Mathematics Commons^™

Quantum Hooks And Mirror Symmetry For Flag Varieties, Linda Chen, E. Kalashnikov

Mathematics & Statistics Faculty Works

Given a flag variety F1 (n; r₁,...,r_p), there is natural ring morphism from the symmetric polynomial ring in r₁ variables to the quantum cohomology of the flag variety. In this paper, we show that for a large class of partitions λ, the image of s_λ under the ring homomorphism is a Schubert class which is described by partitioning λ into a quantum hook (or q-hook) and a tuple of smaller partitions. We use this result to show that the Plücker coordinate mirror of the flag variety describes quantum cohomology relations. This gives new …

Structure And Dynamics That Specialize Neurons For High-Frequency Coincidence Detection In The Barn Owl Nucleus Laminaris, Ben Drucker , '22, Joshua H. Goldwyn

Mathematics & Statistics Faculty Works

A principal cue for sound source localization is the difference in arrival times of sounds at an animal’s two ears (interaural time difference, ITD). Neurons that process ITDs are specialized to compare the timing of inputs with submillisecond precision. In the barn owl, ITD processing begins in the nucleus laminaris (NL) region of the auditory brain stem. Remarkably, NL neurons are sensitive to ITDs in high-frequency sounds (kilohertz-range). This contrasts with ITD-based sound localization in analogous regions in mammals where ITD sensitivity is typically restricted to lower-frequency sounds. Guided by previous experiments and modeling studies of tone-evoked responses of NL …

Generalized Sasakian Structures From A Poisson Geometry Viewpoint, Janet Talvacchia

Mathematics & Statistics Faculty Works

In this paper we define a canonical Poisson structure on a normal generalized contact metric space and use this structure to define a generalized Sasakian structure. We show also that this canonical Poisson structure enables us to distinguish generalized Sasakian structures from generalized coKähler structures.

The Square Roots Of Some Classical Operators, Javad Mashreghi, Marek Ptak, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper we give complete descriptions of the set of square roots of certain classical operators, often providing specific formulas. The classical operators included in this discussion are the square of the unilateral shift, the Volterra operator, certain compressed shifts, the unilateral shift plus its adjoint, the Hilbert matrix, and the Cesàro operator.

Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated …

Complete Study Of An Original Power-Exponential Transformation Approach For Generalizing Probability Distributions, Mustafa S. Shama, Farid El Ktaibi, Jamal N. Al Abbasi, Christophe Chesneau, Ahmed Z. Afify

All Works

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are …

Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.

Peer-To-Peer Energy Trading In Smart Residential Environment With User Behavioral Modeling, Ashutosh Timilsina

Theses and Dissertations--Computer Science

Electric power systems are transforming from a centralized unidirectional market to a decentralized open market. With this shift, the end-users have the possibility to actively participate in local energy exchanges, with or without the involvement of the main grid. Rapidly reducing prices for Renewable Energy Technologies (RETs), supported by their ease of installation and operation, with the facilitation of Electric Vehicles (EV) and Smart Grid (SG) technologies to make bidirectional flow of energy possible, has contributed to this changing landscape in the distribution side of the traditional power grid.

Trading energy among users in a decentralized fashion has been referred …

Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong

Honors Theses

Stable polynomials, in the context of this research, are two-variable polynomials like $p(z_1,z_2) = 2 - z_1 - z_2$ that are guaranteed to be non-zero if both input variables have an absolute value less than one in the complex plane. Stable polynomials are used in a variety of mathematical fields, thus finding ways to construct stable polynomials is valuable. An important property of these polynomials is whether they have boundary zeros, which are points in the complex plane where the polynomial equals zero and both variables have an absolute value of 1. Overall, it is challenging to find stable polynomials …

Some Estimates On The Exponential Stability Of Solutions Of Nonlinear Neutral Type Systems With Periodic Coefficients, Yener Altun

Turkish Journal of Mathematics

In this present study, we pay attention to a class of nonlinear neutral type systems (NNSs) with periodic coefficients and construct some assumptions guaranteeing the exponential stability (ES) of the trivial solutions of the system considered. To get specific conditions guaranteeing the ES, we use a modified Lyapunov functional. In conclusion, we get some estimates for the exponential decay of the solutions at infinity with the constructed sufficient conditions. We give two examples to demonstrate the applicability of the results obtained with the constructed assumptions.

