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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Minimal Surfaces, Maria Guadalupe Chaparro
Minimal Surfaces, Maria Guadalupe Chaparro
Theses Digitization Project
The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.
Construction Of Finite Homomorphic Images, Jane Yoo
Construction Of Finite Homomorphic Images, Jane Yoo
Theses Digitization Project
The purpose of this thesis is to construct finite groups as homomorphic images of progenitors.
Conics In The Hyperbolic Plane, Trent Phillip Naeve
Conics In The Hyperbolic Plane, Trent Phillip Naeve
Theses Digitization Project
An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.
Stone's Representation Theorem, Ion Radu
Stone's Representation Theorem, Ion Radu
Theses Digitization Project
The thesis analyzes some aspects of the theory of distributive lattices, particularly two representation theorems: Birkhoff's representation theorem for finite distributive lattices and Stone's representation theorem for infinite distributive lattices.
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Theses Digitization Project
The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.
Tutte Polynomial In Knot Theory, David Alan Petersen
Tutte Polynomial In Knot Theory, David Alan Petersen
Theses Digitization Project
This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
Theses Digitization Project
This thesis covers improvements on the upperbounds for ropelength of a specific class of algebraic knots.
Primary Decomposition Of Ideals In A Ring, Sola Oyinsan
Primary Decomposition Of Ideals In A Ring, Sola Oyinsan
Theses Digitization Project
The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.