共查询到20条相似文献,搜索用时 837 毫秒
1.
Misha Verbitsky 《Selecta Mathematica, New Series》2005,10(4):551-559
For any subvariety of a compact holomorphic symplectic K?hler manifold, we define the symplectic Wirtinger number W(X). We show that
W(X) \leqslant 1,W(X) \leqslant 1, and the equality is reached if and only if the subvariety
X ì MX \subset M is trianalytic, i.e. compatible with the hyperk?hler structure on M. For a sequence
X1 ? X2 ? ?Xn ? MX_1 \to X_2 \to \ldots X_n \to M of immersions of simple holomorphic symplectic manifolds, we show that
W( X1 ) \leqslant W( X2 ) \leqslant ?\leqslant W( Xn ).W\left( {X_1 } \right) \leqslant W\left( {X_2 } \right) \leqslant \ldots \leqslant W\left( {X_n } \right). 相似文献
2.
Marino Badiale Lorenzo Pisani Sergio Rolando 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(4):369-405
We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (W,A,m){(\Omega ,\mathcal{A},\mu)} and investigating the main properties of both the Banach space
L( W) = {u1+u2:u1 ? Lq1 (W),u2 ? Lq2 ( W) }, Lqi ( W) :=Lqi ( W,dm),L\left( \Omega \right) =\left\{u_{1}+u_{2}:u_{1} \in L^{q_{1}} \left(\Omega \right),u_{2} \in L^{q_{2}} \left( \Omega \right) \right\}, L^{q_{i}} \left( \Omega \right) :=L^{q_{i}} \left( \Omega ,d\mu \right), 相似文献
3.
We consider generalized Morrey type spaces Mp( ·),q( ·),w( ·)( W) {\mathcal{M}^{p\left( \cdot \right),\theta \left( \cdot \right),\omega \left( \cdot \right)}}\left( \Omega \right) with variable exponents p(x), θ(r) and a general function ω(x, r) defining a Morrey type norm. In the case of bounded sets
W ì \mathbbRn \Omega \subset {\mathbb{R}^n} , we prove the boundedness of the Hardy–Littlewood maximal operator and Calderón–Zygmund singular integral operators with
standard kernel. We prove a Sobolev–Adams type embedding theorem Mp( ·),q1( ·),w1( ·)( W) ? Mq( ·),q2( ·),w2( ·)( W) {\mathcal{M}^{p\left( \cdot \right),{\theta_1}\left( \cdot \right),{\omega_1}\left( \cdot \right)}}\left( \Omega \right) \to {\mathcal{M}^{q\left( \cdot \right),{\theta_2}\left( \cdot \right),{\omega_2}\left( \cdot \right)}}\left( \Omega \right) for the potential type operator I
α(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x, r) with respect to r. Bibliography: 40 titles. 相似文献
4.
Given a weighted graph, letW
1,W
2,W
3,... denote the increasing sequence of all possible distinct spanning tree weights. Settling a conjecture due to Kano, we prove that every spanning tree of weightW
1 is at mostk–1 edge swaps away from some spanning tree of weightW
k
. Three other conjectures posed by Kano are proven for two special classes of graphs. Finally, we consider the algorithmic complexity of generating a spanning tree of weightW
k
.This work was supported in part by a grant from the AT&T foundation and NSF grant DCR-8351757.Primarily supported by a 1967 Science and Engineering Scholarship from the Natural Sciences and Engineering Research Council of Canada. 相似文献
5.
A. Borrelli M. C. Patria 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(6):880-893
The aim of this paper is to investigate the behaviour of the total energy of a magnetoelastic conductor occupying a semi-infinite prismatic cylinder in dynamical conditions. Precisely, we deduce some estimates for the energyW(x
3,t) of the portion of the medium at distance greater thanx
3 from the base in terms of the data. First of all, we prove that the total energyW(0,t) is finite for allt > 0 providedW(0, 0) is finite. Then, using the first Korn inequality, we obtain that the estimate forW(x
3,t) depends only on the initial data ift<x
3/V (V=computable positive material constant); ift>x
3/V then the bound forW(x
3,t) depends on all the data of the problem. 相似文献
6.
Oliver D. Eng 《Journal of Algebraic Combinatorics》2001,13(1):29-40
For a finite reflection group W and parabolic subgroup W
J, we establish that the quotient of Poincaré polynomials \frac{W(t)}{W_J(t)}, when evaluated at t=–1, counts the number of cosets of W
J in W fixed by the longest element. Our case-by-case proof relies on the work of Stembridge (Stembridge, Duke Mathematical Journal, 73 (1994), 469–490) regarding minuscule representations and on the calculations of
of Tan (Tan, Communications in Algebra, 22 (1994), 1049–1061). 相似文献
7.
Jrmie Guilhot 《Journal of Algebra》2007,318(2):893-917
Let W be a Coxeter group and L be a weight function on W. Following Lusztig, we have a corresponding decomposition of W into left cells which have important applications in representation theory. We study the case where W is an affine Weyl group of type . Using explicit computation with COXETER and CHEVIE, we show that (1) there are only finitely many possible decompositions into left cells and (2) the number of left cells is finite in each case, thus confirming some of Lusztig's conjectures in this case. A key ingredient of the proof is a general result which shows that the Kazhdan–Lusztig polynomials of affine Weyl group are invariant under (large enough) translations. 相似文献
8.
