共查询到20条相似文献,搜索用时 31 毫秒
1.
In this Note, we demonstrate that the image of a base point of a rational surface defined in is a set of rational curves defined in . A base point is a parameter value for which the rational parametrization takes the value of (see [4,5]). This result was studied by Clebsch in [1]. Here, we use the formalism of massic vectors introduced by Fiorot and Jeannin in [3]. This allows us to give explicitly these rational curves via their massic vectors. These massic vectors are proportional to those whose indices belong to the Newton polygon of the surface. Moreover, it is shown that by using fractional changes of variables, it is possible to obtain any image curve directly without having to apply successive changes of variables as usually done in algebraic geometry. To cite this article: O. Gibaru, J.-C. Fiorot, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 283–288. 相似文献
2.
Baohua Fu 《Comptes Rendus Mathematique》2003,337(9):593-596
Let be an elliptic fibration on a K3 surface S. Then the composition gives an Abelian fibration on S[n]. Let E be the exceptional divisor of π, then symnφ°π(E) is of dimension n?1. We prove the inverse in this Note. To cite this article: B. Fu, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
3.
Bent Fuglede 《Journal of Functional Analysis》1974,16(1):101-121
In Rn let Ω denote a Nikodym region (= a connected open set on which every distribution of finite Dirichlet integral is itself in . The existence of n commuting self-adjoint operators such that each Hj is a restriction of (acting in the distribution sense) is shown to be equivalent to the existence of a set Λ ?Rn such that the restrictions to Ω of the functions exp i ∑ λjxj form a total orthogonal family in . If it is required, in addition, that the unitary groups generated by H1,…, Hn act multiplicatively on , then this is shown to correspond to the requirement that Λ can be chosen as a subgroup of the additive group Rn. The measurable sets Ω ?Rn (of finite Lebesgue measure) for which there exists a subgroup Λ ?Rn as stated are precisely those measurable sets which (after a correction by a null set) form a system of representatives for the quotient of Rn by some subgroup Γ (essentially the dual of Λ). 相似文献
4.
In this Note we give a generalization of Hardy's theorem for the Dunkl transform on . More precisely, for all a>0, b>0 and p,q∈[1,+∞], we determine the measurable functions f such that and , where are the Lp spaces associated with the Dunkl transform. To cite this article: L. Gallardo, K. Trimèche, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 849–854. 相似文献
5.
George Hutchinson 《Journal of Pure and Applied Algebra》1977,10(2):115-119
Let R be a ring with 1, Rop the opposite ring, and R-Mod the category of left unitary R-modules and R-linear maps. A characterization of well-powered abelian categories such that there exists an exact embedding functor →R-Mod is given. Using this characterization and abelian category duality, the following duality principles can be established.Theorem. There exists an exact embedding functor →R-Mod if and only if there exists an exact embedding functor op→Rop-Mod.Corollary. If R-Mod has a specified diagram-chasing property, then Rop-Mod has the dual property.A lattice L is representable by R-modules if it is embeddable in the lattice of submodules of some unitary left R-module; (R) denotes the quasivariety of all lattices representable by R-modules.Theorem. A lattice L is representable by R-modules if and only if its order dual L1 is representable by Rop-modules. That is, .If is a commutative ring with 1 and a specified diagram-chasing result is satisfied in R-Mod, then the dual result is also satisfied in R-Mod. Furthermore, is self-dual: 相似文献
6.
7.
L.R. Haff 《Journal of multivariate analysis》1977,7(3):374-385
Let Sp×p ~ Wishart (Σ, k), Σ unknown, k > p + 1. Minimax estimators of Σ?1 are given for L1, an Empirical Bayes loss function; and L2, a standard loss function (Ri ≡ E(Li ∣ Σ), i = 1, 2). The estimators are , a, b ≥ 0, r(·) a functional on . Stein, Efron, and Morris studied the special cases and , for certain, a, b. From their work , a = k ? p ? 1, b = p2 + p ? 2; whereas, we prove . The reversal is surprising because a.e. (for a particular L2). Assume (compact) ? , the set of p × p p.s.d. matrices. A “divergence theorem” on functions Fp×p : → implies identities for Ri, i = 1, 2. Then, conditions are given for , i = 1, 2. Most of our results concern estimators with r(S) = t(U)/tr(S), U = p ∣S∣1/p/tr(S). 相似文献
8.
We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps . We show that the L2 distance of ?v from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 173–178 相似文献
9.
We study here a biharmonic equation in an exterior domain of . We give in Lp theory, with 1<p<∞ existence, uniqueness and regularity results. To cite this article: C. Amrouche, M. Fontes, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
10.
