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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Orthogonal Polynomials, George Gevork Antashyan
Orthogonal Polynomials, George Gevork Antashyan
Theses Digitization Project
This thesis will show work on Orthogonal Polynomials. In mathematics, the type of polynomials that are orthogonal to each other under inner product are called orthogonal polynomials. Jacobi polynomials, Laguerre polynomials, and Hermite polynomials are examples of classical orthogonal polynomials that was invented in the nineteenth century. The theory of rational approximations is one of the most important applications of orthogonal polynomials.
Cassini Ovals As Elliptic Curves, Nozomi Arakaki
Cassini Ovals As Elliptic Curves, Nozomi Arakaki
Theses Digitization Project
The purpose of this project is to show that Cassini curves that are not lemniscates, when b does not equal 1, represent elliptic curves. It is also shown that the cross-ratios of these elliptic curves are either real numbers or represented by complex numbers on the unit circle on the conplex plane.
An Investigation Of Air Resistance On Projectile Motion From Aristotle To Euler, Michael Edward Clayton
An Investigation Of Air Resistance On Projectile Motion From Aristotle To Euler, Michael Edward Clayton
Theses Digitization Project
From antiquity until today, mathematicians have tried to develop a theory of projectile motion. The development of a theory of projectile motion began with just a basic observation of motion by the great Greek mathematician Aristotle and has evolved to become more than conjecture or hypothesis, but a well developed science of prediciting the flight and accuracy of a projectile in motion. This thesis traces the development of the theory of projectile motion from Greek antiquity to about the mid 1700's.
Leonhard Euler's Contribution To Infinite Polynomials, Jack Dean Meekins
Leonhard Euler's Contribution To Infinite Polynomials, Jack Dean Meekins
Theses Digitization Project
This thesis will focus on Euler's famous method for solving the infinite polynomial. It will show how he manipulated the sine function to find all possible points along the sine function such that the sine A would equal to y; these would be roots of the polynomial. It also shows how Euler set the infinite polynomial equal to the infinite product allowing him to determine which coefficients were equal to which reciprocals of the roots, roots squared, roots cubed, etc.
Solutions To A Generalized Pell Equation, Kyle Christopher Castro
Solutions To A Generalized Pell Equation, Kyle Christopher Castro
Theses Digitization Project
This study aims to extend the notion of continued fractions to a new field Q (x)*, in order to find solutions to generalized Pell's Equations in Q [x] . The investigation of these new solutions to Pell's Equation will begin with the necessary extensions of theorems as they apply to polynomials with rational coefficients and fractions of such polynomials in order to describe each "family" of solutions.
Prouhet-Tarry-Escott Problem, Juan Manuel Gutierrez
Prouhet-Tarry-Escott Problem, Juan Manuel Gutierrez
Theses Digitization Project
The purpose of this research paper is to gain a deeper understanding of a famous unsolved mathematical problem known as the Prouhet-Terry-Escott Problem. The Prouhet-Terry-Escott Problem is a complex problem that still has much to be discovered. This fascinating problem shows up in many areas of mathematics such as the study of polynomials, graph theory, and the theory of integral quadratic forms.
Closure Operations In Commutative Rings, Chloette Joy Samsam
Closure Operations In Commutative Rings, Chloette Joy Samsam
Theses Digitization Project
The purpose of this study is to survey different types of closures and closure operations on commutative rings and ideals.
Monomial And Permutation Representation Of Groups, Rebeca Maria Blanquet
Monomial And Permutation Representation Of Groups, Rebeca Maria Blanquet
Theses Digitization Project
The purpose of this project is to introduce another method of working with groups, that is more efficient when the groups we wish to work with are of a significantly large finite order. When we wish to work with small finite groups, we use permutations and matrices. Although these two methods are the general methods of working with groups, they are not always efficient.
Symmetric Generation, Lisa Sanchez
Symmetric Generation, Lisa Sanchez
Theses Digitization Project
The purpose of this project is to conduct a systematic search for finite homomorphic images of infinite semi-direct products mn : N, where m = 2,3,5,7 and N <̲ Sn and construct by hand some of the important homomorphic images that emerge from the search.