Browsing by Author "Broughan, Kevin A."

• An Algorithm for the explicit evaluation of GL(n, R) Kolsterman sums 

  Broughan, Kevin A. (Association for Computing Machinery, 2009)

  An algorithm for the explicit evaluation of Kloosterman sums for GL(n, R) for n ≥2 and an implementation in the Mathematics package GL(n) pack are described

  

• Appendix: The GL(n) pack Manual 

  Broughan, Kevin A. (Cambridge University Press, 2006)

  This appendix is the manual for a set of functions written to assist the reader to understand and apply the theorems on GL(n, R) set out in the main part of the book. The software for the package is provided over the World ...

  

• Asymptotic order of the square free part of n! 

  Broughan, Kevin A. (2002)

  The asymptotic order of the logarithm of the square-free part of n! is shown to be (log 2)n with error O(√n ).

  

• The average order of the Dirichlet series of the gcd-sum function 

  Broughan, Kevin A. (University of Waterloo, Department of Computer Science, 2007)

  Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.

  

• The boundedness principle characterizes second category subsets 

  Broughan, Kevin A. (1977)

  Converses are proved for the Osgood (the Principle of Uniform Boundedness), Dini, and other well known. theorems. The notion of a continuous step function on a topological space is defined and a class of spaces identified ...

  

• Almost weak Asplund spaces 

  Somasundaram, Sivajah (The University of Waikato, 2004)

  Continuous convex functions have long been known to be generically differentiable on Euclidean spaces. However, in 1968 Asplund decided to investigate and classify those Banach spaces that possess this Euclidean space ...

  

• Computational and empirical thermal modelling of a proposed SOFC stack housing design 

  Fenton, Basil (The University of Waikato, 2004)

  Solid oxide fuel cells (SOFC) generate electricity cleanly, efficiently and quietly. There has been much effort in commercialising planar and large tubular SOFCs in the past two decades. Some research has involved modelling ...

  

• Critical sets of full Latin squares 

  Raass, Petelo Vaipuna (University of Waikato, 2016)

  This thesis explores the properties of critical sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes. In Chapter 3 we study ...

  

• Brocard's problem and variations 

  Liu, Yi (University of Waikato, 2013)

  This thesis examines the work which has been done on Brocard’s problem which is to study solutions to n! + 1 = x², and related problems of the form n! = f(x) or n! = f(x, y), where f is a polynomial with integer ...

  

• Comparison between the RSA cryptosystem and elliptic curve cryptography 

  Abdullah, Kamilah (The University of Waikato, 2010)

  In the globalization era, cryptography becomes more popular and powerful; in fact it is very important in many areas (i.e. mathematics, computer science, networks, etc). This thesis provides an overview and comparison ...

  

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