in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

There are examples of algorithms which allow the e cient computation of the concepts of a given formal context. However, when one wants to apply those algorithms to an arbitrary closure operator, which might not be given by a formal context, those algorithms cannot be applied directly. Therefore we want to discuss the problem of nding an appropriate formal context for a given closure operator, ...

A pathogen is usually defined as a microorganism that causes, or can cause, disease. We have defined a pathogen as a microbe that can cause damage in a host. However, this definition immediately raises the question of what it is about the microorganism that enables it to cause disease or damage; and this takes us to an ongoing debate that dates back to the late 19th century when the germ theory...

Although individual ants have an extremely basic intelligence, and are completely incapable of surviving on their own, colonies of ants can develop remarkably sophisticated and biologically successful behavior. This paper discusses a set of experiments which attempt to simulate one of these behaviors, namely the ability of ants to place pheromones as a way of communication. These experiments in...