106,219 research outputs found
Multiplicity one theorems: the Archimedean case
Let be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C),
\oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and
let be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q),
\oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in in the
standard way. We show that every irreducible Casselman-Wallach representation
of occurs with multiplicity at most one in every irreducible
Casselman-Wallach representation of . Similar results are proved for the
Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes
\oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes
\oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective
subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R),
\Sp_{2n}(\C).Comment: To appear in Annals of Mathematic
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Zero-field magnetization reversal of two-body Stoner particles with dipolar interaction
Nanomagnetism has recently attracted explosive attention, in particular,
because of the enormous potential applications in information industry, e.g.
new harddisk technology, race-track memory[1], and logic devices[2]. Recent
technological advances[3] allow for the fabrication of single-domain magnetic
nanoparticles (Stoner particles), whose magnetization dynamics have been
extensively studied, both experimentally and theoretically, involving magnetic
fields[4-9] and/or by spin-polarized currents[10-20]. From an industrial point
of view, important issues include lowering the critical switching field ,
and achieving short reversal times. Here we predict a new technological
perspective: can be dramatically lowered (including ) by
appropriately engineering the dipole-dipole interaction (DDI) in a system of
two synchronized Stoner particles. Here, in a modified Stoner-Wohlfarth (SW)
limit, both of the above goals can be achieved. The experimental feasibility of
realizing our proposal is illustrated on the example of cobalt nanoparticles.Comment: 5 pages, 4 figure
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