6,917 research outputs found
Codimension one decompositions and Chow varieties
A presentation of a degree form in variables as the sum of
homogenous elements ``essentially'' involving variables is called a {\em
codimension one decomposition}. Codimension one decompositions are introduced
and the related Waring Problem is stated and solved. Natural schemes describing
the codimension one decompositions of a generic form are defined. Dimension and
degree formulae for these schemes are derived when the number of summands is
the minimal one; in the zero dimensional case the scheme is showed to be
reduced. These results are obtained by studying the Chow variety
of zero dimensional degree cycles in \PP^n. In particular, an explicit
formula for is determined
A Semi-Lagrangian Scheme with Radial Basis Approximation for Surface Reconstruction
We propose a Semi-Lagrangian scheme coupled with Radial Basis Function
interpolation for approximating a curvature-related level set model, which has
been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces
from sparse, possibly noisy data sets. The main advantages of the proposed
scheme are the possibility to solve the level set method on unstructured grids,
as well as to concentrate the reconstruction points in the neighbourhood of the
data set, with a consequent reduction of the computational effort. Moreover,
the scheme is explicit. Numerical tests show the accuracy and robustness of our
approach to reconstruct curves and surfaces from relatively sparse data sets.Comment: 14 pages, 26 figure
Carmichael Numbers on a Quantum Computer
We present a quantum probabilistic algorithm which tests with a polynomial
computational complexity whether a given composite number is of the Carmichael
type. We also suggest a quantum algorithm which could verify a conjecture by
Pomerance, Selfridge and Wagstaff concerning the asymptotic distribution of
Carmichael numbers smaller than a given integer.Comment: 7 pages, Latex/REVTEX fil
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