We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions the Yang-Baxter equation of small size. show that there are 321931 involutive size nine, 4895272 ten 422449480 non-involutive solution eight. Our method is then used biquandles.

A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·, ·] given by [x,y] = 〈Jx,y〉 , x,y ∈ Cn. Characterizations of the J -chaotic order Log(A) J Log(B) are presented for J -selfadjoint matrices A,B with positive eigenvalues, in terms of operator functions involving the α -power mean and the J -relative entropy. An indefinite complete form of the Furuta inequality and s...

Involutive distributions of evolutionary vector fields that belong to images of matrix operators in total derivatives are considered and some classifications of the operators are obtained. The weak compatibility of these operators is an analog of the Poisson pencils for the Hamiltonian structures, while the commutation closure of sums of the images for N -tuples of the operators, which is the s...

Soliton equations are infinite-dimensional integrable systems described by nonlinear evolution equations. As one of the soliton equations, long wave equation takes on profound significance of theory and reality. By using the method of nonlinearization, the relation between long wave equation and second-order eigenvalue problem is generated. Based on the nonlinearized Lax pairs, Euler-Lagrange f...

We investigate the possibility of giving a computational interpretation of an involutive negation in classical natural deduction. We first show why this cannot be simply achieved by adding ¬¬A = A to typed λ-calculus: the main obstacle is that an involutive negation cannot be a particular case of implication at the computational level. It means that one has to go out typed λ-calculus in order t...

Propositional fuzzy logics given by a combination of a continuous SBL t-norm with finitely many idempotents and of an involutive negation are investigated. A characterization of continuous t-norms which, in combination with different involutive negations, yield either isomorphic algebras or algebras with distinct and incomparable sets of propositional tautologies is presented.

We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice.

In this paper we consider diierent involutive divisions and describe their implementation in Mathematica together with algorithms for the construction of involutive bases for monomial ideals. As a straightforward application, we consider computation of the Hilbert function and the Hilbert polynomial for a monomial ideal, or for a polynomial one represented by its Grr obner basis. This allows on...

Recently it has been shown that elements of the unitary matrix determined by a quantum circuit can be computed by counting the number of common roots in the ˇnite ˇeld Z2 for a certain set of multivariate polynomials over Z2. In this paper we present a C# package that allows a user to assemble a quantum circuit and to generate the multivariate polynomial set associated with the circuit. The gen...