• Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges

      Fries, William D.; Jiang, Miaohua; Univ Arizona, Dept Math (TAYLOR & FRANCIS AS, 2019-06-08)
      For a sequence of adjacency matrices, describing the unfolding of a network from the graph of a star, through graphs of a broom, to the graph of a link with constant vertices and edges, we show that the leading eigenvalue (the spectral radius) satisfies a simple algebraic equation. The equation allows easy numerical computation of the leading eigenvalue as well as a direct proof of its monotonicity in terms of the maximal degree of vertices.
    • Methodology for a dump design optimization in large-scale open pit mines

      Puell Ortiz, Jorge; Univ Arizona, Dept Min & Geol Engn; Department of Mining and Geological Engineering, University of Arizona Tucson USA (TAYLOR & FRANCIS AS, 2017-10-05)
      Modern large-scale open pit mines move hundreds of thousands of tonnes of material daily, from the loading sources to the destination zones, whether these are massive mine dumps or, to a lesser extent, to the grinding mills. Mine dumps can be classified as leach or waste dumps, depending upon their economic viability to be processed in-place, a condition that has experienced great progress in the last decades and has reconfigured the open pit haulage network with an increase in the number of dumps. Therefore, new methods for dump design optimization are of the highest priority in mine planning management. This paper presents a methodology to model and optimize the design of a dump by minimizing the total haulage costs. The location and design of these dumps will be given mainly by the geological characteristics of the mineral, tonnage delivered, topographical conditions, infrastructure capital and transportation costs. Spatial and physical design possibilities, in addition, provide a set of parameters of mathematical and economic relationship that creates opportunities for modelling and thus facilitates the measurement and optimization of ultimate dump designs. The proposed methodology consists of: (1) Formulation of a dump model based on a system of equations relying on multiple relevant parameters; (2) Solves by minimizing the total cost using linear programming and determines a "preliminary" dump design; (3) Through a series of iterations, changes the "preliminary" footprint by projecting it to the topography and creates the ultimate dump design. Finally, an application for a waste rock dump illustrates this methodology.