverse Covariance And Deep Residual Networks, Nachammai Palaniappan

Theses

As with most domains where machine learning methods are applied, correct feature engineering is critical when developing deep learning algorithms for solving the protein folding problem. Unlike the domains such as computer vision and natural language processing, feature engineering is not rigorously studied towards solving the protein folding problem. A recent research has highlighted that input features known as precision matrix are most informative for predicting inter-residue contact map, the key for building three-dimensional models. In this work, we study the significance of the precision matrix feature when very deep residual networks are trained. Using a standard dataset of 3456 …

The Relative Effects Of Forest Amount, Forest Configuration, And Urban Matrix Quality On Forest Breeding Birds, Alexandra V. Shoffner, Andrew M. Wilson, Wenwu Tang, Sara A. Gagné

Environmental Studies Faculty Publications

Urbanization modifies landscape structure in three major ways that impact avian diversity in remnant habitat: habitat amount is reduced and habitat configuration and matrix quality are altered. The relative effects of these three components of landscape structure are relatively well-studied in agricultural landscapes, but little is known about the relative effect of urban matrix quality. We addressed this gap by investigating the relative effects of forest amount, forest configuration, and matrix quality, indicated by degree of urbanization and agriculture amount, on the diversity of three guilds of forest birds using data from 13,763 point counts from Pennsylvania, USA. Forest amount …

Hybrid Recommender For Online Petitions With Social Network And Psycholinguistic Features, Ahmed Elnoshokaty

Masters Theses & Doctoral Dissertations

The online petition has become one of the most important channels of civic participation. Most of the state-of-the-art online platforms, however, tend to use simple indicators (such as popularity) to rank petitions, hence creating a situation where the most popular petitions dominate the rank and attract most people’s attention. For the petitions which focus on specific issues, they are often in a disadvantageous position on the list. For example, a petition for local environment problem may not be seen by many people who are really concerned with it, simply because it takes multiple pages to reach it. Therefore, the simple …

Using Explainability For Constrained Matrix Factorization, Behnoush Abdollahi, Olfa Nasraoui

Commonwealth Computational Summit

Explainable Model

• Black Box (opaque) predictors such as Deep learning and Matrix Factorization are accurate,
• ... but lack interpretability and ability to give explanations.
• White Box models such as rules and decision trees are interpretable (explainable),
• ... but lack accuracy.

Classification Results Of Hadamard Matrices, Gregory Allen Schmidt

Masters Theses

In 1893 Hadamard proved that for any n x n matrix A over the complex numbers, with all of its entries of absolute value less than or equal to 1, it necessarily follows that

|det(A)| ≤ n^n/2 [n raised to the power n divided by two],

with equality if and only if the rows of A are mutually orthogonal and the absolute value of each entry is equal to 1 (See [2], [3]). Such matrices are now appropriately identified as Hadamard matrices, which provides an active area of research in both theoretical and applied fields …

Engineering Electron Superpositions Using A Magnetic Field, Zoe A. Rowley, Bianca R. Gualtieri

Physics and Astronomy Summer Fellows

A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other.

Our goal is to be …

Solving The Yang-Baxter Matrix Equation, Mallory O. Jennings

Honors Theses

The Yang-Baxter equation is one that has been widely used and studied in areas such as statistical mechanics, braid groups, knot theory, and quantum mechanics. While many sets of solutions have been found for this equation, it is still an open problem. In this project, I solve the Yang-Baxter matrix equation that is similar in format to the Yang-Baxter equation. I try to solve the corresponding Yang-Baxter matrix equation, ������=������, where X is an unknown ������ matrix, and ��=[0����0] or [0−��−��0], by using the Jordan canonical form to find infinitely many solutions.

Structured Pseudospectra Of Block Matrix Structures, Richard Eric Ferro

Legacy Theses & Dissertations (2009 - 2024)

The study of pseudospectra Λε(A) dates back to the 1980s when it became an important analytical and graphical alternative for investigating non-normal matrices and operators. The interest in pseudospectra was further stimulated in the 1990s by the increasing avail- ability of numerical software such as Matlab, Eigtool and Seigtool. The main reason for the importance of pseudospectra is that eigenvalue analysis of non-self-adjoint operators can be misleading, which is most easily seen by looking at the 2-norm pseudospectra of non- normal matrices whose eigenvectors are not orthogonal. Many of the advances in the field are due to interactions between pure …

A Stochastic Model For Landscape Patterns Of Biodiversity, Jayme A. Prevedello, Nicholas J. Gotelli, Jean Paul Metzger

College of Arts and Sciences Faculty Publications

Many factors have been proposed to affect biodiversity patterns across landscapes, including patch area, patch isolation, edge distances, and matrix quality, but existing models emphasize only one or two of these factors at a time. Here we introduce a synthetic but simple individual-based model that generates realistic patterns of species richness and density as a function of landscape structure. In this model, we simulated the stochastic placement of home ranges in landscapes, thus combining features of existing random placement and mid-domain effect models. As such, the model allows investigation of whether and how geometric constraints on home range placement of …

Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent

Honors Theses

The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.

