Mathematical Sciences: Rigidity

R·康奈利打算研究刚性结构理论中的一些基本问题。典型的主题包括最小布线，自应力和大风图，一般的整体刚度，以及某些对称“张弦梁”的预应力稳定性。一个已被证明出奇有用的基本概念是与张拉整体框架的自应力相关的能量形式。它的阶数、指数和正定性都与重要的刚性性质有关，在未来应该被证明是有用的。康奈利还计划研究某些包装和覆盖问题，特别是与刚性有关的问题。由刚性杆组成的框架或由拉索加固的此类框架的刚性所依据的数学理论令人惊讶地服从于一般原则的分析，并且具有明显的实际意义。打包和覆盖问题也支持丰富的理论，并且已经被发现与纠错码的设计等相关。

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.