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包括工作站，网络硬件以及编程和象征性代数软件的计算机设备，该设备将致力于支持数学科学中的研究。 该设备将用于多个研究项目，包括：（1）波浪现象的研究，与非线性流体动力学中自由表面问题相关的奇异积分的数值计算，线性波的散射频率以及非线性分散波的不稳定溶液； （2）数字理论和算术几何形状的各种问题，例如Weierstrass点的算术特性，P-Adic动力学系统以及由此类系统的固定点产生的磁场，椭圆曲线上的规范高度在数字字段上以及K3表面的Dioophantine几何形状； （3）边界价值问题和椭圆差分运算符的特征值问题。