Nonexistence of Complete Ferromagnetism

Nonexistence of Solutions In

Consider the KPP-type equation of the form ∆u+f (u) = 0, where f : [0, 1] → R + is a concave function. We prove for arbitrary dimensions that there is no solution bounded in (0, 1). The significance of this result from the point of view of probability theory is also discussed.

Nonexistence of Cusp Cross-section of One-cusped Complete Complex Hyperbolic Manifolds Ii

Long and Reid have shown that some compact flat 3-manifold cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped hyperbolic 4-manifold. Similar to the flat case, we give a negative answer that there exists a 3-dimensional closed Heisenberg infranilmanifold whose diffeomorphism class cannot be arisen as a cusp cross-section of any complete finite volume 1-cusped ...

Nonexistence of Stable Threesome Matchings

Gale and Shapley (1962) proved stability is the rule for ‘marriage’, i.e., matchings of twosomes. This rule says given any society with two kinds of agents to be matched in pairs, each agent having a preference ordering on agents of the opposite kind, there exists at least one stable matching. In this note we show by example that stable matchings may fail to exist in societies with three kinds ...

Nonexistence of Countinuous Peaking Functions

We construct a smoothly bounded pseudoconvex domain such that every boundary point has a p.s.h. peak function but some boundary point admits no (local) holomorphic peak function.

A Theory of Ferromagnetism.