id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-2042	Pavlova, Natalia; Remizov, Alexey	Legendre Transformation and Its Applications	2025	11	.pdf	application/pdf	4678	291	70	This approach allows us to understand some interesting properties of it, in particular, the reason for the appearance of singularities of dual curves. Moreover, the presented geometric approach allows us to understand the meaning of restrictions in the standard definition of the Legendre transformation of functions (for example, the convexity) and the reason for the appearance of singularities of dual curves.	cache/ijassa-2042.pdf	txt/ijassa-2042.txt