共查询到20条相似文献,搜索用时 62 毫秒
1.
2.
Yoshiaki Fukuma 《Geometriae Dedicata》1998,69(2):189-206
Let (X,L) be a polarized surface. If h0(L)>0, then g(L) q(X). In our previous papers, we classified polarized surfaces (X,L) with g(L)=q(X) and h0(L)>0. In this paper, we classify polarized surfaces (X,L) with g(L)=q(X)+1, h0(L)>0, and (X) 0. 相似文献
3.
William Y. C. Chen Larry X. W. Wang Arthur L. B. Yang 《Journal of Algebraic Combinatorics》2010,32(3):303-338
We prove two recent conjectures of Liu and Wang by establishing the strong q-log-convexity of the Narayana polynomials, and showing that the Narayana transformation preserves log-convexity. We begin with a formula of Brändén expressing the q-Narayana numbers as a specialization of Schur functions and, by deriving several symmetric function identities, we obtain the necessary Schur-positivity results. In addition, we prove the strong q-log-concavity of the q-Narayana numbers. The q-log-concavity of the q-Narayana numbers N q (n,k) for fixed k is a special case of a conjecture of McNamara and Sagan on the infinite q-log-concavity of the Gaussian coefficients. 相似文献
4.
Let μ be a compactly suppported positive measure on the real line. A point x∈supp?[μ] is said to be μ-regular, if, as n→∞, Otherwise it is a μ-irregular point. We show that for any such measure, the set of μ-irregular points in {μ′>0} (with a suitable definition of this set) has Hausdorff \(m_{h_{\beta}}\) measure 0, for \(h_{\beta}(t) =\left(\log \frac{1}{t}\right)^{-\beta}\), any β>1.
相似文献
$\sup_{\deg\, (P) \le n}\left(\frac{|P(x)|}{{\|P\|}_{L_{2}(d\mu)}}\right )^{1/n}\to1.$
5.
Let G be a discrete subgroup of PU(1,n). Then G acts on ℙℂ
n
preserving the unit ball ℍℂ
n
, where it acts by isometries with respect to the Bergman metric. In this work we look at its action on all of ℙℂ
n
and determine its equicontinuity region Eq(G). This turns out to be the complement of the union of all complex projective hyperplanes in ℙℂ
n
which are tangent to ∂ℍℂ
n
at points in the Chen-Greenberg limit set Λ(G), a closed G-invariant subset of ∂ℍℂ
n
which is minimal for non-elementary groups. We also prove that the action on Eq(G) is discontinuous. Also , if the limit set is “sufficiently general” (i.e. it is not contained in any proper
k
-chain), then each connected component of Eq(G) is a holomorphy domain and it is a complete Kobayashi hyperbolic space. 相似文献
6.
We complete the study of the supersingular locus Mss\mathcal{M}^{\mathrm{ss}} in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n−1) over ℚ in the case that p is inert. This was started by the first author in Can. J. Math. 62, 668–720 (2010) where complete results were obtained for n=2,3. The supersingular locus Mss\mathcal{M}^{\mathrm{ss}} is uniformized by a formal scheme N\mathcal{N} which is a moduli space of so-called unitary p-divisible groups. It depends on the choice of a unitary isocrystal N. We define a stratification of N\mathcal{N} indexed by vertices of the Bruhat-Tits building attached to the reductive group of automorphisms of N. We show that the combinatorial behavior of this stratification is given by the simplicial structure of the building. The
closures of the strata (and in particular the irreducible components of Nred\mathcal{N}_{\mathrm{red}}) are identified with (generalized) Deligne-Lusztig varieties. We show that the Bruhat-Tits stratification is a refinement
of the Ekedahl-Oort stratification and also relate the Ekedahl-Oort strata to Deligne-Lusztig varieties. We deduce that Mss\mathcal{M}^{\mathrm{ss}} is locally a complete intersection, that its irreducible components and each Ekedahl-Oort stratum in every irreducible component
is isomorphic to a Deligne-Lusztig variety, and give formulas for the number of irreducible components of every Ekedahl-Oort
stratum of Mss\mathcal{M}^{\mathrm{ss}}. 相似文献
7.
