Digital Commons Network^™

Undecidable Properties Of Finite Sets Of Equations, George F. Mcnulty

Faculty Publications

No abstract provided.

Application Of Theorems Of Schur And Albert, Thomas L. Markham

Faculty Publications

No abstract provided.

Scs 15: Continuous Lattices And Universal Algebra, Dana S. Scott

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 14: Scs Memo Of Lawson Dated 7-12-76, Michael Mislove

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 13: Complements To Relations With The Interpolation Properties And Continuous Lattices, Klaus Keimel

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 11: Errata And Corrigenda To Memo "Commentary On Scott's Function Spaces", Karl Heinrich Hofmann, Michael Mislove

Seminar on Continuity in Semilattices

Corrections to version dated 7/20/76 at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Version dated 7/20/76 is in supplemental files.

K₁ Of The Compact Operators Is Zero, L. G. Brown, Claude Schochet

Mathematics Faculty Research Publications

We prove that K₁ of the compact operators is zero. This theorem has the following operator-theoretic formulation: any invertible operator of the form (identity) + (compact) is the product of (at most eight) multiplicative commutators (A_jB_jA_j⁻¹B_j⁻¹)^±1, where each B_j is of the form (identity) + (compact). The proof uses results of L. G. Brown, R. G. Douglas, and P. A. Fillmore on essentially normal operators and a theorem of A. Brown and C. Pearcy on multiplicative …

The Port Of Providence: Perspectives On Development, Jerome F. Mcgourthy

Marine Affairs Theses and Major Papers

The paper identified environmental, technological and socio-political factors which have contributed to the demise of the Providence River Port as a regional dry cargo distribution center and examines plans and policies contemplated by local government and business interests to counteract the Port's decline.

A T-Matrix Analysis For The Scattering Cross Section, Michael J. Linville

Masters Theses

No abstract provided.

Cone-Valued Lyapunov Functions, S. Leela, V. Lakshmikantham

Mathematics Technical Papers - Archive

It is very well known that employing a single Lyapunov function and the theory of scalar differential inequality offers a useful mechanism to study a variety of qualitative problems of differential equations in a unified way [10]. Nevertheless, when using this powerful technique for concrete problems, the main difficulty we face is the lack of general method of constructing a Lyapunov function. This naturally beads to the development of the method of vector Lyapunov functions which utilizes several Lyapunov-like functions and the theory of vector differential inequalities in a fruitful manner [5,8-12]. This method offers a more flexible mechanism to …

A Monotone Method For Infinite System Of Nonlinear Boundary Value Problems, V. Lakshmikantham, Jagdish Chandra, S. Leela

Mathematics Technical Papers - Archive

Monotone iterative methods have been successfully used to generate improvable two-sided point-wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations. While such procedures take a simple form when the nonlinearities are independent of gradient terms [6,9], the extension of such techniques to fully nonlinear problems has been quite formidable. In the case of scalar ordinary differential equations of the type (1.1) [see PDF for equation] such results have been obtained making use of either a linear maximum principle (3,1] or a nonlinear maximum principle [4]. In either case an essential use is made …

Minimal And Maximal Solutions Of Nonlinear Boundary Value Problems, Jagdish Chandra, Stephen R. Bernfeld

Mathematics Technical Papers - Archive

This paper is concerned with the construction of the minimal and the maximal solutions of the nonlinear boundary value problem [see PDF for equation] under tether mild assumptions of f. in particular, no assumption of monotonicity is made on [see PDF for equation] either in u or [see PDF for equation].

Scs 12: Relations With The Interpolation Property And Continuous Lattices, Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Michael Mislove

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

A Study Of Asymptotic Solutions Of Second Order Linear Differential Equations, Toshitake Okada

Masters Theses

No abstract provided.

On Ramsey Numbers Defined By Factorizations Of Regular Complete Multi-Partite Graphs, James M. Benedict

Dissertations

No abstract provided.

Cayley Graph Imbeddings And The Associated Block Designs, Brian L. Garman

Dissertations

No abstract provided.

