Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network™

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 4171 - 4200 of 27205

Full-Text Articles in Entire DC Network

(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi Oct 2022

(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Interleaving permutes the data bits by employing a user defined sequence to reduce burst error which at times exceeds the minimum hamming distance. It serves as the sole medium to distinguish user data in the overlapping channel and is the heart of Interleave Division Multiple Access (IDMA) scheme. Versatility of interleavers relies on various design parameters such as orthogonality, correlation, latency and performance parameters like bit error rate (BER), memory occupancy and computation complexity. In this paper, a comprehensive study of interleaving phenomenon and discussion on numerous interleavers is presented. Also, the BER performance of interleavers using IDMA scheme is …

Go to article

Conflict Dynamics In Scale-Free Networks With Degree Correlations And Hierarchical Structure, Eduardo Jacobo-Villegas, Bibiana Obregón-Quintana, Lev Guzmán-Vargas, Larry S. Liebovitch Oct 2022

Conflict Dynamics In Scale-Free Networks With Degree Correlations And Hierarchical Structure, Eduardo Jacobo-Villegas, Bibiana Obregón-Quintana, Lev Guzmán-Vargas, Larry S. Liebovitch

Publications and Research

We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor’s state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive
interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions …

Go to article

Graph Neural Networks For Inverse Problems With Flexible Meshes, William Herzberg Oct 2022

Graph Neural Networks For Inverse Problems With Flexible Meshes, William Herzberg

Dissertations (1934 -)

This thesis addresses the electrical impedance tomography (EIT) image reconstruction problem where samples may have irregular discretizations and presents two, new, learned reconstruction algorithms which leverage a graph framework. These new frameworks consider the irregular, non-uniform data as a graph thus allowing graph neural networks to be applied directly to the data defined over irregular meshes. Currently in imaging, convolutional neural networks are used most frequently in learned methods because they are spatially invariant and have the ability to leverage localized information. In addition, many images are represented by rows and columns of uniformly sized pixels which can easily be …

Go to article

Transcriptional Profile Of Cohesin Complex Mutations In The Background Of Npm1 And Runx1-Runx1t1 Aml, Jacob Tiegs Oct 2022

Transcriptional Profile Of Cohesin Complex Mutations In The Background Of Npm1 And Runx1-Runx1t1 Aml, Jacob Tiegs

Master's Theses (2009 -)

Acute Myeloid Leukemia is a cancer of the blood, characterized by a heterogenous mixture of disease causing mutations. Mutations of the cohesin complex is a group of such mutations and occur alongside several other driving mutations in the development of Acute Myeloid Leukemia. This thesis specifically focuses on cohesin complex mutations in the context of concurrence with NPM1 mutation and the Core Binding Factor (CBF) mutation RUNX1-RUNX1T1 in three distinct components. The first two components involved Differential Expression Analysis (DEA) to identify significantly differentiated genes in each model, followed by Gene Set Enrichment Analysis (GSEA) to identify Gene Ontology (GO) …

Go to article

A Mathematical Model For The Energy Stored In Green Roofs, Maria Aguareles, Marc Calvo-Schwarzwalder, Francesc Font, Timothy G. Myers Oct 2022

A Mathematical Model For The Energy Stored In Green Roofs, Maria Aguareles, Marc Calvo-Schwarzwalder, Francesc Font, Timothy G. Myers

All Works

A simple mathematical model to estimate the energy stored in a green roof is developed. Analytical solutions are derived corresponding to extensive (shallow) and intensive (deep) substrates. Results are presented for the surface temperature and energy stored in both green roofs and concrete during a typical day. Within the restrictions of the model assumptions the analytical solution demonstrates that both energy and surface temperature vary linearly with fractional leaf coverage, albedo and irradiance, while the effect of evaporation rate and convective heat transfer is non-linear. It is shown that a typical green roof is significantly cooler and stores less energy …

Go to article

A Mesh-Free Method Using Piecewise Deep Neural Network For Elliptic Interface Problems, Cuiyu He, Xiaozhe Hu, Lin Mu Oct 2022

A Mesh-Free Method Using Piecewise Deep Neural Network For Elliptic Interface Problems, Cuiyu He, Xiaozhe Hu, Lin Mu

