MUODILA

MUODILA (arabi —barobari, musovi, barobarqimat, muvofiqat) dar matematika, ifodai tahlili baroi daryoftani on qimati argumentho, ki baroyashon qimathoi du funksiyai dodashuda ba hamdigar barobarand. Argumenthoe, ki funksiyaho ba onho vobastaand, nomal u m h o nomida meshavand; qimathoi nomalumho, ki baroi onho qimathoi funksiyaho barobarand, h a l dh o (reshaho) nom dorand. Masalan, 5kh+ 10 = 0 Muodilai yaknomaluma meboshad, kh=2 halli on ast; kh² + -\-u⁷—25=0 M.uodilai duvomaluma nomida meshavad, kh = 3, u = 4 yake az halhoi on ast. Majmui halhoi Muodilai do­dashuda ba majmui qimathoi imkonpaziri nomalumho M vobasta mebo­shad. Agar Muodila dar majmui M hal nadoshta boshad, onro dar M halnashavanda menomand. Muodila metavonad yak, du va hatto yakchand hal dosh- ta boshad. Masalan, Muodilai l⁴ — 4 = 0 dar sohai adadhoi ratsionali halnashavanda meboshad, vale dar sohai adad­hoi haqiqi du hal: kh, = U2, kh, =» = —u2, dar sohai adadhoi kompleksi chor hal: kh₂ =_^2, kh₂ = —U2, kh$ = tt gu2, kh₄ = —«U2 dorad. Miqdori halhoi Muodilai sinx=0 dar sohai adad­hoi haqiqi beintiho ziyod meboshad: kh_p = kp (* = 0, ±1, ±2, …). Agar Muodila baroi hamai adadhoi sohai M hal doshta boshad, onro dar in soha ayniyat menomand. Masalan, Muodilai kh — ukh² dar sohai adadhoi gayrimanfi ayniyat meboshad, vale dar sohai adad­hoi haqiqi ainiyat nest. Majmui Muodilahoe, ki qimathoi nomalumhoyashon dar yak vaqt hamai Muodidahoro qone megardonand, sistemai Muodilaho nomida meshavand. Qimathoi nomalumhoi dar yak vaqt hamai Muodidahoro qonegardonandaro halhoi sis­tema menomand. Masalan, kh + 2u = 5, 2kh + u — z = 1 sistemai du Muodilai senomaluma meboshad; yake az halhoi in sistema kh = 4, u — 2, kh = 3 ast. Agar dar yak halli yak sistema (yak

Muodila) halli digari sistema (digar Muodila) bo­shad, va baraks, on goh in du sis­temai Muodilaho (yo du Muodila) barobarquvva nomida meshavad; dar in mavrid dar du sistema (Muodila) dar hamon yak soha muoina karda meshavand (nigared Muodilahoi barobarquvva). Har guna sistemai Muodilaho ba sistemai namudi M*i» kh₃, …» kh_p) = 0 (ya – 1, 2, …) barobarquvva meboshad. Odatan prosessi justujui halli muodila bo Muodilai barobarquvva ivaz namudani on ast. Muodilahoe, ki baroi onho  bisyoruzvai tagyiryobandahoi Kh|, kh₂, …, kh_p meboshand, yane muodi­la h o i algebravi beshtar tadqiq shudaand, Masalan, Muodilai algebravii yaknomaluma chunin shakl dorad:

Oo*”+ai*n-i+ •« + a_p = 0 (vo*0),

adadi p darajai Muodila nomida mesha­vad. Justujui halli Muodilai algebravi dar asrhoi 16—17 yake az masalahoi asosii algebra bud. Dar in davra usuli halli Muodilai algebravii darajai 3-yum yofta shud (nigared Algeb­ra, Formulai Kardano), (Usuli hal­li Muodilahoi algebravii darajai 1-um va 2-yum az davrahoi qadim malum budand.) Baroi ifodai reshahoi mu- odilai darajai 5-um va az on bolo formulai umumi mavjud nest, ze­ro onho dar radikalho hal nadorand (N. Abel, 1824). Masala dar borai halpazirii Muodilahoi algebravi dar radikalho boisi paydoishi nazariyai umumii Muodilahoi algebravi gar­did (E. Galua, tadrijan 1830). Soddatarin sistemai Muodilaho sistemai Muodilahoi khatti meboshand, ki dar onho /_k bisyoruzvahoi darajai yakum nisbat ba xi, X}, …, kh„ meboshand. Halli sistemai Muodilaho (khatti budanashon shart nest) umuman ba halli yak Muodila ovarda meshavad (bo usuli pai ham khorij namudani nomalumho). Istilohi «Muodila» dar digar ilmhoi tabiatshinosi niz istifoda meshavad. Nigared Muodilai vaqt (astronomiya), Muodilai holat (fizika).

A. Qurbonov.