Results 11 to 20 of about 236,452 (310)

An Analysis of the Quantum Penny Flip Game using Geometric Algebra [PDF]

Journal of the Physical Society of Japan, 2009
We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy.
Benjamin S. C., Cheon T., Doran C., Du J., Eisert J., Hestenes D., Hestenes D., Hestenes D., Ichikawa T., Ichikawa T., Iqbal A., Johnson N. F., Meyer D. A., Meyer D. A., Nielsen M. A., Piotrowski E. W., Rasmusen E., Shimamura J., Shimamura J., Vaidman L., van Enk S. J., Özdemir Ş. K., Özdemir Ş. K.   +22 more
core   +5 more sources

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.
V. V. FERNÁNDEZ, A. M. MOYA, W. A. RODRIGUES   +2 more
openalex   +5 more sources

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, Aleš Návrat, Petr Vašík, Leo Dorst   +3 more
openaire   +5 more sources

Geometric phases characterise operator algebras and missing information [PDF]

Journal of High Energy Physics, 2023
We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von Neumann algebras.
Souvik Banerjee, Moritz Dorband, Johanna Erdmenger, Anna-Lena Weigel   +3 more
doaj   +2 more sources

Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

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, Zhaoyuan Yu, Linwang Yuan, Zeeshan Zeeshan, Saqib Ali Nawaz, Mughair Bhatti, Anum Mehmood, Qurat Ul Ain, Luo Wen   +8 more
doaj   +3 more sources

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations [PDF]

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
Andronikos Paliathanasis, Sibusiso Moyo, P. G. L. Leach   +2 more
openalex   +2 more sources

Normed algebras and the geometric series test [PDF]

Surveys in Mathematics and its Applications, 2017
The purpose of this article is to survey a class of normed algebras that share many central features of Banach algebras, save for completeness. The likeness of these algebras to Banach algebras derives from the fact that the geometric series test is ...
Robert Kantrowitz, Michael M. Neumann
doaj   +1 more source

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
doaj   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This 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.
europepmc   +2 more sources

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, Hao Guan, Jianguo Jiang, Yu Zou, Yongsheng Rao   +4 more
doaj   +1 more source