301,619 research outputs found
Trade agreements with limited punishments
This paper shows that free trade can never be achieved when punishment for deviation from a trade agreement is limited to ‘a withdrawal of equivalent concessions’. This is where retaliation is not allowed to entail higher tariffs than those set by the initial deviant, and is the most severe form of punishment allowed under WTO rules. If, in addition, deviations from agreements are also limited in some way, then efficient self-enforcing tariff reductions must be gradual
On the resolution power of Fourier extensions for oscillatory functions
Functions that are smooth but non-periodic on a certain interval possess
Fourier series that lack uniform convergence and suffer from the Gibbs
phenomenon. However, they can be represented accurately by a Fourier series
that is periodic on a larger interval. This is commonly called a Fourier
extension. When constructed in a particular manner, Fourier extensions share
many of the same features of a standard Fourier series. In particular, one can
compute Fourier extensions which converge spectrally fast whenever the function
is smooth, and exponentially fast if the function is analytic, much the same as
the Fourier series of a smooth/analytic and periodic function.
With this in mind, the purpose of this paper is to describe, analyze and
explain the observation that Fourier extensions, much like classical Fourier
series, also have excellent resolution properties for representing oscillatory
functions. The resolution power, or required number of degrees of freedom per
wavelength, depends on a user-controlled parameter and, as we show, it varies
between 2 and \pi. The former value is optimal and is achieved by classical
Fourier series for periodic functions, for example. The latter value is the
resolution power of algebraic polynomial approximations. Thus, Fourier
extensions with an appropriate choice of parameter are eminently suitable for
problems with moderate to high degrees of oscillation.Comment: Revised versio
On theories of random variables
We study theories of spaces of random variables: first, we consider random
variables with values in the interval , then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type
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