We introduce a simultaneous decomposition for a matrix triplet (A,B,C
∗), where A=±A
∗ and (⋅)∗ denotes the conjugate transpose of a matrix, and use the simultaneous decomposition to solve some conjectures on the maximal
and minimal values of the ranks of the matrix expressions A−BXC±(BXC)∗ with respect to a variable matrix X. In addition, we give some explicit formulas for the maximal and minimal values of the inertia of the matrix expression A−BXC−(BXC)∗ with respect to X. As applications, we derive the extremal ranks and inertias of the matrix expression D−CXC
∗ subject to Hermitian solutions of a consistent matrix equation AXA
∗=B, as well as the extremal ranks and inertias of the Hermitian Schur complement D−B
∗
A
∼
B with respect to a Hermitian generalized inverse A
∼ of A. Various consequences of these extremal ranks and inertias are also presented in the paper. 相似文献
8.
Frances Y. Kuo Grzegorz W. Wasilkowski Henryk Woźniakowski 《BIT Numerical Mathematics》2009,49(3):543-564
We study approximation of multivariate functions from a general separable reproducing kernel Hilbert space in the randomized
setting with the error measured in the L
∞ norm. We consider algorithms that use standard information consisting of function values or general linear information consisting of arbitrary linear functionals. The power of standard or linear information is defined as, roughly speaking, the optimal rate of convergence of algorithms using n function values or linear functionals. We prove under certain assumptions that the power of standard information in the randomized
setting is at least equal to the power of linear information in the worst case setting, and that the powers of linear and
standard information in the randomized setting differ at most by 1/2. These assumptions are satisfied for spaces with weighted
Korobov and Wiener reproducing kernels. For the Wiener case, the parameters in these assumptions are prohibitively large,
and therefore we also present less restrictive assumptions and obtain other bounds on the power of standard information. Finally,
we study tractability, which means that we want to guarantee that the errors depend at most polynomially on the number of
variables and tend to zero polynomially in n
−1 when n function values are used. 相似文献
9.
Gregorio Moreno 《Journal of Theoretical Probability》2010,23(2):466-477
We consider the model of directed polymers in an i.i.d. Gaussian or bounded environment (Imbrie and Spencer in J. Stat. Phys.
52(3/4), 609–626, 1988; Carmona and Hu in Probab. Theory Relat. Fields 124(3), 431–457, 2002; Comets et al. in Adv. Stud. Pure Math. 39, 115–142, 2004) in the L
2 region. We prove the convergence of the law of the environment seen by the particle. 相似文献
10.
The M/G/K queueing system is one of the oldest models for multiserver systems and has been the topic of performance papers for almost
half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (nonnumerical)
approximations in the literature are based on (at most) the first two moments of the job size distribution. In this paper
we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we
provide a lower bound on the inapproximability ratio, which we refer to as “the gap.” This is the first such result in the
literature to address “the gap.” The proof technique behind this result is novel as well and combines mean value analysis,
sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into
the effect of higher moments of the job size distribution on the mean waiting time. 相似文献
11.
We study some properties of algebras of continuous functions on a locally compact space, these algebras being equipped with the topology defined by a family of multiplication operators (β-uniform algebras). We prove an analog of a theorem due to Sheinberg for β-uniform algebras [see Uspekhi Mat. Nauk, 32:5 (197) (1977), 203–204]. 相似文献
12.
A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is equivalent to computing the discrete homotopy group of the 1-skeleton of the permutahedron. To compute this group we introduce combinatorial techniques that we believe will be helpful in computing discrete fundamental groups of other polytopes. More precisely, we use the language of words, over the alphabet of simple transpositions, to obtain conditions that are necessary and sufficient to characterize the equivalence classes of cycles. The proof requires only simple combinatorial arguments. As a corollary, we also obtain a combinatorial proof of the fact that the first Betti number of the complement of the 3-equal arrangement is equal to 2 n?3(n 2?5n+8)?1. This formula was originally obtained by Björner and Welker in 1995. 相似文献
13.
