Weak coloring numbers generalize the notion of degeneracy a graph. They were introduced by Kierstead & Yang in context games on graphs. Recently, several connections have been uncovered between weak and various parameters studied graph minor theory its generalizations. In this note, we show that for every fixed $k\geq1$, maximum $r$-th number with simple treewidth $k$ is $\Theta(r^{k-1}\log...

In this work we explore the first stages of quantum wire (QWR) formation studying the evolution of the growth front for InAs coverages below the critical thickness, theta(c), determined by reflection high energy electron diffraction (RHEED). Our results obtained by in situ measurement of the accumulated stress evolution during InAs growth on InP(001) show that the relaxation process starts at a...

ww

We have simulated both conventional (V1) and saturation transfer (V'2) electron paramagnetic resonance spectra for the case of Brownian rotational diffusion restricted in angular amplitude. Numerical solutions of the diffusion-coupled Bloch equations were obtained for an axially symmetric 14N nitroxide spin label with its principal axis rotating within a Gaussian angular distribution of full wi...

We study traces of weighted Triebel–Lizorkin spaces F p , q s ( R n w ) $F^s_{p,q}(\mathbb {R}^n,w)$ on hyperplanes − k $\mathbb {R}^{n-k}$ where the weight is Muckenhoupt type. concentrate example α x = | $w_\alpha (x) {\big\vert x_n\big\vert }^\alpha$ when ≤ 1 $\big\vert \le 1$ ∈ $x\in \mathbb {R}^n$ and (x)=1$ otherwise, > $\alpha >-1$ . Here we use some refined atomic decomposition argument...

For a given pseudo-Brewster angle phi(pB) of minimum reflectance |r(p)| of p-polarized light at a dielectric-conductor interface, the second-Brewster angle phi(2B) of minimum reflectance ratio |rho|=|r(p)|/|r(s)| of the p and s polarizations is determined for all possible values of the complex relative dielectric function epsilon that lead to the same phi(pB). The difference phi(2B)-phi(pB) is ...

We classify simply-connected, orientable, complete Willmore surfaces with vanishing Gaussian curvature. also study the cones in $${\mathbb {R}}^{3}$$ and give a classification. As an application, we show that for embedding $$f:{\mathbb {R}}^{2} \rightarrow {\mathbb , if its corresponding curvature is nonnegative image of Gauss map lies $$\big \{\theta \in {S}}^{2}: d_{{\mathbb {S}}^{2}}(\theta ...

Neural networks with the rectified linear unit (ReLU) nonlinearity are described by a vector of parameters $$\theta $$ and realized as piecewise continuous function $$\varvec{R}_{\theta }: x \in \mathbb {R}^{d} \mapsto \varvec{R}_{\theta }(x) {R}^{k}$$ . Natural scalings permutations operations on leave realization unchanged, leading to equivalence classes that yield same realization. These con...