We construct Nijenhuis operators from particular bialgebras called dendriform-Nijenhuis bialgebras. It turns out that such Nijenhuis operators commute with TD-operators, a kind of Baxter-Rota operators, and are therefore closely related to dendriform trialgebras. This allows the construction of associative algebras, called dendriform-Nijenhuis algebras, made out of nine operations and presentin...

In [4] we characterize the class of countable completey representable relation and cylindric algebras via special neat embeddings. In this note we provide a counterexample showing that the condition of countability cannot be omitted.

We obtain the class N A of noncommutative cylindric algebras from the class CA of cylindric algebras by weakening the axiom C 4 of commuta-tivity of cylindrifications (to C * 4 , see below, and we obtain N CA from CA by omitting C 4 completely). Some motivation for studying noncommutative cylindric algebras: Noncommutative cylindric algebras (N A's) have the same " substi-tutional structure " a...

Several new formulations of the notion of cylindric algebra are presented. The class CA of all cylindric algebras of degree a is shown to be definitionally equivalent to a class of algebras in which only substitutions (together with the Boolean +, •, and — ) are taken to be primitive operations. Then CA is shown to be definitionally equivalent to an equational class of algebras in which only su...

This paper classifies the blocks of the affine Hecke algebras of type A and the blocks of the cyclotomic Hecke algebras of type G(r, 1, n) over an arbitrary algebraically closed field. Rather than working with the Hecke algebras directly we work instead with the cyclotomic Schur algebras. The advantage of these algebras is that the cyclotomic Jantzen sum formula gives an easy combinatorial char...

We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited.

We study fusion rings for degenerate minimal models (p = q case) for N = 0 and N = 1 (super)conformal algebras. We consider a distinguished family of modules at the level c = 1 and c = 3 2 and show that the corresponding fusion rings are isomorphic to the representation rings for sl(2, C) and osp(1|2) respectively.

In a recent work, thanks to the use of Cliiord algebras and designants, we have shown that Wynn's vector "-algorithm can be written as a ratio of two designants. The present work, according to these new results, has the aim of 1. Finding easily and diierently the results of some authors in this scope, particularly those of Wynn, D.E. Roberts and P.R. Graves-Morris. 2. Computing explicitly the e...

We introduce the notion of pie algebra for a 2-monad, these bearing the same relationship to the flexible and semiflexible algebras as pie limits do to flexible and semiflexible ones. We see that in many cases, the pie algebras are precisely those ‘‘free at the level of objects’’ in a suitable sense; so that, for instance, a strict monoidal category is pie just when its underlying monoid of obj...