For every continuous $f$ there is an absolutely continuous $g$ such that $[f=g]$ is not bilaterally strongly porous

Why Believe That There Is a God?

This article presents an argument for the existence of God, showing that the evident phenomena are best explained by supposing that a God causes them. The argument is based on the inductive force of four very evident general phenomena: that there is a physical Universe; that it is governed by very simple natural laws; that those laws are such as to lead to the existence of human bodies; and tha...

Now f is continuous (exercise!)

Absolutely Continuous Invariant Measures That Are Maximal

Let A be a certain irreducible 0-1 matrix and let t denote the family of piecewise linear Markov maps on [0,1] which are consistent with A. The main result of this paper characterizes those maps in t whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.

Computable real function F such that F is not polynomial time computable on [0, 1]

A computable real function F on [0,1] is constructed such that there exists an exponential time algorithm for the evaluation of the function on [0,1] on Turing machine but there does not exist any polynomial time algorithm for the evaluation of the function on [0,1] on Turing machine (moreover, it holds for any rational point on (0,1))

Academic nepotism – all that glitters is not gold

Dear Editor With increasing emphasis on publications forfaculty recruitment, career advancementand obtaining research grants, the issues relatedto author kinship and academic nepotism havegrown significantly and these probably reflectthe inflationary growth rather than the optimalgrowth warranted due to increasing researchcomplexity. Allesina S (1) measured the fullmagnitude of nepotism in the ...