Clifford algebra and discretizable distance geometry
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DOI: 10.1002/mma.4422
Abstract: Protein structure calculations using nuclear magnetic resonance (NMR) experiments are one of the most important applications of distance geometry. The chemistry of proteins and the NMR data allow us to define an atomic order, such… read more here.
Keywords: discretizable distance; geometry; distance geometry; clifford algebra ... See more keywords
Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials
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DOI: 10.1007/s00006-015-0596-z
Abstract: Recently, systems of Clifford algebra-valued orthogonal polynomials have been studied from different points of view. We prove in this paper that for their building blocks there exist some three-term recurrence relations, similar to that for… read more here.
Keywords: valued orthogonal; clifford; clifford algebra; orthogonal polynomials ... See more keywords
Using the Symmetries of the Cube and Tetrahedron as a Vehicle for Introducing Some Clifford Algebra to High School Students and Undergraduate College Students
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DOI: 10.1007/s00006-015-0607-0
Abstract: This paper outlines how Clifford Algebra can be presented to high school or college students to deal with the symmetries of the Platonic solids. I concentrate on the cube but all five solids are discussed. read more here.
Keywords: clifford algebra; high school; college students;
On Complex Representations of Clifford Algebra
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DOI: 10.1007/s00006-018-0930-3
Abstract: We show that complex representations of Clifford algebra can always be reduced either to a real or to a quaternionic algebra depending on signature of complex space thus showing that spinors are unavoidably either real… read more here.
Keywords: complex representations; representations clifford; algebra; clifford algebra ... See more keywords
Two-State Quantum Systems Revisited: A Clifford Algebra Approach
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DOI: 10.1007/s00006-020-01116-1
Abstract: We revisit the topic of two-state quantum systems using the Clifford Algebra in three dimensions $$Cl_3$$ . In this description, both the quantum states and Hermitian operators are written as elements of $$Cl_3$$ . By… read more here.
Keywords: two state; state quantum; clifford algebra; approach ... See more keywords
Clifford Algebra-Valued Segal–Bargmann Transform and Taylor Isomorphism
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DOI: 10.1007/s00006-021-01171-2
Abstract: Classical Segal-Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and the configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued functions. We establish the unitary isomorphisms… read more here.
Keywords: clifford algebra; segal bargmann; space; algebra valued ... See more keywords
The Clifford Algebra of Physical Space and Elko Spinors
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DOI: 10.1007/s10773-017-3591-4
Abstract: Elko spinors are eigenspinors of the charge conjugation operator. In this work we use the Clifford algebra of the physical space in order to formulate the theory of Elko spinors and use a procedure analog… read more here.
Keywords: algebra physical; elko spinors; clifford algebra; equation ... See more keywords
Hardy spaces of Clifford algebra-valued monogenic functions in exterior domains and a higher dimensional version of Cauchy’s vanishing theorem
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DOI: 10.1080/17476933.2016.1250915
Abstract: We introduce and study Hardy spaces consisting of Clifford algebra-valued functions annihilated by perturbed Dirac operators in exterior uniformly rectifiable (UR) domains, and which radiate at infinity. In this context, we establish a higher dimensional… read more here.
Keywords: clifford algebra; version; hardy spaces; algebra valued ... See more keywords
Support vector machine skin lesion classification in Clifford algebra subspaces
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DOI: 10.21136/am.2019.0292-18
Abstract: The present study develops the Clifford algebra Cl5,0 within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV… read more here.
Keywords: machine; vector; classification; support vector ... See more keywords