Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.

A taxonomia de Phasmatodea baseia-se essencialmente em caracteres de morfologia externa e características do ovo. A genitália masculina, estrutura com grande relevância taxonômica em outras ordens de insetos, foi examinada em poucas espécies de bicho-pau, sendo a sua morfologia ainda muito pobremente explorada para fins taxonômicos e filogenéticos. Das poucas análises filogenéticas realizadas até hoje em Phasmatodea, a maioria foi baseada em dados moleculares e focou nas relações entre grandes grupos, com apenas dois estudos abordando relações intragenéricas. Paraphasma Redtenbacher, 1906 é um gênero neotropical de bichos-paus pequenos e de aspecto delicado, com ambos os sexos possuindo asas posteriores bem desenvolvidas. Incluía, até o início deste estudo, dez espécies válidas, oito das quais com registro para o Brasil; trata-se de um gênero relativamente bem representado nas coleções brasileiras de Phasmatodea. Porém, assim como grande parte dos gêneros brasileiros de bichos-paus, Paraphasma encontrava-se taxonomicamente mal definido, e o conhecimento sobre suas espécies era praticamente restrito às descrições originais, normalmente muito superficiais, e a informações vagas de distribuição geográfica. O objetivo deste estudo foi realizar uma revisão taxonômica e análise filogenética de Paraphasma, buscando explorar o potencial taxonômico da genitália masculina de Phasmatodea. Foram examinados 407 exemplares (incluindo 38 tipos), estando representadas todas as espécies de Paraphasma e 18 espécies como grupo-externo da análise filogenética. A genitália masculina foi examinada e ilustrada para 22 espécies; foram verificadas prováveis homologias entre as espécies e propostos nomes para as regiões e estruturas da genitália. Foram definidos 80 caracteres morfológicos para a análise filogenética, dos quais 32 referemse à genitália masculina. Como resultado, Paraphasma passa a ter uma configuração bastante distinta da inicial, incluindo nove espécies, das quais três são espécies novas identificadas durante o estudo. O gênero foi redescrito, com base em morfologia externa e em características da genitália masculina e do ovo. Foram descritas as três espécies novas e redescritas as demais espécies de Paraphasma, incluindo a primeira descrição do macho de Paraphasma minus, do ovo de seis espécies e da genitália masculina de oito. Foram propostos dois novos gêneros (chamados aqui pelos nomes fictícios \"Aus\" e \"Bus\") para duas espécies previamente em Paraphasma, resultando nas novas combinações \"Aus\" amabilis e \"Bus\" cognatus. As decisões taxonômicas propostas incluem também outras cinco novas combinações [Paraphasma laterale, Paraphasma trianguliferum, Paraphasma umbretta, Prexaspes (Elasia) paulensis, Tithonophasma cancellatum], seis novas sinonímias de espécie [Phasma hopii, Phasma lineolatum e Stratocles dentatus sinônimos de Paraphasma laterale; Phasma quadratum sinônimo de Prexaspes (Elasia) pholcus; Phasma perspicillaris sinônimo de Stratocles xanthomela; Metriotes pericles sinônimo de Perliodes sexmaculatus], uma nova sinonímia de gênero (Oestrophora sinônimo de Paraphasma), uma espécie revalidada (Paraphasma umbretta) e um nome de espécie considerado nomen dubium (Paraphasma fasciatum). A genitália masculina correspondeu à principal fonte de informações para delimitação das espécies de Paraphasma. Além disso, os caracteres genitais foram, de forma geral, mais consistentes com a hipótese filogenética obtida do que os de morfologia externa, que se mostraram bastante homoplásticos. Os resultados da análise filogenética sugerem que as três subfamílias de Pseudophasmatidae (Pseudophasmatinae, Stratocleinae, Xerosomatinae) são polifiléticas. / The taxonomy of Phasmatodea relies largely on external morphology and features of the egg. The male genitalia, which is highly relevant for the taxonomy of other insect orders, has been examined in only a few species of stick insects, and its morphology remains very poorly explored for taxonomic and phylogenetic purposes. Of the few phylogenetic analyses performed so far in Phasmatodea, most were based on molecular data and focused on the relations among large groups, with only two studies having addressed intrageneric relationships. Paraphasma Redtenbacher, 1906 is a Neotropical genus of small and delicate stick insects, with both sexes having well-developed hind wings. Until the beginning of this study Paraphasma included ten valid species, eight of which recorded from Brazil; the genus is relatively well represented in Brazilian Phasmatodea collections. However, like most Brazilian genera of stick insects, Paraphasma was taxonomically poorly defined, and the current knowledge