‎‎The investigation of equational compactness was initiated by‎ ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎ ‎equivalent to equational compactness‎. ‎Here we define the so‎ ‎called sequentially compact acts over semigroups and study‎ ‎some of their categorical and homological properties‎. ‎Some‎ ‎Baer conditions for injectivity of S-acts are also presented‎.

In terms of storage capacity and containment efficiency, deep saline aquifers are among the best candidates for CO2 storage. However, salt precipitation in the wellbore vicinity and fines mobilization ensued from in situ mineral dissolution could impair CO2 injectivity and reduce the quality and capacity of deep saline reservoirs for CO2 storage. The mechanisms of salt precipitation and its imp...

Characterizations of quasi-continuousmodules and continuousmodules are given. A non-trivial generalization of injectivity (distinct from p-injectivity) is considered.

Characterizations of quasi-continuousmodules and continuousmodules are given. A non-trivial generalization of injectivity (distinct from p-injectivity) is considered.

Essentiality is an important notion closely related to injectivity. Depending on a class M of morphisms of a category A, three different types of essentiality are considered in literature. Each has its own benefits in regards with the behaviour of M-injectivity. In this paper we intend to study these different notions of essentiality and to investigate their relations to injectivity and among t...

In this paper we provide sufficient conditions that ensure the convexity of the inverse images of an operator, monotone in some sense. Further, conditions that ensure the monotonicity, respectively the local injectivity of an operator are also obtained. Combining the conditions that provide the local injectivity, respectively the convexity of the inverse images of an operator, we are able to ob...

Given an order-enriched category, it is known that all its KZ-monadic subcategories can be described by Kan-injectivity with respect to a collection of morphisms. We prove the analogous result for Kan-injectivity with respect to a collection H of commutative squares. A square is called a Kan-injective consequence of H if by adding it to H Kan-injectivity is not changed. We present a sound logic...

We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrixand graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite multigraph, termed the “DSR graph”, is shown to be a useful representation of an interaction network when discussing questions of injectivity. A graph-theoreti...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...