Let C be a full-dimensional pointed closed convex cone in R obtained by taking the conic hull of a strictly convex set. Given A ∈ Qm×n1 , B ∈ Qm×n2 and b ∈ Q, a simple conic mixed-integer set (SCMIS) is a set of the form {(x, y) ∈ Z1 ×R2 | Ax+By− b ∈ C}. In this paper, we give a complete characterization of the closedness of convex hulls of SCMISs. Under certain technical conditions on the cone...

In this paper we reconsider the question of when the continuous linear image of a closed convex cone is closed in Euclidean space. In particular, we show that although it is not true that the closedness of the image is preserved under small perturbations of the linear mappings it is “almost” true that the closedness of the image is preserved under small perturbations, in the sense that, for “al...

The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we deand reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively...

Mourgues and Ressayre [10] showed that any real closed field is isomorphic to a truncation closed subfield of a Hahn field over R. The papers [5, 6, 7, 4] continue the study of truncation closedness. The results are typically that truncation closedness is robust in the sense of being preserved under a variety of extensions. One significance of truncation closedness is that it enables transfinit...

We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discret...

Some research works have mentioned the similarity of autopoiesis with (M,R) systems proposed by Rosen, from the perspective of closedness of the systems. However, there are some difference between the aspects of closedness required for autopoiesis and (M,R) systems. This paper aims at clarifying these differences to investigate the possibility of algebraic description of living systems, based o...

In this paper, we obtain several new generalized KKM-type theorems under a new coercivity condition and the condition of intersectionally closedness which improves condition of transfer closedness. As applications, we obtain new versions of equilibrium problem, minimax inequality, coincidence theorem, fixed point theorem and an existence theorem for an 1-person game.

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that  the category $L$-$mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.

We introduce a new formalism to define compositions of interacting heterogeneous systems, described by extended motion description languages (MDLes). The novelty of the formalism is in producing a composed system with a behavior that could be a superset of the union of the behaviors of its generators. We prove closedness of MDLes under this composition and we show that in the class of systems m...