An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.

This paper aims to investigate properties of strictly involution binary relations, which are generalizations of the classical notions of binary relations. We study the concepts of involution spanning subsets and give some examples related to different involution binary relations. Moreover, the involution independence with code is also considered in this paper.

Permutative automorphisms of the Cuntz algebra O n are in bijection with a class permutations k elements, that called stable, and further partitioned by rank. In this work we mainly focus on stable cycles quadratic case (i.e., = 2 ). More precisely, such provide characterization rank one (so proving Conjecture 12.1 [3] ), exhibit closed formula for number r -cycles (valid all characterize enume...

Lactation is under homeostatic control, and sustained milk stasis or weaning leads to mammary gland involution. This transition is under the control of systemic and local factors. Of all the phases of mammary gland development, involution is the least well understood. Recent epidemiological observations suggest that involution events promote breast diseases, including breast cancer. This has re...

We introduce the effectual topological complexity (ETC) of a [Formula: see text]-space text]. This is text]-equivariant homotopy invariant sitting in between effective pair text] and (regular) orbit space study ETC for spheres surfaces with antipodal involution, obtaining full computation case torus. allows us to prove vanishing twice nontrivial obstruction responsible fact that Klein bottle In...

We classify surfaces of general type S with pg = q = 1 having an involution i such that S/i is non-ruled and the bicanonical map of S factors through the natural cover S → S/i. We prove that the minimal model of S/i is either a K3 surface or a surface of Kodaira dimension 1 (in this last case S has a genus 2 fibration). We also show that these cases do occur. In particular we construct a surfac...

We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation. This new approach relies on developing the theory of k-tableaux, and includes the introduction of a weight-permuting involution on these tableaux that generalizes the Bender-Knuth involution. This work lays the groundwork needed to prove that the set of k-Schur Li...

This paper considers Darboux transformations of a bispectral operator which preserve its bispectrality. A sufficient condition for this to occur is given, and applied to the case of generalized Airy operators of arbitrary order r > 1. As a result, the bispectrality of a large family of algebras of rank r is demonstrated. An involution on these algebras is exhibited which exchanges the role of s...

The involutory dimension, if it exists, of an involution poset P := (P,≤,′ ) is the minimum cardinality of a family of linear extensions of ≤, involutory with respect to ′, whose intersection is the ordering ≤. We show that the involutory dimension of an involution poset exists iff any pair of isotropic elements are orthogonal. Some characterizations of the involutory dimension of such posets a...