We study observables as r-D-homomorphisms de®ned on Boolean D-posets of subsets into a Boolean Dposet. We show that given an atomic r-complete Boolean D-poset P with the countable set of atoms there exist a r-complete Boolean D-poset of subsets S and a r-D-homomorphism h from S onto P, more precisely we can choose S ˆ B…R†, which gives an analogy of the Loomis± Sikorski representation theorem f...

The paper contains results that characterize the Donkin–Koppinen filtration of coordinate superalgebra K[G] general linear supergroup G = GL(m|n) by its subsupermodules CΓ OΓ(K[G]). Here, supermodule is largest subsupermodule whose composition factors are irreducible supermodules highest weight ⋋, where ⋋ belongs to a finitely-generated ideal Γ poset X(T)+ dominant weights G. A decomposition as...

We show that if C is a class of graphs which is nowhere dense then rst-order model-checking is xed-parameter tractable on C. As all graph classes which exclude a xed minor, or are of bounded local tree-width or locally exclude a minor are nowhere dense, this generalises algorithmic meta-theorems obtained for these classes in the past (see [11, 13, 4]). Conversely, if C is not nowhere dense and ...

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...

In this manuscript we study inclusion posets of Borel orbit closures on (symmetric) matrices. In particular, we show that the Bruhat poset of partial involutions is a lexicographically shellable poset. We determine which subintervals of the Bruhat posets are Eulerian, and moreover, by studying certain embeddings of the symmetric groups and their involutions into rook matrices and partial involu...

In this paper we are using the poset representation to describe the complex answers given by IR systems after a clustering and ranking processes. The answers considered may be given by cartographical representations or by thematic sub-lists of documents. The poset representation, with the graph theory and the relational representation opens many perspectives in the definition of new similarity ...

Poset games are two-player impartial combinatorial games, with normal play convention. Starting with any poset, the players take turns picking an element of the poset, and removing that and all larger elements from the poset. Examples of poset games include Chomp, Nim, Hackendot, Subset-Takeaway, and others. We prove a general theorem about poset games, which we call the Poset Game Perioidicity...

In his study of a Hochschild complex arising in connection with the free loop fibration, S. Saneblidze defined freehedron, certain polytope constructed via truncation process from hypercube. It was recently conjectured by F. Chapoton and proven C. Combe that orientation 1-skeleton freehedron carries lattice structure. The resulting dubbed it is interval constructable extremal. These properties ...

provide the notation and terminology for this paper. 1. POSET RETRACTS One can prove the following propositions: (1) For all binary relations a, b holds a · b = a b. (2) Let X be a set, L be a non empty relational structure, S be a non empty relational substruc-ture of L, f , g be functions from X into the carrier of S, and f , g be functions from X into the carrier of L. If f = f and g = g and...