title: Flat primes and thin primes

authors: Broughan, Kevin A.

subjects: flat prime

abstract: A number is called upper (lower) flat if its shift by +1 ( −1) is a power of 2 times a squarefree number. If the squarefree number is 1 or a single odd prime then the original number is called upper (lower) thin. Upper flat numbers which are primes arise in the study of multi-perfect numbers. Here we show that the lower or upper flat primes have asymptotic density relative to that of the full set of primes given by twice Artin’s constant, that more than 53% of the primes are both lower and upper flat, and that the series of reciprocals of the lower or the upper thin primes converges.

text: Flat primes and thin primes A number is called upper (lower) flat if its shift by +1 ( −1) is a power of 2 times a squarefree number. If the squarefree number is 1 or a single odd prime then the original number is called upper (lower) thin. Upper flat numbers which are primes arise in the study of multi-perfect numbers. Here we show that the lower or upper flat primes have asymptotic density relative to that of the full set of primes given by twice Artin’s constant, that more than 53% of the primes are both lower and upper flat, and that the series of reciprocals of the lower or the upper thin primes converges.

year: 2010

title: Children’s perceptions of unfair reward and punishment

authors: Evans, Ian M.

subjects: child development

abstract: Being able to judge the fairness of a personal encounter and having an appreciation of the associated feelings are important components of prosocial development. This study explored a common feature of everyday experience: unfair reward and unfair punishment. Scenarios depicting 4 possible variants of unfairness were read to children aged 9 to 11 years, who then made judgments regarding the degree of unfairness and the nature and strength of the feelings experienced by the characters. Our hypothesis that children with classroom conduct problems would judge the non-receipt of a deserved reward as worse than the receipt of an undeserved punishment was not confirmed. This differentiation, however, did prove to be characteristic of boys in general, but not girls. Being asked to think of unfair things that had actually happened did not appear to influence the children's responses to hypothetical unfair situations, but did reveal that children experience and remember a variety of unfair events in everyday family contexts. This study provides evidence that children actively monitor the receipt of social reward and punishment according to their perception of fairness.

text: Children’s perceptions of unfair reward and punishment Being able to judge the fairness of a personal encounter and having an appreciation of the associated feelings are important components of prosocial development. This study explored a common feature of everyday experience: unfair reward and unfair punishment. Scenarios depicting 4 possible variants of unfairness were read to children aged 9 to 11 years, who then made judgments regarding the degree of unfairness and the nature and strength of the feelings experienced by the characters. Our hypothesis that children with classroom conduct problems would judge the non-receipt of a deserved reward as worse than the receipt of an undeserved punishment was not confirmed. This differentiation, however, did prove to be characteristic of boys in general, but not girls. Being asked to think of unfair things that had actually happened did not appear to influence the children's responses to hypothetical unfair situations, but did reveal that children experience and remember a variety of unfair events in everyday family contexts. This study provides evidence that children actively monitor the receipt of social reward and punishment according to their perception of fairness.

year: 2001

title: Coaching for the game of life: Driving coaching with mana

authors: Were, Brandyn Māia

subjects: Kaupapa Māori

abstract: Coaching needs to account for culture. This indigenous autoethnography explores personal experience to show how I, a young Māori male coach in Aotearoa New Zealand, navigates the complex nature of coaching. By weaving together Kaupapa Māori, established coaching knowledge, and experiences from my playing and coaching journey to date, a Kaupapa Māori coaching framework emerges – Driving Coaching with Mana.

As I reflect on the teachings of my coach, Mr. Mel Young, combined with my cultural identity, I reconnect to critical moments in my life that have shaped the person I am today and the values I hold, elevating the centrality of culture through the practice of Kaupapa, Ako, Manaakitanga, Whanaungatanga, Wairuatanga, and self-reflection as Āta-kaiako (a reflective coach).

Driven to enhance the development of rangatahi (youth) through sport, and informed by literature and experience, Driving Coaching with Mana is personally and culturally grounded – a way of thinking about coaching differently and in a more holistic way. There is more to the people we coach than their lives as athletes. Coaching is more than skill acquisition.

text: Coaching for the game of life: Driving coaching with mana Coaching needs to account for culture. This indigenous autoethnography explores personal experience to show how I, a young Māori male coach in Aotearoa New Zealand, navigates the complex nature of coaching. By weaving together Kaupapa Māori, established coaching knowledge, and experiences from my playing and coaching journey to date, a Kaupapa Māori coaching framework emerges – Driving Coaching with Mana.

As I reflect on the teachings of my coach, Mr. Mel Young, combined with my cultural identity, I reconnect to critical moments in my life that have shaped the person I am today and the values I hold, elevating the centrality of culture through the practice of Kaupapa, Ako, Manaakitanga, Whanaungatanga, Wairuatanga, and self-reflection as Āta-kaiako (a reflective coach).

Driven to enhance the development of rangatahi (youth) through sport, and informed by literature and experience, Driving Coaching with Mana is personally and culturally grounded – a way of thinking about coaching differently and in a more holistic way. There is more to the people we coach than their lives as athletes. Coaching is more than skill acquisition.

year: 2023