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A Proof Of Convergence For The Tridiagonal Ql Algorithm In Floating-Point Arithmetic, James George Sanderson

Mathematics & Statistics ETDs

Numerous routines are available to find the eigenvalues of a real symmetric tridiagonal matrix. Since it is known to converge in exact arithmetic, the tridiagonal QL algorithm with origin shift is widely used. Here we analyze the algorithm in floating-point arithmetic. This analysis suggests two modifications to the EISPACK implementation TQLl that enable one to prove correctness and hence convergence of the routine.

Also, it is known that the implicit and explicit versions of the QL algorithm produce the same results in exact arithmetic. A counter-example to the floating-point analog of this theorem is presented.

Graph Multiplicities, David Burns

Masters Theses

No abstract provided.

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

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.

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

Masters Theses

No abstract provided.

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

Dissertations

No abstract provided.

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

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 …

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

Doctoral Theses

No abstract provided.

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.

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.

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 …

Price, Income, Interest In A Two Sector Model Of Agriculture And Non-Agriculture: A Theoretical And Empirical Analysis For Indian Economy., Pradip Maiti Dr.

Doctoral Theses

A macroeconometric model seeks to portray the functioning of an economy at an aggregative level, i.e., in terms of important macrovariables and their interrelationships. The empirical counterpart of such a model is what is called a macroeconometric model when the macrorelations are posited statistically, employing probabilistic methods of estimation and/or hypothesis testing. The present study covers both aspects of a macromodel. On the theoretical side, it builds up a macroeconomic model which may be relevant for a country like India. On the empirical-statistical side, it goes on to formulate a macroeconometric model. There is a clear interdependence between these two …

Contributions To The Theory Of Optimum Utilisation Of Auxiliary Information In Survey Sampling., V. N. Reddy Dr.

Doctoral Theses

The main problem of Survey sapling fron finite populations consista of devistng an appropriate procodure for solecting a rapresentative srple frøn a glven popalation and dornloping an apprepriate procedure for the estimation of the population parceeter of interest guch as po pulation nean or total or population ratto with a viev to naxinising the preofsion of the estinstor vithin the available resources of tino and ooat or 6iternati vely minimising the aost for achieving a giren level of prestsion, Towards the solution of this problen 1t is only during the thirties ond forties that a nore systematie develop- nant has …

System Of Imprimitivity For Ergodic Actions Of Locally Compact Abelian Groups., Joseph Mathew Dr.

Doctoral Theses

Mackeys theorem on inducud representation gives all the systems of imprimitivity for a locally compact second countable group G, acting in a separable Hilbert space and based on a transitive G-space X. These systems of imprimitivity are obtained from the unitary representationg of the closed subgroup H of G defining the transitive G-space X. The main tool for this study is a class of functions called cocycles. Maçkey showed that the (G, x) systems of imprimitivity are connected in a one-one way to unitary operator valued cocycles on GXX: This cocycle in turn gives a representation of the closed subgroup …

International Tea Economy:An Econometric Description., Samir K. Majumder Dr.

Doctoral Theses

No abstract provided.

Employment And Output Objectives In Project Selection., Basudeb Sen Dr.

Doctoral Theses

Alarmingly high and increasing rates of unemployment among the fast growing labour force has, in the recent years, becmne a serious threat to the social, political and economic envirorment in developing countries like India. Despite planned efforts at economic development, the percentage of unemployed in the labour force is estimated to have increased fron 9.0 per cent in 1962 to 1o.4 per cent in 1971 and 11.0 per cent in 1972 Dutt and Sundharam (1975) 7. Eradication of unemployme nt through creation of large-scale job opportuni ti es has come to establish itself as a major objective of the country. …

Contribution To The Analysis Of Consumer Behaviour., Dipankor Coondoo Dr.

Doctoral Theses

Studies on consumer behavicur : 4 surveyThis Chapter briefly reviews the methodology, implications and limitations of various approaches to empirical demand analysis and also sunmarises the important Indian contributions to this branch of econo- metric applications.The Hicks-Allen theory of consumer equil ibrium has been outlined first to indicate the nature of empirically ob servable restrictione that ensure consistent consumer behaviour in an essentially static world deal- ing solely with non-durable oommodities. The role of the assumption of separability of the utility function in quantitative applications has al so been stressed here. Finally, the sope and limitation of this theory has …

Group Of Point Transformations Of Time Dependent Harmonic Oscillators, Jose Ricardo Bernal

University of the Pacific Theses and Dissertations

In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.

The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest's adiabatic principle and the later treatments on exact and adiabatic invariants will be presented.

Some Applications Of Lie Transformation Groups To Classical Hamiltonian Dynamics, Donald Robert Peterson

University of the Pacific Theses and Dissertations

Recent work has established that a group theoretical viewpoint of completely integrable dynamical systems with N degrees of freedom yields an algorithm that provides new information concerning the symmetry transformation group structure of this class of dynamical systems. The work presented here rests heavily on the results presented in reference and it is recommended that the reader consult this reference for a more rigorous discussion of the results given in this thesis.