Normality Of Very Even Nilpotent Varieties In D-2l, 2011 University of Massachusetts - Amherst

#### Normality Of Very Even Nilpotent Varieties In D-2l, E Sommers

*Eric N Sommers*

For the classical groups, Kraft and Procesi have resolved the question of which nilpotent orbits have closures that are normal and which do not, with the exception of the very even orbits in D2l that have partitions of the form (a2k, b2) for a > b even natural numbers satisfying ak + b = 2l.

B-Stable Ideals In The Nilradical Of A Borel Subalgebra, 2011 University of Massachusetts - Amherst

#### B-Stable Ideals In The Nilradical Of A Borel Subalgebra, En Sommers

*Eric N Sommers*

Let $G$G be a connected simple algebraic group over the complex numbers and $B$B a Borel subgroup. Let $\germ g$g be the Lie algebra of $G$G and $\germ b$b the Lie algebra of $B$B . A subspace of the nilradical of $\germ b$b which is stable under the action of $B$B is called a $B$B -stable ideal of the nilradical. It is called strictly positive if it intersects the simple root spaces trivially. The author counts the number of strictly positive $B$B -stable ideals in the nilradical of a Borel subalgebra ...

Exterior Powers Of The Reflection Representation In Springer Theory, 2011 University of Massachusetts - Amherst

#### Exterior Powers Of The Reflection Representation In Springer Theory, E Sommers

*Eric N Sommers*

We give a proof of a conjecture of Lehrer and Shoji regarding the occurrences of the exterior powers of the reflection representation in the cohomology of Springer fibers. The actual theorem proved is a slight extension of the original conjecture to all nilpotent orbits and also takes into account the action of the component group. The method is to use Shoji's approach to the orthogonality formulas for Green functions to relate the symmetric algebra to a sum over Green functions. In the second part of the paper we give an explanation of the appearance of the Orlik-Solomon exponents using ...

Normality Of Nilpotent Varieties In E-6, 2011 University of Massachusetts - Amherst

#### Normality Of Nilpotent Varieties In E-6, E Sommers

*Eric N Sommers*

We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [E. Sommers, Comm. Math. Univ. Sancti Pauli 49 (1) (2000) 101–104] concerning functions on non-special nilpotent orbits for E6.

Exponents For B-Stable Ideals, 2011 University of Massachusetts - Amherst

#### Exponents For B-Stable Ideals, E Sommers, J Tymoczko

*Eric N Sommers*

Let be a simple algebraic group over the complex numbers containing a Borel subgroup . Given a -stable ideal in the nilradical of the Lie algebra of , we define natural numbers which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types and some other types. When , we recover the usual exponents of by Kostant (1959), and one of our conjectures reduces to a well-known factorization of the Poincaré polynomial of the Weyl group. The other conjecture reduces to a well-known result of Arnold-Brieskorn on the factorization of the characteristic polynomial of the ...

Local Systems On Nilpotent Orbits And Weighted Dynkin Diagrams, 2011 University of Massachusetts - Amherst

#### Local Systems On Nilpotent Orbits And Weighted Dynkin Diagrams, Promad Achar, E Sommers

*Eric N Sommers*

We study the Lusztig-Vogan bijection for the case of a local system. We compute the bijection explicitly in type A for a local system and then show that the dominant weights obtained for different local systems on the same orbit are related in a manner made precise in the paper. We also give a conjecture (putatively valid for all groups) detailing how the weighted Dynkin diagram for a nilpotent orbit in the dual Lie algebra should arise under the bijection.

Pieces Of Nilpotent Cones For Classical Groups, 2011 University of Massachusetts - Amherst

#### Pieces Of Nilpotent Cones For Classical Groups, Promad Achar, Anthony Henderson, E Sommers

*Eric N Sommers*

We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$, and Kato's exotic nilpotent cone. We prove that the number of $\F_q$-points in each nilpotent orbit of type $B_n$ or $C_n$ equals that in a corresponding union of orbits, called a type-$B$ or type-$C$ piece, in the exotic nilpotent cone. This is a finer version of Lusztig's result that corresponding special pieces in types $B_n$ and $C_n$ have the same number of $\F_q$-points. The proof requires studying the case of characteristic 2, where more direct connections between the three nilpotent ...

Dark-Bright Discrete Solitons: A Numerical Study Of Existence, Stability And Dynamics, 2011 UMass, Amherst

#### Dark-Bright Discrete Solitons: A Numerical Study Of Existence, Stability And Dynamics, A. Alvarez, J. Cuevas, F. Romero, Panos Kevrekidis

*Panos Kevrekidis*

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions ...

A New Summation Formula For Wp-Bailey Pairs, 2011 West Chester University of Pennsylvania

#### A New Summation Formula For Wp-Bailey Pairs, James Mclaughlin

*Mathematics*

No abstract provided.

Quantitative Stability Of Linear Infinite Inequality Systems Under Block Perturbations With Applications To Convex Systems, 2011 Miguel Hernández University of Elche, Alicante, Spain

#### Quantitative Stability Of Linear Infinite Inequality Systems Under Block Perturbations With Applications To Convex Systems, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

*Mathematics Research Reports*

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is loo(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system ...

2011 (Spring), 2011 University of Dayton

#### 2011 (Spring), University Of Dayton. Department Of Mathematics

*Colloquia*

Abstracts of the talks given at the 2011 Spring Colloquium.

The Theory Of Discrete Fractional Calculus: Development And Application, 2011 University of Nebraska-Lincoln

#### The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm

*Dissertations, Theses, and Student Research Papers in Mathematics*

The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.

