21,315 research outputs found
On the enumeration of closures and environments with an application to random generation
Environments and closures are two of the main ingredients of evaluation in
lambda-calculus. A closure is a pair consisting of a lambda-term and an
environment, whereas an environment is a list of lambda-terms assigned to free
variables. In this paper we investigate some dynamic aspects of evaluation in
lambda-calculus considering the quantitative, combinatorial properties of
environments and closures. Focusing on two classes of environments and
closures, namely the so-called plain and closed ones, we consider the problem
of their asymptotic counting and effective random generation. We provide an
asymptotic approximation of the number of both plain environments and closures
of size . Using the associated generating functions, we construct effective
samplers for both classes of combinatorial structures. Finally, we discuss the
related problem of asymptotic counting and random generation of closed
environemnts and closures
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
Inverse scattering of Canonical systems and their evolution
In this work we present an analogue of the inverse scattering for Canonical
systems using theory of vessels and associated to them completely integrable
systems. Analytic coefficients fits into this setting, significantly expanding
the class of functions for which the inverse scattering exist. We also derive
an evolutionary equation, arising from canonical systems, which describes the
evolution of the logarithmic derivative of the tau function, associated to
these systemsComment: arXiv admin note: substantial text overlap with arXiv:1303.532
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