scholarly journals Eulerian Dynamics in Multidimensions with Radial Symmetry

2021 ◽  
Vol 53 (3) ◽  
pp. 3040-3071
Author(s):  
Changhui Tan
Keyword(s):  
Radial Symmetry ◽  
Eulerian Dynamics

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

Pollen characterization of ornamental species of Mammillaria Haw. (Cactaceae/Cactoideae)

2019 ◽  
Vol 6 (1) ◽  
pp. 13 ◽  
Author(s):  
Denise M. D. S. Mouga ◽  
Gabriel R. Schroeder ◽  
Nilton P. Vieira Junior ◽  
Enderlei Dec
Keyword(s):  
Pollen Morphology ◽  
Pollen Grains ◽  
Radial Symmetry ◽  
Morphological Data ◽  
Medium Size ◽  
Ornamental Species

The pollen morphology of thirteen species of Cactaceae was studied: M. backebergiana F.G. Buchenau, M. decipiens Scheidw, M. elongata DC, M. gracilis Pfeiff., M. hahniana Werderm., M. marksiana Krainz, M. matudae Bravo, M. nejapensis R.T. Craig & E.Y. Dawson, M. nivosa Link ex Pfeiff., M. plumosa F.A.C. Weber, M. prolifera (Mill.) Haw, M. spinosissima var. “A Peak” Lem. and M. voburnensis Scheer. All analysed pollen grains are monads, with radial symmetry, medium size (M. gracilis, M. marksiana, M. prolifera, large), tricolpates (dimorphs in M. plumosa [3-6 colpus] and M. prolifera [3-6 colpus]), with circular-subcircular amb (quadrangular in M. prolifera and M. plumosa with six colpus). The pollen grains presented differences in relation to the shape and exine thickness. The exine was microechinate and microperforated. The pollen morphological data are unpublished and will aid in studies that use pollen samples. These pollen grains indicate ornamental cacti.

scholarly journals Infinitely many positive solutions of nonlinear Schrödinger equations

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Riccardo Molle ◽  
Donato Passaseo
Keyword(s):  
Positive Solutions ◽  
Radial Symmetry ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

AbstractThe paper deals with the equation $$-\Delta u+a(x) u =|u|^{p-1}u $$ - Δ u + a ( x ) u = | u | p - 1 u , $$u \in H^1({\mathbb {R}}^N)$$ u ∈ H 1 ( R N ) , with $$N\ge 2$$ N ≥ 2 , $$p> 1,\ p< {N+2\over N-2}$$ p > 1 , p < N + 2 N - 2 if $$N\ge 3$$ N ≥ 3 , $$a\in L^{N/2}_{loc}({\mathbb {R}}^N)$$ a ∈ L loc N / 2 ( R N ) , $$\inf a> 0$$ inf a > 0 , $$\lim _{|x| \rightarrow \infty } a(x)= a_\infty $$ lim | x | → ∞ a ( x ) = a ∞ . Assuming that the potential a(x) satisfies $$\lim _{|x| \rightarrow \infty }[a(x)-a_\infty ] e^{\eta |x|}= \infty \ \ \forall \eta > 0$$ lim | x | → ∞ [ a ( x ) - a ∞ ] e η | x | = ∞ ∀ η > 0 , $$ \lim _{\rho \rightarrow \infty } \sup \left\{ a(\rho \theta _1) - a(\rho \theta _2) \ :\ \theta _1, \theta _2 \in {\mathbb {R}}^N,\ |\theta _1|= |\theta _2|=1 \right\} e^{\tilde{\eta }\rho } = 0 \quad \text{ for } \text{ some } \ \tilde{\eta }> 0$$ lim ρ → ∞ sup a ( ρ θ 1 ) - a ( ρ θ 2 ) : θ 1 , θ 2 ∈ R N , | θ 1 | = | θ 2 | = 1 e η ~ ρ = 0 for some η ~ > 0 and other technical conditions, but not requiring any symmetry, the existence of infinitely many positive multi-bump solutions is proved. This result considerably improves those of previous papers because we do not require that a(x) has radial symmetry, or that $$N=2$$ N = 2 , or that $$|a(x)-a_\infty |$$ | a ( x ) - a ∞ | is uniformly small in $${\mathbb {R}}^N$$ R N , etc. ....

A ten-faced hexangulaconulariid from Cambrian Stage 2 of South China

2021 ◽  
pp. 1-8
Author(s):  
Junfeng Guo ◽  
Jian Han ◽  
Heyo Van Iten ◽  
Zuchen Song ◽  
Yaqin Qiang ◽  
...  
Keyword(s):  
New Genus ◽  
Radial Symmetry ◽  
New Taxon ◽  
Three Gorges ◽  
Substantial Variation ◽  
The Three Gorges ◽  
Apical Half ◽  
Lateral Margins ◽  
Number Of Faces ◽  
Extinct Group

