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2011 •
Abstract We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two polar vortices.
Mathematical Proceedings of the …
Group Theoretic Conditions for Existence of Robust Relative Homoclinic Trajectories2002 •
2011 •
(Abridged abstract) For a finite real reflection group W and a W-orbit O of flats in its reflection arrangement---or equivalently a conjugacy class of its parabolic subgroups---we introduce a statistic on elements of W. We then study the operator of right-multiplication within the group algebra of W by the element whose coefficients are given by this statistic. We reinterpret the operators geometrically in terms of the arrangement of reflecting hyperplanes for W. We show that they are self-adjoint and positive semidefinite. via two explicit factorizations into a symmetrized form A^t A. In one such factorization, A is a generalization of the projection of a simplex onto the linear ordering polytope. In the other factorization, A is the transition matrix for one of the well-studied Bidigare-Hanlon-Rockmore random walks on the chambers of an arrangement. We study the family of operators in which O is the conjugacy classes of Young subgroups of type (k,1^{n-k}). A special case within this family is the operator corresponding to random-to-random shuffling. We show in a purely enumerative fashion that these operators pairwise commute. We furthermore conjecture that they have integer spectrum, generalizing a conjecture of Uyemura-Reyes for the case k=n-1. We use representation theory to show that if O is a conjugacy class of rank one parabolics in W, the corresponding operator has integer spectrum. Our proof makes use of an (apparently) new family of twisted Gelfand pairs for W. We also study the family of operators in which O is the conjugacy classes of Young subgroups of type (2^k,1^{n-2k}). Here the construction of a Gelfand model for the symmetric group shows that these operators pairwise commute and that they have integer spectrum. For the symmetric group, we conjecture that apart from the two commuting families above, no other pair of operators of this form commutes.
2008 •
International Journal of Bifurcation and Chaos
Symmetry and Synchrony in Coupled Cell Networks 1: Fixed-Point Spaces2006 •
Journal of Mathematical Biology
Stochastic population growth in spatially heterogeneous environments2013 •
NATO Science Series II: Mathematics, Physics and Chemistry
Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries2005 •
Duke Mathematical Journal
Finiteness and quasi-simplicity for symmetric $K3$ -surfaces2004 •
Journal of Statistical Physics
Ising Correlations and Elliptic Determinants2011 •
Journal of Dynamics and Differential Equations
Pattern Formation for the Swift-Hohenberg Equation on the Hyperbolic Plane2013 •
International Symposium on Physical Design
Heteroclinic cycles in rings of coupled cells2000 •
Journal of Physics A: Mathematical and Theoretical
Factorized finite-size Ising model spin matrix elements from separation of variables2009 •
Inventiones Mathematicae
Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism2002 •
2005 •
Lecture Notes in Computer Science
Recursive MDS-Codes and Pseudogeometries1999 •
Lecture Notes in Computer Science
On the Structure of Inversive Pseudorandom Number Generators2000 •
Annales Henri Poincare
Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions2007 •
2007 •
2003 •
Linear Algebra, Theory and Applications.
Linear Algebra, Theory And Applications The Saylor Foundation2011 •
Applied Mathematics and Computation
Euclidean graph distance matrices of generalizations of the star graph2014 •
Structured Matrices in Numerical Linear Algebra
Structured Matrices in Numerical Linear Algebra Analysis Algorithms and Applications-Springer Interna2018 •