Results 211 to 220 of about 33,078 (239)

A Brunn–Minkowski-Type Inequality

Geometriae Dedicata, 1999
For convex bodies \(K,L\) in \(\mathbb{R}^n\), let \(M(K,L): =\max_{x\in \mathbb{R}^n}|K\cap(x+L)|\) (where \(|\cdot|\) denotes volume). The author conjectures that \[ |K+L |^{1/n}\geq M(K,L)^{1/n} +{|K |^{1/n} |L|^{1/n}\over M(K,L)^{1/n}}, \] which would be a useful improvement of the Brunn-Minkowski theorem.
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Companions to the Brunn–Minkowski inequality

Positivity
Let \(\mathcal{C}\) be the family of all compact convex sets in \(\mathbb{R}^n\). For \(A, B \in \mathcal{C}\) denote by \(\operatorname{Vol}(A)\) the Lebesque measure of \(A\) and by \(\Delta (A,B) = \big[\operatorname{Vol}(A)\big]^{1/n} + \big[\operatorname{Vol}(B)\big]^{1/n} - \big[\operatorname{Vol}(A + B)\big]^{1/n}\). An \((m + 1)\)-tuple \((B_0,
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More Generalizations of Hartfiel’s Inequality and the Brunn–Minkowski Inequality

Bulletin of the Iranian Mathematical Society, 2020
Let \(A,B\in\mathbb{C}^{n\times n}\) be positive definite. Minkowski's determinant inequality (also known as the matrix form of the Brunn-Minkowski inequality) states that \[ (\det{(A+B)})^\frac{1}{n}\ge(\det{A})^\frac{1}{n}+(\det{B})^\frac{1}{n}. \] It has several refinements and generalizations. Some of them are extended to sector matrices. A matrix \
Dong, Sheng, Wang, Qing-Wen
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Brunn-Minkowski inequality

2000
This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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Convexity and Minkowski's Inequality

The American Mathematical Monthly, 2005
(2005). Convexity and Minkowski's Inequality. The American Mathematical Monthly: Vol. 112, No. 8, pp. 740-742.
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Inequalities of Minkowski type

Real analysis exchange, 1994
Let f be a real nonnegative, nondecreasing function defined on segment a, b, and x_i are nonnegative nondecreasing functions with continuous first derivative. If p>1, then (\int_a^b (\sum_{; ; i=1}; ; ^n x_i^p(t))'f(t)dt)^{; ; 1/p}; ; \geq \sum_{; ; i=1}; ; ^n (\int_a^b (x_i^p(t))'f(t)dt)^{; ; 1/p}; ; .
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Approximate solutions for the inextensible Heisenberg antiferromagnetic flow and solitonic magnetic flux surfaces in the normal direction in Minkowski space

Optik, 2021
Talat Körpınar, Rıdvan Cem Demirkol, Zeliha Körpınar   +2 more
exaly  

Hölder’s Inequality, Minkowski’s Inequality and Their Variants

2012
In this chapter we’ll introduce two very useful inequalities with broad practical usage: Holder’s inequality and Minkowski’s inequality. We’ll also present few variants of these inequalities. For that purpose we will firstly introduce the following theorem.
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Regular Black Holes with Asymptotically Minkowski Cores

Universe, 2020
Alexander Marcus Simpson, Matt Visser
exaly  

Resolution of the Abraham-Minkowski Dilemma

Physical Review Letters, 2010
Stephen M Barnett
exaly