title: There are asymptotically the same number of Latin squares of each parity

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: A Latin square is reduced if its first row and column are in natural order. For Latin squares of a particular order n there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality between the numbers of reduced Latin squares of each possible parity as the order n → ∞.

text: There are asymptotically the same number of Latin squares of each parity A Latin square is reduced if its first row and column are in natural order. For Latin squares of a particular order n there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality between the numbers of reduced Latin squares of each possible parity as the order n → ∞.

year: 2016

title: The reactivity of [Pt₂(μ-S)₂(PPh₃)₄] towards difunctional chloroacetamide alkylating agents: Formation of cyclized or bridged products

authors: Ujam, Oguejiofo Theophilus

subjects: platinum complexes

abstract: The reactions of [Pt₂(μ-S)₂(PPh₃)₄] towards some bis(chloroacetamide) alkylating agents have been investigated. Reaction with one mole equivalent of the hydrazine-derived compound ClCH₂C(O)NHNHC(O)CH₂Cl led to the cyclized product [Pt₂{SCH₂C(O)NHNHC(O)CH₂S}(PPh₃)₄]²⁺ which showed two different PPh₃ environments in the ³¹P{1H} NMR spectrum, as a result of non-fluxional behavior of the dithiolate ligand in solution. Reactions of [Pt₂(μ-S)₂(PPh₃)₄] with the ortho and para isomers of the phenylenediamine-derived bis(chloroacetamides) ClCH2C(O)NHC6H4NHC(O)CH2Cl gave tetrametallic complexes containing two {Pt₂S₂} moieties spanned by the CH₂C(O)NHC₆H₄NHC(O)CH₂ group. Both the ortho and para isomers were crystallographically characterized; in the ortho isomer there is intramolecular CO=H–N and S•••H–N hydrogen bonding involving the two amide groups.

text: The reactivity of [Pt₂(μ-S)₂(PPh₃)₄] towards difunctional chloroacetamide alkylating agents: Formation of cyclized or bridged products The reactions of [Pt₂(μ-S)₂(PPh₃)₄] towards some bis(chloroacetamide) alkylating agents have been investigated. Reaction with one mole equivalent of the hydrazine-derived compound ClCH₂C(O)NHNHC(O)CH₂Cl led to the cyclized product [Pt₂{SCH₂C(O)NHNHC(O)CH₂S}(PPh₃)₄]²⁺ which showed two different PPh₃ environments in the ³¹P{1H} NMR spectrum, as a result of non-fluxional behavior of the dithiolate ligand in solution. Reactions of [Pt₂(μ-S)₂(PPh₃)₄] with the ortho and para isomers of the phenylenediamine-derived bis(chloroacetamides) ClCH2C(O)NHC6H4NHC(O)CH2Cl gave tetrametallic complexes containing two {Pt₂S₂} moieties spanned by the CH₂C(O)NHC₆H₄NHC(O)CH₂ group. Both the ortho and para isomers were crystallographically characterized; in the ortho isomer there is intramolecular CO=H–N and S•••H–N hydrogen bonding involving the two amide groups.

year: 2011

title: Indigenous epistemology in a national curriculum framework?

authors: Macfarlane, Angus

subjects: curriculum competencies

abstract: In this article, a group of four indigenous Māori educators and one non-Māori educator comment on a proposed amendment to the New Zealand National Curriculum Framework to replace the current separate sets of skills, values and attitudes with five generic performance-based key competencies. The paper discusses important parallels between western/European sociocultural theorizing on human development and learning (on which the key competencies seemed to be based), and the values, beliefs and preferred practices that are embodied within an indigenous Māori cultural worldview (Te Ao Māori). A Māori worldview is characterized by an abiding concern for the quality of human relationships that need to be established and maintained if learning contexts are to be effective for Māori students, and for these relationships to balance individual learning and achievement against responsibilities for the well-being and achievement of the group. Within such a worldview, education is understood as holistic, collective, experiential and dependent upon a free exchanging of teaching and learning roles. The article describes five specific cultural constructs within this worldview that highlight Māori traditional understandings of human development and learning and teaching, and aligns and compares these constructs with the five key competencies proposed. The article argues that the worldviews of Māori people in New Zealand provide an extensive and coherent framework for theorizing about human development and education, and are able to contribute strongly and positively to the development of a national school curriculum for the benefit all students. Implications for other contexts can also be drawn.

text: Indigenous epistemology in a national curriculum framework? In this article, a group of four indigenous Māori educators and one non-Māori educator comment on a proposed amendment to the New Zealand National Curriculum Framework to replace the current separate sets of skills, values and attitudes with five generic performance-based key competencies. The paper discusses important parallels between western/European sociocultural theorizing on human development and learning (on which the key competencies seemed to be based), and the values, beliefs and preferred practices that are embodied within an indigenous Māori cultural worldview (Te Ao Māori). A Māori worldview is characterized by an abiding concern for the quality of human relationships that need to be established and maintained if learning contexts are to be effective for Māori students, and for these relationships to balance individual learning and achievement against responsibilities for the well-being and achievement of the group. Within such a worldview, education is understood as holistic, collective, experiential and dependent upon a free exchanging of teaching and learning roles. The article describes five specific cultural constructs within this worldview that highlight Māori traditional understandings of human development and learning and teaching, and aligns and compares these constructs with the five key competencies proposed. The article argues that the worldviews of Māori people in New Zealand provide an extensive and coherent framework for theorizing about human development and education, and are able to contribute strongly and positively to the development of a national school curriculum for the benefit all students. Implications for other contexts can also be drawn.

year: 2008