共查询到20条相似文献,搜索用时 578 毫秒
1.
Throughout this paper G(k) denotes a Chevalley group of rankn defined over the field k, where n3. Let be the root systemassociated with G(k) and let ={1, 2, ..., n} be a set of fundamentalroots of , with + being the set of positive roots of with respectto . For and +, let n() be the coefficient of in the expressionof as a sum of fundamental roots; so =n(). Also we recall thatht(), the height of , is given by ht()=n(). The highest rootin + will be denoted by . We additionally assume that the Dynkindiagram of G(k) is connected. 相似文献
2.
We study concentration phenomena for the system
in the unit ball B1 of 3 with Dirichlet boundaryconditions. Here , , > 0 and p > 1. We prove the existenceof positive radial solutions (, ) such that concentrates ata distance (/2)|log | away from the boundary B1 as the parameter tends to 0. The approach is based on a combination of LyapunovSchmidtreduction procedure together with a variational method. 相似文献
3.
Let f be a continuous function on an open subset of R2 suchthat for every x there exists a continuous map : [1,1] with (0) = x and f increasing on [1, 1]. Thenfor every there exists a continuous map : [0, 1) suchthat (0) = y, f is increasing on [0; 1), and for every compactsubset K of , max{t : (t) K} < 1. This result gives an answerto a question posed by M. Ortel. Furthermore, an example showsthat this result is not valid in higher dimensions. 相似文献
4.
Betti Numbers of Semialgebraic and Sub-Pfaffian Sets 总被引:1,自引:0,他引:1
Let X be a subset in [1,1]n0Rn0 defined by the formula X={x0|Q1x1Q2x2...Qx ((x0,x1,...x)X)}, where Qi{ }, Qi Qi+1, xi [1, 1]ni, and X may be eitheran open or a closed set in [1,1]n0+...+n, being the differencebetween a finite CW-complex and its subcomplex. An upper boundon each Betti number of X is expressed via a sum of Betti numbersof some sets defined by quantifier-free formulae involving X. In important particular cases of semialgebraic and semi-Pfaffiansets defined by quantifier-free formulae with polynomials andPfaffian functions respectively, upper bounds on Betti numbersof X are well known. The results allow to extend the boundsto sets defined with quantifiers, in particular to sub-Pfaffiansets. 相似文献
5.
The paper shows that any graph G with the maximum degree (G) 8, which is embeddable in a surface of Euler characteristic() 0, is totally ((G)+2)-colorable. In general, it is shownthat any graph G which is embeddable in a surface and satisfiesthe maximum degree (G) (20/9) (3())+1 is totally ((G)+2)-colorable. 相似文献
6.
Buff Xavier; Fagella NuRia; Geyer Lukas; Henriksen Christian 《Journal London Mathematical Society》2005,72(3):689-716
For (,a) C* x C, let f,a be the rational map defined by f,a(z)= z2 (az+1)/(z+a). If R/Z is a Brjuno number, we let D bethe set of parameters (,a) such that f,a has a fixed Hermanring with rotation number (we consider that (e2i,0) D). Resultsobtained by McMullen and Sullivan imply that, for any g D, theconnected component of D(C* x (C/{0,1})) that contains g isisomorphic to a punctured disk. We show that there is a holomorphic injection F:DD such thatF(0) = (e2i ,0) and , where r is the conformal radius at 0 of the Siegel disk of the quadraticpolynomial z e2i z(1+z). As a consequence, we show that for a (0,1/3), if fl,a has afixed Herman ring with rotation number and if ma is the modulusof the Herman ring, then, as a0, we have e ma=(r/a) + O(a). We finally explain how to adapt the results to the complex standardfamily z e(a/2)(z-1/z). 相似文献
7.
The close relationship between the notions of positive formsand representations for a C*-algebra A is one of the most basicfacts in the subject. In particular the weak containment ofrepresentations is well understood in terms of positive forms:given a representation of A in a Hilbert space H and a positiveform on A, its associated representation is weakly containedin (that is, ker ker ) if and only if belongs to the weak*closure of the cone of all finite sums of coefficients of .Among the results on the subject, let us recall the followingones. Suppose that A is concretely represented in H. Then everypositive form on A is the weak* limit of forms of the typex ki=1 i, xi with the i in H; moreover if A is a von Neumannsubalgebra of (H) and is normal, there exists a sequence (i)i 1 in H such that (x) = i 1 i, xi for all x. 相似文献
8.
Let 1 < p < , 0 < v < p', let be a bounded domainin Rn, and denote by id the limiting compact embedding of theBesov space (Rn) into the exponentialOrlicz space Lexp(tv)(), mapping a function f onto its restrictionf|. In 1993 Triebel established, among others, two-sided estimatesfor the entropy numbers of id, which are even asymptoticallyoptimal for small . The aim of the paper is toimprove the upper bounds in the case of large, where Triebel's estimates are not yet sharp, thus making afurther step towards the conjectured correct asymptotic behaviour. 相似文献
9.
