Identifying Half-Twists Using Randomized Algorithm Methods

Since the braid group was discovered by E. Artin, the question of its conjugacy problem has been solved by Garside and Birman, Ko and Lee. However, the solutions given thus far are difficult to compute with a computer, since the number of operations needed is extremely large. Meanwhile, random algorithms used to solve difficult problems such as primality of a number were developed, and the random practical methods have become an important tool. We give a random algorithm, along with a conjecture of how to improve its convergence speed, in order to identify elements in the braid group, which are conjugated to its generators for a given power. These elements of the braid group, the half-twists, are important in themselves, as they are the key players in some geometrical and algebraical methods, the building blocks of quasipositive braids and they construct endless sets of generators for the group.Comment: 18 pages, 4 Postscript figures; Last proof read corrections before printing - Paper accepted for publicatio

Investigation of a hopping transporter concept for lunar exploration

Performance and dynamic characteristics determined for hopping transporter for lunar exploratio

Executive Compensation: Six Questions that Need Answering

In this article, we focus on how recent research advances can be used to address the following six questions: (1) How much does executive compensation cost the firm? (2) How much is executive compensation worth to the recipient? (3) How well does executive compensation work? (4) What are the effects of executive compensation? (5) How much executive compensation is enough? (6) Could executive compensation be improved? We stress the formal link between executive pay and performance that is provided by stock options and equivalent forms of long term compensation. We compare executive compensation in 12 OECD countries for the period from 1984-1996. There are good reasons why the answers to the first two questions are different. Executive compensation research should be very careful to distinguish the concepts of employer cost and the value to the executive. Agency theory remains the only viable candidate for answering the question about how executive compensation works but the empirical research to date cannot explain very much about the structure of the optimal contract. For this reason, it is also hard to answer the questions about the effects of executive compensation and the adequacy of the amounts of executive compensation, although it is clear that companies can provide both too little and too much contingent compensation, in the context of agency theory. We suggest two fertile areas for research regarding the improvement of executive compensation.

Spacecraft control/flexible structures interaction study

An initial study to begin development of a flight experiment to measure spacecraft control/flexible structure interactions was completed. The approach consisted of developing the equations of motion for a vehicle possessing a flexible solar array, then linearizing about some nominal motion of the craft. A set of solutions is assumed for array deflection using a continuous normal mode method and important parameters are identified. Interrelationships between these parameters, measurement techniques, and input requirements are discussed which assure minimization of special vehicle maneuvers and optimization of data to be obtained during the normal flight sequence. Limited consideration is given to flight data retrieval and processing techniques as correlated with the requirements imposed by the measurement system. Results indicate that inflight measurement of the bending and torsional mode shapes and respective frequencies, and damping ratios, is necessary. Other parameters may be measured from design data