Robert MacDuff, Ph.D., President, InfoDynamics Applications Ltd. (Phone) 480-205-6135 Feb. 2, 2009 draft. jj The Paradise Valley Unified School District in Arizona, in northern Phoenix, has been administering Standard Aligned Measures (SAM) tests in mathematics since 2005. The SAMs tests, three during the year, have shown a high degree of correlation with the state’s “Arizona's Instrument to Me...

We prove that any partition of an n-dimensional discrete box into nontrivial sub-boxes must consist of at least 2 sub-boxes, and consider some extensions of this theorem.

Extra items added to a list cause memory for the other items to decrease (the list-length effect). In one of the present studies we show that strengthening (or weakening) some items on a list harms (helps) free recall of the remaining list items. This is termed the list-strength effect. However, in seven recognition studies the list-strength effect was either absent or negative. This held wheth...

We discuss an efficient hardware implementation of the Rijndael S-box.

In this paper, we present several new constructions of differentially 4-uniform permutations over F22m by modifying the values of the inverse function on some subsets of F22m . The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of crytographic substitution boxes.

We show that every R–diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu’s S–transform is multiplicative. Our considerations base on a new concept of R–diagonality with amalgamation, for which we give several equivalent characterizat...