Showing papers in "Tohoku Mathematical Journal in 1970"
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TL;DR: In this article, the authors studied equations of type Xn-aX + b = 0, and obtained some results on unramified extensions of quadratic number fields.
Abstract: We have studied equations of type Xn-aX + b =0, and have obtained some results on unramified extensions of quadratic number fields [3]. In this paper we have further results which include almost all of [3]. We do not refer to [3] in the following, though the techniques of proofs are almost equal to those of [3], Theorems proved here are the following." Notice that "unramified" means in this paper that every finite prime is unramified. THEOREM 1. Let k be an algebraic number field o f finite degree. Let a and b be integers of k. K denotes the minimal splitting field of a polynomial
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TL;DR: In this paper, Remoundos et al. pointed out that le nombre de valeurs exceptionnelles est limite par le nomes des relations lineaires homogenes a coefficients constants and distinctes entre les fonctions A0,•c,An.
Abstract: ou A0,•c,An sont des fonctions entieres telles qu'au moms un rapport mutuel entre les fonctions A0,•c,An est transcendant. Alors, on sait que f(z) n'admet que 2n valeurs exceptionnelles au sens de Picard ou de Borel en general ([12], [13]). Mais, Varopoulos ([16]) s'est aperucu que le nombre de valeurs exceptionnelles est limite par le nombre des relations lineaires homogenes a coefficients constants et distinctes entre les fonctions A0,•c,An puis Remoundos
TL;DR: In this article, a local rigidity theorem for minimal hypersurfaces on a Riemannian manifold of constant curvature has been proposed, where the curvature tensor of the Ricci tensor is defined.
Abstract: [ 1 ] S. S. CHERN, Minimal submanifolds in a Riemannian manifold, Lecture note, 1968.[2] S. S.CHERN, M.P. Do Carmo, S. KOBAYASHI, Minimal submanifolds of a sphere withsecond fundamental form of constant length, to appear.[ 3 ] E. T. DA VIES, On the second and third fundamental forms of a subspace, J. London Math.Soc, 12(1937), 290-295.[ 4 ] H. B. LAWSON, JR, Local rigidity theorems for minimal hypersurfaces, Ann. of Math., 89(1969), 187-197.[ 5 ] K. NOMIZU, On hypersurfaces satisfying a certain condition on the curvature tensor,Tδhoku Math. J., 20(1968), 46-59.[ 6 ] T. OTSTJKI, Minimal hypersurfaces in a Riemannian manifold of constant curvature, toappear.[7] J.SlMONS, Minimal varieties in riemannian manifolds, Ann. of Math., 88(1968), 62-105.[8] S. TANNO, Hypersurfaces satisfying a certain condition on the Ricci tensor, Tόhoku Math.J., 21(1969), 297-303.[9] S. TANNO, T. TAKAHASHI, Some hypersurfaces of a sphere, Tόhoku Math. J., 22(1970),212-219.[10] Y. TOMONAGA, Pseudo-Jacobi fields on minimal varieties, Tohoku Math. J., 21(1969),539-547.MATHEMATICAL INSTITUTETOHOKU UNIVERSITYS::NDAI, JAPAN
TL;DR: In this paper, the authors propose a 1.1.1-approximation algorithm for the problem of concatenation of 2.0-2.5.0.
Abstract: 1.