Digital Commons Network^™

On Strategies Of Sampling Finite Populations In One And Two Phases., Arun Kumar Adhikary Dr.

Doctoral Theses

This thesis is being submitted to the Indi an Statibtical Institute (ISI) in fulfilment of the primary requirements for the award of the degree of Doctor of Philosophy in Statistics.No part of this theais was submitted to any other Inatitute for any degree, diploma, certifioate etc.In this thesis we have mainly presented results of our investigation on optimal strategles for surveying finite populations in two phanes using selection procedures with varying probabilities. Incidentally we have added a few more resulta to the available literature on uni-phase sampling as are conaidered important in formulating appropriate doutbe sampling plans. Optimal and pragnatically …

Optimal Block Designs In One And Multi-Way Settings., Sunanda Bagchi Dr.

Doctoral Theses

The study of optimality of block designs formally began with wald (1943) proving a very important optimality property, designated as D-optimality of Iatin Square. Desi gns in a given physical set up. Next Ehrenfield (1955) proved the E-optimality property of Latin Square Designs. Since then, the work in: the area has primarily consisted in evolving a number of useful opti- mality oriteria for oomparing block design in a reasonable set up given and oharacterizing and/or constructing desi gns saiisfying the so called optimality criteria developed. But it was not until 1958, when the theory was given a proper and precise …

Some Results About Basic Elements, Cancellation And Efficient Generation Of Modules Over Laurent Polynomial Rings., S. Mandal Dr.

Doctoral Theses

Unless otherwise stated all rings are assumed to be commutative and Noetherian with finite Krull dimension and modules are finitely generated. There are three related questions in commutative algebra. They are about the existence of unimodular elements in projective modules, cancellation of projective modules and minimal number of generators for finitely generated modules. In particular, determining the minimal number of generators of ideals is also of great interest in this area.In this thesis we shall be concerned with the above questions in the case of Laurent polynomial rings.The thesis consists of three Chapters. The main results are presented in Chapters …

Pattern And Mathematics: Math Enrichment Activities For Gifted Fourth, Fifth And Sixth Grade Children, Janet K. Zuber

All Graduate Projects

The purpose of this project is to provide assistance to the elementary math teacher in meeting the needs of the student gifted in the area of math. A collection of activities is provided to use with gifted intermediate students and should serve as an example of the type of activities appropriate for the gifted student. These activities would be most appropriately used with gifted students in grades four through six. The activities would be of greatest benefit if students were grouped in a homogeneous manner with one teacher taking responsibility for their math needs, Homogeneous grouping would allow for faster-paced …

Computer Banking And Cross-Referencing Of Mathematical Materials For The Elementary Grades, Daniel Jordan Martin

All Graduate Projects

The specific area and focus of this project will be that of arranging District and program math learning objectives for eventual computer banking along with materials cross-referenced to those objectives. In addition, the cross-referenced materials will be labeled as to grade level, interest level, mode of learning, and time needed for their use. The computer banking will facilitate use and prescriptive accessibility to given objectives.

The justification for such a project can be broken down into several areas: (1) the need of the elementary math teachers to have a bank of supplementary materials cross-referenced to facilitate their instruction of math …

Numerical Solution Of Three Instability Problems, Jacob Greydanus

Digitized Theses

This thesis obtains numerical solutions for three instability problems.;The first is a Rayleigh-Taylor interfacial instability problem. Numerical solutions are obtained using a co-ordinate transformation technique and two approaches are tested for use in solving the field equation: (a) transformation and extremization of the variational integral, and (b) transformation of the differential equation itself. The latter is also tested with the use of higher order finite difference formulae. Solutions are generated with the most suitable method and compared with the predictions of Nayfeh's non-linear perturbation theory. While there is good qualitative agreement it is found that the quantitative agreement degrades with …

Boundary Layer Flow In Streamwise Concave Corners, Steven Ray Wilkinson

Digitized Theses

Laminar boundary-layer theory has been correctly developed for streamwise corners using singular perturbation techniques. Theoretical predictions, however, do not compare well with experimental measurements due to the observed breakdown of flow stability and similarity. Both of these properties appear as basic assumptions of the boundary-layer theory, thereby providing needed simplification as well as imposing limitations upon the mathematical model.;Any theoretical investigation of similarity breakdown would require knowledge of the similar solution not only as an initial condition, but also for insight into how to proceed. Examination of the cross-flow behavior, which affects the onset of similarity breakdown, may suggest ways …