As has been known for many years (see, e.g., K. Mahler, /. Reine Angew. Math., v. 166, 1932, pp. 118-150), a real or complex number f is transcendental if and only if the following condition is satisfied. To every positive number co there exists a positive integer n and an infinite sequence of distinct polynomials {p,(z)} = {pr + pr z + • • • + p z } at most of 0 1 n degree n with integral coef...

This paper examines the possibility for two contestants to agree on a peace settlement thereby avoiding a contest, in which each would exert a costly effort given the posterior distributions inferred from the negotiation. I find a necessary and sufficient condition of the prior distributions for there to exist a negotiation mechanism that admits a peace-ensuring perfect Bayesian equilibrium. Th...

In this paper, it is proved that a symmetric tensor is (strictly) copositive if and only if each of its principal subtensors has no (non-positive) negative H++-eigenvalue. Necessary and sufficient conditions for (strict) copositivity of a symmetric tensor are also given in terms of Z++-eigenvalues of the principal sub-tensors of that tensor. This presents a method for testing (strict) copositiv...