Let G be a separable locally compact group and let be its dualspace with Fell's topology. It is well known that the set P(G)of continuous positive-definite functions on G can be identifiedwith the set of positive linear functionals on the group C*-algebraC*(G). We show that if is discrete in , then there exists anonzero positive-definite function associated with such that is a w*-strongly exposed point of P(G)0, where P(G)0={f P(G):f(e)1. Conversely, if some nonzero positive-definite function associatedwith is a w*-strongly exposed point of P(G)0, then is isolatedin . Consequently, G is compact if and only if, for every ,there exists a nonzero positive-definite function associatedwith that is a w*-strongly exposed point of P(G)0. If, in addition,G is unimodular and , then is isolated in if and only if somenonzero positive-definite function associated with is a w*-stronglyexposed point of P(G)0, where is the left regular representationof G and is the reduced dual space of G. We prove that if B(G)has the RadonNikodym property, then the set of isolatedpoints of (so square-integrable if G is unimodular) is densein . It is also proved that if G is a separable SIN-group, thenG is amenable if and only if there exists a closed point in. In particular, for a countable discrete non-amenable groupG (for example the free group F2 on two generators), there isno closed point in its reduced dual space . 相似文献
10.
We consider operators on the matrix-valued disc algebra. Weshow that any bounded linear operator to a Banach space X of cotype 2 induces a boundedoperator GX defined on some weighted Bergman space G on theunit disc. We give sufficient conditions on the weight forthe formal inclusion to be 2C*-summing. Decompositions of T with respect to operator-valuedmeasures are obtained. 相似文献
11.
The boundedness of CalderónZygmund operators isproved in the scale of the mixed Lebesgue spaces. As a consequence,the boundedness of the bilinear null forms Qi j (u,) =i uj - j ui , Q0(u,)=ut t -x u· x on various spacetimemixed SobolevLebesgue spaces is shown. 相似文献
12.
If = {1, 2, ..., s}, where 1 2 ... s > 0, is a partitionof n then denotes the associated irreducible character of Sn,the symmetric group on {1, 2, ..., n}, and, if cCSn, the groupalgebra generated by C and Sn, then dc(·) denotes thegeneralized matrix function associated with c. If c1, c2 CSnthen we write c1 c2 in case (A) (A) for each n x n positivesemi-definite Hermitian matrix A. If cCSn and c(e) 0, wheree denotes the identity in Sn, then or denotes (c(e))–1 c. The main result, an estimate for the norms of tensors of a certainanti-symmetry type, implies that if = {1, 2, ..., s, 1t} isa partition of n such that s > 1 and s = 2, and ' denotes{1, 2, ..., s-1, 1t} then (, {2}) where denotes characterinduction from Sn–2 x S2 to Sn. This in turn implies thatif = {1, 2, ..., s, 1t} with s > 1, s = 2, and ßdenotes {1 + 2, 2, ..., s-1, 1t} then ß which,in conjunction with other known results, provides many new inequalitiesamong immanants. In particular it implies that the permanentfunction dominates all normalized immanants whose associatedpartitions are of rank 2, a result which has proved elusivefor some years. We also consider the non-relationship problem for immanants– that is the problem of identifying pairs, (,ß)such that ß and ß are both false. 相似文献
13.
Hayashi Nakao; Kaikina Elena I.; Naumkin Pavel I. 《Journal London Mathematical Society》2005,72(3):663-688
The Cauchy problem is studied for the nonlinear equations withfractional power of the negative Laplacian
where (0,2), with critical = /n and sub-critical (0,/n)powers of the nonlinearity. Let u0 L1,a L C, u0(x) 0 in Rn, = . The case of not small initial data is of interest. It is proved that the Cauchy problemhas a unique global solution u C([0,); L L1,a C) and the largetime asymptotics are obtained. 相似文献
14.
A model (M, <, ...) is -like if M has cardinality but, forall M, the cardinality of {x M : x < a} is strictly lessthan . In this paper we shall give constructions of -like modelsof arithmetic satisfying an arbitrarily large finite part ofPA but not PA itself, for various singular cardinals . The mainresults are: (1) for each countable nonstandard M 2Th(PA)with arbitrarily large initial segments satisfying PA and eachuncountable of cofinality there is a cofinal extension K ofM which is -like; also hierarchical variants of this resultfor nTh(PA); and (2) for every n 1, every singular and every M Bn+exp+¬ In there is a -like model K elementarilyequivalent to M. 相似文献
15.
