43,791 research outputs found
Vanishing Results for Hall-Littlewood Polynomials
No full textIt is well-known that if one integrates a Schur function indexed by a partition λ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of λ have even multiplicity (resp. all parts of λ are even). In a recent work of Rains and Vazirani, Macdonald polynomial generalizations of these identities and several others were developed and proved using Hecke algebra techniques. However at q=0 (the Hall-Littlewood level), these approaches do not directly work; this obstruction was the motivation for this thesis. We investigate three related projects in chapters 2-4 (the first chapter consists of an introduction to the thesis). In the second chapter, we develop a combinatorial technique for proving the results of Rains and Vazirani at q=0. This approach allows us to generalize some of those results in interesting ways and leads us to a finite-dimensional analog of a recent result of Warnaar, involving the Rogers-Szego polynomials. In the third chapter, we provide a new construction for Koornwinder polynomials at q=0, allowing these polynomials to be viewed as Hall-Littlewood polynomials of type BC. This is a first step in building the analogy between the Macdonald and Koornwinder families at the q=0 limit. We use this construction in conjunction with the combinatorial technique of the previous chapter to prove some vanishing results of Rains and Vazirani for Koornwinder polynomials at q=0. In the fourth chapter, we provide an interpretation for vanishing results for Hall-Littlewood polynomials using p-adic representation theory; it is an analog of the Schur case. This p-adic approach allows us to generalize our original vanishing results. In particular, we exhibit a t-analog of a classical vanishing result for Schur functions due to Littlewood and Weyl; our vanishing condition is in terms of Hall polynomials and Littlewood-Richardson coefficients
Tobin's Q and Financial Policy
No full textRecent research in macroeconomics has emphasized the importance of linking the financial and real sectors and the need for working with optimizing models. Tobin’s Q model of investment would appear to provide a framework that can satisfy these two criteria. In contrast to the original presentation of the Q model, the formal development has not recognized that the firm actively participates in a number of financial markets; in this broader context, we show that Q is likely to be an uninformative and possibly misleading signal for investment expenditures . We then endeavor to turn this negative theoretical result to positive advantage in resolving a number of empirical problems with Q models, but the modifications dictated by the theory receive little support from the data.
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
No full textWe introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers.
This study is motivated by their key role in the (reciprocal) expansion of any power of a second order
q-differential operator having the q-classical polynomials as eigenfunctions in terms of other even order operators,
which we explicitly construct in this work. The results here obtained can be viewed as the q-version of
those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a
q-version of the Jacobi–Stirling numbers given by Gelineau and the second author
Parallel simplex benchmarking results
No full textData used to generate results in "Parallelizing the dual revised simplex method" http://www.maths.ed.ac.uk/hall/HuHa13/, a copy of which is attached
Dr Dean Kenning is a Research Fellow in The School of Fine Art at Kingston University. He is also a writer and an artist, most recently writing about art education. We interviewed him at the Royal Festival Hall, London.
No full textInterview with Q-Arts on Professional Practice in Fine Ar
[USF President] Virtual Town Hall
No full textCampus-wide email from the Office of the President reminding the community of the virtual town hall meeting that will occur over Zoom on June 23, 2020
The universal factorial Hall-Littlewood - and -functions
No full textIn this paper, we introduce {\it factorial} analogues of the ordinary
Hall--Littlewood - and -polynomials, which we call the {\it factorial
Hall--Littlewood - and -polynomials}. Using the {\it universal} formal
group law, we further generalize these polynomials to the {\it universal
factorial Hall--Littlewood - and -functions}.
We show that these functions satisfy the {\it vanishing property} which the
ordinary factorial Schur -, -, and -polynomials have. By the vanishing
property, we derive the Pieri-type formula and a certain generalization of the
classical hook formula.
We then characterize our functions in terms of Gysin maps from flag bundles
in the complex cobordism theory. Using this characterization and Gysin formulas
for flag bundles, we can obtain generating functions for the universal
factorial Hall--Littlewood - and -functions. Using our generating
functions, we can show that our factorial Hall--Littlewood - and
-polynomials have a certain {\it cancellation property}.
Further applications such as Pfaffian formulas for -theoretic factorial
-polynomials are also given.Comment: 27 pages, AMSLaTeX; We totally revised the manuscript, focusing on
the introduction of the universal factorial Hall--Littlewood P- and
Q-functions and their basic properties. (Title has been changed slightly
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Network Q
No full textA press release from Network Q announcing that they will begin featuring Brian McNaught, a gay columnist and author, for a monthly segment
Network Q
No full textA press release from Network Q announcing that they will begin featuring Brian McNaught, a gay columnist and author, for a monthly segment
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