Elliptical motions have been defined by three different right-handed coordinate systems. The motion of these systems depends on the time parameter which has great importance in robotics. In particular, it is used a model robot arm manipulator to achieve high performance. Hence, we expressed some theorems and results concerning this elliptical motion. Besides, special cases discussed.

This paper defines a new sequence of finite dimensional algebras as quotients of the group algebras of the braid groups. This sequence depends on three homogeneous parameters and has a one-parameter family of Markov traces, and so gives a three parameter invariant of oriented links.

Many mathematical forms of utility functions have been considered in the economics and finance literature, although, as Xie (2000) has said, by far the most widely employed are those displaying constant relative risk aversion (CRRA). Xie pointed out the dangers implicit in an inappropriate assumption of CRRA and the desirability of more flexible utility functions permitting a greater range of r...