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the interface, we employ different neural networks for each sub-domain. By reformulating the interface problem as a least-squares problem, we discretize the objective function using mean squared error via sampling and solve the proposed deep least-squares method by standard training algorithms such as stochastic gradient descent. The discretized objective function utilizes only the point-wise information on the sampling points and thus no underlying mesh …

Go to article

Innovation Transition Success: Practice Doesn't Make Perfect, Kaitlyn Ryan, Amy M. Cox, Ethan Blake, Clay Koschnick, Alfred E. Thal Jr. Oct 2022

Innovation Transition Success: Practice Doesn't Make Perfect, Kaitlyn Ryan, Amy M. Cox, Ethan Blake, Clay Koschnick, Alfred E. Thal Jr.

Faculty Publications

The authors of this research examine and evaluate organizational factors associated with commercialization under the Air Force Small Business Innovation Research (SBIR) program. Their objective is to improve return on investment. The data set used was the SBIR Phase II program data set, which contains information on 433 SBIR topics with closed contracts reported during Department of Defense (DoD) fiscal years (FYs) 2015 to 2018. Each data point contained characteristics of the topic, including commercialization. Military capability or topic areas were hypothesized to have varying commercialization rates. Incumbency was theorized to be a characteristic of successful programs, while increased company …

Go to article

A Mode-Sum Prescription For The Renormalized Stress Energy Tensor On Black Hole Spacetimes, Peter Taylor, Cormac Breen, Adrian Ottewill Sep 2022

A Mode-Sum Prescription For The Renormalized Stress Energy Tensor On Black Hole Spacetimes, Peter Taylor, Cormac Breen, Adrian Ottewill

Articles

In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semiclassical backreaction.

Go to article

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook Sep 2022

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook

CODEE Journal

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …

Go to article

Modelling The Impacts Of Immigrants On Covid 19 Transmission Dynamics With Control Measures, Alfred K. Hugo, Goodluck M. Mlay, Moses B. Kabigi Sep 2022

Modelling The Impacts Of Immigrants On Covid 19 Transmission Dynamics With Control Measures, Alfred K. Hugo, Goodluck M. Mlay, Moses B. Kabigi

Tanzania Journal of Science

The COVID-19 pandemic began in Wuhan City in the Hubei province of China in December 2019. The disease spread quickly in many countries around the world due to mobility of people from one location to another. As a result, a COVID-19 mathematical model with the impacts on immigrants was proposed to study its transmission dynamics and possible control measures. The reproduction number was determined by using the next-generation technique and found to be 0.636, indicating that the transmission could be minimized in the community if all immigrants were effectively controlled. The Pontryagin's Maximum Principle was applied in analysing control strategies …

Go to article

Dynamical Analysis And Control Strategies For Capturing The Spread Of Covid-19, Mutairu K. Kolawole, Kazeem A. Odeyemi, Adedapo I. Alaje, Asimuyu O. Oladapo, Kehinde A. Bashiru Sep 2022

Dynamical Analysis And Control Strategies For Capturing The Spread Of Covid-19, Mutairu K. Kolawole, Kazeem A. Odeyemi, Adedapo I. Alaje, Asimuyu O. Oladapo, Kehinde A. Bashiru

Tanzania Journal of Science

In this paper, a study of preventive measures capable of curbing the spread of COVID 19 pandemic to avoid its second wave was carried out. The existence and uniqueness of the proposed mathematical model is assured, the basic reproduction number is established, the local and global stability of the disease free equilibrium are well obtained and the variational iteration method is applied to solve the mathematical model. Numerical simulation of the included control parameters are carried out. The obtained results and outcomes are presented graphically. It was revealed that enlightenment to vaccination awareness should be encouraged as vaccination is a …

Go to article

Quantization Of The Boolean Poisson Central Limit Theorem And A Generalized Boolean Bernoulli Sequence, Yungang Lu Sep 2022

Quantization Of The Boolean Poisson Central Limit Theorem And A Generalized Boolean Bernoulli Sequence, Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Go to article

A Question Of Fundamental Methodology: Reply To Mikhail Katz And His Coauthors, Tom Archibald, Richard T. W. Arthur, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper Lützen, Marco Panza, David Rabouin, Gert Schubring Sep 2022

