Non-negative matrices: The open Leontief model

Determination of the largest pit with the non-negative net profit in the open pit mines

The determination of the Ultimate Pit Limit (UPL) is the first step in the open pit mine planning process. In this stage that parts of the mineral deposit that are economic to mine are determined. There are several mathematical, heuristic and meta-heuristic algorithms to determine UPL. The optimization criterion in these algorithms is maximization of the total profit whilst satisfying...

On Non-negative-valued Matrices.

cording to our Theorem, if (4) is fulfilled, f3 and a can be so chosen that (2) be fulfilled. This form shows, however, that the lowest term in the determinant Ioua'+ Owa-11, if considered as a polynomial in E, is {nT Hence, the lowest term in the determinant :u ± EWI is I0K-1Iaean-r, i.e., the coefficient of (n7r in the determinant |u + Ew| does not vanish. Conversely, let us assume that u and...

Improvements on inequalities for non-negative matrices

We prove that there is an integer k :::; (n 2n + 4) /2 such that the diagonal entries of Ak are all positive for any non-negative irreducible n x n matrix A, and that there are integers i, j with 0 :::; i < j :::; 3n / 2 such that Ai :::; Aj for any non-negative n x n matrix A with no entry in (0,1) and n 2:: 2. The results of Wang and Shallit [Linear Algebra Appl. 290 (1999) 135-144] are thus ...

On Clans of Non-negative Matrices

A clan is a compact connected topological semigroup with identity. Professor A. D. Wallace has raised the following question [9]: Is a clan of real »X» matrices with non-negative entries, which contains the identity matrix, necessarily acyclic? That is to say, do all of the Alexander-Cech cohomology groups with arbitrary coefficients (in positive dimensions) vanish? In this paper the slightly s...

Contractive inhomogeneous products of non - negative matrices