about its species was essentially limited to superficial original descriptions and vague information concerning geographical distribution. The aim of this study was to perform a taxonomic revision and phylogenetic analysis of Paraphasma, seeking to explore the taxonomic potential of the phasmid male genitalia. A total of 407 specimens were examined (including 38 types), with all species of Paraphasma plus 18 species as outgroups for the phylogenetic analysis. The male genitalia of 22 species was studied and illustrated; probable homologies were found among species and names were proposed for regions and structures of the genitalia. Eighty morphological characters were defined for the phylogenetic analysis, of which 32 refer to male genitalia. As a result, Paraphasma now shows a very different conception, with nine valid species, including three new ones identified during this study. Paraphasma was redescribed, based on external morphology and features of the male genitalia and egg. The three new species were described and the other six species were redescribed, including the first description of the male of Paraphasma minus, the egg of six species and the male genitalia of eight. Two new genera were proposed (herein referred by the symbolic names \"Aus\" and \"Bus\") to include two species previously in Paraphasma, resulting in the new combinations \"Aus\" amabilis and \"Bus\" cognatus. Taxonomic decisions proposed here also include other five new combinations [Paraphasma laterale, Paraphasma trianguliferum, Paraphasma umbretta, Prexaspes (Elasia) paulensis, Tithonophasma cancellatum], six new species synonymys [Phasma hopii, Phasma lineolatum and Stratocles dentatus under Paraphasma laterale; Phasma quadratum under Prexaspes (Elasia) pholcus; Phasma perspicillaris under Stratocles xanthomela; Metriotes pericles under Perliodes sexmaculatus], one new genus synonymy (Oestrophora under Paraphasma), one resurrected species (Paraphasma umbretta) and one species name regarded as a nomen dubium (Paraphasma fasciatum). Male genitalia was the main source of information for species delimitation in Paraphasma. Furthermore, genital characters were generally more consistent with the phylogenetic hypothesis obtained than characters of external morphology, which turned out to be quite homoplastic. The results of the phylogenetic analysis suggest that the three subfamilies of Pseudophasmatidae (Pseudophasmatinae, Stratocleinae and Xerosomatinae) are polyphyletic.

<p><img src="file:///C:/DOCUME~1/staff/LOCALS~1/Temp/moz-screenshot-13.jpg" alt="" /> <meta http-equiv="Content-Type" content="text/html / charset=utf-8"> <meta name="ProgId" content="Word.Document"> <meta name="Generator" content="Microsoft Word 12"> <meta name="Originator" content="Microsoft Word 12"> <link rel="File-List" href="file:///C:DOCUME~1staffLOCALS~1Tempmsohtmlclip11clip_filelist.xml" /> <link rel="themeData" href="file:///C:DOCUME~1staffLOCALS~1Tempmsohtmlclip11clip_themedata.thmx" /> <link rel="colorSchemeMapping" href="file:///C:DOCUME~1staffLOCALS~1Tempmsohtmlclip11clip_colorschememapping.xml" /><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves /> <w:TrackFormatting /> <w:PunctuationKerning /> <w:ValidateAgainstSchemas /> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF /> <w:LidThemeOther>EN-US</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables /> <w:SnapToGridInCell /> <w:WrapTextWithPunct /> <w:UseAsianBreakRules /> <w:DontGrowAutofit /> <w:SplitPgBreakAndParaMark /> <w:DontVertAlignCellWithSp /> <w:DontBreakConstrainedForcedTables /> <w:DontVertAlignInTxbx /> <w:Word11KerningPairs /> <w:CachedColBalance /> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math" /> <m:brkBin m:val="before" /> <m:brkBinSub m:val="&#45 / -" /> <m:smallFrac m:val="off" /> <m:dispDef /> <m:lMargin m:val="0" /> <m:rMargin m:val="0" /> <m:defJc m:val="centerGroup" /> <m:wrapIndent m:val="1440" /> <m:intLim m:val="subSup" /> <m:naryLim m:val="undOvr" /> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true" DefSemiHidden="true" DefQFormat="false" DefPriority="99" LatentStyleCount="267"> <w:LsdException Locked="false" Priority="0" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Normal" /> <w:LsdException Locked="false" Priority="9" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="heading 1" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9" /> <w:LsdException Locked="false" Priority="39" Name="toc 1" /> <w:LsdException Locked="false" Priority="39" Name="toc 2" /> <w:LsdException Locked="false" Priority="39" Name="toc 3" /> <w:LsdException Locked="false" Priority="39" Name="toc 4" /> <w:LsdException Locked="false" Priority="39" Name="toc 5" /> <w:LsdException Locked="false" Priority="39" Name="toc 