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Del i v er y H er o setz t sei n en sta r k en W a c h stu m sk u r s i m d r i tten Q u a r ta l 2 0 2 0 f or t, B estel l u n g en i m V er g l ei c h z u m V or j a h r a u f 3 6 2 M i l. Soit f un morphisme de groupes f Q !Q >0, Q étant muni de l’addition et Q >0 muni de la multiplication Calculer f(n) en fonction de f(1) pour tout entier n>0 Montrer que les deux groupes précédents ne sont pas isomorphes Correction H Exercice 16 Trouver tous les morphismes du groupe additif Q dans lui même Même question de Q dans Z Même question de Z=mZ dans Z. Q Z jg jq dm< 1 (62) Donc, f g 2L 1 Pour montrer (61), on distingue maintenant 3 cas 134 Cas 1 On suppose kf kp =0 ou kg kq =0 On a alors f =0 pp ou g =0 pp On en déduit f g =0 pp, donc kf g k1 =0 et (61) est vraie Cas 2On suppose kf kp =1 et kg kq =1 On a alors, avec (62), kf g k1 = Z jf g jdm 1 p 1 q =1= kf kp kg kq L'inégalité (61) est donc vraie Cas 3 On.
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R d Z n u k b k l _ f u m i j Z \ e _ g b y i h ^ t _ f g h c f Z r b g u g Z w e _ f _ g l g h c Z a _ n b j f u 6LHPHQV \ l h f q b k e _ d h g l j h e e _ j u. / 0 1 * 2 !. In this video we learn about function composition Composite functions are combinations of more than one function In this video we learn about f(g(x)) and g.
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On pose le cadre on travaille dans C0(a,b,R) muni du produit scalaire ˙ f,g ¨˘ Z b a f (t)g(t) dt On applique alors l’inégalité de CauchySchwarz à f x 7!1 et g x 7!. Zx 4Supposons que d = pgcd Qx (f;g) soit le pgcd dans l’anneau Qx de deux polynômes primitifs f et g de Zx Soit d = a d 0 sa représentation de type 1) Montrer que d 0 = pgcd Zx (f;g) dans l’anneau Zx 5Soient f, g2Zx, f =c(f)f 0, g=c(g)g 0 Alors pgcd Zx (f;g)=pgcd Z (c(f);c(g))pgcd Zx (f 0;g 0) Correction H Exercice 2 Démontrer que tout morphisme. Chercher alors la base et la direction de pq Exercice 12 f g= fet g f= g Soit Eun Kev Trouver tous les couples (f,g) d’endomorphismes de Etels que f g= fet g f= g Exercice 13 f g= id Soit Eun espace vectoriel et f,g∈ L(E) tels que f g= id E Montrer que g fest une projection et déterminer ses éléments Exercice 14 Projection pq−q p Soient p,qdeux projections telles que p q.
Dans cet oral XCachan Psi 15, on étudie l'équation fonctionnelle f(qz)f(z)=g(z), avec g (DSE) donnée, et en fonction de q.
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