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Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence 2015 Boise State University

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

Mathematics Faculty Publications and Presentations

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pn whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.


Minimum Rank Of Graphs With Loops, Chassidy Bozeman, AnnaVictoria Ellsworth, Leslie Hogben, Jephian Chin-Hung Lin, Gabi Maurer, Kathleen Nowak, Aaron Rodriguez, James Strickland 2015 Iowa State University

Minimum Rank Of Graphs With Loops, Chassidy Bozeman, Annavictoria Ellsworth, Leslie Hogben, Jephian Chin-Hung Lin, Gabi Maurer, Kathleen Nowak, Aaron Rodriguez, James Strickland

Electronic Journal of Linear Algebra

A loop graph $\mf G$ is a finite undirected graph that allows loops but does not allow multiple edges. The set $\sym(\lG)$ of real symmetric matrices associated with a loop graph $\lG$ of order $n$ is the set of symmetric matrices $A=[a_{ij}]\in\Rnn$ such that $a_{ij}\ne 0$ if and only if $ij\in E(\lG)$. The minimum (maximum) rank of a loop graph is the minimum (maximum) of the ranks of the matrices in $\sym(\lG)$. We characterize loop graphs having minimum rank at most two (by forbidden induced subgraphs and graph complements) and ...


Rationality Of The Spectral Action For Robertson-Walker Metrics And The Geometry Of The Determinant Line Bundle For The Noncommutative Two Torus, Asghar Ghorbanpour 2015 The University of Western Ontario

Rationality Of The Spectral Action For Robertson-Walker Metrics And The Geometry Of The Determinant Line Bundle For The Noncommutative Two Torus, Asghar Ghorbanpour

University of Western Ontario - Electronic Thesis and Dissertation Repository

In noncommutative geometry, the geometry of a space is given via a spectral triple $(\mathcal{A,H},D)$. Geometric information, in this approach, is encoded in the spectrum of $D$ and to extract them, one should study spectral functions such as the heat trace $\Tr (e^{-tD^2})$, the spectral zeta function $\Tr(|D|^{-s})$ and the spectral action functional, $\Tr f(D/\Lambda)$.

The main focus of this thesis is on the methods and tools that can be used to extract the spectral information. Applying the pseudodifferential calculus and the heat trace techniques, in addition to computing the newer ...


Improving University Students' Perception Of Mathematics And Mathematics Ability, Shelly L. Wismath, Alyson Worrall 2015 University of Lethbridge

Improving University Students' Perception Of Mathematics And Mathematics Ability, Shelly L. Wismath, Alyson Worrall

Numeracy

Although mathematical and quantitative reasoning skills are an essential part of adult life in our society, many students arrive at post-secondary education without such skills. Taking a standard mathematics course such as calculus may do little to improve those skills. Using a modification of the Tapia & Marsh questionnaire, we surveyed 62 students taking a broad quantitative reasoning course designed to develop quantitative skills, with respect to two broad attitudinal areas: students’ perception of their own ability, confidence and anxiety, and their perception of the value of mathematics in their studies and their lives. Pre- to post-course comparisons were done by ...


A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson 2015 Utah State University

A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson

Tutorials on... in 1 hour or less

Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .


Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson 2015 Utah State University

Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson

Tutorials on... in 1 hour or less

In this worksheet we shall review the basic definitions and properties of Cartan involutions and Cartan decompositions and illustrate these using the DifferentialGeometry software package for Lie algebras.


Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik 2014 The University of Western Ontario

Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik

University of Western Ontario - Electronic Thesis and Dissertation Repository

Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by triangular sets) and then, with some generic assumptions, to l many hypersurfaces.

Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at points on curves.


Positive Semidefinite 3 X 3 Block Matrices, Minghua Lin, Pauline van den Driessche 2014 University of Victoria

Positive Semidefinite 3 X 3 Block Matrices, Minghua Lin, Pauline Van Den Driessche

Electronic Journal of Linear Algebra

Several results related to positive semidefinite 3 by 3 block matrices are presented. In particular, a question of Audenaert is answered affirmatively and some determinantal inequalities are proved.


High-Order Green Operators On The Disk And The Polydisc, Yifei Pan 2014 Indiana University – Purdue University Fort Wayne

High-Order Green Operators On The Disk And The Polydisc, Yifei Pan

Mathematical Sciences Faculty Publications

In this paper, we give the explicit expressions of high-order Green operators on the disk and the polydisc, and hence the kernel functions of high-order Green operators are also presented. As applications, we present the explicit integral expressions of all the solutions for linear high-order partial differential equations in the disk.


