Search results for "ERG"

The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems

2020

Abstract In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.

Some approximation properties of a Durrmeyer variant ofq-Bernstein-Schurer operators

2016

On the Coefficients of Multiple Series with Respect to Vilenkin System

2017

Abstract We give a sufficient condition for coefficients of double series Σ Σ n,m an,m χ n,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.

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…

Controlled turbulence regime of electron cyclotron resonance ion source for improved multicharged ion performance

2020

Fundamental studies of excitation and non-linear evolution of kinetic instabilities of strongly nonequlibrium hot plasmas confined in open magnetic traps suggest new opportunities for fine-tuning of conventional electron cyclotron resonance (ECR) ion sources. These devices are widely used for the production of particle beams of high charge state ions. Operating the ion source in controlled turbulence regime allows increasing the absorbed power density and therefore the volumetric plasma energy content in the dense part of the discharge surrounded by the ECR surface, which leads to enhanced beam currents of high charge state ions. We report experiments at the ECR ion source at the JYFL accel…

Effect of space charge on the negative oxygen flux during reactive sputtering

2017

Negative ions often play a distinctive role in the phase formation during reactive sputter deposition. The path of these high energetic ions is often assumed to be straight. In this paper, it is shown that in the context of reactive magnetron sputtering space charge effects are decisive for the energetic negative ion trajectories. To investigate the effect of space charge spreading, reactive magnetron sputter experiments were performed in compound mode with target materials that are expected to have a high secondary ion emission yield (MgO and CeO2). By the combination of energy flux measurements, and simulations, a quantitative value for the negative oxygen ion yield can be derived.

First principles hybrid Hartree-Fock-DFT calculations of bulk and (001) surface F centers in oxide perovskites and alkaline-earth fluorides

2020

Valuable discussions with E. A. Kotomin are gratefully acknowledged. Research contribution of R. E. and A. I. P. has been performed within the framework of the EUROfusion Enabling Research project: ENR-MFE19.ISSP-UL-02 “Advanced experimental and theoretical analysis of defect evolution and structural disordering in optical and dielectric materials for fusion applications.” The views and opinions expressed herein do not necessarily reflect those of the European Commission.

Plastic yielding of glass in high-pressure torsion apparatus

2018

International audience; Hardness measurements performed at room temperature have demonstrated that glass can flow under elevated pressure, whereas the effect of high pressure on glass rheology remains poorly quantified. Here, we applied a high-pressure torsion (HPT) apparatus to deform SCHOTT SF6 â glass and attempted to quantify the effect of pressure and temperature on the shear deformation of glass subjected to pressures from 0.3 GPa to 7 GPa and temperatures from 25 ℃ to 496 ℃. Results show that the plastic yield deformation was occurring during the HPT experiments on the SF6 glass at elevated temperature from 350 ℃ to 496 ℃. The yield stress of SF6 glass decreases with increasing tempe…

Structural characterization and electrochemical hydrogen storage properties of Ti2LxZrxNi (x [ 0, 0.1, 0.2) alloys prepared by mechanical alloying

2013

International audience; Nominal Ti2Ni was synthesized under argon atmosphere at room temperature using a planetary high-energy ball mill. The effect of milling time and Zr substitution for Ti on the microstructure was characterized by XRD, SEM and TEM, and the discharge capacities of Ti2xZrxNi (x 1/4 0, 0.1, 0.2) were examined by electrochemical measurements at galvanostatic conditions. XRD analysis shows that amorphous phase of Ti2Ni can be elaborated by 60 h of milling, whereas Zr substitution hinders amorphization process of the system. The products of ball milling nominal Ti2xZrxNi (x 1/4 0.1, 0.2) were austenitic (Ti, Zr)Ni and partly TiO, despite the fact that the operation was carrie…

Pressure-induced instability of the fergusonite phase of EuNbO4 studied by in situ Raman spectroscopy, x-ray diffraction, and photoluminescence spect…

2020

In this article, we present high-pressure experimental investigations on EuNbO4, an interesting technologically important material, using synchrotron based x-ray powder diffraction, Raman spectroscopy, and europium photoluminescence measurements up to 39.2, 31.6, and 32.4 GPa, respectively. All three techniques show the stability of the ambient monoclinic phase until 20 GPa. Beyond that, a pressure-induced structural phase transition takes place with the coexistence of two phases over a wide pressure range. The structure of the high-pressure phase has been determined as orthorhombic (space group: Imma) with a volume discontinuity of nearly 9% at the transition indicating the nature of trans…