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Let kk be a field of characteristic zero and RR a factorial affine kk-domain. Let BB be an affineRR-domain. In terms of locally nilpotent derivations, we give criteria for BB to be RR-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y]R[X1,X2,Y] over RR by the ideal (X1X2−φ(Y))(X1X2φ(Y)) for φ(Y)∈R[Y]?Rφ(Y)R[Y]?R.  相似文献   

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A quasiplane f(V)f(V) is the image of an n-dimensional Euclidean subspace V   of RNRN (1≤n≤N−11nN1) under a quasiconformal map f:RN→RNf:RNRN. We give sufficient conditions in terms of the weak quasisymmetry constant of the underlying map for a quasiplane to be a bi-Lipschitz n  -manifold and for a quasiplane to have big pieces of bi-Lipschitz images of RnRn. One main novelty of these results is that we analyze quasiplanes in arbitrary codimension N−nNn. To establish the big pieces criterion, we prove new extension theorems for “almost affine” maps, which are of independent interest. This work is related to investigations by Tukia and Väisälä on extensions of quasisymmetric maps with small distortion.  相似文献   

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Let AA be a connected graded noncommutative monomial algebra. We associate to AA a finite graph Γ(A)Γ(A) called the CPS graph of AA. Finiteness properties of the Yoneda algebra ExtA(k,k)ExtA(k,k) including Noetherianity, finite GK dimension, and finite generation are characterized in terms of Γ(A)Γ(A). We show that these properties, notably finite generation, can be checked by means of a terminating algorithm.  相似文献   

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We prove that, unless assuming additional set theoretical axioms, there are no reflexive spaces without unconditional sequences of the density continuum. We show that for every integer nn there are normalized weakly-null sequences of length ωnωn without unconditional subsequences. This together with a result of Dodos et al. (2011) [7] shows that ωωωω is the minimal cardinal κκ that could possibly have the property that every weakly null κκ-sequence has an infinite unconditional basic subsequence. We also prove that for every cardinal number κκ which is smaller than the first ωω-Erd?s cardinal there is a normalized weakly-null sequence without subsymmetric subsequences. Finally, we prove that mixed Tsirelson spaces of uncountable densities must always contain isomorphic copies of either c0c0 or ?p?p, with p≥1p1.  相似文献   

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Let ηtηt be a Poisson point process of intensity t≥1t1 on some state space YY and let ff be a non-negative symmetric function on YkYk for some k≥1k1. Applying ff to all kk-tuples of distinct points of ηtηt generates a point process ξtξt on the positive real half-axis. The scaling limit of ξtξt as tt tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the mm-th smallest point of ξtξt is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener–Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen–Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as kk-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry.  相似文献   

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