Let $D \subset \mathbb{R}^d$ be a bounded, connected domain with smooth boundary, and let $-\Delta u = \mu\_1 u$ the first nontrivial eigenfunction of Laplace operator Neumann boundary conditions. We prove that $$ \max\_{x \in D} \~u(x) \leq 60 \cdot \partial we emphasize this constant is uniform among all domains in dimensions. In particular, hot spots conjecture cannot fail by an arbitrarily ...

<p style='text-indent:20px;'>In this paper, we use the exponential transform to give a unified formal upper bound for asymptotic rate of spread population propagating in one dimensional habitat. We show through examples how can be obtained directly discrete and continuous time models. This has form <inline-formula><tex-math id="M1">\begin{document}$ \min_{s>0} \ln (\rho...