Results 51 to 60 of about 1,448 (158)
An Improved Discrete Hardy Inequality [PDF]
The American Mathematical Monthly, 2018 We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{n=1}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{n=1}^{\infty }\left({\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}\right)^{2}, \end{equation*} where $\{a_n\}_{n=1}^\infty$ is any sequence of non-negative real numbers.
Keller, Matthias (Prof. Dr.) +2 more
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Subuniformity of harmonic mean p$$ p $$‐values
Canadian Journal of Statistics, EarlyView.Abstract We obtain several inequalities on the generalized means of dependent p$$ p $$‐values. In particular, the weighted harmonic mean of p$$ p $$‐values is strictly subuniform under several dependence assumptions of p$$ p $$‐values, including independence, negative upper orthant dependence, the class of extremal mixture copulas, and some Clayton ...
Yuyu Chen +3 more
wiley +1 more source
A test of Local Realism with entangled kaon pairs and without inequalities
, 2002 We propose the use of entangled pairs of neutral kaons, considered as a promising tool to close the well known loopholes affecting generic Bell's inequality tests, in a specific Hardy-type experiment.
A. Afriat +14 more
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Weighted discrete Hardy's inequalities
Ukrains’kyi Matematychnyi Zhurnal, 2023 UDC 517.5 We give a short proof of a weighted version of the discrete Hardy inequality. This includes the known case of classical monomial weights with optimal constant. The proof is based on the ideas of the short direct proof given recently in [P. Lefèvre, Arch. Math. (Basel), <strong>114</strong>, № 2, 195–198 (2020)].
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Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity
Mathematische Nachrichten, EarlyView.Abstract We consider the quasi‐geostrophic equation with its principal part (−Δ)α${(-\mathrm{\Delta})^{\alpha}}$ for α>1/2$\alpha >1/2$ in Rn$\mathbb {R}^n$ with n≥2$n \ge 2$. We show that for every initial data θ0∈Ḃr,q1−2α+nr$\theta _0 \in \dot{B}^{1-2\alpha + \frac{n}{r}}_{r, q}$ with 1
Hideo Kozono +2 more
wiley +1 more source
Sharp Hardy–Sobolev inequalities
Comptes Rendus. Mathématique, 2004 Let Ω be a smooth bounded domain in RN, N⩾3. We show that Hardy's inequality involving the distance to the boundary, with best constant (14), may still be improved by adding a multiple of the critical Sobolev norm.
Filippas, S. +2 more
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Hardy Martingales and Jensen's inequality [PDF]
Bulletin of the Australian Mathematical Society, 1997 Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus 𝕋N, where analyticity is defined using a lexicographic order on the dual group ℤN. We show how, by using basic properties of orders on ℤN, we can apply Garling's method in the study of analytic functions on an arbitrary compact Abelian group ...
Asmar, Nakhlé H. +1 more
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Life after herbarium digitisation: Physical and digital collections, curation and use
PLANTS, PEOPLE, PLANET, EarlyView.Societal Impact Statement Collections of dried plant specimens (herbaria) provide an invaluable resource for the study of many areas of scientific interest and conservation globally. Digitisation increases access to specimens and metadata, enabling efficient use across a broad spectrum of research.
Alan James Paton +39 more
wiley +1 more source
Optimizing Improved Hardy Inequalities
Journal of Functional Analysis, 2002 Let \(N\geq 3\) and \(\Omega\) be a bounded domain in \({\mathbb R}^N\) such that \(0\in \Omega\). The goal of the authors is to study a general improved Hardy inequality: For all \(u\in H^1_0(\Omega)\), \[ \int_{\Omega} \left|\nabla u\right|^2\geq \left(\frac{N-2}2\right)^2\int_{\Omega} \frac{\left|u\right|^2}{\left|x\right|^2}dx+b\int_{\Omega} Vu^2dx
Filippas, Stathis, Tertikas, Achilles
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International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT This paper focuses on state estimation for a fairly general class of systems, involving nonlinear functions and disturbances in both the process dynamics and output equations. A nonlinear observer that satisfies a H∞$$ {\boldsymbol{H}}_{\boldsymbol{\infty}} $$ disturbance attenuation constraint in addition to providing asymptotic stability in ...
Hamidreza Movahedi +2 more
wiley +1 more source