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1.
We prove that the crossed product C*-algebra C*r(, ) of a freegroup with its boundary sits naturally between the reducedgroup C*-algebra C*r and its injective envelope I(C*r). In otherwords, we have natural inclusion C*r C*r(, ) I(C*r) of C*-algebras. 相似文献
2.
Let be a non-elementary Kleinian group acting on the closedn-dimensional unit ball and assume that its Poincaréseries converges at the exponent . Let M be the -quotient ofthe open unit ball. We consider certain families = {E1, ...,Ep} of open subsets of M such that is compact. The sets Ei are the ends of M and is a completecollection of ends for M. We associate to each end E an -conformalmeasure such that the measures corresponding to different endsare mutually singular if non-trivial. Additionally, each -conformalmeasure for on the limit set () of can be written as a sumof such conformal measures associated to ends E . In dimension3, our results overlap with some results of Bishop and Jones(The law of the iterated logarithm for Kleinian groups, Cont.Math. 211 (1997), 1750.). 相似文献
3.
A cycle C of a graph embedded in a 3-manifold M is said tobe trivial in if it bounds a disk with interior disjoint from. Let e be an edge of with ends on C. We shall study the relationbetween triviality of cycles in and that of e and/e. Let C1 be one of the two cycles in C e containing e. Themain theorem says that if C is trivial in e and C1/eis trivial in /e, then either C or C1 is trivial in . Some applicationsto cycle trivial graphs will be given in Section 2. 相似文献
4.
This paper considers the finite-element approximation of theelliptic interface problem: -?(u) + cu = f in Rn (n = 2 or3), with u = 0 on , where is discontinuous across a smoothsurface in the interior of . First we show that, if the meshis isoparametrically fitted to using simplicial elements ofdegree k - 1, with k 2, then the standard Galerkin method achievesthe optimal rate of convergence in the H1 and L2 norms overthe approximations l4 of l where l 2. Second, since itmay be computationally inconvenient to fit the mesh to , weanalyse a fully practical piecewise linear approximation ofa related penalized problem, as introduced by Babuska (1970),based on a mesh that is independent of . We show that, by choosingthe penalty parameter appropriately, this approximation convergesto u at the optimal rate in the H1 norm over l4 and in the L2norm over any interior domain l* satisfying l* l** l4 for somedomain l**.
Present address: School of Mathematical and Physical Sciences,University of Sussex, Brighton BN1 9QH 相似文献
5.
An elliptic boundary-value problem on a domain with prescribedDirichlet data on I is approximated using a finite-elementspace of approximation power hK in the L2 norm. It is shownthat the total flux across I can be approximated with an errorof O(hK) when is a curved domain in Rn (n = 2 or 3) and isoparametricelements are used. When is a polyhedron, an O(h2K2)approximation is given. We use these results to study the finite-elementapproximation of elliptic equations when the prescribed boundarydata on I is the total flux.
Present address: School of Mathematical and Physical Sciences,University of Sussex, Brighton, Sussex BN1 9QH. 相似文献
6.
The plasma problem studied is: given R+ find (, d, u) R ?R ? H1() such that
Let 1 < 2 be the first two eigenvalues of the associatedlinear eigenvalue problem: find $$\left(\lambda ,\phi \right)\in\mathrm{R;}\times {\hbox{ H }}_{0}^{1}\left(\Omega \right)$$such that
For 0(0,2) it is well known that there exists a unique solution(0, d0, u0) to the above problem. We show that the standard continuous piecewise linear Galerkinfinite-element approximatinon $$\left({\lambda }_{0},{\hbox{d }}_{0}^{k},{u}_{0}^{h}\right)$$, for 0(0,2), converges atthe optimal rate in the H1, L2, and L norms as h, the mesh length,tends to 0. In addition, we show that dist (, h)Ch2 ln 1/h,where $${\Gamma }^{\left(h\right)}=\left\{x\in \Omega :{u}_{0}^{\left(h\right)}\left(x\right)=0\right\}$$.Finally we consider a more practical approximation involvingnumerical integration. 相似文献
7.
