Search results for "Linear combination"
showing 10 items of 132 documents
Characterizations of {K,s+1}-Potent Matrices and Applications
2012
Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idempotent matrix, widely useful in many applications. In this paper, we introduce a new kind of matrices called {K,s+1}-potent, as an extension of the aforementioned ones. First, different properties of {K,s+1}-potent matrices have been developed. Later, the main result developed in this paper is the characterization of this kind of matrices from a spectral point of view, in terms of powers of the ma…
Algorithms for {K, s+1}-potent matrix constructions
2013
In this paper, we deal with {K, s + 1}-potent matrices. These matrices generalize all the following classes of matrices: k-potent matrices, periodic matrices, idempotent matrices, involutory matrices, centrosymmetric matrices, mirrorsymmetric matrices, circulant matrices, among others. Several applications of these classes of matrices can be found in the literature. We develop algorithms in order to compute {K, s + 1}-potent matrices and {K, s + 1}-potent linear combinations of {K, s + 1}-potent matrices. In addition, some examples are presented in order to show the numerical performance of the method. (C) 2012 Elsevier B.V. All rights reserved.
The formation of silica high temperature polymorphs from quartz: Influence of grain size and mineralising agents
2015
Abstract The formation of high-temperature silica polymorphs in presence of Na and K has been studied at various temperatures and soaking times, starting from quartzes of different grain size, ex situ as well as in situ. The results show that cristobalite and tridymite formation is strongly influenced by the nature and the amount of mineraliser added. In particular, K seems to discriminate more between the two structures, as it produces the largest observed amount of cristobalite. The disappearance of quartz can be controlled by the proper combination of mineraliser/temperature/time, which in turn control the amount and the type of polymorph formed, together with the amount of amorphous mat…
Theoretical and Experimental Study of (Ba,Sr)TiO 3 Perovskite Solid Solutions and BaTiO 3 /SrTiO 3 Heterostructures
2019
This study was supported by the ERA-NET HarvEnPiez project. The authors would like to thank their national funding agencies (Latvian State Education Development Agency, Slovenian Ministry of Higher Education, Science and Technology, Romanian National Authority for Scientific Research and Innovation, CCCDI-UEFISCDI, project number 49/2016 within PNCDI III – M-ERA NET Program).
Ab initio simulation of (Ba,Sr)TiO3 and (Ba,Ca)TiO3 perovskite solid solutions
2019
Abstract The results of ab initio (first-principles) computations of structural, elastic and piezoelectric properties of Ba(1−x)SrxTiO3 (BSTO) and Ba(1−x)CaxTiO3 (BCTO) perovskite solid solutions are presented, discussed and compared. Calculations are performed with the CRYSTAL14 computer code within the linear combination of atomic orbitals (LCAO) approximation, using advanced hybrid functionals of the density-functional-theory (DFT). Supercell model allows us to simulate solid solutions with different chemical compositions (x = 0, 0.125 and 0.25) within ferroelectric tetragonal phases (x
Four-faceted nanowires generated from densely-packed TiO2 rutile surfaces: Ab initio calculations
2013
Abstract Two-dimensional (2D) slabs and monoperiodic (1D) nanowires orthogonal to the slab surface of rutile-based TiO 2 structure terminated by densely-packed surfaces and facets, respectively, have been simulated in the current study. The procedure of structural generation of nanowires (NWs) from titania slabs (2D → 1D) is described. We have simulated: ( i ) (110), (100), (101) and (001) slabs of different thicknesses as well as ( ii ) [001]- and [110]-oriented nanowires of different diameters terminated by either four types of related {110} facets or alternating { 1 1 ¯ 0 } and {001} facets, respectively. Nanowires have been described using both the Ti atom-centered rotation axes as well…
Origin of pressure-induced insulator-to-metal transition in the van der Waals compound FePS3 from first-principles calculations
2020
The authors acknowledge the assistance of the University Computer Center of Saint‐Petersburg State University in the accomplishment of high‐performance computations. A.K. is grateful to the Latvian Council of Science project no. lzp‐2018/2‐0353 for financial support.
First-principles modeling of oxygen interaction with SrTiO3(001) surface: Comparative density-functional LCAO and plane-wave study
2011
Large scale first-principles calculations based on density functional theory (DFT) employing two different methods (atomic orbitals and plane wave basis sets) were used to study the energetics, geometry, the electronic charge redistribution and migration for adsorbed atomic and molecular oxygen on defect-free SrTiO3(001) surfaces (both SrO- and TiO2-terminated), which serves as a prototype for many ABO3-type perovskites. Both methods predict substantial binding energies for atomic O adsorption at the bridge position between the oxygen surface ions and an adjacent metal ion. A strong chemisorption is caused by formation of a surface molecular peroxide ion. In contrast, the neutral molecular …
Ab initio calculations of charged point defects in GaN
2005
The Generalized Gradient Approximation (GGA) of a Density Functional Theory (DFT) in LCAO basis is used to determine electronic structure of charged point defects in hexagonal GaN. Impurities of MgGa, ZnGa, SiN and CN (the most common dopants) were considered for charge states 0, ±1, –2. The vacancies of VGa and VN were considered for charge states 0 and 0, ±1, ±2 respectively. The defects in consideration are compared from the point of view of the one-electron states localization. All the calculations were performed for a supercell containing 96 atoms. The divergence due to periodically repeated charges has been eliminated by the use of a uniform background charge of an opposite sign. (© 2…
Effect of Pressure and Temperature on the Local Structure and Lattice Dynamics of Copper(II) Oxide
2016
Abstract Microcrystalline and nanocrystalline (6 nm) CuO were studied in situ by the Cu K-edge X-ray absorption spectroscopy as a function of pressure (0-20 GPa) and temperature (10-300 K). Pressure dependence of X-ray absorption near edge structure (XANES) was interpreted within the full-multiple-scattering formalism based on the relaxed atomic structure determined by ab initio linear combination of atomic orbital (LCAO) calculations. Temperature dependence of the mean-square relative displacement (MSRD) for the four shortest Cu–O distances was obtained from the analysis of extended X-ray absorption fine structure (EXAFS) and described by the correlated Einstein model with the characterist…