In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the Möbius function and topology of such pattern posets. We prove our results using a poset fibration based on the embeddings of the poset, where embeddings are representations of occurrences. We show that the Möbius ...

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

Let Sn and Bn denote the respective sets of ordinary and bigrassmannian permutations of order n, and let (Sn,≤) denote the Bruhat ordering permutation poset. We extensively study the structural properties of the restricted poset (Bn,≤), showing among other things that it is ranked, symmetric, and possesses the Sperner property. We also give formulae for the number of bigrassmannian permutations...

The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset T of two agents, which are partially ordered by the capabilities available in the system. We build up a formal system and we elaborate suitable semantic models in order to derive information from the poset. The system is related to three-valued Heyting algebras with Boolean ...

It is shown that Aut(L ~ is naturally isomorphic to Aut(L) x Aut(Q) when L is a directly and exponentially indecomposable lattice, Q a non-empty connected poset, and one of the following holds: Q is arbitrary but L is a jm-lattice, Q is finitely factorable and L is complete with a join-dense subset of completely join-irreducible elements, or L is arbitrary but Q is finite. A problem of J6nsson ...

The adsorption of hydrogen sulfide molecule on undoped and N-doped TiO2/Au nanocomposites was investigated by density functional theory (DFT) calculations. The results showed that the adsorption energies of H2S on the nanocomposites follow the order of 2N doped (Ti site)>N-doped (Ti site)>Undoped (Ti site). The structural properties including bond lengths, angles<span id="...

We prove a conjecture of Thomas Lam that the face posets stratified spaces planar resistor networks are shellable. These called uncrossing partial orders. This shellability result combines with Lam's previous these same Eulerian to imply they CW posets, namely regular complexes. Certain subposets orders shown be isomorphic type A Bruhat order intervals; our shelling is coincide on intervals whi...

Suppose P is a partially ordered set that is locally finite, has a least element, and admits a rank function. We call P a weighted-relation poset if all the covering relations of P are assigned a positive integer weight. We develop a theory of covering maps for weighted-relation posets, and in particular show that any weighted-relation poset P has a universal cover P̃ → P , unique up to isomorph...