Results 61 to 70 of about 251 (170)

Introduction to Clifford's Geometric Algebra

, 2013
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing, tracking, geographic information systems and neural computing.
openaire   +2 more sources

Transient Hydrology in Amazonis Planitia (Mars) in the Aftermath of the Tooting Impact

Journal of Geophysical Research: Planets, Volume 130, Issue 11, November 2025.
Abstract Hydrological flows generated by meteoroid impact are still largely unexplored on Mars and may also have implications for Earth. We reconstructed the hydrological sequence initiated on Mars by a less than 3 Ma old meteoroid impact that formed the 28 km‐wide Tooting crater on Amazonis Planitia, an ice‐bearing region.
Fabio Vittorio De Blasio, Andrea Caccia, Giovanni Battista Crosta   +2 more
wiley   +1 more source

Square Root of a Multivector of Clifford Algebras in 3D: A Game with Signs

Mathematics
An algorithm is presented to extract the square root from a multivector (MV) in real Clifford algebras Clp,q, where n=p+q≤3, in radicals. It is shown that in Cl3,0, Cl1,2, and Cl0,3 algebras, there are up to four isolated square roots in a case of the ...
Arturas Acus, Adolfas Dargys
doaj   +1 more source

Clifford-based spectral action and renormalization group analysis of the gauge couplings

European Physical Journal C: Particles and Fields, 2019
The Spectral Action Principle in noncommutative geometry derives the actions of the Standard Model and General Relativity (along with several other gravitational terms) by reconciling them in a geometric setting, and hence offers an explanation for their
Ufuk Aydemir
doaj   +1 more source

Advanced Graph Neural Networks for Smart Mining: A Systematic Literature Review of Equivariant, Topological, Symplectic, and Generative Models

Mathematics
The transition of the mining industry towards Industry 5.0 demands predictive models capable of strictly adhering to physical laws and modeling complex, non-Euclidean geometries—capabilities often lacking in standard graph neural networks.
Luis Rojas, Lorena Jorquera, José Garcia   +2 more
doaj   +1 more source

A Study of LFT Embeddings in the Second Order Clifford Algebra Cl(R²,º)

IEEE Access
Knowledge graph embedding models represent entities as vectors in continuous spaces and their relations by geometric transformations, mainly translation, and rotation.
Kossi Amouzouvi, Sahar Vahdati, Bowen Song, Bernard O. Bainson, Nur A. Zarin Nishat, Jens Lehmann   +5 more
doaj   +1 more source

On the Continuity Equation in Space–Time Algebra: Multivector Waves, Energy–Momentum Vectors, Diffusion, and a Derivation of Maxwell Equations

Mathematics
Historically and to date, the continuity equation (C.E.) has served as a consistency criterion for the development of physical theories. In this paper, we study the C.E. employing the mathematical framework of space–time algebra (STA), showing how common
Manuel Beato Vásquez, Melvin Arias Polanco   +1 more
doaj   +1 more source

Elastic Curves and Euler–Bernoulli Constrained Beams from the Perspective of Geometric Algebra

Mathematics
Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the formalism of ...
Dimiter Prodanov
doaj   +1 more source

Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras

Advances in Applied Clifford Algebras
33 ...
Ekaterina Filimoshina, Dmitry Shirokov
openaire   +2 more sources

A representation of twistors within geometric (Clifford) algebra

, 2006
33 pages, 7 figures.
Arcaute, Elsa, Lasenby, Anthony, Doran, Chris   +2 more
openaire   +2 more sources