This paper is devoted to the initial value problems for semilinear wave equations of derivative type with spatial weights in one space dimension. The lifespan estimates classical solutions are quite different from those nonlinearity unknown function itself as global-in-time existence can be established by decay.

The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type for Hausdorff dimension: For any $0<\beta<\alpha$, compact metric space $X$ of dimension $\alpha$ contains a subset which is biLipschitz equivalent to an and has at least $\beta$. In this note we present simple proof in doubling spaces using Bartal's Ramsey decompositions [Ba...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4. We prove in a direct way the equivalence of these two constructions for p ~ 31. In dimension 32, we obtain an extremal lattice of type II not isometric...