Physical Sciences and Mathematics Commons^™

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Implementasi Geometric Brownian Motion Dalam Memprediksi Harga Minyak Mentah Pada Masa Pandemi Covid-19, Feby Seru, Christian Dwi Suhendra, Agung Dwi Saputra

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Minyak mentah atau crude oil memiliki peranan yang vital dalam pertumbuhan ekonomi suatu negara, karena minyak mentah merupakan sumber energi penggerak perekonomian. Untuk menjaga kestabilan perekonomian, maka harga minyak mentah pada periode mendatang perlu diantisipasi dengan cara melakukan prediksi terhadap harga komoditas minyak mentah dunia. Salah satu model yang dapat digunakan untuk memprediksi harga minyak mentah dalam jangka waktu pendek adalah Geometric Brownian Motion (GBM). Tujuan dari penelitian ini adalah mengimplementasikan model GBM dalam memprediksi harga minyak mentah di masa pandemi Covid-19, serta mengukur keakuratan model tersebut. Pada penelitian ini, prediksi harga minyak menggunakan model GBM dilakukan dengan 50, 100, …

Analisa Kestabilan Bebas Kecanduan Pada Penyebaran Penggunaan Media Sosial Berdasarkan Model Searqs, Ratna Widayati, Intrada Reviladi

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Penelitian ini membahas mengenai model penyebaran penggunaan media sosial dan analisa kestabilan di sekitar titik ekuilibrium serta simulasi numeriknya dengan mengasumsikan populasi individu dibagi menjadi 5 kelas yaitu individu yang rentan terhadap kecanduan media sosial, individu yang menggunakan media sosial tetapi belum timbul kecanduan, individu kecanduan/adiktif media sosial, individu sembuh dari kecanduan media dan individu yang berhenti menggunakan media sosial. Model matematika yang digunakan adalah SEARQS dengan asumsi tidak ada kematian karena kecanduan media sosial. Selain itu, individu yang telah berhenti dari kecanduan media sosial, dapat kembali menjadi individu rentan. Permasalahan yang timbul dari penyebaran penggunaan media sosial yang berlebihan …

Analisis Sentimen Terhadap Kalimat Finansial Pada Fiqa Dan The Financial Phrasebank, Maximilianus Noel Brilianto, Yuliana Susanti, Etik Zukhronah

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Analisis sentimen atau bisa disebut juga opinion mining merupakan salah satu tugas utama dari Natural Language Processing (NLP) yang merupakan studi komputasi yang mempelajari tentang pendapat seseorang terhadap suatu topik bahasan atau entitas. Analisis dilakukan dengan algoritma machine learning (pembelajaran mesin) Naïve Bayes, Decision Tree, dan K-Nearest Neighbor dengan membagi sentimen ke dalam dua kategori sentimen yaitu sentimen positif dan sentimen negatif. Data analisis diambil dari Financial Opinion Mining and Question Answering (FiQA) dan The Financial PhraseBank yang terdiri dari 4.840 kalimat yang dipilih dari berbagai berita keuangan dan dianotasi oleh 16 annotator berbeda yang berpengalaman dalam domain finansial. Penelitian …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Difference Of Facial Achromatic Numbers Between Two Triangular Embeddings Of A Graph, Kengo Enami, Yumiko Ohno

Theory and Applications of Graphs

A facial $3$-complete $k$-coloring of a triangulation $G$ on a surface is a vertex $k$-coloring such that every triple of $k$-colors appears on the boundary of some face of $G$. The facial $3$-achromatic number $\psi_3(G)$ of $G$ is the maximum integer $k$ such that $G$ has a facial $3$-complete $k$-coloring. This notion is an expansion of the complete coloring, that is, a proper vertex coloring of a graph such that every pair of colors appears on the ends of some edge.

For two triangulations $G$ and $G'$ on a surface, $\psi_3(G)$ may not be equal to $\psi_3(G')$ even if $G$ …

The Ricci Curvature On Simplicial Complexes, Taiki Yamada

Theory and Applications of Graphs

We define the Ricci curvature on simplicial complexes modifying the definition of the Ricci curvature on graphs, and prove upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on simplicial complexes by the Ricci curvature.

Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise

Masters Theses

The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price

Feminist Pedagogy

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

Limit Distributions Of Products Of Independent And Identically Distributed Random 2 × 2 Stochastic Matrices: A Treatment With The Reciprocal Of The Golden Ratio, Santanu Chakraborty

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Consider a sequence (Xn)n≥1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first column of Xn and for a given real r with 012 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r=√5−12 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation.

