Following the landmark 2015 United Nations Paris Agreement, a growing number of countries are committing to transition net-zero emissions. Carbon capture and storage (CCS) has been consistently heralded directly address emissions from energy industrial sectors forms significant component plans reach net-zero. However, despite critical importance technology substantial research development date,...

Let A be the arrangement of hyperplanes consisting of the re ecting hyperplanes for the root system An 1. Let B = B(q) be the Varchenko matrix for this arrangement with all hyperplane parameters equal to q. We show that B is the matri x with rows and columns indexed by permutations with ; entry equal to qi( 1) where i( ) is the number of inversions of . Equivalently B is the matrix for left mul...

Every function on a nite residue class ring D=I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a nite commutative local ring with maximal ideal P of nilpotency N satisfying for all a; b 2 R, if ab 2 Pn then a 2 P k , b 2 P j with k + j min(n;N), we determine the number of functions (as...

This article investigates the geometric and algebraic foundations of exponential product expansions in nonlinear control. A survey of historic developments in geometric control theory on one side, and algebraic combinatorics on the other side exhibits parallel developments and demonstrates how respective ndings translate into powerful tools on the other side. Chronological algebras are shown to...