Search results for "Affine transformation"
showing 10 items of 99 documents
Algebraicity of analytic maps to a hyperbolic variety
2018
Let $X$ be an algebraic variety over $\mathbb{C}$. We say that $X$ is Borel hyperbolic if, for every finite type reduced scheme $S$ over $\mathbb{C}$, every holomorphic map $S^{an}\to X^{an}$ is algebraic. We use a transcendental specialization technique to prove that $X$ is Borel hyperbolic if and only if, for every smooth affine curve $C$ over $\mathbb{C}$, every holomorphic map $C^{an}\to X^{an}$ is algebraic. We use the latter result to prove that Borel hyperbolicity shares many common features with other notions of hyperbolicity such as Kobayashi hyperbolicity.
On base loci of higher fundamental forms of toric varieties
2019
We study the base locus of the higher fundamental forms of a projective toric variety $X$ at a general point. More precisely we consider the closure $X$ of the image of a map $({\mathbb C}^*)^k\to {\mathbb P}^n$, sending $t$ to the vector of Laurent monomials with exponents $p_0,\dots,p_n\in {\mathbb Z}^k$. We prove that the $m$-th fundamental form of such an $X$ at a general point has non empty base locus if and only if the points $p_i$ lie on a suitable degree-$m$ affine hypersurface. We then restrict to the case in which the points $p_i$ are all the lattice points of a lattice polytope and we give some applications of the above result. In particular we provide a classification for the se…
On Mardia’s Tests of Multinormality
2004
Classical multivariate analysis is based on the assumption that the data come from a multivariate normal distribution. The tests of multinormality have therefore received very much attention. Several tests for assessing multinormality, among them Mardia’s popular multivariate skewness and kurtosis statistics, are based on standardized third and fourth moments. In Mardia’s construction of the affine invariant test statistics, the data vectors are first standardized using the sample mean vector and the sample covariance matrix. In this paper we investigate whether, in the test construction, it is advantageous to replace the regular sample mean vector and sample covariance matrix by their affi…
Monothetic algebraic groups
2007
AbstractWe call an algebraic group monothetic if it possesses a dense cyclic subgroup. For an arbitrary field k we describe the structure of all, not necessarily affine, monothetic k-groups G and determine in which cases G has a k-rational generator.
Affine compensation of illumination in hyperspectral remote sensing images
2009
A problem when working with optical satellite or airborne images is the need to compensate for changes in the illumination conditions at the time of acquisition. This is particularly critical when working with time series of data. Atmospheric correction strategies based on radiative transfer codes may provide a rigorous solution but it may not be the best solution for situations where a huge amount of hyperspectral images may need to be processed and computational time is a critical factor. The GMES (”Global Monitoring for Environment and Security”) initiative has promoted the creation of a new generation of satellites (the SENTINEL series) with ”ultra-high resolution” and ”superspectral im…
Monotonic solution of heterogeneous anisotropic diffusion problems
2013
Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…
Metric-affine f(R,T) theories of gravity and their applications
2018
We study $f(R,T)$ theories of gravity, where $T$ is the trace of the energy-momentum tensor ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine $f(R)$ relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the nonconservatio…
Black holes in five-dimensional Palatinif(R)gravity and implications for the AdS/CFT correspondence
2014
We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (the Palatini approach). We illustrate this fact by considering the case of Palatini $f(R)$ gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to ad hoc quasitopological constructions.
Observable traces of non-metricity: new constraints on metric-affine gravity
2018
Relaxing the Riemannian condition to incorporate geometric quantities such as torsion and non-metricity may allow to explore new physics associated with defects in a hypothetical space-time microstructure. Here we show that non-metricity produces observable effects in quantum fields in the form of 4-fermion contact interactions, thereby allowing us to constrain the scale of non-metricity to be greater than 1 TeV by using results on Bhabha scattering. Our analysis is carried out in the framework of a wide class of theories of gravity in the metric-affine approach. The bound obtained represents an improvement of several orders of magnitude to previous experimental constraints.
Ghosts in metric-affine higher order curvature gravity
2019
We disprove the widespread belief that higher order curvature theories of gravity in the metric-affine formalism are generally ghost-free. This is clarified by considering a sub-class of theories constructed only with the Ricci tensor and showing that the non-projectively invariant sector propagates ghost-like degrees of freedom. We also explain how these pathologies can be avoided either by imposing a projective symmetry or additional constraints in the gravity sector. Our results put forward that higher order curvature gravity theories generally remain pathological in the metric-affine (and hybrid) formalisms and highlight the key importance of the projective symmetry and/or additional co…