Turing Patterns In A P-Adic Fitzhugh-Nagumo System On The Unit Ball, L. F. Chacón-Cortés, C. A. Garcia-Bibiano, Wilson A. Zuniga-Galindo

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We introduce discrete and p-adic continuous versions of the FitzHugh-Nagumo system on the one-dimensional p-adic unit ball. We provide criteria for the existence of Turing patterns. We present extensive simulations of some of these systems. The simulations show that the Turing patterns are traveling waves in the p-adic unit ball.

A Map-Algebra-Inspired Approach For Interacting With Wireless Sensor Networks, Cyber-Physical Systems Or Internet Of Things, David Almeida

Electronic Theses and Dissertations

The typical approach for consuming data from wireless sensor networks (WSN) and Internet of Things (IoT) has been to send data back to central servers for processing and analysis. This thesis develops an alternative strategy for processing and acting on data directly in the environment referred to as Active embedded Map Algebra (AeMA). Active refers to the near real time production of data, and embedded refers to the architecture of distributed embedded sensor nodes. Network macroprogramming, a style of programming adopted for wireless sensor networks and IoT, addresses the challenges of coordinating the behavior of multiple connected devices through a …

Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we study holomorphic motion of Julia sets of polynomial-like maps. In particular, we prove that in the stable family of polynomial-like maps if all the continuos functions move continuously by parameter then the Julia sets move holomorphically. Moreover, we also study the relation between continuity of regular compact sets and their Green functions.

An Analogue Of Hartogs Lemma For Separately Harmonic Functions With Variable Radius Of Harmonicity, Sevdiyor Imomkulov, Sultanbay Abdikadirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this note we prove that if a function u(x,y) is separately harmonic in a domain D × V_r = D × {y∈ℝ²:|y|<r,  r>1} ⊂ ℝⁿ × ℝ² and for each fixed point x⁰ ∈ D the function u(x⁰,y) of variable y continues harmonically into the great circle {y∈ℝ²:|y|<R(x⁰),  R(x⁰)>r}, then it continues harmonically into a domain {(x …

Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, Sindor Ashurov, Satimboy Palvanov, Abror Tuymuradov, Dilmurod Tuymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Bremsstrahlung radiation, a pivotal phenomenon in high-energy physics, presents numerous applications and implications in both theoretical studies and practical scenarios. This article explores the Bremsstrahlung radiation of electrons in tungsten (W) targets of varying widths subjected to different energy beams using GEANT4 simulations. By systematically altering the target widths and electron beam energies, we assess the corresponding effects on radiation yield and spectrum. The findings contribute to a deeper understanding of Bremsstrahlung processes in high-$Z$ materials and offer valuable insights for applications ranging from radiation therapy to materials analysis.

Toughness Of Recursively Partitionable Graphs, Calum Buchanan, Brandon Du Preez, K. E. Perry, Puck Rombach

Theory and Applications of Graphs

A simple graph G = (V,E) on n vertices is said to be recursively partitionable (RP) if G ≃ K1, or if G is connected and satisfies the following recursive property: for every integer partition a₁, a₂, . . . , a_k of n, there is a partition {A₁,A₂, . . . ,A_k} of V such that each |A_i| = a_i, and each induced subgraph G[A_i] is RP (1 ≤ i ≤ k). We show that if S is a …

Translation-Invariant Gibbs Measures For Potts Model With Competing Interactions With A Countable Set Of Spin Values On Cayley Tree, Zarinabonu Mustafoyeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider of an infinite system of functional equations for the Potts model with competing interactions and countable spin values Φ = {0, 1, ..., } on a Cayley tree of order k. We study translation-invariant Gibbs measures that gives the description of the solutions of some infinite system of equations. For any k ≥ 1 and any fixed probability measure ν we show that the set of translation-invariant splitting Gibbs measures contains one and two points for odd k and even k, respectively, independently on parameters of the Potts model with a countable …

The Tor Algebra Of Trimmings Of Gorenstein Ideals, Luigi Ferraro, Alexis Hardesty

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Let (R,\mathfrak m,\Bbbk ) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by \mathfrak m; we say that J is a trimming of I. Building on a recent paper of Vandebogert, we construct an explicit free resolution of R/J and compute a partial DG algebra structure on this …

Cyclically Compact Operators In Banach Modules Over L0(B), Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper the properties of linear cyclically compact operators in Banach modules over space L⁰(B) are given.

