Mathematical Sciences: Computations in Mathematical Research

夏威夷大学数学系将购买专门用于支持数学科学研究的计算机设备和软件。该设备将用于几个研究项目，特别包括：函数的零点的微分和分布；格子理论；一阶逻辑的学习、推广和模型构建；常微分方程式和偏微分方程式的符号和数值分析。第一个项目涉及多项式的零点分布和某些其他函数的微分的影响。涉及几何映射性质的新技术将被用来研究几个著名的猜想。第二个项目将利用自由和有限表示格的最新进展来研究格论中尚未解决的问题，包括求解自由格中的方程和寻找有限生成格簇的覆盖。第三个项目将研究机器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范式和自然几何结构。

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.