title: Row-column block designs: Efficiency and structure

authors: Nie, Xiao

subjects: Latin Squares

abstract: A row-column design is any rearrangement of the blocks of a combinatorial design into a rectangular array. A row-column block design is a row-column design in which the blocks form a balanced incomplete block design; that is, each pair of elements occurs in a constant number of blocks. In this thesis we study the efficiency and structure of row-column block designs. In particular, we use solutions to Heffter’s difference problem to give construct row-column block designs with 3 elements per cell with optimal regularity in rows and columns.
In Section 1 we review definitions and theorems related to Latin squares. We introduce related concepts of balanced incomplete block designs and incidence matrix and concurrence matrix of designs. In Section 2 we give our main results of row-column block designs with block size 3. In Section 3 we use Heffter’s difference problem to give some solutions. In Section 4 we explain efficiency measures for block designs. In Section 5 we introduce Trojan semi-Latin squares. We give efficiency measures for Trojan semi-Latin squares. In Section 6 we show the applications to experimental design. Original results are given in the following theorems: Theorem 2.9, Theorem 3.1, Theorem 3.3, Theorem 3.4, Theorem 4.2, Theorem 5.2, Theorem 5.12.
Results from Section 2 and Section 3 have been submitted as a manuscript for publication [17] (Xiao Nie, Row-column block designs with blocks of size three, Ars Combinatoria, submitted).

text: Row-column block designs: Efficiency and structure A row-column design is any rearrangement of the blocks of a combinatorial design into a rectangular array. A row-column block design is a row-column design in which the blocks form a balanced incomplete block design; that is, each pair of elements occurs in a constant number of blocks. In this thesis we study the efficiency and structure of row-column block designs. In particular, we use solutions to Heffter’s difference problem to give construct row-column block designs with 3 elements per cell with optimal regularity in rows and columns.
In Section 1 we review definitions and theorems related to Latin squares. We introduce related concepts of balanced incomplete block designs and incidence matrix and concurrence matrix of designs. In Section 2 we give our main results of row-column block designs with block size 3. In Section 3 we use Heffter’s difference problem to give some solutions. In Section 4 we explain efficiency measures for block designs. In Section 5 we introduce Trojan semi-Latin squares. We give efficiency measures for Trojan semi-Latin squares. In Section 6 we show the applications to experimental design. Original results are given in the following theorems: Theorem 2.9, Theorem 3.1, Theorem 3.3, Theorem 3.4, Theorem 4.2, Theorem 5.2, Theorem 5.12.
Results from Section 2 and Section 3 have been submitted as a manuscript for publication [17] (Xiao Nie, Row-column block designs with blocks of size three, Ars Combinatoria, submitted).

year: 2024-09-23

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: Ngā maihi o Te Whare Hukahuka, ngā maihi o Te Whare o Ruamano: Te whare kōrero o ngā maihi o Tuteao

authors: Hona, Hakahaka Charlie Barlow

subjects: Tuteao

abstract: Ko Pūtauaki te maunga
Ko Rangitāiki te awa
Ko Hekerangi te papa whenua
Ko Tuteao te marae
Ko Ngā Maihi te hapū
Ko Ngāti Awa te iwi
Ko Mataatua te waka
Tihe mauri-ora
Ko tōku kāwai rangatira tēnei. E mōhio ai te tangata ko wai ahau; nō hea ahau, nā wai hoki ahau. Ā, nā whai anō taku urupounamu, ko wai a Ngā Maihi o Tuteao? E mea ana ngā pākeke, he iwi tawhito a Ngā Maihi i heke mai i ngā tātai whakapapa o Tangaroa, o Pōtiki, o Mahutapoanui, o Toroa, o Tuteao. Hēoi, kua kore e rangona ōna kōrero i runga marae ātea. Kua kore e wānangahia i roto i te poho o te whare o Tuteao. Kua ngū ngā poupou o te whare kōrero. Ka mutu, i roto i ngā tau tata nei kua riro tītapu ngā puna o te kī, ngā whītiki o te kupu, o te hapū; kua kore e rangona ngā kōrero o Ngā Maihi i runga marae ātea. Ko te haumate o te reo i runga o Tuteao tētahi take i pēnei ai. Nō reira, kai te imu te ruhi, kai te imu te ngēngē. E noho pōhara ana a Ngā Maihi ki ngā tāonga o tōna whare kōrero. Hei te tau 2027, ka whakanuia te rautau o te whare tīpuna a Tuteao, ā i tēnei tau tonu 2022, e whai whakaaro ana te hapū ki taua kaupapa otirā ki te hanga whare tīpuna hou; he whare kaitā e uru ai te tokomaha. Nō reira, e whakaaro ana hoki ki ngā kōrero ka whakairohia ki ngā pakitara o te whare. I tēnei tau hoki kua mana te whakaako i ngā kōrero hītori o te Māori i roto i ngā kura, nō reira he aha rā ngā kōrero e wātea ana ki ngā tamariki o ngā kura e pā ana ki a Ngā Maihi? He maramara, he kongakonga, he putunga kōrero e noho marara ana i ngā wāhi tūmatanui. He uaua te kitea o ētahi atu, kei ngā wāhi tūmataiti, pēnei i te Kōti Whenua Māori, i ngā tuhinga ā-whānau, kei ngā pukapuka wānanga o te marae. Nō reira, he uaua te kite atu i tōna whānuitanga, i tōna hohonutanga. Tīmata ake i ngā kohinga kōrero o te hapū tonu o Ngā Maihi, i ōna kaumātua, i ōna wānanga, i ōna whānau. I tua atu i wā te whare pukapuka, kei ngā wāhi tūmataiti ētahi putunga kōrero hei ō mo te whare kōrero o Ngā Maihi o Tuteao. Ka mutu, kei ngā waiata, ngā haka, ngā mōteatea. Kai ngā kōrero hoki o iwi kē, e pā ana ki wō mātou tīpuna. I reira i tōtō mai i te kōrero.