6" /> <w:LsdException Locked="false" Priority="39" Name="toc 7" /> <w:LsdException Locked="false" Priority="39" Name="toc 8" /> <w:LsdException Locked="false" Priority="39" Name="toc 9" /> <w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption" /> <w:LsdException Locked="false" Priority="10" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Title" /> <w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font" /> <w:LsdException Locked="false" Priority="11" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtitle" /> <w:LsdException Locked="false" Priority="22" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Strong" /> <w:LsdException Locked="false" Priority="20" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Emphasis" /> <w:LsdException Locked="false" Priority="59" SemiHidden="false" UnhideWhenUsed="false" Name="Table Grid" /> <w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text" /> <w:LsdException Locked="false" Priority="1" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="No Spacing" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 1" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 1" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 1" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 1" /> <w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision" /> <w:LsdException Locked="false" Priority="34" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="List Paragraph" /> <w:LsdException Locked="false" Priority="29" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Quote" /> <w:LsdException Locked="false" Priority="30" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Quote" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 1" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 1" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 1" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 1" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 1" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 2" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 2" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 2" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 2" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 2" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 2" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 2" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 2" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 2" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 3" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 3" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 3" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 3" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 3" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 3" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 3" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 3" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 3" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 4" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 4" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 4" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 4" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 4" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 4" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 4" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 4" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 4" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 5" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 5" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 5" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 5" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 5" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 5" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 5" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 5" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 5" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 6" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 6" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 6" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 6" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 6" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 6" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 6" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 6" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 6" /> <w:LsdException Locked="false" Priority="19" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis" /> <w:LsdException Locked="false" Priority="21" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis" /> <w:LsdException Locked="false" Priority="31" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference" /> <w:LsdException Locked="false" Priority="32" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Reference" /> <w:LsdException Locked="false" Priority="33" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Book Title" /> <w:LsdException Locked="false" Priority="37" Name="Bibliography" /> <w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading" /> </w:LatentStyles> </xml><![endif]--><style type="text/css"> <!