title: On square values of the product of the Euler totient and sum of divisors functions

authors: Broughan, Kevin A.

subjects: Euler function

abstract: If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m≤n. We put m = n - a and we study the positive integers a arising in this way.

text: On square values of the product of the Euler totient and sum of divisors functions If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m≤n. We put m = n - a and we study the positive integers a arising in this way.

year: 2012

title: Vacuum-assisted infiltration of chitosan or polycaprolactone as a structural reinforcement for sintered cancellous bovine bone graft

authors: Laird, Dougal Frazer

subjects: Sintered cancellous bovine bone

abstract: Sintered cancellous bovine bone (SCBB) offers numerous advantages as a bone graft substitute material; however, its mechanical properties require improvement. In this study, SCBB was infiltrated with ε-polycaprolactone (PCL) or chitosan/monetite to improve mechanical properties while retaining valuable SCBB structure. Organic infiltrating solutions consisted of (i) chitosan and monetite (CaHPO₄) dissolved in hydrochloric acid; (ii) chitosan, monetite (CaHPO₄), and genipin dissolved in hydrochloric acid; or (iii) PCL polymer dissolved in tetrahydrofuran (THF). Porous SCBB materials were infiltrated with one of the three solutions using vacuum-assisted infiltration. Chitosan and CaHPO₄ were immobilized in the SCBB structure by reprecipitation following a pH increase in an ammonia atmosphere. Genipin was used in one sample group to immobilize chitosan via crosslinking. PCL was immobilized by evaporating the THF carrier solvent. Mechanical compression testing showed an improvement in ultimate stress for the SCBB with chitosan/CaHPO₄ infiltrates, whereas PCL samples showed an increase in modulus. All SCBB samples were found to demonstrate favorable in vitro biocompatibility when subjected to L929 mouse fibroblast cells but required a vigorous washing regime to eradicate toxic ammonia residue. In conclusion, infiltration of SCBB with a polymeric or organic/mineral composite matrix positively modifies SCBB mechanical properties in favor of bone grafting applications.

text: Vacuum-assisted infiltration of chitosan or polycaprolactone as a structural reinforcement for sintered cancellous bovine bone graft Sintered cancellous bovine bone (SCBB) offers numerous advantages as a bone graft substitute material; however, its mechanical properties require improvement. In this study, SCBB was infiltrated with ε-polycaprolactone (PCL) or chitosan/monetite to improve mechanical properties while retaining valuable SCBB structure. Organic infiltrating solutions consisted of (i) chitosan and monetite (CaHPO₄) dissolved in hydrochloric acid; (ii) chitosan, monetite (CaHPO₄), and genipin dissolved in hydrochloric acid; or (iii) PCL polymer dissolved in tetrahydrofuran (THF). Porous SCBB materials were infiltrated with one of the three solutions using vacuum-assisted infiltration. Chitosan and CaHPO₄ were immobilized in the SCBB structure by reprecipitation following a pH increase in an ammonia atmosphere. Genipin was used in one sample group to immobilize chitosan via crosslinking. PCL was immobilized by evaporating the THF carrier solvent. Mechanical compression testing showed an improvement in ultimate stress for the SCBB with chitosan/CaHPO₄ infiltrates, whereas PCL samples showed an increase in modulus. All SCBB samples were found to demonstrate favorable in vitro biocompatibility when subjected to L929 mouse fibroblast cells but required a vigorous washing regime to eradicate toxic ammonia residue. In conclusion, infiltration of SCBB with a polymeric or organic/mineral composite matrix positively modifies SCBB mechanical properties in favor of bone grafting applications.

year: 2012

title: From the rākau to the ngākau

authors: Derby, Melissa

subjects: research

abstract: The Ministry of Business, Innovation and Employment (MBIE) in Aotearoa New Zealand has funded 11 National Science Challenges (NSC), which aim to tackle a series of big questions affecting wellbeing in society. One Challenge, A Better Start: E Tipu E Rea, is investigating four key focus areas that children encounter in their early development and is seeking to identify the factors that contribute to forming a solid foundation for fostering wellbeing and lifelong success. Central to the principles of this Challenge is the Treaty of Waitangi in that the Treaty provides a framework to guide whānau engagement, policy change, and praxis. This article describes how a ‘ngākau’ rather than a ‘rākau’ approach to shaping research inquiry within this Challenge facilitates more authentic and mana-enhancing whānau engagement in research interactions (Macfarlane, 2019). The development of a whānau questionnaire is drawn on to illustrate the ngākau approach in practice.

text: From the rākau to the ngākau The Ministry of Business, Innovation and Employment (MBIE) in Aotearoa New Zealand has funded 11 National Science Challenges (NSC), which aim to tackle a series of big questions affecting wellbeing in society. One Challenge, A Better Start: E Tipu E Rea, is investigating four key focus areas that children encounter in their early development and is seeking to identify the factors that contribute to forming a solid foundation for fostering wellbeing and lifelong success. Central to the principles of this Challenge is the Treaty of Waitangi in that the Treaty provides a framework to guide whānau engagement, policy change, and praxis. This article describes how a ‘ngākau’ rather than a ‘rākau’ approach to shaping research inquiry within this Challenge facilitates more authentic and mana-enhancing whānau engagement in research interactions (Macfarlane, 2019). The development of a whānau questionnaire is drawn on to illustrate the ngākau approach in practice.

year: 2021