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Property (H*) and Differentiability in Banach Spaces

Description: A continuous convex function on an open interval of the real line is differentiable everywhere except on a countable subset of its domain. There has been interest in the problem of characterizing those Banach spaces where the continuous functions exhibit similar differentiability properties. In this paper we show that if a Banach space E has property (H*) and B_E• is weak* sequentially compact, then E is an Asplund space. In the case where the space is weakly compactly generated, it is shown th… more
Date: August 1993
Creator: Obeid, Ossama A.
Item Type: Refine your search to only Thesis or Dissertation
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Tensor Products of Banach Spaces

Description: Tensor products of Banach Spaces are studied. An introduction to tensor products is given. Some results concerning the reciprocal Dunford-Pettis Property due to Emmanuele are presented. Pelczyriski's property (V) and (V)-sets are studied. It will be shown that if X and Y are Banach spaces with property (V) and every integral operator from X into Y* is compact, then the (V)-subsets of (X⊗F)* are weak* sequentially compact. This in turn will be used to prove some stronger convergence results for … more
Date: August 1996
Creator: Ochoa, James Philip
Item Type: Refine your search to only Thesis or Dissertation
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Gateaux Differentiable Points of Simple Type

Description: Every continuous convex function defined on a separable Banach space is Gateaux differentiable on a dense G^ subset of the space E [Mazur]. Suppose we are given a sequence (xn) that Is dense in E. Can we always find a Gateaux differentiable point x such that x = z^=^anxn.for some sequence (an) with infinitely many non-zero terms so that Ση∞=1||anxn|| < co ? According to this paper, such points are called of "simple type," and shown to be dense in E. Mazur's theorem follows directly from the res… more
Date: December 1982
Creator: Oh, Seung Jae
Item Type: Refine your search to only Thesis or Dissertation
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Multifractal Measures

Description: The purpose of this dissertation is to introduce a natural and unifying multifractal formalism which contains the above mentioned multifractal parameters, and gives interesting results for a large class of natural measures. In Part 2 we introduce the proposed multifractal formalism and study it properties. We also show that this multifractal formalism gives natural and interesting results when applied to (nonrandom) graph directed self-similar measures in Rd and "cookie-cutter" measures in R. I… more
Date: May 1994
Creator: Olsen, Lars
Item Type: Refine your search to only Thesis or Dissertation
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A Topological Uniqueness Result for the Special Linear Groups

Description: The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Date: August 1997
Creator: Opalecky, Robert Vincent
Item Type: Refine your search to only Thesis or Dissertation
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Measure Functions

Description: This thesis examines measure functions. A measure function has as its domain of definition a class of sets. It also must satisfy a certain additive condition. To state a concise definition of a measure function, it is convenient to define set function and completely additive set function.
Date: August 1965
Creator: Ottwell, Otho F.
Item Type: Refine your search to only Thesis or Dissertation
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Semi-supervised and Self-evolving Learning Algorithms with Application to Anomaly Detection in Cloud Computing

Description: Semi-supervised learning (SSL) is the most practical approach for classification among machine learning algorithms. It is similar to the humans way of learning and thus has great applications in text/image classification, bioinformatics, artificial intelligence, robotics etc. Labeled data is hard to obtain in real life experiments and may need human experts with experimental equipments to mark the labels, which can be slow and expensive. But unlabeled data is easily available in terms of web pa… more
Date: December 2012
Creator: Pannu, Husanbir Singh
Item Type: Refine your search to only Thesis or Dissertation
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A Comparative Study of Non Linear Conjugate Gradient Methods

Description: We study the development of nonlinear conjugate gradient methods, Fletcher Reeves (FR) and Polak Ribiere (PR). FR extends the linear conjugate gradient method to nonlinear functions by incorporating two changes, for the step length αk a line search is performed and replacing the residual, rk (rk=b-Axk) by the gradient of the nonlinear objective function. The PR method is equivalent to FR method for exact line searches and when the underlying quadratic function is strongly convex. The PR method … more
Date: August 2013
Creator: Pathak, Subrat
Item Type: Refine your search to only Thesis or Dissertation
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Traveling Wave Solutions of the Porous Medium Equation

Description: We prove the existence of a one-parameter family of solutions of the porous medium equation, a nonlinear heat equation. In our work, with space dimension 3, the interface is a half line whose end point advances at constant speed. We prove, by using maximum principle, that the solutions are stable under a suitable class of perturbations. We discuss the relevance of our solutions, when restricted to two dimensions, to gravity driven flows of thin films. Here we extend the results of J. Iaia and S… more
Date: May 2013
Creator: Paudel, Laxmi P.
Item Type: Refine your search to only Thesis or Dissertation
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A Development of the Peano Postulates

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 p… more
Date: May 1963
Creator: Peek, Darwin Eugene
Item Type: Refine your search to only Thesis or Dissertation
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Some Generalizations in the Theory of Summable Series

Description: 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.
Date: August 1950
Creator: Penner, Jimmie G.
Item Type: Refine your search to only Thesis or Dissertation
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Some Properties of Dini Derivatives

Description: 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.
Date: August 1953
Creator: Pinkerton, Jane W.
Item Type: Refine your search to only Thesis or Dissertation
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The Runge-Kutta Method

Description: This paper investigates the Runge-Kutta method of numerically integrating ordinary differential equations. An existence theorem is given insuring a solution to the differential equation, then the theorem is modified to yield an analytic solution. The derivation of the method itself is followed by an analysis of the inherent error.
Date: June 1961
Creator: Powell, Don Ross
Item Type: Refine your search to only Thesis or Dissertation
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Finite Dimensional Vector Space

Description: The object of this thesis is to examine properties of an abstract vector space of finite dimension n. The properties of the set of complex numbers are assumed, and the definition of a field and of an abelian group are not stated, although reference to these systems is made.
Date: August 1960
Creator: Power, Billy Joe
Item Type: Refine your search to only Thesis or Dissertation
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Some Diophantine Equations

Description: This paper will be devoted to an examination of several general and specific equations and systems of equations of the diophantine type. Only algebraic equations with integral coefficients, not all zero, will considered. The elementary properties of the integers will be assumed.
Date: January 1960
Creator: Pressly, Kirby Smith
Item Type: Refine your search to only Thesis or Dissertation
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