Mathematical Sciences: Rigidity

R.康奈利打算研究一些基本问题， 刚性结构理论 典型的受试者包括 最小布线、自应力和Gale图，通用 整体刚度和预应力稳定性的某些 对称的“张量网格”。 一个基本概念已经证明 令人惊讶地有用的是， 张拉整体框架的自应力。 它的排名、指数和 正定性都与重要刚性有关 这些特性在将来会证明是有用的。 康奈利 还计划研究某些包装和覆盖问题， 特别是与刚性相关的那些。 数学理论下的刚性 由刚性杆组成的框架或这种框架 由拉索加固， 既有一般原理分析，又有明显的实用性分析， 本案无关 包装和覆盖问题也支持丰富的 理论，并已被发现相关的设计 纠错码等等。

R. Connelly intends to study some fundamental problems in the theory of rigid structures. Typical subjects include minimal cabling, self-stresses and Gale diagrams, generic global rigidity, and the pre-stress stability of certain symmetric "tensegrids". A basic concept that has proved surprisingly useful is the energy form associated to a self-stress for a tensegrity framework. Its rank, index, and positive definiteness are all related to important rigidity properties and should prove useful in the future. Connelly also plans to study certain packing and covering problems, particularly those related to rigidity. The mathematical theory underlying the rigidity of frameworks composed of rigid rods or of such frameworks reinforced by bracing cables is surprisingly amenable to analysis by general principles as well as of obvious practical relevance. Packing and covering problems also support a rich theory and have been found relevant to the design of error-correcting codes among other things.