Proposals
Below are some proposals for talks from the past (and current). By clicking on the ID number, more details are shown. By default, these are sorted chronologically (recent first) and by then by last name. The data can be sorted by alternate means by using the links at the top right, each allowing ascending or descending orders.
Displaying 121-140 of 471 results.
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ID:
200
Year: 2007
Name: Jonathan Botts
Institution: Drake University
Subject area(s):
Title of Talk: On the Weakly Sign Symmetric Matrix Completion Problems
Abstract: An n x n matrix is called a P-matrix if all its principal minors are positive. An n x n matrix, A = [a_{ij}], is sign symmetric, if for each i,j \in \{1, 2, \dots, n }, either a_{ij} = 0 = a_{ji}$ or a_{ij}a_{ji}>0; the matrix is weakly sign symmetric if a_{ij}a_{ji}\ge 0. In this talk we show that an n x n partial (weakly) sign symmetric P-matrix specifying an asymmetric acyclic digraph can be completed to a (weakly) sign symmetric P-matrix. We also show that a partial n x n (weakly) sign symmetric P-matrix specifying an asymmetric digraph with no 3-cycles, can be completed to a (weakly) sign symmetric P-matrix for n >= 5.
Year: 2007
Name: Jonathan Botts
Institution: Drake University
Subject area(s):
Title of Talk: On the Weakly Sign Symmetric Matrix Completion Problems
Abstract: An n x n matrix is called a P-matrix if all its principal minors are positive. An n x n matrix, A = [a_{ij}], is sign symmetric, if for each i,j \in \{1, 2, \dots, n }, either a_{ij} = 0 = a_{ji}$ or a_{ij}a_{ji}>0; the matrix is weakly sign symmetric if a_{ij}a_{ji}\ge 0. In this talk we show that an n x n partial (weakly) sign symmetric P-matrix specifying an asymmetric acyclic digraph can be completed to a (weakly) sign symmetric P-matrix. We also show that a partial n x n (weakly) sign symmetric P-matrix specifying an asymmetric digraph with no 3-cycles, can be completed to a (weakly) sign symmetric P-matrix for n >= 5.
ID:
201
Year: 2007
Name: Henry Walker
Institution: Grinnell College
Subject area(s):
Title of Talk: Ethics and Standards
Abstract: The MAA Committee on the Profession (CotP) has been asked by the MAA Board of Governors to draft a Statement of Ethics Standards. This talk will provide an overview to the work on this project and encourage reactions to the current working draft.
Year: 2007
Name: Henry Walker
Institution: Grinnell College
Subject area(s):
Title of Talk: Ethics and Standards
Abstract: The MAA Committee on the Profession (CotP) has been asked by the MAA Board of Governors to draft a Statement of Ethics Standards. This talk will provide an overview to the work on this project and encourage reactions to the current working draft.
ID:
202
Year: 2007
Name: Luz De Alba Guerra
Institution: Drake University
Subject area(s):
Title of Talk: Minimum Rank of Powers of Some Special Graphs
Abstract: For an n x n symmetric matrix A the graph of A, G(A) =(V, E) is a simple undirected graph with vertex set {1, 2, ..., n }, where {i, j } is in E, if and only if a_{ij} is not 0. For a graph G, with vertex set V = {1, 2, ..., n }, and edge set E, the r-th power of G is the graph G^r = (V, F), where {u, v } is in F if and only if there is a walk of length r from u to v. The minimum rank of a graph G is mr(G) = min{ rank(A) : A = A^T, and G(A) = G }. In this talk we determine the minimum rank of certain powers of two special families of graphs: paths and trees in general. We will also present a onjecture on the minimum rank of powers of cycles.
Year: 2007
Name: Luz De Alba Guerra
Institution: Drake University
Subject area(s):
Title of Talk: Minimum Rank of Powers of Some Special Graphs
Abstract: For an n x n symmetric matrix A the graph of A, G(A) =(V, E) is a simple undirected graph with vertex set {1, 2, ..., n }, where {i, j } is in E, if and only if a_{ij} is not 0. For a graph G, with vertex set V = {1, 2, ..., n }, and edge set E, the r-th power of G is the graph G^r = (V, F), where {u, v } is in F if and only if there is a walk of length r from u to v. The minimum rank of a graph G is mr(G) = min{ rank(A) : A = A^T, and G(A) = G }. In this talk we determine the minimum rank of certain powers of two special families of graphs: paths and trees in general. We will also present a onjecture on the minimum rank of powers of cycles.
