Acquisition of Mathematical Sciences Research Equipment

本项目是数学科学项目科学计算研究设备资助项目下的设备资助项目。该项目涉及购买专门用于支持数学科学研究的专用设备。一般来说，这种设备是几个研究项目共同需要的，很难单独用于一个项目。这项由国家科学基金会提供的研究设备支持与制造商提供的设备折扣和贡献以及提交机构的大量费用分摊相结合。这个项目是大学、工业和政府合作支持数学科学基础研究的一个很好的例子。该设备将用于支持以下研究：(1)利用MACSYMA、MACAULY、BMDP和SPSSx研究有理平面曲线的数值不变量之间的关系；(2)用图形方法研究不变二次微分复维族的参数空间；(3)研究全函数和亚纯函数的Julia集以及Kleinian群的稳定集。(4)研究涉及正交多项式的测度与递归系数之间的关系。这些项目涉及高速多精度算法、大内存需求和人工智能。

This project is an equipment grant under the activity Grants For Scientific Computing Research Equipment For The Mathematical Sciences program. The project involves the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required jointly by several research projects and would be difficult to justify on one project alone. This research equipment support from the National Science Foundation is coupled with discounts and contributions of equipment from manufacturers and significant cost-sharing from the submitting institution. This project provides a good example of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. This equipment will be utilized to support the following research: (1) MACSYMA, MACAULY, BMDP, and SPSSx will be used to study the relationship between numerical invariants of rational plane curves, (2) parameter spaces of complex dimensional families of invariant quadratic differentials will be examined graphically, (3) Julia sets of entire and meromorphic functions and stable sets of Kleinian groups will be examined, and (4) the connection between measures and recurrence coefficients involving orthogonal polynomials will be studied. The projects involve high speed multiple precision arithmetic, large memory requirements, and artificial intelligence.