R. A. Bandaliev 《Mathematical Notes》2014,95(3-4):450-462
The main purpose of this paper is to study the weight space L p(x),ω for 0 < p(x) < 1 as well as the topology of this space. Embeddings between different Lebesgue spaces with variable exponent of summability are established. In particular, it is proved that the set of all linear continuous functionals over L p(x),ω for 0 < p(x) < 1 consists only of the zero functional. 相似文献
14.
Yury A. Neretin 《Algebras and Representation Theory》2018,21(5):1087-1117
Consider a restriction of an irreducible finite dimensional holomorphic representation of \(\text {GL}(n + 1,\mathbb {C})\) to the subgroup \(\text {GL}(n,\mathbb {C})\). We write explicitly formulas for generators of the Lie algebra \(\mathfrak {g}\mathfrak {l}(n + 1)\) in the direct sum of representations of \(\text {GL}(n,\mathbb {C})\). Nontrivial generators act as differential-difference operators, the differential part has order n ??1, the difference part acts on the space of parameters (highest weights) of representations. We also formulate a conjecture about unitary principal series of \(\text {GL}(n,\mathbb {C})\). 相似文献
15.
L. D. Faddeev 《Functional Analysis and Its Applications》2008,42(4):330-335
The modular double of the quantum group U q (sl(2)) with deformation parameter q = e iπτ is a natural object explicitly taking into account the duality τ ? 1/τ. The use of the modular double in conformal field theory allows one to consider the region 1 < c < 25 for the central charge of the Virasoro algebra when |τ| = 1. In this paper, a new discrete series of representations for the modular double of U q (sl(2, ?)) is found for such τ. 相似文献
16.
The prime graph of a finite group was introduced by Gruenberg and Kegel. The degree pattern of a finite group G associated to its prime graph was introduced in [1] and denoted by D(G). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions (1) |G| = |H| and (2) D(G) = D(H). Moreover, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Till now a lot of finite simple groups were shown to be OD-characterizable, and also some finite groups especially the automorphism
groups of some finite simple groups were shown not being OD-characterizable but k-fold OD-characterizable for some k > 1. In the present paper, the authors continue this topic and show that the automorphism groups of orthogonal groups O
10+(2) and O
10−(2) are OD-characterizable. 相似文献
17.
We point out that it is consistent with ZFC that 2
ω
> ℵ1 and every subset of ℝ is the ω
1 limit of a sequence of G
δ
sets in ℝ. We prove also that assuming cov (
) > ℵ1, not every set in ℝ is the ω
1 limit of a sequence of measurable sets. This solves two problems of T. Natkaniec and J. Wesołowska.
相似文献
18.
Aladár Heppes 《Discrete and Computational Geometry》2011,45(2):321-328
Let K denote an oval, a centrally symmetric compact convex domain with non-empty interior. A family of translates of K is said to have property T(k) if for every subset of at most k translates there exists a common line transversal intersecting all of them. Property T means that a transversal exists for all members of the family. Two translates, K i and K j are said to be φ-disjoint, φ>0, if the concentric φ-enlarged copies of K i and K j are disjoint. It is well known that in a φ-disjoint family of congruent discs T(3)?T if \(\varphi>\sqrt{2}\), and \(T(3)\not\Rightarrow T\) if \(\varphi<\sqrt{2}\). In this note finite φ-disjoint T(3)-families of translates of an oval will be investigated. 相似文献
19.
BINOD KUMAR SAHOO 《Proceedings Mathematical Sciences》2016,126(2):143-151
In [5], a new combinatorial model with four types of points and nine types of lines of the slim dense near hexagon Q(5,2)?Q(5,2) was provided and it was then used to construct a non-abelain representation of Q(5,2)?Q(5,2) in the extraspecial 2-group \(2_{-}^{1+18}\). In this paper, we give a direct proof for the existence of a non-abelian representation of Q(5,2)?Q(5,2) in \(2_{-}^{1+18}\). 相似文献