Search results for " Transformation"
showing 10 items of 1043 documents
Self-affine sets in analytic curves and algebraic surfaces
2018
We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces do not contain non-trivial self-affine sets. peerReviewed
Compactifying Torus Fibrations Over Integral Affine Manifolds with Singularities
2021
This is an announcement of the following construction: given an integral affine manifold B with singularities, we build a topological space X which is a torus fibration over B. The main new feature of the fibration X → B is that it has the discriminant in codimension 2.
Flat lightlike hypersurfaces in Lorentz–Minkowski 4-space
2009
Abstract The lightlike hypersurfaces in Lorentz–Minkowski space are of special interest in Relativity Theory. In particular, the singularities of these hypersurfaces provide good models for the study of different horizon types. We introduce the notion of flatness for these hypersurfaces and study their singularities. The classification result asserts that a generic classification of flat lightlike hypersurfaces is quite different from that of generic lightlike hypersurfaces.
Local structure of self-affine sets
2011
The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self-affine Cantor sets E of the type studied by Bedford, McMullen, Gatzouras and Lalley, for which the projection onto the horizontal axis is an interval. We show that within small square neighborhoods of almost each point x in E, with respect to many product measures on address space, E is well approximated by product sets of an interval and a Cantor set. Even though E is totally disconnected, the limit sets have the product structure with interval fibres, reminiscent to the view of attractors of chaotic differentia…
Hyperbolicity as an obstruction to smoothability for one-dimensional actions
2017
Ghys and Sergiescu proved in the $80$s that Thompson's group $T$, and hence $F$, admits actions by $C^{\infty}$ diffeomorphisms of the circle . They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of piecewise projective homeomorphisms, and Lodha-Moore defined finitely presentable groups of piecewise projective homeomorphisms. These groups are of particular interest because they are nonamenable and contain no free subgroup. In contrast to the result of Ghys-Sergiescu, we prove that the groups of Monod and Lodha-Moore are not topologically conjugate to a group of $C^1$ diffeomorphisms. Fur…
A group analysis via weak equivalence transformations for a model of tumor encapsulation
2004
A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach. The presence in the model of three arbitrary functions suggests the use of Lie symmetries by using the weak equivalence transformations. An invariant classification is given which allows us to reduce the initial PDEs system to an ODEs system. Numerical simulations show a realistic enough description of the physical process.
Skeleta of affine hypersurfaces
2014
A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.
Tests of Independence Based on Sign and Rank Covariances
2003
In this paper three different concepts of bivariate sign and rank, namely marginal sign and rank, spatial sign and rank and affine equivariant sign and rank, are considered. The aim is to see whether these different sign and rank covariances can be used to construct tests for the hypothesis of independence. In some cases (spatial sign, affine equivariant sign and rank) an additional assumption on the symmetry of marginal distribution is needed. Limiting distributions of test statistics under the null hypothesis as well as under interesting sequences of contiguous alternatives are derived. Asymptotic relative efficiencies with respect to the regular correlation test are calculated and compar…
Functorial Test Modules
2016
In this article we introduce a slight modification of the definition of test modules which is an additive functor $\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual definition of test modules. Furthermore, we show that for a smooth morphism $f \colon X \to Y$ of $F$-finite schemes one has a natural isomorphism $f^! \circ \tau \cong \tau \circ f^!$. If $f$ is quasi-finite and of finite type we construct a natural transformation $\tau \circ f_* \to f_* \circ \tau$.
Affine Algebraic Varieties
2000
Algebraic geometers study zero loci of polynomials. More accurately, they study geometric objects, called algebraic varieties, that can be described locally as zero loci of polynomials. For example, every high school mathematics student has studied a bit of algebraic geometry, in learning the basic properties of conic sections such as parabolas and hyperbolas.