Latest content added for UNT Digital Library Collection: UNT Theses and Dissertationshttp://digital.library.unt.edu/explore/collections/UNTETD/browse/?fq=str_degree_discipline:Mathematics&fq=untl_decade:1950-19592012-12-27T22:03:54-06:00UNT LibrariesThis is a custom feed for browsing UNT Digital Library Collection: UNT Theses and DissertationsSome Generalizations in the Theory of Summable Series2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130256/<p><a href="/ark:/67531/metadc130256/"><img alt="Some Generalizations in the Theory of Summable Series" title="Some Generalizations in the Theory of Summable Series" src="/ark:/67531/metadc130256/thumbnail/"/></a></p><p>It will be our purpose to study a generalized definition of sum of a series and the restrictions which must be placed upon it in order that it shall satisfy the generally accepted requirements of any generalized definition of sum of a series. We shall then proceed to investigate the possibilities of further generalizing this process.</p>Some Properties of Dini Derivatives2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130342/<p><a href="/ark:/67531/metadc130342/"><img alt="Some Properties of Dini Derivatives" title="Some Properties of Dini Derivatives" src="/ark:/67531/metadc130342/thumbnail/"/></a></p><p>The purpose of this paper is to derive certain of the fundamental properties of the Dini derivatives of an arbitrary real function. To this end it will be necessary to investigate the properties of the limits superior and inferior of real functions and to prove the Vitali Covering Theorem as well as a fundamental theorem on the metric density of arbitrary point sets.</p>A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130370/<p><a href="/ark:/67531/metadc130370/"><img alt="A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions" title="A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions" src="/ark:/67531/metadc130370/thumbnail/"/></a></p><p>The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.</p>Some Properties of the Perron Integral2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130430/<p><a href="/ark:/67531/metadc130430/"><img alt="Some Properties of the Perron Integral" title="Some Properties of the Perron Integral" src="/ark:/67531/metadc130430/thumbnail/"/></a></p><p>The purpose of this thesis is to restate the definition of the integral as given by O. Perron, to establish some of the fundamental properties of the Perron integral, and to prove the equivalence between the Perron and Lebesgue integrals in the bounded case. </p>Random Sampling2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130442/<p><a href="/ark:/67531/metadc130442/"><img alt="Random Sampling" title="Random Sampling" src="/ark:/67531/metadc130442/thumbnail/"/></a></p><p>The purpose of this study is to show the use of random sampling in solving certain mathematical problems. The origin of random numbers to be used in sampling is discussed and methods of sampling from known distributions are then given together with an indication that the sampling procedures are unbiased.</p>Random Variables of One Dimension2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130444/<p><a href="/ark:/67531/metadc130444/"><img alt="Random Variables of One Dimension" title="Random Variables of One Dimension" src="/ark:/67531/metadc130444/thumbnail/"/></a></p><p>This thesis examines random variables of one dimension.</p>Exhaustibility and Related Set Properties2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130236/<p><a href="/ark:/67531/metadc130236/"><img alt="Exhaustibility and Related Set Properties" title="Exhaustibility and Related Set Properties" src="/ark:/67531/metadc130236/thumbnail/"/></a></p><p>The purpose of this paper is to develop certain fundamental properties of exhaustible sets and their complements and to examine various set properties which are generalizations, with respect to exhaustible neglect, or well-known set properties.</p>Some Results of Two Topological Spaces2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130437/<p><a href="/ark:/67531/metadc130437/"><img alt="Some Results of Two Topological Spaces" title="Some Results of Two Topological Spaces" src="/ark:/67531/metadc130437/thumbnail/"/></a></p><p>This thesis explores some results of two topological spaces.</p>The Lebesgue and Equivalent Integrals2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130387/<p><a href="/ark:/67531/metadc130387/"><img alt="The Lebesgue and Equivalent Integrals" title="The Lebesgue and Equivalent Integrals" src="/ark:/67531/metadc130387/thumbnail/"/></a></p><p>The purpose of this thesis is to present a study of the Lebesgue definite integral, defined in four different ways.</p>Fundamental Properties of Fourier Series2012-12-27T22:03:54-06:00http://digital.library.unt.edu/ark:/67531/metadc130383/<p><a href="/ark:/67531/metadc130383/"><img alt="Fundamental Properties of Fourier Series" title="Fundamental Properties of Fourier Series" src="/ark:/67531/metadc130383/thumbnail/"/></a></p><p>This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.</p>