ID:
203
Year: 2007
Name: In-Jae Kim
Institution: Minnesota State University, Mankato
Subject area(s):
Title of Talk: Sign patterns that allow a positive or nonnegative left inverse
Abstract: An m x n sign pattern S is an m x n matrix with entries in {+,-,0}. An m x n sign pattern S allows a positive (resp., nonnegative) left inverse provided that there exist an m x n matrix A with sign pattern S and an m x n matrix with only positive (resp., nonnegative) entries satisfying BA=I_{n}, where I_{n} is the n x n identity matrix. Using associated bipartite digraphs, we characterize m x n (m >= n >= 2) sign patterns that allow a positive left inverse. This generalizes the known result for the square case. Some results on sign patterns allowing a nonnegative left inverse are also presented. (This is joint work with D.D. Olesky, B.L. Shader and P. van den Driessche.)
Year: 2007
Name: In-Jae Kim
Institution: Minnesota State University, Mankato
Subject area(s):
Title of Talk: Sign patterns that allow a positive or nonnegative left inverse
Abstract: An m x n sign pattern S is an m x n matrix with entries in {+,-,0}. An m x n sign pattern S allows a positive (resp., nonnegative) left inverse provided that there exist an m x n matrix A with sign pattern S and an m x n matrix with only positive (resp., nonnegative) entries satisfying BA=I_{n}, where I_{n} is the n x n identity matrix. Using associated bipartite digraphs, we characterize m x n (m >= n >= 2) sign patterns that allow a positive left inverse. This generalizes the known result for the square case. Some results on sign patterns allowing a nonnegative left inverse are also presented. (This is joint work with D.D. Olesky, B.L. Shader and P. van den Driessche.)
ID:
204
Year: 2007
Name: Joseph A. Gallian
Institution: University of Minnesota, Duluth
Subject area(s):
Title of Talk: Using groups and graphs to create symmetry patterns, Parts 1
Abstract: Part 1 concerns the problem of traversing an m by n directed grid embedded on a torus so that each vertex is visited exactly once before returning to the starting position. We also consider generalizations and variations on this theme.
Year: 2007
Name: Joseph A. Gallian
Institution: University of Minnesota, Duluth
Subject area(s):
Title of Talk: Using groups and graphs to create symmetry patterns, Parts 1
Abstract: Part 1 concerns the problem of traversing an m by n directed grid embedded on a torus so that each vertex is visited exactly once before returning to the starting position. We also consider generalizations and variations on this theme.
ID:
205
Year: 2007
Name: Joseph A. Gallian
Institution: University of Minnesota, Duluth
Subject area(s):
Title of Talk: Using groups and graphs to create symmetry patterns, Part 2
Abstract: Part 2 is a discussion of how Hamiltonian paths, spanning trees, cosets in groups, and factor groups can be used to create computer generated symmetry patterns in hyperbolic and Euclidean planes. These methods were used to create the image for the 2003 Mathematics Awareness Month poster.
Year: 2007
Name: Joseph A. Gallian
Institution: University of Minnesota, Duluth
Subject area(s):
Title of Talk: Using groups and graphs to create symmetry patterns, Part 2
Abstract: Part 2 is a discussion of how Hamiltonian paths, spanning trees, cosets in groups, and factor groups can be used to create computer generated symmetry patterns in hyperbolic and Euclidean planes. These methods were used to create the image for the 2003 Mathematics Awareness Month poster.
ID:
206
Year: 2007
Name: M Anne Dow
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Mathematics for Sustainable Living: Pre-Calculus Basics
Abstract: This talk describes a new math course I am designing for our Sustainable Living students. The purpose of the Sustainable Living major is to equip students to design, build, and maintain sustainable communities. The prerequisite for the new math course is Intermediate Algebra. It will cover simple linear models, exponential and logarithmic functions, graphs of functions, trigonometry of triangles, and elementary probability, all in the context of problems and topics arising in our Sustainable Living major.
