Space Reduction for Linear Systems with Local Symmetry

2021 ◽  
Vol 89 (3) ◽  
Author(s):  
Jia Yin ◽  
Chunxiong Zheng
Keyword(s):  
Linear Systems ◽  
Local Symmetry ◽  
Space Reduction

ELNES of Iron Compounds

1990 ◽  
Vol 48 (2) ◽  
pp. 28-29
Author(s):  
Hiroki Kurata ◽  
Kazuhiro Nagai ◽  
Seiji Isoda ◽  
Takashi Kobayashi
Keyword(s):  
Energy Loss ◽  
Metal Ions ◽  
Energy Resolution ◽  
Transition Metal Oxides ◽  
Local Symmetry ◽  
Iron Compounds ◽  
Fine Structures ◽  
Electron Energy Loss ◽  
Fe Ions ◽  
Electron Energy Loss Spectra

Electron energy loss spectra of transition metal oxides, which show various fine structures in inner shell edges, have been extensively studied. These structures and their positions are related to the oxidation state of metal ions. In this sence an influence of anions coordinated with the metal ions is very interesting. In the present work, we have investigated the energy loss near-edge structures (ELNES) of some iron compounds, i.e. oxides, chlorides, fluorides and potassium cyanides. In these compounds, Fe ions (Fe2+ or Fe3+) are octahedrally surrounded by six ligand anions and this means that the local symmetry around each iron is almost isotropic.EELS spectra were obtained using a JEM-2000FX with a Gatan Model-666 PEELS. The energy resolution was about leV which was mainly due to the energy spread of LaB6 -filament. The threshole energies of each edges were measured using a voltage scan module which was calibrated by setting the Ni L3 peak in NiO to an energy value of 853 eV.

The limits of strain and lattice parameter measurements by CBED

1989 ◽  
Vol 47 ◽  
pp. 518-519
Author(s):  
Hamish L. Fraser
Keyword(s):  
Electron Beam ◽  
Mirror Symmetry ◽  
Local Symmetry ◽  
Lattice Parameter ◽  
Growth Direction ◽  
Surface Relaxation ◽  
Strained Layer ◽  
Axis Parallel ◽  
Local Lattice ◽  
Strained Layer Superlattice

The topic of strain and lattice parameter measurements using CBED is discussed by reference to several examples. In this paper, only one of these examples is referenced because of the limitation of length. In this technique, scattering in the higher order Laue zones is used to determine local lattice parameters. Work (e.g. 1) has concentrated on a model strained-layer superlattice, namely Si/Gex-Si1-x. In bulk samples, the strain is expected to be tetragonal in nature with the unique axis parallel to [100], the growth direction. When CBED patterns are recorded from the alloy epi-layers, the symmetries exhibited by the patterns are not tetragonal, but are in fact distorted from this to lower symmetries. The spatial variation of the distortion close to a strained-layer interface has been assessed. This is most readily noted by consideration of Fig. 1(a-c), which show enlargements of CBED patterns for various locations and compositions of Ge. Thus, Fig. 1(a) was obtained with the electron beam positioned in the center of a 5Ge epilayer and the distortion is consistent with an orthorhombic distortion. When the beam is situated at about 150 nm from the interface, the same part of the CBED pattern is shown in Fig. 1(b); clearly, the symmetry exhibited by the mirror planes in Fig. 1 is broken. Finally, when the electron beam is positioned in the center of a 10Ge epilayer, the CBED pattern yields the result shown in Fig. 1(c). In this case, the break in the mirror symmetry is independent of distance form the heterointerface, as might be expected from the increase in the mismatch between 5 and 10%Ge, i.e. 0.2 to 0.4%, respectively. From computer simulation, Fig.2, the apparent monocline distortion corresponding to the 5Ge epilayer is quantified as a100 = 0.5443 nm, a010 = 0.5429 nm and a001 = 0.5440 nm (all ± 0.0001 nm), and α = β = 90°, γ = 89.96 ± 0.02°. These local symmetry changes are most likely due to surface relaxation phenomena.

Well-Posed Linear Systems

2005 ◽  
Author(s):  
Olof Staffans
Keyword(s):  
Linear Systems ◽  
Well Posed

Principles of Linear Systems

1997 ◽  
Author(s):  
Philip E. Sarachik
Keyword(s):  
Linear Systems

Particularities of overdetermined linear systems arising in particle size analysis

1992 ◽  
Vol 2 (8) ◽  
pp. 1547-1555
Author(s):  
D. M. Calistru ◽  
R. Mondescu ◽  
I. Baltog
Keyword(s):  
Particle Size ◽  
Linear Systems ◽  
Particle Size Analysis ◽  
Size Analysis ◽  
Overdetermined Linear Systems

LOCAL SYMMETRY AT THE 3d METAL SITE AND CHEMICAL ORDER IN AMORPHOUS AND CRYSTALLINE Ni1-xBx

1985 ◽  
Vol 46 (C8) ◽  
pp. C8-217-C8-221 ◽  
Author(s):  
M. Maurer ◽  
A. Mehdaoui ◽  
J. M. Friedt
Keyword(s):  
Local Symmetry ◽  
Chemical Order ◽  
Metal Site

A COMINRES-QLP Method for Solving Complex Symmetric Linear Systems

2020 ◽  
Vol 140 (12) ◽  
pp. 832-841
Author(s):  
Lijun Liu ◽  
Kazuaki Sekiya ◽  
Masao Ogino ◽  
Koki Masui
Keyword(s):  
Linear Systems ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric

Fast iterative solvers for large compressed-sparse row linear systems on graphics processing unit

2015 ◽  
Vol 10 (1) ◽  
pp. 3-18 ◽  
Author(s):  
Frédéric Magoulès ◽  
Abal-Kassim Cheik Ahamed ◽  
Roman Putanowicz
Keyword(s):  
Linear Systems ◽  
Graphics Processing Unit ◽  
Iterative Solvers ◽  
Processing Unit ◽  
Compressed Sparse Row ◽  
Graphics Processing
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