69,743 research outputs found
Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient
The Cauchy problem for a multidimensional linear transport equation with
discontinuous coefficient is investigated. Provided the coefficient satisfies a
one-sided Lipschitz condition, existence, uniqueness and weak stability of
solutions are obtained for either the conservative backward problem or the
advective forward problem by duality. Specific uniqueness criteria are
introduced for the backward conservation equation since weak solutions are not
unique. A main point is the introduction of a generalized flow in the sense of
partial differential equations, which is proved to have unique jacobian
determinant, even though it is itself nonunique.Comment: 19-03-200
Fourier phase analysis in radio-interferometry
Most statistical tools used to characterize the complex structures of the
interstellar medium can be related to the power spectrum, and therefore to the
Fourier amplitudes of the observed fields. To tap into the vast amount of
information contained in the Fourier phases, one may consider the probability
distribution function (PDF) of phase increments, and the related concepts of
phase entropy and phase structure quantity. We use these ideas here with the
purpose of assessing the ability of radio-interferometers to detect and recover
this information. By comparing current arrays such as the VLA and Plateau de
Bure to the future ALMA instrument, we show that the latter is definitely
needed to achieve significant detection of phase structure, and that it will do
so even in the presence of a fair amount of atmospheric phase fluctuations. We
also show that ALMA will be able to recover the actual "amount'' of phase
structure in the noise-free case, if multiple configurations are used.Comment: Accepted for publication in "Astronomy & Astrophysics
The Codimension-Three conjecture for holonomic DQ-modules
We prove an analogue for holonomic DQ-modules of the codimension-three
conjecture for microdifferential modules recently proved by Kashiwara and
Vilonen. Our result states that any holonomic DQ-module having a lattice
extends uniquely beyond an analytic subset of codimension equal to or larger
than three in a Lagrangian subvariety containing the support of the DQ-module.Comment: 37 pages, several minor correction
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