Introducing the notions of (inner) σ-derivation, (inner) σ-endomorphism and oneparameter group of σ-endomorphisms (σ-dynamics) on a Banach algebra, we correspond to each σ-dynamics a σ-derivation named as its σ-infinitesimal generator. We show that the σ-infinitesimal generator of a σ-dynamics of inner σ-endomorphisms is an inner σ-derivation and deal with the converse. We also establish a nice...

For V a vector space over a field, or more generally, over a division ring, it is well-known that every x ∈ End(V ) has an inner inverse; that is, that there exists y ∈ End(V ) satisfying xyx = x. We show here that a large class of such x have inner inverses y that satisfy with x an infinite family of additional monoid relations, making the monoid generated by x and y what is known as an invers...

Let A1 = K〈X,Y | [Y,X] = 1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(Y X) of A1 is Z. Let A1 → A1, X 7→ x, Y 7→ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of theWeyl algebra A1 is Z and the eigenvector algebra of ad(yx) is K〈x...

Stable equilibrium study cascaded one bit sigma-delta modulator In the paper defines a boundary of stability zone for sigma-delta modulator. The boundary depends from inner sigma-delta modulator coefficients. For designing purposes such result could use to find or compare some appropriate schemes with each other. It's proved some statements and showed that boundary could be found theoretically ...

Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

A relational structure is called reversible iff every bijective endomorphism of that an automorphism. We characterize property in the class disconnected binary structures, and one its subclasses—posets are disjoint union chains. Also, using concept a monotone function from structures preordered by monomorphism into well founded relation, we detect additional classes posets. further give equival...

In this paper, the endomorphisms, the half-strong endomorphisms, the locally strong endomorphisms, the quasi-strong endomorphisms, the strong endomorphisms and the automorphisms of a join of cycle n C and a vertex y are investigated. Some enumerative problems concerning these graphs are solved. In particular, the endomorphism spectrums and the endomorphism types of these graphs are given. It ha...

We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an algebra constant rank with center $C$ and $\sigma$ automorphism $D$, such that $\sigma|_{C}$ has finite order. The automorphisms these are canonically induced by ring the $D[t;\sigma]$ used in their construction. achieve description inner automorphisms. Results on ...

Extracytoplasmic function (ECF) sigma factors constitute a diverse family of proteins, within the class of the sigma 70 subunit of RNA polymerase. Most members of the family studied to date are known to regulate gene expression in response to stress conditions. The Bacillus subtilis genome encodes at least 17 distinct sigma factors, seven of which are members of the ECF subfamily. Among these, ...