A.G Ramm 《Journal of Mathematical Analysis and Applications》1984,98(1):92-98
Consider the exterior boundary value problem (▽2 + K2) u = 0, in Ω, k >0. , where Γ is a smooth closed connected surface in 3, , ∝ is called the radiation pattern. We prove that when h runs through any dense set in L2(Γ) the corresponding radiation pattern ∝(k,n) runs through a dense set in L2(S2) for any k >0, where S2 is the unit sphere in 3. 相似文献
11.
If the Riemann–Christoffel tensor associated with a field of class of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset , then this field is the metric tensor field associated with a deformation of class of the set , uniquely determined up to isometries of . We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493. 相似文献
12.
This paper deals with asymptotic behavior for (weak) solutions of the equation , on + × Ω; u(t, x) = 0, on + × ?Ω. If and β is coercive, we prove that the solutions are bounded in the energy space, under weaker assumptions than those used by G. Prouse in a previous work. If in addition and ? is srongly almost-periodic, we prove for strongly monotone β that all solutions are asymptotically almost-periodic in the energy space. The assumptions made on β are much less restrictive than those made by G. Prouse: mainly, we allow β to be multivalued, and in the one-dimensional case β need not be defined everywhere. 相似文献
13.
We study a continuous time growth process on (d?1) associated to the following interacting particle system: initially there is only one simple symmetric continuous time random walk of total jump rate one located at the origin; then, whenever a random walk visits a site still unvisited by any other random walk, it creates a new independent random walk starting from that site. Let us call Pd the law of such a process and S0d(t) the set of sites, visited by all walks by time t. We prove that there exists a bounded, non-empty, convex set , such that for every ε>0, Pd-a.s. eventually in t, the set Sd0(t) is within an ε neighborhood of the set [Cdt], where for we define . Moreover, for d large enough, the set Cd is not a ball under the Euclidean norm. We also show that the empirical density of particles within Sd0(t) converges weakly to a product Poisson measure of parameter one. To cite this article: A.F. Ram??rez, V. Sidoravicius, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 821–826. 相似文献
14.
Yuliang Wen 《Comptes Rendus Mathematique》2004,338(3):229-234
Let M2n be a 2n-dimensional compact, simply connected Riemannian manifold without boundary and S2n be the unit sphere of 2n+1 dimension Euclidean space . We prove in this note that if the sectional curvature KM varies in (0,1] and the volume V(M) is not larger than for some positive number η depending only on n, then M2n is homeomorphic to S2n. To cite this article: Y. Wen, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
15.
We show that the Föppl–von Kármán theory arises as a low energy Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [5] that for maps , the L2 distance of ?v from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 201–206. 相似文献
16.
We study questions of the following type: Given positive semi-definite matrix , does there exist a sequence of vectors in whose Grammian equals to and which has some specified additional properties (typically related to the sup norm)? In particular, we show that the answer to the 1947 Knaster problem about real functions on spheres is negative for sufficiently large dimensions. To cite this article: B.S. Kashin, S.J. Szarek, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
17.
Chérif Amrouche 《Comptes Rendus Mathematique》2002,335(2):151-156
We study here the nonhomogeneous Neumann problem in the half-space with N?2. We give in Lp theory, with 1<p<∞, a basic existence and regularity results in weighted Sobolev spaces. To cite this article: C. Amrouche, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 151–156. 相似文献
18.
David Gurarie 《Journal of Mathematical Analysis and Applications》1985,108(1):223-229
For elliptic operators on Rn and certain of their singular perturbations relative compactness of B with respect to A is established. This result applies to the study of Lp-spectra of elliptic operators for different p. 相似文献
19.
Harry Dym 《Journal of Functional Analysis》1978,28(1):33-57
Let PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of exponential type ? T which are square summable on the line with respect to the measure , and let G denote the operator of multiplication by a suitably restricted complex valued function g. It is shown that if is summable, if is locally summable, and if belongs to the span in L∞ of e?iyTH∞:T ? 0, in which h is chosen to be an outer function and h#(γ) agrees with the complex conjugate of h(γ) on the line, then exists and is independent of h for every positive integer n. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special case h = 1 using a different formalism. It also extends earlier results of the author which were established under more stringent conditions on h. The conclusions are based in part upon a preliminary study of a more general class of projections. 相似文献
20.
Nicolae Dinculeanu 《Journal of Functional Analysis》1973,12(3):229-235
Let (X, ∑, μ) be a measure space and S be a semigroup of measure-preserving transformations T:X → X. In case μ(X) < ∞, Aribaud [1] proved the existence of a positive contractive projection P of L1(μ) such that for every belongs to the closure of the convex hull of the set {}. In this paper we extend this result in three directions: we consider infinite measure spaces, vector-valued functions, and Lp spaces with 1 ? p < ∞, and prove that P is in fact the conditional expectation with respect to the σ-algebra Λ of sets of ∑ which are invariant with respect to all T?S. 相似文献