Mathematics Commons^™

Performance Of Bootstrap Confidence Intervals For L-Moments And Ratios Of L-Moments., Suzanne Glass

Electronic Theses and Dissertations

L-moments are defined as linear combinations of expected values of order statistics of a variable.(Hosking 1990) L-moments are estimated from samples using functions of weighted means of order statistics. The advantages of L-moments over classical moments are: able to characterize a wider range of distributions; L-moments are more robust to the presence of outliers in the data when estimated from a sample; and L-moments are less subject to bias in estimation and approximate their asymptotic normal distribution more closely.

Hosking (1990) obtained an asymptotic result specifying the sample L-moments have a multivariate normal distribution as n approaches infinity. The standard …

Vertices In Total Dominating Sets., Robert Elmer Dautermann Iii

Electronic Theses and Dissertations

Fricke, Haynes, Hedetniemi, Hedetniemi, and Laskar introduced the following concept. For a graph G = (V,E), let rho denote a property of interest concerning sets of vertices. A vertex u is rho-good if u is contained in a {minimum, maximum} rho-set in G and rho-bad if u is not contained in a rho-set. Let g denote the number of rho-good vertices and b denote the number of rho-bad vertices. A graph G is called rho-excellent if every vertex in V is rho-good, rho-commendable if g > b > 0, rho-fair if g = b, and …

Mode Vertices And Mode Graphs., Jobriath Scott Kauffman

Electronic Theses and Dissertations

The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some …

The Spieker Circle And Certain Related Configurations, Berthola Elmo Lumzy

Electronic Theses and Dissertations

This thesis, presented to the Department of Mathematics at Xavier University in partial fulfillment of requirements for the degree of Master of Arts in 1952, examines the Spieker circle, a circle inscribed in the median triangle of a given triangle, and extends its defining properties to related geometric configurations. Lumzy first establishes a series of analogies between the Spieker circle and the nine-point circle, demonstrating parallel relationships involving radius, center, harmonic conjugates, and homothetic centers relative to the incenter, median point, and Nagel point of a triangle.

The thesis then proves that the Spieker circle is inscribed in two congruent …

A Study Of Fermat's Last Theorem., Jerome L. Krumpelman

Electronic Theses and Dissertations

This work is intended primarily for the student of mathematics who may not necessarily wish to delve into the complete theory of the problem. but who may wish to get a picture of the work necessary to study and understand it. For a complete history of the problem until 1919, refer to Chapter XXVI of Dickson's History of the Theory of Numbers, II, and for the work primarily connected with Irregular Cyclotomic Fields and Fermat's Last Theorem through part of 1927, refer to Algebraic Numbers, II, National Research Council Bulletin, # 62. For a Short presentation of the problem refer …

Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean

Electronic Theses and Dissertations

Geometry, the science of space and its relations which exist between its various elements, linear, superficial and solid, develops and helps society.

Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean

Electronic Theses and Dissertations

No abstract provided.

General Steps In The Evolution Of The Calculus From The Time Of The Ancients To The Present, Sister Mary Virginia Ssf

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This thesis, submitted to Xavier University in partial fulfillment of requirements for a Bachelor of Science degree in 1931, traces the historical development of the calculus from ancient Greek mathematics through the early twentieth century. The study is organized chronologically across eight sections. The introduction defines key mathematical terms including calculus, variable, and limit, and situates the calculus as the most powerful instrument of mathematical investigation. The thesis then examines the Method of Exhaustion developed by Greek mathematicians including Antiphon (430 B.C.), Eudoxus (370 B.C.), and Archimedes (225 B.C.), whose summation of infinite series represents the nearest ancient approach to …

History Of Applied Geometry, Evelyn Jackson

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Mathematics: Just what does the word mean to us? After a moment of thought many different meanings may present themselves to our minds. At first we are inclined to say that the word mathematics covers a vast field. We are justified in so thinking because mathematics embraces a wide scope of study. Were we to say that it is a science we should place it in its proper genius, for it is truly a science of numbers and space. However, could not the science be the art of calculation or the art of computation?

History Of Applied Geometry, Evelyn Jackson

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No abstract provided.

The Utility Of Mathematics, Jack R. Dunn

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No abstract provided.