A singular multi-dimensional piston problem in compressible flow

AbstractThis paper concerns the multi-dimensional piston problem, which is a special initial boundary value problem of multi-dimensional unsteady potential flow equation. The problem is defined in a domain bounded by two conical surfaces, one of them is shock, whose location is also to be determined. By introducing self-similar coordinates, the problem can be reduced to a free boundary value problem of an elliptic equation. The existence of the problem is proved by using partial hodograph transformation and nonlinear alternating iteration. The result also shows the stability of the structure of shock front in symmetric case under small perturbation

Competitive service market: modeling, storage and management

In order to capture the business dynamics underlying SOA-based service systems, we propose and formalize the concept of a competitive service market (CSM). A CSM is composed of a set of composite service providers, each managing a collection of atomic service providers. With the help of service composition protocol, composite service providers are able to invoke atomic services and aggregate them into value-added composite services for servicing various types of customers\u27 requests. Centering around the setting of a competitive service market, our research is separated into three parts: 1. Aiming to support the quantitative-based decision processes of different market players, we construct stochastic models to conduct performance analysis at various levels spanning vertically on the structural hierarchy of the service market. 2. In the context of requirements analysis, we classify the concept of service and service instance in terms of their respective functional and non-functional features. Hereafter, we identify the related storage issues and propose a counting Bloom filter-based hybrid storage architecture for the service registry design underlying the service market. A feature-based service discovery protocol is developed to demonstrate the usefulness of this design. 3. The business relationship between different market players are typically framed through the service level agreements (SLAs), which specify the attributes of QoS-based metrics and service costs for the realized service provisioning. SLAs constitute the backbone structure for managing the CSM. We identify several SLA design patterns in terms of different business scenarios that can occur in the life cycle of a service market. Against each pattern we study the corresponding SLA design scheme that can meet its unique requirements. In addition, we systematically investigate the application of Bayes estimator in these schemes, since the knowledge of their negotiation counterpart or market competitors is essential for reaching the goal of utility optimization. At the end, we cast the hybrid SLA design framework into a stochastic model that allows decision makers to obtain evaluations of performance of interest