7,314 research outputs found
On uniform convergence of Fourier series
We consider the space of all continuous functions on the
circle with uniformly convergent Fourier series. We show that if
is a continuous piecewise linear but
not linear map, then
Theory of the Spatio-Temporal Dynamics of Transport Bifurcations
The development and time evolution of a transport barrier in a magnetically
confined plasma with non-monotonic, nonlinear dependence of the anomalous flux
on mean gradients is analyzed. Upon consideration of both the spatial
inhomogeneity and the gradient nonlinearity of the transport coefficient, we
find that the transition develops as a bifurcation front with radially
propagating discontinuity in local gradient. The spatial location of the
transport barrier as a function of input flux is calculated. The analysis
indicates that for powers slightly above threshold, the barrier location
where is the local transition
power threshold and is the neoclassical diffusivity . This result
suggests a simple explanation of the high disruptivity observed in reversed
shear plasmas. The basic conclusions of this theory are insensitive to the
details of the local transport model.Comment: 21 page Tex file, 10 postscript file
Sequential quantum-enhanced measurement with an atomic ensemble
We propose a quantum-enhanced iterative (with steps) measurement scheme
based on an ensemble of two-level probes which asymptotically approaches
the Heisenberg limit , the number of quantum
resources. The protocol is inspired by Kitaev's phase estimation algorithm and
involves only collective manipulation and measurement of the ensemble. The
iterative procedure takes the shot-noise limited primary measurement with
precision to increasingly precise results
. A straightforward implementation of the algorithm
makes use of a two-component atomic cloud of Bosons in the precision
measurement of a magnetic field.Comment: 5 pages, 1 figur
On the Fourier transform of the characteristic functions of domains with -smooth boundary
We consider domains with -smooth boundary and
study the following question: when the Fourier transform of the
characteristic function belongs to ?Comment: added two references; added footnotes on pages 6 and 1
Estimates in Beurling--Helson type theorems. Multidimensional case
We consider the spaces of functions on the
-dimensional torus such that the sequence of the Fourier
coefficients belongs to
. The norm on is defined by
. We study the rate of
growth of the norms as
for -smooth real
functions on (the one-dimensional case was investigated
by the author earlier). The lower estimates that we obtain have direct
analogues for the spaces
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