We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a seminorm two-dimensional subspace of algebra generating algebra. In terms structure constants and Minkowski support function unit ball which defines quasimetric, we establish criterion for strict abnormality these extremals.

in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

The functions of Computable Analysis are defined by enhancing the capacities of normal Turing Machines to deal with real number inputs. We consider characterizations of these functions using function algebras, known as Real Recursive Functions. Bournez and Hainry 2006 [5] used a function algebra to characterize the twice continuously differentiable functions of Computable Analysis, restricted t...

Given a nite graded poset with labeled Hasse diagram, we construct a quasi-symmetric generating function for chains whose labels have xed descents. This is a common generalization of a generating function for the ag f-vector de-ned by Ehrenborg and of a symmetric function associated to certain edge-labeled posets which arose in the theory of Schubert polynomials. We show this construction gives...

We introduce a generalization of the Heisenberg algebra which is written in terms of a functional of one generator of the algebra, f(J0), that can be any analytical function. When f is linear with slope θ, we show that the algebra in this case corresponds to q-oscillators for q = tan θ. The case where f is a polynomial of order n in J0 corresponds to a n-parameter deformed Heisenberg algebra. T...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

We deene an algebra on matrix pencils that is a natural extension of sums, products and quotients of real numbers. The classical algebra of linear transformations may be regarded as a special case of the algebra of pencils. The sum and product deened here preserve right deeating subspaces. We show below that the matrix sign function and the inverse-free algorithms can be derived from an algebra...