This paper considers solutions $u_\alpha$ of the three-dimensional Navier--Stokes equations on periodic domains $Q_\alpha:=(-\alpha,\alpha)^3$ as domain size $\alpha\to\infty$, and compares them to same whole space. For compactly-supported initial data $u_\alpha^0\in H^1(Q_\alpha)$, an appropriate extension converges a solution $u$ ${\mathbb R}^3$, strongly in $L^r(0,T;H^1({\mathbb R}^3))$, $r\...

objective: alpha-thalassemia is one of the most prevalent hemoglobin disorders in the world and it is a common hereditary condition caused by deletion of one or more α-globin genes. common α-thalassemia deletions like 3.7 kb, 4.2 kb, 20.5 kb and med can be detected by multiplex pcr. there are, however, some unknown deletions that can not be detected by the mentioned method or even by direct dna...

For a given irrational number $\alpha$ one can define an irrationality measure function $\psi_{\alpha}^{[2]}(t) = \min\limits_{\substack{(q, p)\colon q, p \in\mathbb{Z}, 1\leqslant q\leqslant t, \\ (p, q) \neq (p_n, q_n) ~\forall n\in\mathbb{Z_{+}}}} |q\alpha -p|$, related to the second-best approximations $\alpha$. In 2017 Moshchevitin studied corresponding Diophantine constant $\mathfrak{k}(\...

Chelkak introduced $s$-embeddings as tilings by tangential quads which provide the right setting to study Ising model with arbitrary coupling constants on planar graphs. We prove existence and uniqueness of a local transformation for called cube move, consists in flipping three quadrilaterals such way that resulting tiling is also class $s$-embeddings. In passing, we give new simpler formula ch...

Through an extensive series of high-precision numerical computations the optimal complete photonic band gap (PBG) as a function dielectric contrast $\ensuremath{\alpha}$ for variety crystal and disordered heterostructures, we reveal striking universal behaviors sensitivity $\mathcal{S}(\ensuremath{\alpha})\ensuremath{\equiv}d\mathrm{\ensuremath{\Delta}}(\ensuremath{\alpha})/d\ensuremath{\alpha}...