ar X iv : c ha o - dy n / 99 06 00 4 v 1 3 1 M ay 1 99 9 Lagrangian Reduction , the Euler – Poincaré Equations , and Semidirect Products

ar X iv : c ha o - dy n / 99 10 00 5 v 1 6 O ct 1 99 9 The Finite - Difference Analysis and Time Flow

. SG ] 1 5 Ju n 19 99 Discrete Lagrangian reduction , discrete Euler – Poincaré equations , and semidirect products

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on G×G, where G is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of an isotropy subgroup of a fixed element in the representation space of G. In this context the reduction of the discrete Euler–Lagrange equations is shown to lead to th...

ar X iv : m at h / 99 07 08 5 v 1 [ m at h . G R ] 1 3 Ju l 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS

ar X iv : m at h / 99 07 08 5 v 2 [ m at h . G R ] 1 7 D ec 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS

ar X iv : c ha o - dy n / 99 05 03 6 v 1 21 M ay 1 99 9 Restart Strategies and Internet Congestion

We recently presented a methodology for quantitatively reducing the risk and cost of executing electronic transactions in a bursty network environment such as the Internet. In the language of portfolio theory, time to complete a transaction and its variance replace the expected return and risk associated with a security, whereas restart times replace combinations of securities. While such a str...