Results 61 to 70 of about 4,868,795 (209)
Visibility and Intersection Density for Boolean Models in Hyperbolic Space
ABSTRACT For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally considered in the analysis of Boolean models in Euclidean space. In particular, we determine a necessary and sufficient condition for the finiteness of the mean visible ...
Tillmann Bühler +2 more
wiley +1 more source
Real Cubic Hypersurfaces and Group Laws
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Isoparametric and Dupin Hypersurfaces
A hypersurface $M^{n−1}$ in a real space-form $R^n$, $S^n$ or $H^n$ is isoparametric if it has constant principal curvatures. For $R^n$ and $H^n$, the classification of isoparametric hypersurfaces is complete and relatively simple, but as Élie Cartan ...
Thomas E. Cecil
doaj +1 more source
Recent advances in CR (Cauchy-Riemann) geometry have raised interesting fine questions about the regularity of CR mappings between real analytic hypersurfaces.
Joël Merker
doaj +1 more source
The three‐step test in international copyright—a global framework for generative AI training
Abstract The training of generative artificial intelligence (genAI) models involves the processing of large datasets, which often include copyrighted materials, thereby raising questions of copyright infringement. These questions tend to center on whether such use constitutes fair use or falls under text and data mining (TDM) exceptions.
Nicola Lucchi +2 more
wiley +1 more source
In this paper we apply for the first time a new method for multivariate equation solving which was developed in for complex root determination to the real case.
Heintz, Joos +3 more
core +1 more source
Singularity of non‐pluripolar cohomology classes
Abstract We establish a relation between Lelong numbers and the full mass property of relative non‐pluripolar products. We use this relation to prove that if the restricted volume of a big class α$\alpha$ along an effective divisor D$D$ has full mass, then the Lelong numbers of the non‐pluripolar class ⟨αn−1⟩$\langle \alpha ^{n-1}\rangle$ at every ...
Duc‐Bao Nguyen +2 more
wiley +1 more source
Topology of random real hypersurfaces
18 pages, notes of the course I gave during the CIMPA summer school at Villa de Leyva, Colombia, in July ...
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Refinements on higher order Weil–Oesterlé bounds via a Serre type argument
Abstract Weil's theorem gives the most standard bound on the maximum number of points Nq(g)$N_q(g)$ of a curve of genus g$g$ over a finite field Fq$\mathbb {F}_q$. This bound was improved by Ihara and Oesterlé for larger genus. A recent point of view allows one to recover these bounds by solving a sequence of semi‐definite programs, and the first two ...
Emmanuel Hallouin +2 more
wiley +1 more source
Real hypersurfaces of a complex projective space
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