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Marcus Carlsson 《Expositiones Mathematicae》2021,39(1):149-157
von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(8):106948
Let be a Henselian discrete valued field with residue field of characteristic , and be the Brauer p-dimension of K. This paper shows that if , for some . It proves that if and only if . 相似文献
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Diego Maldonado 《Journal of Differential Equations》2018,264(2):624-678
We prove a Harnack inequality for nonnegative strong solutions to degenerate and singular elliptic PDEs modeled after certain convex functions and in the presence of unbounded drifts. Our main theorem extends the Harnack inequality for the linearized Monge–Ampère equation due to Caffarelli and Gutiérrez and it is related, although under different hypotheses, to a recent work by N.Q. Le.Since our results are shown to apply to the convex functions with and their tensor sums, the degenerate elliptic operators that we can consider include subelliptic Grushin and Grushin-like operators as well as a recent example by A. Montanari of a nondivergence-form subelliptic operator arising from the geometric theory of several complex variables. In the light of these applications, it follows that the Monge–Ampère quasi-metric structure can be regarded as an alternative to the usual Carnot–Carathéodory metric in the study of certain subelliptic PDEs. 相似文献
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In this paper, we investigate the permutation behavior of a class of quadrinomials. Each term of these quadrinomials has a Niho-type exponent, and two sets of coefficient triples making the quadrinomials to be permutations are obtained. We use a substitution to transform the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations. 相似文献
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使用改进后的四球摩擦磨损试验机考察了不同电磁场强度和不同载荷条件下菜籽油的摩擦学性能,结合扫描电子显微镜(SEM)、X射线能谱仪(EDS)和X射线光电子能谱仪(XPS)分析了磨斑的表面形貌及表面典型元素的化学状态,并对摩擦学机理进行了初步探讨.结果表明:在所考察的工况下,电磁场有利于改善菜籽油的抗磨减摩性能,其强度越大,对菜籽油抗磨减摩性能的改善效果越好;电磁场通过促进吸附膜的吸附作用和O元素与金属表面作用,有利于在磨斑表面生成更厚、更致密的摩擦化学反应膜,从而增强了菜籽油的抗磨减摩性能;不同强度的电磁场可能会改变长链菜籽油分子在摩擦界面的吸附形态而影响其减摩性能. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(14):5691-5710
We consider a 2 time scale nonlinear system of ordinary differential equations. The small parameter of the system is the ratio ϵ of the time scales. We search for an approximation involving only the slow time unknowns and valid uniformly for all times at order O(ϵ2). A classical approach to study these problems is Tikhonov's singular perturbation theorem. We develop an approach leading to a higher order approximation using the renormalization group (RG) method. We apply it in 2 steps. In the first step, we show that the RG method allows for approximation of the fast time variables by their RG expansion taken at the slow time unknowns. Next, we study the slow time equations, where the fast time unknowns are replaced by their RG expansion. This allows to rigorously show the second order uniform error estimate. Our result is a higher order extension of Hoppensteadt's work on the Tikhonov singular perturbation theorem for infinite times. The proposed procedure is suitable for problems from applications, and it is computationally less demanding than the classical Vasil'eva‐O'Malley expansion. We apply the developed method to a mathematical model of stem cell dynamics. 相似文献