In [M. Klin, A. Munemusa, M. Muzychuk, P.-H. Zieschang Directed strongly regular graphs obtained from coherent algebras. Linear Algebra and its Applications 337, (2004) 83-109] the flag algebra of a given balanced incomplete block design with parameters (ν, b, r, k, λ) where λ = 1, has been constructed. In this paper, we consider the association scheme which is related to this flag algebra. By ...

Integrable σ-models, such as the principal chiral model, ZT -coset models for T ∈ Z≥2 and their various integrable deformations, are examples of non-ultralocal integrable field theories described by r/s-systems with twist function. In this general setting, and when the Lie algebra g underlying the r/s-system is of classical type, we construct an infinite algebra of local conserved charges in in...

This paper studies the homological determinants and Nakayama automorphisms of not-necessarily-noetherian m-Koszul twisted Calabi-Yau or, equivalently, m-Koszul Artin-Schelter regular, algebras. Dubois-Violette showed that such an algebra is isomorphic to a derivation quotient algebra D(w, i) for a unique-up-to-scalar-multiples twisted superpotential w. By definition, D(w, i) is the quotient of ...

We consider a strongly regular graph, G, with adjacency matrix A, and associate a three dimensional Euclidean Jordan algebra to A. Then, by considering convergent series of Hadamard powers of the idempotents of the unique complete system of orthogonal idempotents of the Euclidean Jordan algebra associated to A, we establish new admissibility conditions for the existence of strongly regular grap...

Many functions on context-free languages can be expressed in the form of the least fixed point of a function whose definition mimics the grammar of the given language. Examples include the function returning the length of the shortest word in a language, and the function returning the smallest number of edit operations required to transform a given word into a word in a language. This paper pre...

We consider three forms of non-regular iteration in process algebra: the push-down operation $, de5ned by xy = x((xy)(xy)) + y, the nesting operation ], de5ned by xy = x((xy)x) + y, and the back and forth operation , de5ned by x y= x((x y)y) + y. In the process algebraic framework ACP with abstraction and one of $, ] or we provide de5nitions of the following standard processes: stack, context-f...

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point. In [Co] Cole gave a counterexample to the peak point conjecture by constructing a non-trivial uniform algebra A with co...

The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a...

A new homology is defined for a non-self-adjoint operator algebra with a distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra. Under natural hypotheses the zeroth order group coincides with the K0 group of the generated C ∗-algebra. Several identifications and applications are given, and in particular it is shown how ...

While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is...