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1.
B. Et-Taoui 《Geometriae Dedicata》1996,63(3):297-308
Résumé On étudie dans P
n
les m-uples de points, appelés F-réguliers, dont les sous-triplets ordonnés sont deux à deux isométriques. On montre qu'il existe au plus deux classes d'isométrie de quintuplets F-réguliers contenant un triangle équilatère T donné. On étudie aussi les m-uples F-réguliers, dont les sous k-uples (k<m) non ordonnés sont deux à deux isométriques. Ces m-uples sont appelés k-réguliers. On montre que la 4-régularité implique la k-régularité pour tous les k5.
We investigate in P n m-tuples of points in which all ordered triples are pairwise isometric. Such m-tuples are called F-regular. We show that for a given triangle T there exist at most two isometry classes of F-regular quintuples containing T. We also investigate F-regular m-tuples in which all (unordered) k-tuples (k<m) are pairwise isometric. Such m-tuples are called k-regular. We show that 4-regularity implies k-regularity for all k5.相似文献
2.
Cédric Pépin 《Mathematische Annalen》2013,355(1):147-185
Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X K can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as Néron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the Néron property of its Picard functor. In particular, one can recover the Néron model of the Picard variety ${{\rm Pic}_{X_K/K,{\rm red}}^0}$ of X K from the Picard functor Pic X/S , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X. 相似文献
3.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(12):1425-1430
We present several limit models for genuinely clamped elastic beams obtained from linear three-dimensional elasticity using an asymptotic method, and we prove the existence and the uniqueness of the solution for these models. We also obtain convergence to the usual clamped beam model. 相似文献
4.
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(7):777-782
Let F. be a connected amd locally connected locally compact group having a countable basis for its topology. Does E admit a translation invariant Brelot harmonic sheaf? For which E does the elliptic Bauer theory coincides with the Brelot theory for all invariant harmonic elliptic sheaves? This note announces the following solutions: (a) Any E carries invariant Brelot harmonic sheaves; (b) Any invariant elliptic Bauer harmonic elliptic sheaf is a Brelot sheaf if and only if E is a finite dimensional Lie group. These results are obtained by studying product diffusions on infinite products of manifolds. e.g.. compacts Lie groups. 相似文献
6.
Dr. Jean-Pierre Kahane 《Monatshefte für Mathematik》1982,93(4):289-292
Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero. 相似文献
7.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(7):833-838
We study in this Note ordinary differential equations for divergence-free vector-fields with a limited regularity. We first observe that it is equivalent to solve the associated transport equations (i.e. Liouville equations). Then, we show existence, uniqueness, and stability results for generic vector-fields in L1 or for “piecewise” W1.1 vector-fields. 相似文献
8.
9.
Sans résuméPrésenté par G. Alexits 相似文献
10.
Marianne Peyron 《Comptes Rendus Mathematique》2013,351(9-10):353-356
The Poincaré–Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly pseudoconvex homogeneous domain is biholomorphic to the unit ball. In an almost complex manifold, the unit ball is not the only strongly pseudoconvex homogeneous domain. A strongly pseudoconvex homogeneous domain is biholomorphic to a model domain. The aim of this paper is to extend this theorem to model domains. 相似文献
11.
Andre Marchaud 《Annali di Matematica Pura ed Applicata》1961,56(1):131-157
Résumé Sur la droite projective, la notion de connexité est intuitive. Dans un espace projectif En, un ensemble est dit:linéairement connexe, si toutes ses traces sur les droites de En sont connexes. Deux ensembles complémentaires sont simultanément linéairement connexes ou non.
On définit l'index (d'expansion linéaire intérieure) d'un ensemble linéairement connexe, possèdant des points intérieurs, comme le nombre maximum de dimensions des multiplicités
linéaires qu'on peut mener à l'intérieur de l'ensemble. C'est uń nombre positif ou nul.
Soient dans En deux ensembles complémentaires linéairement connexes possèdant chacun des points intérieurs: An et Bn. Leurs index respectifs αn et βn, satisfont à la relation: αn + βn +1 ≤ n.
