We establish alternative theorems for quadratic inequality systems. Consequently, we obtain Lagrange multiplier characterizations of global optimality for classes of non-convex quadratic optimization problems. We present a generalization of Dine’s theorem to a system of two homogeneous quadratic functions with a regular cone. The class of regular cones are cones K for which (K∪−K) is a subspace...

Brouwer and Wilbrink [3] showed the nonexistence of regular near octagons whose parameters s, t2, t3 and t satisfy s ≥ 2, t2 ≥ 2 and t3 = t2(t2 + 1). Later an arithmetical error was discovered in the proof. Because of this error, the existence problem was still open for the near octagons corresponding with certain values of s, t2 and t3. In the present paper, we will also show the nonexistence ...

LetG be a finite group acting on a finite-dimensional vector space V , such that the ring of invariants is polynomial. The purpose of this note is to describe exactly the finitely generated inverse systems such that the associated G-representation is the direct sum of copies of the regular representation of G. This generalizes work of Steinberg, Bergeron, Garsia, and Tesler. Related results are...

We use the Lorenz system, the Rikitake model and the nonlinear Schrödinger equation to demonstrate that for completely integrable systems, there exist what we call regular mirror systems near movable singularities. The method for finding the mirror systems is very similar to the original Weiss et al’s (1983 J. Math. Phys. 24 522–6) version of the Painlevé test. It tests the complete integrabili...

Gambling is a common recreational activity that becomes dysfunctional in a subset of individuals, with DSM "pathological gambling" regarded as the most severe form. During gambling, players experience a range of cognitive distortions that promote an overestimation of the chances of winning. Near-miss outcomes are thought to fuel these distortions. We observed previously that near misses recruit...