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 …

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 …

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, …

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.

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.

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 …

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.

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 …

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 …

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 …

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 …

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

The Negative Stigma Surrounding Mathematics, Marissa A. Greisen

PSU McNair Scholars Online Journal

There is a negative stigma that surrounds mathematics in our education system. It is important to bring notice to this for the benefit of future students. There is a lot of research claiming that math is looked down on, but they do not answer why, or what we can do to fix it. Why is there a greater negative stigma around math and not other subjects? What roles to teachers, parents, and peers play in this stigma? In this article, I created a survey for people to answer questions regarding their opinion on math, who they believe typically does well …

Eigenvalue Algorithm For Hausdorff Dimension On Complex Kleinian Groups, Jacob Linden, Xuqing Wu

Rose-Hulman Undergraduate Mathematics Journal

In this manuscript, we present computational results approximating the Hausdorff dimension for the limit sets of complex Kleinian groups. We apply McMullen's eigenvalue algorithm \cite{mcmullen} in symmetric and non-symmetric examples of complex Kleinian groups, arising in both real and complex hyperbolic space. Numerical results are compared with asymptotic estimates in each case. Python code used to obtain all results and figures can be found at \url{https://github.com/WXML-HausDim/WXML-project}, all of which took only minutes to run on a personal computer.

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

Combinatorially Orthogonal Paths, Sean A. Bailey, David E. Brown, Leroy Beaseley

Communications on Number Theory and Combinatorial Theory

Vectors x=(x₁,x₂,...,x_n)^T and y=(y₁,y₂,...,y_n)^T are combinatorially orthogonal if |{i:x_iy_i≠0}|≠1. An undirected graph G=(V,E) is a combinatorially orthogonal graph if there exists f:V→ℝⁿ such that for any u,v∈V, uv∉E iff f(u) and f(v) are combinatorially orthogonal. We will show that every graph has a combinatorially orthogonal representation. We will show …

An Extensive Note On Characteristic Properties And Possible Implications Of Some Operators Designated By Various Type Derivatives, Ömer Faruk Kulali, Hüseyi̇n Irmak

Turkish Journal of Mathematics

In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined.

Fibonomial Matrix And Its Domain In The Spaces $\Ell_P$ And $\Ell_{\Infty}$, Muhammet Ci̇hat Dağli, Taja Yaying

Turkish Journal of Mathematics

In this paper, we introduce the fibonomial sequence spaces $b_{p}^{r,s,F}$ and $b_{\infty}^{r,s,F},$ and show that these are BK-spaces. Also, we prove that these new spaces are linearly isomorphic to $\ell_{p}$ and $\ell_{\infty}.$ Moreover, we determine the $\alpha$-, $\beta$-, $\gamma$-duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space $b_{p}^{r,s,F}.$

Best Proximity For Proximal Operators On $B$-Metric Spaces, Ariana Pitea, Monica Stanciu

Turkish Journal of Mathematics

The paper presents existence results of $(\phi,\varphi)$ best proximity points for operators that fulfill implicit type inequalities. Classes of mappings endowed with continuity, monotone or monotone-type properties, and which additionally satisfy some adequate inequalities are studied from this point of view. Applications of our results are given with regard to fixed point theory.

Multiplication Of Closed Balls In $\Mathbb{C}^N$, Patrícia Damas Beites, Alejandro Piñera Nicolás, José Da Silva Lourenço Vitória

Turkish Journal of Mathematics

Motivated by circular complex interval arithmetic, some operations on closed balls in $\mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $\mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n \in \{3, 7\}$, are studied. In addition, certain equations involving the defined multiplications are solved.

On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic

Turkish Journal of Mathematics

This paper presents a generalization of the concepts of partial-$A$-isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field [5, 30, 31]. By extending the definition of partial-$A$-isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left $p$-partial-$A$-isometry as a broader class of operators, including partial-$A$-isometry and left polynomially partial isometry. Some basic properties of a left $p$-partial-$A$-isometry are proven, as well as its relation with $A$-isometry. Several decompositions of a left $p$-partial-$A$-isometry are developed. We consider spectral properties and matrix representation …

Various Types Of Continuity And Their Interpretations In Ideal Topological Spaces, Anika Njamcul, Aleksandar Pavlovi?

Turkish Journal of Mathematics

In this paper we work on preserving various types of continuity in ideal topological spaces. The accent will be on $\theta$-continuity and weak continuity. We will give their translations in ideal topological spaces. As a consequence of those results, we will prove that every $\theta$-continuous function is continuous if topologies are generated by $\theta$-open sets and we will give an example of a weakly continuous function which is not $\tau_\theta$-continuous. This will complete the diagram of relations between continuous, $\tau_\theta$-continuous, $\theta$-continuous, weakly continuous, and faintly continuous functions.

A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar

Turkish Journal of Mathematics

This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating $y^{\prime}(u)$ using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to …

Involutive Automorphisms And Derivations Of The Quaternions, Eyüp Kizil, Adriano Da Silva, Okan Duman

Turkish Journal of Mathematics

Let $Q=(\frac{a,b}{{\Bbb R}})$ denote the quaternion algebra over the reals which is by the Frobenius Theorem either split or the division algebra $H$ of Hamilton's quaternions. We have presented explicitly in \cite{Kizil-Alagoz} the matrix of a typical derivation of $Q$. Given a derivation $d\in Der(H)$, we show that the matrix $D\in M_{3}({\Bbb R})$ that represents $d$ on the linear subspace $% H_{0}\simeq {\Bbb R}^{3}$ of pure quaternions provides a pair of idempotent matrices $AdjD$ and $-D^{2}$ that correspond bijectively to the involutary matrix $\Sigma $ of a quaternion involution $\sigma $ and present several equations involving these matrices. In particular, …

Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product, Mübari̇z T. Garayev

Turkish Journal of Mathematics

The Berezin symbol $\tilde{A}$ of an operator $A$ on the reproducing kernel Hilbert space $\mathcal{H}\left( \Omega\right) $ over some set $\Omega$ with the reproducing kernel $k_{\lambda}$ is defined by \[ \tilde{A}(\lambda)=\left\langle {A\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}}\right\Vert }},\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}% }\right\Vert }}}\right\rangle ,\ \lambda\in\Omega. \] We study the existence of invariant subspaces for Bergman space operators in terms of Berezin symbols.