829 research outputs found
Doug O’Donnell
No full textAuthor, professor and church planter Doug O\u27Donnell brings a message on on Luke 7
Workshop with Doug Buehl
No full textDoug Buehl is a teacher, author, and national literacy consultant. He is the author of the national bestseller Classroom Strategies for Interactive Learning, 4th Edition, 2014, and Developing Readers in the Academic Disciplines, 2011. He is co-author of Reading and the High School Student: Strategies to Enhance Literacy, 2nd Edition, 2007; and Strategies to Enhance Literacy and Learning in Middle School Content Area Classrooms 3rd Edition, 2007
Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces
No full textThis paper is a sequel to [Caine A., Pickrell D., Int. Math. Res. Not., to appear, arXiv:0710.4484], where we studied the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. In this paper we consider loop space analogues. Many of the results extend in a relatively routine way to the loop space setting, but new issues emerge. The main point of this paper is to spell out the meaning of the results, especially in the SU(2) case. Applications include integral formulas and factorizations for Toeplitz determinants
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Factorization in unitary loop groups and reduced words in affine Weyl groups.
No full textThe purpose of this dissertation is to elaborate, with specific examples and calculations, on a new refinement of triangular factorization for the loop group of a simple, compact Lie group K, first appearing in Pickrell & Pittman-Polletta 2010. This new factorization allows us to write a smooth map from the unit circle into K (having a triangular factorization) as a triply infinite product of loops, each of which depends on a single complex parameter. These parameters give a set of coordinates on the loop group of K.The order of the factors in this refinement is determined by an infinite sequence of simple generators in the affine Weyl group associated to K, having certain properties. The major results of this dissertation are examples of such sequences for all the classical Weyl groups.We also produce a variation of this refinement which allows us to write smooth maps from the unit circle into the special unitary group of n by n matrices as products of 2n+1 infinite products. By analogy with the semisimple analog of our factorization, we suggest that this variation of the refinement has simpler combinatorics than that appearing in Pickrell & Pittman-Polletta 2010
Dr. Doug Hicks – Faculty Author Interview
No full textThe Podcasts@Boatwright debut author is Dr. Doug Hicks, associate professor of leadership studies and religion and executive director of the Bonner Center for Civic Engagement. His new book, With God on All Sides: Leadership in a Devout and Diverse America, describes how our various religious traditions can help build common ground in America and how leaders can and should deal with religious diversity
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Werner's Measure on Self-Avoiding Loops and Representations of the Virasoro Algebra
No full textWerner has proven the existence and essential uniqueness of a conformally invariant family of locally-finite measures on self-avoiding loops on Riemann surfaces. The measures can be thought of as self-avoiding loop analogues of Schramm-Loewner evolution with parameter κ=8/3. This family is determined by a single measure on (normalized) holomorphic univalent functions on the unit disk. We will devise an algorithm for calculating moments of their Taylor coefficients. And in special cases, we can present closed-form solutions. Essentially, our algorithm arises as a consequence of non-degeneracy for a newly-realized family of highest-weight representations of the Virasoro algebra (we provide an explicit isomorphism between these representations and those constructed by Kirillov and Yuriev). Moreover, our algorithm leads to an alternate proof of essential uniqueness of Werner's family, as first seen in the author's joint work with Douglas Pickrell. Kontsevich and Suhov have conjectured the existence and essential uniqueness of a one-parameter deformation of Werner's family to a family of measures having values in powers of determinant line bundles (the deformation parameter is given by the real parameter κ satisfying 0 ≤ κ ≤ 4). Benoist and Dubédat recently proved the existence part of this conjecture for κ=2. We will provide an outline of how the argument for the Werner case can be adapted to prove the uniqueness part of Kontsevich and Suhov's conjecture
Inaugural address : January 5, 2015
No full textabstract: Gov. Doug Ducey promised "serious reform" of Arizona's public schools in an inaugural address in which he repeated a commitment to limited government. Arizona's 23rd governor struck an optimistic and determined
tone, noting the state's imminent budget deficit but promising it, and other challenges, are "entirely within our power to overcome.
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The c-function for affine Kac-Moody algebras
No full textIn this paper, we will first study the Harish-Chandra transform and the c-function for finite type Kac-Moody groups. The Harish-Chandra transform is essentially the Gelfand transform on L¹( K\G/K). From our point of view, the c-function arises as the Fourier transform of the diagonal distribution for Haar measures of K. A brief account of Kac-Moody algebras, especially affine Kac-Moody algebras, is also presented. Then we use a formula of Harish-Chandra for the c-function for finite type Kac-Moody groups to discuss the definition of the c-function for affine Kac-Moody algebras, especially the twisted affine Kac-Moody algebras. It turns out the c-function for an affine Kac-Moody algebra can be written as a product of trigonometric functions over the positive roots of the corresponding finite type Kac-Moody algebra. This finite type Kac-Moody algebra is the Lie algebra of a finite type Kac-Moody group G. Then the c-function can be thought as the Fourier transform of the diagonal distribution for a Haar type measure of G. For the affine Kac-Moody algebra of type A⁽¹⁾₁ , G is SL(2, C) and the measure is (trace(g* g))⁻³. This leads to the question of whether (trace( g* g))⁻ᵐ on SL(n, C) is that measure for the affine Kac-Moody algebra of type A⁽¹⁾(n-1). In the last part, for any positive integer l, the Harish-Chandra transform of (trace(g* g) ⁻⁽⁽ⁿ⁽ⁿ⁻¹⁾⁾/²⁾⁻¹ on SL(n, C) is calculated to check if the Fourier transform of the diagonal distribution for (trace(g* g) ⁻⁽⁽ⁿ⁽ⁿ⁻¹⁾⁾/²⁾⁻¹ is the c-function for the affine Kac-Moody algebra of type A⁽¹⁾(n-1).This item was digitized from a paper original and/or a microfilm copy. If you need higher-resolution images for any content in this item, please contact us at [email protected] file replaced with corrected file October 2023
On Campus Video, Featuring Doug Manning.
No full textA videorecording of an interview with author, lecturer, and counselor Doug Manning, conducted by Dr. Gary McCaleb of Abilene Christian University in 1984. Manning discusses the topics of grief, marriage, and self-esteem
Loops in SU(2) and factorization
No full textAbstractWe discuss analytic issues associated with a refinement of triangular factorization for the loop group of SU(2). This factorization is of interest because (1) Toeplitz determinants factor in the associated coordinates, and (2) the factorization is intimately related to the critical degree of smoothness for loops, W1/2,L2
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