Abstract: A reduced order model of a distributed time invariant system is produced by projecting system matrices onto smaller matrices, interpolating the matrices and placing into a state-space system. The system matrices are an internal representation of the distributed time invariant system which comprises a description of the system to be modeled, mainly, for example, its inputs and outputs. The method is applied to distributed systems and guarantees accuracy in complicated systems and produces well-behaved models appropriate for use in simulators and simulations.

Abstract: A Baccarat wagering method in which provision is made for placing a bet for a round of play to end in a tie between a player hand and a banker hand, wherein there are a plurality of different payment ratios for a successful tie bet, with each possible card total on which a tie can occur having a pre-defined payment ratio associated therewith. Also bets on the banker hand or player hand to win also have a plurality of different payment ratios for a winning bet, each possible card total on which a winning hand can occur having a pre-defined payment ratio associated therewith. Baccarat playing surfaces for carrying out these wagering methods are also disclosed.