N. A. Shirokov 《Journal of Mathematical Sciences》2001,107(4):4125-4142
For a family of domains
Wt ì \mathbbCn ,t ? [ 0,1 ]\Omega _t \subset \mathbb{C}^n ,t \in \left[ {0,1} \right]
, a formula for B
1
(z,s)-B_0(z,s) is established, where B
0
and B
1
are the Bergman kernels for
W0\Omega _0
and
W1\Omega _1
. As an application of this formula, we obtain two terms in the asymptotics of B(z,z) as
z ? ?Wz \to \partial \Omega
for a special class of domains. Bibliography: 4 titles. 相似文献
9.
C.K. Fan 《Journal of Algebraic Combinatorics》1996,5(3):175-189
Let (W, S) be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let H be the corresponding Hecke Algebra. We define a certain quotient \-H of H and show that it has a basis parametrized by a certain subset W
cof the Coxeter group W. Specifically, W
cconsists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommuting generators in S. We determine which Coxeter groups have finite W
cand compute the cardinality of W
cwhen W is a Weyl group. Finally, we give a combinatorial application (which is related to the number of reduced expressions for w W
cof an exponential formula of Lusztig which utilizes a specialization of a subalgebra of \-H. 相似文献
10.
《复变函数与椭圆型方程》2012,57(12):837-843
Let W be a nonnegative summable function whose logarithm is also summable with respect to the Lebesgue measure on the unit circle. For 0?<?p?<?∞ , Hp (W) denotes a weighted Hardy space on the unit circle. When W?≡?1, H p(W) is the usual Hardy space Hp . We are interested in Hp ( W)+ the set of all nonnegative functions in Hp ( W). If p?≥?1/2, Hp + consists of constant functions. However Hp ( W)+ contains a nonconstant nonnegative function for some weight W. In this paper, if p?≥?1/2 we determine W and describe Hp ( W)+ when the linear span of Hp ( W)+ is of finite dimension. Moreover we show that the linear span of Hp (W)+ is of infinite dimension for arbitrary weight W when 0?<?p?<?1/2. 相似文献
11.
Etsuko Bannai 《Graphs and Combinatorics》2001,17(4):589-598
It is known that for each matrix W
i
and it's transpose
t
W
i
in any four-weight spin model (X, W
1, W
2, W
3, W
4; D), there is attached the Bose-Mesner algebra of an association scheme, which we call Nomura algebra. They are denoted by N(W
i
) and N(
t
W
i
) = N′(W
i
) respectively. H. Guo and T. Huang showed that some of them coincide with a self-dual Bose-Mesner algebra, that is, N(W
1) = N′(W
1) = N(W
3) = N′(W
3) holds. In this paper we show that all of them coincide, that is, N(W
i
), N′(W
i
), i=1, 2, 3, 4, are the same self-dual Bose-Mesner algebra.
Received: June 17, 1999 Final version received: Januray 17, 2000 相似文献
12.
Let {β(s), s ≥ 0} be the standard Brownian motion in ℝ
d
with d ≥ 4 and let |W
r
(t)| be the volume of the Wiener sausage associated with {β(s), s ≥ 0} observed until time t. From the central limit theorem of Wiener sausage, we know that when d ≥ 4 the limit distribution is normal. In this paper, we study the laws of the iterated logarithm for
| Wr (t) | - \mathbbE| Wr (t) |\left| {W_r (t)} \right| - \mathbb{E}\left| {W_r (t)} \right| in this case. 相似文献
13.
We introduce W‐spin structures on a Riemann surface Σ and give a precise definition to the corresponding W‐spin equations for any quasi‐homogeneous polynomial W. Then we construct examples of nonzero solutions of spin equations in the presence of Ramond marked points. The main result of the paper is a compactness theorem for the moduli space of the solutions of W‐spin equations when W = W(x1, …, xt) is a nondegenerate, quasi‐homogeneous polynomial with fractional degrees (or weights) qi < ½ for all i. In particular, the compactness theorem holds for the superpotentials E6, E7, E8 or An ? 1, Dn + 1 for n ≥ 3. © 2008 Wiley Periodicals, Inc. 相似文献
14.
This note is the first part of consecutive two papers concerning with a length function and Demazure operators for the complex reflection group W = G(e, 1, n). In this first part, we study the word problem on W based on the work of Bremke and Malle [BM]. We show that the usual length function ?(W) associated to a given generator set S is completely described by the function n(W), introduced in [BM], associated to the root system of W.In the second part, we will study the Demazure operators of W on the symmetric algebra. We define a graded space HW in terms of Demazure operators, and show that HW is isomorphic to the coinvariant algebra SW, which enables us to define a homogeneous basis on SW parametrized by w?W. 相似文献
15.
N. M. Ivochkina 《Journal of Mathematical Sciences》2010,170(4):496-509
We construct an a priori estimate of the seminorm
á uxx
ña, [`(W)] {\left\langle {{u_{xx}}} \right\rangle_{\alpha, \bar{\Omega }}} for solutions to the problem
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