Tags » Math.OA

the influence of real world history on fantasy lore

Sometimes, fantasy worlds apply elements to themselves that very closely resemble historical events of our own world. Of course there’s the valid line of thought that constitutes┬áthat we have come up with nothing new, and that we simply only can pull from our past, or knowledge that we have acquired. 524 more words

PA Lore

Constructing one the most resilient races of Project Alternatum

This race has a very small population compared to all other civilized races, and in fact is the most indifferent towards others as well. As the laws of nature would have it, they are also the most disciplined and strongest of all. 1,149 more words

PA Lore

The integration of irreligious and unspiritual practices into a fantasy world

In Bejaan, the world that most of Project Alternatum takes place in, religious influence is the cause of many cultural ideologies and societal structures. Some societies have very strict theological pantheons, and are willing to die for their beliefs. 1,015 more words

PA Lore

The origins of human civilization and the Desert Magnus

The Human race is not ubiquitous throughout the world (Bejaan), and is in fact suppressed into a corner of it. They inhabit what is now the Desert Magnus and the small mountain range (The Funteina Mountains) to the North of it. 834 more words

PA Lore

Discretised wave equations

The wave equation is usually expressed in the form

where is a function of both time and space , with being the Laplacian operator. One can generalise this equation in a number of ways, for instance by replacing the spatial domain with some other manifold and replacing the Laplacian with the Laplace-Beltrami operator or adding lower order terms (such as a potential, or a coupling with a magnetic field). 1,149 more words


A Banach algebra proof of the prime number theorem

The prime number theorem can be expressed as the assertion

as , where

is the von Mangoldt function. It is a basic result in analytic number theory, but requires a bit of effort to prove. 1,967 more words