Given a monoid string rewriting system M , one way of obtaining a complete rewriting system for M is to use the classical Knuth-Bendix critical pairs completion algorithm. It is well known that this algorithm is equivalent to computing a noncommutative Gröbner basis for M . This article develops an alternative approach, using noncommutative involutive basis methods to obtain a complete involuti...

In this paper, we consider a non-posetal analogue of the notion of involutive quantale [MP92]; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order of tensoring. We study the coherence issues that inevitably result when passing from posets to categories; we also link our subject with other notions already in the literature, such as balanced mon...

Involutive bases are a special kind of non-reduced Gröbner bases. They have been introduced by Gerdt and collaborators for polynomial ideals (see e.g. Zharkov and Blinkov, 1993; Gerdt and Blinkov, 1998a,b) based on ideas from the Janet–Riquier theory of differential equations (Janet, 1929; Riquier, 1910). Involutive bases possess special combinatorial properties: in particular, they define Stan...

A dozen papers have considered the concept of negation probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point functions defined on a set values and called here negators. Recently class pd-independent linear negators has been characterized using Yager’s negator. The open problem was how to introduce involutive generating pd. To solve this problem...

Some generalizations of BCI algebras (the RM, BH, CI, BCH,
 BH**, BCH**, and *aRM** algebras) satisfying the identity $(x \rightarrow
 1)\rightarrow y = (y \rightarrow 1) x$ are considered. The connections these algebras
 various commutative groups (such as, for
 example, involutive moons (weakly)
 goops) described. In particular, it is proved that an RM
 algebra v...

The notion of microsupport and regularity for ind-sheaves was introduced by M. Kashiwara and P. Schapira in [4]. In this paper we study the behaviour of the microsupport under several functorial operations and characterize “microlocally” the ind-sheaves that are regular along involutive manifolds. As an application we prove that if a coherent D-module M is regular along an involutive manifold V...

Among P-pseudo-Hermitian Hamiltonians H = P−1H† P with real spectra, the “weakly pseudo-Hermitian” ones (i.e., those employing non-self-adjoint P 6 = P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P 6 = P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasip...

We focus on Θ-rich and almost Θ-rich words over a finite alphabet A, where Θ is an involutive antimorphism over A∗. We show that any recurrent almost Θ-rich word u is an image of a recurrent Θ′-rich word under a suitable morphism, where Θ′ is also an involutive antimorphism. Moreover, if the word u is uniformly recurrent, we show that Θ′ can be set to the reversal mapping. We also treat one spe...