-- /* Font Definitions */ @font-face {font-family:"Cambria Math" / panose-1:2 4 5 3 5 4 6 3 2 4 / mso-font-charset:0 / mso-generic-font-family:roman / mso-font-pitch:variable / mso-font-signature:-1610611985 1107304683 0 0 159 0 / } @font-face {font-family:Calibri / panose-1:2 15 5 2 2 2 4 3 2 4 / mso-font-alt:Calibri / mso-font-charset:0 / mso-generic-font-family:swiss / mso-font-pitch:variable / mso-font-signature:-1610611985 1073750139 0 0 159 0 / } /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no / mso-style-qformat:yes / mso-style-parent:"" / margin-top:0in / margin-right:0in / margin-bottom:10.0pt / margin-left:0in / line-height:115% / mso-pagination:widow-orphan / font-size:11.0pt / font-family:"Calibri","sans-serif" / mso-ascii-font-family:Calibri / mso-ascii-theme-font:minor-latin / mso-fareast-font-family:"Times New Roman" / mso-hansi-font-family:Calibri / mso-hansi-theme-font:minor-latin / mso-bidi-font-family:"Times New Roman" / mso-bidi-theme-font:minor-bidi / } .MsoChpDefault {mso-style-type:export-only / mso-default-props:yes / font-family:"Univers Condensed","sans-serif" / mso-ascii-font-family:Calibri / mso-ascii-theme-font:minor-latin / mso-hansi-font-family:Calibri / mso-hansi-theme-font:minor-latin / mso-bidi-font-family:Calibri / mso-bidi-theme-font:minor-latin / } .MsoPapDefault {mso-style-type:export-only / margin-bottom:10.0pt / line-height:115% / } @page WordSection1 {size:8.5in 11.0in / margin:1.0in 1.0in 1.0in 1.0in / mso-header-margin:.5in / mso-footer-margin:.5in / mso-paper-source:0 / } div.WordSection1 {page:WordSection1 / } --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal" / mso-tstyle-rowband-size:0 / mso-tstyle-colband-size:0 / mso-style-noshow:yes / mso-style-priority:99 / mso-style-qformat:yes / mso-style-parent:"" / mso-padding-alt:0in 5.4pt 0in 5.4pt / mso-para-margin-top:0in / mso-para-margin-right:0in / mso-para-margin-bottom:10.0pt / mso-para-margin-left:0in / line-height:115% / mso-pagination:widow-orphan / font-size:11.0pt / font-family:"Calibri","sans-serif" / mso-ascii-font-family:Calibri / mso-ascii-theme-font:minor-latin / mso-fareast-font-family:"Times New Roman" / mso-fareast-theme-font:minor-fareast / mso-hansi-font-family:Calibri / mso-hansi-theme-font:minor-latin / mso-bidi-font-family:"Times New Roman" / mso-bidi-theme-font:minor-bidi / } </style> <![endif]--> </meta> </meta> </meta> </meta> </p> <p class="MsoNormal"><span style="font-size: 12pt / line-height: 115% / font-family: &quot / Times New Roman&quot / ,&quot / serif&quot / ">This study has reveled the levels of knowledge and compliance towards Universal Precautions and examined the factors that are influential in having a positive and negative effect on their adoption by healthcare practitioners in practice. Despite acceptable knowledge regarding the potential for infection and mechanisms to prevent these infections, this study has found out that health care workers are not as compliant with universal precautions as they need to be. The findings that compliance correlated directly with knowledge, with in-service training and with availability of protective equipment, provide important indications for future interventions. Therefore a regular on job refreshing training program on Universal Precautions, a written guideline and reminder poster on Universal Precautions and personal protective equipment need to be made available for all health care providers in every department of the hospital for better compliance. <span style="">&nbsp / </span><span style="">&nbsp / </span><span style="">&nbsp / </span><o:p></o:p></span></p> <p>&nbsp / </p>