L'essentiel des résultats du Mémoire est le suivant: Si αn et βn sont tout deux nuls ou positifs, la frontière commune Fn, à An et Bn, estalgébrique et du secoud degré; si un seul est nul, Fn estconvexe, dégénérée ou non, mais pas nécessairement algébrique. Dans tous les cas la connaissance de αn et βn permet de préciser la nature de Fn. En particulier, si αn + βn +1 = n, Fn est sans singularité, et réciproquement. 相似文献
12.
Mohamed Hmissi 《Potential Analysis》1994,3(1):145-152
Let (X, ) be a continuous dynamical system on a locally compact spaceX with countable base. In this note we prove the equivalence of the following statements:
As application, every unstable dynamical system possesses a sectionS in the formS={p=q}, such thatp andq are lower semicontinuous and >0 onX. 相似文献
1. | (X, ) is unstable; |
2. | The kernelf Vf= 0 f((t, ·)) dt, is a proper kernel. |
13.
If K/k
is a finite purely inseparable extension of fields, we are interested in the factorizations
of K as a tensor product over
k of intermediates fields of
K/k.
We introduce the notion of e-factorization
that generalizes the notion of modular factorization. Contrary to modular
factorization, K/k
has always an e-factorization and its factors, when their number
is maximum, are quasi-invariants.Received: 4 April 2002 相似文献
14.
15.
For simply connected nilpotent Lie groups, we show that a probability measure is gaussian in the sense of Bernstein (for a definition thereof which in a natural way involves non-commutativity) iff it is a gaussian measure in the classical sense concentrated on an abelian subgroup. Furthermore we carry over the Skitovic̆-Darmois theorem to symmetric spaces of non-compact type. 相似文献
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18.
Françoise Chatelin 《Numerische Mathematik》1979,32(3):233-246
Summary The theoretical framework of this study is presented in Sect. 1, with a review of practical numerical methods. The linear operatorT and its approximationT
n are defined in the same Banach space, which is a very common situation. The notion of strong stability forT
n is essential and cannot be weakened without introducing a numerical instability [2]. IfT (or its inverse) is compact, most numerical methods are strongly stable. Without compactness forT(T
–1) they may not be strongly stable [20].In Sect. 2 we establish error bounds valid in the general setting of a strongly stable approximation of a closedT. This is a generalization of Vainikko [24, 25] (compact approximation). Osborn [19] (uniform and collectivity compact approximation) and Chatelin and Lemordant [6] (strong approximation), based on the equivalence between the eigenvalues convergence with preservation of multiplicities and the collectively compact convergence of spectral projections. It can be summarized in the following way: , eigenvalue ofT of multiplicitym is approximated bym numbers,
n
is their arithmetic mean.-
n
and the gap between invariant subspaces are of order
n
=(T-T
n)P. IfT
n
*
converges toT
*, pointwise inX
*, the principal term in the error on -
n
is
. And for projection methods, withT
n=
n
T, we get the bound
. It applies to the finite element method for a differential operator with a noncompact resolvent. Aposteriori error bounds are given, and thegeneralized Rayleigh quotient
TP
n appears to be an approximation of of the second order, as in the selfadjoint case [12].In Sect. 3, these results are applied to the Galerkin method and its Sloan variant [22], and to approximate quadrature methods. The error bounds and the generalized Rayleigh quotient are numerically tested in Sect. 4.
Sur les bornes d'erreur a posteriori pour les éléments propres d'opérateurs linéaires相似文献
19.
S. Marcus 《Acta Mathematica Hungarica》1963,14(3-4):269-281
20.
Jean-Paul Bézivin 《Aequationes Mathematicae》1992,43(2-3):159-176
Summary In this paper, we study the convergence of formal power series solutions of functional equations of the formP
k(x)([k](x))=(x), where
[k]
(x) denotes thek-th iterate of the function.We obtain results similar to the results of Malgrange and Ramis for formal solutions of differential equations: if(0) = 0, and(0) =q is a nonzero complex number with absolute value less than one then, if(x)=a(n)x
n is a divergent solution, there exists a positive real numbers such that the power seriesa(n)q
sn(n+1)2
x
n has a finite and nonzero radius of convergence. 相似文献