1. Constructional tasks of conics with GeoGebra

    Lenka Juklova

    Department of Algebra and Geometry, Faculty of Natural Sciences, Palacky University, Olomouc, Czech Republic.

    Abstract: This paper is devoted to the teaching of conics at the grammar school and at the college in Czech Republic. There are presented GeoGebra work-sheets which can to help teach constructional tasks about conic sections both at grammar school and solving more challenging tasks at college.

    Keywords: Administrative sources, Statistical purposes, National Strategy.

    Pages: 167 – 174 | Full PDF Paper
  2. A Topological Multiple Correspondence Analysis

    Rafik Abdesselam

    COACTIS-ISH Management Sciences Laboratory – Human Sciences Institute, University of Lyon, Lumiere Lyon 2, Campus Berges du Rhone, 69635 Lyon Cedex 07, France.

    Abstract: Topological Multiple Correspondence Analysis (TMCA) studies a group of categorical variables defined on the same set of individuals. Its a topological method of data analysis that consists of exploring, analyzing and representing the associations between several qualitative variables in the context of multiple correspondence analysis. It compares and classifies proximity measures to select the best one according to the data under consideration, then analyzes, interprets and visualizes with graphic representations, the possible associations between several categorical variables relat-ing to, the known problem of Multiple Correspondence Analysis (MCA). Based on the notion of neighborhood graphs, some of these proximity measures are more-or-less equivalent. A topological equivalence index between two measures is defined and statistically tested according to the degree of description of the associations between the modalities of these qualitative variables.
    We compare proximity measures and propose a topological criterion for choosing the best association measure, adapted to the data considered, from among some of the most widely used proximity measures for categorical data. The principle of the proposed approach is illustrated using a real data set with conventional proximity measures for binary variables from the literature. The first step is to find the proximity measure that can best adapted to the data; the second step is to use this measure to perform the TMCA.

    Keywords: Burt table, proximity measure, neighborhood graph, adjacency matrix, topological equivalence, graphical representations.

    Pages: 175 – 192 | Full PDF Paper
  3. The Benders Decomposition for the Dual of the b- Complementary Multi-Semigroup Problem

    Eleazar Gerardo Madriz Lozada

    CETEC-UFRB, Cruz da Almas, BA, Brazil.

    Abstract: Multi-valued Additive Systems defined by Araoz and Johnson in 1982, these finite algebraic structures are a generalization of finite groups and semigroups. A particular case of these systems are the b-complemetary multisemigroups. In 1980 Johnson studied the dual primal problem over a semigroup, and in 1985 Araoz and Johnson presented a study that classifies the polyhedron associated with an additive system, a study that features vertices and faces of this polyhedron. Madriz in 2016 presents the duality results for the primal problem over a b-complementary multisemigroup. In this work, we show that systems of two different bases of the cone associated with an integer linear programming problem under a b-complementary Multisemigroup are equivalent. We also present the decomposition of Benders for the dual problem of the a b-Complementary Multisemigroup.

    Keywords: Additive System, Multisemigruop, b-Complementary, Duality, Benders Decompostion.

    Pages: 193 – 205 | Full PDF Paper
  4. An Unexpected Random Walk

    Thomas J. Osler and Marcus Wright

    Mathematics Department, Rowan University, Glassboro, NJ 08028.

    Pages: 206 – 211 | Full PDF Paper