I declare that this essay is work done as part of the Part III Examination. I have read and understood the Statement on Plagiarism for Part III and Graduate Courses issued by the Faculty of Mathematics, and have abided by it. This essay is the result of my own work, and except where explicitly stated otherwise, only includes material undertaken since the publication of the list of essay titles,...

The deducibility problem, i.e., the problem, how to test whether a formula of a formalized Iheory is or is not a theorem, is investigated from the statistical point of view. A model is proposed in which the corresponding statistical decision problem can be converted into a parametric test of a simple hypothesis against a simple alternative. Some results following from this possibility are formu...

In two-phase slug flow pattern, the bulk of the gas is trapped inside large bubbles that are separated by liquid slugs, which may contain small dispersed bubbles. The unsteady nature of slug flow makes the prediction of pressure drop and heat and mass transfer a difficult task. Earlier models that deal with steady slug flow assume constant lengths and shapes of liquid slugs and elongated bubble...

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Using a set of confidence intervals, we develop a common approach, to construct a fuzzy set as an estimator for unknown parameters in statistical models. We investigate a method to derive the explicit and unique membership function of such fuzzy estimators. The proposed method has been used to derive the fuzzy estimators of the parameters of a Normal distribution and some functions of parameter...

The construction of optimal keywords dictionary is one of the most important tasks in developing of thesaurusbased Informational Retrieval Systems and some other NLP applications. The problem is, which parameters of keywords dictionaries may be rated as consistent ones from statistical point of view (that is not dependent on sample size)? Analysis of the recent scientific works and the results ...

We consider passive polarimetric near infra-red imaging systems that measure the three first elements of the Stokes vector and deduce from them the degree of linear polarization and the angle of polarization in near infra-red spectrum for analyzing plant leaves. By using the variance of the angel of polarization from each sample leaf, we identify the curl of the leaf surface and compare it to o...