Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique c...

Biologists view life as transient while theologians see it as eternal. An unbiased definition for life would respect both views until one or both were eliminated by evidence. This paper identifies pre-requisites for such a definition. First among these is that all assumptions be made explicit. Currently "life" is surrounded by implicit assumptions, e.g., that it is what organisms lose at death ...

Abstract. Eternal solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one eternal solution – the trivial solution. While solutions to the heat equation exist for all forward time, they cannot be extended backwards in time. Nonlinearities exasperate the situation somewhat, in that solutions may form singula...

Friedrich Nietzsche’s theory of eternal recurrence is an essential part of his mature philosophy, but the theory’s metaphysical commitments and practical implications are both obscure. In this essay I consider only the metaphysical elements of the theory, with the aim of determining whether it is possible that we live our lives infinitely many times, as the theory maintains. I argue that the po...