title: Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation ψtt-Δ3ψ = 0

authors: Kalnins, Ernie G.

abstract: A detailed classification is made of orthogonal coordinate systems for which the wave equation ψtt - Δ3ψ = 0 admits an R -separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have been found in previous articles. We find 106 new coordinates to give a total of 367 conformally inequivalent orthogonal coordinates for which the wave equation admits an R -separation of variables.

text: Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation ψtt-Δ3ψ = 0 A detailed classification is made of orthogonal coordinate systems for which the wave equation ψtt - Δ3ψ = 0 admits an R -separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have been found in previous articles. We find 106 new coordinates to give a total of 367 conformally inequivalent orthogonal coordinates for which the wave equation admits an R -separation of variables.

year: 1977

title: The effect of silane coupling agent on iron sand for use in magnetorheological elastomers Part 1: Surface chemical modification and characterization

authors: Pickering, Kim L.

subjects: Science & Technology

abstract: Bis-(3-triethoxysilylpropyl) tetrasulphane (TESPT) was employed for surface modification of iron sand for use in magnetorheological elastomers (MREs). The amount of TESPT was varied at five levels (2, 4, 6, 8 and 10 wt%) relative to iron sand content to assess the optimum amount of coupling agent for interfacial bonding and damping performance. Evidence that coupling had occurred between iron sand and TESPT was identified by Raman Spectroscopy and the grafting percentage was determined by thermogravimetric analysis. Subsequently, isotropic MREs containing unmodified and modified iron sand particles and natural rubber were prepared. Crosslink density assessment by swelling testing provided evidence that the tetrasulphane group of TESPT formed crosslinks with the rubber chains. The results exhibited the advantages of TESPT as a coupling agent between iron sand particles and rubber and also revealed that 6% TESPT content produced the highest crosslink density. The effects of the amount of TESPT on dynamic mechanical properties the morphological characteristics of the MREs were also investigated.

text: The effect of silane coupling agent on iron sand for use in magnetorheological elastomers Part 1: Surface chemical modification and characterization Bis-(3-triethoxysilylpropyl) tetrasulphane (TESPT) was employed for surface modification of iron sand for use in magnetorheological elastomers (MREs). The amount of TESPT was varied at five levels (2, 4, 6, 8 and 10 wt%) relative to iron sand content to assess the optimum amount of coupling agent for interfacial bonding and damping performance. Evidence that coupling had occurred between iron sand and TESPT was identified by Raman Spectroscopy and the grafting percentage was determined by thermogravimetric analysis. Subsequently, isotropic MREs containing unmodified and modified iron sand particles and natural rubber were prepared. Crosslink density assessment by swelling testing provided evidence that the tetrasulphane group of TESPT formed crosslinks with the rubber chains. The results exhibited the advantages of TESPT as a coupling agent between iron sand particles and rubber and also revealed that 6% TESPT content produced the highest crosslink density. The effects of the amount of TESPT on dynamic mechanical properties the morphological characteristics of the MREs were also investigated.

year: 2015-01-01

title: E tama Hikairo

authors: Maxwell, Te Kahautu

subjects: Oriori

abstract: He oriori tēnei mō Hikairo, te mokopuna tuatahi a Kīngi Tūheitia. He oriori tēnei e whakanui ana i a Hikairo, tōna whakapapa, tōna tūranga i te ao Māori me te ao Kīngitanga. He mokopuna Ringatū anō a Hikairo, nā Kīngi Tūheitia i tuku mai a Hikairo kia tūātia e Te Hāhi Ringatū ki te Poukai o Wāhi Pā i te tuawaru o Whiringa-ā-Nuku 2014. Ka whakaaturia tōna whakapono Hāhi Ringatū ki roto i te oriori nei e kupu whakaaritia ana. I tohua hoki e Kīngi Tūheitia a Te Kāhautu hai pou whakaruruhau1 mō Hikairo koinei ia i titoa ai tēnei oriori mō tana tamaiti mokopuna, mō Hikairo. He aroha nui nō te matua mō wai oti, mō Hikairo.

I titoa tēnei oriori hai waiatatanga mā te kapa haka o Ōpōtiki Mai Tawhiti. I waiatatia e Ōpōtiki Mai Tawhiti tēnei ki Te Matatini i tū ki Ōtautahi te tau rua mano tekau mā rima. He huarahi anō tēnei mā Te Kāhautu ki te whakamānawa i tana mokopuna i a Hikairo, nara nā te kapa haka a Te Kāhautu i waiata, i whakanui a Hikairo ki te maraenui o te iwi Māori, ko Te Matatini. Ana i tuatahi a Hikairo i te wehenga o Te Waiata Tira. “E Tama Hikairo, haere mai rā.”

text: E tama Hikairo He oriori tēnei mō Hikairo, te mokopuna tuatahi a Kīngi Tūheitia. He oriori tēnei e whakanui ana i a Hikairo, tōna whakapapa, tōna tūranga i te ao Māori me te ao Kīngitanga. He mokopuna Ringatū anō a Hikairo, nā Kīngi Tūheitia i tuku mai a Hikairo kia tūātia e Te Hāhi Ringatū ki te Poukai o Wāhi Pā i te tuawaru o Whiringa-ā-Nuku 2014. Ka whakaaturia tōna whakapono Hāhi Ringatū ki roto i te oriori nei e kupu whakaaritia ana. I tohua hoki e Kīngi Tūheitia a Te Kāhautu hai pou whakaruruhau1 mō Hikairo koinei ia i titoa ai tēnei oriori mō tana tamaiti mokopuna, mō Hikairo. He aroha nui nō te matua mō wai oti, mō Hikairo.

I titoa tēnei oriori hai waiatatanga mā te kapa haka o Ōpōtiki Mai Tawhiti. I waiatatia e Ōpōtiki Mai Tawhiti tēnei ki Te Matatini i tū ki Ōtautahi te tau rua mano tekau mā rima. He huarahi anō tēnei mā Te Kāhautu ki te whakamānawa i tana mokopuna i a Hikairo, nara nā te kapa haka a Te Kāhautu i waiata, i whakanui a Hikairo ki te maraenui o te iwi Māori, ko Te Matatini. Ana i tuatahi a Hikairo i te wehenga o Te Waiata Tira. “E Tama Hikairo, haere mai rā.”

year: 2016