Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation

1992 ◽  
Vol 9 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Christoph R�cker ◽  
Gerta R�cker
Keyword(s):  
Orthogonal Relation

scholarly journals Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity

2018 ◽  
Vol 2 (7) ◽  
pp. 075007 ◽  
Author(s):  
Kyu-Won Park ◽  
Songky Moon ◽  
Hyunseok Jeong ◽  
Jaewan Kim ◽  
Kabgyun Jeong
Keyword(s):  
Orthogonal Relation

scholarly journals Orthogonal relation between wavefield polarization and fastSwave direction in the Val d'Agri region: An integrating method to investigate rock anisotropy

2014 ◽  
Vol 119 (1) ◽  
pp. 396-408 ◽  
Author(s):  
M. Pischiutta ◽  
M. Pastori ◽  
L. Improta ◽  
F. Salvini ◽  
A. Rovelli
Keyword(s):  
Rock Anisotropy ◽  
Orthogonal Relation

The energy orthogonal relation between conforming and non-conforming displacements of triangular element

1999 ◽  
Vol 20 (6) ◽  
pp. 660-665
Author(s):  
Nie Yufeng ◽  
Zhou Tianxiao ◽  
Nie Tiejun
Keyword(s):  
Triangular Element ◽  
Orthogonal Relation

scholarly journals Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding

2020 ◽  
Author(s):  
Yun Tang ◽  
Jing Huang ◽  
Guangtao Wang ◽  
Xiaodong He ◽  
Bowen Zhou
Keyword(s):  
Graph Embedding ◽  
Knowledge Graph ◽  
Context Modeling ◽  
Orthogonal Relation

Fluorescence Fluoride Ion Sensor Utilizing Desilylation of N-Silylated 9- Aminoanthracene

2020 ◽  
Vol 7 (2) ◽  
pp. 249-254
Author(s):  
Yosuke Uchiyama ◽  
Yu Yasuda ◽  
Hideyo Matsuzawa
Keyword(s):  
Color Change ◽  
Crystallographic Analysis ◽  
Fluoride Ion ◽  
Amino Group ◽  
Green Fluorescence ◽  
Tetrabutylammonium Fluoride ◽  
Fluorescence Color ◽  
Fluoride Sensor ◽  
Layer Chromatography ◽  
Orthogonal Relation

N,N-Bis(trimethylsilyl)-9-aminoanthracene (Si9AA) was synthesized by deprotonation of 9-aminoanthracne (9AA) with n-BuLi followed by the addition of trimethylsilyl chloride (TMSCl). Under ultraviolet, Si9AA showed blue fluorescence originated from the anthracene skeleton due to orthogonal relation between anthracene skeleton and bis(trimethylsilyl)amino group, which was determined by X-ray crystallographic analysis, while 9AA, in which conjugation exists between the anthracene and the amino group, showed green fluorescence. In a THF solution, Si9AA was converted to 9AA by desilylation of bis(trimethylsilyl)amino group with fluoride ion, which was contained in tetrabutylammonium fluoride (TBAF) or KF-18-crown-6 complex, resulting in fluorescence color change from blue to green. Si9AA was found to utilize as a sensor to detect fluoride ion in THF solution or on a thin layer chromatography (TLC) via the fluorescence color change without any metals, regarding a metal free fluorescence fluoride sensor in green chemistry.

Geometric regularity of some oblique sculptures in pectinid and other bivalves: recognition by computer simulations

Paleobiology ◽  
1986 ◽  
Vol 12 (4) ◽  
pp. 433-449 ◽  
Author(s):  
Itaru Hayami ◽  
Takashi Okamoto
Keyword(s):  
Computer Simulations ◽  
External Surface ◽  
Uniform Density ◽  
Mutual Relationship ◽  
Growth Increments ◽  
Geometric Regularity ◽  
Orthogonal Relation

The geometric regularity of oblique sculptures in pectinids and some other bivalves was examined both theoretically and empirically. Camptonectes microsculpture occurs exclusively on the external surface of foliated calcite, and is well characterized by an invariably orthogonal relation to growth increments and almost uniform density over the surface. It is genetically unrelated to radial and other sculpturing. According to our SEM observations, its divergent orientation seems to be controlled primarily by the growth of calcite laths. In contrast, the shagreen microsculpture of pectinids is characterized by a quincunx arrangement of scales on the diagonal network. Shagreen microsculpture can be regarded as a variant of diagonal sculpture together with the simple oblique, divaricate, V-shaped, and zigzag patterns that are widespread in other bivalves. The geometric regularity of these variations as well as their mutual relationship can be readily recognized by computer simulations. All of these diagonal sculptures may result from interference between radial and commarginal elements. The formation of diagonal sculptures seems to occur by the periodic activation of regularly arranged sculpture-producing cells on the mantle margin.

Damaged Structural Vibration Analysis Using the Hamiltonian Matrix Perturbation Theory

2008 ◽  
Vol 44-46 ◽  
pp. 91-96
Author(s):  
Long Liu ◽  
Fu Zhen Xuan
Keyword(s):  
Numerical Simulation ◽  
Perturbation Theory ◽  
Vibration Analysis ◽  
Structural Vibration ◽  
Hamiltonian Matrix ◽  
Perturbation Approach ◽  
Matrix Perturbation ◽  
State Variables ◽  
Matrix Perturbation Theory ◽  
Orthogonal Relation

This paper proposes a Hamiltonian perturbation approach for analyzing the dynamic characteristics of the damaged structure. Firstly, structural vibration governing equation is transformed to the general expression of state variables composed of displacement and momentum. On the basis of the conjugate symplectic orthogonal relation, the first-, and second- order perturbation expression of the damaged structural eigensolution are obtained. Finally, the numerical simulation and cantilever experiment prove the effectiveness of this approach.

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