In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and...

We consider Krammer’s representation of the pure braid group on three strings: P3 → GL 3, Z t±1, q±1 , where t and q are indeterminates. As it was done in the case of the braid group, B3, we specialize the indeterminates t and q to nonzero complex numbers. Then we present our main theorem that gives us a necessary and sufficient condition that guarantees the irreducibility of the complex specia...

This is a continuation of [7] in which we proved irreducibility of spaces of rational curves on a general hypersurface X d ⊂ P n of degree d < n+1 2. In this paper, we prove that if d 2 + d + 2 ≤ n and if d ≥ 3, then the spaces of rational curves are themselves rationally connected.

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to diierent ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.

This paper shows the existence of a collateral equilibrium without assuming any hypotheses on the strict positivity, be they individual initial endowments, including the ex post initial endowments, or aggregated initial endowments. Because of dropping the strict positivity of social initial endowment we fail to get an equilibrium. Instead, we get a quasi-equilibrium. Then, appealing to the conc...

We study C?-irreducibility of inclusions reduced twisted group C?-algebras and C?-algebras. characterize in the case an inclusion arising from a normal subgroup, exhibit many new examples C?-irreducible inclusions.

Our goal is to compute the minimal-order recurrence of the colored Jones polynomial of the 74 knot, as well as for the first four double twist knots. As a corollary, we verify the AJ Conjecture for the simplest knot 74 with reducible non-abelian SL(2,C) character variety. To achieve our goal, we use symbolic summation techniques of Zeilberger’s holonomic systems approach and an irreducibility c...

Several theories of emergence will be distinguished. In particular, these are synchronic, diachronic, and weak versions of emergence. While the weaker theories are compatible with property reductionism, synchronic emergentism and strong versions of diachronic emergentism are not. Synchronic emergentism is of particular interest for the discussion of downward causation. For such a theory, a syst...

An operator is said to be strongly irreducible if its commutant has no nontrivial idempotent. This paper first shows that if an operator is not strongly irreducible then the set of idempotents in its commutant is either finite or uncountable. The second part of the paper focuses on the Jordan block which is a well-known class of irreducible operators, and determines when a Jordan block is stron...