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《Journal of Pure and Applied Algebra》2022,226(12):107140
We explore explicit virtual resolutions, as introduced by Berkesch, Erman, and Smith, for ideals of finite sets of points in . Specifically, we describe a virtual resolution for a sufficiently general set of points X in that only depends on . We also improve an existence result of Berkesch, Erman, and Smith in the special case of points in ; more precisely, we give an effective bound for their construction that gives a virtual resolution of length two for any set of points in . 相似文献
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As an application of the method of [4], we find the metric and connection on the space of conics in determined as the solution space of the ODE (1). These calculations underpin the twistor construction of the Radon transform on conics in described in [5]. Two further examples of the method are provided. 相似文献
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We present a generalization of a family of points on , the Diamond ensemble, containing collections of N points on with very small logarithmic energy for all . We extend this construction to the real projective plane and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space. 相似文献
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A new a priori estimate for solutions to Navier–Stokes equations is derived. Uniqueness and existence of these solutions in for all is proved in a class of solutions locally differentiable in time with values in , where is the Sobolev space. By the solution a solution to an integral equation is understood. No smallness restrictions on the data are imposed. 相似文献
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Jian Wang 《Comptes Rendus Mathematique》2019,357(3):284-290
The goal of this paper is to investigate the topological structure of open simply connected 3-manifolds whose scalar curvature has a slow decay at infinity. In particular, we show that the Whitehead manifold does not admit a complete metric whose scalar curvature decays slowly, and in fact that any contractible complete 3-manifolds with such a metric is diffeomorphic to . Furthermore, using this result, we prove that any open simply connected 3-manifold M with and a complete metric as above is diffeomorphic to . 相似文献
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《Discrete Mathematics》2020,343(3):111721
The -additive codes are subgroups of , and can be seen as a generalization of linear codes over and . A -linear Hadamard code is a binary Hadamard code which is the Gray map image of a -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some -linear Hadamard codes of length are equivalent, once is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to , this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on , the full classification of the -linear Hadamard codes of length is established by giving the exact number of such codes. 相似文献
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We present several existence and nonexistence results for permutation binomials of the form , where and . As a consequence, we obtain a complete characterization of such permutation binomials over , , , , and , where p is an odd prime. 相似文献
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