Search results for "classical"
showing 10 items of 2294 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…
Topological two-dimensional Su–Schrieffer–Heeger analog acoustic networks: Total reflection at corners and corner induced modes
2021
In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edg…
Thermal cloaking of complex objects with the neutral inclusion and the coordinate transformation methods
2019
We explore the cloaking of a complex shape by either the neutral inclusion or the transformation thermodynamics (TT) methods. Thin cloaks are built and the heat cloaking efficiency is investigated for both the steady-state and the transient regimes. We show that the neutral inclusion cloak is more efficient in both regimes, though it has the drawback that the thermal conductivity of the cloaked shape must be known. In practice, the neutral inclusion method is more flexible and easier to implement than the coordinate transformation method, especially for complex shapes.We explore the cloaking of a complex shape by either the neutral inclusion or the transformation thermodynamics (TT) methods…
High-resolution spectroscopy and analysis of the nu3/2nu4 dyad of CF4
2011
International audience; CF4 is a strong greenhouse gas of both anthropogenic and natural origin [D.R. Worton et al., Environ. Sci. Technol. 41, 2184 (2007)]. However, high-resolution infrared spectroscopy of this molecule has received only a limited interest up to now. Until very recently, the public databases only contained cross-sections for this species, but no detailed line list. We reinvestigate here the strongly absorbing ν3 region around 7.8 μm. New Fourier transform infrared (FTIR) spectra up to a maximal resolution of 0.0025 cm−1 have been recorded: (i) room-temperature spectra in a static cell and (ii) a supersonic expansion jet spectrum at a 23 K estimated temperature. Following …
Line parameters and shapes of high clusters: R-branch of the nu3 band of CH4 in He mixtures
2002
International audience; The IR absorption spectra of CH4 in pure gas and in mixture with helium were studied in the region of nu3 band at higher J line clusters R(17)-R(22). The frequencies and intensities of rotation-vibration lines were estimated from the experimental spectra at Doppler shape conditions. The line frequencies and intensities were calculated and used for the attribution of overlapped lines in clusters. The calculated line intensities are close to the experimental values. The calculated frequency structure of the higher J manifolds are somewhat wider than the observed one. The shapes of helium-broadened line clusters were compared with those calculated accounting for line mi…
Biological control of invasive stink bugs: review of global state and future prospects
2020
International audience; Invasive stink bugs (Hemiptera: Pentatomidae) are responsible for high economic losses to agricul-ture on a global scale. The most important species, dating from recent to old invasions, includeBagrada hilaris (Burmeister), Halyomorpha halys (Stal), Piezodorus guildinii (Westwood), Nezara vir-idula (L.), and Murgantia histrionica (Hahn). Bagrada hilaris, H. halys,andN. viridula are nowalmost globally distributed. Biological control of these pests faces a complex set of challenges thatmust be addressed to maintain pest populations below the economic injury level. Several case studiesof classical and conservation biological control of invasive stink bugs are reported …
Squamation and ecology of thelodonts
2017
Thelodonts are an enigmatic group of Paleozoic jawless vertebrates that have been well studied from taxonomical, biostratigraphic and paleogeographic points of view, although our knowledge of their ecology and mode of life is still scant. Their bodies were covered by micrometric scales whose morphology, histology and the developmental process are extremely similar to those of extant sharks. Based on these similarities and on the well-recognized relationship between squamation and ecology in sharks, here we explore the ecological diversity and lifestyles of thelodonts. For this we use classic morphometrics and discriminant analysis to characterize the squamation patterns of a significant num…
European Formalism and Empiriocriticism : Formalism within the International Empiriocritical Movement
2020
Abstract This paper argues that Russian Formalism is to be considered a constitutive part of the international empiriocritical movement—Ernst Mach (1838—1916) and Richard Avenarius’s (1843—1896). The conceptual parallelism between Empiriocriticism and Formalism is striking indeed. Thus, the cornerstones of the empiriocritical approach—the concept of series [Reihe] and the concept of elements [Elemente], understood as sensations [Empfindungen]—are plainly recognizable within formalist theories: the notion of ‘series’ (for example, the notion of ‘literary series’ or ‘poetic series’, leading to the famous concept of ‘literariness’, literaturnost’) and the very formalist idea of a necessarily p…
Modelling chemical composition in electric systems - implications to the dynamics of dye-sensitised solar cells
2010
International audience; Classical electromagnetism provides limited means to model electric generators. To extend the classical theory in this respect, additional information on microscopic processes is required. In semiconductor devices and electrochemical generators such information may be obtained by modelling chemical composition. Here we use this approach for the modelling of dye-sensitised solar cells. We simulate the steady-state current-voltage characteristics of such a cell, as well as its transient response. Dynamic simulations show optoelectronic hysteresis in these cells under transient light pulse illumination.