Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching: for a given text the goal is to find its factors having the same “shape” as a given pattern. The known results include a linear-time algorithm for this problem (in case of polynomially-bounded alphabet) and a generalization to multiple patterns. We exte...

Let (X, ν) be a probability space and suppose a free group Fm withm generators acts on (X, ν) by measure-preserving transformations. Let {a1, . . . , am} be a set of free generators for Fm and let T1, . . . , Tm : X → X be transformations corresponding to the generators. Write T−i = T −1 i for i = 1, . . . ,m, and set A = {−m, . . . ,−1, 1, . . . ,m}. We also have the action Fm on L1(X, ν), def...

Let X be a chain, OP (X) the order-preserving partial transformation semigroup on X and OI(X) the order-preserving 1–1 partial transformation semigroup on X. It is known that both OP (X) and OI(X) are regular semigroups. We extend these results by characterizing the regular elements of the semigroups OP (X,Y ), OI(X,Y ), OP (X,Y ) and OI(X,Y ) where ∅ = Y ⊆ X,OP (X,Y ) = {α ∈ OP (X) | ranα ⊆ Y ...

The aim of this paper is to show that if an order preserving bijective transformation of the Hilbert space effect algebra also preserves the probability with respect to a fixed pair of mixed states, then it is an ortho-order automorphism. A similar result for the orthomodular lattice of all sharp effects (i.e., projections) is also presented.

It is well known that increasing functions do not preserve operator order in general; nor decreasing reverse order. However, monotone or do. In this article, we employ a convex approach to discuss preserving conversing functions. As an easy consequence of more general results, find nonnegative constants γ and ψ such A≤B implies f(B)≤f(A)+γ1ℋ andf(A)≤f(B)+ψ1ℋ, for the self-adjoint operators A, B...

Abstract Several properties of subspaces $$J \subset X$$ J ⊂ X in a pair ( X , J ) with quotient lifting different types are derived, giving emphasis to order-preserving for order unit spaces and affine continuous functions on Choquet simplexes.

Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains applications used to represent ordered relations between entities the domains. Examples task dependencies a project plan, transaction order distributed ledgers execution sequences of tasks computer programs, just mention few. We study problem preserving hierarchical cluster...