Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras. Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k...

This paper provides a unifying mathematical framework for orders of magnitude models used in Qualitative Physics. An axiomatic of the qualitative equality is provided and a general algebraic structure called qualita­ tive algebra is defined. It is shown that the usual model (+,-,0,?) and the extended model recently introduced by Dubois and Prade are particular cases in the class of mo­ dels tha...

We investigate the expressive power of the typed-calculus when expressing computations over nite structures, i.e., databases. We show that the simply typed-calculus can express various database query languages such as the relational algebra, xpoint logic, and the complex object algebra. In our embeddings, inputs and outputs are-terms encoding databases, and a program expressing a query is a-ter...

In a previous paper the authors generalized classical results on minimal realizations of non-commutative (nc) rational functions, using nc Fornasini–Marchesini which are centred at an arbitrary matrix point. particular, it was proved that domain regularity function is contained in invertibility set corresponding pencil any realization function. this we prove equality between and its realization...

It was proposed recently that the near-horizon states of an extremal four-dimensional Kerr black hole could be identified with a certain chiral conformal field theory whose Virasoro algebra arises as an asymptotic symmetry algebra of the near-horizon Kerr geometry. Supportive evidence for the proposed duality came from the equality of the microscopic entropy of the CFT, calculated by means of t...

It was proposed recently that the near-horizon states of an extremal four-dimensional Kerr black hole could be identified with a certain chiral conformal field theory whose Virasoro algebra arises as an asymptotic symmetry algebra of the near-horizon Kerr geometry. Supportive evidence for the proposed duality came from the equality of the microscopic entropy of the CFT, calculated by means of t...

Salomaa ((1969) Theory of Automata, page 143) asked whether the equational theory of regular expressions over a singleton alphabet has a finite equational base. In this paper, we provide a negative answer to this long standing question. The proof of our main result rests upon a modeltheoretic argument. For every finite collection of equations, that are sound in the algebra of regular expression...

The lambda calculus is fundamental in computer science. It resists an algebraic treatment because of capture-avoidance sideconditions. Nominal algebra is a logic of equality designed for specifications involving binding. We axiomatize the lambda calculus using nominal algebra, demonstrate how proofs with these axioms reflect the informal arguments on syntax and we prove the axioms to be sound a...

The bene ts of the object, logic (or relational), functional, and constraint paradigms can be obtained from our previous combination of the object and functional paradigms in hidden algebra, by combining it with existential queries over the states and attributes of objects, and then lifting to hidden Horn clause logic with equality, using an extension of a result due to Diaconescu. We call this...

The ability to decide whether or not two objects are the same is a fundamental requirement of any database query language. Because no single equality deenition is appropriate for all object types, many languages permit users to deene their own. The query algebra, AQUA 14] goes so far as to allow user-deened equalities to be supplied as arguments to query operators. These operators generalize st...