Some Observations On Scientific Epistemology With Applications To Conflict Resolution And Constructive Controversy, Judith Puncochar, Don Faust 2014 Northern Michigan University

Some Observations On Scientific Epistemology With Applications To Conflict Resolution And Constructive Controversy, Judith Puncochar, Don Faust

Other Presentations

An overview, by Judy and Don (published in 2013 in the BULLETIN OF SYMBOLIC LOGIC):

Explorationism is a perspective wherein all of our knowledge is (so far) less than certain, and naturally would come equipped with a base logic entailing machinery for representing and processing evidential knowledge. One such base logic is Evidence Logic, which strives to deal with the phenomenon of the gradational presence of both confirmatory and refutatory evidence. From this perspective, we will address questions surrounding sociological problem areas that we see as deeply infused with substantial epistemological factors. By defining a framework as any theory, in ...


Cohomology Of Absolute Galois Groups, Claudio Quadrelli 2014 The University of Western Ontario

Cohomology Of Absolute Galois Groups, Claudio Quadrelli

University of Western Ontario - Electronic Thesis and Dissertation Repository

The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group.

We define a new class of pro-p groups ...


A Schwarz-Pick Lemma For The Modulus Of Holomorphic Mappings From The Polydisk Into The Unit Ball, Yifei Pan 2014 Indiana University – Purdue University Fort Wayne

A Schwarz-Pick Lemma For The Modulus Of Holomorphic Mappings From The Polydisk Into The Unit Ball, Yifei Pan

Mathematical Sciences Faculty Publications

In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.


Gifted Students In Mathematics: A Problem Solving Approach To Enrichment, Caylin DePuy 2014 Brockport College

Gifted Students In Mathematics: A Problem Solving Approach To Enrichment, Caylin Depuy

Education and Human Development Master's Theses

In the United States mathematically gifted students frequently go unnoticed and most often receive the same education as their at-level peers (Ysseldyke, Tardrew, Betts, Thill, Hannigan, 2004). There is very limited funding available for gifted students and the identification and classification varies by state, often being decided by school district (National Association, 2014). Gifted American students are exposed to less challenging problems than those in other countries and, as a result, are falling behind in academic performance (Ross, 1993). This curriculum is designed to supplement the existing Geometry curriculum by offering eight unique, challenging problems that can be used for ...


An Algebra Unit On Quadratics For Teachers With Students With Ebd, Christopher Williams 2014 State University of Brockport

An Algebra Unit On Quadratics For Teachers With Students With Ebd, Christopher Williams

Education and Human Development Master's Theses

The number of students identified as having an emotional and behavioral disorder (EBD) are increasing rapidly and still underreported. These students often have significant behavioral, social and academic deficits that pose challenges within and outside the school setting and are among some of the most difficult students to teach with the bleakest post-school success or employment rates. Research reveals several effective procedures for conducting interventions to increase performance, participation and engagement and in lowering the number of inappropriate behavior occurrences within the classroom. Based on these findings, an algebra unit plan on quadratics has been developed to assist and direct ...


The Structure And Properties Of Clique Graphs Of Regular Graphs, Jan Burmeister 2014 University of Southern Mississippi

The Structure And Properties Of Clique Graphs Of Regular Graphs, Jan Burmeister

Master's Theses

In the following thesis, the structure and properties of G and its clique graph clt (G) are analyzed for graphs G that are non-complete, regular with degree δ , and where every edge of G is contained in a t -clique. In a clique graph clt (G), all cliques of order t of the original graph G become the clique graph’s vertices, and the vertices of the clique graph are adjacent if and only if the corresponding cliques in the original graph have at least 1 vertex in common. This thesis mainly investigates if properties of regular graphs ...


Ogden College News, Cheryl Stevens, Dean, Odgen College of Science & Engineering, Western Kentucky University 2014 Western Kentucky University

Ogden College News, Cheryl Stevens, Dean, Odgen College Of Science & Engineering, Western Kentucky University

Ogden College of Science & Engineering Publications

No abstract provided.


Classical And Motivic Adams Charts, Daniel C. Isaksen 2014 Wayne State University

Classical And Motivic Adams Charts, Daniel C. Isaksen

Mathematics Research Reports

This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 59-stem and contain partial results to the 70-stem. In the classical context, we believe that these are the most accurate charts of their kind. We also include Adams charts for the motivic homotopy groups of the cofiber of τ.


Classical And Motivic Adams-Novikov Charts, Daniel C. Isaksen 2014 Wayne State University

Classical And Motivic Adams-Novikov Charts, Daniel C. Isaksen

Mathematics Research Reports

This document contains large-format Adams-Novikov charts that compute the classical 2-complete stable homotopy groups. The charts are essentially complete through the 59-stem. We believe that these are the most accurate and extensive charts of their kind. We also include a motivic Adams-Novikov E∞ chart.


The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen 2014 Brigham Young University - Provo

The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen

All Theses and Dissertations

Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We ...


An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench 2014 Trinity University

An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench

William F. Trench

No abstract provided.


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