Smarandache Multi-Space Theory(III)--Map geometries and pseudo-plane geometries [PDF]
arXiv, 2006 A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This is the third part on multi-spaces concertrating on Smarandache geometries, including those of map ...
arxiv
NEUF: Learning Point Cloud Quality by Non-Euclidean Fast Filtering
IEEE AccessThis paper addresses the problem of no reference visual quality assessment in point clouds, useful for extended reality communication service such as remote surgery and education. Accurate, computationally efficient metrics for point cloud visual quality
Eleonora Di Salvo +5 more
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Stringy Geometry and Topology of Orbifolds [PDF]
arXiv, 2000 This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.
arxiv
The notion of dimension in geometry and algebra [PDF]
arXiv, 2005 This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are invoked and compared.
arxiv
The Bolyai-Lobatschewsky Non-Euclidean Geometry: an Elementary Interpretation of this Geometry, and some Results which follow from this Interpretation [PDF]
, 1909 H. S. Carslaw
openalex +1 more source
Book Review: The Elements of Non-Euclidean Geometry [PDF]
, 1915 J. L. Coolidge
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Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces
, 2006 We discover suprising connections between three seemingly different problems: finding right triangles with rational sides in a non-Euclidean geometry, finding three integers such that the difference of the squares of any two is a square, and the problem ...
Robin Hartshorne, Ronald, Van Luijk
core +1 more source
Learning neural operators on Riemannian manifolds
National Science OpenLearning mappings between functions (operators) defined on complex computational domains is a common theoretical challenge in machine learning. Existing operator learning methods mainly focus on regular computational domains, and have many components ...
Chen Gengxiang +5 more
doaj +1 more source
Foundations of Euclidean and Non-Euclidean Geometry. by Ellery B. Golos. Holt, Rinehart and Winston, Toronto (1968). xiii + 225 pp. [PDF]
, 1970 Cyril W. L. Garner
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A history of non-euclidean geometry: evolution of the concept of a geometric space [PDF]
, 1989 openalex +1 more source