54 research outputs found
Transfinite thin plate spline interpolation
Duchon's method of thin plate splines defines a polyharmonic interpolant to
scattered data values as the minimizer of a certain integral functional. For
transfinite interpolation, i.e. interpolation of continuous data prescribed on
curves or hypersurfaces, Kounchev has developed the method of polysplines,
which are piecewise polyharmonic functions of fixed smoothness across the given
hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has
introduced boundary conditions of Beppo Levi type to construct a semi-cardinal
model for polyspline interpolation to data on an infinite set of parallel
hyperplanes. The present paper proves that, for periodic data on a finite set
of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi
boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon
type functional
Quantum optics in the phase space - A tutorial on Gaussian states
In this tutorial, we introduce the basic concepts and mathematical tools
needed for phase-space description of a very common class of states, whose
phase properties are described by Gaussian Wigner functions: the Gaussian
states. In particular, we address their manipulation, evolution and
characterization in view of their application to quantum information.Comment: Tutorial. 23 pages, 1 figure. Updated version accepted for
publication in EPJ - ST devoted to the memory of Federico Casagrand
Group therapy with adolescents who have learning disabilities and social/emotional problems
Land fauna composition of small mammals of a fragment of Atlantic Forest in the State of Sao Paulo, Brazil
Investigation of different target's microâvibration feature based on a coherent shotânoise limited LIDAR
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