2,634 research outputs found
Weyl group multiple Dirichlet series constructed from quadratic characters
We construct multiple Dirichlet series in several complex variables whose
coefficients involve quadratic residue symbols. The series are shown to have an
analytic continuation and satisfy a certain group of functional equations.
These are the first examples of an infinite collection of unstable Weyl group
multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment
Crystal constructions in Number Theory
Weyl group multiple Dirichlet series and metaplectic Whittaker functions can
be described in terms of crystal graphs. We present crystals as parameterized
by Littelmann patterns and we give a survey of purely combinatorial
constructions of prime power coefficients of Weyl group multiple Dirichlet
series and metaplectic Whittaker functions using the language of crystal
graphs. We explore how the branching structure of crystals manifests in these
constructions, and how it allows access to some intricate objects in number
theory and related open questions using tools of algebraic combinatorics
Metaplectic Ice
Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over
a nonarchimedean local field containing n distinct n-th roots of unity may be
expressed as the partition functions of statistical mechanical systems that are
variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika
formula this fact is related to Tokuyama's deformation of the Weyl character
formula. It is shown that various properties of these Whittaker functions may
be expressed in terms of the commutativity of row transfer matrices for the
system. Potentially these properties (which are already proved by other
methods, but very nontrivial) are amenable to proof by the Yang-Baxter
equation
Application of advanced technologies to small, short-haul aircraft
The results of a preliminary design study which investigates the use of selected advanced technologies to achieve low cost design for small (50-passenger), short haul (50 to 1000 mile) transports are reported. The largest single item in the cost of manufacturing an airplane of this type is labor. A careful examination of advanced technology to airframe structure was performed since one of the most labor-intensive parts of the airplane is structures. Also, preliminary investigation of advanced aerodynamics flight controls, ride control and gust load alleviation systems, aircraft systems and turbo-prop propulsion systems was performed. The most beneficial advanced technology examined was bonded aluminum primary structure. The use of this structure in large wing panels and body sections resulted in a greatly reduced number of parts and fasteners and therefore, labor hours. The resultant cost of assembled airplane structure was reduced by 40% and the total airplane manufacturing cost by 16% - a major cost reduction. With further development, test verification and optimization appreciable weight saving is also achievable. Other advanced technology items which showed significant gains are as follows: (1) advanced turboprop-reduced block fuel by 15.30% depending on range; (2) configuration revisions (vee-tail)-empennage cost reduction of 25%; (3) leading-edge flap addition-weight reduction of 2500 pounds
Constructing habitus: promoting an international arts trend at the Singapore Arts Festival
The Singapore Arts Festival (SAF) is Singapore’s largest government-supported international arts festival. SAF presents the best in international and local arts, in an attempt, to develop what it perceives to be a lack of cultural knowledge of the Singaporean arts-going public. Using Pierre Bourdieu’s key concept of ‘habitus’ together with an analysis of the programming of the festival, this paper will highlight how the festival seeks to create a specific cultural taste in Singaporean art-goers through privileging and promoting works that are internationally marketable to European countries. The paper will conclude that this programming style occurs at the expense of Singaporean artists and hinders the development of the city’s state cultural and artistic development
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