Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Studies on the propagation of errors in physical oceanographic computations

The results of an investigation on the limits of the random errors contained in the basic data of Physical Oceanography and their propagation through the computational procedures are presented in this thesis. It also suggest a method which increases the reliability of the derived results. The thesis is presented in eight chapters including the introductory chapter. Chapter 2 discusses the general theory of errors that are relevant in the context of the propagation of errors in Physical Oceanographic computations. The error components contained in the independent oceanographic variables namely, temperature, salinity and depth are deliniated and quantified in chapter 3. Chapter 4 discusses and derives the magnitude of errors in the computation of the dependent oceanographic variables, density in situ, gt, specific volume and specific volume anomaly, due to the propagation of errors contained in the independent oceanographic variables. The errors propagated into the computed values of the derived quantities namely, dynamic depth and relative currents, have been estimated and presented chapter 5. Chapter 6 reviews the existing methods for the identification of level of no motion and suggests a method for the identification of a reliable zero reference level. Chapter 7 discusses the available methods for the extension of the zero reference level into shallow regions of the oceans and suggests a new method which is more reliable. A procedure of graphical smoothening of dynamic topographies between the error limits to provide more reliable results is also suggested in this chapter. Chapter 8 deals with the computation of the geostrophic current from these smoothened values of dynamic heights, with reference to the selected zero reference level. The summary and conclusion are also presented in this chapter.

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

THE THEORY OF FUNCTION OF POETRY PROPOUNDED BY T. S. ELIOT AND S. H. VATSYAYAN

Hindi

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

Development and applications of density matrix functional theory of generalized Hubbard Models

In dieser Doktorarbeit wird eine akkurate Methode zur Bestimmung von Grundzustandseigenschaften stark korrelierter Elektronen im Rahmen von Gittermodellen entwickelt und angewandt. In der Dichtematrix-Funktional-Theorie (LDFT, vom englischen lattice density functional theory) ist die Ein-Teilchen-Dichtematrix γ die fundamentale Variable. Auf der Basis eines verallgemeinerten Hohenberg-Kohn-Theorems ergibt sich die Grundzustandsenergie Egs[γgs] = min° E[γ] durch die Minimierung des Energiefunktionals E[γ] bezüglich aller physikalischer bzw. repräsentativer γ. Das Energiefunktional kann in zwei Beiträge aufgeteilt werden: Das Funktional der kinetischen Energie T[γ], dessen lineare Abhängigkeit von γ genau bekannt ist, und das Funktional der Korrelationsenergie W[γ], dessen Abhängigkeit von γ nicht explizit bekannt ist. Das Auffinden präziser Näherungen für W[γ] stellt die tatsächliche Herausforderung dieser These dar. Einem Teil dieser Arbeit liegen vorausgegangene Studien zu Grunde, in denen eine Näherung des Funktionals W[γ] für das Hubbardmodell, basierend auf Skalierungshypothesen und exakten analytischen Ergebnissen für das Dimer, hergeleitet wird. Jedoch ist dieser Ansatz begrenzt auf spin-unabhängige und homogene Systeme. Um den Anwendungsbereich von LDFT zu erweitern, entwickeln wir drei verschiedene Ansätze zur Herleitung von W[γ], die das Studium von Systemen mit gebrochener Symmetrie ermöglichen. Zuerst wird das bisherige Skalierungsfunktional erweitert auf Systeme mit Ladungstransfer. Eine systematische Untersuchung der Abhängigkeit des Funktionals W[γ] von der Ladungsverteilung ergibt ähnliche Skalierungseigenschaften wie für den homogenen Fall. Daraufhin wird eine Erweiterung auf das Hubbardmodell auf bipartiten Gittern hergeleitet und an sowohl endlichen als auch unendlichen Systemen mit repulsiver und attraktiver Wechselwirkung angewandt. Die hohe Genauigkeit dieses Funktionals wird aufgezeigt. Es erweist sich jedoch als schwierig, diesen Ansatz auf komplexere Systeme zu übertragen, da bei der Berechnung von W[γ] das System als ganzes betrachtet wird. Um dieses Problem zu bewältigen, leiten wir eine weitere Näherung basierend auf lokalen Skalierungseigenschaften her. Dieses Funktional ist lokal bezüglich der Gitterplätze formuliert und ist daher anwendbar auf jede Art von geordneten oder ungeordneten Hamiltonoperatoren mit lokalen Wechselwirkungen. Als Anwendungen untersuchen wir den Metall-Isolator-Übergang sowohl im ionischen Hubbardmodell in einer und zwei Dimensionen als auch in eindimensionalen Hubbardketten mit nächsten und übernächsten Nachbarn. Schließlich entwickeln wir ein numerisches Verfahren zur Berechnung von W[γ], basierend auf exakten Diagonalisierungen eines effektiven Vielteilchen-Hamilton-Operators, welcher einen von einem effektiven Medium umgebenen Cluster beschreibt. Dieser effektive Hamiltonoperator hängt von der Dichtematrix γ ab und erlaubt die Herleitung von Näherungen an W[γ], dessen Qualität sich systematisch mit steigender Clustergröße verbessert. Die Formulierung ist spinabhängig und ermöglicht eine direkte Verallgemeinerung auf korrelierte Systeme mit mehreren Orbitalen, wie zum Beispiel auf den spd-Hamilton-Operator. Darüber hinaus berücksichtigt sie die Effekte kurzreichweitiger Ladungs- und Spinfluktuationen in dem Funktional. Für das Hubbardmodell wird die Genauigkeit der Methode durch Vergleich mit Bethe-Ansatz-Resultaten (1D) und Quanten-Monte-Carlo-Simulationen (2D) veranschaulicht. Zum Abschluss wird ein Ausblick auf relevante zukünftige Entwicklungen dieser Theorie gegeben.