A Question Of Fundamental Methodology: Reply To Mikhail Katz And His Coauthors, Tom Archibald, Richard T. W. Arthur, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper Lützen, Marco Panza, David Rabouin, Gert Schubring

Philosophy Faculty Articles and Research

This paper is a response by several historians of mathematics to a series of papers published from 2012 onwards by Mikhail Katz and various co-authors, the latest of which was recently published in the Mathematical Intelligencer, “Two-Track Depictions of Leibniz’s Fictions” (Katz, Kuhlemann, Sherry, Ugaglia, and van Atten, 2021). At issue is a question of fundamental methodology. These authors take for granted that non-standard analysis provides the correct framework for historical interpretation of the calculus, and castigate rival interpretations as having had a deleterious effect on the philosophy, practice, and applications of mathematics. Rather than make this case by reasoned …

Go to article

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway Sep 2022

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Go to article

Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 3: Spherical Triangles, Jyotirmoy Sarkar, Mamunur Rashid Sep 2022

Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 3: Spherical Triangles, Jyotirmoy Sarkar, Mamunur Rashid

Mathematics Faculty Publications

What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, …

Go to article

Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia Sep 2022

Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia

SMU Data Science Review

In this paper, machine learning techniques are used to reconstruct particle collision pathways. CERN (Conseil européen pour la recherche nucléaire) uses a massive underground particle collider, called the Large Hadron Collider or LHC, to produce particle collisions at extremely high speeds. There are several layers of detectors in the collider that track the pathways of particles as they collide. The data produced from collisions contains an extraneous amount of background noise, i.e., decays from known particle collisions produce fake signal. Particularly, in the first layer of the detector, the pixel tracker, there is an overwhelming amount of background noise that …

Go to article

A First-Passage Problem For Exponential Integrated Diffusion Processes, Mario Lefebvre Sep 2022

A First-Passage Problem For Exponential Integrated Diffusion Processes, Mario Lefebvre

Journal of Stochastic Analysis

No abstract provided.

Go to article

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser Sep 2022

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

Go to article

Euler's Navigation Variational Problem, Sylvio R. Bistafa Sep 2022

Euler's Navigation Variational Problem, Sylvio R. Bistafa

Euleriana

In a 1747 publication, De motu cymbarum remis propulsarum in fluviis (“On the motion of boats propelled by oars in rivers”), Leonhard Euler (1707-1783) works out various instances of a boat moving at constant speed across a stream flowing in straight streamlines at assigned speeds, in which one of these gives rise to a variational problem consisting of finding the quickest crossing path between two points on opposite side of the river banks, which is generally known as the navigation variational problem. This problem together with the well-known catenary and brachistochrone problems, are considered classical examples in the calculus …

Go to article

Basel Problem: Historical Perspective And Further Proofs From Stochastic Processes, Uwe Hassler, Mehdi Hosseinkouchack Sep 2022

Basel Problem: Historical Perspective And Further Proofs From Stochastic Processes, Uwe Hassler, Mehdi Hosseinkouchack

Euleriana

In this note, we offer a historical perspective on solutions of the Basel problem. In particular, we have a closer look at some of the less famous results by Euler E41 and provide a review of a selection of the assemblage of earlier proofs. Moreover, we show how to generate further proofs using Karhunen-Lo\`{e}ve expansions of stochastic processes.

Go to article

Answer To A Question Concerning Euler's Paper "Variae Considerationes Circa Series Hypergeometricas", Alexander Aycock Sep 2022

Answer To A Question Concerning Euler's Paper "Variae Considerationes Circa Series Hypergeometricas", Alexander Aycock

Euleriana

We solve a problem concerning Euler's paper "Variae considerationes circa series hypergeometricas" (\cite{E661}), as suggested by G. Faber in the preface to Volume 16,2 of the first series of Euler's Opera Omnia. Our solution employs methods introduced by Euler at other places.

Go to article

Euler Archive Spotlight, Cynthia Huffman Ph.D. Sep 2022

Euler Archive Spotlight, Cynthia Huffman Ph.D.

Euleriana

This issue we spotlight the translations of Jordan Bell, one of the most prolific translators for the Euler Archive.

