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In this paper we show how a variant of Stone and Brook's continuum regression criterion may be used to define the least variance ratio estimator of the slope parameters of the simultaneous equations model of econometrics. As a by-product of this approach we identify a family of estimators (distinct from the family of k-class estimators) to which it and two variants of the orthogonal least squares estimator belong. We also take the opportunity to mention several features of linear unbiased scalar residuals omitted from an earlier paper. [ABSTRACT FROM AUTHOR]

The two-variable orthogonal least squares procedure was developed independently by Julius Ludwig Weisbach (1806–1871) and Robert Jackson Adcock (1826–1895). In this article we discuss aspects of two recent articles concerned with the contributions of these individuals. We also identify a prototype of the orthogonal minimax fitting procedure due to August Beyer (1677–1753). [ABSTRACT FROM AUTHOR]

Following a brief critique of the wording of Lewis Carroll's Alice's Adventures in Wonderland, this article offers some supplementary remarks relating to the solution of a 3×3 pseudo-magic square problem posed by Lewis Carroll, a generalisation of the 3×3 Lo-Su or luoshu magic square, the problem of installing m² = 25 or m² = 36 offcers of m different ranks and m different regiments in a m × m Graeco-Latin square (with apposite remarks on the military career of Leonhard Euler's third son and the recent coinage of the Empress Maria Theresa) and a list of fourteen portraits of mathematicians on banknotes paying particular attention to those of Sir Isaac Newton and Florence Nightingale. [ABSTRACT FROM AUTHOR]

We establish that there are a total of 48 distinct ordered sets of three 4×4 (skew-symmetric) signed permutation matrices which will serve as the basis of an algebra of quaternions. [Copyright &y& Elsevier]

Describes the geometrical representation of allocations of quantities of goods, votes or probabilities between two or more persons, parties or strategies. Representation of the time-varying allocation of votes between political parties; Allocation of goods between persons; Identification of probabilities between strategies.

In this paper we show that a set of conditions that are sufficient to ensure the stability of a univariate linear difference equation are closely related to the corresponding set of necessary and sufficient conditions established by Samuelson and Wise. [ABSTRACT FROM AUTHOR]

The article reviews the book "In the Dark on the Sunny Side: A Memoir of an Out-Of-Sight Mathematician" by Larry W. Baggett.