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Mathematics and Statistics Faculty Research & Creative Works

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Articles 421 - 443 of 443

Full-Text Articles in Mathematics

Regular Singular Differential Equations Whose Conjugate Equation Has Polynomial Solutions, Leon M. Hall Jan 1977

Regular Singular Differential Equations Whose Conjugate Equation Has Polynomial Solutions, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

Consider the n -dimensional singular differential system defined by the operator $L:(Ly)(z) = z^p y'(z) + A(z)y(z)$, where z is a complex variable and p is a positive integer. The solvability of the nonhomogeneous system $Ly = g$ depends on the solutions of the homogeneous conjugate system, $L^ * f = 0$, where $L^ * $ is the operator conjugate to L. We show that $L^ * f = 0$ has polynomial solutions if the constant matrix in the series expansion of $A(z)$ has at least one nonpositive integer eigenvalue. Also, we show that if $L^ * f = 0$ …


A Class Of Functional Equations And Mielnik Probability Spaces, S. J. Guccione, Caslav V. Stanojevic Jan 1976

A Class Of Functional Equations And Mielnik Probability Spaces, S. J. Guccione, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

Let S be the unit sphere of a normed real linear space N and let (S, p) be a Mielnik space of dimension two. For p(x, y) = f(‖x+y‖), x, yєS, where /is a continuous, strictly increasing function from [0, 2] onto [0, 1], it has been shown that (S, p) being two dimensional is equivalent to N being an inner product space. In some polarization problems modeled on the unit sphere of an inner product space, the transition probability p(x, y) may not be as well behaved as p(x, y) = f(‖x + y‖). In order to provide a …


Quasi-Unmixedness And Integral Closure Of Rees Rings, Peter G. Sawtelle Jan 1976

Quasi-Unmixedness And Integral Closure Of Rees Rings, Peter G. Sawtelle

Mathematics and Statistics Faculty Research & Creative Works

For certain Rees rings ℛ of a local domain R, the quasiunmixedness of R is characterized in terms of a certain transform of ℛ being contained in the integral closure of ℛ. © 1976 American Mathematical Society.


On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic Jan 1976

On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that to a certain cosine series f, a Rees-Stanojević cosine sumn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for L1 convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Other corollaries are given concerning the well-known integrability conditions. © 1975, American Mathematical Society.


On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic Jan 1976

On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

Rees and Stanojevic introduced a new class of modified cosine sums (equation omitted) and found a necessary and sufficient condition for integrability of these modified cosine sums. Here we show that to every classical cosine series f with coefficients of bounded variation, a Rees-Stanqjevic cosine sum gn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for Lx convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Examples are given using the well-known integrability conditions. © 1976 American …


Univalence Of Derivatives Of Functions Defined By Gap Power Series. Ii, S. M. Shah, S. Y. Trimble Jan 1976

Univalence Of Derivatives Of Functions Defined By Gap Power Series. Ii, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


The Extremal Structure Of Locally Compact Convex Sets, J. C. Hankins, Roy M. Rakestraw Jan 1976

The Extremal Structure Of Locally Compact Convex Sets, J. C. Hankins, Roy M. Rakestraw

Mathematics and Statistics Faculty Research & Creative Works

Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved.


Univalence Of Derivatives Of Functions Defined By Gap Power Series, S. M. Shah, S. Y. Trimble Jan 1975

Univalence Of Derivatives Of Functions Defined By Gap Power Series, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


A Coefficient Inequality For Convex Univalent Functions, S. Y. Trimble Jan 1975

A Coefficient Inequality For Convex Univalent Functions, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

A short proof of formula presented is given for normalized convex univalent functions. © 1975, American Mathematical Society.


On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic Jan 1975

On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that the method used by C. V. Stanojevic to obtain a characterization of inner product spaces in terms of a Mielnik probability space of dimension 2 does not admit a generalization to dimension n > 2. © 1975 American Mathematical Society.


Stiefel-Whitney Homology Classes And Bordism, Ethan Akin Jan 1975

Stiefel-Whitney Homology Classes And Bordism, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

We develop the theory of mod 2 Stiefel-Whitney homology classes for Euler polyhedral. We then describe a simple method of obtaining pJ. bordism theories. Finally, we define the ungraded bordism theory of Euler spaces and show that it is isomorphic to ordinary total homology. © 1975 American Mathematical Society.


The Order Of An Entire Function With Some Derivatives Univalent, S. M. Shah, S. Y. Trimble Jan 1974

The Order Of An Entire Function With Some Derivatives Univalent, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


A Note On T, Topologies, Wilson R. Crisler, Troy L. Hicks Jan 1974

A Note On T, Topologies, Wilson R. Crisler, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Let t be a T. topology for a set X. The problem of representing t as the lattice product (intersection) of stronger topologies is considered. © 1974 American Mathematical Society.


Quasi-Unmixed Local Rings And Quasi-Subspaces, Peter G. Sawtelle Jan 1973

Quasi-Unmixed Local Rings And Quasi-Subspaces, Peter G. Sawtelle

Mathematics and Statistics Faculty Research & Creative Works

The concept of a quasi-subspace is defined so that it plays a role relative to quasi-unmixedness analogous to that of subspace to unmixedness. This definition is used to characterize quasi-unmixed local rings. © 1973 American Mathematical Society.


A First Order Method For Differential Equations Of Neutral Type, R. N. Castleton, L. J. Grimm Jan 1973

A First Order Method For Differential Equations Of Neutral Type, R. N. Castleton, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

A first order method is presented for solution of the initial-value problem for a differential equation of neutral type with implicit delay in the critical case where the time-lag is zero and the method of stepwise integration does not apply. A convergence theorem is proved, and numerical examples are given. © 1973, American Mathematical Society.


Some Quasi-Uniform Space Examples, Troy L. Hicks, J. W. Carlson Jan 1972

Some Quasi-Uniform Space Examples, Troy L. Hicks, J. W. Carlson

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


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.


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.


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.


On Semigroups Of Functions On Topological Spaces, Troy L. Hicks, A. G. (Glen) Haddock Jan 1969

On Semigroups Of Functions On Topological Spaces, Troy L. Hicks, A. G. (Glen) Haddock

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


Manifold Phenomena In The Theory Of Polyhedra, Ethan Akin Jan 1969

Manifold Phenomena In The Theory Of Polyhedra, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


Rings Of Continuous Functions On Open Convex Subsets Of R, Lyle E. Pursell Jan 1968

Rings Of Continuous Functions On Open Convex Subsets Of R, Lyle E. Pursell

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


Tolerance Regions For A Joint Exponential Distribution, Lee J. Bain Jan 1967

Tolerance Regions For A Joint Exponential Distribution, Lee J. Bain

Mathematics and Statistics Faculty Research & Creative Works

The evaluation of the reliability of a system of components, when the components are assumed to follow a joint exponential distribution, is considered. The approach used is to develop tolerance regions for the joint exponential distribution or to estimate the probability content of the appropriate specification region. Copyright © 1968 by The Institute of Electrical and Electronics Engineers, Inc.