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...

In this work, a novel quaternary algebra has been proposed that can be used to implement any quaternary logic function. Unlike other variants of quaternary algebra, this algebra is closely related to Boolean algebra and can be used to convert any binary function into quaternary without any significant modification. For this purpose, we have defined a set of quaternary operators and developed tw...

The Kontsevich integral of a knot is a powerful invariant which takes values in an algebra of trivalent graphs with legs. Given a Lie algebra, the Kontsevich integral determines an invariant of knots (the so-called colored Jones function) with values in the symmetric algebra of the Lie algebra. Recently A. Kricker and the author constructed a rational form of the Kontsevich integral which takes...

A celebrated contribution of Bellantoni and Cook was a function algebra to capture FPTIME. This algebra uses recursion on notation. Later, Oitavem showed that including primitive recursion, an algebra is obtained which captures FPSPACE. The main results of this paper concern variants of the latter algebra. First, we show that iteration can replace primitive recursion. Then, we consider the resu...

An approach to combining type-structured algebraic speciications with Gure-vich Machines (evolving algebras) is proposed. A type-structured algebraic speci-cation, in its simplest form, consists of data type speciications and independent function (detached operation) speciications. Concrete and generic speciication components (data types and functions) are distinguished in a more developed case...

We construct a basis for the right quantum algebra introduced by Garoufalidis, Lê and Zeilberger and give a method making it possible to go from an algebra subject to commutation relations (without the variable q) to the right quantum algebra by means of an appropriate weight-function. As a consequence, a strong quantum MacMahon Master Theorem is derived. Besides, the algebra of biwords is syst...

The Kontsevich integral of a knot is a powerful invariant which takes values in an algebra of trivalent graphs with legs. Given a Lie algebra, the Kontsevich integral determines an invariant of knots (the so-called colored Jones function) with values in the symmetric algebra of the Lie algebra. Recently A. Kricker and the author constructed a rational form of the Kontsevich integral which takes...

in this paper, we associate canonically a precyclic mod- ule to a regular multiplier hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition