JOURNAL ARTICLE

Applications of Clifford ratios unaffected by the local Schwarz paradox.

  • Published In: Mathematical Methods in the Applied Sciences, 2024, v. 47, n. 14. P. 11321 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Roselli, Paolo 3 of 3

Abstract

We show that the gradient of a strongly differentiable function at a point is the limit of a single coordinate‐free Clifford quotient between a multidifference pseudo‐vector and a pseudo‐scalar, or of a sum of Clifford quotients between scalars (as numerators) and vectors (as denominators), both evaluated at the vertices of a same non‐degenerate simplex contracting to that point. Such result allows to fix an issue with a defective definition of pseudo‐scalar field in Sobczyck's simplicial calculus. Then, we provide some consequences and conjectures implied by the foregoing results. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Mathematical Methods in the Applied Sciences. 2024/09, Vol. 47, Issue 14, p11321
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0170-4214
  • DOI:10.1002/mma.9431
  • Accession Number:179110444
  • Copyright Statement:Copyright of Mathematical Methods in the Applied Sciences is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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