By combining a spiral zone plate (SZP) and grating, we propose single optical element, termed composited grating (CSZPG), to generate flower mode vortices with the equicohesive petals has long focal depths. Theoretical analysis reveals that CSZPG can approximately petals, it longer depths compared conventional SZP. Moreover, performance of on period, length radius is investigated. The experimen...

A sunflower with p petals consists of sets whose pairwise intersections are identical. The goal the problem is to find smallest r=r(p,k) such that any family rk distinct k-element contains a petals. Building upon breakthrough Alweiss, Lovett, Wu and Zhang from 2019, Rao proved r=O(plog(pk)) suffices; this bound was reproved by Tao in 2020. In short note we record r=O(plogk) suffices, using mino...

A sunflower with $r$ petals is a collection of sets so that the intersection each pair equal to all them. Erd?s and Rado proved lemma: for any fixed $r$, family size $w$, at least about $w^w$ sets, must contain petals. The famous conjecture states bound on number can be improved $c^w$ some constant $c$. In this paper, we improve $\mathrm{log}\ w)^w$. fact, prove result robust notion sunflowers,...

Angular distribution of light diffracted out of the plane of two-dimensional photonic crystals (PhC) has been studied in the azimuthal direction with a specially designed waveguide structure. The optical images of the light extraction patterns from the guided photoluminescence light are obtained with laser excitation in the center of the annual structure made on GaN multilayer. For increasing l...

To study the movement characteristics and separation mechanism of safflower petals their impurities under action airflow lower impurity rate in cleaning operation process, integration computational fluid dynamics (CFD) discrete element method (DEM) codes was performed to motion sorting behavior particles different inclination angles, dust removal angles inlet velocities by establishing a true p...