The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

The goal of coronary revascularization, indeed of all medical treatments, is to improve outcomes for patients, but what does “improve outcomes” mean? Usually, there are many outcomes to a treatment, relief of symptoms, reduced risk of death and disability, major complications, minor nuisances, financial impact, pain, recovery time, and so on. How do we weigh these different aspects of outcome t...

Let f ∈ Z[x] be a polynomial of degree d. We establish the paucity of non-trivial positive integer solutions to the equation f(x1) + f(x2) = f(x3) + f(x4), provided that d ≥ 7. We also investigate the corresponding situation for equal sums of three like polynomials. Mathematics Subject Classification (2000): 11D45 (11P05)