Parameter Estimation in Minification Processes

In this article it is proved that the stationary Markov sequences generated by minification models are ergodic and uniformly mixing. These results are used to establish the optimal properties of estimators for the parameters in the model. The problem of estimating the parameters in the exponential minification model is discussed in detail.

Fluorescent Superparamagnetic Iron Oxide Core–Shell Nanoprobes for Multimodal Cellular Imaging

Multimodal imaging agents that combine magnetic and fluorescent imaging capabilities are desirable for the high spatial and temporal resolution. In the present work, we report the synthesis of multifunctional fluorescent ferrofluids using iron oxide as the magnetic core and rhodamine B as fluorochrome shell. The core–shell structure was designed in such a way that fluorescence quenching due to the inner magnetic core was minimized by an intermediate layer of silica. The intermediate passive layer of silica was realized by a novel method which involves the esterification reaction between the epoxy group of prehydrolysed 3-Glyidoxypropyltrimethoxysilane and the surfactant over iron oxide. The as-synthesized ferrofluids have a high saturation magnetization in the range of 62–65 emu/g and were found to emit light of wavelength 640 nm ( excitation = 446 nm). Time resolved life time decay analysis showed a bi-exponential decay pattern with an increase in the decay life time in the presence of intermediate silica layer. Cytotoxicity studies confirmed the cell viability of these materials. The in vitro MRI imaging illustrated a high contrast when these multimodal nano probes were employed and the R2 relaxivity of these ∗Author to whom correspondence should be addressed. Email: smissmis@gmail.com sample was found to be 334 mM−1s−1 which reveals its high potential as a T2 contrast enhancing agent

Studies on Pseudoscalar Meson Bound States and Semileptonic Decays in a Relativistic Potential Model

In this thesis quark-antiquark bound states are considered using a relativistic two-body equation for Dirac particles. The mass spectrum of mesons includes bound states involving two heavy quarks or one heavy and one light quark. In order to analyse these states within a unified formalism, it is desirable to have a two-fermion equation that limits to one body Dirac equation with a static interaction for the light quark when the other particle's mass tends to infinity. A suitable two-body equation has been developed by Mandelzweig and Wallace. This equation is solved in momentum space and is used to describe the complete spectrum of mesons. The potential used in this work contains a short range one-gluon exchange interaction and a long range linear confining and constant potential terms. This model is used to investigate the decay processes of heavy mesons. Semileptonic decays are more tractable since there is no final state interactions between the leptons and hadrons that would otherwise complicate the situation. Studies on B and D meson decays are helpful to understand the nonperturbative strong interactions of heavy mesons, which in turn is useful to extract the details of weak interaction process. Calculation of form factors of these semileptonic decays of pseudo scalar mesons are also presented.

Bayesian Inference in Exponential and Pareto populations in the presence of Outliers

This thesis Entitled Bayesian inference in Exponential and pareto populations in the presence of outliers. The main theme of the present thesis is focussed on various estimation problems using the Bayesian appraoch, falling under the general category of accommodation procedures for analysing Pareto data containing outlier. In Chapter II. the problem of estimation of parameters in the classical Pareto distribution specified by the density function. In Chapter IV. we discuss the estimation of (1.19) when the sample contain a known number of outliers under three different data generating mechanisms, viz. the exchangeable model. Chapter V the prediction of a future observation based on a random sample that contains one contaminant. Chapter VI is devoted to the study of estimation problems concerning the exponential parameters under a k-outlier model.