Go to article

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part Ii, Janet H. Barnett, Dominic Klyve, Dave Ruch Sep 2022

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part Ii, Janet H. Barnett, Dominic Klyve, Dave Ruch

Euleriana

This article and its prequel together highlight a set of nine classroom-ready projects that draw on the remarkable writing of Leonhard Euler (1707--1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom use.

Go to article

On The Motion Of Boats Propelled By Oars In Rivers, Sylvio R. Bistafa Sep 2022

On The Motion Of Boats Propelled By Oars In Rivers, Sylvio R. Bistafa

Euleriana

Euler considers the following problem: A boat with a perfect rudder moves at constant speed across a stream flowing in straight streamlines at assigned speeds. Assuming that the downstream velocity of the boat equals that of the river, how should the rudder be set so that the boat traverses a given path? He works out various instances, one of which gives rise to a variational problem, in detail. (From Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)

Go to article

A Method For Calculating The Equation Of Noon (An English Translation Of Methodus Computandi Aequationem Meridiei), Patrick T. Headley Sep 2022

A Method For Calculating The Equation Of Noon (An English Translation Of Methodus Computandi Aequationem Meridiei), Patrick T. Headley

Euleriana

In this paper Euler presents a method for determining solar noon, the time at which the Sun crosses the meridian. The method requires the times of two observations of the Sun, one in the morning and one in the afternoon, at equal altitudes above the horizon. Solar noon is approximately the midpoint between two such observations, but, since the declination of the Sun will have changed during the day, a correction term, called the equation of noon, is required. Euler explains that this term is too large to ignore and discusses the table of values constructed by de la Hire; …

Go to article

Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou Sep 2022

Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou

Euleriana

Review of The History of Mathematics: A Source-Based Approach (Vol. 2), Part I, by June Barrow-Green, Jeremy Gray, and Robin Wilson. MAA Press, 2022, 330 + xiv pages.

Go to article

Variety And Variation, Christopher Goff, Erik R. Tou Sep 2022

Variety And Variation, Christopher Goff, Erik R. Tou

Euleriana

Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.

Go to article

Generalizations Of Commutativity In Dihedral Groups, Noah A. Heckenlively Sep 2022

Generalizations Of Commutativity In Dihedral Groups, Noah A. Heckenlively

Rose-Hulman Undergraduate Mathematics Journal

The probability that two elements commute in a non-Abelian finite group is at most 5 8 . We prove several generalizations of this result for dihedral groups. In particular, we give specific values for the probability that a product of an arbitrary number of dihedral group elements is equal to its reverse, and also for the probability that a product of three elements is equal to a permutation of itself or to a cyclic permutation of itself. We also show that for any r and n, there exists a dihedral group such that the probability that a product of n …

Go to article

On The Linear Independence Of Finite Gabor And Wavelet Systems, Abdelkrim Bourouihiya Sep 2022

On The Linear Independence Of Finite Gabor And Wavelet Systems, Abdelkrim Bourouihiya

Mathematics Colloquium Series

Gabor and Wavelet Systems are some of the most important families of integrable functions with great potential in applications. Those applications include numerical analysis, signal processing (sound, images), and many other areas of physics and engineering. In this talk, we will present some partial results on a conjecture that states each finite Gabor system is linearly independent. We will also present cases of linearly independent and cases of linearly dependent finite wavelet systems.

Go to article

Applications Of The Harary-Sachs Theorem For Hypergraphs, Gregory J. Clark, Joshua N. Cooper Sep 2022

Applications Of The Harary-Sachs Theorem For Hypergraphs, Gregory J. Clark, Joshua N. Cooper

Faculty Publications

The Harary-Sachs theorem for k-uniform hypergraphs equates the codegree-d coefficient of the adjacency characteristic polynomial of a uniform hypergraph with a weighted sum of subgraph counts over certain multi-hypergraphs with d edges. We begin by showing that the classical Harary-Sachs theorem for graphs is indeed a special case of this general theorem. To this end we apply the generalized Harary-Sachs theorem to the leading coefficients of the characteristic polynomial of various hypergraphs. In particular, we provide explicit and asymptotic formulas for the contribution of the k-uniform simplex to the codegree-d coefficient. Moreover, we provide an explicit formula for the leading …

Go to article

First Prev Next Last