Physical Sciences and Mathematics Commons^™

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

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

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

Doctoral Theses

No abstract provided.

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

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

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.

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 …

Scs 5: Notes On Chains In Cl-Objects, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

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

Finite-Difference Approach To The Hodge Theory Of Harmonic Forms, Jozef Dodziuk

Publications and Research

No abstract provided.

Scs 4: Note On Continuous Lattices, Dana S. Scott

Seminar on Continuity in Semilattices

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

Fixed Point Theorems On Closed Sets Through Abstract Cones, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers

Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of an iterative sequence whose limit is a fixed point in D. If X is a Banach space then a classical approach is to set G = I - T and use a numerical search method to minimize ||GX|| in D. Another approach, which does not require a Banach space structure, was recently introduced by Caristi and Kirk ([1],[2]). They prove that a metrically inward …

The Method Of Quasilinearization And Positivity Of Solutions In Abstract Cones, V. Lakshmikantham, Dolores D. Sety, A. Richard Mitchell

Mathematics Technical Papers

The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the method can be found in (Ref. 3). This method has been very useful in providing an analytic approach to obtain approximate solutions of non-linear equations, or more specifically, to derive upper and lower bounds for the solutions.

Weak Type Multipliers For Hankel Transforms, William C. Connett, Alan L. Schwartz

UMSL Emeritus

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 …

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. …

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 …

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 …

A Nonlinear Variation Of Constants Method For Integro-Differential And Integral Equations, M. E. Lord, Stephen R. Bernfeld

Mathematics Technical Papers

It is well known that a very important technique in obtaining the asymptotic behavior of solutions of linear and nonlinear ordinary differential equations under perturbations is through the use of the variation of constants formula (see [1] and [14]). Miller [16] used a well known representation formula for perturbed linear Volterra integral equations in terms of the resolvent which has been successfully used in recent years to analyze stability behavior of solutions (see, for example, [12] and [17] and references therein). In addition, Bownds and Cushing [4] obtained another variation of constants formula for linear integral equations utilizing a fundamental …

On The Construction Of A Norm Associated With The Measure Of Noncompactness, Stephen R. Bernfeld, V. Lakshmikantham, Jerome Eisenfeld

Mathematics Technical Papers

It is shown that the bounded, nonempty subsets of a reflexive Banach space g can be imbedded in another Banach space B(E) in such a manner so that the measure of noncompactness corresponds to the norm in B(E). The results are applied to ordinary differential equations theory.

Scs 3: Equationally Compact Sendos Are Retracts Of Compact Ones, Klaus Keimel, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

Memo by Klaus Keimel, with a Remark by K.H. Hofmann, February 10, 1976.

Scs 1: More Notes On Spread, Jimmie D. Lawson

Seminar on Continuity in Semilattices

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

Scs 2: Notes On Notes By Jdl (Concerning What He Calls The 'Spread'), Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

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