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We construct a generalisation of Bakry–Émery curvature to prove twisted intertwining relations for Markov semigroups. These relations are applied to Brascamp–Lieb type inequalities and spectral gap results. It extends the method of Arnaudon, Bonnefont and Joulin, to Riemannian manifolds and to a wider class of twists. These results are illustrated with several examples. [ABSTRACT FROM AUTHOR]

This article examines a way to define left and right versions of the large class of “ ( b , c ) -inverses” introduced by the writer in (2012) [6] : Given any semigroup S and any a , b , c ∈ S , then a is called left ( b , c ) - invertible if b ∈ S c a b , and x ∈ S is called a left ( b , c ) - inverse of a if x ∈ S c and x a b = b , and dually c ∈ c a b S , z ∈ S b and c a z = z for right ( b , c ) -inverses z of a . It is shown that left and right ( b , c ) -invertibility of a together imply ( b , c ) -invertibility, in which case every left ( b , c ) -inverse of a is also a right ( b , c ) -inverse, and conversely, and then all left or right ( b , c ) -inverses of a coincide. When b = c (e.g. for the Moore-Penrose inverse or for the pseudo-inverse of the author) left ( b , b ) -invertibility coincides with right ( b , b ) -invertibility in every strongly π -regular semigroup. A fundamental result of Vaserstein and Goodearl, which guarantees the left-right symmetry of Bass's property of stable range 1, is extended from two-sided inverses to left or right inverses, and, for central b , to left or right ( b , b ) -inverses. [ABSTRACT FROM AUTHOR]

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation. [ABSTRACT FROM AUTHOR]

Abstract: Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or ‘hockles’ are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively, by the dynamic conversion of twist (Tw) to writhe (Wr). [Copyright &y& Elsevier]