Capacities, surface area, and radial sums

Capacities , Surface Area , and Radial Sums

A dual capacitary Brunn-Minkowski inequality is established for the (n − 1)capacity of radial sums of star bodies in R. This inequality is a counterpart to the capacitary Brunn-Minkowski inequality for the p-capacity of Minkowski sums of convex bodies in R, 1 ≤ p < n, proved by Borell, Colesanti, and Salani. When n ≥ 3, the dual capacitary BrunnMinkowski inequality follows from an inequality of...

Water-stable zirconium-based metal-organic framework material with high-surface area and gas-storage capacities.

We designed, synthesized, and characterized a new Zr-based metal-organic framework material, NU-1100, with a pore volume of 1.53 ccg(-1) and Brunauer-Emmett-Teller (BET) surface area of 4020 m(2) g(-1) ; to our knowledge, currently the highest published for Zr-based MOFs. CH4 /CO2 /H2 adsorption isotherms were obtained over a broad range of pressures and temperatures and are in excellent agreem...

Toric Surface Codes and Minkowski Sums

Toric codes are evaluation codes obtained from an integral convex polytope P ⊂ R and finite field Fq. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently in [6], [8], [9], and [12]. In this paper, we obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon P ⊂ R by examining Minkowski sum decompositions of subpo...

The Valuative Capacities of the Sets of Sums of Two and of Three Squares

If A is a subset of Z, then the n-th characteristic ideal of A is the fractional ideal of Z consisting of 0 and the leading coe cients of polynomials in Q[x] of degree no more than n which are integer-valued on A. The valuative capacity with respect to a prime p of A is a measure of the rate of growth of the p-adic part of these characteristic ideals of A and is defined, for a given p, to be th...

Choquet-like integrals with respect to level-dependent capacities and φ-ordinal sums of aggregation function