The Reanalysis Method of Weighted Generalized Inverse for Topological Modification of Plane Structures

Using a weighed decomposition of the stiffness matrix and the weighed generalized inverse theory, a reanalysis method is presented for the topological modification of plane structures, and a set of formulae of elementary topology change are obtained. These formulae are explicit one and using them one can reanalyze the modified structures in topological optimal design. Finally an example is given to verify the valid of this method.

Elementary topology and universal computation

This paper attempts to define a general framework for computability on an arbitrary topological space X . The elements of X are taken as primitives in this approach—also for the coding of functions — and, except when X = N, the natural numbers are not used directly.

Cauchy completeness in elementary logic

The inverse of the distance between two structures≢of finite typeτis naturally measured by the smallest integerqsuch that a sentence of quantifier rankq− 1 is satisfied bybut not by. In this way the space Strτof structures of typeτis equipped with a pseudometric. The induced topology coincides with the elementary topology of Strτ. Using the rudiments of the theory of uniform spaces, in this elementary note we prove the convergence of every Cauchy net of structures, for any typeτ.

BRAID GROUP REPRESENTATIONS ASSOCIATED WITH ${\mathfrak{sl}}_m$

It has been seen elsewhere how elementary topology may be used to construct representations of the Iwahori-Hecke algebra associated with two-row Young diagrams, and how these constructions are related to the production of the same representations from the monodromy of n-point correlation functions in the work of Tsuchiya & Kanie and to the construction of the one-variable Jones polynomial. This paper investigates the extension of these results to representations associated with arbitrary multi-row Young diagrams and a functorial description of the two-variable Jones polynomial of links in S3.