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Applications of Clifford ratios unaffected by the local Schwarz paradox
  • Paolo Roselli
Paolo Roselli
Universita degli Studi di Roma Tor Vergata Dipartimento di Matematica

Corresponding Author:[email protected]

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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 multi-difference 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 a 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.
28 Nov 2022Submitted to Mathematical Methods in the Applied Sciences
28 Nov 2022Submission Checks Completed
28 Nov 2022Assigned to Editor
09 Dec 2022Review(s) Completed, Editorial Evaluation Pending
09 Dec 2022Reviewer(s) Assigned
21 Mar 2023Editorial Decision: Revise Major
30 Mar 20231st Revision Received
05 Apr 2023Submission Checks Completed
05 Apr 2023Assigned to Editor
05 Apr 2023Review(s) Completed, Editorial Evaluation Pending
05 Apr 2023Reviewer(s) Assigned
14 May 2023Editorial Decision: Accept