<prompt> Mutsara 1: Iyi-vector ndiyo Hodge yemukati ye, uye ndiyo mufananidzo weiyo fomura _ 31 pasi peiyo isomorphism inokonzerwa neyakagadzirwa kaviri. Mutsara wechipiri: Vector iyi ndiyo hodge-dual uye mufananidzo wefomura iri pasi pe isomorphism inokonzerwa nechigadzirwa chemukati. Mubvunzo: Mutsara wokutanga nomutsara wechipiri unoreva chinhu chimwe chete here? Hungu kana kuti Aiwa?  <response>: Kwete 