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.

Studies on the digestive enzymes of the cultivable grey mullet liza parsia (hamilton buchanan, 1822)

Culturing of fish in captivity demands a detailed knowledge on well balanced diet and adequate feeding. Formulation and production of nutritionally balanced diets for fish require research, quality control and biological evaluation. It is often assuemed that what is ingested is also digested, but this is not always be the case. Digestion depends upon both the physical state of the food and the kind and quantity of enzymes in the digestive tract. The ability of fish to digest a particular component of diet can be ascertained by investigating the complement of digestive enzymes present along the digestive tract. Investigations on the basic digestive physiology will not only enhance our present knowledge on nutrition and feed development, but will also contribute in understanding the digestive functions of lower vertebrates. It is against this background that the present topic of investigation "Studies on the digestive enzymes of the cultivable grey mullet Liza parsia Hamilton Buchanan, l822" has been selected. The thesis is arranged and presented in eight chapters.

"Effects of some heavy metals copper. zinc and lead on certain tissues of £153 Qarsia (Hamilton and Buchanan) in different environments

The research investigations on pollution, particularly in coastal/ estuarine environments are recent ones and started only in 1970s. Hence the informations available are fragmentary and scattered. They throw some light only on either the concentration of heavy metals in water or in sediment or in organisms. No concerted efforts have been made to consolidate and correlate the results between the environment and biota. Literature on the level of concentration of heavy metals in different tissues of organisms with regard to their availability in the living media, their ratio, their inter—relationship, tolerance limit of organisms, etc. are very few or rather nil. in view of the importance enumerated above, the candidate has selected the topic "Effects of some heavy metals copper, zinc and lead on certain tissues of E E (Hamilton and Buchanan) in different environments" for detailed studies and to understand systematically (i) the source of effluents and wastes, (ii) the concentration of heavy metals copper, zinc and lead in water, in sediments and in tissues of the test animal, (iii) their effects, (iv) capacity of tolerance and accumulation in different tissues of the animal, and (V) the "Bioaccumulation Factor", etc.

El lenguaje vectorial en geometría : los pioneros William Rowan Hamilton y Herman Günther Grassmann.

Resumen del autor. Este artículo pertenece a un número en homenaje a Gonzalo Sánchez Vázquez

Hamilton : la liberación del álgebra.

Se hace un recorrido por la figura de William Rowan Hamilton. Además de aspectos biográficos, se hace referencia a sus principales teorías relacionadas con las matemáticas como son los números irracionales, el álgebra de parejas o los cuaterniones.

Análisis del comportamiento de la inflación trimestral en Colombia bajo cambios de régimen: Una evidencia a través del modelo "Switching" de Hamilton.

Este trabajo tiene como propósito estudiar la evolución de la inflación trimestral en Colombia, durante el período comprendido entre 1954 y 1996, a través de la metodología de Hamilton(1989) y segundo presentar algunos conceptos relacionados con dicha metodología, la cual introduce cambios de régimen en el análisis convencional de series de tiempo. En general, esta metodología permite estimar modelos ARIMA con parámetros o varianzas cambiantes en el tiempo. En este caso, tales cambios en el modelo de la inflación se suponen asociados a posibles regímenes distintos donde la inflación presenta cambios en su nivel o en su variabilidad. Esta modelación posibilita el reconocimiento de los distintos regímenes a través del tiempo (por ejemplo dos regímenes: inflación alta e inflación baja) en lo referente a su tiempo promedio de duración y a la probabilidad asociada de cada uno de ellos, es decir, la probabilidad de estar en un régimen particular en un momento dado del tiempo. Las probabilidades de transición estimadas, permiten concluir, por ejemplo, que al estar en un régimen de inflación trimestral moderado, la probabilidad de permanecer en éste es muy alta (0.94), en tanto que pasar de éste a un régimen de inflación promedio alta tiene una probabilidad de (0.05), la cual es cinco veces mayor que la estimada para la transición de moderada a baja (0.01). Adicionalmente, se puede observar que la máxima probabilidad de permanecer en un mismo régimen se tiene en aquel caracterizado como de inflación y variabilidad moderadas.