Physical Sciences and Mathematics Commons^™

Distinct Products Of Triples In Finite Groups, Curtis Z. Mitchell

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let D_i(G) be the proportion of triples ( x , y , z ) of elements in G such that the cardinality of { xyz , xzy , yxz, yzx , zxy , zyx } is i. In this paper we show that:

i) The average value of D_i is either 1 or at least 53/32.

ii) D₂= 0 ==> D₃ = D₄ = D₅ = D₆ = 0;

iii) D₃= 0 ==> D₄ = D₅ = 0

An Inverse Problem In Thermal Language, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring of the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has of data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Robot Space Coordinate Representation Of Objects In Euclidean Space, Justin Gallagher

Mathematical Sciences Technical Reports (MSTR)

Robot motion control strategies generally center around trajectory planning schemes which are point-to-point. This paper explores the problem of planning robot trajectories which sweep an area in a two-link robot's work space. A diffeomorphism which transforms the linear coordinates of Euclidean space to the non-linear angular coordinates which represent the displacements of the joint motors is developed. It is used to determine the distortion of an object's area at different locations in the robot's work space and for different robot link length geometries. Study of such distortions may lead to an optimization scheme by which the placement of the object …