Adviser: Lynn Erbe and Allan Peterson

Hamming Codes And The Mceliece Cryptosystem, 2011 Carroll College, Helena, MT

#### Hamming Codes And The Mceliece Cryptosystem, Ben Dill

*Mathematics, Engineering and Computer Science Undergraduate Theses*

In this paper, we seek to understand some basic principles of coding theory. Specifically, we define and explore binary codes, Hamming codes, and a special application of coding theory known as the McEliece cryptosystem. We describe the meaning and usage of generator matrices and parity check matrices and present bounds on the number of codewords in codes of a given minimum distance and length. We present and prove several known results about Hamming codes, including the fact that they are necessarily perfect codes. We show how to construct a cryptosystem using any linear code and discuss the strength of the ...

A Geometric Framework For Analyzing The Performance Of Multiple-Antenna Systems Under Finite-Rate Feedback, 2011 University of Colorado at Boulder

#### A Geometric Framework For Analyzing The Performance Of Multiple-Antenna Systems Under Finite-Rate Feedback, Rajesh Tembarai Krishnamachari

*Electrical, Computer & Energy Engineering Graduate Theses & Dissertations*

We study the performance of multiple-antenna systems under finite-rate feedback of some function of the current channel realization from a channel-aware receiver to the transmitter. Our analysis is based on a novel geometric paradigm whereby the feedback information is modeled as a source distributed over a Riemannian manifold. While the right singular vectors of the channel matrix and the subspace spanned by them are located on the traditional Stiefel and Grassmann surfaces, the optimal input covariance matrix is located on a new manifold of positive semi-definite matrices - specified by rank and trace constraints - called the Pn manifold. The geometry of ...

Characterization Of Thethreshold For Nad(P)H:Quinone Oxidoreductase Activity In Intact Sulforaphane-Treated Pulmonary Arterial Endothelial Cells, 2011 Medical College of Wisconsin

#### Characterization Of Thethreshold For Nad(P)H:Quinone Oxidoreductase Activity In Intact Sulforaphane-Treated Pulmonary Arterial Endothelial Cells, Robert D. Bongard, Gary S. Krenz, Adam J. Gastonguay, Carol L. Williams, Brian J. Lindemer, Marilyn P. Merker

*Mathematics, Statistics and Computer Science Faculty Research and Publications*

Treatment of bovine pulmonary arterial endothelial cells in culture with the phase II enzyme inducer sulforaphane (5 μM, 24 h; sulf-treated) increased cell-lysate NAD(P)H:quinone oxidoreductase (NQO1) activity by 5.7 ± 0.6 (mean ± SEM)-fold, but intact-cell NQO1 activity by only 2.8 ± 0.1-fold compared to control cells. To evaluate the hypothesis that the threshold for sulforaphane-induced intact-cell NQO1 activity reflects a limitation in the capacity to supply NADPH at a sufficient rate to drive all the induced NQO1 to its maximum activity, total KOH-extractable pyridine nucleotides were measured in cells treated with duroquinone to stimulate ...

Rank One Perturbations Of Self-Adjoint Operators, 2011 University of Richmond

#### Rank One Perturbations Of Self-Adjoint Operators, Haoxuan Zheng

*Honors Theses*

No abstract provided.

Results In Lattices, Ortholattices, And Graphs, 2011 Louisiana Tech University

#### Results In Lattices, Ortholattices, And Graphs, Jianning Su

*Doctoral Dissertations*

This dissertation contains two parts: lattice theory and graph theory. In the lattice theory part, we have two main subjects. First, the class of all distributive lattices is one of the most familiar classes of lattices. We introduce "π-versions" of five familiar equivalent conditions for distributivity by applying the various conditions to 3-element antichains only. We prove that they are inequivalent concepts, and characterize them via exclusion systems. A lattice *L* satisfies D0π, if *a* ✶ (*b* ✶ *c*) ≤ (*a* ✶ *b*) ✶ *c* for all 3-element antichains {* a, b, c*}. We consider a congruence relation ∼ whose blocks are the maximal autonomous chains and ...

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science, 2011 Old Dominion University

#### Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

*Virginia Journal of Science*

Abstracts for the Astronomy, Mathematics, and Physics with Materials Science Section for the 89th Annual Meeting of the Virginia Academy of Science, May 25-27, 2011, University of Richmond, Richmond VA.

Teaching Statistics To Elementary Children: Using A Problem-Solving Approach To Enhance Learning, 2011 Rhode Island College

#### Teaching Statistics To Elementary Children: Using A Problem-Solving Approach To Enhance Learning, Kayla Lee Botelho

*Honors Projects Overview*

When teaching statistics (or data analysis) to elementary children, it is beneficial to use a problem-solving approach that incorporates meaningful tasks to enhance the students' learning. This was determined through a careful review of literature, observations of elementary teachers, and the creation and instruction of data analysis unit. The unit required the students to collect data on heights, organize the data in charts, and display the data in line plots. In addition, the students analyzed the data to recalculate the average and other measures of central tendency and to answer questions that arose through the implementation of the lessons. In ...

Phase Retrieval For Characteristic Functions Of Convex Bodies And Reconstruction From Covariograms, 2011 Università di Firenze

#### Phase Retrieval For Characteristic Functions Of Convex Bodies And Reconstruction From Covariograms, Gabriele Bianchi, Richard J. Gardner, Markus Kiederlen

*Mathematics*

The Phase Retrieval Problem of Fourier analysis involves determining a function f on Rn from the modulus |f�| of its Fourier transform f�. This problem arises naturally and frequently in various areas of science, such as X-ray crystallography, electron microscopy, optics, astronomy, and remote sensing, in which only the magnitude of the Fourier transform can be measured and the phase is lost.