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An adaptive evolutionary algorithm based on non-euclidean geometry for many-objective optimization
Annual Conference on Genetic and Evolutionary Computation, 2019In the last decade, several evolutionary algorithms have been proposed in the literature for solving multi- and many-objective optimization problems.
Annibale Panichella
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2006
Abstract Euclidean geometry was the first branch of mathematics to be treated in anything like the modern fashion (with postulates, definitions, theorems, and so forth); and even now geometry is conducted in a very logical, tightly knit fashion.
Valerio Scarani, Rachael Thew
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Abstract Euclidean geometry was the first branch of mathematics to be treated in anything like the modern fashion (with postulates, definitions, theorems, and so forth); and even now geometry is conducted in a very logical, tightly knit fashion.
Valerio Scarani, Rachael Thew
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Euclidean-Geometry-Based Space-Time Block Coded Spatial Modulation
IEEE Journal on Selected Topics in Signal Processing, 2019In this paper, we propose Euclidean geometric schemes to construct the codebooks for the space-time block coded spatial modulation system. The new codebook-constructing schemes are more efficient than the previous exhaustive searching scheme.
Xueqin Jiang +4 more
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1993
Abstract Let S be an affine space. We saw in the last chapter that if we also assume that S has the extra structure of an absolute distance |AB| between two points A and B, then it is possible to define a dot product u • v between any two vectors u and V in S.
H. S. M. Coxeter, George Beck
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Abstract Let S be an affine space. We saw in the last chapter that if we also assume that S has the extra structure of an absolute distance |AB| between two points A and B, then it is possible to define a dot product u • v between any two vectors u and V in S.
H. S. M. Coxeter, George Beck
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Euclidean and Non-Euclidean Geometry
Visual Differential Geometry and Forms, 2021openaire +2 more sources
Autoformalizing Euclidean Geometry
International Conference on Machine LearningAutoformalization involves automatically translating informal math into formal theorems and proofs that are machine-verifiable. Euclidean geometry provides an interesting and controllable domain for studying autoformalization. In this paper, we introduce
Logan Murphy +5 more
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Eighteen Essays in Non-Euclidean Geometry
, 2019This book consists of a series of self-contained essays on non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski geometries ...
Vincent Alberge, A. Papadopoulos
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SLE as a Mating of Trees in Euclidean Geometry
Communications in Mathematical Physics, 2016The mating of trees approach to Schramm–Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier et al. (Liouville quantum gravity as a mating of trees, 2014. arXiv:1409.7055).
N. Holden, Xin Sun
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1989
Surprisingly, the geometry of curved surfaces throws light on the geometry of the plane. More than 2000 years after Euclid formulated axioms for plane geometry, differential geometry showed that the parallel axiom does not follow from the other axioms of Euclid.
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Surprisingly, the geometry of curved surfaces throws light on the geometry of the plane. More than 2000 years after Euclid formulated axioms for plane geometry, differential geometry showed that the parallel axiom does not follow from the other axioms of Euclid.
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Mathematical Gazette, 1901
Non-Euclidean geometry began as an inquiry into a possible weakness in Euclid’s Elements and became the source of the ideas that there are geometries of spaces other than the one imagined in elementary geometry and that many mathematical theories, not ...
G. Halsted
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Non-Euclidean geometry began as an inquiry into a possible weakness in Euclid’s Elements and became the source of the ideas that there are geometries of spaces other than the one imagined in elementary geometry and that many mathematical theories, not ...
G. Halsted
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