Results 71 to 80 of about 636,012 (237)

The General Minkowski Inequality for Mixed Volume

Journal of Function Spaces
Mixed volume is an important notion in convex geometry, which is the extension of volume and surface area. The Minkowski inequality for mixed volume plays a vital role in convex geometry.
Yusha Lv
doaj   +1 more source

State‐dependent dynamic tube MPC: A novel tube MPC method with a fuzzy model of disturbances

International Journal of Robust and Nonlinear Control, Volume 35, Issue 4, Page 1319-1354, 10 March 2025.
Abstract Most real‐world systems are affected by external disturbances, which may be impossible or costly to measure. For instance, when autonomous robots move in dusty environments, the perception of their sensors is disturbed. Moreover, uneven terrains can cause ground robots to deviate from their planned trajectories.
Filip Surma, Anahita Jamshidnejad
wiley   +1 more source

Inequalities for dual affine quermassintegrals

Journal of Inequalities and Applications, 2006
For star bodies, the dual affine quermassintegrals were introduced and studied in several papers. The aim of this paper is to study them further. In this paper, some inequalities for dual affine quermassintegrals are established, such as the Minkowski ...
Jun Yuan, Gangsong Leng
doaj  

A discrete version and stability of Brunn Minkowski inequality [PDF]

arXiv, 2007
In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for length spaces. Our new definition based only on distance properties allows us also to deal with discrete spaces. Then we show the stability of our new inequality under a convergence of metric measure spaces.
arxiv  

Rectifiability, finite Hausdorff measure, and compactness for non‐minimizing Bernoulli free boundaries

Communications on Pure and Applied Mathematics, Volume 78, Issue 3, Page 545-591, March 2025.
Abstract While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent ...
Dennis Kriventsov, Georg S. Weiss
wiley   +1 more source

Uniqueness and continuity of the solution to $L_p$ dual Minkowski problem [PDF]

arXiv, 2021
Lutwak, Yang and Zhang \cite{LYZ2018} introduced the $L_p$ dual curvature measure that unifies several other geometric measures in dual Brunn-Minkowski theory and Brunn- Minkowski theory. Motivated by works in \cite{LYZ2018}, we consider the uniqueness and continuity of the solution to the $L_p$ dual Minkowski problem.
arxiv  

A new class of nonparametric tests for second‐order stochastic dominance based on the Lorenz P–P plot

Scandinavian Journal of Statistics, Volume 52, Issue 1, Page 480-512, March 2025.
Abstract Given samples from two non‐negative random variables, we propose a family of tests for the null hypothesis that one random variable stochastically dominates the other at the second order. Test statistics are obtained as functionals of the difference between the identity and the Lorenz P–P plot, defined as the composition between the inverse ...
Tommaso Lando, Sirio Legramanti
wiley   +1 more source

Inequalities of Hardy Type via Superquadratic Functions with General Kernels and Measures for Several Variables on Time Scales

Journal of Function Spaces, 2020
We use the properties of superquadratic functions to produce various improvements and popularizations on time scales of the Hardy form inequalities and their converses.
H. M. Rezk, H. A. Abd El-Hamid, A. M. Ahmed, Ghada AlNemer, M. Zakarya   +4 more
doaj   +1 more source

Brunn-Minkowski inequalities in product metric measure spaces [PDF]

arXiv, 2017
Given one metric measure space $X$ satisfying a linear Brunn-Minkowski inequality, and a second one $Y$ satisfying a Brunn-Minkowski inequality with exponent $p\ge -1$, we prove that the product $X\times Y$ with the standard product distance and measure satisfies a Brunn-Minkowski inequality of order $1/(1+p^{-1})$ under mild conditions on the measures
arxiv  

On volume and surface area of parallel sets. II. Surface measures and (non)differentiability of the volume

Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 895-912, March 2025.
Abstract We prove that at differentiability points r0>0$r_0>0$ of the volume function of a compact set A⊂Rd$A\subset \mathbb {R}^d$ (associating to r$r$ the volume of the r$r$‐parallel set of A$A$), the surface area measures of r$r$‐parallel sets of A$A$ converge weakly to the surface area measure of the r0$r_0$‐parallel set as r→r0$r\rightarrow r_0 ...
Jan Rataj, Steffen Winter
wiley   +1 more source