Piezoelectric actuators (PEA) hold the most promise for precision positioning applications due to their capability of producing extremely small displacements down to 10 pm (1 pm = 10-12 m) as well as their high stiffness and force output. The piezoelectric-driven stick-slip (PDSS) actuator, working on the friction-inertia concept, has the capacity of accomplishing an unlimited range of motion. It also holds the promises of simple configuration and low cost. On the other hand, the PDSS actuator has a relatively low efficiency and low loading capability, which greatly limits its applications. The purpose of this research is to improve the performance of the PDSS actuators by employing specially-designed working surfaces.<p> The working surfaces, referred as anisotropic friction (AF) surfaces in this study, can provide different friction forces depending on the direction of relative motion of the two surfaces, and are used in this research to accomplish the aforementioned purpose. To fabricate such surfaces, two nanostructure technologies are employed: hot filament chemical vapour deposition (HFCVD) and ion beam etching (IBE). The HFCVD is used to deposit diamond on silicon substrates; and the IBE is used to etch the diamond crystalloid with a certain angle with respect to the coating surface to obtain an unsymmetrical-triangle microstructure. <p> A PDSS actuator prototype containing the AF surfaces was developed in this study to verify the function of the AF surfaces and characterize the performance of PDSS actuators. The designed surfaces were mounted on the prototype; and the improvement in performance was characterized by conducting a set of experiments with both the normal isotropic friction (IF) surfaces and the AF surfaces, respectively. The results illustrate that the PDSS actuator with the AF surface has a higher efficiency and improved loading capability compared to the one with the IF surfaces.<p> A model was also developed to represent the displacement of the novel PDSS actuator. The dynamics of the PEA and the platform were approximated by using a second order dynamic system. The pre-sliding friction behaviour involved was investigated by modifying the LuGre friction model, in which six parameters (Note that three parameters are used in the LuGre model) were employed to represent the anisotropic friction. By combining the PEA mechanism model, the modified friction model, and the dynamics of end-effector, a model for the PDSS actuator with the AF surface was developed. The model with the identified parameters was simulated in MATLAB Simulink and the simulation results obtained were compared to the experimental results to verify the model. The comparison suggests that the model developed in this study is promising to represent the displacement of the novel PDSS actuators with AF surfaces.

Previous studies show that the Piezoelectric-Driven Stick-Slip (PDSS) actuator is a promising device in many micropositioning and micromanipulation applications, where positioning with a long range and a high resolution is required. However, research in this area is still in its early stage and many issues remain to be addressed. One key issue is the representation of the dynamic displacement of the end-effector. It is known that such factors as the dynamics of piezoelectric actuator (PEA) and the presliding friction involved can significantly contribute to the displacement dynamics. Although this has been widely accepted, specific quantitative relationship between the aforementioned factors and the displacement dynamics has rarely been defined. The aim of this research is to develop a model to represent the displacement of the end-effecter of the PDSS actuators, in which both the presliding friction and the PEA dynamics are addressed. <p>In order to represent the presliding friction, the models reported in literatures, including Dahl model [Olsson, et al., 1998], Reset Integrator model [Haessig and Friedland 1991], LuGre model [Canudas de Wit et al., 1995] and Elastoplastic model [Dupont et al., 2002] were reviewed and examined; and the LuGre model was chosen to be used because of its efficiency and simple formulation. On the other hand, a linear second order dynamic system model was employed to represent the combination of a PEA and its driven mechanism. On the basis of the pre-sliding friction model and the linearized PEA dynamics model, a model representative of the end-effector displacement of the PDSS actuator model was developed. <p>In order to validate experimentally the developed PDSS model, a displacement measuring and data acquisition experiment system was established and a prototype was developed based on dSPACE and Simulink. On the prototyped actuator, two experiments were designed and conducted to identify the parameters involved in the model. One experiment is for the determination of the parameters of the second order system for the dynamics of the combination of a PEA and its driven mechanism; and other one is for the determination of the parameters of the chosen friction model. The identified parameters were then employed in the developed PDSS model to simulate the displacements and the results were compared with the experimental results that were obtained under the same operating conditions as the simulation. The comparison suggests that the model developed in this study is promising for the end-effector displacement of the PDSS actuator.

