A sufficient and necessary condition for $${\mathcal {A}}$$-quasiaffinity

A Necessary and Sufficient Condition for Transcendency

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...

A Necessary and Sufficient Condition for Peace∗

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...

A Necessary Condition for Weyl-Heisenberg Frames

A necessary and sufficient minimality condition for uncertain systems

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFT’s) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well...

A Necessary and Sufficient Condition for Peace An Extended Abstract

Under what conditions can potential contestants avoid conflicts through a peace settlement? This question is relevant to real world situations such as international conflicts and pre-litigation negotiations. In the spirit of Myerson and Satterthwaite [4] on bilateral trade, where information asymmetry is the impediment to mutually beneficial negotiation outcomes, a natural approach to address t...