text: Ngā maihi o Te Whare Hukahuka, ngā maihi o Te Whare o Ruamano: Te whare kōrero o ngā maihi o Tuteao Ko Pūtauaki te maunga
Ko Rangitāiki te awa
Ko Hekerangi te papa whenua
Ko Tuteao te marae
Ko Ngā Maihi te hapū
Ko Ngāti Awa te iwi
Ko Mataatua te waka
Tihe mauri-ora
Ko tōku kāwai rangatira tēnei. E mōhio ai te tangata ko wai ahau; nō hea ahau, nā wai hoki ahau. Ā, nā whai anō taku urupounamu, ko wai a Ngā Maihi o Tuteao? E mea ana ngā pākeke, he iwi tawhito a Ngā Maihi i heke mai i ngā tātai whakapapa o Tangaroa, o Pōtiki, o Mahutapoanui, o Toroa, o Tuteao. Hēoi, kua kore e rangona ōna kōrero i runga marae ātea. Kua kore e wānangahia i roto i te poho o te whare o Tuteao. Kua ngū ngā poupou o te whare kōrero. Ka mutu, i roto i ngā tau tata nei kua riro tītapu ngā puna o te kī, ngā whītiki o te kupu, o te hapū; kua kore e rangona ngā kōrero o Ngā Maihi i runga marae ātea. Ko te haumate o te reo i runga o Tuteao tētahi take i pēnei ai. Nō reira, kai te imu te ruhi, kai te imu te ngēngē. E noho pōhara ana a Ngā Maihi ki ngā tāonga o tōna whare kōrero. Hei te tau 2027, ka whakanuia te rautau o te whare tīpuna a Tuteao, ā i tēnei tau tonu 2022, e whai whakaaro ana te hapū ki taua kaupapa otirā ki te hanga whare tīpuna hou; he whare kaitā e uru ai te tokomaha. Nō reira, e whakaaro ana hoki ki ngā kōrero ka whakairohia ki ngā pakitara o te whare. I tēnei tau hoki kua mana te whakaako i ngā kōrero hītori o te Māori i roto i ngā kura, nō reira he aha rā ngā kōrero e wātea ana ki ngā tamariki o ngā kura e pā ana ki a Ngā Maihi? He maramara, he kongakonga, he putunga kōrero e noho marara ana i ngā wāhi tūmatanui. He uaua te kitea o ētahi atu, kei ngā wāhi tūmataiti, pēnei i te Kōti Whenua Māori, i ngā tuhinga ā-whānau, kei ngā pukapuka wānanga o te marae. Nō reira, he uaua te kite atu i tōna whānuitanga, i tōna hohonutanga. Tīmata ake i ngā kohinga kōrero o te hapū tonu o Ngā Maihi, i ōna kaumātua, i ōna wānanga, i ōna whānau. I tua atu i wā te whare pukapuka, kei ngā wāhi tūmataiti ētahi putunga kōrero hei ō mo te whare kōrero o Ngā Maihi o Tuteao. Ka mutu, kei ngā waiata, ngā haka, ngā mōteatea. Kai ngā kōrero hoki o iwi kē, e pā ana ki wō mātou tīpuna. I reira i tōtō mai i te kōrero.

year: 2022