Mathematics Commons^™

High-Risk Behavior Of Students Carrying Weapon To School, Nan Lin Wah Sin Htoo, Naima Shifa

Annual Student Research Poster Session

The rise of personal and mental issues in students has been accompanied by an increase in the number of students carrying guns and the frequency of mass shootings at schools in the US. A recent study (Dong, 2021) pointed out that future researchers should focus on recognizing high-risk youths and tackle their issues early on in life most appropriately according to individual differences such as age and personal circumstances.This research discusses the contributing factors to youths carrying guns to schools and analyzes the high-risk behaviors of students. It was hypothesized that their personal issues such as their mental wellness, high-risk …

On Equivariant Flag F-Vectors For Balanced Relative Simplicial Complexes, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We study the equivariant flag f-vector and equivariant flag h-vector of a balanced relative simplicial complex with respect to a group action. When the complex satisfies Serre's condition (Sℓ), we show that the equivariant flag h-vector, the equivariant h-vector, and the equivariant f-vector satisfy several inequalities.
We apply these results to the study of P-partitions of double posets, and weak colorings of mixed graphs.

(Si10-063) Number Of Automorphisms Of Some Non-Abelian P-Groups Of Order P^4, Muniya ., Harsha Arora, Mahender Singh

Applications and Applied Mathematics: An International Journal (AAM)

The automorphism of a group is a way of mapping the object to itself while preserving all of its structure, and the set of automorphisms of an object forms a group called the automorphism group. It is simply a bijective homomorphism. One of the earliest group automorphism was given by Irish mathematician William Rowan Hamilton in 1856, in his icosian calculus where he discovered an order two automorphism. In this paper, we compute the automorphisms of some non-Abelian groups of order p⁴, where p is an odd prime and GAP (Group Algorithm Programming) software has been used for …

(Si10-089) Integer Cordial Labeling Of Alternate Snake Graph And Irregular Snake Graph, Pratik Shah, Dharamvirsinh Parmar

Applications and Applied Mathematics: An International Journal (AAM)

If a graph G admits integer cordial labeling, it is called an integer cordial graph. In this paper we prove that Alternate m-triangular Snake graph, Quadrilateral Snake graph, Alternate m- quadrilateral Snake graph, Pentagonal Snake graph, Alternate m-pentagonal Snake graph, Irregular triangular Snake graph, Irregular quadrilateral Snake graph, and Irregular pentagonal Snake graphs are integer cordial graphs.

(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.

Why 1/(1+D) Is An Effective Distance-Based Similarity Measure: Two Explanations, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most of our decisions are based on the notion of similarity: we use a decision that helped in similar situations. From this viewpoint, it is important to have, for each pair of situations or objects, a numerical value describing similarity between them. This is called a similarity measure. In some cases, the only information that we can use to estimate the similarity value is some natural distance measure d(a,b). In many such situations, empirical data shows that the similarity measure 1/(1+d) is very effective. In this paper, we provide two explanations for this effectiveness.

How To Describe Variety Of A Probability Distribution: A Possible Answer To Yager's Question, Vladik Kreinovich

Departmental Technical Reports (CS)

Entropy is a natural measure of randomness. It progresses from its smallest possible value 0 -- when we have a deterministic case in which one alternative i occurs with probability 1 (pi = 1), to the largest possible value which is attained at a uniform distribution p1 = ... = pn = 1/n. Intuitively, both in the deterministic case and in the uniform distribution case, there is not much variety in the distribution, while in the intermediate cases, when we have several different values pi, there is a strong variety. Entropy does not seem to capture this notion of variety. …

How The Pavement Strength Changes With Time: Ai Ideas Help To Explain Semi-Empirical Formulas, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we use AI ideas to provide a theoretical explanation for semi-empirical formulas that describe how the pavement strength changes with time, and how we can predict the pavement lifetime.

