共查询到20条相似文献,搜索用时 15 毫秒
1.
Linus Carlsson 《Mathematische Zeitschrift》2009,261(1):189-200
We show a sufficient condition for a domain in to be a H
∞-domain of holomorphy. Furthermore if a domain has the Gleason property at a point and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several
other interesting properties.
相似文献
2.
Euisung Park 《Mathematische Zeitschrift》2007,256(3):685-697
In this article we study nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay. Note that for a rational normal curve and a point . Our main result is about the relation between the geometric properties of X and the position of P with respect to . We show that the graded Betti numbers of X are uniquely determined by the rank of P with respect to . In particular, X satisfies property N
2,p
if and only if . Therefore property N
2,p
of X is controlled by and conversely can be read off from the minimal free resolution of X. This result provides a non-linearly normal example for which the converse to Theorem 1.1 in (Eisenbud et al., Compositio
Math 141:1460–1478, 2005) holds. Also our result implies that for nondegenerate projective curves of degree d which are not arithmetically Cohen–Macaulay, there are exactly distinct Betti tables. 相似文献
3.
A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
We consider the 2m-th order elliptic boundary value problem Lu = f (x, u) on a bounded smooth domain with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic operator of order 2m given by . For the nonlinearity we assume that , where are positive functions and q > 1 if N ≤ 2m, if N > 2m. We prove a priori bounds, i.e, we show that for every solution u, where C > 0 is a constant. The solutions are allowed to be sign-changing. The proof is done by a blow-up argument which relies on
the following new Liouville-type theorem on a half-space: if u is a classical, bounded, non-negative solution of ( − Δ)
m
u = u
q
in with Dirichlet boundary conditions on and q > 1 if N ≤ 2m, if N > 2m then .
相似文献
4.
Michele Bolognesi 《Mathematische Zeitschrift》2009,261(1):149-168
Let C be a genus 2 curve and the moduli space of semi-stable rank 2 vector bundles on C with trivial determinant. In Bolognesi (Adv Geom 7(1):113–144, 2007) we described the parameter space of non stable extension
classes of the canonical sheaf ω of C by ω−1. In this paper, we study the classifying rational map that sends an extension class to the corresponding rank two vector bundle. Moreover, we prove that, if we blow up along a certain cubic surface S and at the point p corresponding to the bundle , then the induced morphism defines a conic bundle that degenerates on the blow up (at p) of the Kummer surface naturally contained in . Furthermore we construct the -bundle that contains the conic bundle and we discuss the stability and deformations of one of its components. 相似文献
5.
Jens Habermann 《Mathematische Zeitschrift》2008,258(2):427-462
For weak solutions of higher order systems of the type , for all , with variable growth exponent p : Ω → (1,∞) we prove that if with , then . We should note that we prove this implication both in the non-degenerate (μ > 0) and in the degenerate case (μ = 0). 相似文献
6.
Andreas Rosenschon 《K-Theory》2008,38(2):235-241
We give examples of smooth projective complex varieties of dimension d ≥ 4 and primes ℓ such that the morphic cohomology group is infinite, and is not finitely generated as a rational vector space. In particular, for these examples the semi-topological K-group has infinite dimension. 相似文献
7.
Michael Struwe 《Mathematische Zeitschrift》2007,256(2):397-424
For concentrating solutions weakly in H
2(Ω) to the equation on a domain with Navier boundary conditions the concentration energy is shown to be strictly quantized in multiples of the number . 相似文献
8.
Yu. I. Lyubich 《Designs, Codes and Cryptography》2009,51(1):21-31
It is shown that among all tight designs in , where is or , or (quaternions), only 5-designs in (Lyubich, Shatalora Geom Dedicata 86: 169–178, 2001) have irrational angle set. This is the only case of equal ranks of the
first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
相似文献
9.
10.
J. Ruppenthal 《Mathematische Zeitschrift》2009,263(2):447-472
Let X be a regular irreducible variety in , Y the associated homogeneous variety in , and N the restriction of the universal bundle of to X. In the present paper, we compute the obstructions to solving the -equation in the L
p
-sense on Y for 1 ≤ p ≤ ∞ in terms of cohomology groups . That allows to identify obstructions explicitly if X is specified more precisely, for example if it is equivalent to or an elliptic curve.
相似文献
11.
Let be a C
2 map and let Spec(Y) denote the set of eigenvalues of the derivative DY
p
, when p varies in . We begin proving that if, for some ϵ > 0, then the foliation with made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case
of Jelonek’s Jacobian Conjecture for polynomial maps of
The first author was supported by CNPq-Brazil Grant 306992/2003-5. The first and second author were supported by FAPESP-Brazil
Grant 03/03107-9. 相似文献
12.
