Guanzhong Ma

Dec 6, 2024 | mdpi.com | Guanzhong Ma |Jun Luo |Xiao Zhou

1. IntroductionLet M d ( R ) be the set of all d × d matrices with entries in R, and let A ∈ M d ( R ) be an expanding matrix. Let N ≥ 2 and n 1 , … , n N be positive integers. Write A j = A n j , 1 ≤ j ≤ N and D = { d 1 , … , d N } ⊂ R d . Then, we can define a self-affine iterated function system (IFS) { S j } j = 1 N on R d by S j ( x ) = A j − 1 ( x + d j ) , j = 1 , … , N .

Aug 11, 2023 | mdpi.com | Yujun Liu |Guanzhong Ma

1. IntroductionThe concept of entropy was first introduced by Rudolf Clausius in the mid-19th century as a measure of the disorder or randomness in a system. In 1948, Shannon [1] inaugurated information entropy in information theory, which measures the unpredictability of the realization of a random variable. Subsequently, information entropy developed into an essential tool in information theory (see Gray [2]).