297 research outputs found
On the total curvatures of a tame function
Given a definable function f, enough differentiable, we study the continuity
of the total curvature function t --> K(t), total curvature of the level {f=t},
and the total absolute curvature function t-->|K| (t), total absolute curvature
of the level {f=t}. We show they admits at most finitely many discontinuities
Development after international adoption
This thesis examined the development of adopted children to shed more light on the effects of deprivation on child development and the potential for catch-up and recovery after placement in the more advantageous environment of an adoptive family. In the first part of the thesis a meta-analysis is presented in which we compared adopted children’s attachment relationships with the normative attachment distribution of nonadopted children raised by their biological parents, and - as a comparison - we also compared the attachment distribution of foster children with the normative distribution. The second and third parts of the thesis focus on the development of former foster and post-institutionalized children, 11 to 16 months old at arrival, two and six months after their adoption from China. Several salient developmental domains were studied: attachment, cognitive and motor development, physical growth, stress regulation, and social-emotional behavior.LEI Universiteit LeidenNetherlands Organization for Scientific Research (NWO 400-03-208). Additional support was received from
Wereldkinderen, and for the meta-analysis described in Chapter 2 from VSBfonds,
Fonds Psychische Gezondheid, and Stichting Kinderpostzegels Nederland.FSW - Gezinsopvoeding - Ou
Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem
Let f be a definable function, enough differentiable. Under the condition of
having strongly isolated singularities at infinity at a regular value c we give
a sufficient condition expressed in terms of the total absolute curvature
function to ensure the local triviality of the function f over a neighbourhood
of c and doing so providing the tame version of Parusinski's Theorem on complex
polynomials with isolated singularities at infinity.Comment: 20 page
Monotone functions and maps
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2
(2011)] we defined semi-monotone sets, as open bounded sets, definable in an
o-minimal structure over the reals, and having connected intersections with all
translated coordinate cones in R^n. In this paper we develop this theory
further by defining monotone functions and maps, and studying their fundamental
geometric properties. We prove several equivalent conditions for a bounded
continuous definable function or map to be monotone. We show that the class of
graphs of monotone maps is closed under intersections with affine coordinate
subspaces and projections to coordinate subspaces. We prove that the graph of a
monotone map is a topologically regular cell. These results generalize and
expand the corresponding results obtained in Basu et al. for semi-monotone
sets.Comment: 30 pages. Version 2 appeared in RACSAM. In version 3 Corollaries 1
and 2 were corrected. In version 4 Theorem 3 is correcte
\Lambda-buildings and base change functors
We prove an analog of the base change functor of \Lambda-trees in the setting
of generalized affine buildings. The proof is mainly based on local and global
combinatorics of the associated spherical buildings. As an application we
obtain that the class of generalized affine building is closed under ultracones
and asymptotic cones. Other applications involve a complex of groups
decompositions and fixed point theorems for certain classes of generalized
affine buildings.Comment: revised version, 29 pages, to appear in Geom. Dedicat
Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers
We prove decidability of univariate real algebra extended with predicates for
rational and integer powers, i.e., and . Our decision procedure combines computation over real algebraic
cells with the rational root theorem and witness construction via algebraic
number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated
Deduction, 2015. Proceedings to be published by Springer-Verla
Euler-Bessel and Euler-Fourier Transforms
We consider a topological integral transform of Bessel (concentric
isospectral sets) type and Fourier (hyperplane isospectral sets) type, using
the Euler characteristic as a measure. These transforms convert constructible
\zed-valued functions to continuous -valued functions over a vector
space. Core contributions include: the definition of the topological Bessel
transform; a relationship in terms of the logarithmic blowup of the topological
Fourier transform; and a novel Morse index formula for the transforms. We then
apply the theory to problems of target reconstruction from enumerative sensor
data, including localization and shape discrimination. This last application
utilizes an extension of spatially variant apodization (SVA) to mitigate
sidelobe phenomena
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