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71.
An efficient method of achieving flexibility in the length of discrete convolutions, computed using Fourier and Fourier-like fast transform algorithms, is described. Then this method is extended to discrete multidimensional convolutions computed using polynomial transforms. 相似文献
72.
The Brownian loop soup 总被引:6,自引:0,他引:6
Gregory F.?Lawler Wendelin?WernerEmail author 《Probability Theory and Related Fields》2004,128(4):565-588
We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40 相似文献
73.
Robert S. Maier 《Journal of statistical physics》2003,111(5-6):1027-1048
Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for the expected number of crossing clusters. It is shown that for lattices where conformal invariance holds, they simplify when the spatial domain is taken to be the interior of an equilateral triangle. The two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry. This suggests that rigorous proofs of Watts's formula and Cardy's new formula will be easiest to construct if the underlying lattice is triangular. The simplification in a triangular domain of Schramm's bulk Cardy's formula is also studied. 相似文献
74.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
75.
Po-Hsun Hsieh 《Geometriae Dedicata》2003,97(1):99-113
We study a nonidentity transvection (i.e. (strictly) hyperbolic isometry) or nonidentity Heisenberg translation f of complex hyperbolic space H
n and a Dirichlet polyhedron P of the cyclic group f. We have four main results: (a) If z & in H
n and the axis of a nonidentity transvection are not complex collinear, then, roughly speaking, any two distinct 'naturally arising' geodesics passing through z are not complex collinear. (b) If g is also a transvection or Heisenberg translation of H
n and z & in H
n such that f(z)=g(z) and f
–1(z)=g
–1(z), then f=g. (c) We classify all this kind of polyhedra up to congruence in H
n. (d) We obtain an equivalent condition for P to be cospinal (which means that the complex spines of the two sides of P coincide) in terms of the distance of the spines of the two sides of P. 相似文献
76.
We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the
set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty. 相似文献
77.
Frances Y. Jackson W. A. J. Luxemburg 《Proceedings of the American Mathematical Society》2003,131(1):185-199
We characterize the first three sundual spaces of , with respect to the translation group of .
78.
We present a detailed proof of the existence-theorem for noncommutative spectral sections (see the noncommutative spectral flow, unpublished preprint, 1997). We apply this result to various index-theoretic situations, extending to the noncommutative context results of Booss–Wojciechowski, Melrose–Piazza and Dai–Zhang. In particular, we prove a variational formula, in K*(Cr*(Γ)), for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula involves a noncommutative spectral flow for the boundary family. Next, we establish an additivity result, in K*(Cr*(Γ)), for the index class defined by a Dirac-type operator associated to a closed manifold M and a map r:M→BΓ when we assume that M is the union along a hypersurface F of two manifolds with boundary M=M+ F M−. Finally, we prove a defect formula for the signature-index classes of two cut-and-paste equivalent pairs (M1,r1:M1→BΓ) and (M2,r2:M2→BΓ), whereand φjDiff(F). The formula involves the noncommutative spectral flow of a suitable 1-parameter family of twisted signature operators on F. We give applications to the problem of cut-and-paste invariance of Novikov's higher signatures on closed oriented manifolds. 相似文献
M1=M+ (F,φ1) M−, M2=M+ (F,φ2) M−
79.
Thomas Schick 《Transactions of the American Mathematical Society》2001,353(8):3247-3265
A standing conjecture in -cohomology says that every finite -complex is of -determinant class. In this paper, we prove this whenever the fundamental group belongs to a large class of groups containing, e.g., all extensions of residually finite groups with amenable quotients, all residually amenable groups, and free products of these. If, in addition, is -acyclic, we also show that the -determinant is a homotopy invariant -- giving a short and easy proof independent of and encompassing all known cases. Under suitable conditions we give new approximation formulas for -Betti numbers.
80.
A spread of
is a set of l-dimensional subspaces L V partitioning V {0}. We construct examples of compact spreads that are identical with their sets of orthogonal spaces L
. In the corresponding topological translation planes, every Euclidean sphere is a unital with the additional property that every point at infinity has flat feet. 相似文献