Untitled Research Article: Difference between revisions
Created page with "Title: Untitled Research Article Research Question: How can we verify the termination and error-freedom of logic programs with block declarations? Methodology: The researchers presented two approaches to verify the termination and error-freedom of logic programs with block declarations. The first approach aimed to eliminate the problem of speculative output bindings. The second approach was based on identifying predicates that do not require the textual position of an..." |
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Title: Untitled Research Article | Title: Untitled Research Article | ||
Abstract: This research article explores the development of a curve on a plane, specifically focusing on the intersection of a plane with a polytope. The main result is that slice curves always develop to simple curves, i.e., they do not self-intersect. The authors achieve this by generalizing Cauchy's arm lemma, allowing for nonconvex "openings" of a planar convex chain. This generalization is crucial in proving that the hand cannot enter the forbidden disk D(a), ensuring that the curve develops without self-intersection. | |||
Research Question: How do slice curves develop on a plane without self-intersection? | |||
Methodology: The authors employ a generalization of Cauchy's arm lemma, which permits opening of the angles beyond π. This generalization is used to prove that slice curves always develop to simple curves, preventing self-intersection. | |||
Results: The main result of this paper is that slice curves always develop to simple curves, i.e., they do not self-intersect. This is achieved by proving that the hand cannot enter the forbidden disk D(a) in any reconfiguration of the chain, ensuring that the curve develops without self-intersection. | |||
Link to Article: https://arxiv.org/abs/ | Implications: This research has significant implications for the field of geometry, particularly in the study of curve development and self-intersection. The generalization of Cauchy's arm lemma used in this study can be applied to other areas of mathematics and may lead to further advancements in the field. | ||
Conclusion: In conclusion, the authors have successfully generalized Cauchy's arm lemma to permit nonconvex "openings" of a planar convex chain. This generalization has been used to prove that slice curves always develop to simple curves, preventing self-intersection. This research has significant implications for the field of geometry and may lead to further advancements in the study of curve development and self-intersection. | |||
Link to Article: https://arxiv.org/abs/0006035v3 | |||
Authors: | Authors: | ||
arXiv ID: | arXiv ID: 0006035v3 | ||
Revision as of 00:41, 24 December 2023
Title: Untitled Research Article
Abstract: This research article explores the development of a curve on a plane, specifically focusing on the intersection of a plane with a polytope. The main result is that slice curves always develop to simple curves, i.e., they do not self-intersect. The authors achieve this by generalizing Cauchy's arm lemma, allowing for nonconvex "openings" of a planar convex chain. This generalization is crucial in proving that the hand cannot enter the forbidden disk D(a), ensuring that the curve develops without self-intersection.
Research Question: How do slice curves develop on a plane without self-intersection?
Methodology: The authors employ a generalization of Cauchy's arm lemma, which permits opening of the angles beyond π. This generalization is used to prove that slice curves always develop to simple curves, preventing self-intersection.
Results: The main result of this paper is that slice curves always develop to simple curves, i.e., they do not self-intersect. This is achieved by proving that the hand cannot enter the forbidden disk D(a) in any reconfiguration of the chain, ensuring that the curve develops without self-intersection.
Implications: This research has significant implications for the field of geometry, particularly in the study of curve development and self-intersection. The generalization of Cauchy's arm lemma used in this study can be applied to other areas of mathematics and may lead to further advancements in the field.
Conclusion: In conclusion, the authors have successfully generalized Cauchy's arm lemma to permit nonconvex "openings" of a planar convex chain. This generalization has been used to prove that slice curves always develop to simple curves, preventing self-intersection. This research has significant implications for the field of geometry and may lead to further advancements in the study of curve development and self-intersection.
Link to Article: https://arxiv.org/abs/0006035v3 Authors: arXiv ID: 0006035v3