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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris
Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris
Theses Digitization Project
Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.
A Topological Approach To Nonlinear Analysis, Wendy Ann Peske
A Topological Approach To Nonlinear Analysis, Wendy Ann Peske
Theses Digitization Project
A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.
Survival Analysis, Mohammad Alif Wardak
Survival Analysis, Mohammad Alif Wardak
Theses Digitization Project
Survival analysis pertains to a statistical approach designed to take into account the amount of time an experimental unit contributes to a study. A Mayo Clinic study of 418 Primary Biliary Cirrhosis patients during a ten year period was used. The Kaplan-Meier Estimator, a non-parametric statistic, and the Cox Proportional Hazard methods were the tools applied. Kaplan-Meier results include total values/censored values.
Symmetric Generation Of Finite Homomorphic Images?, Lee Farber
Symmetric Generation Of Finite Homomorphic Images?, Lee Farber
Theses Digitization Project
The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.
Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle
Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle
Theses Digitization Project
In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.
The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau
The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau
Theses Digitization Project
This project centers around finding specific examples of quintic polynomials that were and were not solvable. This helped to devise a method for finding examples of solvable and unsolvable quintics.
Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer
Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer
Theses Digitization Project
This paper defines generalized binomial coefficients and shows that they can be used to generate generalized Pascal's Triangles and have properties analogous to binomial coefficients. It uses the generalized binomial coefficients to compute the Dilworth number and the Sperner number of certain rings.
Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt
Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt
Theses Digitization Project
Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.
Symmetrically Generated Groups, Benny Nguyen
Symmetrically Generated Groups, Benny Nguyen
Theses Digitization Project
This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.
Root Subgroups Of The Rank Two Unitary Groups, Matthew Thomas Henes
Root Subgroups Of The Rank Two Unitary Groups, Matthew Thomas Henes
Theses Digitization Project
Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.