共查询到20条相似文献,搜索用时 31 毫秒
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Steven Hoehner 《Journal of Mathematical Analysis and Applications》2022,505(2):125506
For a convex body K in , we introduce and study the extremal general affine surface areas, defined by where and are the and affine surface area of K, respectively. We prove that there exist extremal convex bodies that achieve the supremum and infimum, and that the functionals and are continuous. In our main results, we prove Blaschke-Santaló type inequalities and inverse Santaló type inequalities for the extremal general affine surface areas. This article may be regarded as an Orlicz extension of the recent work of Giladi, Huang, Schütt and Werner (2020), who introduced and studied the extremal affine surface areas. 相似文献
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Saeed Nasseh Sean Sather-Wagstaff Ryo Takahashi Keller VandeBogert 《Journal of Pure and Applied Algebra》2019,223(3):1272-1287
We construct a local Cohen–Macaulay ring R with a prime ideal such that R satisfies the uniform Auslander condition (UAC), but the localization does not satisfy Auslander's condition (AC). Given any positive integer n, we also construct a local Cohen–Macaulay ring R with a prime ideal such that R has exactly two non-isomorphic semidualizing modules, but the localization has non-isomorphic semidualizing modules. Each of these examples is constructed as a fiber product of two local rings over their common residue field. Additionally, we characterize the non-trivial Cohen–Macaulay fiber products of finite Cohen–Macaulay type. 相似文献
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Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献
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《Journal of Pure and Applied Algebra》2022,226(10):107074
For a commutative ring A we consider a related graph, , whose vertices are the unimodular rows of length 2 up to multiplication by units. We prove that is path-connected if and only if A is a -ring, in the terminology of P. M. Cohn. Furthermore, if denotes the clique complex of , we prove that is simply connected if and only if A is universal for . More precisely, our main theorem is that for any commutative ring A the fundamental group of is isomorphic to the group modulo the subgroup generated by symbols. 相似文献
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Julia Semikina 《Journal of Pure and Applied Algebra》2019,223(10):4509-4523
I. Hambleton, L. Taylor and B. Williams conjectured a general formula in the spirit of H. Lenstra for the decomposition of for any finite group G and noetherian ring R. The conjectured decomposition was shown to hold for some large classes of finite groups. D. Webb and D. Yao discovered that the conjecture failed for the symmetric group , but remarked that it still might be reasonable to expect the HTW-decomposition for solvable groups. In this paper we show that the solvable group is also a counterexample to the conjectured HTW-decomposition. Nevertheless, we prove that for any finite group G the rank of does not exceed the rank of the expression in the HTW-decomposition. We also show that the HTW-decomposition predicts correct torsion for for any finite group G. Furthermore, we prove that for any degree other than the conjecture gives a correct prediction for the rank of . 相似文献
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Yinshan Chang Yiming Long Jian Wang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(1):75-102
We consider a continuously differentiable curve in the space of real symplectic matrices, which is the solution of the following ODE: where and is a continuous path in the space of real matrices which are symmetric. Under a certain convexity assumption (which includes the particular case that is strictly positive definite for all ), we investigate the dynamics of the eigenvalues of when t varies, which are closely related to the stability of such Hamiltonian dynamical systems. We rigorously prove the qualitative behavior of the branching of eigenvalues and explicitly give the first order asymptotics of the eigenvalues. This generalizes classical Krein–Lyubarskii theorem on the analytic bifurcation of the Floquet multipliers under a linear perturbation of the Hamiltonian. As a corollary, we give a rigorous proof of the following statement of Ekeland: is a discrete set. 相似文献
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Tadahiro Miyao 《Journal of Functional Analysis》2019,276(6):1948-1977
We consider the renormalized Nelson model at a fixed total momentum P: ; the Hamiltonian is defined through an infinite energy renormalization. We prove that is positivity improving for all and in the Fock representation. 相似文献
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Jacques Darné 《Journal of Pure and Applied Algebra》2019,223(12):5484-5525
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