657 research outputs found
Nonalgebraizable real analytic tubes in C^n
We give necessary conditions for certain real analytic tube generic
submanifolds in C^n to be locally algebraizable. As an application, we exhibit
families of real analytic non locally algebraizable tube generic submanifolds
in C^n. During the proof, we show that the local CR automorphism group of a
minimal, finitely nondegenerate real algebraic generic submanifold is a real
algebraic local Lie group. We may state one of the main results as follows. Let
M be a real analytic hypersurface tube in C^n passing through the origin,
having a defining equation of the form v = \phi(y), where (z,w)= (x+iy,u+iv)
\in C^{n-1} \times C. Assume that M is Levi nondegenerate at the origin and
that the real Lie algebra of local infinitesimal CR automorphisms of M is of
minimal possible dimension n, i.e. generated by the real parts of the
holomorphic vector fields \partial_{z_1}, ..., \partial_{z_{n-1}}, \partial_w.
Then M is locally algebraizable only if every second derivative
\partial^2_{y_ky_l}\phi is an algebraic function of the collection of first
derivatives \partial_{y_1} \phi,..., \partial_{y_m} \phi.Comment: 36 pages, 4 figure
On the convergence of S-nondegenerate formal CR maps
We introduce S-nondegenerate formal CR maps and establish their convergence
(revision of a preliminary version).Comment: 38 page
Deformable Prototypes for Encoding Shape Categories in Image Databases
We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.Office of Naval Research (Young Investigator Award N00014-06-1-0661
A general framework for Noetherian well ordered polynomial reductions
Polynomial reduction is one of the main tools in computational algebra with
innumerable applications in many areas, both pure and applied. Since many years
both the theory and an efficient design of the related algorithm have been
solidly established.
This paper presents a general definition of polynomial reduction structure,
studies its features and highlights the aspects needed in order to grant and to
efficiently test the main properties (noetherianity, confluence, ideal
membership).
The most significant aspect of this analysis is a negative reappraisal of the
role of the notion of term order which is usually considered a central and
crucial tool in the theory. In fact, as it was already established in the
computer science context in relation with termination of algorithms, most of
the properties can be obtained simply considering a well-founded ordering,
while the classical requirement that it be preserved by multiplication is
irrelevant.
The last part of the paper shows how the polynomial basis concepts present in
literature are interpreted in our language and their properties are
consequences of the general results established in the first part of the paper.Comment: 36 pages. New title and substantial improvements to the presentation
according to the comments of the reviewer
Coherence for Modalities
Positive modalities in systems in the vicinity of S4 and S5 are investigated
in terms of categorial proof theory. Coherence and maximality results are
demonstrated, and connections with mixed distributive laws and Frobenius
algebras are exhibited.Comment: 43 pages, minor addition
Modular categories of types B,C and D
We construct four series of modular categories from the two-variable Kauffman
polynomial, without use of the representation theory of quantum groups at roots
of unity. The specializations of this polynomial corresponding to quantum
groups of types B, C and D produce series of pre-modular categories. One of
them turns out to be modular and three others satisfy Brugui\`eres'
modularization criterion. For these four series we compute the Verlinde
formulas, and discuss spin and cohomological refinements.Comment: 32 pages, LaTeX with figures, Comment. Math. Helv. 200
Panorama of p-adic model theory
ABSTRACT. We survey the literature in the model theory of p-adic numbers since\ud
Denef’s work on the rationality of Poincaré series. / RÉSUMÉ. Nous donnons un aperçu des développements de la théorie des modèles\ud
des nombres p-adiques depuis les travaux de Denef sur la rationalité de séries de Poincaré,\ud
par une revue de la bibliographie
Tiling groupoids and Bratteli diagrams
Let T be an aperiodic and repetitive tiling of R^d with finite local
complexity. Let O be its tiling space with canonical transversal X. The tiling
equivalence relation R_X is the set of pairs of tilings in X which are
translates of each others, with a certain (etale) topology. In this paper R_X
is reconstructed as a generalized "tail equivalence" on a Bratteli diagram,
with its standard AF-relation as a subequivalence relation.
Using a generalization of the Anderson-Putnam complex, O is identified with
the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is
built from this sequence, and its set of infinite paths dB is homeomorphic to
X. The diagram B is endowed with a horizontal structure: additional edges that
encode the adjacencies of patches in T. This allows to define an etale
equivalence relation R_B on dB which is homeomorphic to R_X, and contains the
AF-relation of "tail equivalence".Comment: 34 pages, 4 figure
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