The relation of semiadjacency on ∩-semigroups of transformations

Abstract

We consider two relations on a ∩-semigroup of partial functions on a given set: the inclusion of domains and semiadjacency (i.e., the inclusion of the image of the first function in the domain of the second). These are characterized from an abstract point of view via a system of elementary axioms, i.e., conditions expressed in the language of pure predicate calculus with equality.

Lattice study of quark distribution amplitudes in the pion and its excitations

“…[12]; our present calculation does not include operator mixing that they find largely responsible for the quark mass dependence of the excited-state decay constants, but note that the anisotropic lattice used in this calculation has fine spacing in the temporal direction. Furthermore, our basis of interpolating operators includes only "single-hadron" operators, whose coupling to multihadron decay states is expected to be suppressed by the volume; we note that the second excited state is at or above the energy level of the lowest-lying non-interacting two-meson state on each of our lattices [2]. Future work will therefore include the inclusion of the operator improvement term and calculations at larger volumes to expose any contributions from multihadron states.…”

“…Such experiments are the aim of the 12 GeV upgrade of the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab [1] with, in particular, a meson spectroscopy program based on the photoproduction of meson excitations. The expectation is that new data produced in this upcoming experiment, combined with recent lattice QCD results aimed to extracting the spectrum of meson excited states [2,3], will represent a unique opportunity for the study of the nature of confinement mechanism and for determining the role of the gluonic field in the hadron spectrum.…”

Axioms for function semigroups with agreement quasi-order

“…Function ∩-semigroups equipped with one or more additional relations have been considered, for example as in [1,2,25], where the relations considered are semicompatibility (relating those f, g which agree wherever both are defined) and semiadjacency (relating f to g if the range of f is a subset of the domain of g).…”

The relations of semiadjacency and semicompatibility in $$\cap $$ ∩ -semigroups of transformations

“…Later, in [5], an abstract characterization of the algebraic system (Φ, •, ξ Φ , δ Φ ) was given, and in [2] ∩-semigroups of transformations with the semiadjacency relation were characterized. The semiadjacency relation on algebras of multiplace functions was investigated in [11].…”

“…Later, in [5], was found an abstract characterization of semigroups of transformations containing these two relations, i.e., an abstract characterization of an algebraic system (Φ, •, ξ Φ , δ Φ ). The ∩-semigroup of transformations with the semiadjacency relation was described in [2]. The semiadjacency relation on algebras of multiplace functions was investigated in [11].…”