abstract The notion of invariant subspaces is useful in a number of theoretical and practical applications. In this paper we give an elementary treatment of invariant subspaces that stresses their connection with simple eigenvalues and their eigenvectors.

one of the most important issues of abrahamic religions is faith. paul the apostle and fakhr rāzī, two thinkers in two religious fields of christianity and islam, have expressed their opinions in details in this regard. in discussing the consequences of faith, paul the apostle talks about salvation, justness, new life, security from devils and enemies, calmness and reception of god’s promises. ...

the present study seeks to explain and analyse some of the fundamentals of hick’s discussion of the problem of evil or theodicy. in this study, while analysing john hick’s solution to the problem of the existence of evil in the world, we will see that he begins his exposition of the discussion of theodicy by interpreting the notion of primordial fall (and sin) as a myth and opines that moral ev...

Eternal inflation is a term that describes a number of different phenomena which have been classified by Winitzki. According to Winitzki’s classification these phases can be characterized by the topology of the percolating structures in the inflating, “white,” region. In this paper we discuss these phases, the transitions between them, and the way they are seen by a “Census Taker”; a hypothetic...

Experiments have shown that punishment enhances socially beneficial cooperation but that the costs of punishment outweigh the gains from cooperation. This challenges evolutionary models of altruistic cooperation and punishment, which predict that punishment will be beneficial. We compared 10- and 50-period cooperation experiments. With the longer time horizon, punishment is unambiguously benefi...

We present an interpretation of the physics of space-times undergoing eternal inflation by repeated nucleation of bubbles. In many cases the physics can be interpreted in terms of the quantum mechanics of a system with a finite number of states. If this interpretation is correct, the conventional picture of these space-times is misleading.

The Economics of Altruistic Punishment and the Demise of Cooperation Explaining the evolution and maintenance of cooperation among unrelated individuals is one of the fundamental problems in biology and the social sciences. Recent experimental evidence suggests that altruistic punishment is an important mechanism to maintain cooperation among humans. In this paper we explore the boundary condit...