Development of the human kidney begins at the end of the first month, and the kidney becomes functional in the course of the second month of antenatal life. In the last trimester, the fetal kidney already manifests first involutive changes. From then on to its adult maturity, the kidney is characterised by intensive processes of maturation, but also evident involutive changes. The dynamism of t...

In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Möller et al. [21], we present a more efficient variant of Gerdt’s algorithm (than the algorithm presented in [17]) to compute minimal involutive bases. Further, by using the involutive version of Hilbert driven technique, along with the new variant of Gerdt’s algorit...

In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present pa...

Applying a classical theorem of Smith, we show that the poset property of being Gorenstein∗ over Z2 is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. ...

We list some reasons why among P−pseudo-Hermitian Hamiltonians H = P HP with real spectra, the “weakly pseudo-Hermitian” ones (i.e., those employing P 6 = P, even when belonging to the former class) form such an interesting special family that they deserve a special name and attention. In particular we show that for P 6 = P, the current auxiliary involutive operator of charge C gets complemente...

We prove that differentials of lattice coordinate functions x must be algebraic independent to their involutive conjugate, else no correct continuum limit exists. PACS: 02.40.Gh, 11.15.Ha

Abstract In [4, 5], it was introduced a logic (called Six) associated to class of algebraic structures known as involutive Stone algebras. This algebras, denoted by S, considered the first time in [6] tool for study certain problems connected theory finite-valued Łukasiewicz–Moisil fact, Six is that preserves degrees truth with respect S. Among other things, proved 6-valued Logic Formal Inconsi...

Employing the algebraic structure of left brace and dynamical extensions cycle sets, we investigate a class indecomposable involutive set-theoretic solutions Yang–Baxter equation having specific imprimitivity blocks. Moreover, study one-generator braces multipermutation level 2.

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

We characterize, classify and axiomatize all subvarieties of IMTL(3), the variety of IMTL-algebras given by the equation ¬(x3) ∨ x ≈ >. We also give a canonical set of generators for each one. Introduction and preliminaries An IMTL-algebra is a bounded residuated lattice A = 〈A,∧,∨, ∗,→,¬,⊥,>〉, where ∧ and ∨ are meet and join, 〈∗,→〉 is a residuated pair, ¬ is the associated negation (i.e. ¬x =d...