981 research outputs found
H\"older Regularity of Geometric Subdivision Schemes
We present a framework for analyzing non-linear -valued
subdivision schemes which are geometric in the sense that they commute with
similarities in . It admits to establish
-regularity for arbitrary schemes of this type, and
-regularity for an important subset thereof, which includes all
real-valued schemes. Our results are constructive in the sense that they can be
verified explicitly for any scheme and any given set of initial data by a
universal procedure. This procedure can be executed automatically and
rigorously by a computer when using interval arithmetics.Comment: 31 pages, 1 figur
Least Squares Approximation of Bezier Coefficients provides Best Degree Reduction in the L 2-Norm
Feasibility of intraventricular administration of etoposide in patients with metastatic brain tumours
As the systemic administration of etoposide is effective in the treatment of relapsed and metastatic brain tumours, a pilot trial was designed to study the feasibility of intraventricular administration of etoposide in such patients. 14 patients aged 2.1 to 33.2 years were treated with intraventricular etoposide simultaneously with either oral or intravenous chemotherapy with trofosfamide or carboplatin and etoposide. In 59 courses (1–12/patient) 0.5 mg etoposide was administered daily via an indwelling subcutaneous reservoir for 5 consecutive days every 2–5 weeks over a period of 0–11 months. During 15 courses in 5 patients serial CSF samples were obtained and etoposide levels were determined by reversed-phase HPLC. Side effects included transient headache and bacterial meningitis, each during 2 courses. Pharmacokinetic data analysis in the CSF (11 courses, 4 patients) revealed a terminal half-life of 7.4±1.2 hours and an AUC of 25.0 ± 9.5 μg h ml–1(mean ± standard deviation). The volume of distribution at steady state and total clearance exhibited a large interindividual variability with mean values of 0.16 l and 0.46 ml min–1respectively. Intraventricularly administered etoposide is well tolerated. CSF peak levels exceed more than 100-fold those achieved with intravenous infusions. Further studies should be focused on optimizing the dose and schedule and on determining the effectiveness of intraventricularly administered etoposide. © 2001 Cancer Research Campaign http://www.bjcancer.co
Quantum Interactive Proofs with Competing Provers
This paper studies quantum refereed games, which are quantum interactive
proof systems with two competing provers: one that tries to convince the
verifier to accept and the other that tries to convince the verifier to reject.
We prove that every language having an ordinary quantum interactive proof
system also has a quantum refereed game in which the verifier exchanges just
one round of messages with each prover. A key part of our proof is the fact
that there exists a single quantum measurement that reliably distinguishes
between mixed states chosen arbitrarily from disjoint convex sets having large
minimal trace distance from one another. We also show how to reduce the
probability of error for some classes of quantum refereed games.Comment: 13 pages, to appear in STACS 200
Extraction of shear viscosity in stationary states of relativistic particle systems
Starting from a classical picture of shear viscosity we construct a
stationary velocity gradient in a microscopic parton cascade. Employing the
Navier-Stokes ansatz we extract the shear viscosity coefficient . For
elastic isotropic scatterings we find an excellent agreement with the analytic
values. This confirms the applicability of this method. Furthermore for both
elastic and inelastic scatterings with pQCD based cross sections we extract the
shear viscosity coefficient for a pure gluonic system and find a good
agreement with already published calculations.Comment: 17 pages, 7 figure
Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach
We study the effects of dissipation and decoherence induced on a harmonic
oscillator by the coupling to a chaotic system with two degrees of freedom.