An Abstract Matrix Model: The Column Model, Tomas Eufracio Salazar

Mathematics & Statistics ETDs

In this dissertation we introduce an abstract model for matrix theory, The Column Model. We investigate some properties of the special class of partially ordered linear algebras that satisfy the conditions of the Model. We use the order structure of the Model to obtain some results on: idempotents in the Model, nonnegative elements of the Model having nonnegative generalized inverses, factor theorems in the Model and concepts in the Model that are related to the usual notion of eigenvalues of an m-by-m matrix. Since the set of m-by-m matrices belongs to the special class of partially ordered linear algebras satisfying …

Scs 10: Points With Small Semilattices, Jimmie D. Lawson

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 9: Commentary On Scott's Function Spaces, Karl Heinrich Hofmann, Michael Mislove

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Sequential Methods In Estimation And Prediction., Nitis Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

Scs 8: On The Theorem Of Lawson's That All Compact Locally Connected Finite Dimensional Semilattices Are Cl, Karl Heinrich Hofmann, Michael Mislove

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 7: Still More Notes On Chains In Cl-Objects, James H. Carruth

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Generalized Stability Of Motion And Vector Lyapunov Functions, Deborah A. Pace, Roger W. Mitchell

Mathematics Technical Papers - Archive

The direct theory for stability of motion in terms of vector Lyapunov functions and the general comparison method is well-developed [4, 5, 6, 7] and effectively applied for large scale dynamical systems [1, 3]. However, the problem of constructing vector Lyapunov functions and developing appropriate perturbation theory has seen very little progress. Perhaps one of the reasons for this situation is that the stability definitions by means of the standard norm are not flexible enough for such a venture.

Optimum Structural Probability Bounds For The Right-Tail Of The Paretian Law, Danny D. Dyer

Mathematics Technical Papers - Archive

The two-parameter Pareto density function [see PDF for equation] is widely used in applied statistics. For example, in reliability theory (1.1) represents the failure-time distribution of a "work-hardened" component whose.hazard function is inversely proportional to time. Because of its long right-tail, (1.1) is often a probability model for certain socioeconomic phenomena (e.g., distribution of city population sizes, distribution of personal incomes which exceed tax-exempt levels). One of the more recent characterizations of the Pareto distribution is due to Revankar, et. at. [15]. They show that within the population of individuals that under-report their income for income tax purposes, the average …

Scs 6: More Notes On Chains In Cl-Objects, James H. Carruth, Charles E. Clark, J. Winston Crawley, E. L. Evans, R. L. Wilson

Seminar on Continuity in Semilattices

No abstract provided.

Interpretation And Application Of Elements Of Differential Geometry And Lie Theory, James R. Brannan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Basic concepts of differential geometry and Lie theory are introduced. Lie transformation groups are applied to linear systems of differential equations and the problem of describing rigid body orientation. Linear Hamiltonian systems are then treated as a Lie system of differential equations. This theory is applied to a particular Hamiltonian system arising from a problem in control theory, the linear state regulator problem.

Positive Controllability Of Systems With Nearly-Non-Negative Matrices, Theodore Sonne Perry

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper analyzes the controllability of constant coefficient linear differential equations and presents two proofs of a major theorem on controllability. Properties of nearly-non-negative matrices are discussed and in particular a theorem on the behavior of the exponential matrix of nearly-non-negative matrices is proven. These results are then used to prove that the reachable set for systems with nearly-non-negative matrices is limited to the positive hyperoctant.

Shooting Method For Two-Point Boundary Value Problems, John D. Baumann

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to develop the shooting method as a technique for approximating the solution to the two-point boundary value problem on the interval [a,b] with the even order differential equation {i.e. n is even)

u⁽ⁿ⁾(t) + f(t, u(t), u⁽ⁱ⁾(t, ),..., u^(n-1)(t)) = 0

and boundary conditions

u(a) = A

u(b) = B

and with at most n-2 other boundary conditions specified at either a or b. The basic proceedure will be illustrated by the following example.

Consider the two-point boundary value problem (0.1) (0.2) (0.3) with the additional boundary conditions …

Random Ergodic Sequences And P-Occupancy Sets, Jacob Israel Reich

Mathematics & Statistics ETDs

In this paper we study the behavior of random probability measures...

A Metric Graph Structure For Information Retrieval, Karl Jerry Melendez

Mathematics & Statistics ETDs

Document retrieval systems accept a user request for information and respond with a list of documents which contain information relevant to the request. When the documents (or abstracts of the documents) are stored in a computer memory, a function can be defined which estimates the semantic distance between documents. If this function together with the set of documents forms a metric space, a graph, which I call a progressive graph, can be constructed to aid the search for the documents with relevant information.

Progressive graphs are studied and the search algorithms which use this graph structure are presented. The search …