Results 11 to 20 of about 140,252 (207)
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc +2 more sources
, 2022 <p>Equivalence, duality, and invariance are the pin-points of unification in modern theoretical physics that got the twist of topologies when going beyond the notions of differential and conformal domains to geometries to the symplectic norm of topologies with the pillars being the algebraic geometry taking the counting of specified states ...
openaire +1 more source
The mapping class group of a genus two surface is linear
, 2001 In this paper we construct a faithful representation of the mapping class group of the genus two surface into a group of matrices over the complex numbers.
Farkas +6 more
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A mapping theorem for topological complexity [PDF]
, 2015 Peer reviewedPublisher ...
Grant, Mark +2 more
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Advanced Engineering Materials, EarlyView.This study reports lightweight polyetherimide triply periodic minimal surfaces lattices coated with carbon nanotube‐reinforced epoxy that combine mechanical robustness with self‐sensing. The conformal coating enhances stiffness, strength and energy absorption while enabling reliable strain monitoring.
A. Triay +3 more
wiley +1 more source
Advanced Engineering Materials, EarlyView.Additive manufacturing provides precise control over the placement of continuous fibres within polymer matrices, enabling customised mechanical performance in composite components. This article explores processing strategies, mechanical testing, and modelling approaches for additive manufactured continuous fibre‐reinforced composites.
Cherian Thomas, Amir Hosein Sakhaei
wiley +1 more source
On several varieties of cacti and their relations
, 2005 Motivated by string topology and the arc operad, we introduce the notion of quasi-operads and consider four (quasi)-operads which are different varieties of the operad of cacti.
Kassel, Penner, Ralph M Kaufmann
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Advanced Functional Materials, EarlyView.Cuttlebone‐inspired metamaterials exploit a septum‐wall architecture to achieve excellent mechanical and functional properties. This review classifies existing designs into direct biomimetic, honeycomb‐type, and strut‐type architectures, summarizes governing design principles, and presents a decoupled design framework for interpreting multiphysical ...
Xinwei Li, Zhendong Li
wiley +1 more source
Alexander polynomial, finite type invariants and volume of hyperbolic knots
, 2004 We show that given n>0, there exists a hyperbolic knot K with trivial Alexander polynomial, trivial finite type invariants of order 0, there exists a sequence of hyperbolic knots with trivial finite type invariants of order
Adams +7 more
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Algorithmic Design of Disordered Networks With Arbitrary Coordination: Application to Biophotonics
Advanced Functional Materials, EarlyView.Predictive Design of Disordered Networks: Disordered network‐like morphologies are abundant in nature, from cytoskeletal networks to bone structures and chalcogenide glasses. These structures are naturally hard to characterize. A new algorithmic tool extends the established Wooten–Weaire–Winer (WWW) algorithm to valencies above 4.
Florin Hemmann +3 more
wiley +1 more source