Catarina P. Avelino

Spherical f-tilings by scalene triangles and isosceles trapezoids, I

The study of the dihedral f-tilings of the sphere S^2 whose prototiles are an equilateral or isosceles triangle and an isosceles trapezoid was described in [C.P. Avelino, A.F. Santos, Spherical f-tilings by (equilateral and isosceles) triangles and isosceles trapezoids, 2008 (submitted for publication)]. In this paper we generalize this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in some cases of adjacency.

DEFORMATION OF F-TILINGS VERSUS DEFORMATION OF ISOMETRIC FOLDINGS

We present some relations between deformation of spherical isometric foldings and deformation of spherical f-tilings. The natural way to deform f-tilings is based on the Hausdorff metric on compact sets. It is conjectured that any f-tiling is (continuously) deformable in the standard f-tiling τs = {(x, y, z) ∈ S2 : z = 0} and it is shown that the deformation of f-tilings does not induce a continuous deformation on its associated isometric foldings.

Lot-sizing and scheduling in a glass container manufacture company

We consider a real production planning problem occurring in a glass container manufacturing company. The goal is to minimise the average stock level during a planning horizon of one year, maintaining customers satisfaction and keeping the production at its maximum rate. Besides the production capacity, the main constraints considered are related to the number of setup changes in machines, which is restricted in each factory. The main goal is to find the best balance between the number of setups and the average stock level. We propose a decomposition of the problem into two interrelated problems: a lot-sizing problem and a scheduling problem. For each problem we propose a mathematical model that can be solved using a commercial solver package. To be an efficient managerial tool, the method should provide quickly good solutions. Therefore we solve the lot-sizing problem through a relax-and-fix heuristic and discuss the results.

Geometric and combinatorial structure of a class of spherical folding tessellations — I

A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed. The combinatorial structure of each tiling is also analysed.

Spherical folding tessellations by kites and isosceles triangles IV

The classification of the dihedral folding tessellations of the sphere and the plane whose prototiles are a kite and an equilateral triangle were obtained in [C. Avelino and A. Santos, Spherical and planar folding tessellations by kites and equilateral triangles, Australasian Journal of Combinatorics, 53 (2012), 109–125.]. Recently, this classification was extended to isosceles triangles so that the classification of spherical folding tesselations by kites and isosceles triangles in three cases of adjacency was presented in [C. Avelino and A. Santos, Spherical Folding Tessellations by Kites and Isosceles Triangles: a case of adjacency, Mathematical Communications, 19 (2014), 1–28.; C. Avelino and A. Santos, Spherical Folding Tessellations by Kites and Isosceles Triangles II, International Journal of Pure and Applied Mathematics, 85 (2013), 45–67.; C.Avelino and A.Santos, Spherical Folding Tessellations by Kites and Isosceles Triangles III, submitted.]. In this paper we finalize this classification presenting all the dihedral folding tessellations of the sphere by kites and isosceles triangles in the remaining three cases of adjacency, that consists of five sporadic isolated tilings. A list containing these tilings including its combinatorial structure is presented at the end of this paper.

Dihedral f‐Tilings of the Sphere by Isosceles Triangles and Isosceles Trapezoids

We present the study of dihedral f‐tilings of the sphere, with prototiles a spherical isosceles triangle and a spherical isosceles trapezoid. The combinatorial structure, including the symmetry group of each tiling, is given in Table 1.