Full Isolation Number Of Matrices: Some Extremal Results, David Tate, David Brown

David C. Brown

A set of nonzero entries of a (0,1)-matrix is an isolated set if no two entries belong to the same row, no two entries belong to the same column, and no two entries belong to a submatrix of the form [1 1; 1 1]. The isolation number of a matrix is the maximum size over all isolated sets. The isolation number of a matrix is a well-known and well-used lower bound for the matrix's Boolean rank. We will discuss the isolation number of the adjacency matrix of various graphs and develop some extremal results for n x n matrices with …

On A Generalization Of Kelly's Combinatorial Lemma, Aymen Ben Amira, Jamel Dammak, Hamza Si Kaddour

Turkish Journal of Mathematics

Kelly's combinatorial lemma is a basic tool in the study of Ulam's reconstruction conjecture. A generalization in terms of a family of t -elements subsets of a v -element set was given by Pouzet. We consider a version of this generalization modulo a prime p. We give illustrations to graphs and tournaments.

Effect Of Director Distortions On Morphologies Of Phase Separation In Liquid Crystals, D. Voloschenko, Oleg P. Pishnyak, Sergij V. Shiyanovskii, Oleg Lavrentovich

Oleg Lavrentovich

We study phase separation from a nematic liquid crystal with spatially nonuniform director gradients. Particles of a phase-separated component, which is either an isotropic fluid (silicone oil) or a nonmesogenic photopolymer, accumulate in the regions with the strongest director distortions, thus reducing the overall energy of the system.

Orientation Distribution Of Highly Oriented Type I Collagen Deposited On Flat Samples With Different Geometries, Qamrun Nahar, David Minh Luan Quach, Behafarid Darvish, Harvey A. Goldberg, Bernd Grohe, Silvia Mittler

Physics and Astronomy Publications

The structural arrangement of type I collagen in vivo is critical for the normal functioning of tissues, such as bone, cornea, tendons and blood vessels. At present, there are no established low-cost techniques for fabricating aligned collagen structures for applications in regenerative medicine. Here, we report on a straightforward approach to fabricate collagen films, with defined orientation distributions of collagen fibrillar aggregates within a matrix of oriented collagen molecules on flat sample surfaces. Langmuir Blodgett (LB) technology was used to deposit thin films of oriented type I collagen onto flat substrates exhibiting various shapes. By varying the shapes of the …

Age Estimation Based On Extended Non-Negative Matrix Factorization, Ce Zhan, Wanqing Li, Philip Ogunbona

Associate Professor Wanqing Li

Previous studies suggested that local appearance-based methods are more efficient than geometric-based and holistic methods for age estimation. This is mainly due to the fact that age information are usually encoded by the local features such as wrinkles and skin texture on the forehead or at the eye corners. However, the variations of theses features caused by other factors such as identity, expression, pose and lighting may be larger than that caused by aging. Thus, one of the key challenges of age estimation lies in constructing a feature space that could successfully recovers age information while ignoring other sources of …

Estimation In A Multiplicative Mixed Model Involving A Genetic Relationship Matrix, Alison M. Kelly, Brian R. Cullis, Arthur R. Gilmour, John A. Eccleston, Robin Thompson

Dr Arthur Gilmour

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we …

Estimation In A Multiplicative Mixed Model Involving A Genetic Relationship Matrix, Alison M. Kelly, Brian R. Cullis, Arthur R. Gilmour, John A. Eccleston, Robin Thompson

Professor Brian Cullis

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we …

Age Estimation Based On Extended Non-Negative Matrix Factorization, Ce Zhan, Wanqing Li, Philip Ogunbona

Professor Philip Ogunbona

Previous studies suggested that local appearance-based methods are more efficient than geometric-based and holistic methods for age estimation. This is mainly due to the fact that age information are usually encoded by the local features such as wrinkles and skin texture on the forehead or at the eye corners. However, the variations of theses features caused by other factors such as identity, expression, pose and lighting may be larger than that caused by aging. Thus, one of the key challenges of age estimation lies in constructing a feature space that could successfully recovers age information while ignoring other sources of …