The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on non-commutative two dimensional hierarchy. Further we generalize to extended To survey its integrability, construct bi-Hamiltonian structure and conserved densities means R-matrix formalism. This can be reduced multicomponent hierarchy, ZN -Toda respectively reductions Lie algebras.

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

We discuss Hamiltonian formulations for integrable couplings, particularly biand tri-integrable couplings, based on zero curvature equations. The basic tools are the variational identities over non-semisimple Lie algebras consisting of block matrices. Illustrative examples include dark equations and biand tri-integrable couplings of the KdV equation and the AKNS equations, generated from the en...

Fà a di Bruno (Hopf, bi)algebras appear in several branches of mathematics and physics, and may be introduced in several ways. Here we start from exponential power series like f (t) = ∞ n=1 f n n! t n , with f 1 > 0. In view of Borel's theorem, one may regard them as local representatives of orientation-preserving diffeomorphisms of R leaving 0 fixed. On the group G of these diffeomorphisms we ...

In this paper, we have established bi-approximation semantics for lattice-based logics with the De Morgan negation (unbounded orthologic), and their morphisms. In addition, we have discussed the dual representation between unbounded ortholattices with strict homomorphisms and polarity frames and d-morphisms. Apart from the abstract construction of dual algebras in the series of the present auth...

Abstract. SL2-tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL2-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 × 2– submatrix has determinant 1. We construct a large class of new SL2-tilings which contains the previously known ones. More precisely, we show that there is a bijection...

We improve on the results of [Vel] and give some examples. In [Jech], a number of infinite games on (complete) Boolean algebras were defined. Among them was the following Prikry-style “cut and choose” game Gc&c : I p, b0 b1 . . . . . . . . . bi . . . . . . . . . . i < ω II r0 r1 . . . . . . . . . ri . . . . . . . . . . where p, bi’s are elements of the Boolean algebra B in question and ri ∈ 2 f...

A finite latin square is an n × n matrix whose entries are elements of the set {1, . . . , n} and no element is repeated in any row or column. Given equivalence relations on the set of rows, the set of columns, and the set of symbols, respectively, we can use these relations to identify equivalent rows, columns and symbols, and obtain an amalgamated latin square. There is a set of natural equat...