Search results for "Lips"
showing 10 items of 414 documents
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Amorphous ultra-wide bandgap ZnOx thin films deposited at cryogenic temperatures
2020
Crystalline wurtzite zinc oxide (w-ZnO) can be used as a wide band gap semiconductor for light emitting devices and for transparent or high temperature electronics. The use of amorphous zinc oxide (a-ZnO) can be an advantage in these applications. In this paper we report on X-ray amorphous a-ZnOx thin films (~500 nm) deposited at cryogenic temperatures by reactive magnetron sputtering. The substrates were cooled by a nitrogen flow through the copper substrate holder during the deposition. The films were characterized by X-ray diffraction (XRD), Raman, infrared, UV-Vis-NIR spectroscopies, and ellipsometry. The a-ZnOx films on glass and Ti substrates were obtained at the substrate holder temp…
Band gap of corundumlike α−Ga2O3 determined by absorption and ellipsometry
2017
The electronic structure near the band gap of the corundumlike $\ensuremath{\alpha}$ phase of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ has been investigated by means of optical absorption and spectroscopic ellipsometry measurements in the ultraviolet (UV) range (400--190 nm). The absorption coefficient in the UV region and the imaginary part of the dielectric function exhibit two prominent absorption thresholds with wide but well-defined structures at 5.6 and 6.3 eV which have been ascribed to allowed direct transitions from crystal-field split valence bands to the conduction band. Excitonic effects with large Gaussian broadening are taken into account through the Elliott-Toyozawa model, which y…
Determination of refractive index of submicron-thick films using resonance shift in a four-layer slab waveguide
2017
The measurement of refractive index of very thin films at the order of ten to hundred nanometers is cumbersome and usually requires employing sophisticated techniques such as the spectral ellipsometry. In this paper we describe a simple contact method for measuring the refractive index of thin films. Here we have used the prism-coupling technique for characterizing samples prepared as four-layer slab waveguides. The waveguide resonance condition can be calculated by solving simple analytic transcendental equations for the slab waveguide. Then the captured mode position as a function of cladding thickness is used for probing the refractive index of cladding layer. We used indium-tin-oxide la…
Three X-ray Flares Near Primary Eclipse of the RS CVn Binary XY UMa
2016
We report on an archival X-ray observation of the eclipsing RS CVn binary XY UMa ($\rm P_{orb}\approx$ 0.48d). In two $\emph{Chandra}$ ACIS observations spanning 200 ks and almost five orbital periods, three flares occurred. We find no evidence for eclipses in the X-ray flux. The flares took place around times of primary eclipse, with one flare occurring shortly ($<0.125\rm P_{orb}$) after a primary eclipse, and the other two happening shortly ($<0.05\rm P_{orb}$) before a primary eclipse. Two flares occurred within roughly one orbital period ($\Delta \phi\approx1.024\rm P_{orb}$) of each other. We analyze the light curve and spectra of the system, and investigate coronal length scales both…
Modelling Complex Volume Shape Using Ellipsoid: Application to Pore Space Representation
2017
Natural shapes have complex volume forms that are usually difficult to model using simple analytical equations. The complexity of the representation is due to the heterogeneity of the physical environment and the variety of phenomena involved. In this study we consider the representation of the porous media. Thanks to the technological advances in Computed Topography scanners, the acquisition of images of complex shapes becomes possible. However, and unfortunately, the image data is not directly usable for simulation purposes. In this paper, we investigate the modeling of such shapes using a piece wise approximation of image data by ellipsoids. We propose to use a split-merge strategy and a…
Extended two-body problem for rotating rigid bodies
2021
A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for pairs of spheroids and ellipsoids with 12 degrees of freedom. We demonstrate the method with two dimensionless test scenarios, one where tumbling motion develops, and one where the motion of the bodies resemble spinning tops. We also test the method on the asteroid binary (66391) 1999 KW4, where both components are modelled either as spheroids or ellipsoids. The two different shape models have negligible effects on the eccentricity and semi-major axis, but…
Integrative taxonomy of root aphid parasitoids from the genus Paralipsis (Hymenoptera, Braconidae, Aphidiinae) with description of new species
2019
Species from the genus Paralipsis are obligatory endoparasitoids of root aphids in the Palaearctic. It is known that these species are broadly distributed, parasitizing various aphid hosts and showing great biological and ecological diversity. On the other hand, this group of endoparasitoids is understudied and was thought to be represented by a single species in Europe, viz., Paralipsisenervis (Nees). However, recent description of two new species indicated the possibility of cryptic speciation and recognition of additional Paralipsis species in Europe. In this research, Paralipsis specimens collected during the last 60 years from eight European countries, as well as one sample from Morocc…
Development of a low-alcoholic fermented beverage employing cashew apple juice and non-conventional yeasts
2019
Cashew apples are by-products in the production of cashew nuts, which are mostly left to rot in the fields. Cashew apple juice (CAJ), a highly nutritious beverage, can be produced from them. It is rich in sugars and ascorbic acid, but its high polyphenol content makes it bitter and astringent, and therefore difficult to commercialize. The kingdom of fungi contains more than 2000 yeast species, of which only a few species have been studied in relation to their potential to produce aroma compounds. The aim of this research was to develop a new low-alcoholic fermented beverage to valorize cashew apples. For this purpose, a screening was carried out employing non-conventional yeast species and …