Object Detection And Image Categorization By Transferring Commonsense Knowledge With Premises And Quantifiers, Irina Chernyavsky

Theses, Dissertations and Culminating Projects

Domestic, or household robots, are autonomous robots designed to make our home-life easier by performing chores and mundane tasks such as cleaning, or cooking. Currently domestic robots are specialized to complete a specific task and, therefore, are confined by factors such as mobility, size, and complexity. With the fast development of computer vision and robotics, the need for more compact, advanced and multi-task robots has emerged. Therefore, the robot needs to be multi-functional, able to discern the environment and the tasks. The aim of this paper is to categorize images in domestic robots as relevant to the culinary, laundry, vacuum …

Clusters, Curves, And Centroids: Stellar Flare Morphology In The Ultraviolet, Vera Berger

Pomona Senior Theses

With a novel sample of 495 high-cadence light curves for stellar flares in the near-ultraviolet, I explore similarity measures, clustering algorithms, averaging methods, and curve fitting techniques for time series. This work seeks to provide insight into whether stellar flares are similar across stars, if we can identify physically meaningful patterns in their light curves, and how to construct a comprehensive model for flares. I construct the first empirical template for flare light curves in the ultraviolet, and compute ``average elements" of flares displaying complex features such as quasi-periodic oscillations and multipeak structures. Developing accurate models for flares in the …

Cayley Map Embeddings Of Complete Graphs With Even Order, Michael O'Connor

Honors Program Theses

German mathematician Claus Michael Ringel used voltage graphs to embed complete graphs onto orientable surfaces such that none of the graph's edges cross each other. Cayley maps do the same whilst being simpler to work with. The goal is to determine the efficiency of Cayley maps in embedding complete graphs onto orientable surfaces. This article focus on complete graphs of even order with an emphasis on graphs whose orders are congruent to 6 modulo 12 and 0 modulo 12. We establish 12 distinct classes that each have their own unique qualities. Through the generalization of a previous technique, we prove …

Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek

Turkish Journal of Mathematics

he problem of list $M$-ary hypothesis testing with fixed list size $L< M$ is considered. Based on some random observation, the test outputs a list of $L$ candidates out of $M$ possible hypotheses. The probability of list error is defined as the probability of the event that the list output by the test does not contain the true hypothesis that has generated the observation. An identity is derived that relates the minimum average probability of error of the optimal list hypothesis test to the minimum average probability of error of an optimal maximum a posteriori probability decision rule. The latter decides among an alternative set of hypotheses corresponding to all possible $L$-component mixtures of the distributions that characterize the observation under the original $M$ candidate hypotheses. As an application, the proposed identity is employed to obtain novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing.

Locally Product-Like Statistical Submersions, Kazuhi̇ko Takano, Esra Erkan, Mehmet Gülbahar

Turkish Journal of Mathematics

In this paper, the main identities on locally product-like statistical submersions are obtained with the aid of statistical structures and their Riemannian curvature tensors. Some examples of locally product-like statistical submersions are presented. Some results on $F$-invariant, $F^{\ast}$-invariant and antiinvariant locally product-like statistical submersions are given.

On Generalized Darboux Frame Of A Spacelike Curve Lying On A Lightlike Surface In Minkowski Space $\Mathbb{E}^{3}_{1}$, Jelena Djordjevic, Emilija Nesovic, Ufuk Öztürk

Turkish Journal of Mathematics

In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on a lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that $\alpha$ has two such frames and obtain generalized Darboux frame's equations. We find the relations between the curvature functions $k_g$, $k_n$, $\tau_g$ of $\alpha$ with respect to its Darboux frame and the curvature functions $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on …

Global Existence, Asymptotic Behavior And Blow Up Of Solutions For A Kirchhoff-Type Equation With Nonlinear Boundary Delay And Source Terms, Houria Kamache, Nouri Boumaza, Billel Gheraibia

Turkish Journal of Mathematics

The main goal of this work is to study an initial boundary value problem for a Kirchhoff-type equation with nonlinear boundary delay and source terms. This paper is devoted to prove the global existence, decay, and the blow up of solutions. To the best of our knowledge, there are not results on the Kirchhoff type-equation with nonlinear boundary delay and source terms.