Previous studies show that the Piezoelectric-Driven Stick-Slip (PDSS) actuator is a promising device in many micropositioning and micromanipulation applications, where positioning with a long range and a high resolution is required. However, research in this area is still in its early stage and many issues remain to be addressed. One key issue is the representation of the dynamic displacement of the end-effector. It is known that such factors as the dynamics of piezoelectric actuator (PEA) and the presliding friction involved can significantly contribute to the displacement dynamics. Although this has been widely accepted, specific quantitative relationship between the aforementioned factors and the displacement dynamics has rarely been defined. The aim of this research is to develop a model to represent the displacement of the end-effecter of the PDSS actuators, in which both the presliding friction and the PEA dynamics are addressed. <p>In order to represent the presliding friction, the models reported in literatures, including Dahl model [Olsson, et al., 1998], Reset Integrator model [Haessig and Friedland 1991], LuGre model [Canudas de Wit et al., 1995] and Elastoplastic model [Dupont et al., 2002] were reviewed and examined; and the LuGre model was chosen to be used because of its efficiency and simple formulation. On the other hand, a linear second order dynamic system model was employed to represent the combination of a PEA and its driven mechanism. On the basis of the pre-sliding friction model and the linearized PEA dynamics model, a model representative of the end-effector displacement of the PDSS actuator model was developed. <p>In order to validate experimentally the developed PDSS model, a displacement measuring and data acquisition experiment system was established and a prototype was developed based on dSPACE and Simulink. On the prototyped actuator, two experiments were designed and conducted to identify the parameters involved in the model. One experiment is for the determination of the parameters of the second order system for the dynamics of the combination of a PEA and its driven mechanism; and other one is for the determination of the parameters of the chosen friction model. The identified parameters were then employed in the developed PDSS model to simulate the displacements and the results were compared with the experimental results that were obtained under the same operating conditions as the simulation. The comparison suggests that the model developed in this study is promising for the end-effector displacement of the PDSS actuator.

Piezoelectric actuators (PEA) hold the most promise for precision positioning applications due to their capability of producing extremely small displacements down to 10 pm (1 pm = 10-12 m) as well as their high stiffness and force output. The piezoelectric-driven stick-slip (PDSS) actuator, working on the friction-inertia concept, has the capacity of accomplishing an unlimited range of motion. It also holds the promises of simple configuration and low cost. On the other hand, the PDSS actuator has a relatively low efficiency and low loading capability, which greatly limits its applications. The purpose of this research is to improve the performance of the PDSS actuators by employing specially-designed working surfaces.<p> The working surfaces, referred as anisotropic friction (AF) surfaces in this study, can provide different friction forces depending on the direction of relative motion of the two surfaces, and are used in this research to accomplish the aforementioned purpose. To fabricate such surfaces, two nanostructure technologies are employed: hot filament chemical vapour deposition (HFCVD) and ion beam etching (IBE). The HFCVD is used to deposit diamond on silicon substrates; and the IBE is used to etch the diamond crystalloid with a certain angle with respect to the coating surface to obtain an unsymmetrical-triangle microstructure. <p> A PDSS actuator prototype containing the AF surfaces was developed in this study to verify the function of the AF surfaces and characterize the performance of PDSS actuators. The designed surfaces were mounted on the prototype; and the improvement in performance was characterized by conducting a set of experiments with both the normal isotropic friction (IF) surfaces and the AF surfaces, respectively. The results illustrate that the PDSS actuator with the AF surface has a higher efficiency and improved loading capability compared to the one with the IF surfaces.<p> A model was also developed to represent the displacement of the novel PDSS actuator. The dynamics of the PEA and the platform were approximated by using a second order dynamic system. The pre-sliding friction behaviour involved was investigated by modifying the LuGre friction model, in which six parameters (Note that three parameters are used in the LuGre model) were employed to represent the anisotropic friction. By combining the PEA mechanism model, the modified friction model, and the dynamics of end-effector, a model for the PDSS actuator with the AF surface was developed. The model with the identified parameters was simulated in MATLAB Simulink and the simulation results obtained were compared to the experimental results to verify the model. The comparison suggests that the model developed in this study is promising to represent the displacement of the novel PDSS actuators with AF surfaces.

Tattooing in the federal Indian boarding school system appears to have been common among the student body, but the practice is not well documented. A search of the literature on Native education, focusing on boarding schools, yielded only fragments of references to tattooing because there has been no substantive or detailed research on Indian boarding school tattoos. One brief narrative from Celia Haig-Brown (1988), however, illustrates the commonality and the dangers of tattooing. This study examines tattoos among female students who attended Indian boarding schools in the Southwest during the 1960s-1970s. The personal accounts of my mother's experience in tattooing at the Phoenix Indian School provide a baseline for this study. My study explores an undocumented area of boarding school history and student experiences. Many students from various tribes tattooed. The tattoos most often included small initials and markings, and my analysis concludes that the meanings were mostly related to resistance.

