Search results for "Lysis"
showing 10 items of 34769 documents
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
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.
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
A combined three-dimensional digitisation and subsurface defect detection data using active infrared thermography
2016
International audience; In recent years, NonDestructive Testing (NDT) systems have been upgraded with three-dimensional information. Indeed, combine the three-dimensional and thermal information allows a more meaningful analysis. In the literature, the data for NDT and three-dimensional (3D) reconstruction analysis are commonly acquired from independent systems. However, the use of two such systems leads to error analysis during the data registration. In an attempt to overcome such problems, we propose a single system based on active thermography approach using heat point-source stimulation to get the 3D digitization as well as subsurface defect detection. The experiments are conducted on s…
Optimum Design and Performance of an Electron Gun for a Ka-Band TWT
2019
This paper deals with optimum design and development of a thermionic electron gun to meet specified beam requirements within defined electric and geometric constraints for a Ka -band traveling wave tube (TWT) for space applications. The electron gun design is based on the Pierce method and carried out according to the iterative process indicated by Vaughan. The design of a periodic permanent magnet (PPM) beam focusing system for the stability of the beam is also required. A sensitivity analysis, by varying electric parameters and geometric parameters, is presented and taken into account as a fundamental role to the aim of optimizing the design of the Pierce gun. A cathode current value of 5…
Batch-to-Melt Conversion Kinetics in Sodium Aluminosilicate Batches Using Different Alumina Raw Materials
2016
The batch-to-melt conversion in batches of sand, soda ash and corundum (C), alumina spinel (A), boehmite (B), or gibbsite (G) as Al2O3 carrier are studied using thermal analysis, X-ray diffraction, and 27Al nuclear magnetic resonance spectroscopy. Laboratory-scaled batches are either heated continuously or quenched from 1600°C in a series of increasing dwell times. The results show that the conversion from the raw materials to the fresh melt proceeds in two kinetic stages. During the first stage (3–5 min), fast conversion of nearly 95% by mass occurs and the conversion coefficient increases in the order G < C ≈ A < B. The second stage is controlled by the slow dissolution of intermediate cr…
The filter and calibration wheel for the ATHENA wide field imager
2016
The planned filter and calibration wheel for the Wide Field Imager (WFI) instrument on Athena is presented. With four selectable positions it provides the necessary functions, in particular an UV/VIS blocking filter for the WFI detectors and a calibration source. Challenges for the filter wheel design are the large volume and mass of the subsystem, the implementation of a robust mechanism and the protection of the ultra-thin filter with an area of 160 mm square. This paper describes performed trade-offs based on simulation results and describes the baseline design in detail. Reliable solutions are envisaged for the conceptual design of the filter and calibration wheel. Four different varian…
A General Mathematical Formulation for the Determination of Differential Leakage Factors in Electrical Machines with Symmetrical and Asymmetrical Ful…
2018
This paper presents a simple and general mathematical formulation for the determination of the differential leakage factor for both symmetrical and asymmetrical full and dead-coil windings of electrical machines. The method can be applied to all multiphase windings and considers Gorges polygons in conjunction with masses geometry in order to find an easy and affordable way to compute the differential leakage factor, avoiding the adoption of traditional methods that refer to the Ossanna's infinite series, which has to be obviously truncated under the bound of a predetermined accuracy. Moreover, the method described in this paper allows the easy determination of both the minimum and maximum v…
Superparamagnetic recoverable flowerlike Fe3O4@Bi2O3 core–shell with g-C3N4 sheet nanocomposite: synthesis, characterization, mechanism and kinetic s…
2019
In the present research study, a simple method was developed for the synthesis of three-dimensional flowerlike Fe3O4@Bi2O3 core–shell with g-C3N4 sheet nanocomposites. The X-ray diffraction, Fourier transform infrared spectroscopy, scanning electronic microscopy, transmission electron microscope, vibrating sample magnetometer, dynamic laser scattering analyzer and UV–Vis diffuse reflection spectroscopy were employed for the characterization of structure, purity and morphology of the resultant samples. The degradation of indigo carmine as a model of organic dye pollutant is applied for photo-catalytic activity. The parameters which are affecting the efficiency of various parameters, such as;…