scholarly journals Algebraic higher symmetry and categorical symmetry: A holographic and entanglement view of symmetry

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Liang Kong ◽  
Tian Lan ◽  
Xiao-Gang Wen ◽  
Zhi-Hao Zhang ◽  
Hao Zheng
Keyword(s):  
Higher Symmetry

Some simple theorems concerning crystal lattice sums of electric potential, electric field, and electric field gradient in crystals

1967 ◽  
Vol 20 (12) ◽  
pp. 2551 ◽  
Author(s):  
CK Coogan
Keyword(s):  
Electric Field ◽  
Field Gradient ◽  
Electric Potential ◽  
Higher Symmetry ◽  
Lattice Sums ◽  
Symmetry Properties ◽  
Lattice Sum ◽  
Direct Lattice ◽  
Electric Potential Field ◽  
Conver Gence

The conditions under which direct lattice sums of electric potential, field, and field gradient converge are discussed. The analogous conditions under which differences in these lattice sums, for two points in the crystal, converge are also outlined. These conditions are applied to direct lattice sum calculations in crystals in which the ideal lattice is distorted close to a defect of some kind. The conver- gence conditions are then applied to the case of determining the direct lattice sums in crystals in which higher symmetry properties can be invoked, which leads to a knowledge by inspection of the lattice sum at one point in the unit cell.

Temperature Dependent Raman Scattering in CsTiOAsO4 Single Crystal

1995 ◽  
Vol 398 ◽  
Author(s):  
A.R. Guo ◽  
C.-S. Tu ◽  
Ruiwu Tao ◽  
R.S. Katiyar ◽  
Ruyan Guo ◽  
...  
Keyword(s):  
Soft Mode ◽  
Low Frequency ◽  
High Mobility ◽  
Vibrational Modes ◽  
Frequency Range ◽  
Temperature Dependent ◽  
Higher Symmetry ◽  
Phonon Spectra ◽  
Symmetry Structure ◽  
Increasing Temperature

ABSTRACTThe longitudinal (LO) and transverse (TO) A1 vibrational modes have been measured between 30-1200 cm−1 as a function of temperature (30–1240 K) for CsTiOAsO4 (CTA). The frequencies for all corresponding Raman components shifted to lower frequencies on increasing the temperature, however, there is no typical soft-mode like behavior observed in the measured frequency range. The relative intensities of the low frequency bands increase dramatically with increasing temperature due to high mobility of Cs+ ion. A higher symmetry structure taking place above 940K has been confirmed by changes in the phonon spectra.

Dimorphic ThNi2P2 with BaCu2S2 and CaBe2Ge2 Type Structure

1994 ◽  
Vol 49 (8) ◽  
pp. 1074-1080 ◽  
Author(s):  
Jörg H. Albering ◽  
Wolfgang Jeitschko
Keyword(s):  
Phase Transformation ◽  
High Temperature ◽  
Crystal Structures ◽  
Type Structure ◽  
Variable Parameters ◽  
Higher Symmetry ◽  
X Ray ◽  
Coordination Numbers ◽  
Structure Factors ◽  
High Temperature Form

Two modifications of ThNi2P2 were prepared in a tin flux at 850 °C (α-ThNi2P2) and 1000 °C (β-ThNi2P2). The crystal structures of both modifications were refined from single­crystal X-ray data. α-ThNi2P2 (BaCu2S2 type structure): Pnma. a = 819.69(5), b = 394.28(3), c = 981.54(7) pm. R = 0.028 for 32 variables and 654 structure factors: β-ThNi2P2 (CaBe2Ge2 type structure): P4/nmm, a = 408.5(1), c = 908.0(3) pm, R = 0.033 for 15 variable parameters and 261 F values. Although the two structures are closely related, they can be transformed into each other only by a reconstructive phase transformation. The differences and similari­ties of the two structures are discussed. The high temperature form has higher symmetry, a smaller number of variable positional parameters, and a tendency for higher coordination numbers.

