Eric Lander conjectured that if G is an abelian group of order v containing a difference set of order n and p is a prime dividing v and n, then the Sylow p-subgroup of G cannot be cyclic. This paper verifies a version of this conjecture for k < 6500. A special case of this version is the non-existence of Menon-Hadamard-McFarland difference sets in 2-groups. We also give an algorithm that easily...

In this article we prove a collection of new non-linear and non-local integral inequalities. As an example for u ≥ 0 and p ∈ (0,∞) we obtain ∫ R3 dx u(x) ≤ ( p+ 1 p )2 ∫ R3 dx {(−4)−1u(x)}|∇u p 2 (x)|. We use these inequalities to deduce global existence of solutions to a non-local heat equation with a quadratic non-linearity for large radial monotonic positive initial conditions. Specifically,...

We prove the nonexistence of ovoids in finite orthogonal spaces of type O2n+1(q) for n ≥ 4.

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...

In this paper, the parabolic problem $$u_t - div(\omega (x) \nabla u)= h(t) f(u) + l(t) g(u)$$ with non-negative initial conditions pertaining to $$C_b({\mathbb {R}}^N)$$ , will be studied, where weight $$\omega $$ is an appropriate function that belongs Muckenhoupt class $$A_{1 \frac{2}{N}}$$ and functions f, g, h l are continuous. The main goal establish global non-global existence of solutio...

Abstract A fundamental question in the field of cohomology dynamical systems is to determine when there are solutions coboundary equation: $$ \begin{align*} f = g - \circ T. \end{align*} In many cases, T given be an ergodic invertible measure-preserving transformation on a standard probability space $(X, {\mathcal B}, \mu )$ and contained $L^p$ for $p \geq 0$ . We extend previous results by sho...