# School of Mathematical Sciences

• Globalization and advances in communications technology, notably satellite television and broadband internet, have greatly expanded the potential marketplace for professional sport teams. As a resu...
• Background: Life-threatening illnesses in young people are traumatic for patients and their families. Support services can help patients and families deal with various non-medical impacts of diagno...
• Let τ(n) denote the number of positive divisors of a natural number n > 1 and let σ(n) denote their sum. Then n is superharmonic if σ(n) | nκτ(n) for some positive integer κ. We deduce numerous pro...
• A number n > 1 is harmonic if σ(n) σ nτ(n), where τ(n) and σ(n) are the number of positive divisors of n and their sum, respectively. It is known that there are no odd harmonic numbers up to 1015. ...
• This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a pena...
• Let n > 2 be a positive integer and let φ denote Euler's totient function. Define φ1(n) = φ(n) and φk(n) = φ(φk-1(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ2(n)...
• © 2014 IEEE. Pointing is a typical means of directing a human's attention to a specific object or event. Robot pointing behaviours that direct the attention of humans are critical for human-robot i...
• We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No odd perfect numbers are known, but it is well known that if such a number exists, it must have pr...