11,949 research outputs found
The Schwartz algebra of an affine Hecke algebra
For a general affine Hecke algebra H we study its Schwartz completion S. The
main theorem is an exact description of the image of S under the Fourier
isomorphism. An important ingredient in the proof of this result is the
definition and computation of the constant terms of a coefficient of a
generalized principal series representation. Finally we discuss some
consequences of the main theorem for the theory of tempered representations of
H
A two-axis laser boresight system for a shuttle experiment
A two-axis gimballed laser pointing mechanism is being developed for the Lidar In-space Technology Experiment (LITE) to be flown on the National Space Transportation System (NSTS) Space Shuttle in February 1993. This report describes the design requirements and goals, the configuration, analysis, and testing plans for this laser pointing device
The Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory
Fractional Brownian motion is a non-Markovian Gaussian process , indexed
by the Hurst exponent . It generalises standard Brownian motion
(corresponding to ). We study the probability distribution of the
maximum of the process and the time at which the maximum is
reached. They are encoded in a path integral, which we evaluate perturbatively
around a Brownian, setting . This allows us to derive
analytic results beyond the scaling exponents. Extensive numerical simulations
for different values of test these analytical predictions and show
excellent agreement, even for large .Comment: 5 pages, 7 figure
Continuants and some decompositions into squares
In 1855 H. J. S. Smith proved Fermat's two-square using the notion of
palindromic continuants. In his paper, Smith constructed a proper
representation of a prime number as a sum of two squares, given a solution
of , and vice versa. In this paper, we extend the use of
continuants to proper representations by sums of two squares in rings of
polynomials on fields of characteristic different from 2. New deterministic
algorithms for finding the corresponding proper representations are presented.
Our approach will provide a new constructive proof of the four-square theorem
and new proofs for other representations of integers by quaternary quadratic
forms.Comment: 21 page
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