Bestvina–Brady groups arise as kernels of length homomorphismsG from right-angled Artin groups to the integers. Under someconnectivity assumptions on the flag complex , we compute severalalgebraic invariants of such a group N, directly from the underlyinggraph . As an application, we give examples of finitely presentedBestvina–Brady groups which are not isomorphic to anyArtin group or arrangement group. 相似文献
8.
Let denote the unit disk, viewed as a model for the hyperbolicplane. Under rescaling, takes on the appearance of a tree,with an additional ribbon structure coming from the cyclic orderingof its ends. In this paper, we show that branched coverings of ribbon treesnaturally compactify the space of proper holomorphic maps f: (, 0) (, 0), and use the structure of these ribbon treesto describe the limiting moduli of f. Received December 1, 2007. 相似文献
9.
Let be a singular cardinal of regular uncountable cofinality. Let {(): < } be a continuous increasing sequence withlimit , and let =()+(), < be regular cardinals. Let I be a normal ideal on , and assume that the reduced product</I admits a cofinal -scale of ordinal functions. Then +, where =||||I is the I-norm of . 相似文献
10.
The main part of the paper deals with local existence and globalexistence versus blow-up for solutions of the Laplace equationin bounded domains with a non-linear dynamical boundary condition.More precisely, we study the problem consisting in: (1) theLaplace equation in (0, ) x ; (2) a homogeneous Dirichlet condition(0, ) x 0; (3) the dynamical boundary condition ; (4) the initial condition u(0, x) = u0 (x) on . Here is a regular and bounded domain in Rn, with n 1, and0 and 1 endow a measurable partition of . Moreover, m>1,2 p < r, where r = 2 (n 1) / (n 2) whenn 3, r = when n = 1,2, and u0 H1/2 , u0 = 0 on 0. The final part of the paper deals with a refinement of a globalnon-existence result by Levine, Park and Serrin, which is appliedto the previous problem. 2000 Mathematics Subject Classification35K55 (primary), 35K90, 35K77 (secondary). 相似文献
11.
Higher Generation Subgroup Sets and the Virtual Cohomological Dimension of Graph Products of Finite Groups 总被引:1,自引:0,他引:1
We introduce panels of stabilizer schemes (K, G*) associatedwith finite intersection-closed subgroup sets of a given groupG, generalizing in some sense Davis' notion of a panel structureon a triangulated manifold for Coxeter groups. Given (K, G*),we construct a G-complex X with K as a strong fundamental domainand simplex stabilizers conjugate to subgroups in . It turnsout that higher generation properties of in the sense of Abels-Holzare reflected in connectivity properties of X. Given a finite simplicial graph and a non-trivial group G()for every vertex of , the graph product G() is the quotientof the free product of all vertex groups modulo the normal closureof all commutators [G(), G(w)] for which the vertices , w areadjacent. Our main result allows the computation of the virtualcohomological dimension of a graph product with finite vertexgroups in terms of connectivity properties of the underlyinggraph . 相似文献
12.
We prove that the Novikov assembly map for a group factorizes,in low homological degree, through the algebraicK-theory of its integral group ring. In homological degree 2,this answers a question posed by N. Higson and P. Julg. As adirect application, we prove that if is torsion-free and satisfiesthe Baum-Connes conjecture, then the homology group H1(; Z)injects in and in , for any ring A such that . If moreover B is of dimension lessthan or equal to 4, then we show that H2(; Z) injects in and in , where A is as before, and 2 is generated by the Steinberg symbols{,}, for . 2000 Mathematical Subject Classification: primary 19D55, 19Kxx,58J22; secondary: 19Cxx, 19D45, 43A20, 46L85. 相似文献
13.
BARRETT JOHN W.; CHAKRABARTI ROMA; ELLIOTT CHARLES M. 《IMA Journal of Numerical Analysis》1991,11(4):579-594
Optimal order H1 and L error bounds are obtained for a continuouspiecewise linear finite element approximation of an obstacleproblem, where the obstacle's height as well as the contactzone, c, are a priori unknown. The problem models the indentationof a membrane by a rigid punch. For R2, given ,g R+ and an obstacle defined over E we consider the minimization of |v|21,+gµover (v, µ) H10() x R subject to v+µ on E. In additionwe show under certain nondegeneracy conditions that dist (c,hc)Ch ln 1/h, where hc is the finite element approximation toc. Finally we show that the resulting algebraic problem canbe solved using a projected SOR algorithm. 相似文献
14.
