18,103 research outputs found
Piecewise Constant Policy Approximations to Hamilton-Jacobi-Bellman Equations
An advantageous feature of piecewise constant policy timestepping for
Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation
schemes, and indeed different meshes, can be used for the resulting linear
equations for different control parameters. Standard convergence analysis
suggests that monotone (i.e., linear) interpolation must be used to transfer
data between meshes. Using the equivalence to a switching system and an
adaptation of the usual arguments based on consistency, stability and
monotonicity, we show that if limited, potentially higher order interpolation
is used for the mesh transfer, convergence is guaranteed. We provide numerical
tests for the mean-variance optimal investment problem and the uncertain
volatility option pricing model, and compare the results to published test
cases
An Investigation of the Factor Structure of the HARVARD GROUP SCALE OF HYPNOTIC SUSCEPTIBILITY, Form A (HGSHS:A)
In order to investigate the effects of the hypnotic state a standardized hypnosis session
was conducted with 144 subjects in a controlled laboratory study. The induction of a
hypnotic trance in the German version of the Harvard Group Scale of Hypnotic Susceptibility
(HGSHS:A by Shor and Orne, 1962) was tape-recorded and used as the
treatment.
The HGSHS:A seems to be a reliable measure of suggestibility and hypnotizability. This
is underlined by the consistent results of a factor analysis on the depths of hypnosis that
is in agreement with former studies. Descriptive data analyses with a sufficient number
of subjects of high and low suggestibility suggest that our hypnosis induction by tape is
an effective method of producing a hypnotic trance. Analyses of within-subjects variables
did not reveal any valid predictors of hypnotizability, thereby confirming the need of
screening instruments such as the HGSHS
Artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane
We discuss artificial boundary conditions for stationary Navier-Stokes flows
past bodies in the half-plane, for a range of low Reynolds numbers. When
truncating the half-plane to a finite domain for numerical purposes, artificial
boundaries appear. We present an explicit Dirichlet condition for the velocity
at these boundaries in terms of an asymptotic expansion for the solution to the
problem. We show a substantial increase in accuracy of the computed values for
drag and lift when compared with results for traditional boundary conditions.
We also analyze the qualitative behavior of the solutions in terms of the
streamlines of the flow. The new boundary conditions are universal in the sense
that they depend on a given body only through one constant, which can be
determined in a feed-back loop as part of the solution process
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