125,623 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
A Semi-Blind Source Separation Method for Differential Optical Absorption Spectroscopy of Atmospheric Gas Mixtures
Differential optical absorption spectroscopy (DOAS) is a powerful tool for
detecting and quantifying trace gases in atmospheric chemistry
\cite{Platt_Stutz08}. DOAS spectra consist of a linear combination of complex
multi-peak multi-scale structures. Most DOAS analysis routines in use today are
based on least squares techniques, for example, the approach developed in the
1970s uses polynomial fits to remove a slowly varying background, and known
reference spectra to retrieve the identity and concentrations of reference
gases. An open problem is to identify unknown gases in the fitting residuals
for complex atmospheric mixtures.
In this work, we develop a novel three step semi-blind source separation
method. The first step uses a multi-resolution analysis to remove the
slow-varying and fast-varying components in the DOAS spectral data matrix .
The second step decomposes the preprocessed data in the first step
into a linear combination of the reference spectra plus a remainder, or
, where columns of matrix are known reference spectra,
and the matrix contains the unknown non-negative coefficients that are
proportional to concentration. The second step is realized by a convex
minimization problem ,
where the norm is a hybrid norm (Huber estimator) that helps to
maintain the non-negativity of . The third step performs a blind independent
component analysis of the remainder matrix to extract remnant gas
components. We first illustrate the proposed method in processing a set of DOAS
experimental data by a satisfactory blind extraction of an a-priori unknown
trace gas (ozone) from the remainder matrix. Numerical results also show that
the method can identify multiple trace gases from the residuals.Comment: submitted to Journal of Scientific Computin
Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces
We investigate the statistics of the maximal fluctuation of two-dimensional
Gaussian interfaces. Its relation to the entropic repulsion between rigid walls
and a confined interface is used to derive the average maximal fluctuation and the asymptotic behavior of the whole
distribution for finite with and the interface size and
tension, respectively. The standardized form of does not depend on
or , but shows a good agreement with Gumbel's first asymptote distribution
with a particular non-integer parameter. The effects of the correlations among
individual fluctuations on the extreme value statistics are discussed in our
findings.Comment: 4 pages, 4 figures, final version in PR
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
- …