Other Mathematics Commons^™

Weak-Star Limits On Polynomials And Their Derivatives, William T. Ross, Joseph A. Ball

Department of Math & Statistics Faculty Publications

Let μ and v be regular finite Borel measures with compact support in the real line ℝ and define the differential operator D :L ∞(μ) → L ∞(v) with domain equal to the polynomials P by Dp = p′. In this paper we will characterize the weak-star closure of the graph of D in ∞(μ) ⊕ ∞(y). As a consequence we will characterize when D is closable (i.e. the weak-star closure of G contains no non-zero elements of the form o ⊕ g) and when g is weak-star dense in L∞(μ) ⊕ …

A Theorem On Reproducing Kernel Hilbert Spaces Of Pairs, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study reproducing kernel Hilbert and Banach spaces of pairs. These are a generalization of reproducing kernel Krein spaces and, roughly speaking, consist of pairs of Hilbert (or Banach) spaces of functions in duality with respect to a sesquilinear form and admitting a left and right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z, ω) analytic in z and ω* there is a neighborhood of the origin that can be associated with a reproducing kernel Hilbert space of pairs with left reproducing kernel K(z, …

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

Some Remarks On Reproducing Kernel Krein Spaces, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

The one-to-one correspondence between positive functions and reproducing kernel Hilbert spaces was extended by L. Schwartz to a (onto, but not one-to-one) correspondence between difference of positive functions and reproducing kernel Krein spaces. After discussing this result, we prove that matrix value function K(z,ω) symmetric and jointly analytic in z and ω in a neighborhood of the origin is the reproducing kernel of a reproducing kernel Krein space. We conclude with an example showing that such a function can be the reproducing kernel of two different Krein spaces.

Linear Programming By G.V. Shenoy, New Delhi: Wiley Eastern Limited, 1989., A K Rao

IIMB Management Review

No abstract provided.

Partially Confluent Maps And N-Ods, Van C. Nall

Department of Math & Statistics Faculty Publications

Let f : X-->Y be a map between topological spaces. A Wf-set in Y is a continuum in Y which is the image under f of a continuum in X. The map f is partially confluent if each continuum in Y is the union of a finite number of Wf-sets, and n-partially confluent if each continuum in Y is the union of n Wf-sets. In this paper, it is shown that every partially confluent map onto an n-cell is weakly confluent. Also, the relationship between partially confluent maps and continua which …

Dilatations Des Commutants D'Opérateurs Pour Des Espaces De Krein De Fonctions Analytiques, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

Let K1 and K2 be two Krein spaces of functions analytic in the unit disk and invariant for the left shift operator R0(R0f(z)=(f(z)−f(0))/z), and let A be a linear continuous operator from K1 into K2 whose adjoint commutes with R0. We study dilations of A which preserve this commuting property and such that the Hermitian forms defined by I−AA∗ and I−BB∗ have the same number of negative squares. We thus obtain a version of the commutant lifting theorem in the framework of Krein spaces of analytic functions. To prove this result we suppose that the graph of the operator A∗, …

Organizational Inducements And Social Motives: A Game Theoretic Analysis, Richard G. Davis

Dissertations and Theses

Game theory was used to analyze compensation systems based on individual and group incentives. Payoff formulas were developed for these incentives assuming different preferences for individual and social outcomes. Two levels of contributions were considered: (1) Defection. The minimum acceptable level of contributions, and (2) Cooperation. A level of discretionary contributions above the minimum. The discretionary contributions associated with cooperation were represented as a cost to the individual.

A classification scheme for uniform n-person games was developed using the approach of Rappaport and Guyer (1966) for 2 x 2 games. This classification scheme defines the natural outcome (cooperation or defection) …

Maps Which Preserve Graphs, Van C. Nall

Department of Math & Statistics Faculty Publications

In 1976 Eberhart, Fúgate, and Gordh proved that the weakly confluent image of a graph is a graph. A much weaker condition on the map is introduced called partial confluence, and it is shown that the image of a graph is a graph if and only if the map is partially confluent.

In addition, it is shown that certain properties of one-dimensional continua are preserved by partially confluent maps, generalizing theorems of Cook and Lelek, Tymchatyn and Lelek, and Grace and Vought. Also, some continua in addition to graphs are shown to be the images of partially confluent maps only.

Reproducing Kernel Krein Spaces Of Analytic Functions And Inverse Scattering, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

The purpose of this thesis is to study certain reproducing kernel Krein spaces of analytic functions, the relationships between these spaces and an inverse scattering problem associated with matrix valued functions of bounded type, and an operator model.

Roughly speaking, these results correspond to a generalization of earlier investigations on the applications of de Branges' theory of reproducing kernel Hilbert spaces of analytic functions to the inverse scattering problem for a matrix valued function of the Schur class.

The present work considers first a generalization of a portion of de Branges' theory to Krein spaces. We then formulate a general …

U.S. Input-Output Data: A 1984 Update, Ronald E. Miller

Accounts and Data

This paper calls attention to the U.S. national input-output data for 1977 and the U.S. multiregional input-output data for the same year; both of these data sets became available during 1984. In particular, the commodity-by- industry accounting scheme which underpins both the 1972 and 1977 U.S. national models (as well as the U.S. 1977 multiregional model), is contrasted with the industry-by-industry approach of the original Leontief framework, which was the basis of the pre-1972 U.S. national tables.

Generalisations Et Generalites, Florentin Smarandache, Eleonora Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

"Généralisations et Généralités" , pourquoi ce titre? Parce Que l'auteur a voulu rassembler ici Quelques-unes de ses recherches originales C Qui sont donc des "s~n:§rali tés") , df'2ls diverses branches des mathématiques (algèl)re, thôorie des nombres, Gométrie, analyse, linguistique, mathématiQues distrayantes) , mêlne si les articles qui composent ce recueil n'ont pas toujours de liaison entre eux.

