10,111 research outputs found
Some characterizations of spheres and elliptic paraboloids II
We show some characterizations of hyperspheres in the -dimensional
Euclidean space with intrinsic and extrinsic properties such
as the -dimensional area of the sections cut off by hyperplanes, the
-dimensional volume of regions between parallel hyperplanes, and the
-dimensional surface area of regions between parallel hyperplanes. We also
establish two characterizations of elliptic paraboloids in the
-dimensional Euclidean space with the -dimensional
area of the sections cut off by hyperplanes and the -dimensional volume
of regions between parallel hyperplanes. For further study, we suggest a few
open problems.Comment: 10 page
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling
We study the collective behaviors in a ring of coupled nonidentical nonlinear
oscillators with unidirectional coupling, of which natural frequencies are
distributed in a random way. We find the amplitude death phenomena in the case
of unidirectional couplings and discuss the differences between the cases of
bidirectional and unidirectional couplings. There are three main differences;
there exists neither partial amplitude death nor local clustering behavior but
oblique line structure which represents directional signal flow on the
spatio-temporal patterns in the unidirectional coupling case. The
unidirectional coupling has the advantage of easily obtaining global amplitude
death in a ring of coupled oscillators with randomly distributed natural
frequency. Finally, we explain the results using the eigenvalue analysis of
Jacobian matrix at the origin and also discuss the transition of dynamical
behavior coming from connection structure as coupling strength increases.Comment: 14 pages, 11 figure
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