Mathematical Sciences: Computations in Mathematical Research

夏威夷大学数学系将购买计算机设备和软件，专门用于支持数学科学的研究。这些设备将用于若干研究项目，特别是：函数的微分和零的分布；晶格理论;一阶逻辑的学习、泛化与模型构建常微分方程和偏微分方程的符号和数值分析。第一个项目是关于多项式和某些其他函数的零点分布的微分效应。涉及几何映射性质的新技术将用于研究几个众所周知的猜想。第二个项目将利用自由晶格和有限晶格的最新进展来研究晶格理论中未解决的问题，包括在自由晶格中求解方程和寻找有限生成晶格变体的覆盖。第三个项目将研究力学定理证明的各个方面。第四个项目将寻找与控制系统相关的标准形式和自然几何结构。

The Department of Mathematics at the University of Hawaii will purchase computer equipment and software which will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular: Differentiation and the Distribution of Zeros of Functions; Lattice Theory; Learning, Generalization and Model Construction in First-Order Logic; and Symbolic and Numerical Analysis of Ordinary and Partial Differential Equations. The first project is concerned with the effect of differentiation of the distribution of zeros of polynomials and certain other functions. New techniques involving geometric mapping properties will be employed to study several well-- known conjectures. The second project will use recent advances in free and finitely presented lattices to study unsolved problems in lattice theory, including solving equations in free lattices and finding the covers of finitely generated lattice varieties. The third project will study various aspects of mechanical theorem proving. The fourth project will search for normal forms and natural geometric structures associated with control systems.