The local Gauss law of quantum chromodynamics on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant Z3-valued global charge in QCD. The total charge contained in a region of the lattice is equal to the flux through its boundary of a certain Z3-valued, additive quantity. Implications for continuous QCD are discussed.

Hopf solitons in the Skyrme-Faddeev model — S 2-valued fields on R 3 with Skyrme dynamics — are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S 2-valued fields on the cubic lattice Z 3 with a nearest-neighbour interaction. For suitable choices of the interaction, topological solitons exist on the lattice. Their appearance is remarkably simil...

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued fram...

Our starting point is the Mosco-convergence result due to Hess ((He'89]) for integrable multivalued supermartingales whose values may be unbounded, but are majorized by a w-ball-compact-valued function. It is shown that the convergence takes place also in the slice topology. In the case when both the underlying space X and its dual X have the Radon-Nikodym property a weaker compactness assumpti...

In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

In this paper, based on viscosity technique with perturbation, we introduce a new non-linear viscosity algorithm for finding a element of the set of fixed points of nonexpansivemulti-valued mappings in a Hilbert space. We derive a strong convergence theorem for thisnew algorithm under appropriate assumptions. Moreover, in support of our results, somenumerical examples (u...

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension of this reducibility for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice with the disjoint union of multi-valued functions as greatest ...