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Integrating Path-Dependent Functionals On Yeh-Wiener Space, Ian Pierce, David Skough
Integrating Path-Dependent Functionals On Yeh-Wiener Space, Ian Pierce, David Skough
Department of Mathematics: Faculty Publications
Denote by Ca,b(Q) the generalized two-parameter Yeh-Wiener space with associated Gaussian measure. We investigate several scenarios in which integrals of functionals on this space can be reduced to integrals of related functionals over an appropriate single-parameter generalized Wiener space Cˆa,ˆb[0, T ]. This extends some interesting results of R. H. Cameron and D. A. Storvick.
Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai
Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai
Department of Mathematics: Faculty Publications
We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindstr¨om-Gessel- Viennot methodology to find the number of tilings of a quartered lozenge hexagon.
Von Neumann Algebras And Extensions Of Inverse Semigroups, Allan P. Donsig, Adam H. Fuller, David R. Pitts
Von Neumann Algebras And Extensions Of Inverse Semigroups, Allan P. Donsig, Adam H. Fuller, David R. Pitts
Department of Mathematics: Faculty Publications
In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan MASAs using measured equivalence re- lations and 2-cocycles on such equivalence relations. In this paper, we give a new classification in terms of extensions of inverse semigroups. Our approach is more algebraic in character and less point-based than that of Feldman-Moore. As an application, we give a restatement of the spectral theorem for bimodules in terms of subsets of inverse semigroups. We also show how our viewpoint leads naturally to a description of maximal subdiagonal algebras.
A Mentoring Program For Inquiry-Based Teaching In A College Geometry Class, Nathaniel Miller, Nathan Wakefield
A Mentoring Program For Inquiry-Based Teaching In A College Geometry Class, Nathaniel Miller, Nathan Wakefield
Department of Mathematics: Faculty Publications
This paper describes a mentoring program designed to prepare novice instructors to teach a college geometry class using inquiry-based methods. The mentoring program was used in a medium-sized public university with approximately 12,000 undergraduate students and 1,500 graduate students. The authors worked together to implement a mentoring program for the first time. One author was an associate professor and experienced using inquiry-based learning. The other author was a graduate student in mathematics education. During the course of the year the graduate student first observed and then taught a college level inquiry-based geometry course for pre-service teachers. This article describes the …
A Generalization Of Aztec Diamond Theorem, Part I, Tri Lai
A Generalization Of Aztec Diamond Theorem, Part I, Tri Lai
Department of Mathematics: Faculty Publications
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagonals drawn in. By proving that the number of tilings of the new regions is given by a power 2, we generalize both Aztec diamond theorem and Douglas’ theorem. The proof extends an idea of Eu and Fu for Aztec diamonds, by using a bijection between domino tilings and non-intersecting Schr¨oder paths, then applying Lindstr¨om-Gessel-Viennot methodology.
A Simple Proof For The Number Of Tilings Of Quartered Aztec Diamonds, Tri Lai
A Simple Proof For The Number Of Tilings Of Quartered Aztec Diamonds, Tri Lai
Department of Mathematics: Faculty Publications
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the number of tilings of quartered Aztec diamonds is given by simple product formulas. In this paper we present a simple proof for this result.
Downhill Domination In Graphs, Teresa W. Haynes, Stephen T. Hedetniemi, Jessie D. Jamieson, William B. Jamieson
Downhill Domination In Graphs, Teresa W. Haynes, Stephen T. Hedetniemi, Jessie D. Jamieson, William B. Jamieson
Department of Mathematics: Faculty Publications
A path π = (v1, v2, . . . , vk+1) iun a graph G = (V, E) is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi) ≥ deg(vi+1), where deg(vi) denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S …