An implementation of the algebra of pseudo diierential operators in the computer algebra system AXIOM is described. In several examples the application of the package to typical computations in the theory of integrable systems is demonstrated. Nature of physical problem: Generation of integrable systems solvable by the Inverse Scattering Method and determination of conservation laws Method of s...

This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras such that the differential Gerstenhaber algebra of its complex structure is quasi-isomorphic to that of its symplectic...

A set E equipped with a partial, commutative and associative operation ⊕, containing elements 0 and 1, in which the existence of a unique inverse element x′ to any x ∈ E is guaranteed, and a⊕ 1 is admitted only if a = 0 is well known as effect algebra. Effect algebras were introduced by Foulis and Bennet [3] and simultaneously by Kôpka and Chovanec [7] as D-posets. An effect algebra equipped wi...

The notion of pseudo-valuations (valuations) on a BCC-algebra is introduced by using the Buşneag’s model ([1–3]), and a pseudo-metric is induced by a pseudo-valuation on BCC-algebras. Conditions for a real-valued function to be an BCK-pseudo-valuation are provided. The fact that the binary operation in BCC-algebras is uniformly continuous is provided based on the notion of (pseudo) valuation.

The framework. In 1956, G. Birkhoff G. and R.S. Pierce [1] conjectured the following: do the algebra of piecewise polynomial functions with real coefficients and the algebra of functions that can be written as Inf and Sup of finitely many polynomials coincide? The conjecture – that can be equivalently stated asking for the free n-generated lattice-ordered algebra to be isomorphic with the algeb...

We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are the wound-rounds of lattice-ordered groups. It follows some results about can be stated in terms MV-algebras. For example, study together with cyclic order allows to get first-order characterization unimodular complex numbers finite deduce pseudofinite MV-chains pseudo-si...

Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling and solving systems of linear differe...

In this note, we show that there is no Hopf algebra structure onQ∞, the algebra of pseudo-roots of noncommutative polynomials, which extends the one existing on NSym (one of its famous subalgebras).

In this note, we show that there is no Hopf algebra structure onQ∞, the algebra of pseudo-roots of noncommutative polynomials, which extends the one existing on NSym (one of its famous subalgebras).

MV-algebras were introduced by Chang in 1958 preliminary to his providing an algebraic completeness proof for the K0-vaΓued Lukasiewicz propositional logic, LXo. In this paper a method is given for determining, for an arbitrary normal extension of LKo, an MV-algebra characteristic for the extension. The characteristic algebras are finite direct products of two sets of linearly ordered MV-algebr...