Jonathan Arbib

Papers & Research


Circuits in Complete Graphs and the Dwyer Function

by on May.30, 2008, under Papers & Research

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.

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Counting the Number of Euler Circuits in Complete Graphs

by on May.29, 2008, under Papers & Research

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

News Item

Author: Professor John Dwyer

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Security Measures in GSM Networks and Possible Attack Methods

by on May.17, 2008, under Papers & Research

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

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Euler Circuits White Board Fun

by on Mar.23, 2007, under Papers & Research

Having some fun on the White board at Richmond University after working for a few hours on Euler Circuits… 🙂

euler1

euler2

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