Gruppen von Restklassen nach Restpolynomidealen in mehreren Unbestimmten

Ohne Zusammenfassung     

Explicit construction of regular graphs without small cycles

For every integerd>2 we give an explicit construction of infinitely many Cayley graphsX of degreed withn(X) vertices and girth >0.4801...(logn(X))/log (d−1)−2. This improves a result of Margulis. Dedicated to Paul Erdős on his seventieth birthday     

On The Cauchy Problem for The Equation u′ − Δu = u¦u¦γ−1 In The Supercritical Case

We prove global existence of classical solutions to the above problem, whenever the initial function is continuous and can be enclosed between a sub- and a supersolution of the corresponding stationary problem, where the latter are assumed to be smooth bounded functions lying in some L^p(?ⁿ) (Theorem 1). In addition we study the large-time behaviour of the solutions. As an example, it turns out from this that in case of the critical exponent γ = (n+2)/(n?2) the corresponding positive stationary solutions are unstable w.r.t. arbitrarily slight variations either from above or from below (Theorems 5 and 9).     

Associative products of graphs

It is shown that there exist exactly twenty products of graphs defined on the Cartesian product of the vertex sets of the factors where the adjacencies of the vertices only depend on the adjacencies in the factors.