Results 61 to 70 of about 84,048 (226)
Differential Geometry and Matrix-Based Generalizations of the Pythagorean Theorem in Space Forms
MathematicsIn this work, we consider Pythagorean triples and quadruples using fundamental form matrices of hypersurfaces in three- and four-dimensional space forms and illustrate various figures. Moreover, we generalize that an immersed hypersphere Mn with radius r
Erhan Güler +2 more
doaj +1 more source
Characteristic Varieties of Hypersurface Complements [PDF]
, 2016 We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface.
Liu, Yongqiang, Maxim, Laurentiu
core
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1656-1702, September 2025.Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli +2 more
wiley +1 more source
Angewandte Chemie International Edition, Volume 64, Issue 32, August 4, 2025.This minireview discusses the facilitation of E─C bond homolysis of main group compounds with visible light by the coordination of redox non‐innocent ligands. Important conceptual coherencies, potential applications, and future challenges are highlighted with respect to selected literature reports.
Jonas O. Wenzel +2 more
wiley +1 more source
Motivic Milnor fiber of a quasi-ordinary hypersurface [PDF]
, 2011 Let $f$ be a germ of complex analytic function at $({\mathbf{C}}^{d+1}, 0)$ such that its zero level defines an irreducible germ of quasi-ordinary hypersurface $(S,0)$.
Perez, Pedro Daniel Gonzalez +1 more
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Topology in Biological Piezoelectric Materials
Advanced Materials, Volume 37, Issue 32, August 14, 2025.This review summarizes the topological structures in biological piezoelectric materials, covering morphology evolution, spatial arrangement, and biomimetic strategies. These topologies modulate structure‐property relationships across multiple scales, enabling performance enhancement and multifunctional integration.
Chen Chen +7 more
wiley +1 more source
Lightlike Hypersurfaces and Canal Hypersurfaces of Lorentzian Surfaces
Abstract and Applied Analysis, 2014 The lightlike hypersurfaces in semi-Euclidean space are of special interest in Relativity Theory. In particular, the singularities of these lightlike hypersurfaces provide good models for the study of different horizon types. And we obtain some geometrical propositions of the canal hypersurfaces of Lorentzian surfaces.
Donghe Pei, Jianguo Sun, Jianguo Sun
openaire +3 more sources
Bis[1]benzothieno[1,4]thiazine‐S‐oxides–Luminescence of the Anti‐Anti‐Regioisomer
Asian Journal of Organic Chemistry, Volume 14, Issue 8, August 2025.Three regioisomeric bis[1]benzothieno[1,4]thiazine‐S‐oxides were synthesized by mild oxidation. Crystal structures reveal S‐extra‐oxide, N‐intra conformers with paired‐like substructures, and intermolecular distances as low as 3.30 Å. UV–vis absorption and emission spectroscopy identifies the anti‐anti‐regioisomer as a strong blue light emitter ...
Simone T. Hauer +3 more
wiley +1 more source