In a regular category $$\mathbb {E}$$ , the direct image along epimorphism f of preorder is not in general. Set, its best approximation then cocartesian above f. category, existence such S actually equivalent to supremum $$R[f]\vee S$$ among preorders. We investigate here some conditions ensuring these images or equivalently suprema. They apply two very dissimilar contexts: any topos with supre...

Abstract We study permutability properties of matrix semigroups over commutative bipotent semirings (of which the best-known example is tropical semiring ). prove that every such semigroup weakly permutable (a result previous stated in literature, but with an erroneous proof) and then proceed to depth question when they are strongly (which turns out depend heavily on semiring). Along way we cla...

Orientation-invariant feature descriptors are widely used for image matching. We propose a new method of computing and comparing Histogram of Gradients (HoG) descriptors which allows for re-orientation through permutation. We do so by moving the orientation processing to the distance comparison, rather than the descriptor computation. This improves upon prior work by increasing spatial distinct...

The permutability equation G(G(x, y), z) = G(G(x, z), y) is satisfied by many scientific and geometric laws. A few examples among many are: The LorentzFitzGerald Contraction, Beer’s Law, the Pythagorean Theorem, and the formula for computing the volume of a cylinder. If we required that a permutable law be meaningful, the possible forms of a law are considerably restricted. The class of example...

We consider Markovian GSMPs (generalized semi-Markov processes) in which the rates of events are subject to control. A control is monotone if the rate of one event is increasing or decreasing in the number of occurrences of other events. We give general conditions for the existence of monotone optimal controls. The conditions are functional properties for the one-step cost functions and, more i...

It is proved that every (universal) algebra A with distributive and permutable structure lattice is isomorphic with the algebra of all global sections with compact supports of a sheaf of homomorphic images of A over a topological space. This completely generalises the corresponding result of Klaus Keimel for /-rings. Introduction. The following note is a preliminary report on the investigations...