Additionally, \({{{\boldsymbol{\varepsilon }}}\left({{{\boldsymbol{\omega }}}{{{\boldsymbol{,}}}{{{\bf{k}}}\right)\) is the dielectric tensor, and \({{{\bf{D}}}\left({{{\boldsymbol{\omega }}}{{{\boldsymbol{,}}}{{{\bf{k}}}\right)\) is the coefficient matrix, ...
For all $\varepsilon > 0$, we show that there exists a $\delta > 0$ such that there are $n$-vertex $O(n)$-edge graphs $G$ where adding any shortcut set of size $O(n^{2-\varepsilon})$ keeps the diameter of $G$ at $\Omega(n^\delta)$. This improves the sparsity of ...
We study under which conditions the pseudo-differential operator with the symbol gives rise to a Feller semigroup if the symbol of the perturbation B depends merely measurably on x. If the symbol—or, equivalently, the characteristics—of a Lévy-type operator satisfies suitable smoothness ...
On the other hand, knowing the value of(and that it is attained for), we can define a further notion of optimal-constantA, “relative” to. More precisely we define For the sake of generality we will actually consideralso in the so-calledsubcritical case, meaning that we enlarge the class...
Let\(\varSigma \)be a finite non-empty alphabet of symbols. Then\(\varSigma ^*\)denotes the set of strings over the alphabet\(\varSigma \)including the empty string\(\varepsilon \). The length of a stringwis denoted by |w|, and the number of occurrences of a symbolain a string...