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Start Over Search Limiters Academic (Peer-Reviewed) Journals Topic knot theory Journal plos one
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1. Geometric analysis of non-degenerate shifted-knots Bézier surfaces in Minkowski space.

Author

Bashir, Sadia and Ahmad, Daud

Subjects
MINKOWSKI space, GEOMETRIC analysis, COMPUTER graphics, MICROSOFT Surface (Computer), KNOT theory, COMPUTER engineering
Abstract

In this paper, we investigate the properties of timelike and spacelike shifted-knots Bézier surfaces in Minkowski space- E13. These surfaces are commonly used in mathematical models for surface formation in computer science for computer-aided geometric design and computer graphics, as well as in other fields of mathematics. Our objective is to analyze the characteristics of timelike and spacelike shifted-knots Bézier surfaces in Minkowski space- E13. To achieve this, we compute the fundamental coefficients of shifted-knots Bézier surfaces, including the Gauss-curvature, mean-curvature, and shape-operator of the surface. Furthermore, we present numerical examples of timelike and spacelike bi-quadratic (m = n = 2) and bi-cubic (m = n = 3) shifted-knots Bézier surfaces in Minkowski space- E13 to demonstrate the applicability of the technique in Minkowski space. [ABSTRACT FROM AUTHOR]

Published
2024
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2. The braid index of DNA double crossover polyhedral links

Author

Yuanan Diao and Xiao-Sheng Cheng

Subjects
Models, Molecular, Computer and Information Sciences, Molecular biology, Science, Mathematical properties, Plant Science, 010402 general chemistry, 01 natural sciences, Infographics, Polynomials, Biochemistry, Topology, Combinatorics, Polyhedron, Knot Theory, Braid, Genetics, Flower Anatomy, Mathematics, Multidisciplinary, 010405 organic chemistry, Data Visualization, Plant Anatomy, Double crossover, Chemical Compounds, Biology and Life Sciences, DNA structure, Graph theory, DNA, Graph, Hydrocarbons, 0104 chemical sciences, Knot theory, Nucleic acids, Macromolecular structure analysis, Chemistry, Petals, Algebra, Graph Theory, Physical Sciences, Nucleic Acid Conformation, Medicine, Graphs, Research Article
Abstract

In this paper, the authors study the mathematical properties of a class of alternating links called polyhedral links which have been used to model DNA polyhedra. The motivation of such studies is to provide guidance and aid in the research of the properties of certain DNA molecules. For example, such studies can provide characterizations of the structural complexity of DNA molecules. In an earlier work, Cheng and Jin studied the mathematical properties of such polyhedral links and were able to determine the braid index of a double crossover polyhedral link with 4 turn. However, the braid index of a double crossover polyhedral link with 4.5 turn remained an unsolved problem to this date, even though the graphs that admit the double crossover polyhedral links with 4.5 turn have been synthesized. In this paper, we provide a complete formulation of the braid index of a double crossover polyhedral link with an arbitrary turn number. Our approach is more general and it allows us to completely determine the braid indices for a much larger class of links. In the case of the double crossover polyhedral links, our formulation of the braid index is a simple formula based on a simpler graph used as a template to build the double crossover polyhedral links.

Published
2020