21,104 research outputs found
How to project onto extended second order cones
The extended second order cones were introduced by S. Z. N\'emeth and G.
Zhang in [S. Z. N\'emeth and G. Zhang. Extended Lorentz cones and variational
inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for
solving mixed complementarity problems and variational inequalities on
cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended second
order cones. Journal of Global Optimization, 66(3):585-593, 2016] determined
the automorphism groups and the Lyapunov or bilinearity ranks of these cones.
S. Z. N\'emeth and G. Zhang in [S.Z. N\'emeth and G. Zhang. Positive operators
of Extended Lorentz cones. arXiv:1608.07455v2, 2016] found both necessary
conditions and sufficient conditions for a linear operator to be a positive
operator of an extended second order cone. This note will give formulas for
projecting onto the extended second order cones. In the most general case the
formula will depend on a piecewise linear equation for one real variable which
will be solved by using numerical methods
On the spherical convexity of quadratic functions
In this paper we study the spherical convexity of quadratic functions on
spherically convex sets. In particular, conditions characterizing the spherical
convexity of quadratic functions on spherical convex sets associated to the
positive orthants and Lorentz cones are given
Faceted anomalous scaling in the epitaxial growth of semiconductor films
We apply the generic dynamical scaling theory (GDST) to the surfaces of CdTe
polycrystalline films grown in glass substrates. The analysed data were
obtained with a stylus profiler with an estimated resolution lateral resolution
of m. Both real two-point correlation function and power spectrum
analyses were done. We found that the GDST applied to the surface power spectra
foresees faceted morphology in contrast with the self-affine surface indicated
by the local roughness exponent found via the height-height correlation
function. This inconsistency is explained in terms of convolution effects
resulting from the finite size of the probe tip used to scan the surfaces. High
resolution AFM images corroborates the predictions of GDST.Comment: to appear in Europhysics Letter
Transition on the entropic elasticity of DNA induced by intercalating molecules
We use optical tweezers to perform stretching experiments on DNA molecules
when interacting with the drugs daunomycin and ethidium bromide, which
intercalate the DNA molecule. These experiments are performed in the low-force
regime from zero up to 2 pN. Our results show that the persistence length of
the DNA-drug complexes increases strongly as the drug concentration increases
up to some critical value. Above this critical value, the persistence length
decreases abruptly and remains practically constant for larger drug
concentrations. The contour length of the molecules increases monotonically and
saturates as drugs concentration increases. Measured in- tercalants critical
concentrations for the persistence length transition coincide with reported
values for the helix-coil transition of DNA-drug complexes, obtained from
sedimentation experiments.Comment: This experimental article shows and discuss a transition observed in
the persistence length of DNA molecules when studied as a function of some
intercalating drug concentrations, like daunomycin and ethidium bromide. It
has 15 pages and 4 figures. The article presented here is in preprint forma
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