id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-1996	Sandeep Sharma	Mathematical Analysis of Some (3+1)-D Models via Rangaig Transform	2024	17	.pdf	application/pdf	5108	267	68	= ( 1 𝜛4 − 1 𝜛5 ) sin 𝜋𝑥 sin𝜋𝑦 sin 𝜋𝑧, ⋮ Therefore, 𝜇1(Υ, 𝑡) = − sin 𝜋𝑥 sin𝜋𝑦 sin 𝜋𝑧, 𝜇2(Υ, 𝑡) = 𝑡2 2! sin 𝜋𝑥 sin𝜋𝑦 sin 𝜋𝑧, 𝜇3(Υ, 𝑡) = − 𝑡3 3! sin 𝜋𝑥 sin𝜋𝑦 sin 𝜋𝑧, ⋮ Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 394 https://internationalpubls.com [19-22] The following part introduces the fundamental principles and features of another transform, the “Rangaig Transform”, which will be introduced in this work.	cache/cana-1996.pdf	txt/cana-1996.txt