Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ea n (t)’s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time...

Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation K+ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “meas...

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual s...

A factorization of a Galois connection investigated earlier is used to give a definition of a connectedness-disconnectedness Galois connection that is free of the notion of constant morphism. A new notion of N -fixed morphism with respect to a classN of monomorphisms is presented. This is used to characterize the connectedness-disconnectedness Galois connection in the case that N is closed unde...

• unify, and generalize seemingly disparate, classical sufficient conditions: polyhedrality of the cone, and “Slater” type conditions; • are necessary and sufficient, when the dual cone belongs to a class, that we call nice cones. Nice cones subsume all cones amenable to treatment by efficient optimization algorithms: for instance, polyhedral, semidefinite, and p-cones. • provide similarly attr...

In this note, we study how the depths of multiplier ideals behave under restriction. We also study possible values of the depths of multiplier ideals in the filtrations induced from maximal ideal sheaves. We then use it to give a sufficient condition for the integral closedness of the product of a multiplier ideal and a power of maximal ideal sheaf in the spirit of Huneke.

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfillment of two different formulae involving the εsubdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recent...

In this paper, we first construct the function space of (L, M)-fuzzy Q-convergence spaces to show Cartesian-closedness category M)-QC spaces. Secondly, introduce several subcategories M)-QC, including M)-KQC Kent spaces, M)-LQC Q-limit and M)-PQC pretopological investigate their relationships.