Year: 2007
Name: M Anne Dow
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Mathematics for Sustainable Living: Pre-Calculus Basics
Abstract: This talk describes a new math course I am designing for our Sustainable Living students. The purpose of the Sustainable Living major is to equip students to design, build, and maintain sustainable communities. The prerequisite for the new math course is Intermediate Algebra. It will cover simple linear models, exponential and logarithmic functions, graphs of functions, trigonometry of triangles, and elementary probability, all in the context of problems and topics arising in our Sustainable Living major.
ID:
207
Year: 2007
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Geometry for the Artist: A General Education Course
Abstract: This paper will describe the course Geometry for the Artist that I have been teaching for over 20 years at M.U.M. The topics covered symmetry, Euclidean geometry, perspective, fractals, non-Euclidean geometry, and topology. For each topic, we discuss applications in the visual arts with an emphasis on M. C. Escher. This course satisfies the distribution requirement for mathematics.
Year: 2007
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Geometry for the Artist: A General Education Course
Abstract: This paper will describe the course Geometry for the Artist that I have been teaching for over 20 years at M.U.M. The topics covered symmetry, Euclidean geometry, perspective, fractals, non-Euclidean geometry, and topology. For each topic, we discuss applications in the visual arts with an emphasis on M. C. Escher. This course satisfies the distribution requirement for mathematics.
ID:
208
Year: 2007
Name: James Fiedler
Institution: Iowa State University
Subject area(s):
Title of Talk: On a Group Associated With Projective Planes
Abstract: A pair of orthogonal Latin squares of order n is equivalent to a permutation on the set of ordered pairs of integers 1, ..., n. Since a projective plane of order n exists if and only if there exists a set of n-1 mutually orthogonal Latin squares of order n, the group generated by the above permutations may be of some interest in the study of projective planes. Relevant definitions and results of some investigations concerning these groups will be presented.
Year: 2007
Name: James Fiedler
Institution: Iowa State University
Subject area(s):
Title of Talk: On a Group Associated With Projective Planes
Abstract: A pair of orthogonal Latin squares of order n is equivalent to a permutation on the set of ordered pairs of integers 1, ..., n. Since a projective plane of order n exists if and only if there exists a set of n-1 mutually orthogonal Latin squares of order n, the group generated by the above permutations may be of some interest in the study of projective planes. Relevant definitions and results of some investigations concerning these groups will be presented.
ID:
209
Year: 2007
Name: Erick Hofacker
Institution: University of Wisconsin - River Falls
Subject area(s):
Title of Talk: Teaching tools in the MAA digital library
Abstract: The purpose of the workshop was to inform participants of the teaching tools available through the MAA digital library. Participants at the session are able to do some exploring of sites on their own while I am discussing the vast number of resources that are available.
Year: 2007
Name: Erick Hofacker
Institution: University of Wisconsin - River Falls
Subject area(s):
Title of Talk: Teaching tools in the MAA digital library
Abstract: The purpose of the workshop was to inform participants of the teaching tools available through the MAA digital library. Participants at the session are able to do some exploring of sites on their own while I am discussing the vast number of resources that are available.
ID:
210
Year: 2007
Name: Stephen Willson
Institution: Iowa State University
Subject area(s):
Title of Talk: On the Mathematics of Juggling
Abstract: The mathematical analysis of juggling gives interesting examples of permutations and uses of modular arithmetic. Simple mathematical notation can be used to describe many different ways of juggling. The descriptions can tell which periodic patterns give valid juggling methods.
Year: 2007
Name: Stephen Willson
Institution: Iowa State University
Subject area(s):
Title of Talk: On the Mathematics of Juggling
Abstract: The mathematical analysis of juggling gives interesting examples of permutations and uses of modular arithmetic. Simple mathematical notation can be used to describe many different ways of juggling. The descriptions can tell which periodic patterns give valid juggling methods.
ID:
211
Year: 2007
Name: Rana Mikkelson
Institution: Iowa State University
Subject area(s):
Title of Talk: An Introduction to Minimum Rank of a Graph
Abstract: Given a graph, we can associate a set of matrices therewith: the set of all symmetric matrices A over R where aij = 0 ? G has an edge between vertex i and j . We define the minimum rank of a graph is then the minimum among the ranks of all the matrices in this set. There is no one easy formula for computing this value given any graph, but for certain types graphs we can find the minimum rank exactly, and for others we can at least determine a few bounds. This talk introduces the topic and begins to explore the known results.
