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《Indagationes Mathematicae》2022,33(2):322-333
We apply the techniques developed by I. Panin for the proof of the equicharacteristic case of the Serre–Grothendieck conjecture for isotropic reductive groups (Panin et al., 2015; Panin, 2019) to obtain similar injectivity and -invariance theorems for non-stable -functors associated to isotropic reductive groups. Namely, let be a reductive group over a commutative ring . We say that has isotropic rank , if every non-trivial normal semisimple -subgroup of contains . We show that if has isotropic rank and is a regular domain containing a field, then , where is the corresponding non-stable -functor, also called the Whitehead group of . If is, moreover, local, then we show that is injective, where is the field of fractions of . 相似文献
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We define a ribbon category , depending on a parameter β, which encompasses Cautis, Kamnitzer and Morrison's spider category, and describes for the monoidal category of representations of generated by exterior powers of the vector representation and their duals. We identify this category with a direct limit of quotients of a dual idempotented quantum group , proving a mixed version of skew Howe duality in which exterior powers and their duals appear at the same time. We show that the category gives a unified natural setting for defining the colored link invariant (for ) and the colored HOMFLY-PT polynomial (for β generic). 相似文献
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Lionel Nguyen Van Thé 《Expositiones Mathematicae》2019,37(2):192-199
Say that a graph is representable in if there is a map from its vertex set into the Euclidean space such that iff and are both edges or both non-edges in . The purpose of this note is to present the proof of the following result, due to Einhorn and Schoenberg in Einhorn and Schoenberg (1966): if finite is neither complete nor independent, then it is representable in . A similar result also holds in the case of finite complete edge-colored graphs. 相似文献
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We consider the following Schrödinger equation where , , and is superlinear and subcritical nonlinear term. We show that if attains local minimum and attains global maximum at the same point or attains global minimum and attains local maximum at the same point, then there exists a positive solution for sufficiently small . 相似文献
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Qichun Wang 《Discrete Mathematics》2019,342(12):111625
It was proved by J. Schatz that the covering radius of the second order Reed–Muller code is 18 (Schatz (1981)). However, the covering radius of has been an open problem for many years. In this paper, we prove that the covering radius of is 40, which is the same as the covering radius of in . As a corollary, we also find new upper bounds for the covering radius of , . 相似文献
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《Indagationes Mathematicae》2023,34(3):637-642
We prove a sharp Schwarz lemma type inequality for the Weierstrass–Enneper parameterization of minimal disks. It states the following. If is a conformal harmonic parameterization of a minimal disk , where is the unit disk and , then . If for some the previous inequality is equality, then the surface is an affine image of a disk, and is linear up to a Möbius transformation of the unit disk. 相似文献
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《Discrete Mathematics》2019,342(10):2834-2842
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Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields with values in are invariant in law under operator-scaling in both the time-domain and the state-space. The construction is based on operator-stable random measures utilizing certain homogeneous functions. 相似文献