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Missouri University of Science and Technology

1971

Mathematics

Articles 1 - 9 of 9

Full-Text Articles in Physical Sciences and Mathematics

Existence And Uniqueness For Nonlinear Neutral-Differential Equations, L. J. Grimm Jan 1971

Existence And Uniqueness For Nonlinear Neutral-Differential Equations, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

Fixed point theorems are used to prove existence and uniqueness of the C1 solution of the initial-value problem for a functional-differential equation of neutral type. © 1971, American Mathematical Society. All Rights Reserved.

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On Completeness In Quasi-Uniform Spaces, John W. Carlson, Troy L. Hicks Jan 1971

On Completeness In Quasi-Uniform Spaces, John W. Carlson, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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Existence And Continuous Dependence For A Class Of Nonlinear Neutraldifferential Equations, L. J. Grimm Jan 1971

Existence And Continuous Dependence For A Class Of Nonlinear Neutraldifferential Equations, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

This paper presents existence, uniqueness, and continuous dependence theorems for solutions of initial-value problems for neutral-differential equations of the form (equation omited), where f, g, and h are continuous functions with g(0, x0)=h(0, x0) = 0. The existence of a continuous solution of the functional equation z(t) =f(t, z(h(t))) is proved as a corollary. © 1971 American Mathematical Society.

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Some Statistical Inferences For The Bivariate Exponential Distribution, Bruce Mohr Bemis Jan 1971

Some Statistical Inferences For The Bivariate Exponential Distribution, Bruce Mohr Bemis

Doctoral Dissertations

"The bivariate exponential distribution is neither absolutely continuous nor discrete due to the property that there is a positive probability that the two random variables may be equal. Basic properties of the distribution are presented as well as methods of parameter estimation including maximum likelihood. The distribution is shown to satisfy the usual regularity conditions in spite of its possession of a singularity. The maximum likelihood estimates are asymptotically efficient. Two other methods of estimation are compared with the maximum likelihood method in terms of efficiency. Tests of the hypothesis that two random variables each have independent exponential distributions versus …

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Integrability Of The Sums Of The Trigonometric Series 1/2 Aₒ + ∞ [Over] Σ [Over] N=1 AN Cos Nθ And ∞ [Over] Σ [Over] N=1 AN Sin Nθ, John William Garrett Jan 1971

Integrability Of The Sums Of The Trigonometric Series 1/2 Aₒ + ∞ [Over] Σ [Over] N=1 AN Cos Nθ And ∞ [Over] Σ [Over] N=1 AN Sin Nθ, John William Garrett

Masters Theses

"The trigonometric series C = 1/2 aₒ + ∞ [over] Σ [over] [n=1] a[subscript n] cos nΘ and S = ∞ [over] Σ [over] n=1 a[subscript n] sin nΘ, where {a[subscript n]} monotonically decreases to zero both converge almost everywhere to functions f and g respectively. f (or g) is L iff C (or S) is the Fourier series of f (or g) iff term-by-term integration of C (or S) is valid. There are three equivalent conditions, each of which implies that C is the Fourier series of f...."--Abstract, page ii.

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Inclusion Theorems For Boundary Value Problems For Delay Differential Equations, Leon M. Hall Jan 1971

Inclusion Theorems For Boundary Value Problems For Delay Differential Equations, Leon M. Hall

Masters Theses

"In this thesis existence and uniqueness of solutions to certain second and third order boundary value problems for delay differential equations is established. Sequences of upper and lower solutions similar to those used by Kovač and Savčenko are defined by means of an integral operator, and conditions are given under which these sequences converge monotonically from above and below to the unique solution of the problem. Some numerical examples for the second order case are presented. Existence and uniqueness is also proved for the case where the delay is a function of the solution as well as the independent variable"--Abstract, …

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Special Subrings Of Real, Continuous Functions, Paul Marlin Harms Jan 1971

Special Subrings Of Real, Continuous Functions, Paul Marlin Harms

Doctoral Dissertations

"Some lattice-ordered subrings of C(X) containing C*(X) are examined where X is a completely regular space. Each realcompact spaceY between [v]x and ßx is associated with a lattice-ordered subring of C(X) which is isomorphic to C(Y) and contains C*(X). The cardinal number of (ßX - [v]X) is a lower bound for the cardinal number of these subrings. Every prime ideal in each of these subrings is comparable with the intersection of the subring and a maximal ideal in C(X). The structure space of maximal ideals is studied for special subrings in C(X) containing CK(X), the continuous functions of …

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Characterizing Topologies By Classes Of Functions And Multifunctions, Alexander Hamlin Cramer Jan 1971

Characterizing Topologies By Classes Of Functions And Multifunctions, Alexander Hamlin Cramer

Doctoral Dissertations

"Topological spaces are characterized by the algebraic and topological structures of their classes of continuous selfmaps. The problem of determining the topology of a set given certain classes of multifunctions or relations is considered. The algebraic structure of the upper semicontinuous multifunctions is shown to determine the topology of T₁ spaces. A partial order for classes of topologies for the real numbers is defined and relationships between various classes are established"--Abstract, page ii.

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Modeling The Visual Pathway For Interactive Diagnosis Of Visual Fields, Chiam Geoffrey Goldbogen Jan 1971

Modeling The Visual Pathway For Interactive Diagnosis Of Visual Fields, Chiam Geoffrey Goldbogen

Doctoral Dissertations

"Visual fields are an important tool for the ophthalmologist in the detection, diagnosis, and monitoring of certain diseases and maladies of the visual pathway. The aim of the present research is to build a computer system which utilizes a learning machine to develop a mathematical model of the visual pathway. It is hoped that this system may be used in the field of ophthalmology as a teaching aid, or may assist in various aspects of diagnosis. Faults corresponding to blind or impaired areas of visual fields are extracted from medical records of a patient's condition. The structure of the model …

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