flynn017

I thought I would wrote a small article on some numbers which I find interesting, I may expand upon this topic in the future, but for this article I'm going to restrict myself to three forms of number: Kaprekar's Constant, Polygonal Numbers and Highly Composite Numbers. Kaprekar's Constant:  Kaprekar's Constant is a special constant discovered by the Indian Mathematician called D.R.Kaprekar. The constant has the value of 6174. The constant comes from a simple algorithm known as Kaprekar's Routine. The constant can be produced from at most 7 iterations. Kaprekar's Constant will always be produced after iterating through Kaprekar's Routine, when given an arbitrary 4 digit integer, providing that at least two of the digits are different otherwise the constant will not be produced. For example, using 3524 from Wikipedia (since the number of steps is knowingly small), arrange the number in descending order and then ascending order. Subtract these two numbers, and...

As with Bull Graphs, House Graphs are simple graphs (not the Graph Theoretic definition) which have been neglected. They may not be interesting or yield any important findings to professional research mathematicians, but I haven't been able to find a paper or website which lists or shows any of the House Graphs properly at all. My intention is simply to state and prove of these properties. Please note I'm not a professional mathematician and I'm not even studying for a Mathematics degree (Computer Science), and therefore may make mistakes or misunderstandings. There are two main variants of House Graphs, and in this article I will listing the Vertex Colouring and Edge Colouring properties of such graphs. The two graphs are the House Graph and the House-X Graph. House Graph House-X Graph Both of the graphs are simple graphs, and the same number of vertices. In terms of the structure of the graph, the only difference between the graphs are the number of edges. The number edge...

Windows needs to ensure that untrusted code and untrusted users aren't accessing important areas of the operating system, and creating problems which would ultimately lead to a vast number of BSODs. Windows manages this through Access Tokens which are used to identify the security context of a process/thread and a user. Access Tokens take two main forms: a Primary access token and a Impersonation access token. The Access Token additionally has two important features which are integral to security validation: SIDs (Security Identifiers) and a Privilege Array which contains the privileges allowed for that object. The token type can be found within a enumeration called TOKEN_TYPE.   The data structure can be found under the TokenType field within the _TOKEN structure. The Primary type determines the security context of the process for the currently logged on user, and the Impersonation type allows a thread to temporarily use a different security context. The Token type can also ...