We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are obtained for
the expansion of a polynomial in terms of m-polynomials. We conclude this article by an implementation in MATHEMATICA of m-polynomials and the results obtained for them.
We propose a two parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai (1985) and Singh and Ruiz Esp
ejo (2003). The bias and mean square error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean square error than the sample mean, ratio and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using groundwater data taken from a geological site in the state of Florida.
Our goal in this article is to review the known properties of the mysterious Kolakoski sequence and at the same time look at generalizations of it over arbitrary two letter alphabets. Our primary focus will here be the case where one of the letters i
s odd while the other is even, since in the other cases the sequences in question can be rewritten as (well-known) primitive substitution sequences. We will look at word and letter frequencies, squares, palindromes and complexity.
