A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector (n ≥ 3) is decomposable iff all its contractions with up to n − 2 covectors are decomposable. In the last years, several authors have studied ...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza's theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford's work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

We study projective dimension, a graph parameter (denoted by pd(G) for a graph G), introduced by Pudlák and Rödl [13], who showed that proving lower bounds for pd(Gf ) for bipartite graphs Gf associated with a Boolean function f imply size lower bounds for branching programs computing f . Despite several attempts [13, 17], proving super-linear lower bounds for projective dimension of explicit f...

ACstract--In the eight-point linear algorithm for determining 3-D motion/structure from two perspective views using point correspondences, the E matrix occupies a central role. The E matrix is defined as a skew-symmetrical matrix (containing the translation components) postmultiplied by a rotation matrix. In this correspondence, we show that a necessary and sufficient condition for a 3 x 3 matr...

The main result of this paper completely settles Bermond's conjecture for bipartite graphs of odd degree by proving that if G is a bipartite (2k+1)-regular graph that is Hamilton decomposable, then the line graph, L(G), of G is also Hamilton decomposable. A similar result is obtained for 5-regular graphs, thus providing further evidence to support Bermond's conjecture.

We extend F.Pastjin's construction of uniform decomposable chains of finite rank to those of rank 'finite over a limit' and investigate infinite (length ω) products and unions of such chains. We derive an extension of Pastjin's characterisation to uniform decomposable chains of small transfinite rank (≤ ω + ω).

In this paper we translate Ramsey-type problems into the language of decomposable hereditary properties of graphs. We prove a distribu-tive law for reducible and decomposable properties of graphs. Using it we establish some values of graph theoretical invariants of decompos-able properties and show their correspondence to generalized Ramsey numbers.

We define the decomposable extensions of difference fields and study the irreducibility of q-Painlevé equation of type A 7 ′ . Every strongly normal extension or Liouville-Franke extension, the latter of which is a difference analogue of the Liouvillian extension, satisfies that its appropriate algebraic closure is a decomposable extension.

The present paper considers discrete probability models with exact computational properties. In relation to contingency tables this means closed form expressions of the maksimum likelihood estimate and its distribution. The model class includes what is known as decomposable graphical models, which can be characterized by a structured set of conditional independencies between some variables give...