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Articles 1 - 12 of 12
Full-Text Articles in Mathematics
Continuous Trace C*-Algebras, Gauge Groups And Rationalization, John R. Klein, Claude Schochet, Samuel B. Smith
Continuous Trace C*-Algebras, Gauge Groups And Rationalization, John R. Klein, Claude Schochet, Samuel B. Smith
Mathematics Faculty Research Publications
Let ζ be an n-dimensional complex matrix bundle over a compact metric space X and let Aζ denote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UAζ, the group of unitaries of Aζ. The answer turns out to be independent of the bundle ζ and depends only upon n and the rational cohomology of X. We prove analogous results for the gauge group and the projective gauge group of a principal bundle over a compact metric space X.
Flattening A Cone, Sean A. Broughton
Flattening A Cone, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
We want to manufacture a cut-off slanted cone from a flat sheet of metal. If the cone were a normal right cone we know that we would simply cut out a sector of a circle and roll it up. However the cone is slanted. We want to know what the flattened shape looks like so that we can cut it out and roll it up to closely approximate correct final shape. We also want to minimize the amount of wasted metal after the shape is cut out.
The problem, and it generalizations may be solved analytically but the analytical solution …
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Department of Mathematics: Dissertations, Theses, and Student Research
Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf KqT on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …
Some Properties Of Yao Y4 Subgraphs, Joseph O'Rourke
Some Properties Of Yao Y4 Subgraphs, Joseph O'Rourke
Computer Science: Faculty Publications
The Yao graph for k = 4, Y4, is naturally partitioned into four subgraphs, one per quadrant. We show that the subgraphs for one quadrant differ from the subgraphs for two adjacent quadrants in three properties: planarity, connectedness, and whether the directed graphs are spanners.
The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers
The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers
FIU Electronic Theses and Dissertations
The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics …
Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov
Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov
Conference papers
A class of equations describing the geodesic flow for a right-invariant metric on the group of diffeomorphisms of Rn is reviewed from the viewpoint of their Lie-Poisson structures. A subclass of these equations is analogous to the Euler equations in hydrodynamics (for n = 3), preserving the volume element of the domain of fluid flow. An example in n = 1 dimension is the Camassa-Holm equation, which is a geodesic flow equation on the group of diffeomorphisms, preserving the H1 metric.
Galois Structure And De Rhan Invariants Of Elliptic Curves, Darren B. Glass, Sonin Kwon
Galois Structure And De Rhan Invariants Of Elliptic Curves, Darren B. Glass, Sonin Kwon
Math Faculty Publications
Let K be a number field with ring of integers OK. Suppose a finite group G acts numerically tamely on a regular scheme X over OK. One can then define a de Rham invariant class in the class group Cl(OK[G]), which is a refined Euler characteristic of the de Rham complex of X. Our results concern the classification of numerically tame actions and the de Rham invariant classes. We first describe how all Galois etale G-covers of a K-variety may be built up from finite Galois extensions of K and from geometric covers. When X is a curve of positive …
Banach Algebras And Rational Homotopy Theory, Gregory Lupton, N. Christopher Phillips, Claude Schochet, Samuel B. Smith
Banach Algebras And Rational Homotopy Theory, Gregory Lupton, N. Christopher Phillips, Claude Schochet, Samuel B. Smith
Mathematics Faculty Research Publications
Let A be a unital commutative Banach algebra with maximal ideal space Max(A). We determine the rational H-type of GLn(A), the group of invertible n x n matrices with coefficients in A, in terms of the rational cohomology of Max(A). We also address an old problem of J. L. Taylor. Let Lcn(A) denote the space of "last columns" of GLn(A). We construct a natural isomorphism
Ȟs(Max(A);ℚ) ≅ π2n-1-s(Lcn(A)) ⊗ ℚ …
Using Non-Euclidean Geometry In The Euclidean Classroom, Kelli Jean Wasserman
Using Non-Euclidean Geometry In The Euclidean Classroom, Kelli Jean Wasserman
Theses Digitization Project
This study is designed to explore the ramifications of supplementing the basic Euclidean geometry, with spherical geometry, a non-Eugledian geometry curriculum. This project examined different aspects of the impact of spherical geometry on the high school geometry classroom.
Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams
Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams
Dissertations
Problem
Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …
Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich
Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich
Scholarship and Professional Work - LAS
We have noticed a certain kind of n-gon dissection into triangles that has a wonderful property of interest to most puzzlists. Namely that any two triangles have at least one edge in common yet no two triangles need be congruent. In an informal poll of specialists at a recent convention, none of them saw immediately how this could be accomplished. But in fact it is very straightforward.
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
Theses Digitization Project
The purpose of the project is to examine the action of the composition of split inversions on the hyperbolic plane, H². The model that is used is the poincoŕe disk.