Inverse SturmLiouville problems with eigenparameter-dependentboundary conditions are considered. Theorems analogous to thoseof both Hochstadt and Gelfand and Levitan are proved. In particular, let ly = (1/r)((py')'+qy), ,
where det = > 0, c 0, det > 0, t 0 and (cs + dr au tb)2 < 4(cr ta)(ds ub). Denoteby (l; ; ) the eigenvalue problem ly = y with boundary conditionsy(0)cos+y'(0)sin = 0 and (a+b)y(1) = (c+d)(py')(1). Define (; ; ) as above but with l replacedby . Let wn denote the eigenfunctionof (l; ; ) having eigenvalue n and initial conditions wn(0)= sin and pw'n(0) = cos and let n = awn(1)+cpw'n(1).Define n and n similarly. As sample results, it is proved that if (l; ; ) and (; ; ) have the same spectrum, and (l;; ) and (; ; ) have the samespectrum or for all n, thenq/r = /. 相似文献
16.
For reciprocation with respect to a sphere x2=c in Euclideann-space, there is a unitary analogue: Hermitian reciprocationwith respect to an antisphere u=c. This is now applied, forthe first time, to complex polytopes. When a regular polytope has a palindromic Schläfli symbol,it is self-reciprocal in the sense that its reciprocal ', withrespect to a suitable concentric sphere or antisphere, is congruentto . The present article reveals that and ' usually have togetherthe same vertices as a third polytope + and the same facet-hyperplanesas a fourth polytope (where + and are againregular), so as to form a compound, +[2].When the geometry is real, + is the convex hull of and ', while is their common content or core. For instance,when is a regular p-gon {p}, the compound is
The exceptions are of two kinds. In one, + and are notregular. The actual cases are when is an n-simplex {3, 3, ...,3} with n4 or the real 4-dimensional 24-cell {3, 4, 3}=2{3}2{4}2{3}2or the complex 4-dimensional Witting polytope 3{3}3{3}3{3}3.The other kind of exception arises when the vertices of arethe poles of its own facet-hyperplanes, so that , ', + and all coincide. Then is said to be strongly self-reciprocal. 相似文献
17.
Let G be a permutation group on a set , and let m and k be integerswhere 0<m<k. For a subset of , if the cardinalities ofthe sets g\, for gG, are finite and bounded, then is said tohave bounded movement, and the movement of is defined as move()=maxgG|g\|. If there is a k-element subset such that move()m, it is shown that some G-orbit has length at most (k2m)/(km).When combined with a result of P. M. Neumann, this result hasthe following consequence: if some infinite subset has boundedmovement at most m, then either is a G-invariant subset withat most m points added or removed, or nontrivially meets aG-orbit of length at most m2+m+1. Also, if move ()m for allk-element subsets and if G has no fixed points in , then either||k+m (and in this case all permutation groups on have thisproperty), or ||5m2. These results generalise earlierresults about the separation of finite sets under group actionsby B. J. Birch, R. G. Burns, S. O. Macdonald and P. M. Neumann,and groups in which all subsets have bounded movement (by theauthor). 相似文献
18.
On a smooth curve a theta-characteristic is a line bundle L,the square of which is the canonical line bundle . The equivalentcondition om(L, ) L generalizes well to singular curves, asapplications show. More precisely, a theta-characteristic isa torsion-free sheaf of rank 1 with om(, ) . If the curvehas non-ADE singularities, then there are infinitely many theta-characteristics.Therefore, theta-characteristics are distinguished by theirlocal type. The main purpose of this article is to compute thenumber of even and odd theta-characteristics (that is withh0(C, ) 0 and h0(C, ) 1 modulo 2, respectively) in terms ofthe geometric genus of the curve and certain discrete invariantsof a fixed local type. 相似文献
19.
Let =(n)n1 be a log concave sequence such that lim infn+n/nc>0for some c>0 and ((log n)/n)n1 is nonincreasing for some<1/2. We show that, if T is a contraction on the Hilbertspace with spectrum a Carleson set, and if ||Tn||=O(n)as n tends to + with n11/(n log n)=+, then T is unitary. Onthe other hand, if n11/(n log n)<+, then there exists a (non-unitary)contraction T on the Hilbert space such that the spectrum ofT is a Carleson set, ||Tn||=O(n) as n tends to +, andlim supn+||Tn||=+. 相似文献
20.
Haller-Dintelmann Robert; Heck Horst; Hieber Matthias 《Journal London Mathematical Society》2006,74(3):717-736
Consider a parabolic NxN-system of order m on n with top-ordercoefficients a VMOL. Let 1 < p, q < and let be a Muckenhouptweight. It is proved that systems of this kind possess a uniquesolution u satisfying
whereAu = ||m a Du and J = [0,). In particular, choosing = 1, therealization of A in Lp(n)N has maximal Lp – Lq regularity. 相似文献