Search results for "LINE"

Abstracts from the CECAM workshop on computer simulations of cellular automata

1989

Voronovskaya type results and operators fixing two functions

2021

The present paper deals with positive linear operators which fix two functions. The transfer of a given sequence (Ln) of positive linear operators to a new sequence (Kn) is investigated. A general procedure to construct sequences of positive linear operators fixing two functions which form an Extended Complete Chebyshev system is described. The Voronovskaya type formula corresponding to the new sequence which is strongly influenced by the nature of the fixed functions is obtained. In the last section our results are compared with other results existing in literature.

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.

Constant sign and nodal solutions for nonlinear robin equations with locally defined source term

2020

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States

2012

We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…

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.

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.

Evolution of the microstructure of sputter deposited TaAlON thin films with increasing oxygen partial pressure

2021

Abstract Recently, quaternary oxynitrides of transition metals and aluminum have attracted increasing interest due to their tunable properties. Within the present work, a series of TaAl(O)N films was sputter deposited using constant nitrogen and varying oxygen partial pressures. The films were grown from single element Ta and Al targets. The deposition parameters were adjusted to obtain a Ta/Al atomic ratio of ~50/50 for the oxygen-free film and were held constant for the following depositions, with the exception of the increasing oxygen partial pressure and compensatory decreasing argon partial pressure. Elastic recoil detection analysis revealed oxygen contents of up to ~26 at.%, while th…

Long-term evolution of luminescent properties in CdI2 crystals

2016

Fresh and aged melt-grown or gas-phase grown CdI2 crystals are studied by means of low-temperature photoluminescence spectroscopy. Noticeable transformations of emission spectra are observed after long-term aging. The formation of nanostructures containing cadmium oxide and cadmium hydroxide as well as the changes in local surrounding of iodine atoms and the possible growth of polytypic modifications of CdI2 are taken into account when considering the diversity of optical spectra.

Comparative Theoretical Analysis of BN Nanotubes Doped with Al, P, Ga, As, In, and Sb

2013

SUMMARY AND CONCLUDING REMARKS We have performed large-scale first-principles calculations ofthe electronic structure of (5,5) boron nitride nanotubescontaining the following substitutional impurity atoms: Al, P,Ga, As, In, and Sb. Calculations have been performed using thetwo methods: (i) linear combination of atomic orbitals(LCAO) with the atomic-centered Gaussian-type functions asa basis set and (ii) linearized augmented cylindrical wave(LACW) accompanied with the local density functional andmuffin-tin approximations for the electronic potential. In arelatively good qualitative agreement, both methods predict lowformation energies and, thus, relative stability of point defectsthat are assoc…