College Algebra Slide Decks, Bader Abukhodair, Michelle Zeng

All Open Educational Resources

This collection of slide decks is designed to be used in concert with the following Open Eduational Resources:

- OpenStax College Algebra 2e Open Texbook

- Department of Mathematics Video Playlist

- Homework questions from myOpenMath

Concepts include are: A study of equations, graphs, and inequalities for linear, quadratic, polynomial, rational, logarithmic, exponential, and absolute value functions. Transformations on graphs, complex numbers, circles, systems of inequalities, and systems of equations including matrices.

(Si10-068) Performance Analysis Of Cosine Window Function, Vikas Misra, Narendra Singh, M. Shukla

Applications and Applied Mathematics: An International Journal (AAM)

This paper reviews the mathematical functions called the window functions which are employed in the Finite Impulse Response (FIR) filter design applications as well as spectral analysis for the detection of weak signals. The characteristic properties of the window functions are analyzed and parameters are compared among the known conventional cosine window (CW) functions (Rectangular, Hamming, Hanning, and Blackman) and the variable Kaiser window function. The window function expressed in the time domain can be transformed into the frequency domain by taking the Discrete Fourier Transform (DFT) of the time domain window function. The frequency response of the window function …

(Si10-054) Nonsplit Edge Geodetic Domination Number Of A Graph, P. Arul Paul Sudhahar, J. Jeba Lisa

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have defined an inventive parameter called the nonsplit edge geodetic domination number of a graph, and some of its general properties are studied. The nonsplit edge geodetic domination number of some standard graph is obtained. In this work, we also determine the realization results of the nonsplit edge geodetic domination number and the edge geodetic number of a graph.

(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the authors discusses the numerical simulations of higher-order differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.

Implicit Surface Reconstruction With A Curl-Free Radial Basis Function Partition Of Unity Method, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set) approximation for an oriented point cloud using only information about (approximate) normals to the surface. The technique exploits the fundamental result from vector calculus that the normals to an implicit surface are curl-free. By using curl-free radial basis function (RBF) interpolation of the normals, we can extract a potential for the vector field whose zero-level surface approximates the point cloud. We use curl-free …

Bounds On Cohomological Support Varieties, Benjamin Briggs, Eloisa Grifo, Josh Pollitz

Department of Mathematics: Faculty Publications

Over a local ring R, the theory of cohomological support varieties attaches to any bounded complex M of finitely generated R-modules an algebraic variety VR(M) that encodes homological properties of M. We give lower bounds for the dimension of VR(M) in terms of classical invariants of R. In particular, when R is Cohen-Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When M has finite projective dimension, we also give an upper bound for dimVR(M) in terms of the dimension of the radical of the homotopy …

(Si10-130) On Regular Inverse Eccentric Fuzzy Graphs, N. Meenal, J. Jeromi Jovita

Applications and Applied Mathematics: An International Journal (AAM)

Two new concepts of regular inverse eccentric fuzzy graphs and totally regular inverse eccentric fuzzy graphs are established in this article. By illustrations, these two graphs are compared and the results are derived. Equivalent condition for the existence of these two graphs are found. The exact values of Order and Size for some standard inverse eccentric graphs are also derived.

(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 …

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 …

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) …

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 …

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 …

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 …

Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, Katharine Larsen

Doctoral Dissertations and Master's Theses

Accurate characterization of fragment fly-out properties from high-speed warhead detonations is essential for estimation of collateral damage and lethality for a given weapon. Real warhead dynamic detonation tests are rare, costly, and often unrealizable with current technology, leaving fragmentation experiments limited to static arena tests and numerical simulations. Stereoscopic imaging techniques can now provide static arena tests with time-dependent tracks of individual fragments, each with characteristics such as fragment IDs and their respective position vector. Simulation methods can account for the dynamic case but can exclude relevant dynamics experienced in real-life warhead detonations. This research leverages machine learning methodologies to …

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 …

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.

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 …

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 …

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 …

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

Journal of Stochastic Analysis

No abstract provided.

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 …

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.