Results 11 to 20 of about 231,503 (267)
Chirality in Geometric Algebra
Mathematics, 2021 We define chirality in the context of chiral algebra. We show that it coincides with the more general chirality definition that appears in the literature, which does not require the existence of a quadratic space.
Michel Petitjean
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Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra [PDF]
Advances in Applied Clifford Algebras, 2021 We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat duality in PGA. This leads to unification of PGA and CGA objects which is important especially for software implementation and symbolic calculations.
Jaroslav Hrdina +3 more
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A Machine Proof System of Point Geometry Based on Coq
Mathematics, 2023 An important development in geometric algebra in recent years is the new system known as point geometry, which treats points as direct objects of operations and considerably simplifies the process of geometric reasoning.
Siran Lei +4 more
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GEOMETRIC ALGEBRAS AND EXTENSORS [PDF]
International Journal of Geometric Methods in Modern Physics, 2007 This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field.
Fernández, V. V. +2 more
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An approach to adaptive filtering with variable step size based on geometric algebra
IET Communications, 2022 Recently, adaptive filtering algorithms have attracted much more attention in the field of signal processing. By studying the shortcoming of the traditional real‐valued fixed step size adaptive filtering algorithm, this paper proposed the novel approach ...
Haiquan Wang +3 more
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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.
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A multi‐channel geometric algebra residual network for traffic data prediction
IET Intelligent Transport Systems, 2022 Traffic data prediction offers a significant way to evaluate the future traffic congestion status; many deep learning based approaches have been widely applied in this field. Most current methods only consider short‐term traffic data forecasting; however,
Di Zang +6 more
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IEEE Access, 2020 With the increasing demand for multidimensional data processing, Geometric algebra (GA) has attracted more and more attention in the field of geographical information systems.
Uzair Aslam Bhatti +8 more
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Geometric-algebra affine projection adaptive filter
EURASIP Journal on Advances in Signal Processing, 2021 Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine projection algorithm (APA) in the GA domain to provide fast convergence against hypercomplex ...
Yuetao Ren, Yongfeng Zhi, Jun Zhang
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Aplikasi Aljabar Geometris Pada Teori Elektrodinamika Klasik
Jurnal Fourier, 2012 In this paper geometric algebra and its aplication in the theory of classical electrodynamic will be studied. Geometric algebra provide many simplification and new insight in the theoretical formulation and physical aplication of theory.
Joko Purwanto
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