Abstract In this paper we continue the study of spaces $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) and O}_...

Let L be a complete lattice. We introduce and characterize the prime L-submodules of a unitary module over a commutative ring with identity. Finally, we investigate the Zariski topology on the prime L-Spectrum of a unitary module, consisting of the collection of all prime L-submodules, and prove that for L-top modules the Zariski topology on L-Spec(M) exists. © 2007 Elsevier B.V. All rights res...

We prove that the Büchi topology, the automatic topology, the alphabetic topology and the strong alphabetic topology are Polish, and provide consequences of this. 1998 ACM Subject Classification F.1.1 Models of Computation, F.1.3 Complexity Measures and Classes, F.4.1 Mathematical Logic, F.4.3 Formal Languages

Graph pattern matching is to find all matches in a data graph for a given pattern graph, and it is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow graph pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of d...

A major challenge in systems biology is to understand interactions within biological systems. Such a system often consists of units with various levels of activities that evolve over time, mathematically represented by the dynamics of the system. The interaction between units is mathematically represented by the topology of the system. We carry out some mathematical analysis on the connections ...

We prove that if {φt}t≥0 is a CP-semigroup acting on a von Neumann algebra M ⊆ B(H), then for every A ∈ M and ξ ∈ H , the map t 7→ φt(A)ξ is norm-continuous. We discuss the implications of this fact to the existence of dilations of CPsemigroups to semigroups of endomorphisms.

In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC)L or (TC)R axioms and the L-relations induced by two L-fuzzy topologi...