Cohomology of Fuchsian groups and non-Euclidean crystallographic groups
Sign Up to like & getrecommendations! Published in 2022 at "manuscripta mathematica"
DOI: 10.1007/s00229-022-01369-z
Abstract: For each geometrically finite 2-dimensional non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology. read more here.
Keywords: group; cohomology fuchsian; euclidean crystallographic; cohomology ... See more keywords
The sphere packing problem into bounded containers in three-dimension non-Euclidean space
Sign Up to like & getrecommendations! Published in 2018 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2018.11.450
Abstract: Abstract This paper deals with the problem of optimal packing a given number of equal spheres into different closed sets. We consider the problem both in three-dimensional Euclidean and non-Euclidean spaces. The special algorithm based… read more here.
Keywords: space; problem bounded; non euclidean; problem ... See more keywords
Computing the signatures of subgroups of non-Euclidean crystallographic groups
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2017.01.017
Abstract: Abstract A (planar and cocompact) non-Euclidean crystallographic (NEC) group Δ is a subgroup of the group of, conformal and anti-conformal, isometries of the hyperbolic plane H 2 such that H 2 / Δ is compact.… read more here.
Keywords: subgroups non; computing signatures; euclidean crystallographic; crystallographic groups ... See more keywords
Generalised rigid body motions in non-Euclidean planes with applications to global rigidity
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2022.126259
Abstract: A bar-joint framework (G, p) in a (non-Euclidean) real normed plane X is the combination of a finite, simple graph G and a placement p of the vertices in X . A framework (G, p)… read more here.
Keywords: non euclidean; global rigidity; rigidity; rigid body ... See more keywords
Topological Hyperbolic Lattices.
Sign Up to like & getrecommendations! Published in 2020 at "Physical review letters"
DOI: 10.1103/physrevlett.125.053901
Abstract: Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general theory of relativity. Notably, an infinite… read more here.
Keywords: non euclidean; geometry; topological hyperbolic; hyperbolic lattices ... See more keywords
Fractional Excitations in Non-Euclidean Elastic Plates.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review letters"
DOI: 10.1103/physrevlett.127.098001
Abstract: We show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such elastic plates support fractional excitations, which take the form of charge-1/2 solitons… read more here.
Keywords: euclidean elastic; non euclidean; fractional excitations; elastic plates ... See more keywords
Observation of Topological p-Orbital Disclination States in Non-Euclidean Acoustic Metamaterials.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review letters"
DOI: 10.1103/physrevlett.129.154301
Abstract: Disclinations-topological defects ubiquitously existing in various materials-can reveal the intrinsic band topology of the hosting material through the bulk-disclination correspondence. In low-dimensional materials and nanostructure such as graphene and fullerenes, disclinations yield curved surfaces and… read more here.
Keywords: topology; disclination; physics; acoustic metamaterials ... See more keywords
A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Signal Processing"
DOI: 10.1109/tsp.2018.2870353
Abstract: We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity, as well as practical faster convergence. Under mild… read more here.
Keywords: non euclidean; matrix; framework non; non convex ... See more keywords
Kriging models for linear networks and non‐Euclidean distances: Cautions and solutions
Sign Up to like & getrecommendations! Published in 2018 at "Methods in Ecology and Evolution"
DOI: 10.1111/2041-210x.12979
Abstract: There are now several examples in the ecological literature where, for spatial prediction like kriging, non-Euclidean distances were used in autocorrelation models developed under a Euclidean distance assumption. This leads to a problem where prediction… read more here.
Keywords: linear networks; euclidean distances; networks non; models linear ... See more keywords
Non-Euclidean navigation
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Experimental Biology"
DOI: 10.1242/jeb.187971
Abstract: ABSTRACT A basic set of navigation strategies supports navigational tasks ranging from homing to novel detours and shortcuts. To perform these last two tasks, it is generally thought that humans, mammals and perhaps some insects… read more here.
Keywords: spatial knowledge; map; navigation; graph ... See more keywords
Learning trajectory of non-Euclidean geometry through ethnomathematics learning approaches to improve spatial ability
Sign Up to like & getrecommendations! Published in 2023 at "Eurasia Journal of Mathematics, Science and Technology Education"
DOI: 10.29333/ejmste/13269
Abstract: Non-Euclidean geometry is an abstract subject and difficult to learn, but mandatory for students. The ethnomathematics approach as a learning approach to improve students’ spatial abilities. The aim of this research is to discover new… read more here.
Keywords: spatial ability; spatial abilities; learning trajectory; geometry ... See more keywords