Let M be a smooth, compact, oriented, odd-dimensional Riemannianmanifold and let M be anormal covering of M. It is proved that the relative von Neumanneta-invariant (2)() of Cheeger and Gromov is a homotopy invariant when is torsion-free, discreteand the BaumConnes assembly map µmax:K0(B) K0(C*)is an isomorphism. 相似文献
15.
We consider a Hamiltonian setup M, , H, L, , P, where M, isa symplectic manifold, L is a distribution of Lagrangian subspacesin M, P is a Lagrangian submanifold of M, H is a smooth time-dependentHamiltonian function on M, and :[a,b] M is an integral curveof the Hamiltonian flow starting at P. We do not require any convexity property of the Hamiltonianfunction H. Under the assumption that (b) is not P-focal, weintroduce the Maslov index imaslov of given in terms of thefirst relative homology group of the Lagrangian Grassmannian;under generic circumstances imaslov() is computed as a sortof algebraic count of the P-focal points along . We prove thefollowing version of the Index Theorem: under suitable hypotheses,the Morse index of the Lagrangian action functional restrictedto suitable variations of is equal to the sum of imaslov()and a convexity term of the Hamiltonian H relative to the submanifoldP. When the result is applied to the case of the cotangent bundleM = TM* of a semi-Riemannian manifold (M, g) and to the geodesicHamiltonian , we obtain a semi-Riemannian version of the celebrated Morse Index Theorem for geodesicswith variable endpoints in Riemannian geometry. 2000 MathematicalSubject Classification: 37J05, 53C22, 53C50, 53D12, 70H05. 相似文献
16.
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
17.
Asymptotic Cones of Finitely Generated Groups 总被引:1,自引:0,他引:1
Answering a question of Gromov [7], we shall present an exampleof a finitely generated group and two non-principal ultrafiltersA, B such that the asymptotic cones ConA and ConB are nothomeomorphic. 1991 Mathematics Subject Classification 20F06,20F32. 相似文献
18.
Let be a bounded connected open set in RN, N 2, and let 0be the Dirichlet Laplacian defined in L2(). Let > 0 be thesmallest eigenvalue of , and let > 0 be its correspondingeigenfunction, normalized by ||||2 = 1. For sufficiently small>0 we let R() be a connected open subset of satisfying
Let 0 be the Dirichlet Laplacian on R(), and let >0and >0 be its ground state eigenvalue and ground state eigenfunction,respectively, normalized by ||||2=1. For functions f definedon , we let Sf denote the restriction of f to R(). For functionsg defined on R(), we let Tg be the extension of g to satisfying
1991 Mathematics SubjectClassification 47F05. 相似文献
19.
The Hardy operator Ta on a tree is defined by Properties of Ta as a map from Lp() into itselfare established for 1 p . The main result is that, with appropriateassumptions on u and v, the approximation numbers an(Ta) ofTa satisfy for a specified constant p and 1 p < . This extends results of Naimark, Newmanand Solomyak for p = 2. Hitherto, for p 2, (*) was unknowneven when is an interval. Also, upper and lower estimates forthe lq and weak-lq norms of an(Ta) are determined. 2000 MathematicalSubject Classification: 47G10, 47B10. 相似文献
20.
In this paper, the behaviour of the positive eigenfunction of in u| = 0, p > 1, isstudied near its critical points. Under some convexity and symmetryassumptions on , is seen to have a unique critical point atx = 0; also, the behaviour of both and is determined nearby.Positive solutions u to some general problems pu = f(u)in , u| = 0, are also considered, with some convexity restrictionson u. 2000 Mathematics Subject Classification 35B05 (primary),35J65, 35J70 (secondary). 相似文献