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...

Basic problems of complex systems are outlined with an emphasis on irreducibility and dynamic many-to-many correspondences. We discuss the importance of a constructive approach to artificial reality and the significance of an internal observer.

we consider a 2-dimensional representation of the hecke algebra h(g7; u), whereg7 is the complex re ection group and u is the set of indeterminatesu = (x1; x2; y1; y2; y3; z1; z2; z3):after specializing the indetrminates to non zero complex numbers, we then determine a nec-essary and sucient condition that guarantees the irreducibility of the complex specializationof the representation of the ...