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...

The classical Ulm theory provides a complete set of invariants for countable abelian p-groups, and hence also for countable torsion abelian groups. These invariants involve countable ordinals. One can read off many simple structural properties of such groups directly from the Ulm theory. We...

The theory of hypernumbers is a novel approach in functional analysis aimed at the development of such mathematically correct technique, which allows operations with divergent integrals and series. Although, it resembles nonstandard analysis, there are several distinctions between these...

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...

The probability for a device to work properly after a certain period of time will be considered using the Strehler-Mildvan model. We will suppose that the functionality of a device depends on an unknown parameter , which decreases progressively in time. The device stops working if goes below a...