First Order Approximation On The Basilica Julia Set, Xintan Xia, Taryn Flock

Mathematics, Statistics, and Computer Science Honors Projects

We consider the basilica Julia set of the quadratic polynomial P (z) = z^2 - 1, with its successive graph approximations defined in terms of the external ray parametrization of the set. Following the model of Kigami and later Strichartz, we exploit these graph approximations to define derivatives of functions defined on the fractal, an endeavor complicated by asymmetric neighborhood behaviors at approximated vertex points across levels, and by the topology of these vertices. We hence differentiate even and odd levels of approximations of the Julia set and construct, accordingly, normal derivatives corresponding to each level category at the vertices, …

Wiener Index In Graphs Given Girth, Minimum, And Maximum Degrees, Fadekemi J. Osaye, Liliek Susilowati, Alex S. Alochukwu, Cadavious Jones

Theory and Applications of Graphs

Let $G$ be a connected graph of order $n$. The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. The well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n \choose 2}$ on the Wiener index of a graph of order $n$ and minimum degree $\delta$ by Kouider and Winkler \cite{Kouider} was improved significantly by Alochukwu and Dankelmann \cite{Alex} for graphs containing a vertex of large degree $\Delta$ to $W(G) \leq {n-\Delta+\delta \choose 2} \big( \frac{n+2\Delta}{\delta+1}+4 \big)$. In this paper, we give upper bounds on the Wiener index of $G$ in terms of order …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …

On The Hardness Of The Balanced Connected Subgraph Problem For Families Of Regular Graphs, Harsharaj Pathak

Theory and Applications of Graphs

The Balanced Connected Subgraph problem (BCS) was introduced by Bhore et al. In the BCS problem we are given a vertex-colored graph G = (V, E) where each vertex is colored “red” or “blue”. The goal is to find a maximum cardinality induced connected subgraph H of G such that H contains an equal number of red and blue vertices. This problem is known to be NP-hard for general graphs as well as many special classes of graphs. In this work we explore the time complexity of the BCS problem in case of regular graphs. We prove that the BCS …

The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson

Cybersecurity Undergraduate Research Showcase

The RSA encryption algorithm has secured many large systems, including bank systems, data encryption in emails, several online transactions, etc. Benefiting from the use of asymmetric cryptography and properties of number theory, RSA was widely regarded as one of most difficult algorithms to decrypt without a key, especially since by brute force, breaking the algorithm would take thousands of years. However, in recent times, research has shown that RSA is getting closer to being efficiently decrypted classically, using algebraic methods, (fully cracked through limited bits) in which elliptic-curve cryptography has been thought of as the alternative that is stronger than …

Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor

Articles

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …

Laterally Complete Regular Modules, Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we introduce the notion laterally complete regular modules and study some properties of theese modules.

A Review On Possible Physical Meaning Of Elastic-Electromagnetic Mathematical Equivalences, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known, despite special theory of relativity has been widely accepted, in our recent draft submitted to this journal it is shown that some experiments have been carried out suggesting superluminal wave propagation, which make Minkowski lightcone not valid anymore. Therefore, it seems worth to reconsider the connection between elastic wave and electromagnetic wave equations, as in their early development. In this paper we will start with Maxwell-Dirac isomorphism, then we will find its connection with elastic wave equations.

The Construction Of Khovanov Homology, Shiaohan Liu

Master's Theses

Knot theory is a rich topic in topology that studies the how circles can be embedded in Euclidean 3-space. One of the main questions in knot theory is how to distinguish between different types of knots efficiently. One way to approach this problem is to study knot invariants, which are properties of knots that do not change under a standard set of deformations. We give a brief overview of basic knot theory, and examine a specific knot invariant known as Khovanov homology. Khovanov homology is a homological invariant that refines the Jones polynomial, another knot invariant that assigns a Laurent …

Pappus Of Alexandria, Book Iii Of The Mathematical Collection, Pappus Of Alexandria, John B. Little

Holy Cross Bookshelf

John B. Little is the translator.

This is a translation of Book III of the Mathematical Collection by Pappus of Alexandria (ca. 290 - 350 CE) from the original Greek to English, following the edition of Friedrich Hultsch. While other books of the Mathematical Collection have been translated into English and short quotations from Book III have appeared in a number of places (see the Introduction), to my knowledge, no complete English translation of Book III has been published. Pappus was very influential as a sort of conduit between knowledge preserved from ancient Greek mathematics and European mathematicians in the …