Azizi, Tahmineh and Alali, Bacim and Kerr, Gabriel
(2020)
*A Detailed Study: Using Parametric Mathematical
Modeling to Develop a Geometric and Topological
Intuition for Molecular Knots.*
B P International.
ISBN 978-93-90431-07-6

## Abstract

Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in

different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space

which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have

been applied to synthetic molecular design. Mathematics and chemistry together can work to

determine, characterize and create knots which help to understand different molecular designs and

then forecast their physical features. In this study, we provide an introduction to the knot theory and its

topological concepts, and then we extend it to the context of chemistry. We present parametric

representations for several synthetic knots. The main goal of this paper is to develop a geometric and

topological intuition for molecular knots using parametric equations. Since parameterizations are nonunique;

there is more than one set of parametric equations to specify the same molecular knots. This

parametric representation can be used easily to express geometrically molecular knots and would be

helpful to find out more complicated molecular models. Parametric equations are convenient for

describing different synthetic molecular knots and can be considered as manifolds and algebraic

varieties of higher dimension. It is always possible to convert a set of parametric equations to a single

implicit equation through implicitization which can be done easily by eliminating the variable t from the

equations. This study brings more mathematical intuitions in studying the synthetic molecular knots

and will help chemists and biophysicists to discover more complicated properties of them.

Item Type: | Book |
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Subjects: | Eurolib Press > Mathematical Science |

Depositing User: | Managing Editor |

Date Deposited: | 10 Nov 2023 05:33 |

Last Modified: | 10 Nov 2023 05:33 |

URI: | http://info.submit4journal.com/id/eprint/3009 |