Thesis (M.A.) -- Central Connecticut State University, 2006. / Thesis advisor: Yuanquian Chen. "... in partial fulfillment of the requirements for the degree of Master of Art in Mathematics." Includes bibliographical references (leaf 43). Also available via the World Wide Web.

Intercalates and the maximum number of intercalates are presented. We introduced partially intercalate complete Latin squares and results on the existence of some infinite families as well as Latin squares of smaller size is given. The second part of our work summarizes the main results on orthogonal Latin squares. Special type of Latin squares, gerechte designs, are introduced and proof for the existence of such orthogonal Latin squares of prime orders is also presented.

A spline function of degree k with knots S₀, S₁,...,Sr is a C[superscript]k-1 function which is a polynomial of degree at most k in each of the intervals (-∞, S₀), (S₀, S₁),…, (Sr,+∞). The Gauss-Markoff Theorem can be used to estimate by least squares the coefficients of a spline function of given degree and knots. Estimating a spline function of known knots without full knowledge of the degree entails an extension of the Gauss-Markoff technique. The estimation of the degree when the knots are also unknown has a possible solution in a method employing finite differences. The technique of minimizing sums of squared residuals forms the basis for a method of estimating the knots of a spline function of given degree. Estimates for the knots may also be obtained by a method of successive approximation, provided additional information about the spline function is known. / Science, Faculty of / Mathematics, Department of / Graduate

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Methods of constructing orthogonal Latin of squares and incomplete balanced block designs are developed. The analysis of these designs is then derived. Particular care is taken in the determination of the number of degrees of freedom involved, a point which is usually neglected in other sources. The principle source of material for this thesis has been H.B. Mann's book, Analysis and Design of Experiments. / Thesis / Master of Arts (MA)

Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard 1 l -minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of simulation results strongly confirming the utility of their approach, they did not rigorously establish the convergence properties of their algorithm. In this paper, we introduce prior information on the support of the sparse domain of the solution into the algorithm of Daubechies et al. We then provide a rigorous proof of the convergence of the resulting algorithm.

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