Then the binary map (m^{sigma}), defined by (m^{sigma}(a,a)=a) and bigl(m^{sigma}(a,b) bigr)^{-1}= { frac{1}{b-a} int_{1}^{b/a} m biggl(1,frac{1}{t^{2}} biggr)},dt (1.1) for all (a,b>0) with (aneq b), is a continuous homogeneous symmetric mean (called the integral mean-transform of m).
Let g be a continuous function, homogeneous of degree p, real, and strictly Schur-convex (see [28] for the definition of Schur-convex functions and related properties).
Geotechnical investigations, laboratory tests and geological mapping showed that the rock mass could be considered as a continuous, homogeneous, isotropic and linearly elastic (CHILE) material.
It is well known that ξ q is a continuous, positively homogeneous, subadditive and convex function on Y, and it is monotone (that is, y 2 − y 1 ∈ C ⇒ ξ q ( y 1 ) ≤ ξ q ( y 2 ) ) and strictly monotone (that is, y 2 − y 1 ∈ − int C ⇒ ξ q ( y 1 ) < ξ q ( y 2 ) ) (see [25, 26]).
The results showed that the aluminum alloy surface is coated with a continuous, homogeneous, and compact aluminum (hydr oxide silane hybrid film, which is composed of ca. 200 nm particle array that was tightly and regularly packed.
Let P n (t) be the probability that n components fail at time t assuming n ∊ {0, 1, 2, 3} where t ≥ 0 and the process is a continuous-time homogeneous Markov chain in which the transition rates matrix is as follows.
Let be a right-continuous homogeneous Markov process on the probability space which take values in the finite space satisfying and its generator is given by.
Moreover, for each (i 1, …, i m ), the coefficient of λ 1 i 1 ⋯ λ m i m is a continuous translation invariant and homogeneous valuation of degree i j in K j.
A continuous homogeneous symmetric mean will be called regular mean, for the sake of simplicity.
