We perform the group classification of a bond-pricing partial differential equation of mathematical finance to discover the combinations of arbitrary parameters that allow the partial differential equation to admit a nontrivial symmetry Lie algebra. As a result of the group classification we propose "natural" values for the arbitrary parameters in the partial differential equation, some of which validate the choices of parameters in such classical models as that of Vasicek and Cox-Ingersoll-Ross. For each set of these natural parameter values we compute the admitted Lie point symmetries, identify the corresponding symmetry Lie algebra and solve the partial differential equation.

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AMQP (Advanced Message Queuing Protocol) was born out of my own experience and frustrations in developing front-and back-office processing systems at investment banks. It seemed to me that we were living in integration Groundhog Day-the same problems of connecting systems together would crop up with depressing regularity. Each time the same discussions about which products to use would happen, and each time the architecture of some system would be curtailed to allow for the fact that the chosen middleware was reassuringly expensive. From 1996 through to 2003 I was waiting for the solution to this obvious requirement to materialize as a standard, and thereby become a commodity. But that failed to happen, and I grew tired of waiting. Consequently, AMQP was created and had its first mission-critical deployment to production in mid-2006. That project paid for itself with its first deployment, serves 2,000 users, and processes 300 million messages per day. This article sets out the motivations, capabilities, and credentials of AMQP and offers it as a practical solution for a standards-based messaging infrastructure. AMQP is a binary wire protocol and well-defined set of behaviors for transmitting application messages between systems using a combination of store-and-forward, publish-and-subscribe, and other techniques. 1 I use the term application messages to distinguish AMQP from instant messaging or other forms of end-user messaging. AMQP addresses the scenario where there is likely to be some economic impact if a message is lost, does not arrive in a timely manner, or is improperly processed. The protocol is designed to be usable from different programming environments, operating systems, and hardware devices, as well as making high-performance implementations possible on various network transports including TCP, SCTP (Stream Control Transmission Protocol), and InfiniBand.

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