The quality of indoor environment depends upon combined effects of architectural constructive elements’ functions (for example: daylight level, thermal comfort, acoustical comfort, load bearing capacity, aesthetic value, price, etc.). Those functions at the same time are defined by their parameters (geometrical parameters of the building elements, parameters of the building materials, etc.). We...

This lecture continues our discussion of the constructive reals and intuitionistic reals. We look at other options beyond the approach taken in the book Constructive Analysis by Bishop and Bridges which is a resource for this course available on the PRL project page (www.nuprl.org). Another resource is the calculator for the constructive reals provided in Nuprl as a public resource. It uses alg...

We introduce a constructive model for algebraic tori based on reduced divisors on singular curves. By using a singular hyperelliptic model, this provides an alternative representation, and computational model, for groups of rational points on an algebraic tori [4]. We obtain a represention of elements on certain tori of dimension r in compact representation using r +1 elements. By embedding the...

Kitaev et al. (2019) described how to shorten universal words for permutations, length n!+n−1−i(n−1) any i∈[(n−2)!], by introducing incomparable elements. They conjectured that it is also possible use elements cycles permutations n!−i(n−1) i∈[(n−2)!]. In this note we prove their conjecture. The proof constructive, and, on the way, show a new method constructing permutations.