Mathematical Computation in Analysis and Number Theory

分析与数论中的数学计算

• 批准号: 9105220
• 负责人: Joseph Silverman
• 金额: $ 3.38万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105220&HistoricalAwards=false
• 关键词: Mathematical; Computation; Analysis; Number; Theory

The Department of Mathematics at Brown University will purchase computer equipment consisting of workstations, networking hardware, and programming and symbolic algebra software which will be dedicated to support research in the mathematical sciences. The equipment will be used for several research projects, including in particular: (1) the study of wave phenomena, the numerical computation of singular integrals related to free surface problems in non-linear fluid dynamics, the scattering frequency of linear waves, and the unstable solutions of nonlinear dispersive waves; (2) various problems in number theory and arithmetic geometry, such as arithmetic properties of Weierstrass points, p-adic dynamical systems and the fields generated by the fixed points of such systems, canonical heights on elliptic curves over number fields, and the Diophantine geometry of K3 surfaces; (3) boundary value problems and eigenvalue problems for elliptic differential operators.

布朗大学数学系将购买 计算机设备，包括工作站、网络 硬件，编程和符号代数软件， 将致力于支持数学研究， 以理工科为重 该设备将用于几项研究 项目，特别是包括：（1）波的研究 现象，奇异积分的数值计算 涉及非线性流体动力学中的自由表面问题， 线性波的散射频率，以及不稳定的 非线性色散波的解;（2） 数论和算术几何，如算术 Weierstrass点的性质，p-adic动力系统和 由这种系统的固定点产生的场， 数域上椭圆曲线的正则高， K3曲面的丢番图几何;（3）边值问题 椭圆型微分算子的特征值问题