We show that the blow-ups of compact solutions to mean curvature flow in $\mathbb{R}^N$ initially satisfying pinching condition $|A|^2 < c |H|^2$ for a suitable constant $c = c(n)$ must be codimension one.

Abstract In this paper, we prove convergence of the high codimension mean curvature flow in sphere to either a round point or totally geodesic assuming pinching condition between norm squared second fundamental form and background sphere. We show that is sharp for dimension $$n\ge 4$$ n ≥ <mml...

OCULAR DISORDERS choroidoretinal defects choroidal coloboma, retinal coloboma, macular coloboma, retinal pigmentation changes, retinal flecks corneal defects not including dystrophy microphthalmos (anteposterior globe diameter less than 20 mm, in adult), anophthalmos eye, motility defects nystagmus strabismus convergent, esotropia, misalignment of the visual axes of the eyes eyelids, anomalies ...

Recently, novel findings have been published, according to which some mem-systems excited by harmonic signals can be characterised by the so-called ‘non-crossing-type pinched hysteretic loops’. Presented is a proof that this phenomenon cannot occur in ideal memristors, memcapacitors and meminductors which are defined axiomatically via the corresponding constitutive relations or via other equiva...

Preliminary results on the fabrication of a memristive device made of zinc oxide (ZnO) over a mesoporous silicon substrate have been reported. Porous silicon (PS) substrate is employed as a template to increase the formation of oxygen vacancies in the ZnO layer and promote suitable grain size conditions for memristance. Morphological and optical properties are investigated using scanning electr...

Here, we report an enhanced separation of colloidal particles using a novel type AsPFF (asymmetric pinched flow fractionation) device with two additional features (t-AsPFF-v). Particularly, by adding a tilted sidewall and vertical focusing channels to the conventional AsPFF device, a significant enhancement in the separation resolution (R(m,n)) has been achieved, which was estimated to be 10.4 ...

Using the Landau-Ginzburg-Devonshire approach, we study stress-induced transformations of polarization switching in ferrielectric CuInP2S6 nanoparticles for three different shapes: a disk, sphere, and needle. Semiconducting properties nanoparticle are modeled by surface charge layer, whose effective screening length can be rather small due to field-effect. We reveal very strong unusual influenc...