This thesis is addressed to the understanding of the mechanisms at the origin of the contact wave fields at frictional interfaces and its relationship with the local characteristics of the surfaces in contact, as well as with the global dynamics and macroscopic frictional behaviour of the system. The aim of this work is to provide insights on the generation and propagation of the waves through the contact both to avoid instabilities and to control their effect on friction. The work is organized in two main parts. The first part presents the development of a non-linear finite element analysis in large transformations of the dynamic rupture at the interface with contact friction separating two bodies (isotropic and elastic) without relative motion. A rupture is considered when an initially sticking zone shifts in sliding state. The properties of the obtained ruptures are analyzed for a flat interface between dissimilar materials in function of the nucleation energy; then the effect of the interface roughness is analyzed. The differentiated rupture inside the asperities and the conditions for coupling and uncoupling between the waves radiating in the two bodies have been also investigated. In the second part, the analysis deals with the sliding onset between two bodies in contact. The sliding between two bodies made of different isotropic elastic materials and separated by a frictional interface is simulated. The evolution along the time of the global normal and tangential forces is analyzed, relating it to the local phenomena occurring at the interface. This part tries to investigate how micro-slips at the interface, acting as distributed ruptures, trigger the macro-slips between the two bodies. The interaction between local and global dynamics is also studied. Finally a numerical parameter space study is carried out, as a function of several system parameters (contact law, friction coefficient, material damping, normal load, translational velocity and regularization time). The results show the key role of the micro-slips and precursors (detectable wave propagations that occur at tangential global force well below the critical value expected by the friction law) in triggering the macro-slip between the two bodies. Depending on their distribution and magnitude the evolution of the contact forces passes from stick-slip-like behaviour to continuous sliding. The local dynamics at the contact (wave and rupture propagation) is linked to the global behaviour of the system (stick-slip, continuous sliding, induced vibrations); the effect of the contact and system parameters on the transfer of vibrational energy between the sliding contact and the system is investigated. The numerical results obtained by the two parts of the work show a good agreement with experimental results in literature.

Les pieds d'aubes de soufflantes de turboréacteurs font face à des sollicitations de type fretting. Il en résulte deux types d'endommagements: (i) l'amorçage et la propagation de fissures, (ii) l'usure des surfaces en contact. OBJECTIF: Afin de fournir les outils permettant de répondre à la problématique industrielle, une méthode semi-analytique permettant de traiter des problèmes de contacts élasto-plastiques revêtus et/ou hétérogènes est développé à partir d'éléments existants et de solutions analytiques et numériques novatrices. METHODE: La structure est simplifiée en supposant un contact entre deux massifs élastiques semi-infinis. Des solutions analytiques donnant pour: + les contributions élémentaires de chargements normaux et tangentiels constants sur une surface rectangulaire + les contributions élémentaires de déformations plastiques supposées constantes sur un volume parallélépipédique + les contributions élémentaires de déformations d'incompatibilité liées à un problème hétérogène (inclusions, revêtements, endommagement,...) supposées constantes sur un volume parallélépipédique. >> les déplacements en surface ou les contraintes dans le volume. Les déplacements en surface ou les contraintes dans le volume sont alors exprimés en utilisant des produits de convolution discrets entre des coefficients d'influence et la source surfacique (chargements en surface) ou volumique (déformations plastiques ou d'incompatibilité). Le problème normal et le problème tangentiel en glissement total ou en glissement partiel peuvent alors être résolus, en prenant en compte les effets plastiques et hétérogènes. L'algorithme d'optimisation sous contrainte utilisé (contact elastique) est celui développé par L.Gallego tandis que la base du solver plastique utilisé a été développé par C. Jacq (contact elasto-plastique sans frottement) RESULTATS: De nouvelles solutions analytiques sont obtenues pour le calcul des déplacements résiduels tangentiels.