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 ...

From Windows Vista onwards, Microsoft has placed a substantially greater focus on the security of the operating system, which is one of the areas most users will neglect and then later come to complain about. In this article I'm going to talk about Windows Integrity Levels, and how we can view this information in WinDbg and through some SysInternals Tools. In another article, I will going into more depth about access tokens and how they are used to increase system security. These security measures were introduced since it was relatively easy to modify memory and remove any security identification, thus leads to code modification and injection being used to allow illegitimate access to important system data structures etc. User-Mode processes often require the use of system services and system resources which reside within the Kernel-Mode. To stop any illegitimate access or any poor programming from creating havoc in Kernel-Mode, some security validation procedures have been introd...

This post is a little irrelevant to general contents of my blog, but I found this to be a interesting geometry problem and it does have some ties with Computational Geometry, which is form a of theoretical computer science. There is additionally some connection with Computational Complexity Theory too. The Bin Packing Problem isn't difficult to explain, and yet can be difficult to find a optimal solution. With Discrete Mathematics, I personally find that the branches within this field are more accessible but the problems are difficult enough to be interesting and form a field of serious mathematical study. I'm only a amateur mathematician and a student, so if there are any problems then please highlight them in the comments section. Bin Packing Problem: The Bin Packing Problem is an example of a optimization problem which has a surprisingly large number of applications, especially in logistics and data management. The Bin Packing Problem asks to minimize the number of bins need...

The !podev , !poreqlist and !poaction aren't documented within WinDbg for some reason, but there is a person which has written about them thankfully. These extensions are a must for Stop 0x0A and debugging any issues related to power like Stop 0x9F. !popolicy  The !popolicy displays information related to the current power policy of the current user.  !pocaps The !pocaps extensions displays information in relation to the power capabilities of the system, this is ideal for checking if drivers are attempting to use a unsupported sleep state. !poreqlist The !poreqlist extension will list all outstanding power IRPs from any driver which has called the PoRequestPowerIrp function. The function will create a Power IRP and then send it to the top of the device stack for a given device object.  The list of power IRPs will be shown under the FieldOffset field. The extension will provide the device object, driver object and the nature of the power IRP. !poaction  The !p...

I thought I would create a list of Maths topics which were relevant for those who are wishing to study Computer Science. I've seen most people on online communities referring to topics which have very little relevance or completely pointless in relation to Computer Science. This list is based upon my experiences and a friend who studies Computer Science at University. I've listed the most popular Computer Science fields and their Maths topics below. General Computer Science: These are the topics which you will typically study in your first year, and therefore will have to do. Graph Theory Linear Algebra (Matrices and Vectors) Calculus I and maybe some Calculus II  Analytical Geometry Set Theory Big O Notation Radicals, Logarithms and Polynomials Logic Computer Graphics:  I'm not too sure about Graphics, but these are the subjects which do have some relevance. Fractal Geometry Linear Algebra Analytical Geometry Differentiable Geometry Hyperbolic Geometry Differential Equati...