Many-body theory of laser-induced ultrafast demagnetization and angular momentum transfer in ferromagnetic transition metals

An electronic theory is developed, which describes the ultrafast demagnetization in itinerant ferromagnets following the absorption of a femtosecond laser pulse. The present work intends to elucidate the microscopic physics of this ultrafast phenomenon by identifying its fundamental mechanisms. In particular, it aims to reveal the nature of the involved spin excitations and angular-momentum transfer between spin and lattice, which are still subjects of intensive debate. In the first preliminary part of the thesis the initial stage of the laser-induced demagnetization process is considered. In this stage the electronic system is highly excited by spin-conserving elementary excitations involved in the laser-pulse absorption, while the spin or magnon degrees of freedom remain very weakly excited. The role of electron-hole excitations on the stability of the magnetic order of one- and two-dimensional 3d transition metals (TMs) is investigated by using ab initio density-functional theory. The results show that the local magnetic moments are remarkably stable even at very high levels of local energy density and, therefore, indicate that these moments preserve their identity throughout the entire demagnetization process. In the second main part of the thesis a many-body theory is proposed, which takes into account these local magnetic moments and the local character of the involved spin excitations such as spin fluctuations from the very beginning. In this approach the relevant valence 3d and 4p electrons are described in terms of a multiband model Hamiltonian which includes Coulomb interactions, interatomic hybridizations, spin-orbit interactions, as well as the coupling to the time-dependent laser field on the same footing. An exact numerical time evolution is performed for small ferromagnetic TM clusters. The dynamical simulations show that after ultra-short laser pulse absorption the magnetization of these clusters decreases on a time scale of hundred femtoseconds. In particular, the results reproduce the experimentally observed laser-induced demagnetization in ferromagnets and demonstrate that this effect can be explained in terms of the following purely electronic non-adiabatic mechanism: First, on a time scale of 10–100 fs after laser excitation the spin-orbit coupling yields local angular-momentum transfer between the spins and the electron orbits, while subsequently the orbital angular momentum is very rapidly quenched in the lattice on the time scale of one femtosecond due to interatomic electron hoppings. In combination, these two processes result in a demagnetization within hundred or a few hundred femtoseconds after laser-pulse absorption.

A Theory of Quantitative Inference Applied to a Mechanical Design Compiler

This thesis presents the ideas underlying a computer program that takes as input a schematic of a mechanical or hydraulic power transmission system, plus specifications and a utility function, and returns catalog numbers from predefined catalogs for the optimal selection of components implementing the design. Unlike programs for designing single components or systems, the program provides the designer with a high level "language" in which to compose new designs. It then performs some of the detailed design process. The process of "compilation" is based on a formalization of quantitative inferences about hierarchically organized sets of artifacts and operating conditions. This allows the design compilation without the exhaustive enumeration of alternatives.

