Search results for " MATHEMATICAL"
showing 10 items of 686 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…
Elliptische Integrale, Thetafunktionen und elliptische Funktionen
1948
Es bedeute W die Quadratwurzel aus einem Polynom dritten oder vierten Grades in einer Veranderlichen z mit lauter verschiedenen Nullstellen, und R (z, W) eine rationale Funktion von z und W. Das unbestimmte Integral von R als Funktion von z heist dann ein elliptisches Integial, falls es sich nicht auf elementare Funktionen reduzieren last.
p −1-Linear Maps in Algebra and Geometry
2012
At least since Habousch’s proof of Kempf’s vanishing theorem, Frobenius splitting techniques have played a crucial role in geometric representation theory and algebraic geometry over a field of positive characteristic. In this article we survey some recent developments which grew out of the confluence of Frobenius splitting techniques and tight closure theory and which provide a framework for higher dimension geometry in positive characteristic. We focus on local properties, i.e. singularities, test ideals, and local cohomology on the one hand and global geometric applicatioms to vanishing theorems and lifting of sections on the other.
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…
Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three
2020
International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.
Generalised bisection method for optimum ultrasonic ray tracing and focusing in multi-layered structures
2021
Ultrasonic testing has been used for many decades, proving itself very efficient for detecting defects in many industrial sectors. The desire to apply ultrasonic testing to geometrically complex structures, and to anisotropic, inhomogeneous materials, together with the advent of more powerful electronics and software, is constantly pushing the applicability of ultrasonic waves to their limits. General ray tracing models, suitable for calculating the proper incident angle of single element probes and the proper time delay of phased array, are currently required. They can support the development of new imaging techniques, as Full Matrix Capture and Total Focusing Method, and the execution of …
Reversed polarized emission in highly strained a-plane GaN/AlN multiple quantum wells
2010
The polarization of the emission from a set of highly strained $a$-plane GaN/AlN multiple quantum wells of varying well widths has been studied. A single photoluminescence peak is observed that shifts to higher energies as the quantum well thickness decreases due to quantum confinement. The emitted light is linearly polarized. For the thinnest samples the preferential polarization direction is perpendicular to the wurtzite $c$ axis with a degree of polarization that decreases with increasing well width. However, for the thickest well the preferred polarization direction is parallel to the $c$ axis. Raman scattering, x-ray diffraction, and transmission electron microscopy studies have been p…
Viewpoint: Atomic-Scale Design Protocols toward Energy, Electronic, Catalysis, and Sensing Applications
2019
Nanostructured materials are essential building blocks for the fabrication of new devices for energy harvesting/storage, sensing, catalysis, magnetic, and optoelectronic applications. However, because of the increase of technological needs, it is essential to identify new functional materials and improve the properties of existing ones. The objective of this Viewpoint is to examine the state of the art of atomic-scale simulative and experimental protocols aimed to the design of novel functional nanostructured materials, and to present new perspectives in the relative fields. This is the result of the debates of Symposium I "Atomic-scale design protocols towards energy, electronic, catalysis…
District heating networks: enhancement of the efficiency
2019
International audience; During the decades the district heating's (DH) advantages (more cost-efficient heat generation and reduced air pollution) overcompensated the additional costs of transmission and distribution of the centrally produced thermal energy to consumers. Rapid increase in the efficiency of low-power heaters, development of separated low heat density areas in cities reduce the competitiveness of the large centralized DH systems in comparison with the distributed cluster-size networks and even local heating. Reduction of transmission costs, enhancement of the network efficiency by optimization of the design of the DH networks become a critical issue. The methodology for determ…
Regenerative scheduling problem in engineer to order manufacturing: an economic assessment
2021
The dynamic production scheduling is a very complex process that may arise from the occurrence of unpredictable situations such as the arrival of new orders besides the ones already accepted. As a consequence, companies may often encounter several difficulties to make decisions about the new orders acceptance and sequencing along with the production of the existing ones. With this recognition, a mathematical programming model for the regenerative scheduling problem with deterministic processing times is formulated in the present paper to evaluate the economic advantage of accepting a new order in an engineer to order (ETO) manufacturing organization. The real case of an Italian ETO company …