Constrained Selection-Corrigendum and Addendum

Corrigendum an Addendum : “ On the axiomatic theory of spectrum II ”

Recall some notations and terminology from [4]. For closed subspaces M, L of a Banach space X we write M e ⊂L (M is essentially contained in L ) if there exists a finite-dimensional subspace F ⊂ X such that M ⊂ L + F . Equivalently, dim M/(M ∩L) = dim(M + L)/L < ∞. Similarly we write M e =L if M e ⊂L and L e ⊂M . For a (bounded linear) operator T ∈ L(X) write R∞(T ) = ∞n=0 R(T) and N∞(T ) = ⋃∞ ...

Simple and Constrained Selection Indices with and without Calving Interval Included in Selection Goal Function for Holstein Cows of Iran

Two selection goals of inclusion or exclusion of calving interval (CI) in the selection goal function for Holstein cows in Iran, besides milk yield, milk fat percentage, and milk protein percentage, were studied. Four selection indices were composed of using the information on production traits, CI and / or days from calving to first insemination (DFI). The results of the predicted genetic grow...

Corrigendum: Constructing Constrained-Version of Magic Squares Using Selection Hyper-heuristics

Corrigendum and Addendum to: Haar Bases for L2(Rn) and Algebraic Number Theory

We correct an error in the proof of Theorem 1.5 in 4]. We also give a strengthened necessary condition for the existence of a Haar basis of the speciied kind for every integer matrix A that has a given irreducible characteristic polynomial f(x) with jf(0)j = 2: A. Potiopa 7] found that the expanding polynomial g(x) = x 4 +x 2 +2 violates this necessary condition. Thus there exists some 4 4 expa...

Corrigendum and addendum to: Linearly recurrent subshifts have a finite number of non-periodic factors

We prove that a subshift (X, T ) is linearly recurrent if and only if it is a primitive and proper S-adic subshift. This corrects Proposition 6 in F. Durand (Ergod. Th. & Dynam. Sys. 20 (2000), 1061–1078).