Nuclei, Primes and the Random Matrix Connection

Nuclei, Primes and the Random Matrix Connection

In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been fruitfully applied in the other. The exciting branch of modern mathematics – random matrix theory – provides the connection between the two fields. We assume no det...

Raytracing and the camera matrix – a connection

In this section we derive the algebraic equations commonly used in the computer graphics technique of raytracing, where the simulation of geometric propagation of rays in an illuminated scene is used to produce highly realistic renderings of three-dimensional virtual scenes. Somewhat counter-intuitively, but for reasons of efficiency, in practical raytracer implementations, ray trajectories ori...

Finding Four Million Large Random Primes

The Random Connection Model on the Torus

We study the diameter of a family of random graphs on the torus that can be used to model wireless networks. In the random connection model two points x and y are connected with probability g(y − x) where g is a given function. We prove that the diameter of the graph is bounded by a constant, that only depends on ‖g‖1, with high probability as the number of vertices in the graph tends to infinity.

Fast Generation of Random, Strong Rsa Primes

A number of cryptographic standards currently under development call for the use of strong primes in the generation of an RSA key. This paper suggests a fast way of generating random strong primes that also satisfy a number of other cryptographic requirements. The method requires no more time to generate strong primes than it takes to generate random primes.