Meson Resonances 2+, 1+, 0+ in the Higher Symmetry Theory

1966 ◽  
pp. 281-304
Author(s):  
Cao Chi ◽  
Nguyen Van Hieu ◽  
B. Sredniawa
Keyword(s):  
Higher Symmetry ◽  
Symmetry Theory

Towards Sucrose Macrocycles with Higher Symmetry via a ‘Click Chemistry’ Route

Synthesis ◽  
2008 ◽  
Vol 2008 (6) ◽  
pp. 913-916 ◽  
Author(s):  
Sławomir Jarosz ◽  
Bartosz Lewandowski ◽  
Arkadiusz Listkowski
Keyword(s):  
Click Chemistry ◽  
Higher Symmetry

ISOMERS OF COPPER CLUSTERS OBTAINED BY A MOLECULAR DYNAMICS MODEL

2005 ◽  
Vol 19 (15n17) ◽  
pp. 2359-2364
Author(s):  
LING WANG ◽  
XI-JING NING
Keyword(s):  
Molecular Dynamics ◽  
Tight Binding ◽  
Magic Number ◽  
Tight Binding Model ◽  
Dynamics Model ◽  
Binding Model ◽  
Higher Symmetry ◽  
Empirical Potential ◽  
Copper Clusters ◽  
Moment Approximation

A molecular dynamics model was developed to search for stable copper clusters with up to 60 atoms by Gupts empirical potential based on the second-moment approximation to tight-binding model (TB-SMA). We found that isomers do not emerge until the clusters have more than 7 atoms, getting more for clusters with 30~52 atoms, and the magic number, 13, 19, 23, 26, 28, 32, 38, 43, 46, 49, and 55 have ground clusters with higher symmetry and have few isomers.

Atomic resolution structure of a chimeric DNA–RNA Z-type duplex in complex with Ba2+ions: a case of complicated multi-domain twinning

2016 ◽  
Vol 72 (2) ◽  
pp. 211-223 ◽  
Author(s):  
Miroslaw Gilski ◽  
Pawel Drozdzal ◽  
Ryszard Kierzek ◽  
Mariusz Jaskolski
Keyword(s):  
Molecular Replacement ◽  
Higher Symmetry ◽  
Barium Ions ◽  
Space Groups ◽  
Left Handed ◽  
Crystal Twinning ◽  
Using Data ◽  
High Degree ◽  
Packing Analysis ◽  
Resolution Structure

The self-complementary dCrGdCrGdCrG hexanucleotide, in which not only the pyrimidine/purine bases but also the ribo/deoxy sugars alternate along the sequence, was crystallized in the presence of barium cations in the form of a left-handed Z-type duplex. The asymmetric unit of theP21crystal with a pseudohexagonal lattice contains four chimeric duplexes and 16 partial Ba2+sites. The chimeric (DNA–RNA)2duplexes have novel patterns of hydration and exhibit a high degree of discrete conformational disorder of their sugar-phosphate backbones, which can at least partly be correlated with the fractional occupancies of the barium ions. The crystals of the DNA–RNA chimeric duplex in complex with Ba2+ions and also with Sr2+ions exhibit complicated twinning, which in combination with structural pseudosymmetry made structure determination difficult. The structure could be successfully solved by molecular replacement in space groupsP1 andP21but not in orthorhombic or higher symmetry and, after scrupulous twinning and packing analysis, was refined in space groupP21to anRandRfreeof 11.36 and 16.91%, respectively, using data extending to 1.09 Å resolution. With the crystal structure having monoclinic symmetry, the sixfold crystal twinning is a combination of threefold and twofold rotations. The paper describes the practical aspects of dealing with cases of complicated twinning and pseudosymmetry, and compares the available software tools for the refinement and analysis of such cases.

Protonenresonanz-spektroskopische Untersuchungen am Chlor-, Brom- und Methylcyclobutadieneisentricarbonyl / A Proton Magnetic Resonance Investigation on Chloro-, Bromo- and Methyl-cyclobutadiene-irontricarbonyl

1974 ◽  
Vol 29 (3-4) ◽  
pp. 219-227 ◽  
Author(s):  
Hans Albert Brune ◽  
Hans Hanebeck ◽  
Gernot Horlbeck ◽  
Hans Hüther
Keyword(s):  
Magnetic Resonance ◽  
Proton Magnetic Resonance ◽  
Electron Distribution ◽  
Membered Ring ◽  
Bond Orders ◽  
Higher Symmetry ◽  
Resonance Investigation ◽  
Cyclic Diene ◽  
Magnetic Resonance Investigation ◽  
Single Bonds

Proton magnetic resonance spectra including all observable 13C-H-couplings have been measured for chloro-cyclobutadiene-irontricarbonyl.bromo-cyclobutadiene-irontricarbonyl and methyl-cyclobutadiene-irontricarbonyl. The results are discussed with respect to structure and bonding. The structure of a cyclic diene with alternating double and single bonds can be excluded for the four-membered ring of all three compounds. Instead the complex bonded cyclobutadiene contains an electron distribution of higher symmetry with — despite the influence of the substituent — nearly uniform bond orders.

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