Image transforms are used extensively in image processing to convert one image form into another form. These transforms are either point-operation transforms or neighborhood-operation transforms. Injective transforms, also known as reversible or one-to-one transforms, are a subset of point-operation transforms where each intensity value maps to a distinct intensity value. In this paper we prese...

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injec...

We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden shift problem admit this reduction. We show similar results for (non-injective) hidden shift problem for bent functions. We generalize the notion of influence a...

1. We just write out (i). Recall that X1 ∪ X2 = {x : x ∈ X1 or x ∈ X2}. Hence x ∈ X1 =⇒ x ∈ X1 ∪ X2, so that X1 ⊆ X1 ∪ X2. By symmetry, X1 ⊆ X1 ∪ X2. Finally, suppose that Y is a set such that X1 ⊆ Y and X2 ⊆ Y . Let x ∈ X1 ∪X2. Then x ∈ X1 or x ∈ X2. If x ∈ X1, then x ∈ Y since X1 ⊆ Y . Similarly, if x ∈ X2, then x ∈ Y . Thus in either case x ∈ Y , so that X1 ∪X2 ⊆ Y . 2. (i) Injective, not su...

Let X be a smooth Fano variety and Ku(X) its Kuznetsov component. A Torelli theorem for states that is uniquely determined by certain polarized abelian associated to it. An infinitesimal the differential of period map injective. categorical variant morphism η:H1(X,TX)→HH2(Ku(X)) In present article, we use machinery Hochschild (co)homology relate aforementioned three Torelli-type theorems variet...

In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respect...

In the category Top0 of T0-spaces and continuous maps, embeddings are just those morphisms with respect to which the Sierpiński space is Kan-injective, and the Kan-injective hull of the Sierpiński space is the category of continuous lattices and maps preserving directed suprema and arbitrary infima. In the category Loc of locales and localic maps, we give an analogous characterization of flat e...

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

The unit quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, quaternion-based feedback control laws require an additional mechanism that lifts a continuous attitude trajectory to the unit quaternion space. Lifting mechanisms that are memoryless, for example, selecting the quaternion having positive scalar component, h...