Decompositions of Laurent polynomials

In the 1920's, Ritt studied the operation of functional composition g o h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple `prime factorizations' with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving the analogous problem for rational functions. In this paper we use results of Avanzi--Zannier and Bilu--Tichy to prove analogues of Ritt's results for decompositions of Laurent polynomials, i.e., rational functions with denominator a power of x.Comment: 31 page

Factorizations of certain bivariate polynomials

We determine the factorization of X*f(X)-Y*g(Y) over K[X,Y] for all squarefree additive polynomials f,g in K[X] and all fields K of odd characteristic. This answers a question of Kaloyan Slavov, who needed these factorizations in connection with an algebraic-geometric analogue of the Kakeya problem.Comment: 5 page

\u3cem\u3eMartin v. Mott\u3c/em\u3e and the Establishment of Executive Emergency Authority

In August of 1814, a New York farmer named Jacob E. Mott refused to rendezvous with the militia pursuant to the orders of Governor Daniel D. Tompkins as commanded by President James Madison. In 1818, Mott was court martialed and fined ninety-six dollars. One year later, Mott brought an action in replevin in the New York state courts to recover chattel taken from him by a deputy marshal in lieu of the ninety-six dollars. Both the New York trial and appellate courts sided with Mott. In a unanimous opinion authored by Justice Joseph Story, the Supreme Court of the United States reversed and held the marshal’s avowry sufficient. Justice Story’s opinion reiterated the authority of the federal executive, and began a line of cases that culminated in our modern approach to unilateral executive emergency powers

Permutation polynomials induced from permutations of subfields, and some complete sets of mutually orthogonal latin squares

We present a general technique for obtaining permutation polynomials over a finite field from permutations of a subfield. By applying this technique to the simplest classes of permutation polynomials on the subfield, we obtain several new families of permutation polynomials. Some of these have the additional property that both f(x) and f(x)+x induce permutations of the field, which has combinatorial consequences. We use some of our permutation polynomials to exhibit complete sets of mutually orthogonal latin squares. In addition, we solve the open problem from a recent paper by Wu and Lin, and we give simpler proofs of much more general versions of the results in two other recent papers.Comment: 13 pages; many new result

Sometimes the Silence Can Be like the Thunder: Access to Pharmaceutical Data at the FDA

Those committed to the free exchange of scientific information have long complained about various restrictions on access to the FDA\u27s pharmaceutical data and the resultant restrictions on open discourse. A review of open-government procedures and litigation at the FDA demonstrates that the need for transparency at the agency extend well beyond the reach of any clinical trial registry