Other Physical Sciences and Mathematics Commons^™

An Exploration Of The Structure Of The Linear Algebraic Model Of Color, Isaac Martin

University Honors Theses

This thesis surveys the mathematical grounding of linear algebraic models of color. It aims to build from the ground up the framework by which additive color is broadly understood in the digital age. Primarily building on the work of Jozef Cohen, Eric Dubois, David H. Krantz, and Günter Wyszecki, it aims to chart the construction of a model of color that underpins most modern understandings of color. While the construction is certainly established in colorimetric circles, the construction is, in the thesis author's opinion, either obtuse or non-rigorous. Ideally, this thesis serves to make the construction accessible to an audience …

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

Representation Theory And Its Applications In Physics, Max Varverakis

Master's Theses

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …

Frieze And Tiling Groups In The Lorentz-Minkowski Plane, Michael O. Lynch

Honors Undergraduate Theses

In this thesis, there is a presentation of the isometries from the Lorentz-Minkowski Plane and a solution to the Frieze Patterns. There is a suggestion for a solution for the Tiling Patterns. Since the construction of these mathematical structures is well understood in the Euclidean plane, one can follow a similar approach to the construction of such objects to find the unique number of groups that describe all possible frieze patterns while there is a suggestion of the number for the tiling case. There is a reflection of these results in a computational and cosmological context.

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 …

Roots Of Quaternionic Polynomials And Automorphisms Of Roots, Olalekan Ogunmefun

Electronic Theses and Dissertations

The quaternions are an extension of the complex numbers which were first described by Sir William Rowan Hamilton in 1843. In his description, he gave the equation of the multiplication of the imaginary component similar to that of complex numbers. Many mathematicians have studied the zeros of quaternionic polynomials. Prominent of these, Ivan Niven pioneered a root-finding algorithm in 1941, Gentili and Struppa proved the Fundamental Theorem of Algebra (FTA) for quaternions in 2007. This thesis finds the zeros of quaternionic polynomials using the Fundamental Theorem of Algebra. There are isolated zeros and spheres of zeros. In this thesis, we …

Commutators On Fock Spaces, Daniel Alpay, Paula Cerejeiras, Uwe Kähler, Trevor Kling

Mathematics, Physics, and Computer Science Faculty Articles and Research

Given a weighted ℓ2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …

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 …

Geometric Constructions From An Algebraic Perspective, Betzabe Bojorquez

Electronic Theses, Projects, and Dissertations

Many topics that mathematicians study at times seem so unrelated such as Geometry and Abstract Algebra. These two branches of math would seem unrelated at first glance. I will try to bridge Geometry and Abstract Algebra just a bit with the following topics. We can be sure that after we construct our basic parallel and perpendicular lines, bisected angles, regular polygons, and other basic geometric figures, we are actually constructing what in geometry is simply stated and accepted, because it will be proven using abstract algebra. Also we will look at many classic problems in Geometry that are not possible …

255 Compiled And Solved Problems In Geometry And Trigonometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Long Wavelength Analysis Of A Model For The Geographic Spread Of A Disease, Layachi Hadji

Applications and Applied Mathematics: An International Journal (AAM)

We investigate the temporal and spatial evolution of the spread of an infectious disease by performing a long-wavelength analysis of a classical model for the geographic spread of a rabies epidemic in a population of foxes subject to idealized boundary conditions. We consider twodimensional and three-dimensional landscapes consisting of an infinite horizontal strip bounded by two walls a finite distance apart and a horizontal region bounded above and below by horizontal walls, respectively. A nonlinear partial differential evolution Equation for the leading order of infectives is derived. The Equation captures the space and time variations of the spread of the …

New Research On Neutrosophic Algebraic Structures, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures in a broader sense. The indeterminacy element “ I “ gives rise to a more bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three categories: such as neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical …

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …

Dsm Vector Spaces Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of DSm linear algebra of refined labels have been done by Florentin Smarandache, Jean Dezert, and Xinde Li.

In this book the authors introduce the notion of DSm vector spaces of refined labels. The reader is requested to refer the paper as the basic concepts are taken from that paper [35]. This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly …

Introduction To Bimatrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in …

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.