id author title date pages extension mime words sentence flesch summary cache txt american_scientific_journal-3116 I. Abad alrhman, Ibrahim Yousif; A. Abu Aasha, Yonnis; B. M. Hamed, Abdulaziz Hamiltonian System Mechanics on (2,0)-Jet Bundles 2017 6 .pdf application/pdf 2281 58 62 [1]. 𝒁𝒁 = οΏ½π’›π’›π’Šπ’Š,π’™π’™π’Šπ’Š = πœΌπœΌπ’Šπ’Š(𝟏𝟏),π’šπ’šπ’Šπ’Š = πœΌπœΌπ’Šπ’Š(𝟐𝟐)οΏ½ = (π’›π’›π’Šπ’Š,π‘Ώπ‘Ώπ’Šπ’Š,π’€π’€π’Šπ’Š) (πŸ‘πŸ‘) 2.2 Theorem A local basis in �́�𝐓𝐳𝐳�𝐉𝐉(𝟐𝟐,𝟎𝟎)π“œπ“œοΏ½is οΏ½ 𝛛𝛛 𝛛𝛛𝐳𝐳𝐒𝐒 , 𝛛𝛛 𝛛𝛛𝐱𝐱𝐒𝐒𝐒𝐒 , 𝛛𝛛 𝛛𝛛𝐲𝐲𝐒𝐒 οΏ½ 𝐒𝐒=𝟏𝟏;𝐧𝐧����� and in �́́�𝐓𝐳𝐳�𝐉𝐉(𝟐𝟐,𝟎𝟎)π“œπ“œοΏ½ theirs conjugates οΏ½ 𝛛𝛛 𝛛𝛛𝐳𝐳𝐒𝐒� , 𝛛𝛛 𝛛𝛛𝐱𝐱�𝐒𝐒 , 𝛛𝛛 𝛛𝛛𝐲𝐲�𝐒𝐒 οΏ½ 𝐒𝐒=𝟏𝟏;𝐧𝐧����� : Due to holomorphic changes on 𝐉𝐉(𝟐𝟐,𝟎𝟎)π“œπ“œ, that is all of 𝛛𝛛�́�𝐳 𝐒𝐒 𝛛𝛛𝐳𝐳𝐣𝐣� , 𝛛𝛛�́�𝐱 𝐒𝐒 𝛛𝛛𝐳𝐳𝐣𝐣� , 𝛛𝛛�́�𝐲 𝐒𝐒 𝛛𝛛𝐳𝐳𝐣𝐣� , 𝛛𝛛�́�𝐱 𝐒𝐒 𝛛𝛛𝐱𝐱𝐣𝐣� , 𝛛𝛛�́�𝐲 𝐒𝐒 𝛛𝛛𝐱𝐱𝐣𝐣� , 𝛛𝛛�́�𝐲 𝐒𝐒 𝛛𝛛𝐲𝐲𝐣𝐣� j are vanishing, and also theirs conjugates, it follows that local bases from �́�𝐓𝐳𝐳�𝐉𝐉(𝟐𝟐,𝟎𝟎)π“œπ“œοΏ½ change w.r.t. If (𝐳𝐳𝐒𝐒)𝐒𝐒=𝟏𝟏;𝐧𝐧����� are complex coordinates, then 𝐓𝐓𝐳𝐳́ π“œπ“œ is spanned by οΏ½ 𝛛𝛛 𝛛𝛛𝐳𝐳𝐒𝐒 οΏ½ 𝐒𝐒=𝟏𝟏;𝐧𝐧����� and οΏ½ΜΜοΏ½π“π³π³π“œπ“œ is spanned by οΏ½ 𝛛𝛛 𝛛𝛛𝐳𝐳�𝐒𝐒 οΏ½ 𝐒𝐒=𝟏𝟏;𝐧𝐧����� moreover οΏ½ΜοΏ½π“π“œπ“œ is a holomorphic vector bundle let 𝐙𝐙 = (𝐳𝐳𝐒𝐒 ,𝐗𝐗𝐒𝐒 = π›ˆπ›ˆπ’π’(𝟏𝟏) = 𝐝𝐝𝐳𝐳𝐒𝐒 𝐝𝐝𝐝𝐝 ,𝐘𝐘𝐒𝐒 = π›ˆπ›ˆπ’π’(𝟐𝟐) cache/american_scientific_journal-3116.pdf txt/american_scientific_journal-3116.txt