Search results for "Dimension"

Big Vector Bundles on Surfaces and Fourfolds

2019

The aim of this note is to exhibit explicit sufficient criteria ensuring bigness of globally generated, rank-$r$ vector bundles, $r \geqslant 2$, on smooth, projective varieties of even dimension $d \leqslant 4$. We also discuss connections of our general criteria to some recent results of other authors, as well as applications to tangent bundles of Fano varieties, to suitable Lazarsfeld-Mukai bundles on four-folds, etcetera.

Global properties of codimension two spacelike submanifolds in Minkowski space

2009

Abstract We consider codimension two spacelike submanifolds with a parallel normal field (i.e. vanishing normal curvature) in Minkowski space. We use the analysis of their contacts with hyperplanes and hyperquadrics in order to get some global information on them. As a consequence we obtain new versions of Carathéodory's and Loewner's conjectures on spacelike surfaces in 4-dimensional Minkowski space and 4-flattenings theorems for closed spacelike curves in 3-dimensional Minkowski space.

Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model

2020

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…

Dynamics of the scenery flow and geometry of measures

2015

We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a n…

Removable sets for intrinsic metric and for holomorphic functions

2019

We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every totally disconnected set with finite Hausdorff measure of codimension 1 is metrically removable, which answers a question raised by Hakobyan and Herron. The metrically removable sets are shown to be related to other classes of "thin" sets that appeared in the literature. They are also related to the removability problems for classes of holomorphic functions with restrictions on the derivative.

Derivatives not first return integrable on a fractal set

2018

We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.

Assouad dimension, Nagata dimension, and uniformly close metric tangents

2013

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…

DEVELOPMENT OF NONTOXIC BIO-ADHESIVES FOR WET ENVIRONMENTS

2021

Metamagnetism in hydrophobically induced carboxylate (phenylmalonate)-bridged copper(II) layers

2006

Self-assembly of copper(II) ions, phenylmalonate and pyrimidine yields the layered compound [Cu(pym)(Phmal)]n ( 1) where intralayer ferro- and interlayer antiferromagnetic interactions occur with three-dimensional antiferromagnetic ordering at Tc = 2.15 K Lloret Pastor, Francisco, Francisco.Lloret@uv.es ; Julve Olcina, Miguel, Miguel.Julve@uv.es

Monitoring of chicken meat freshness by means of a colorimetric sensor array

2012

A new optoelectronic nose to monitor chicken meat ageing has been developed. It is based on 16 pigments prepared by the incorporation of different dyes (pH indicators, Lewis acids, hydrogenbonding derivatives, selective probes and natural dyes) into inorganic materials (UVM-7, silica and alumina). The colour changes of the sensor array were characteristic of chicken ageing in a modi¿ed packaging atmosphere (30% CO2¿70% N2). The chromogenic array data were processed with qualitative (PCA) and quantitative (PLS) tools. The PCA statistical analysis showed a high degree of dispersion, with nine dimensions required to explain 95% of variance. Despite this high dimensionality, a tridimensional re…