Year: 2007
Name: Rana Mikkelson
Institution: Iowa State University
Subject area(s):
Title of Talk: An Introduction to Minimum Rank of a Graph
Abstract: Given a graph, we can associate a set of matrices therewith: the set of all symmetric matrices A over R where aij = 0 ? G has an edge between vertex i and j . We define the minimum rank of a graph is then the minimum among the ranks of all the matrices in this set. There is no one easy formula for computing this value given any graph, but for certain types graphs we can find the minimum rank exactly, and for others we can at least determine a few bounds. This talk introduces the topic and begins to explore the known results.
ID:
212
Year: 2007
Name: Siu-Hung (Richard) Ng
Institution: Iowa State University
Subject area(s):
Title of Talk: Counting the number of solutions in a finite group
Abstract: The notion of Frobenius-Schur (FS)-indicators of a finite group representation has been developed for more than a century. These indicators can be obtained by counting the number of solutions x of the equation x^n=g in a finite group. Moreover, the second indicators can be used to construct topological invariants of surfaces. It was not known until recently that they are invariants of the tensor categories of finite group representations. In the talk, we will give a brief history of these indicators and their new developments.
Year: 2007
Name: Siu-Hung (Richard) Ng
Institution: Iowa State University
Subject area(s):
Title of Talk: Counting the number of solutions in a finite group
Abstract: The notion of Frobenius-Schur (FS)-indicators of a finite group representation has been developed for more than a century. These indicators can be obtained by counting the number of solutions x of the equation x^n=g in a finite group. Moreover, the second indicators can be used to construct topological invariants of surfaces. It was not known until recently that they are invariants of the tensor categories of finite group representations. In the talk, we will give a brief history of these indicators and their new developments.
ID:
213
Year: 2007
Name: Krishna B. Athreya
Institution: Iowa State University
Subject area(s):
Title of Talk: Preferential Attachment Random Graphs with General Weight Function
Abstract: Start with a graph G_0 = {V_1 , V_2} with one edge connecting the two vertices V_1, V_2. Now create a new vertex V_3 and attach it (i.e. add an edge) to V_1 or V_2 with equal probability. Set G_3={V_1 , V_2, V_3}. Let G_n={V_1,
Year: 2007
Name: Krishna B. Athreya
Institution: Iowa State University
Subject area(s):
Title of Talk: Preferential Attachment Random Graphs with General Weight Function
Abstract: Start with a graph G_0 = {V_1 , V_2} with one edge connecting the two vertices V_1, V_2. Now create a new vertex V_3 and attach it (i.e. add an edge) to V_1 or V_2 with equal probability. Set G_3={V_1 , V_2, V_3}. Let G_n={V_1,
ID:
214
Year: 2007
Name: Kliemann Wolfgang
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
Year: 2007
Name: Kliemann Wolfgang
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
ID:
215
Year: 2007
Name: Wolfgang Kliemann
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
Year: 2007
Name: Wolfgang Kliemann
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
ID:
216
Year: 2007
Name: Scott Searcy
Institution: Waldorf College
Subject area(s):
Title of Talk: The Possible Use of Wavelets in Digital Audio Upsampling
Abstract: The challenge of high fidelity digital to analog conversion of digital audio information is quite challenging. This paper will the possible use of wvaelets to increase the fidelity of the recovered analog signal.
Year: 2007
Name: Scott Searcy
Institution: Waldorf College
Subject area(s):
Title of Talk: The Possible Use of Wavelets in Digital Audio Upsampling
Abstract: The challenge of high fidelity digital to analog conversion of digital audio information is quite challenging. This paper will the possible use of wvaelets to increase the fidelity of the recovered analog signal.
ID:
217
Year: 2007
Name: Dennis Roseman
Institution: University of Iowa
Subject area(s):
Title of Talk: How likely is a lattice link?
Abstract: Lattice points in space are points with integer coordinates. A unit lattice edge is a line segment of unit length between lattice points. A lattice link is a finite collection union of lattice edges whose union is topologically equivalent to a union of disjoint circles. We define a notion of probability for lattice knots and links and use this to frame the question: which is more ``likely'', the square knot or the granny knot. A square knot is obtained by tying a right hand trefoil and a left had trefoil together; the granny knot is obtained by using two identical trefoils. We also discuss our progress towards calculation of these probabilities.
Year: 2007
Name: Dennis Roseman
Institution: University of Iowa
Subject area(s):
Title of Talk: How likely is a lattice link?