Abstract Hexangulaconulariids (Cambrian stages 1–2) are an extinct group of medusozoan polyps having a biradially symmetrical, fan-shaped periderm that is distinct from those of medusozoan polyps showing three-, four-, five-, or six-fold radial symmetry. Hexangulaconulariids exhibit substantial variation in gross morphology, including variation in the number of faces on each of the two major sides of the periderm. An intermediate taxon of hexangulaconulariids with ten faces (five on each major side) was expected. Here we describe a new hexangulaconulariid, Decimoconularia isofacialis new genus new species from Bed 5 of the Yanjiahe Formation (Cambrian Stage 2) in the Three Gorges area of Hubei Province, China. The new taxon differs from other hexangulaconulariids (Arthrochites, Hexaconularia, and Septuconularia) mainly in possessing a total of ten faces. The two lateral margins are each marked by a ridge in about the apertural half of the periderm and by a collinear furrow in about the apical half, while the five faces on each major side are bounded by a furrow in about the apertural half and by a collinear ridge in about the apical half. Among hexangulaconulariids, Decimoconularia and Septuconularia may be more closely related to each other than either genus is to Arthrochites or Hexaconularia. UUID: http://zoobank.org/ca270a3b-25ee-4d1f-bdeb-91a963370e70

Interaction of a Whirling Rotor with a Vibrating Stator across a Clearance Annulus

1968 ◽  
Vol 10 (1) ◽  
pp. 1-12 ◽  
Author(s):  
H. F. Black
Keyword(s):  
Dry Friction ◽  
Ball Bearing ◽  
Radial Symmetry ◽  
Experimental Results ◽  
Equilibrium Conditions ◽  
General Behaviour ◽  
Mass Unbalance ◽  
Jump Phenomena ◽  
Rotor Stator Interaction ◽  
Rotor Mass

Where a rotor runs within a clearance space, the clearance being comparable with rotor mass unbalance, the synchronous whirling behaviour of the rotor may be considerably affected by intermittent interaction with the stator at the clearance position. Discontinuity and jump phenomena may occur: in general, behaviour will be different with increasing speed from that with decreasing speed, and in either case zones may exist in which rotor-stator interaction is possible but not certain. In the analysis here presented, rotor and stator are regarded as linear multi-degree-of-freedom systems including damping; dry friction at the clearance space is taken into account. Discussion is limited to cases with radial symmetry, and interaction is assumed limited to the position of the clearance space. Polar receptances are used to establish equilibrium conditions with interaction, and speed zones are defined within which interaction may occur. Some hypothetical cases are fully explored, demonstrating that rotor-stator interactions may occur in a variety of forms and circumstances. Interactions with dry friction counterwhirling are also considered. Some experimental results on counterwhirl within a ball bearing are given and qualitatively compared with theory.

scholarly journals Die zeitliche Änderung der radialen Elektronendichteverteilung beim Theta-Pinch

1963 ◽  
Vol 18 (8-9) ◽  
pp. 895-900
Author(s):  
Franz Peter Küpper
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Electron Distribution ◽  
Radial Symmetry ◽  
Zero Order ◽  
Time Interval ◽  
Interferometric Method ◽  
Density Distributions ◽  
Theta Pinch

In a θ-pinch the radial symmetry of the electron density distribution as a function of time has been measured by a MACH—ZEHNDER interferometer. In a time interval of 400 nsec during a discharge an image converter made three pictures (exposure times of 10 nsec each) . Up to 100 nsec after the first compression, the experimental results show different density distributions for the cases of trapped parallel and antiparallel magnetic fields. Complete radial symmetry of the electron density distribution was not found.Another interferometric method for measuring the radial symmetry of the electron distribution by observing “zero order” fringes is described.

scholarly journals Trends in flower symmetry evolution revealed through phylogenetic and developmental genetic advances

2014 ◽  
Vol 369 (1648) ◽  
pp. 20130348 ◽  
Author(s):  
Lena C. Hileman
Keyword(s):  
Bilateral Symmetry ◽  
Radial Symmetry ◽  
Plant Evolution ◽  
Flowering Plant ◽  
Developmental Studies ◽  
Developmental Genetic ◽  
Evolutionary Transitions ◽  
Flower Symmetry ◽  
Molecular Phylogenetic ◽  
Developmental Programme

A striking aspect of flowering plant (angiosperm) diversity is variation in flower symmetry. From an ancestral form of radial symmetry (polysymmetry, actinomorphy), multiple evolutionary transitions have contributed to instances of non-radial forms, including bilateral symmetry (monosymmetry, zygomorphy) and asymmetry. Advances in flowering plant molecular phylogenetic research and studies of character evolution as well as detailed flower developmental genetic studies in a few model species (e.g. Antirrhinum majus , snapdragon) have provided a foundation for deep insights into flower symmetry evolution. From phylogenetic studies, we have a better understanding of where during flowering plant diversification transitions from radial to bilateral flower symmetry (and back to radial symmetry) have occurred. From developmental studies, we know that a genetic programme largely dependent on the functional action of the CYCLOIDEA gene is necessary for differentiation along the snapdragon dorsoventral flower axis. Bringing these two lines of inquiry together has provided surprising insights into both the parallel recruitment of a CYC -dependent developmental programme during independent transitions to bilateral flower symmetry, and the modifications to this programme in transitions back to radial flower symmetry, during flowering plant evolution.

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