Results 11 to 20 of about 5,189 (241)
Mathematics teacher candidates’ approaches to using topology in geometry [PDF]
, 2021 When we look at the theoretical relationships between the three types of geometry, we find that the most primitive type is topology and that both Euclidean and projective geometry are derived from this earlier type. Therefore, Piaget described the first
Gedik, Solmaz Damla +6 more
core +1 more source
Smooth constructions of homotopy-coherent actions
, 2022 We prove that, for nice classes of infinite-dimensional smooth groups G , natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G . This yields a bridge between infinite-dimensional smooth groups
OH, YONG GEUN +2 more
core +1 more source
Cellular structures in Topology [PDF]
, 1990 This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type.
Renzo Piccinini +4 more
core +1 more source
Geometric Discretization of Lagrangian Mechanics and Field Theories [PDF]
, 2009 This thesis presents a unified framework for geometric discretization of highly oscillatory mechanics and classical field theories, based on Lagrangian variational principles and discrete differential forms. For highly oscillatory problems in mechanics,
Stern, Ari Joshua
core +1 more source
Tête-à-tête : graphs and twists [PDF]
, 2015 This is a PhD thesis in the mathematical field of low-dimensional topology. Its main purpose is to examine so-called tête-à-tête twists, which were defined by A'Campo.
Graf, Christian
core +1 more source
Discrete Exterior Calculus [PDF]
, 2003 This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complex and its geometric dual.
Hirani, Anil Nirmal
core +1 more source
Geometric Quantization and Foliation Reduction [PDF]
, 2013 A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed ...
Skerritt, Paul Michael
core +1 more source
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
Computational Geometric and Algebraic Topology
, 2015 Computational topology is a young, emerging field of mathematics that seeks out practical algorithmic methods for solving complex and fundamental problems in geometry and topology.
core +2 more sources
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