Number Theory Commons^™

Bridging Discrete And Continuous Systems: Fibonacci Sequences And Exponential Growth From Odes, Martyna Wojcik

Discovery Day - Daytona Beach

Bridging Discrete and Continuous Systems: Fibonacci Sequences and Exponential Growth from Ordinary Differential Equations       It has been observed that nature often exhibits specific patterns of growth and structure in biological systems and spiral formations. The Fibonacci sequence, defined as a discrete recursive sequence where each term is generated as the sum of the two preceding terms, “has been applied extensively to understand some natural phenomena” (Pakdemirli, 2023). In contrast, exponential growth describes a continuous process in which the rate of change of a quantity is proportional to its current value. Such behavior is modeled using differential equations that “produce solutions …

Ambientes De Inclusión Para El Desarrollo Del Pensamiento Numérico Con Población Con Síndrome De Down, Luisa Valeria Escobar Buitrago, Ingry Yuliana Torres Garzón, Juan David Firigua Bejarano

Educación

La importancia de tratar sobre una educación inclusiva es hacer que la humanidad obtenga la aceptación hacia la diversidad, donde se encuentre un mundo lleno de posibilidades reconociendo todos los tipos de población entre ella las personas con Síndrome de Down, lo cual consiste en que la educación esté centrado en el respeto y la valoración de la diversidad, haciendo un enfoque general en las necesidades que esta población tiene, desarrollando habilidades para su desenvolvimiento tanto personal como laboral en determinada sociedad, por lo tanto el objetivo principal de este trabajo es desarrollar el pensamiento numérico de los estudiantes de …

(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 …

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions.

As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari

Applications and Applied Mathematics: An International Journal (AAM)

System of linear equations is applied for solving many problems in various areas of applied sciences. Fuzzy methods constitute an important mathematical and computational tool for modeling real-world systems with uncertainties of parameters. In this paper, we discuss about fully fuzzy linear systems in the form AX = b (FFLS). A novel method for finding the non-zero fuzzy solutions of these systems is proposed. We suppose that all elements of coefficient matrix A are positive and we employ parametric form linear system. Finally, Numerical examples are presented to illustrate this approach and its results are compared with other methods.

A Development Of The Number System, Janet R. Olsen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper is based on Landau's book "Foundations of Analysis" which constitutes a development of the number system founded on the Peano axioms for natural numbers.