354 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
The impact of suspension control on the controllability of the lateral vehicle dynamics
International audienceSince there is a coupling between lateral and vertical dynamics, the interactions between control components must be taken into consideration. The paper presents the effects of vertical load variations on the controlled invariant set of the steering system. In the model the nonlinear characteristics of the tire force are approximated by the polynomial form. The analysis is based on Sum-of-Squares programming method and parameter-dependent polynomial control Lyapunov functions. The Maximum Controlled Invariant Sets of the steering as a function of vertical loads are illustrated through a simulation example. The results of the analysis are built into the control design of the suspension system. A semi-active suspension system using preview control is applied. The operation of the controller is illustrated through simulation examples
Orbital Magnetism in Ensembles of Parabolic Potentials
We study the magnetic susceptibility of an ensemble of non-interacting
electrons confined by parabolic potentials and subjected to a perpendicular
magnetic field at finite temperatures. We show that the behavior of the average
susceptibility is qualitatively different from that of billiards. When averaged
over the Fermi energy the susceptibility exhibits a large paramagnetic response
only at certain special field values, corresponding to comensurate classical
frequencies, being negligible elsewhere. We derive approximate analytical
formulae for the susceptibility and compare the results with numerical
calculations.Comment: 4 pages, 4 figures, REVTE
An outline of an asymmetric two-component theory of aspect
The paper presents the bases of an asymmetric two-component model of aspect. The main theoretical conclusion of the study is that (grammatical) viewpoint aspect and situation aspect are not independent aspectual levels, since the former often modifies the input situation aspect of the phrase/sentence. As it is shown, besides the arguments and adjuncts of the predicate, viewpoint aspect is also an important factor in compositionally marking situation aspect. The aspectual framework put forward in the paper is verified and illustrated on the basis of the aspectual system of Hungarian and some examples taken from English linguistic data
Regular dendritic patterns induced by non-local time-periodic forcing
The dynamic response of dendritic solidification to spatially homogeneous
time-periodic forcing has been studied. Phase-field calculations performed in
two dimensions (2D) and experiments on thin (quasi 2D) liquid crystal layers
show that the frequency of dendritic side-branching can be tuned by oscillatory
pressure or heating. The sensitivity of this phenomenon to the relevant
parameters, the frequency and amplitude of the modulation, the initial
undercooling and the anisotropies of the interfacial free energy and molecule
attachment kinetics, has been explored. It has been demonstrated that besides
the side-branching mode synchronous with external forcing as emerging from the
linear Wentzel-Kramers-Brillouin analysis, modes that oscillate with higher
harmonic frequencies are also present with perceptible amplitudes.Comment: 15 pages, 23 figures, Submitted to Phys. Rev.
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