title: Fair testing revisited: A process-algebraic characterisation of conflicts

authors: Malik, Robi

subjects: computer science

abstract: This paper studies conflicts from a process-algebraic point of view and shows how they are related to the testing theory of fair testing. Conflicts have been introduced in the context of discrete event systems, where two concurrent systems are said to be in conflict if they can get trapped in a situation where they are waiting or running endlessly, forever unable to complete their common task. In order to analyse complex discrete event systems, conflict-preserving notions of refinement and equivalence are needed. This paper characterises an appropriate refinement, called the conflict preorder, and provides a denotational semantics for it. Its relationship to other known process preorders is explored, and it is shown to generalise the fair testing preorder in process-algebra for reasoning about conflicts in discrete event systems.

text: Fair testing revisited: A process-algebraic characterisation of conflicts This paper studies conflicts from a process-algebraic point of view and shows how they are related to the testing theory of fair testing. Conflicts have been introduced in the context of discrete event systems, where two concurrent systems are said to be in conflict if they can get trapped in a situation where they are waiting or running endlessly, forever unable to complete their common task. In order to analyse complex discrete event systems, conflict-preserving notions of refinement and equivalence are needed. This paper characterises an appropriate refinement, called the conflict preorder, and provides a denotational semantics for it. Its relationship to other known process preorders is explored, and it is shown to generalise the fair testing preorder in process-algebra for reasoning about conflicts in discrete event systems.

year: 2004

title: Topics in number theory

authors: Braun, Peter Brendan

abstract: The thesis is concerned mainly with topics in the theory of Riemann’s zeta function, but it also includes some contributions to prime number theory and the study of the Möbius function. New conditions are stated for the validity of the quasi-Riemann hypothesis RH (σ₀), that ζ(s) ≠ O for σ > σ₀. The orders and oscillatory behaviour of a variety of summatory functions are considered in this context. Particular study is made of the sums defined by
[formula]
And
[formula]
(k = 0, 1, 2 ...), incomplete sums of the form
[formula]
and summatory functions associated with the coefficients of the Dirichlet series representations for 
[formula]
On the same topic results are proven about connections between RH (σ₀) and the distribution of the set HN of Farey numbers of order N. Some general theorems concerning the sums
[formula]
are established which allow known results in the cases r = 2, 3 to be extended to r = 4, 5, 6. Other analytic studies include a series representation for Riemann’s function, and a theorem improving earlier results concerning the number of zeros of f(λ + i) with 0 < t < T, and fixed λ between 0 and 1, where f (s) = π⁻ˢ/² г(s/2) ζ (s).
The remaining topics are more arithmetic in nature. An attempt is made to show by elementary methods that the order of the Tchebychef difference ψ(x) - x is not greater than that of the Möbius sum M(x), and although only partially successful, the attempt improves on previously published elementary results. Some theorems are proved which relate the order of J (x), the maximum number of consecutive integers each of which is divisible by at least one prime ≤x, to the problems of the least prime in an arithmetic progression and the order of the difference between consecutive primes. Two sections contain a direct attack by elementary methods on the problem of getting estimates of A₀(T) and B₀(T) which would be equivalent to RH(σ₀) for some σ₀ < 1, and the problem is reduced, roughly speaking, to finding sufficiently large N such that the solutions x₁, x₂, ..., xᴛ of the system 
[formula]
 are predominantly of one sign.
The closing sections in the thesis deal with Möbius functions of ordered semigroups of a certain type, and lead to a conjecture that the Möbius functions in a way characterize the ordered multiplicative structure. Some evidence supporting the conjecture is given in the case of the ordinary Möbius function μ.

text: Topics in number theory The thesis is concerned mainly with topics in the theory of Riemann’s zeta function, but it also includes some contributions to prime number theory and the study of the Möbius function. New conditions are stated for the validity of the quasi-Riemann hypothesis RH (σ₀), that ζ(s) ≠ O for σ > σ₀. The orders and oscillatory behaviour of a variety of summatory functions are considered in this context. Particular study is made of the sums defined by
[formula]
And
[formula]
(k = 0, 1, 2 ...), incomplete sums of the form
[formula]
and summatory functions associated with the coefficients of the Dirichlet series representations for 
[formula]
On the same topic results are proven about connections between RH (σ₀) and the distribution of the set HN of Farey numbers of order N. Some general theorems concerning the sums
[formula]
are established which allow known results in the cases r = 2, 3 to be extended to r = 4, 5, 6. Other analytic studies include a series representation for Riemann’s function, and a theorem improving earlier results concerning the number of zeros of f(λ + i) with 0 < t < T, and fixed λ between 0 and 1, where f (s) = π⁻ˢ/² г(s/2) ζ (s).
The remaining topics are more arithmetic in nature. An attempt is made to show by elementary methods that the order of the Tchebychef difference ψ(x) - x is not greater than that of the Möbius sum M(x), and although only partially successful, the attempt improves on previously published elementary results. Some theorems are proved which relate the order of J (x), the maximum number of consecutive integers each of which is divisible by at least one prime ≤x, to the problems of the least prime in an arithmetic progression and the order of the difference between consecutive primes. Two sections contain a direct attack by elementary methods on the problem of getting estimates of A₀(T) and B₀(T) which would be equivalent to RH(σ₀) for some σ₀ < 1, and the problem is reduced, roughly speaking, to finding sufficiently large N such that the solutions x₁, x₂, ..., xᴛ of the system 
[formula]
 are predominantly of one sign.
The closing sections in the thesis deal with Möbius functions of ordered semigroups of a certain type, and lead to a conjecture that the Möbius functions in a way characterize the ordered multiplicative structure. Some evidence supporting the conjecture is given in the case of the ordinary Möbius function μ.

year: 1979

title: The use of Māori words in National Science Challenge online discourse

authors: Calude, Andreea S.

subjects: Maori loanwords

abstract: New Zealand English is well-known for its heavy borrowing of words from Māori. This lexical component, unique to New Zealand English alone has been studied intensely over the last 50 years, particularly in newspaper media. Current research suggests the use is still increasing today, primarily in Māori-related contexts. Here, we analyse a surprising and unexpected use of Māori loanwords in science digital discourse (neither genre being previously investigated), where we discover a strong presence of Māori borrowings in National Science Challenge website and Twitter content. Using corpus linguistics methods, we argue that the use of Māori loanwords in this genre functions as a national identity building tool, used by various authors to signal that the ‘challenges’ the country faces are uniquely New Zealand’s ‘challenges’.

text: The use of Māori words in National Science Challenge online discourse New Zealand English is well-known for its heavy borrowing of words from Māori. This lexical component, unique to New Zealand English alone has been studied intensely over the last 50 years, particularly in newspaper media. Current research suggests the use is still increasing today, primarily in Māori-related contexts. Here, we analyse a surprising and unexpected use of Māori loanwords in science digital discourse (neither genre being previously investigated), where we discover a strong presence of Māori borrowings in National Science Challenge website and Twitter content. Using corpus linguistics methods, we argue that the use of Māori loanwords in this genre functions as a national identity building tool, used by various authors to signal that the ‘challenges’ the country faces are uniquely New Zealand’s ‘challenges’.

year: 2019