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1.
On a question of Brezis and Marcus   总被引:3,自引:0,他引:3  
Motivated by a question of Brezis and Marcus, we show that the Lp–Hardy inequality involving the distance to the boundary of a convex domain, can be improved by adding an Lq norm qp, with a constant depending on the interior diameter of Ω.  相似文献
2.
Stability of the Picard Bundle   总被引:2,自引:0,他引:2  
Let X be a non-singular algebraic curve of genus g 2, n 2an integer, a line bundle over X of degree d > 2n(g –1) with (n,d) = 1 and M the moduli space of stable bundles ofrank n and determinant over X. It is proved that the Picardbundle W is stable with respect to the unique polarisation ofM. 2000 Mathematics Subject Classification 14H60, 14J60.  相似文献
3.
On the Lebesgue measure of the expressible set of certain sequences   总被引:1,自引:0,他引:1  
The paper gives a condition for the expressible set of a sequence to have Lebesgue measure zero.  相似文献
4.
Approximation algorithms for Hamming clustering problems   总被引:1,自引:0,他引:1  
We study Hamming versions of two classical clustering problems. The Hamming radius p-clustering problem (HRC) for a set S of k binary strings, each of length n, is to find p binary strings of length n that minimize the maximum Hamming distance between a string in S and the closest of the p strings; this minimum value is termed the p-radius of S and is denoted by . The related Hamming diameter p-clustering problem (HDC) is to split S into p groups so that the maximum of the Hamming group diameters is minimized; this latter value is called the p-diameter of S.We provide an integer programming formulation of HRC which yields exact solutions in polynomial time whenever k is constant. We also observe that HDC admits straightforward polynomial-time solutions when k=O(logn) and p=O(1), or when p=2. Next, by reduction from the corresponding geometric p-clustering problems in the plane under the L1 metric, we show that neither HRC nor HDC can be approximated within any constant factor smaller than two unless P=NP. We also prove that for any >0 it is NP-hard to split S into at most pk1/7− clusters whose Hamming diameter does not exceed the p-diameter, and that solving HDC exactly is an NP-complete problem already for p=3. Furthermore, we note that by adapting Gonzalez' farthest-point clustering algorithm [T. Gonzalez, Theoret. Comput. Sci. 38 (1985) 293–306], HRC and HDC can be approximated within a factor of two in time O(pkn). Next, we describe a 2O(p/)kO(p/)n2-time (1+)-approximation algorithm for HRC. In particular, it runs in polynomial time when p=O(1) and =O(log(k+n)). Finally, we show how to find in

time a set L of O(plogk) strings of length n such that for each string in S there is at least one string in L within distance (1+), for any constant 0<<1.  相似文献
5.
We study a number of natural families of binary differential equations (BDE's) on a smooth surface in . One, introduced by G. J. Fletcher in 1996, interpolates between the asymptotic and principal BDE's, another between the characteristic and principal BDE's. The locus of singular points of the members of these families determine curves on the surface. In these two cases they are the tangency points of the discriminant sets (given by a fixed ratio of principle curvatures) with the characteristic (resp. asymptotic) BDE.

More generally, we consider a natural class of BDE's on such a surface , and show how the pencil of BDE's joining certain pairs are related to a third BDE of the given class, the so-called polar BDE. This explains, in particular, why the principal, asymptotic and characteristic BDE's are intimately related.

  相似文献

6.
The Teichmüller space of a finite-type surface is considered.It is shown that Teichmüller distance is not C2 + forany > 0. Furthermore, Teichmüller distance is not C2+ g for any gauge function g with . 2000 Mathematics Subject Classification 30F60.  相似文献
7.
8.
The variational partial differential equation (PDE) approach for image denoising restoration leads to PDEs with nonlinear and highly non-smooth coefficients. Such PDEs present convergence difficulties for standard multigrid methods. Recent work on algebraic multigrid methods (AMGs) has shown that robustness can be achieved in general but AMGs are well known to be expensive to apply. This paper proposes an accelerated algebraic multigrid algorithm that offers fast speed as well as robustness for image PDEs. Experiments are shown to demonstrate the improvements obtained.  相似文献
9.
We consider a single machine scheduling problem with two min-sum objective functions: the sum of completion times and the sum of weighted completion times. We propose a simple polynomial time (1+(1/γ),1+γ)-approximation algorithm, and show that for γ>1, there is no (x,y)-approximation with 1<x<1+(1/γ) and 1<y<1+(γ-1)/(2+γ).  相似文献
10.
I. Biswas 《Topology》2006,45(2):403-419
Let X be a nonsingular algebraic curve of genus g?3, and let Mξ denote the moduli space of stable vector bundles of rank n?2 and degree d with fixed determinant ξ over X such that n and d are coprime. We assume that if g=3 then n?4 and if g=4 then n?3, and suppose further that n0, d0 are integers such that n0?1 and nd0+n0d>nn0(2g-2). Let E be a semistable vector bundle over X of rank n0 and degree d0. The generalised Picard bundle Wξ(E) is by definition the vector bundle over Mξ defined by the direct image where Uξ is a universal vector bundle over X×Mξ. We obtain an inversion formula allowing us to recover E from Wξ(E) and show that the space of infinitesimal deformations of Wξ(E) is isomorphic to H1(X,End(E)). This construction gives a locally complete family of vector bundles over Mξ parametrised by the moduli space M(n0,d0) of stable bundles of rank n0 and degree d0 over X. If (n0,d0)=1 and Wξ(E) is stable for all EM(n0,d0), the construction determines an isomorphism from M(n0,d0) to a connected component M0 of a moduli space of stable sheaves over Mξ. This applies in particular when n0=1, in which case M0 is isomorphic to the Jacobian J of X as a polarised variety. The paper as a whole is a generalisation of results of Kempf and Mukai on Picard bundles over J, and is also related to a paper of Tyurin on the geometry of moduli of vector bundles.  相似文献
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