Using the Feynman-Vernon approach and treating the chaotic system
semiclassically we show that the effects of the low dimensional chaotic
environment are in many ways similar to those produced by thermal baths. The
classical correlation and response functions play important roles in both
classical and quantum formulations. Our results are qualitatively similar to
the high temperature regime of the Caldeira-Leggett model.Comment: 31 pages, 4 figure
Electronic Theory for the Nonlinear Magneto-Optical Response of Transition-Metals at Surfaces and Interfaces: Dependence of the Kerr-Rotation on Polarization and on the Magnetic Easy Axis
We extend our previous study of the polarization dependence of the nonlinear
optical response to the case of magnetic surfaces and buried magnetic
interfaces. We calculate for the longitudinal and polar configuration the
nonlinear magneto-optical Kerr rotation angle. In particular, we show which
tensor elements of the susceptibilities are involved in the enhancement of the
Kerr rotation in nonlinear optics for different configurations and we
demonstrate by a detailed analysis how the direction of the magnetization and
thus the easy axis at surfaces and buried interfaces can be determined from the
polarization dependence of the nonlinear magneto-optical response, since the
nonlinear Kerr rotation is sensitive to the electromagnetic field components
instead of merely the intensities. We also prove from the microscopic treatment
of spin-orbit coupling that there is an intrinsic phase difference of
90 between tensor elements which are even or odd under magnetization
reversal in contrast to linear magneto-optics. Finally, we compare our results
with several experiments on Co/Cu films and on Co/Au and Fe/Cr multilayers. We
conclude that the nonlinear magneto-optical Kerr-effect determines uniquely the
magnetic structure and in particular the magnetic easy axis in films and at
multilayer interfaces.Comment: 23 pages Revtex, preprintstyle, 2 uuencoded figure
Restricted random walk model as a new testing ground for the applicability of q-statistics
We present exact results obtained from Master Equations for the probability
function P(y,T) of sums of the positions x_t of a discrete
random walker restricted to the set of integers between -L and L. We study the
asymptotic properties for large values of L and T. For a set of position
dependent transition probabilities the functional form of P(y,T) is with very
high precision represented by q-Gaussians when T assumes a certain value
. The domain of y values for which the q-Gaussian apply
diverges with L. The fit to a q-Gaussian remains of very high quality even when
the exponent of the transition probability g(x)=|x/L|^a+p with 0<p<<1 is
different from 1, all though weak, but essential, deviation from the q-Gaussian
does occur for . To assess the role of correlations we compare the T
dependence of P(y,T) for the restricted random walker case with the equivalent
dependence for a sum y of uncorrelated variables x each distributed according
to 1/g(x).Comment: 5 pages, 7 figs, EPL (2011), in pres
Magnetization switching in a Heisenberg model for small ferromagnetic particles
We investigate the thermally activated magnetization switching of small
ferromagnetic particles driven by an external magnetic field. For low uniaxial
anisotropy the spins can be expected to rotate coherently, while for sufficient
large anisotropy they should behave Ising-like, i.e., the switching should then
be due to nucleation. We study this crossover from coherent rotation to
nucleation for the classical three-dimensional Heisenberg model with a finite
anisotropy. The crossover is influenced by the size of the particle, the
strength of the driving magnetic field, and the anisotropy. We discuss the
relevant energy barriers which have to be overcome during the switching, and
find theoretical arguments which yield the energetically favorable reversal
mechanisms for given values of the quantities above. The results are confirmed
by Monte Carlo simulations of Heisenberg and Ising models.Comment: 8 pages, Revtex, 11 Figures include
Quantum fields in disequilibrium: neutral scalar bosons with long-range, inhomogeneous perturbations
Using Schwinger's quantum action principle, dispersion relations are obtained
for neutral scalar mesons interacting with bi-local sources. These relations
are used as the basis of a method for representing the effect of interactions
in the Gaussian approximation to field theory, and it is argued that a marked
inhomogeneity, in space-time dependence of the sources, forces a discrete
spectrum on the field. The development of such a system is characterized by
features commonly associated with chaos and self-organization (localization by
domain or cell formation). The Green functions play the role of an iterative
map in phase space. Stable systems reside at the fixed points of the map. The
present work can be applied to self-interacting theories by choosing suitable
properties for the sources. Rapid transport leads to a second order phase
transition and anomalous dispersion. Finally, it is shown that there is a
compact representation of the non-equilibrium dynamics in terms of generalized
chemical potentials, or equivalently as a pseudo-gauge theory, with an
imaginary charge. This analogy shows, more clearly, how dissipation and entropy
production are related to the source picture and transform a flip-flop like
behaviour between two reservoirs into the Landau problem in a constant
`magnetic field'. A summary of conventions and formalism is provided as a basis
for future work.Comment: 23 pages revte
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