John Polhill 《Designs, Codes and Cryptography》2009,52(2):163-169
By modifying a construction for Hadamard (Menon) difference sets we construct two infinite families of negative Latin square
type partial difference sets in groups of the form where p is any odd prime. One of these families has the well-known Paley parameters, which had previously only been constructed in
p-groups. This provides new constructions of Hadamard matrices and implies the existence of many new strongly regular graphs
including some that are conference graphs. As a corollary, we are able to construct Paley–Hadamard difference sets of the
Stanton-Sprott family in groups of the form when is a prime power. These are new parameters for such difference sets.
相似文献
13.
We consider the generalized Gagliardo–Nirenberg inequality in in the homogeneous Sobolev space with the critical differential order s = n/r, which describes the embedding such as for all q with p ≦ q < ∞, where 1 < p < ∞ and 1 < r < ∞. We establish the optimal growth rate as q → ∞ of this embedding constant. In particular, we realize the limiting end-point r = ∞ as the space of BMO in such a way that with the constant C
n
depending only on n. As an application, we make it clear that the well known John–Nirenberg inequality is a consequence of our estimate. Furthermore,
it is clarified that the L
∞-bound is established by means of the BMO-norm and the logarithm of the -norm with s > n/r, which may be regarded as a generalization of the Brezis–Gallouet–Wainger inequality. 相似文献
14.
Juan A. Aledo José M. Espinar José A. Gálvez 《Calculus of Variations and Partial Differential Equations》2007,29(3):347-363
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces and . In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature
c > 0 into and a unique one into when c > 1, up to isometries of the ambient space. Moreover, we show that the hyperbolic plane of constant curvature c < −1 cannot be isometrically immersed into or .
J.A. Aledo was partially supported by Ministerio de Education y Ciencia Grant No. MTM2004-02746 and Junta de Comunidades de
Castilla-La Mancha, grant no. PAI-05-034.
J.M. Espinar and J.A. Gálvez were partially supported by Ministerio de Education y Ciencia grant no. MTM2004-02746 and Junta
de Andalucía Grant No. FQM325. 相似文献
15.
Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W
r
+ W
r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w
r
+ w
r+2 satisfies in Ω the system d
*
w
r
= 0, dw
r
+ d
*
w
r+2 = 0; dw
r+2 = 0.
Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure
theorem is proved for the solutions of the Moisil-Théodoresco system.
相似文献
16.
We give an explicit formula for the subalgebra zeta function of a general three-dimensional Lie algebra over the p-adic integers . To this end, we associate to such a Lie algebra a ternary quadratic form over . The formula for the zeta function is given in terms of Igusa’s local zeta function associated to this form.
We acknowledge support from the Mathematisches Forschungsinstitut Oberwolfach and the Nuffield Foundation. 相似文献
17.
It is classically known that a real cubic surface in cannot have more than one solitary point (or -singularity, locally given by x
2 + y
2 + z
2 = 0) whereas it can have up to four nodes (or -singularity, locally given by x
2 + y
2 − z
2 = 0). We show that on any surface of degree d ≥ 3 in the maximum possible number of solitary points is strictly smaller than the maximum possible number of nodes. Conversely,
we adapt a construction of Chmutov to obtain surfaces with many solitary points by using a refined version of Brusotti’s Theorem.
Combining lower and upper bounds, we deduce: , where denotes the maximum possible number of solitary points on a real surface of degree d in . Finally, we adapt this construction to get real algebraic surfaces in with many singular points of type for all k ≥ 1.
相似文献
18.
Cinzia Bisi 《Mathematische Zeitschrift》2008,258(4):875-891
We characterize the polynomial automorphisms of ${\mathbb{C}}^3We characterize the polynomial automorphisms of , which commute with a regular automorphism. We use their meromorphic extension to and consider their dynamics on the hyperplane at infinity. We conjecture the additional hypothesis under which the same characterization
is true in all dimensions. We give a partial answer to a question of S. Smale that in our context can be formulated as follows:
can any polynomial automorphism of be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer (i.e. )?
Partially supported by Progetto MURST di Rilevante Interesse Nazionale Proprietà geometriche delle varietà reali e complesse. Supported by Istituto Nazionale Alta Matematica, “F. Severi”, Roma and G.N.S.A.G.A., Roma. 相似文献
19.
Neculai Andrei 《Numerical Algorithms》2008,47(2):143-156
Another hybrid conjugate gradient algorithm is subject to analysis. The parameter β
k
is computed as a convex combination of (Hestenes-Stiefel) and (Dai-Yuan) algorithms, i.e. . The parameter θ
k
in the convex combination is computed in such a way so that the direction corresponding to the conjugate gradient algorithm
to be the Newton direction and the pair (s
k
, y
k
) to satisfy the quasi-Newton equation , where and . The algorithm uses the standard Wolfe line search conditions. Numerical comparisons with conjugate gradient algorithms show
that this hybrid computational scheme outperforms the Hestenes-Stiefel and the Dai-Yuan conjugate gradient algorithms as well
as the hybrid conjugate gradient algorithms of Dai and Yuan. A set of 750 unconstrained optimization problems are used, some
of them from the CUTE library.
相似文献
20.
Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1).
This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
and by Leverhulme Research Interchange Grant F/00158/X. 相似文献