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Some Fundamental Properties of Power Series
A study to deduce some fundamental properties of power series.
Date:
August 1939
Creator:
Rogers, Curtis, A.
Object Type:
Thesis or Dissertation
System:
The UNT Digital Library
The Steepest Descent Method Using Finite Elements for Systems of Nonlinear Partial Differential Equations
The purpose of this paper is to develop a general method for using Finite Elements in the Steepest Descent Method. The main application is to a partial differential equation for a Transonic Flow Problem. It is also applied to Burger's equation, Laplace's equation and the minimal surface equation. The entire method is tested by computer runs which give satisfactory results. The validity of certain of the procedures used are proved theoretically. The way that the writer handles finite elements is quite different from traditional finite element methods. The variational principle is not needed. The theory is based upon the calculation of a matrix representation of operators in the gradient of a certain functional. Systematic use is made of local interpolation functions.
Date:
August 1981
Creator:
Liaw, Mou-yung Morris
Object Type:
Thesis or Dissertation
System:
The UNT Digital Library
Gateaux Differentiable Points of Simple Type
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 result and Rybakov's theorem (A countably additive vector measure F: E -* X on a cr-field is absolutely continuous with respect to |x*F] for some x* e Xs) can be shown without deep measure theoretic Involvement.
Date:
December 1982
Creator:
Oh, Seung Jae
Object Type:
Thesis or Dissertation
System:
The UNT Digital Library
Algebraic Numbers and Topologically Equivalent Measures
A set-theoretical point of view to study algebraic numbers has been introduced. We extend a result of Navarro-Bermudez concerning shift invariant measures in the Cantor space which are topologically equivalent to shift invariant measures which correspond to some algebraic integers. It is known that any transcendental numbers and rational numbers in the unit interval are not binomial. We proved that there are algebraic numbers of degree greater than two so that they are binomial numbers. Algebraic integers of degree 2 are proved not to be binomial numbers. A few compositive relations having to do with algebraic numbers on the unit interval have been studied; for instance, rationally related, integrally related, binomially related, B1-related relations. A formula between binomial numbers and binomial coefficients has been stated. A generalized algebraic equation related to topologically equivalent measures has also been stated.
Date:
December 1983
Creator:
Huang, Kuoduo
Object Type:
Thesis or Dissertation
System:
The UNT Digital Library
Nonlinear Boundary Conditions in Sobolev Spaces
The method of dual steepest descent is used to solve ordinary differential equations with nonlinear boundary conditions. A general boundary condition is B(u) = 0 where where B is a continuous functional on the nth order Sobolev space Hn[0.1J. If F:HnCO,l] —• L2[0,1] represents a 2 differential equation, define *(u) = 1/2 IIF < u) li and £(u) = 1/2 l!B(u)ll2. Steepest descent is applied to the functional 2 £ a * + £. Two special cases are considered. If f:lR —• R is C^(2), a Type I boundary condition is defined by B(u) = f(u(0),u(1)). Given K: [0,1}xR—•and g: [0,1] —• R of bounded variation, a Type II boundary condition is B(u) = ƒ1/0K(x,u(x))dg(x).
Date:
December 1984
Creator:
Richardson, Walter Brown
Object Type:
Thesis or Dissertation
System:
The UNT Digital Library
Caring for Indigent Infants in Denton County in Relation to Dallas and Tarrant Counties in Texas
Paper compares care for uninsured infants in Denton County, under a County Indigent Health Care Plan (CIHCP), and in Dallas and Tarrant counties, which have hospital districts.
Date:
2008
Creator:
Grant, Scott
Object Type:
Article
System:
The UNT Digital Library
An Analysis of Preparatory Measures for Mathematical Proof Courses
Paper explores the effectiveness of the methods used to prepare mathematics majors for courses that require proofs.
Date:
2009
Creator:
March, Tonya
Object Type:
Article
System:
The UNT Digital Library