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Full-Text Articles in Physical Sciences and Mathematics
A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell
A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell
Electronic Theses and Dissertations
The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.
Concerning The Construction Of Four-Bar Linkages And Their Topological Configuration-Spaces, Peter K. Servatius
Concerning The Construction Of Four-Bar Linkages And Their Topological Configuration-Spaces, Peter K. Servatius
Senior Projects Spring 2018
For a given linkage with one degree of freedom we can analyze the coupler curve created by any selected tracer point in relation to a driver link. The Watt Engine is a four-bar linkage constructed such that the tracer point draws an approximate straight line along a section of the coupler curve. We will explore the family of linkages that are created using Watt's parameters, along with linkages designed by other inventors; looking at methodologies of creating a linkage and the defining what we mean by approximate straight-line motion. Ultimately we will be creating our own linkage using what we …
Hyperplanes Equipartition With Cascading Makeev, Jialin Zhang
Hyperplanes Equipartition With Cascading Makeev, Jialin Zhang
Senior Projects Spring 2018
Given a finite number of masses in the Euclidean space, one could ask is it possible to equipartition these masses into equal parts. Fixing the collection of masses, and the amount of hyperplanes, the equipartition-ability depends on the dimension, and there exists a dimension of such equipartition is possible. In this paper, topology and combinatorics method are used for estimating the lower bound and upper bound of the dimension. In particular, we are looking equipartition problem together with Cascading Makeev Constrain.