We introduce the notion of an : a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully...

In this article we show that even with the Distributive Law in effect we can still use the TAB Postulate to derive the Distribution Law for the Primes Numbers that was derived in ”TAB Theory and Eratosthenes I”.Dirichlet's Theorem is also discussed here because it too depends on the...

The driving idea of this work is that the test-and-branch operation familiar to computer programmers draws new information into a computation. This idea is used to justify an information-theoretic/probabilistic approach to some problems in the prime numbers. One result is a complete law for the...

The driving idea of this work is that the test-and-branch operation familiar to computer programmers draws new information into a computation. This idea is used to justify an information-theoretic/probabilistic approach to some problems in the prime numbers. We use it here against the Riemann...

We consider identity excluding groups. We first show that motion groups of totally disconnected nilpotent groups are identity excluding. We prove that certain class of p-adic algebraic groups which includes algebraic groups whose solvable radical is type have identity excluding property. We also...

We investigate functions which are solutions of the equation ″ = − 2 and related ones. Solutions which satisfy also the initial conditions (0) = 0, ′(0) = 1 and (0) = 1, ′(0) = 0 are known as lemniscatic sine and cosine functions respectively. Taking our cue from the theory of elementary...

We prove Khinchin's Theorems for Gelfand pairs (, ) satisfying a condition (*): (a) is connected; (b) is almost connected and Ad (/) is almost algebraic for some compact normal subgroup ; (c) admits a compact open normal subgroup; (d) (, ) is symmetric and is 2-root compact; (e) is a...