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Full-Text Articles in Algebraic Geometry

Bridging The Mathematics Gap Through The Use Of Mathematical Apps, Ma. Louise Antonette N. De Las Penas, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Agnes D. Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino Jan 2023

Bridging The Mathematics Gap Through The Use Of Mathematical Apps, Ma. Louise Antonette N. De Las Penas, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Agnes D. Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

During the COVID-19 pandemic, school campuses worldwide were forced to close, and students had to learn primarily from home. This sudden disruption is estimated to have caused significant learning loss among learners. This paper reports the use of mathematical applications (apps) to bridge the mathematical learning gaps in Grades 1 to 11 in the Philippines after the pandemic, as part of a project funded by a national government agency. The apps include those that strengthen foundational concepts in number and fraction sense in grade school mathematics, develop proving skills in geometry, promote mastery in algebraic and trigonometry through drill and …


Local And Global Color Symmetries Of A Symmetrical Pattern, Ma. Louise Antonette N. De Las Peñas, Agatha Kristel Abila, Eduard C. Taganap Aug 2019

Local And Global Color Symmetries Of A Symmetrical Pattern, Ma. Louise Antonette N. De Las Peñas, Agatha Kristel Abila, Eduard C. Taganap

Mathematics Faculty Publications

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern P consisting of disjoint congruent symmetric motifs. The pattern P has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of P ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of P, a coloring that is perfect and transitive under G, satisfying the condition that the coloring …


Classification Of Book Representations Of K6, Dana Rowland Mar 2017

Classification Of Book Representations Of K6, Dana Rowland

Mathematics Faculty Publications

A book representation of a graph is a particular way of embedding a graph in three dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to K6, the complete graph with six vertices. We prove there are exactly 59 distinct book representations for K6, and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of K6 contain between one and seven links, and …


Symmetry Groups Associated With Tilings On A Flat Torus, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Grace M. Estrada, Eko Budi Santoso Jan 2015

Symmetry Groups Associated With Tilings On A Flat Torus, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Grace M. Estrada, Eko Budi Santoso

Mathematics Faculty Publications

This work investigates symmetry and color symmetry properties of Kepler, Heesch and Laves tilings embedded on a flat torus and their geometric realizations as tilings on a round torus in Euclidean 3-space. The symmetry group of the tiling on the round torus is determined by analyzing relevant symmetries of the planar tiling that are transformed to axial symmetries of the three-dimensional tiling. The focus on studying tilings on a round torus is motivated by applications in the geometric modeling of nanotori and the determination of their symmetry groups.


Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces, Hanz Martin C. Cheng, Roden Jason David Jan 2015

Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces, Hanz Martin C. Cheng, Roden Jason David

Mathematics Faculty Publications

The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)Ã(p+q) and exc : M ÃNÃN â M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504â519, 2003.].


Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev Jan 2014

Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev

Mathematics Faculty Publications

No abstract provided.


A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica Jan 2014

A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica

Mathematics Faculty Publications

No abstract provided.


Groups Of Graphs Of Groups, David P. Byrne, Matthew J. Donner, Thomas Q. Sibley Mar 2012

Groups Of Graphs Of Groups, David P. Byrne, Matthew J. Donner, Thomas Q. Sibley

Mathematics Faculty Publications

We classify all groups of color preserving automorphisms (isometries) of edge colored complete graphs derived from finite groups.


Infinitary Equivalence Of Zp- Modules With Nice Decomposition Bases, Rüdiger Göbel, Katrin Leistner, Peter Loth, Lutz Strüngmann Oct 2011

Infinitary Equivalence Of Zp- Modules With Nice Decomposition Bases, Rüdiger Göbel, Katrin Leistner, Peter Loth, Lutz Strüngmann

Mathematics Faculty Publications

Warfield modules are direct summands of simply presented Zp - modules, or, alternatively, are Zp - modules possessing a nice decomposition basis with simply presented cokernel. They have been classified up to isomorphism by theor Ilm-Kaplansky and Warfield invariants. Taking a model theoretic point of view and using infinitary languages we give here a complete theoretic characterization of a large class of Zp - modules having a nice decomposition basis. As a corollary, we obtain the classical classification of countable Warfield modules. This generalizes results by Barwise and Eklof.


Semi-Direct Galois Covers Of The Affine Line, Linda Gruendken, Laura L. Hall-Seelig, Bo-Hae Im, Ekin Ozman, Rachel Pries, Katherine Stevenson Jan 2011

Semi-Direct Galois Covers Of The Affine Line, Linda Gruendken, Laura L. Hall-Seelig, Bo-Hae Im, Ekin Ozman, Rachel Pries, Katherine Stevenson

Mathematics Faculty Publications

Let k be an algebraically closed field of characteristic p > 0. Let G be a semi-direct product of the form (Z/`Z) b o Z/pZ where b is a positive integer and ` is a prime distinct from p. In this paper, we study Galois covers ψ : Z → P 1 k ramified only over ∞ with Galois group G. We find the minimal genus of a curve Z which admits a covering map of this form and we give an explicit formula for this genus in terms of ` and p. The minimal genus occurs when b equals the …


The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle Jan 2011

The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle

Mathematics Faculty Publications

We will give a positive answer for the unimodality of the Hilbert functions in the smallest open case, that of Artinian level monomial algebras of type three in three variables.


On Hyperplanes And Semispaces In Max-Min Convex Geometry, Viorel Nitica, Sergeĭ Sergeev Jan 2010

On Hyperplanes And Semispaces In Max-Min Convex Geometry, Viorel Nitica, Sergeĭ Sergeev

Mathematics Faculty Publications

No abstract provided.


The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis Jan 2003

The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis

Mathematics Faculty Publications

A residuated lattice is an ordered algebraic structure [formula] such that is a lattice, is a monoid, and \ and / are binary operations for which the equivalences [formula] hold for all a,b,c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as "dividing" on the right by b and "dividing" on the left by a. The class of all residuated lattices is denoted by ℛℒ The study of such objects originated in the context of the theory of ring ideals in the 1930s. The …