Statistics and Probability Commons^™

Banach Spaces Of Functions Analytic In A Polydisc, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.

Ada: A New Programming Language., Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

In an attempt to control defense software costs while maintaining system reliability, the DOD (Department of Defense) has sponsored the development of a new programming language, called Ada. While Ada supports many of the features found in Fortran and Pascal, it has additional features making it easier and more reliable to use in large complex engineering software systems. Currently, the DOD is requiring that many new defense software systems be written in Ada. The author reviews the history of Ada's development and examines the primary constructs of the language. The philosophy behind Ada program design is reviewed by designing and …

Approximate Tolerance Limits And Confidence Limits On Reliability For The Gamma Distribution, Lee J. Bain, Max Engelhardt, Wei Kei Shiue

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Lebesgue Integral As The Almost Sure Limit Of Random Riemann Sums, John C. Keffer, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

A method is given for generating random intermediate points for a sequence of partitions. For the corresponding random Riemann sums it is shown that they converge almost surely to the Lebesgue integral. © 1982 American Mathematical Society.

Tauberian Conditions For V-Convergence Of Fourier Series, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is proved that Fourier series with asymptotically even coefficients and satisfying (formula present here), for some 1 < p < 2, con­verge in L1-norm if and only if (formula present here), where En(t) =Σk=0neiktRecent results of Stanojevic [1], Bojanic and Stanojevic [2], and Goldberg and Stanojevic [3] are special cases of some corollaries to the main theorem. © 1982 American Mathematical Society.

Conjugate Type Boundary Value Problems For Functional-Differential Equations, P. W. Eloe, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Class Of L¹-Convergence, R. Bojan1c, C. V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is proved that if the Fourier coefficients (an) of /E L!(0, ir) satisfy (*)L" kp\Aan\p = o(l), for some 1

< 2, then \\sn- f\\ = o(l), if and only if a" lg n * o(l). For cosine trigonometric series with coefficients of bounded variation and satisfying (*) it is proved that a necessary and sufficient condition for the series to be a Fourier series is (an) E 6, where G is the Garrett-Stanojevic [4] class. © 1982 American Mathematical Society.

A Note On Fixed-Point Theorems, Troy L. Hicks, M. D. Humphries

Mathematics and Statistics Faculty Research & Creative Works

In an earlier note, S. P. Singh gave an extension of a theorem of Brosowski in a normed linear space setting. Variants of this theorem are considered in the context of strictly convex, reflexive, and inner product spaces. © 1982.

Sequential Probability Ratio Tests For The Shape Parameter Of A Nonhomogeneous Poisson Process, Lee J. Bain, Max Engelhardt

Mathematics and Statistics Faculty Research & Creative Works

Sequential probability ratio tests for the shape parameter of one or more nonhomogeneous Poisson processes, with power intensity functions, are provided. The tests can be performed when the scale parameter is an unknown nuisance parameter; the effective loss of not knowing the scale parameter is one observation per process. The resulting tests can be expressed in terms of the maximum likelihood estimators of the shape parameters for the usual fixed sample procedure. A further advantage of the present approach is that the scale parameters for different processes, in the multiple sample procedures, need not be equal. Approximations for the operating …

Classes Of L¹-Convergence Of Fourier And Fourier-Stieltjes Series, Časlav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that the Fomin class FP (1

< 2) is a subclass of C ∩ B V, where C is the Garrett-Stanojevic class and B V the class of sequences of bounded variation. Wider classes of Fourier and Fourier-Stieltjes series are found for which an lg n - o(1), n → ∞, is a necessary and sufficient condition for L1-convergence. For cosine series with coefficients in B V and n∆a_n = 0(1), n → ∞, necessary and sufficient integrability conditions are obtained. © 1981 American Mathematical Society.

Integral Identities Of Norms And Characterization Of Inner Product Spaces, Časlav V. Stanojevlć, Ana M. Suchanek

Mathematics and Statistics Faculty Research & Creative Works

Integral identities of norms over compact groups are used to characterize inner product spaces. These integral identities also generalize the Penico- Stanojevic [1] integral form of the parallelogram law. © 1981 American Mathematical Society. © 1981 American Mathematical Society.

Embedding Discrete Flows On R In A Continuous Flow, P. L. Sharma, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

The problem of determining when a given discrete flow on a topological space is embeddable in some continuous flow was mentioned by G. R. Sell ("Topological Dynamics and Ordinary Differential Equations," Van Nostrand, New York, 1971) in his book on topological dynamics. In this book, the theory of generalized dynamical systems is exploited in the qualitative study of differential equations. Even more complicated is the problem of simultaneously embedding two or more discrete flows in a single continuous flow. We examine both of these problems when the underlying topological space is the space R of the real numbers. © 1980.

Tolerance Intervals For A Class Of Ifr Distributions With A Threshold Parameter, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

One-sided upper and lower tolerance intervals based on type II censored data are obtained. Under certain conditions the tolerance factors can be obtained from known results on the 2-parameter exponential distribution. Copyright © 1980 by the Institute of Electrical and Electronics Engineers, Inc.

Newtruck: A Comprehensive Long-Term Project In Computer Science, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Fixed Point Theorems In Generalized Hilbert Spaces, Troy L. Hicks, Ed W. Huffman

Mathematics and Statistics Faculty Research & Creative Works

Some fundamental fixed point theorems are proved for locally convex spaces whose generating family of semi norms satisfies the parallelogram law. © 1978.

Convergent Factorial Series Solutions Of Linear Difference Equations, W. J. Fitzpatrick, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Conjugate Of A Singular Functional Differential Operator, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

An explicit representation of the conjugate of a singular functional differential operator is given. Some theorems and their corollaries are proven.

K-Theory Doesn't Exist, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Convex Cones And Dentability, J. C. Hankins, R. (Roy) M. Rakestraw

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

On The Mann Iteration Process In A Hilbert Space, Troy L. Hicks, John D. Kubicek

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Class Of Singular Neutral-Differential Systems, W. J. Fitzpatrick, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

Noetherian operator theory is used to prove an existence theorem for a singular functional-differential system. An analogue of the standard existence and uniqueness results at an ordinary point follows as a corollary. © 1977 American Mathematical Society.

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

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

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

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

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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.