Weak Confluence And W-Sets, Van C. Nall

Department of Math & Statistics Faculty Publications

A mapping between continua is weakly confluent if for each subcontinuum K of the range some component of the preimage of K maps onto K. Class [W] is the class of all continua which are the images of weakly confluent maps only. The notion of Class [W] was introduced by Andrej Lelek in 1972. Since then it has been widely explored and some characterizations of these continua have been given. J. Grispolakis and E. D. Tymchatyn have given a characterization in terms of hyperspaces [4]. J. Davis has shown that acyclic atriodic continua are in Class [W]i therefore, atriodic tree-like …

Problemes Avec Et, Sans Problemes!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Linear Estimation: The Kalman-Bucy Filter, William Douglas Schindel

Graduate Theses - Mathematics

The problem of linear dynamic estimation, its solution as developed by Kalman and Bucy, and interpretations, properties and illustrations of that solution are discussed. The central problem considered is the estimation of the system state vector X, describing a linear dynamic system governed by

dx/dt = F(t)X(t) + G(t)U(t)

Y(t) = H(t)X(t) + V(t)

for observations of Y (system output), where V is a random observation-corrupting process, and U is a random system driving process.

An extension of the Kalman-Bucy filter to estimation in the absence of priori knowledge of the random process U and V is developed and illustrated.

A Density For A Generalized Likelihood-Ratio Test When The Sample Size Is A Random Varible, Raymond H. Neville

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many articles, books, papers, and abstracts have been published, which describe the analysis and design of experiments. R. A. Fisher's (1951) book, The Design of Experiments, is referred to by D. J. Finney (1960) as the classic for experimental designs. Some of the more outstanding books and publications in this area are those by Cochran and Cox (1957), Cox (1958), Davis et al., (1954), Federer (1955). Quenouille (1953). and Kempthorne (1952).

Decision Problems, Lowell Anderson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

From an intuitive point of view the notion of effective procedure consists of a set of rules or instructions that enables one, in a finite number of steps and in a purely mechanical way, to answer yes or no to any one of a given class of questions. This procedure requires no intelligence to carry out the instructions and, in fact, it is con­ceivable that some mechanical contrivance may be constructed to carry out these instructions. Should such an effective procedure exist, that answers either yes or no, then the group of problems in question is said to be effectively …

Axiomatic Set Theory, Ronald P. Smit

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

An analysis of the well known paradoxes found in intuitive set theory has led to the reconstruction of set theory by axiomatic means. This exposition is devoted to Zermelo-Fraenkel set theory with some changes made by Suppes.

The first order predicate calculus is presupposed. In addition to the usual quantifiers admitted, a unique existential quantifier is used. The primitive notions of the set theory are the empty set and the two place membership predicate.

Laplace, Finite Fourier Sine And Cosine, Transformations, Jan Eugene Wynn

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Laplace and finite Fourier sine transforms can be used to solve certain boundary value problems. Also the Laplace transform is a useful took in solving some integral and integrodifferential equations. This report is composed of transform solutions of seventeen such applied problems, while the author's first report is focused towards the theoretical aspect of these transforms.

Several different types of problems are solved in this report. Among these are Bessel's classical differential equation of index n, two electrical circuit problems, a beam problem, a vibrating string problem, a heat flow problem, and a temperature gradient problem.

One of the …

A Development Of The Number System, Janet R. Olsen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper is based on Landau's book "Foundations of Analysis" which constitutes a development of the number system founded on the Peano axioms for natural numbers.

Pfaffian Differential Expressions And Equations, K. Raman Unni

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

It is needless to point out the necessity and the importance of the study of Pfaffian differential expressions and equations. While it is interesting to consider from the pure mathematical point of view, their applications in many branches of applied mathematics are well known. To mention a few, one may observe that they arise in connection with line integrals (example, determination of work). They provide a more rational formulation of the foundations of thermodynamics as developed by the Greek mathematician Caratheodory. They also arise in the problem of determining the orthogonal trajectories. In many branches of engineering and other physical …

Mathematicians And Royalty: A Historical Survey, Loren W. Pixley

Masters Theses

No abstract provided.

The Solution Of Boundary Value Problems By Use Of The Laplace Transformation As Compared With Classical Methods, Dan W. Stoddard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to present a study of different methods of solving certain boundary value problems. In particular it will be concerned with solutions by classical methods and by operational methods. Of the various operational methods that may be considered, the Laplace transformation appears to be the best⁽¹⁾ and will be used in this paper.

In the 1951 Encyclopedia Americana Annual is this report on the activities in applied mathematics for the previous year:

Progress was made on the general problem of finding the eigenvalues of matrices and systems of differential equations. Considerable effort was also …

Mathematical Short Cuts And Checks, Leon Schram

Bachelors’ Theses

A computer naturally should be the master of short cuts and methods for checking his work. The latter is perhaps of more importance than the former because one must be able to show his employer that he knows that his work is correct.

History Of Applied Geometry, Evelyn Jackson

Electronic Theses and Dissertations

Mathematics: Just what does the word mean to us? After a moment of thought many different meanings may present themselves to our minds. At first we are inclined to say that the word mathematics covers a vast field. We are justified in so thinking because mathematics embraces a wide scope of study. Were we to say that it is a science we should place it in its proper genius, for it is truly a science of numbers and space. However, could not the science be the art of calculation or the art of computation?

Some Contributions Of Pure Math To Science, Herbert B.E. Case

Student and Lippitt Prize Essays

An examination of the connection between math and science through discoveries in the subjects of astronomy, mechanics, physics and chemistry.