scholarly journals Searching for centrally symmetric generating solutions in Hill problem

2018 ◽  
pp. 1-24
Author(s):  
Alexander Borisovich Batkhin
Keyword(s):  
Hill Problem ◽  
Centrally Symmetric

scholarly journals Symmetry-tailored patterns and polarizations of single-photon emission

Nanophotonics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 3557-3565
Author(s):  
Guorui Zhang ◽  
Ying Gu ◽  
Qihuang Gong ◽  
Jianjun Chen
Keyword(s):  
Single Photon ◽  
Photon Emission ◽  
Silver Nanowire ◽  
Emission Rates ◽  
Single Photon Emission ◽  
Emission Pattern ◽  
Single Photon Emitters ◽  
Resonant Modes ◽  
Oriented Dipole ◽  
Centrally Symmetric

AbstractDue to small optical mode volumes and linear polarizations of surface-plasmon-polariton (SPP) resonant modes in metallic antennas, it is very difficult to obtain complex emission patterns and polarizations for single-photon emitters. Herein, nonresonant enhancement in a silver nanowire is used to both enhance emission rates and extract a z-oriented dipole, and then the symmetry of metallic nanostructures is proposed to tailor the patterns and polarizations of single-photon emission. The emission pattern of a quantum dot located close to a metallic nanostructure with a symmetric axis is split into multiple flaps. The number of splitting flaps is equal to the order of the symmetric axis. Moreover, the electric vectors of the emitted photons become centrally symmetric about the symmetric axis. The above phenomena are well explained by both a simulation and an image dipole model. The structural-symmetry-tailoring mechanism may open up a new avenue in the design of multifunctional and novel quantum-plasmonic devices.

scholarly journals Centrally symmetric and magic rectangles

1997 ◽  
Vol 176 (1-3) ◽  
pp. 29-42 ◽  
Author(s):  
Thomas Bier ◽  
Axel Kleinschmidt
Keyword(s):  
Centrally Symmetric

scholarly journals Highly neighborly centrally symmetric spheres

2020 ◽  
Vol 370 ◽  
pp. 107238
Author(s):  
Isabella Novik ◽  
Hailun Zheng
Keyword(s):  
Centrally Symmetric

Ball characterizations in spaces of constant curvature

2018 ◽  
Vol 55 (4) ◽  
pp. 421-478
Author(s):  
Jesus Jerónimo-Castro ◽  
Endre Makai, Jr.
Keyword(s):  
Convex Sets ◽  
Central Symmetry ◽  
Connected Components ◽  
Plane Convex ◽  
Converse Implication ◽  
Plane Convex Body ◽  
Dual Theorem ◽  
Centrally Symmetric ◽  
Whole Space ◽  
Straight Lines

High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical, Euclidean and hyperbolic spaces, under some regularity assumptions. Suppose that in any of these spaces there is a pair of closed convex sets of class C+2 with interior points, different from the whole space, and the intersections of any congruent copies of these sets are centrally symmetric (provided they have non-empty interiors). Then our sets are congruent balls. Under the same hypotheses, but if we require only central symmetry of small intersections, then our sets are either congruent balls, or paraballs, or have as connected components of their boundaries congruent hyperspheres (and the converse implication also holds). Under the same hypotheses, if we require central symmetry of all compact intersections, then either our sets are congruent balls or paraballs, or have as connected components of their boundaries congruent hyperspheres, and either d ≥ 3, or d = 2 and one of the sets is bounded by one hypercycle, or both sets are congruent parallel domains of straight lines, or there are no more compact intersections than those bounded by two finite hypercycle arcs (and the converse implication also holds). We also prove a dual theorem. If in any of these spaces there is a pair of smooth closed convex sets, such that both of them have supporting spheres at any of their boundary points Sd for Sd of radius less than π/2- and the closed convex hulls of any congruent copies of these sets are centrally symmetric, then our sets are congruent balls.

scholarly journals A measure of axial symmetry of centrally symmetric convex bodies

2010 ◽  
Vol 121 (2) ◽  
pp. 295-306 ◽  
Author(s):  
Marek Lassak ◽  
Monika Nowicka
Keyword(s):  
Axial Symmetry ◽  
Convex Bodies ◽  
Symmetric Convex ◽  
Centrally Symmetric
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