Abstract: Lattice points in space are points with integer coordinates. A unit lattice edge is a line segment of unit length between lattice points. A lattice link is a finite collection union of lattice edges whose union is topologically equivalent to a union of disjoint circles. We define a notion of probability for lattice knots and links and use this to frame the question: which is more ``likely'', the square knot or the granny knot. A square knot is obtained by tying a right hand trefoil and a left had trefoil together; the granny knot is obtained by using two identical trefoils. We also discuss our progress towards calculation of these probabilities.
ID:
219
Year: 2008
Name: Haseena Ahmed
Institution: Iowa State University
Subject area(s): Applied Mathematics, Numerical Analysis
Title of Talk: Alternating evolution (AE) schemes for hyperbolic conservation laws
Abstract: An alternating evolution (AE) system is proposed which is an accurate approximation to systems of hyperbolic conservation laws. We develop a class of local Alternating Evolution (AE) schemes, where we take advantage of high accuracy of the proposed AE approximation. Our approach is based on a sliding average of the AE system over an interval of [x − \Delta x, x + \Delta x]. The numerical scheme is then constructed by sampling the averaged system over alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial reconstruction from the obtained averages and a stable Runge-Kutta discretization in time. The AE schemes have the advantage of easier formulation and implementation, and efficient computation of the solution. For the first and second order local AE schemes applied to scalar laws, we prove the numerical stability in the sense of satisfying the maximum principle and total variation diminishing (TVD) property. Numerical tests for both scalar conservation laws and compressible Euler equations are presented to demonstrate the high order accuracy and capacity of these AE schemes.
Year: 2008
Name: Haseena Ahmed
Institution: Iowa State University
Subject area(s): Applied Mathematics, Numerical Analysis
Title of Talk: Alternating evolution (AE) schemes for hyperbolic conservation laws
Abstract: An alternating evolution (AE) system is proposed which is an accurate approximation to systems of hyperbolic conservation laws. We develop a class of local Alternating Evolution (AE) schemes, where we take advantage of high accuracy of the proposed AE approximation. Our approach is based on a sliding average of the AE system over an interval of [x − \Delta x, x + \Delta x]. The numerical scheme is then constructed by sampling the averaged system over alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial reconstruction from the obtained averages and a stable Runge-Kutta discretization in time. The AE schemes have the advantage of easier formulation and implementation, and efficient computation of the solution. For the first and second order local AE schemes applied to scalar laws, we prove the numerical stability in the sense of satisfying the maximum principle and total variation diminishing (TVD) property. Numerical tests for both scalar conservation laws and compressible Euler equations are presented to demonstrate the high order accuracy and capacity of these AE schemes.
ID:
220
Year: 2008
Name: Zhongming WANG
Institution: Iowa State University
Subject area(s):
Title of Talk: Bloch Band Based Level Set Method for the Schrodinger Equation
Abstract: We develop a Bloch band based level set method for capturing the semiclassical limit of one-dimensional Schrodinger equations in periodic medium. A hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. Following the level set methodology , we develop a Bloch band based level set method, which are hybrid numerical schemes -- splitting the solution process into several parts: i) band decomposition of the initial data and construction of the initial level set function; ii) solve the Bloch eigenvalue problem; iii) evolve the band level set equation to compute multi-valued velocity and density on each Bloch band; iv)the total position density over a sample set of bands is evaluated using Bloch waves and band densities obtained in step ii) and iii), respectively. Numerical results with different number of bands are provided to demonstrate the good quality of the method.
Year: 2008
Name: Zhongming WANG
Institution: Iowa State University
Subject area(s):
Title of Talk: Bloch Band Based Level Set Method for the Schrodinger Equation
Abstract: We develop a Bloch band based level set method for capturing the semiclassical limit of one-dimensional Schrodinger equations in periodic medium. A hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. Following the level set methodology , we develop a Bloch band based level set method, which are hybrid numerical schemes -- splitting the solution process into several parts: i) band decomposition of the initial data and construction of the initial level set function; ii) solve the Bloch eigenvalue problem; iii) evolve the band level set equation to compute multi-valued velocity and density on each Bloch band; iv)the total position density over a sample set of bands is evaluated using Bloch waves and band densities obtained in step ii) and iii), respectively. Numerical results with different number of bands are provided to demonstrate the good quality of the method.