Numerical Radius, Berezin Number, And Berezin Norm Inequalities For Sums Of Operators, Najla Altwaijry, Kais Feki, Nicusor Minculete

Turkish Journal of Mathematics

The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space. Finally, we establish a necessary and sufficient condition for the triangle inequality related to the Berezin number to hold.

N-Cylindrical Fuzzy Neutrosophic Topological Spaces, Sarannya Kumari R, Sunny Joseph Kalayathankal, Mathews George, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

Professor Cai Wen’S Extenics ( A Letter To The Editor-In-Chief), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

I had the chance and honor to meet Prof. Dr. Cai Wen (1941 - 2021), the founder of Extenics, in the summer of 2012, at the Guangdong University of Technology (GDUT), Institute of Extenics and Innovative Methods, in Guangzhou, P. R. China, where I was invited by Dr. Xingsen Li to do research on Extenics about solving contradictory problems in science.

I have passed a wonderful time in China (17 May – 15 August, 2012) presenting and listening to many scientific presentations on Extenics and their applications in various fields of knowledge, and studying new papers and book provided to …

Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.

Remark On Regenerative Medicine And Potential Utilization Of Low-Intensity Laser Photobiomodulation To Activate Human Stem Cells, Victor Christianto, Florentin Smarandache, Robert N. Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

Recently, a friend of one of these writers told her story of using one of a healthcare product to activate her stem cells as part of regenerative medicine. Regenerative medicine is a field of medicine that seeks to repair or replace damaged or diseased tissues and organs. This can be done through a variety of methods, including stem cell therapy, tissue engineering, and gene therapy. This is a short review article on this rapid field called regenerative medicine, in particular via a new method called photobiomodulation, especially by virtue of low-intensity laser pen treatment. Hopefully it will attract more research …

Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad

Graduate Theses, Dissertations, and Problem Reports (ETD)

The purpose of this thesis is to present new different spaces as attempts to generalize the concept of topological vector spaces. A topological vector space, a well-known concept in mathematics, is a vector space over a field \mathbb{F} with a topology that makes the addition and scalar multiplication operations of the vector space continuous functions. The field \mathbb{F} is usually \mathbb{R} or \mathbb{C} with their standard topologies. Since every vector space is a finitary matroid, we define two spaces called finite matroidal spaces and matrological spaces by replacing the linear structure of the topological vector space with a finitary matroidal …

On Eulerian Subgraphs And Hamiltonian Line Graphs, Yikang Xie

Graduate Theses, Dissertations, and Problem Reports (ETD)

A graph {\color{black}$G$} is Hamilton-connected if for any pair of distinct vertices {\color{black}$u, v \in V(G)$}, {\color{black}$G$} has a spanning $(u,v)$-path; {\color{black}$G$} is 1-hamiltonian if for any vertex subset $S \subseteq {\color{black}V(G)}$ with $|S| \le 1$, $G - S$ has a spanning cycle. Let $\delta(G)$, $\alpha'(G)$ and $L(G)$ denote the minimum degree, the matching number and the line graph of a graph $G$, respectively. The following result is obtained. {\color{black} Let $G$ be a simple graph} with $|E(G)| \ge 3$. If $\delta(G) \geq \alpha'(G)$, then each of the following holds. \\ (i) $L(G)$ is Hamilton-connected if and only if $\kappa(L(G))\ge …

Longest Path And Cycle Transversal And Gallai Families, James A. Long Jr

Graduate Theses, Dissertations, and Problem Reports (ETD)

