Kent E. Morrison

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1. INTRODUCTION. It is natural to use integer matrices for examples and exercises when teaching a linear algebra course, or, for that matter, when writing a textbook in the subject. After all, integer matrices offer a great deal of algebraic simplicity for particular problems. This, in turn, lets students focus on the concepts. Of course, to insist on(More)
one gets the first actual formula for 7r that mankind ever discovered, dating from 1593 and due to Frangois Viete (1540-1603), whose Latinized name is Vieta. (Was any notice taken of the formula's 400th anniversary, perhaps by the issue of a postage stamp?) From the samples of a function t(x) at equally spaced points x", n E z, one can reconstruct the(More)
A linear operator on a Hilbert space may be approximated with nite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L2 functions are never compact; for them we consider how well the(More)
In 2003 the Motor Neurone Disease (MND) Association, together with The Wellcome Trust, funded the creation of a national DNA Bank specific for MND. It was anticipated that the DNA Bank would constitute an important resource to researchers worldwide and significantly increase activity in MND genetic research. The DNA Bank houses over 3000 high quality DNA(More)
In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences, their generating functions, and examples. Section 2 contains the proofs of the formulas for the coefficients and the(More)
We develop an analog of the exponential families of Wilf in which the label sets are finite dimensional vector spaces over a finite field rather than finite sets of positive integers. The essential features of exponential families are preserved, including the exponential formula relating the deck enumerator and the hand enumerator.
Ted Hill is professor emeritus of mathematics at Georgia Tech, and has held visiting appointments in Costa Rica, Germany (Gauss Professor), Holland (NSF-NATO Fellow), Israel, Italy, and Mexico. He studied at West Point (B.S.), Stanford (M.S.), Göttingen (Fulbright Scholar), and Berkeley (M.A., Ph.D.), and his primary research interests are in mathematical(More)
In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to the target, or a winner can be a player coming closest without guessing higher than the target. We study optimal(More)
You walk into a casino, and just inside the main entrance you see a new game to play—the Multiplication Game. You sit at a table opposite the dealer and place your bet. The dealer hits a button and from a slot in the table comes a slip of paper with a number on it that you cannot see. You use a keypad to choose a number of your own—any positive integer you(More)