UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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2004 - 20102

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    Equivariant Giambelli Formulae for Grassmannians
    (2010) Wilson, Elizabeth McLaughlin; Tamvakis, Harry; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In this thesis we use Young's raising operators to define and study polynomials which represent the Schubert classes in the equivariant cohomology ring of Grassmannians. For the type A and maximal isotropic Grassmannians, we show that our expressions coincide with the factorial Schur S, P, and Q functions. We define factorial theta polynomials, and conjecture that these represent the Schubert classes in the equivariant cohomology of non-maximal symplectic Grassmannians. We prove that the factorial theta polynomials satisfy the equivariant Chevalley formula, and that they agree with the type C double Schubert polynomials of [IMN] in some cases.
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    Sigma Delta Modulation and Correlation Criteria for the Construction of Finite Frames Arising in Communication Theory
    (2004-04-29) Kolesar, Joseph Dennis; Benedetto, John J; Mathematics
    In this dissertation we first consider a problem in analog to digital (A/D) conversion. We compute the power spectra of the error arising from an A/D conversion. We then design various higher dimensional analogs of A/D schemes, and compare these schemes to a standard error diffusion scheme in digital halftoning. Secondly, we study finite frames. We classify certain finite frames that are constructed as orbits of a group. These frames are seen to have subtle symmetry properties. We also study Grassmannian frames which are frames with minimal correlation. Grassmannian frames have an important intersection with spherical codes, erasure channel models, and communication theory. This is the main part of the dissertation, and we introduce new theory and algorithms to decrease the maximum frame correlation and hence construct specific examples of Grassmannian frames. A connection has been drawn between the two parts of this thesis, namely A/D conversion and finite frames. In particular, finite frames are used to expand vectors in $\RR^d$, and then different quantization schemes are applied to the coefficients of these expansions. The advantage is that all possible outcomes of quantization can be considered because of the finite dimensionality.