A longest path transversal in a graph G is a set of vertices S of G such that every longest path in G has a vertex in S. The longest path transversal number of a graph G is the size of a smallest longest path transversal in G and is denoted lpt(G). Similarly, a longest cycle transversal is a set of vertices S in a graph G such that every longest cycle in G has a vertex in S. The longest cycle transversal number of a graph G is the size of a smallest longest cycle transversal in G and …

Feature Extraction Of Footwear Impression Images For Quality Assessment, Alexandra Hill

Graduate Theses, Dissertations, and Problem Reports (ETD)

Forensic footwear impression analysis is a valuable tool in criminal investigations. Extracting useful features from images of footwear impressions is a critical step in this process. However, the quality of these images can vary widely, making feature extraction challenging. In order to give a quality assessment rating to a footwear impression image, the image should first be analyzed to extract features from the impression. In this paper, we present a method to extract features from a 2D grayscale footwear impression image. A Hierarchical Grid Model implementation has been adapted from use on a 3D dataset to assist in finding features, …

Modeling Repairable System Failure Data Using Nhpp Reliability Growth Mode., Eunice Ofori-Addo

EWU Masters Thesis Collection

Stochastic point processes have been widely used to describe the behaviour of repairable systems. The Crow nonhomogeneous Poisson process (NHPP) often known as the Power Law model is regarded as one of the best models for repairable systems. The goodness-of-fit test rejects the intensity function of the power law model, and so the log-linear model was fitted and tested for goodness-of-fit. The Weibull Time to Failure recurrent neural network (WTTE-RNN) framework, a probabilistic deep learning model for failure data, is also explored. However, we find that the WTTE-RNN framework is only appropriate failure data with independent and identically distributed interarrival …

Final Report: Conceptualizing Ethics, Authenticity, And Efficacy Of Simulations In Teacher Education, Carrie Wilkerson Lee, Liza Bondurant, Bima Sapkota, Heather Howell, Yvonne Lai

School of Mathematical & Statistical Sciences Faculty Publications

This working group was a continuation of working groups in 2019 and 2021 that initially aimed to focus on equity in simulations of practice in mathematics teacher education. We began by discussing our conceptualizations of simulations and equity. Next, we reflected on the lack of work that currently exists at the intersection of simulations and equity as well as our limited collective expertise in this space. We proposed the following areas of potential research: Access, Design, Affective Domains, Teaching Practices, Assessment, Critical Conversations. Attendees self-selected into focus groups and met to discuss their current work and how future work could …

Mathematical Mobile Apps Via Rural Casting, Ma Louise Antonette N. De Las Peñas, John Chris T. Kwong, Peter Antonio B. Banzon, Philip A. Martinez, Wilbur Isaac G. Lapada, Julian N. Eballa, John Emil C. Sebastian, Miguel D. Asido, Jan Daryl M. San Juan, Debbie Marie B. Verzosa, Jumela F. Sarmiento, Agnes D. Garciano, Mark Anthony C. Tolentino, Maria Alva Q. Aberin, Juan Carlo F. Mallari

Mathematics Faculty Publications

This paper discusses the distribution, through a digital datacasting framework, of mathematical resources for Grades 1 to 7 to two schools in a community in the Philippines. Among the mathematical resources made available, are mathematical applications (apps), which run on mobile technologies, that have been created to help in the mathematical learning of students in a remote setting. The distribution is facilitated by the RuralCasting set-top box, a developed custom set-top box capable of receiving digital TV broadcasts and providing local content access through its Wi-Fi network. This paper presents the performance of the set-top box in distributing the mobile …

Practice Through Play Using Mobile Technology, Agnes D. Garciano, Debbie Marie B. Verzosa, Ma Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

This paper discusses the Just Keep Solving apps that are designed based on deliberate practice model for developing mathematical skills. Features of deliberate practice include well-defined goals involving areas of weakness as determined by a knowledgeable other such as a teacher. The integration of game design features provides a positive environment wherein the learning goals critical in a deliberate practice model are emphasized. Possible strategies for integrating the apps in a classroom are also discussed using Hughes, Thomas and Scharber’s RAT (Replacement, Amplification, Transformation) framework. The games can replace traditional pen-and-paper classroom activities, amplify learning by personalizing a student’s experience …