Descripción y análisis de la aplicación de la teoría general de las organizaciones en el modelo de gestión del Fondo Nacional de Ahorro, FNA

La tesis que a continuación se presenta corresponde a la Maestría en Dirección y Gerencia de Empresas de la Universidad del Rosario. En ella se revisan y analizan múltiples factores mediante los cuales se determina o no la aplicación de aplicación de la Teoría General de las organizaciones en la gestión del Fondo Nacional de Ahorro, FNA. de la ciudad de Bogotá. En ella se plantean los aspectos que se aplican de cada una de las siguientes teorías organizacionales o administrativas: Administración Científica, Clásica (Administración Moderna), de las Relaciones Humanas, Neoclásica, Administración por Objetivos, Burocrática, Estructuralista, Conductista (del Comportamiento o Behaviorista, X, Y) Desarrollo Organizacional, Cibernética, Matemática, de Sistemas y Contingencial. En consecuencia, la revisión efectuada, las reflexiones, los hallazgos y el análisis correspondiente facilitan la comprensión y el dominio de los postulados teóricos. De modo que los aportes de tan exigente ejercicio real y práctico constituyen una significativa experiencia que revisa la vigencia y la pertinencia de las teorías organizacionales y se convierten en un valioso aporte a las ciencias empresariales y a la sociedad colombiana.

Theory of Numbers

Exercises, exams and solutions for a third year maths course.

Análisis al Proceso de Titulación Minera en Colombia desde TOC (Theory Of Constraints)

El incumplimiento reiterado de la normatividad y políticas relacionadas con los tiempos de respuesta del proceso de contratación minera del país, desarrollado actualmente por la recién creada Agencia Nacional de Minería ANM, ha suscitado que la administración del recurso minero no se realice bajo los principios de eficiencia, eficacia, economía y celeridad. Estas debilidades manifiestas provocan represamientos en la resolución de trámites, congelación de áreas para contratar, sobrecostos, demoras en los tiempos de respuesta establecidos por la normatividad vigente y trae como consecuencia incertidumbre en los inversionistas mineros y pérdidas por concepto de recaudo de canon superficiario, entre otras. El objetivo del presente trabajo de investigación consiste en analizar el proceso de titulación minera de Colombia a partir de la filosofía de mejora continua desarrollado en la teoría de restricciones TOC (Theory Of Constraints), para poder identificar cuáles son los cuellos de botella que no permiten que el proceso fluya de manera adecuada y proponer alternativas de mejora, que con su implementación exploten y subordinen la limitaciones al sistema.

Children' s school study : an experimental theory of verbal information and social attitudes. 'Estudio de la escuela primaria: una teoría experimental de la información verbal y las actitudes sociales'.

Determinar los conceptos diferenciales alcanzados por los alumnos de segunda etapa de EGB con respecto a los alumnos de primera etapa en el area de ciencias sociales. Medir mediante una escala de Likertel cambio de actitudes producido como consecuencia de los aprendizajes en el area de humanidades.. La muestra aleatoria la componían 284 alumnos (145 chicos y 139 chicas) de 5õ y 8õ de EGB y 3õ de BUP, alumnos en centros de un centro urbano (Cáceres) y 3 núcleos rurales de la misma provincia.. La investigación se divide en dos bloques, el primero de ellos, de corte más teórico, estudia la cibernética y la teoría de la información como ciencias y su aplicación en el campo de la psicopedagogía. Se determinan también los esquemas generales para la construcción de escalas de medida de actitudes, y se trata de determinar experimentalmente la existencia de diferencias significativas en el caudal lingüístico entre alumnos procedentes de un medio rural y los procedentes de un medio urbano. El segundo bloque, de corte experimental, analiza el concepto de escala usado en ciencias sociales, y se trata de determinar las actitudes que representan un mayor grado de madurez en la dimensión socio-política. Para ello se aplica a los sujetos de la muestra la Social-responsability Scale.. Escala Likert. Quessing-game method (modificado). Social Responsability Scale de Berkowitz y Lutzeman.. Análisis de Varianza. Análisis de correlación. En terminos de transinsformación didáctica puede considerarse que durante la segunda etapa de EGB hay adquisición de conocimientos que suponen un substancial enriquecimiento del caudal lingüístico. El ambiente posibilita y condiciona el enriquecimiento o desarrollo de las facultades individuales. Pueden establecerse correlaciones parciales entre la adquisión de conceptos y la evolución de actitudes..

Can children with autism spectrum disorders be helped to acquire a theory of mind?. '¿Se puede ayudar a los niños con trastornos del espectro autista a adquirir una teoría de la mente?'.

Resumen en español

Measuring the benefits of employer investments in training : towards a new economic theory of training. 'Medir los beneficios de las inversiones del empresario en formación : hacia una nueva teoría económica de la formación'.

Resumen basado en el de la publicación