id author title date pages extension mime words sentence flesch summary cache txt american_scientific_journal-1433 Qasem, Fahmi Yaseen Abdo; Hadi, Wafa'a Hadi Ali On a Generalized ?R- Birecurrent Finsler Space 2016 10 .pdf application/pdf 3133 223 84 This shows that (2.12) β„¬π‘šπ‘šβ„¬π‘›π‘›π»π»π‘—π‘—π‘—π‘— = π‘Žπ‘Žπ‘šπ‘šπ‘›π‘›π»π»π‘—π‘—π‘—π‘— + (1 βˆ’ 𝑛𝑛)π‘π‘π‘šπ‘šπ‘›π‘›π‘”π‘”π‘—π‘—π‘—π‘—. if and only if (2.13) βˆ’β„¬π‘šπ‘šοΏ½π»π»π‘Ÿπ‘ŸπΊπΊπ‘—π‘—π‘›π‘›π‘—π‘—π‘Ÿπ‘Ÿ οΏ½ βˆ’ (β„¬π‘Ÿπ‘Ÿπ»π»π‘—π‘—)πΊπΊπ‘—π‘—π‘šπ‘šπ‘›π‘›π‘Ÿπ‘Ÿ βˆ’ (β„¬π‘›π‘›π»π»π‘Ÿπ‘Ÿ)πΊπΊπ‘—π‘—π‘šπ‘šπ‘—π‘—π‘Ÿπ‘Ÿ = οΏ½οΏ½Μ‡οΏ½πœ•π‘—π‘—π‘Žπ‘Žπ‘šπ‘šπ‘›π‘›οΏ½π»π»π‘—π‘— + (1 βˆ’ 𝑛𝑛)οΏ½οΏ½Μ‡οΏ½πœ•π‘—π‘—π‘π‘π‘šπ‘šπ‘›π‘›οΏ½π‘¦π‘¦π‘—π‘—. Suppose (2.21b) holds, then (2.18) implies (2.22) βˆ’β„¬π‘šπ‘š οΏ½(π‘›π‘›βˆ’1)𝐻𝐻 𝐹𝐹2 π‘¦π‘¦π‘Ÿπ‘ŸπΊπΊπ‘—π‘—π‘›π‘›π‘—π‘—π‘Ÿπ‘Ÿ οΏ½ βˆ’ οΏ½β„¬π‘Ÿπ‘Ÿ (π‘›π‘›βˆ’1)𝐻𝐻 𝐹𝐹2 𝑦𝑦𝑗𝑗� πΊπΊπ‘—π‘—π‘šπ‘šπ‘›π‘›π‘Ÿπ‘Ÿ βˆ’ �ℬ𝑛𝑛 (π‘›π‘›βˆ’1)𝐻𝐻 𝐹𝐹2 π‘¦π‘¦π‘Ÿπ‘ŸοΏ½ πΊπΊπ‘—π‘—π‘šπ‘šπ‘—π‘—π‘Ÿπ‘Ÿ = 0. cache/american_scientific_journal-1433.pdf txt/american_scientific_journal-1433.txt