 By C.; Hemery, C. Lebosse

Manuel scolaire de mathématiques, niveau seconde C, programmes de 1965. Algèbre. Cet ouvrage fait partie de los angeles assortment Lebossé-Hémery dont les manuels furent à l’enseignement des mathématiques ce que le Bled et le Bescherelle furent à celui du français.

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Additional resources for Algèbre. Classe de Seconde C

Example text

M/ 6,! M/. @M/. jr jn k 2 r / is the n-Laplacian operator and ; ˛; ˇ 2 R and f ; g are smooth functions. x/, respectively. Sobolev-Type Inequalities on Manifolds in the Presence of Symmetries and. . 1 Sharp Sobolev Inequalities on Manifolds in the Presence of Symmetries e g/ In the following, we assume the notations and background material. M; g/ its group of isometries. M; g/. M; g/. M/. P/; 2 Gg be its orbit of dimension k, 0 Ä k < n. According to ([31, § 9 ] or ), the map ˚ W G ! OP , defined by ˚ .

1007/978-3-319-31317-7_3 45 46 A. Cotsiolis and N. M; g/ and the case of the solid torus. We would like at this point to give an explanation as to why we study the solid torus even giving a special emphasis. In recent years, significant progress has been made on the analysis of a number of important features of nonlinear partial differential equations of elliptic and parabolic type. The study of these equations has received considerable attention, because of their special mathematical interest and because of practical applications of the torus in scientific research today.

A; s/d˛ s C a 1, Proof. We proceed by mathematical induction on n. b; s/d˛ s: t Let n D k. R. b; s/d˛ s: a t t u This completes the proof. Corollary 2. 0; 1. 0; 1. In the following we adapt to the ˛-fractional setting some results from  by applying the fractional Steffensen inequality, Theorem 3. Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives 33 Theorem 4. 0; 1 and f W Œa; b ! R be an n C 1 times ˛-fractional n differentiable function such that DnC1 ˛ f is increasing and D˛ f is decreasing on Œa; b.