title: Harmonic sets and the harmonic prime number theorem

authors: Broughan, Kevin A.

subjects: harmonic prime number theorem

abstract: We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2.

text: Harmonic sets and the harmonic prime number theorem We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2.

year: 2005

title: The Routledge handbook of planning for health and well-being: shaping a sustainable and healthy future [Book Review]

authors: Mackness, Kate

subjects: Science & Technology

abstract: This article reviews the book “The Routledge handbook of planning for health and well-being: shaping a sustainable and healthy future”, edited by Hugh Barton, Susan Thompson, Sarah Burgess and Marcus Grant, Abingdon, Oxon, Routledge, 2015, 617 pp.

text: The Routledge handbook of planning for health and well-being: shaping a sustainable and healthy future [Book Review] This article reviews the book “The Routledge handbook of planning for health and well-being: shaping a sustainable and healthy future”, edited by Hugh Barton, Susan Thompson, Sarah Burgess and Marcus Grant, Abingdon, Oxon, Routledge, 2015, 617 pp.

year: 2018

title: Maori thinking with a dead white male: Philosophizing in the realm of Novalis

authors: Mika, Carl Te Hira

subjects: Novalis

abstract: In this paper I shall discuss my experiences of referring to Novalis in the context of Maori postcolonialism and metaphysical philosophy. As with other methods of research, from a Maori perspective one always alights on and then carries the effects of the philosopher that stands behind the method, whether the philosopher is silent or explicit. This important onto-epistemological interaction, in a general sense, acknowledges for the indigenous person that one is always ‘within’ the world and not detached from it. The maligned dead white male hence unavoidably becomes the highly constructive, living impulse behind what is to become fresh and innovative indigenous thinking.

text: Maori thinking with a dead white male: Philosophizing in the realm of Novalis In this paper I shall discuss my experiences of referring to Novalis in the context of Maori postcolonialism and metaphysical philosophy. As with other methods of research, from a Maori perspective one always alights on and then carries the effects of the philosopher that stands behind the method, whether the philosopher is silent or explicit. This important onto-epistemological interaction, in a general sense, acknowledges for the indigenous person that one is always ‘within’ the world and not detached from it. The maligned dead white male hence unavoidably becomes the highly constructive, living impulse behind what is to become fresh and innovative indigenous thinking.

year: 2014