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Janez Mr?un 《Journal of Pure and Applied Algebra》2007,210(1):267-282
For any étale Lie groupoid G over a smooth manifold M, the groupoid convolution algebra of smooth functions with compact support on G has a natural coalgebra structure over the commutative algebra which makes it into a Hopf algebroid. Conversely, for any Hopf algebroid A over we construct the associated spectral étale Lie groupoid over M such that is naturally isomorphic to G. Both these constructions are functorial, and is fully faithful left adjoint to . We give explicit conditions under which a Hopf algebroid is isomorphic to the Hopf algebroid of an étale Lie groupoid G. 相似文献
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We show that the π-equivariant chain complex (), , associated to a Morse-theoretic minimal CW-structure X on the complement of an arrangement , is independent of X. The same holds for all scalar extensions, , a field, where X is an arbitrary minimal CW-structure on a space M. When is a section of another arrangement , we show that the divisibility properties of the first Betti number of the Milnor fiber of obstruct the homotopy realization of as a subcomplex of a minimal structure on .If is aspherical and is a sufficiently generic section of , then may be described in terms of π, L and , for an arbitrary local system L; explicit computations may be done, when is fiber-type. In this case, explicit -presentations of arbitrary abelian scalar extensions of the first non-trivial higher homotopy group of , πp(M), may also be obtained. For nonresonant abelian scalar extensions, the -rank of is combinatorially determined. 相似文献
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Mitsuru Uchiyama 《Journal of Functional Analysis》2006,231(1):221-244
Let P+ be the set of all non-negative operator monotone functions defined on [0,∞), and put . Then and . For a function and a strictly increasing function h we write if is operator monotone. If and and if and , then . We will apply this result to polynomials and operator inequalities. Let and be non-increasing sequences, and put for t≧a1 and for t≧b1. Then v+?u+ if m≦n and : in particular, for a sequence of orthonormal polynomials, (pn-1)+?(pn)+. Suppose 0<r,p and s=0 or 1≦s≦1+p/r. Then 0≦A≦B implies for 0<α≦r/(p+r). 相似文献
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Let G be a simple Lie group of real rank one, with Iwasawa decomposition and Bruhat big cell . Then the space may be (almost) identified with N and with K/M, and these identifications induce the (generalised) Cayley transform . We show that is a conformal map of Carnot-Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplication by appropriate powers of the Jacobian, induces isomorphisms of Sobolev spaces and . We use this to construct uniformly bounded and slowly growing representations of G. 相似文献
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We give a characterization of exponentiable monomorphisms in the categories of ω-complete posets, of directed complete posets and of continuous directed complete posets as those monotone maps f that are convex and that lift an element (and then a queue) of any directed set (ω-chain in the case of ) whose supremum is in the image of f (Theorem 1.9). Using this characterization, we obtain that a monomorphism f:X→B in (, ) exponentiable in w.r.t. the Scott topology is exponentiable also in (, ). We prove that the converse is true in the category , but neither in , nor in . 相似文献
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Let G=(V,E) be a connected graph of order n, t a real number with t?1 and M⊆V(G) with . In this paper, we study the problem of some long paths to maintain their one or two different endpoints in M. We obtain the following two results: (1) for any vertex v∈V(G), there exists a vertex u∈M and a path P with the two endpoints v and u to satisfy , , dG(u)+1-t}; (2) there exists either a cycle C to cover all vertices of M or a path P with two different endpoints u0 and up in M to satisfy , where . 相似文献
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Eli Aljadeff 《Advances in Mathematics》2008,218(5):1453-1495
To any cleft Hopf Galois object, i.e., any algebra obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle α, we attach two “universal algebras” and . The algebra is obtained by twisting the multiplication of H with the most general two-cocycle σ formally cohomologous to α. The cocycle σ takes values in the field of rational functions on H. By construction, is a cleft H-Galois extension of a “big” commutative algebra . Any “form” of can be obtained from by a specialization of and vice versa. If the algebra is simple, then is an Azumaya algebra with center . The algebra is constructed using a general theory of polynomial identities that we set up for arbitrary comodule algebras; it is the universal comodule algebra in which all comodule algebra identities of are satisfied. We construct an embedding of into ; this embedding maps the center of into when the algebra is simple. In this case, under an additional assumption, , thus turning into a central localization of . We completely work out these constructions in the case of the four-dimensional Sweedler algebra. 相似文献
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Xiang-dong Hou 《Journal of Combinatorial Theory, Series A》2007,114(3):522-544
Let Ψn be the number of inequivalent self-dual codes in . We prove that , where . Let Δn be the number of inequivalent doubly even self-dual codes in . We also prove that . 相似文献
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Norbert Ortner 《Bulletin des Sciences Mathématiques》2003,127(10):835-843
L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δx−Δy)u=f, , , then
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Let be the anticipating smooth semimartingale and be its generalized local time. In this paper, we give some estimates about the quasi sure property of Xt and its quadratic variation process t〈X〉. We also study the fractional smoothness of and prove that the quadratic variation process of can be constructed as the quasi sure limit of the form , where is a sequence of subdivisions of [a,b], , i=0,1,…,n2. 相似文献
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Let , B and Aj () be real nonsingular n×n matrices, λk () be real numbers. In this paper we present a sufficient condition for the system to be a frame for . This sufficient condition also shows the stability of the system with respect to the perturbation of matrix dilation parameters and the perturbation of translation parameters . 相似文献