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UNT Theses and Dissertations
A Constructive Method for Finding Critical Point of the Ginzburg-Landau Energy Functional
Date: August 2008
Creator: Kazemi, Parimah
Description: In this work I present a constructive method for finding critical points of the Ginzburg-Landau energy functional using the method of Sobolev gradients. I give a description of the construction of the Sobolev gradient and obtain convergence results for continuous steepest descent with this gradient. I study the Ginzburg-Landau functional with magnetic field and the Ginzburg-Landau functional without magnetic field. I then present the numerical results I obtained by using steepest descent with the discretized Sobolev gradient.
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Permallink:digital.library.unt.edu/ark:/67531/metadc9075/
Continuation of Real Functions Defined by Power Series
Date: 1948
Creator: Strickland, Warren, G.
Description: This thesis looks at power series, particularly in the areas of: radius of convergence, properties of functions represented by power series, algebra of power series, and Taylor's Theorem and continuation by means of power series.
Contributing Partner: UNT Libraries
Permallink:digital.library.unt.edu/ark:/67531/metadc83451/
Convergence Preserving Matrices
Date: August 1961
Creator: Line, Harrell Harvey
Description: This paper is the result of a study of triangular matrices with particular emphasis on those which are convergence preserving transformations.
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Permallink:digital.library.unt.edu/ark:/67531/metadc130470/
Convergence Tests for Infinite Series
Date: 1950
Creator: Latimer, Philip W.
Description: The field of infinite series is so large that any investigation into that field must necessarily be limited to a particular phase. An attempt has been made to develop a number of tests having a wide range of applications. Particular emphasis has been placed on tests for series of positive terms.
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Permallink:digital.library.unt.edu/ark:/67531/metadc83732/
A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions
Date: May 2004
Creator: Vlasic, Andrew
Description: We follow a research paper that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of our main result.
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Permallink:digital.library.unt.edu/ark:/67531/metadc4476/
Determining Properties of Synaptic Structure in a Neural Network through Spike Train Analysis
Date: May 2007
Creator: Brooks, Evan
Description: A "complex" system typically has a relatively large number of dynamically interacting components and tends to exhibit emergent behavior that cannot be explained by analyzing each component separately. A biological neural network is one example of such a system. A multi-agent model of such a network is developed to study the relationships between a network's structure and its spike train output. Using this model, inferences are made about the synaptic structure of networks through cluster analysis of spike train summary statistics A complexity measure for the network structure is also presented which has a one-to-one correspondence with the standard time series complexity measure sample entropy.
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Permallink:digital.library.unt.edu/ark:/67531/metadc3702/
A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions
Date: August 1954
Creator: Allen, Alfred I.
Description: 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.
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Permallink:digital.library.unt.edu/ark:/67531/metadc130370/
A Development of the Exponential and Logarithmic Functions
Date: 1953
Creator: Mackey, Benford B.
Description: This thesis discusses a development of the exponential and logarithmic functions.
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Permallink:digital.library.unt.edu/ark:/67531/metadc107841/
The Development of the Natural Numbers by Means of the Peano Postulates
Date: 1951
Creator: Baugh, Orvil Lee
Description: This thesis covers the development of the natural numbers by means of the peano postulates.
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Permallink:digital.library.unt.edu/ark:/67531/metadc96984/
A Development of the Peano Postulates
Date: May 1963
Creator: Peek, Darwin Eugene
Description: The purpose of this paper is to develop the Peano postulates from a weaker axiom system than the system used by John L. Kelley in General Topology. The axiom of regularity which states "If X is a non-empty set, then there is a member Y of X such that the intersection of X and Y is empty." is not assumed in this thesis. The axiom of amalgamation which states "If X is a set, then the union of the elements of X is a set." is also not assumed. All other axioms used by Kelley relevant to the Peano postulates are assumed. The word class is never used in the thesis, though the variables can be interpreted as classes.
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Permallink:digital.library.unt.edu/ark:/67531/metadc108207/