3,564 research outputs found
SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
We propose a group-theoretical approach to the generalized oscillator algebra
Ak recently investigated in J. Phys. A: Math. Theor. 43 (2010) 115303. The case
k > or 0 corresponds to the noncompact group SU(1,1) (as for the harmonic
oscillator and the Poeschl-Teller systems) while the case k < 0 is described by
the compact group SU(2) (as for the Morse system). We construct the phase
operators and the corresponding temporally stable phase eigenstates for Ak in
this group-theoretical context. The SU(2) case is exploited for deriving
families of mutually unbiased bases used in quantum information. Along this
vein, we examine some characteristics of a quadratic discrete Fourier transform
in connection with generalized quadratic Gauss sums and generalized Hadamard
matrices
Steerable Discrete Fourier Transform
Directional transforms have recently raised a lot of interest thanks to their
numerous applications in signal compression and analysis. In this letter, we
introduce a generalization of the discrete Fourier transform, called steerable
DFT (SDFT). Since the DFT is used in numerous fields, it may be of interest in
a wide range of applications. Moreover, we also show that the SDFT is highly
related to other well-known transforms, such as the Fourier sine and cosine
transforms and the Hilbert transforms
Random projections and the optimization of an algorithm for phase retrieval
Iterative phase retrieval algorithms typically employ projections onto
constraint subspaces to recover the unknown phases in the Fourier transform of
an image, or, in the case of x-ray crystallography, the electron density of a
molecule. For a general class of algorithms, where the basic iteration is
specified by the difference map, solutions are associated with fixed points of
the map, the attractive character of which determines the effectiveness of the
algorithm. The behavior of the difference map near fixed points is controlled
by the relative orientation of the tangent spaces of the two constraint
subspaces employed by the map. Since the dimensionalities involved are always
large in practical applications, it is appropriate to use random matrix theory
ideas to analyze the average-case convergence at fixed points. Optimal values
of the gamma parameters of the difference map are found which differ somewhat
from the values previously obtained on the assumption of orthogonal tangent
spaces.Comment: 15 page
Convergence to suitable weak solutions for a finite element approximation of the Navier-Stokes equations with numerical subgrid scale modeling
In this work we prove that weak solutions constructed by a variational
multiscale method are suitable in the sense of Scheffer. In order to prove this
result, we consider a subgrid model that enforces orthogonality between subgrid
and finite element components. Further, the subgrid component must be tracked
in time. Since this type of schemes introduce pressure stabilization, we have
proved the result for equal-order velocity and pressure finite element spaces
that do not satisfy a discrete inf-sup condition.Comment: 23 pages, no figure
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