5,239 research outputs found
Galaxy Modeling with Compound Elliptical Shapelets
Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have
become important tools in galaxy modeling, particularly for the purpose of
extracting ellipticity and morphological information from astronomical data.
However, the standard shapelet basis functions cannot compactly represent
galaxies with high ellipticity or large Sersic index, and the resulting
underfitting bias has been shown to present a serious challenge for
weak-lensing methods based on shapelets. We present here a new convolution
relation and a compound "multi-scale" shapelet basis to address these problems,
and provide a proof-of-concept demonstration using a small sample of nearby
galaxies.Comment: 14 pages, 7 figure
Parabolic stable surfaces with constant mean curvature
We prove that if u is a bounded smooth function in the kernel of a
nonnegative Schrodinger operator on a parabolic Riemannian
manifold M, then u is either identically zero or it has no zeros on M, and the
linear space of such functions is 1-dimensional. We obtain consequences for
orientable, complete stable surfaces with constant mean curvature
in homogeneous spaces with four
dimensional isometry group. For instance, if M is an orientable, parabolic,
complete immersed surface with constant mean curvature H in
, then and if equality holds, then
M is either an entire graph or a vertical horocylinder.Comment: 15 pages, 1 figure. Minor changes have been incorporated (exchange
finite capacity by parabolicity, and simplify the proof of Theorem 1)
Chiral perturbation theory
The main elements and methods of chiral perturbation theory, the effective
field theory of the Standard Model below the scale of spontaneous chiral
symmetry breaking, are summarized. Applications to the interactions of mesons
and baryons at low energies are reviewed, with special emphasis on developments
of the last three years. Among the topics covered are the strong,
electromagnetic and semileptonic weak interactions of mesons at and beyond
next--to--leading order in the chiral expansion, nonleptonic weak interactions
of mesons, virtual photon corrections and the meson--baryon system. The
discussion is limited to processes at zero temperature, for infinite volume and
with at most one baryon.Comment: 84 pages, Latex, 11 PostScript figures (in separate file) embedded
with epsfig.sty, complete ps file (compressed, uuencoded, 0.6 MB) available
via email on request; to appear in Progr. Part. Nucl. Phys., vol. 3
Feller semigroups, Lp-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols
The question of extending L-p-sub-Markovian semigroups to the spaces L-q, q > P, and the interpolation of LP-sub-Markovian semigroups with Feller semigroups is investigated. The structure of generators of L-p-sub-Markovian semigroups is studied. Subordination in the sense of Bochner is used to discuss the construction of refinements of L-p-sub-Markovian semigroups. The role played by some function spaces which are domains of definition for L-p-generators is pointed out. The problem of regularising powers of generators as well as some perturbation results are discussed
On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity
In this paper, we introduce and study non-local Jacobi operators, which
generalize the classical (local) Jacobi operators. We show that these operators
extend to generators of ergodic Markov semigroups with unique invariant
probability measures and study their spectral and convergence properties. In
particular, we derive a series expansion of the semigroup in terms of
explicitly defined polynomials, which generalize the classical Jacobi
orthogonal polynomials. In addition, we give a complete characterization of the
spectrum of the non-self-adjoint generator and semigroup. We show that the
variance decay of the semigroup is hypocoercive with explicit constants, which
provides a natural generalization of the spectral gap estimate. After a random
warm-up time, the semigroup also decays exponentially in entropy and is both
hypercontractive and ultracontractive. Our proofs hinge on the development of
commutation identities, known as intertwining relations, between local and
non-local Jacobi operators and semigroups, with the local objects serving as
reference points for transferring properties from the local to the non-local
case
Universal Constraints on the Location of Extrema of Eigenfunctions of Non-Local Schr\"odinger Operators
We derive a lower bound on the location of global extrema of eigenfunctions
for a large class of non-local Schr\"odinger operators in convex domains under
Dirichlet exterior conditions, featuring the symbol of the kinetic term, the
strength of the potential, and the corresponding eigenvalue, and involving a
new universal constant. We show a number of probabilistic and spectral
geometric implications, and derive a Faber-Krahn type inequality for non-local
operators. Our study also extends to potentials with compact support, and we
establish bounds on the location of extrema relative to the boundary edge of
the support or level sets around minima of the potential.Comment: 30 pages, To appear in Jour. Diff. Equation, 201
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