Integrated voice/data protocols for satellite channels

Several integrated voice/data protocols for satellite channels are studied. The system consists of two types of traffic: voice calls which are blocked-calls-cleared and the data packets which may be stored when no channel is available. The voice calls are operated under a demand assignment protocol. Three different data protocols for data packets are introduced. Under Random Access Data (RAD), the Aloha random access scheme is used. Due to the nature of random access, the channel utilization is low. Under Demand Assignment Data (DAD), a demand assignment protocol is used to improve channel utilization. Since a satellite channel has long propagation delay, DAD may perform worse than RAD. The two protocols are combined to obtain a new protocol called Hybrid Data (HD). The proposed protocols are fully distributed and no central controller is required. Numerical results show that HD enjoys a lower delay than DAD and provides a much higher channel capacity than RAD. The effects of fixed and movable boundaries are compared in partitioning the total frequency band to voice and data users

Subalgebras of \gc_N and Jacobi polynomials

We classify the subalgebras of the general Lie conformal algebra \gc_N that act irreducibly on \C[\partial]^N and that are normalized by the $\operatorname{sl}_2$--part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials $P_n^{(-\sigma,\sigma)}$, \sigma\in\C. The connection goes both ways -- we use in our classification some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.Comment: 35 pages, LaTe

Closed form asymptotics for local volatility models

We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general closed-form approximate solutions for both the pricing kernel and derivative price. A bootstrap scheme allows us to extend our method to large time. We also perform analytic as well as a numerical error analysis, and compare our results to other known methods.Comment: 30 pages, 10 figure