Jonathan Arbib » Papers & Research http://arbib.it Mzee mulimu; A bit of my work, life, and experiences. Sun, 22 Jan 2012 13:33:31 +0000 en hourly 1 http://wordpress.org/?v=3.3.1 Circuits in Complete Graphs and the Dwyer Function http://arbib.it/2008/05/30/circuits-in-complete-graphs-and-the-dwyer-function-2/ http://arbib.it/2008/05/30/circuits-in-complete-graphs-and-the-dwyer-function-2/#comments Fri, 30 May 2008 15:26:19 +0000 ac3bf1 http://arbib.it/?p=533 CIRCUITS IN COMPLETE GRAPHS AND THEIR RELATIONS TO RAPIDLY-INCREASING SPECIAL FUNCTIONS

Published on http://www.algana.co.uk/Research/research.html

Download Paper – circuits-in-complete-graphs

News item on Richmond Website

This is from work I did last year with class mates. It proved to be really interesting, and possibly the most interesting mathematical topic I ever encountered :-)

ABSTRACT
Author: Professor John Dwyer

In computing, several rapidly-increasing functions are used in areas such as computability, algorithm analysis and tractability. These include Ackerman’s function, Dwyer’s function and Euler’s Gamma function. This paper investigates these functions and compares them asymptotically.

Acknowledgements

Several colleagues and project students contributed to the results detailed in this paper, including Professor Wathek Talebaoui, Danladi Abdulaziz, Karwan Al-Sourchi, Jonathan Arbib, Denka Bancheva, Jordan Berkowitz, Emma Dwyer, Daniel Frincu, Salisu Gambo, Saniul Hossain, Ike Igboanugo, Elyse Loosararian, Alin Petculescu, Vjose Retkoceri, Ademola Shasanya and Long Tran.

]]> http://arbib.it/2008/05/30/circuits-in-complete-graphs-and-the-dwyer-function-2/feed/ 2 Counting the Number of Euler Circuits in Complete Graphs http://arbib.it/2008/05/29/counting-the-number-of-euler-circuits-in-complete-graphs/ http://arbib.it/2008/05/29/counting-the-number-of-euler-circuits-in-complete-graphs/#comments Thu, 29 May 2008 13:03:03 +0000 ac3bf1 http://ac3bf1.org/?p=20 Abstract
In graph theory, a long standing problem has involved finding
a closed form expression for the number of Euler circuits in
Kn. The solution presented here comprises a function D(x,y)
that has several interesting applications in computing.

Download Paper

Author: Professor John Dwyer

]]> http://arbib.it/2008/05/29/counting-the-number-of-euler-circuits-in-complete-graphs/feed/ 0 Security Measures in GSM Networks and Possible Attack Methods http://arbib.it/2008/05/17/security-measures-in-gsm-networks-and-possible-attack-methods/ http://arbib.it/2008/05/17/security-measures-in-gsm-networks-and-possible-attack-methods/#comments Sat, 17 May 2008 11:14:52 +0000 ac3bf1 http://ac3bf1.org/2008/05/17/security-measures-in-gsm-networks-and-possible-attack-methods/ This project was born from the love of computing and communications, and the thrills of being able to overcome security measures in communication systems. The purpose of this project is to prove that it is possible for individuals to break though the barriers of GSM (Global System for Mobile communication) protection systems using common and publicly available tools. It has to be said in advance that devices able to intercept GSM conversations do exist; nonetheless these devices are only available to law enforcement agencies and special services.

Download PDF (2 MB)

Links:

http://lukenotricks.blogspot.com/2008/08/long-tail-of-vulnerability-for-a51.html
http://wiki.thc.org/gsm
http://cryptome.info/0001/a51-bsw/a51-bsw.htm

]]> http://arbib.it/2008/05/17/security-measures-in-gsm-networks-and-possible-attack-methods/feed/ 0 Euler Circuits White Board Fun http://arbib.it/2007/03/23/white-board-math-fun/ http://arbib.it/2007/03/23/white-board-math-fun/#comments Fri, 23 Mar 2007 12:57:19 +0000 ac3bf1 http://ac3bf1.org/?p=129 Having some fun on the White board at Richmond University after working for a few hours on Euler Circuits… :)

euler1

euler2

]]> http://arbib.it/2007/03/23/white-board-math-fun/feed/ 0