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《Comptes Rendus Mathematique》2019,357(9):693-696
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Eduard Curcă 《Comptes Rendus Mathematique》2019,357(4):355-359
Let . If has zero integral, then the equation need not have a solution [6] or even [2]. Using these results, we prove that, whenever and , there exists some ?-form such that and the equation has no solution . This provides a negative answer to a question raised by Baldi, Franchi, and Pansu [1]. 相似文献
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《Annals of Pure and Applied Logic》2022,173(8):103135
We further develop a forcing notion known as Coding with Perfect Trees and show that this poset preserves, in a strong sense, definable P-points, definable tight MAD families and definable selective independent families. As a result, we obtain a model in which , each of , , has a witness and there is a well-order of the reals. Note that both the complexity of the witnesses of the above combinatorial cardinal characteristics, as well as the complexity of the well-order are optimal. In addition, we show that the existence of a well-order of the reals is consistent with and each of the following: , , , where the smaller cardinal characteristics have co-analytic witnesses.Our methods allow the preservation of only sufficiently definable witnesses, which significantly differs from other preservation results of this type. 相似文献
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Roberto Aravire Ahmed Laghribi Manuel ORyan 《Journal of Pure and Applied Algebra》2019,223(1):439-457
Let F be a field of characteristic 2. In this paper we give a complete computation of the kernel of the homomorphism induced by scalar extension, where is a purely inseparable extension (of any degree), is the cokernel of the Artin–Schreier operator given by: , where is the space of absolute m-differential forms over F and d is the differential operator. Other related results are included. 相似文献
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Alex Iosevich Chun-Kit Lai Azita Mayeli 《Applied and Computational Harmonic Analysis》2019,46(1):192-205
Let be an integer, and , , be the vector space over the cyclic space . The purpose of this paper is two-fold. First, we obtain sufficient conditions on such that the inverse Fourier transform of generates a tight wavelet frame in . We call these sets (tight) wavelet frame sets. The conditions are given in terms of multiplicative and translational tilings, which is analogous with Theorem 1.1 ([20]) by Wang in the setting of finite fields. In the second part of the paper, we exhibit a constructive method for obtaining tight wavelet frame sets in , , q an odd prime and (mod 4). 相似文献
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Luigi Ambrosio Shouhei Honda Jacobus W. Portegies David Tewodrose 《Journal of Functional Analysis》2021,280(10):108968
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as of the rescaled pull-back metrics in induced by . Moreover we discuss the behavior of with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative -convergence in the noncollapsed setting for all , a result new even for closed Riemannian manifolds and Alexandrov spaces. 相似文献
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