The solution of some persistent p : −q resonant center problems

The notion of p : −q resonant center was introduced recently and studied by several authors. In this paper we generalize the notion of a persistent center to a persistent p : −q resonant center and find conditions for existence of a persistent p : −q resonant center for several p : −q resonant systems with quadratic nonlinearities. To prove the sufficiency of the obtained conditions we use either the Darboux theory of integrability or look for a formal first integral of the required form or we use the method based on the blow-up transformation

HydroShare – A Case Study of the Application of Modern Software Engineering to a Large Distributed Federally-Funded Scientific Software Development Project

HydroShare is an online collaborative system under development to support the open sharing of hydrologic data, analytical tools, and computer models. With HydroShare, scientists can easily discover, access, and analyze hydrologic data and thereby enhance the production and reproducibility of hydrologic scientific results. HydroShare also takes advantage of emerging social media functionality to enable users to enhance information about and collaboration around hydrologic data and models. HydroShare is being developed by an interdisciplinary collaborative team of domain scientists, university software developers, and professional software engineers from ten institutions located across the United States. While the combination of non–co-located, diverse stakeholders presents communication and management challenges, the interdisciplinary nature of the team is integral to the project’s goal of improving scientific software development and capabilities in academia. This chapter describes the challenges faced and lessons learned with the development of HydroShare, as well as the approach to software development that the HydroShare team adopted on the basis of the lessons learned. The chapter closes with recommendations for the application of modern software engineering techniques to large, collaborative, scientific software development projects, similar to the National Science Foundation (NSF)–funded HydroShare, in order to promote the successful application of the approach described herein by other teams for other projects

Towards a Generalization of Fulton\u27s Intersection Multiplicity Algorithm

In this manuscript we generalize Fulton\u27s bivariate intersection multiplicity algorithm to a partial intersection multiplicity algorithm in the n-variate setting. We extend this generalization of Fulton\u27s algorithm to work at any point, rational or not, using the theory of regular chains. We implement these algorithms in Maple and provide experimental testing. The results indicate the proposed algorithm often outperforms the existing standard basis-free intersection multiplicity algorithm in Maple, typically by one to two orders of magnitude. Moreover, we also provide some examples where the proposed algorithm outperforms intersection multiplicity algorithms which rely on standard bases, indicating the proposed algorithm is a viable alternative as a standard basis-free intersection multiplicity algorithm