We study the isospectral Hilbert scheme , defined as the reduced fiber product of with the Hilbert scheme of points in the plane , over the symmetric power . By a theorem of Fogarty, is smooth. We prove that is normal, Cohen-Macaulay and Gorenstein, and hence flat over . We derive two important consequences.
(1) We prove the strong form of the conjecture of Garsia and the author, giving a representation-theoretic interpretation of the Kostka-Macdonald coefficients . This establishes the Macdonald positivity conjecture, namely that .
(2) We show that the Hilbert scheme is isomorphic to the -Hilbert scheme of Nakamura, in such a way that is identified with the universal family over . From this point of view, describes the fiber of a character sheaf at a torus-fixed point of corresponding to .
The proofs rely on a study of certain subspace arrangements , called polygraphs, whose coordinate rings carry geometric information about . The key result is that is a free module over the polynomial ring in one set of coordinates on . This is proven by an intricate inductive argument based on elementary commutative algebra.
This paper analyzes, and thus reveals the structure of the stable invariant subspace of the related Hamiltonian matrix arising from the measurement feedback H-control problem. Using this, it presents another method for the verification of the admissibility of the controller derived by Doyle et al. in 1989. The method not only eliminates unnecessary assumptions on stabilizability and detectability, but also gives deeper insight into the relationship among the stable parts of the associated matrices. 相似文献
For any stable distribution on the line, recurrence-transience of the selfsimilar additive process {Xt,t0} with (X1)= is determined. Comparison with the stable Lévy process {Yt,t0} with (Y1)= is made: if is not strictly stable, then {Yt} is transient but {Xt} is recurrent except the obviously transient case of monotone sample functions. 相似文献
We study the asymptotic behavior and limit distributions for sums Sn =bn-1i=1ni,where
i, i 1, are i.i.d. random convex compact (cc) sets in a given separable Banach space B and summation is defined in a sense of Minkowski. The following results are obtained: (i) Series (LePage type) and Poisson integral representations of random stable cc sets in B are established; (ii) The invariance principle for processes Sn(t) =bn-1i=1[nt]i, t[0, 1], and the existence of p-stable cc Levy motion are proved; (iii) In the case, where
i are segments, the limit of Sn is proved to be countable zonotope. Furthermore, if B = Rd, the singularity of distributions of two countable zonotopes Yp1, 1,Yp2, 2, corresponding to values of exponents p1, p2 and spectral measures
1,
2, is proved if either p1p2 or
12; (iv) Some new simple estimates of parameters of stable laws in Rd, based on these results are suggested. 相似文献
The structural stability and magnetic properties of the icosahedral Ni13, Ni13^+1 and Ni13^-1 clusters have been obtained by utilizing all-electron density functional theory with the generalized gradient approximations for the exchange-correlation energy. The calculated results show that the ground states of neutral and charged clusters all favour a D3d structure, a distorted icosahedron, due to the Jahn-Teller effect. The radial distortions caused by doping one electron and by doping one hole are opposite to each other. Doping one electron will result in a 1/2 decrease and doping one hole will result in a 1/2 increase of the total spin. Both increasing interatomic spacing and decreasing coordination will lead to an enhancement of the spin magnetic moments for Nil3 clusters. 相似文献
In this paper we present a lower bound of the disjunctive rank of the facets describing the stable set polytope of joined a-perfect graphs. This class contains near-bipartite, t-perfect, h-perfect and complement of fuzzy interval graphs, among others. The stable set polytope of joined a-perfect graphs is described by means of full rank constraints of its node induced prime antiwebs. As a first step, we completely determine the disjunctive rank of all these constraints. Using this result we obtain a lower bound of the disjunctive index of joined a-perfect graphs and prove that this bound can be achieved. In addition, we completely determine the disjunctive index of every antiweb and observe that it does not always coincide with the disjunctive rank of its full rank constraint. 相似文献
In this paper, general conditions of state classification for the total weighted occupation times of a class of infinitely
divisible superprocesses on a bounded domain D in ℝd are given. As an application, some sufficient and necessary conditions are found for the total weighted occupation times
of some special superprocesses on D to be absolutely continuous or singular with respect to the Lebesgue measure on D.
The research of Yan-Xia Ren is supported by NNSF of China (Grant No. 10471003) and Foundation for Authors Awarded Excellent
Ph.D. Dissertation. 相似文献
Assume that the characteristic indexαof stable distribution satisfies 1<α<2,and that the distribution is symmetrical about its mean.We consider the change point estimators for stable distribution withαor scale parameterβshift.For the one case that mean is a known constant,ifαorβchanges,then density function will change too.To this end,we suppose the kernel estimation for a change point.For the other case that mean is an unknown constant,we suppose to apply empirical characteristic function to estimate the change-point location.In the two cases,we consider the consistency and strong convergence rate of estimators.Furthermore,we consider the mean shift case.If mean changes,then corresponding characteristic function will change too.To this end,we also apply empirical characteristic function to estimate change point.We obtain the similar convergence rate.Finally,we consider its application on the detection of mean shift in financial market. 相似文献