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A Generalization Of The Inequality Of Minkowski
Let us suppose that the inequality is true for all the values less or equal to m.
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The Brunn–Minkowski inequality for volume differences
Suppose that \(K\), \(L\), \(D\), \(D'\) are compact domains in \(\mathbb{R}^n\) such that \(D\) and \(D'\) are homothetic and convex and \(D\subset K\), \(D'\subset L\). It is proved (in a more general form) that for the volume \(V\) one has \[ ((V(K+ L)- V(D+ D'))^{1/n}\geq (V(K)- V(D))^{1/n}+ (V(L)- V(D'))^{1/n}.
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Propagation of Memory Parameter from Durations to Counts [PDF]
We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,1/2)$ to ensure that the corresponding counting process $N(t)$ satisfies $\textmd{Var} \, N(t) \sim C t^{2d+1}$ ($C>0$) as $t ...
Clifford Hurvich +3 more
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One for all and all for one: regression checks with many regressors [PDF]
We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of sufficiently rich semiparametric alternatives, namely single-index models.
Lavergne, Pascal, Patilea, Valentin
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The football player and the infinite series
This is the text of an expository talk given at the May 1997 Detroit meeting of the American Mathematical Society. It is a tale of a famous football player and a subtle problem he posed about the uniform convergence of Dirichlet series.
Boas, Harold P.
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Processing and Transmission of Information [PDF]
Contains reports on four research projects.National Science Foundation (Grant G-16526)National Institutes of Health (Grant MH-04737-03)National Aeronautics and Space Administration (Grant NsG-496)Lincoln Laboratory (Purchase Order DDL BB-107)United ...
Holsinger, J. L. +3 more
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Hardy inequalities on metric measure spaces. [PDF]
Ruzhansky M, Verma D.
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Volumetric Minkowski Inequality on Manifolds with Weighted Poincaré Inequality
Abstract In the paper, we establish a volumetric Minkowski inequality for complete manifolds admitting a weighted Poincaré inequality with the weight commensurable to the Ricci curvature lower bound. More precisely, we show that the weighted volume of a compact smooth domain in such manifolds is bounded from above by an integral of the mean ...
Wei-Yi Chiu, Chiung-Jue Anna Sung
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