767 research outputs found
Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix
The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a
matrix with columns that form an orthonormal basis for a subspace \X, and
a Hermitian matrix , the eigenvalues of are called Ritz values of
with respect to \X. If the subspace \X is -invariant then the Ritz
values are some of the eigenvalues of . If the -invariant subspace \X
is perturbed to give rise to another subspace \Y, then the vector of absolute
values of changes in Ritz values of represents the absolute eigenvalue
approximation error using \Y. We bound the error in terms of principal angles
between \X and \Y. We capitalize on ideas from a recent paper [DOI:
10.1137/060649070] by A. Knyazev and M. Argentati, where the vector of absolute
values of differences between Ritz values for subspaces \X and \Y was
weakly (sub-)majorized by a constant times the sine of the vector of principal
angles between \X and \Y, the constant being the spread of the spectrum of
. In that result no assumption was made on either subspace being
-invariant. It was conjectured there that if one of the trial subspaces is
-invariant then an analogous weak majorization bound should only involve
terms of the order of sine squared. Here we confirm this conjecture.
Specifically we prove that the absolute eigenvalue error is weakly majorized by
a constant times the sine squared of the vector of principal angles between the
subspaces \X and \Y, where the constant is proportional to the spread of
the spectrum of . For many practical cases we show that the proportionality
factor is simply one, and that this bound is sharp. For the general case we can
only prove the result with a slightly larger constant, which we believe is
artificial.Comment: 12 pages. Accepted to SIAM Journal on Matrix Analysis and
Applications (SIMAX
Renormalization of hole-hole interaction at decreasing Drude conductivity
The diffusion contribution of the hole-hole interaction to the conductivity
is analyzed in gated GaAs/InGaAs/GaAs heterostructures. We show
that the change of the interaction correction to the conductivity with the
decreasing Drude conductivity results both from the compensation of the singlet
and triplet channels and from the arising prefactor in the
conventional expression for the interaction correction.Comment: 6 pages, 5 figure
Electric fields in plasmas under pulsed currents
Electric fields in a plasma that conducts a high-current pulse are measured
as a function of time and space. The experiment is performed using a coaxial
configuration, in which a current rising to 160 kA in 100 ns is conducted
through a plasma that prefills the region between two coaxial electrodes. The
electric field is determined using laser spectroscopy and line-shape analysis.
Plasma doping allows for 3D spatially resolved measurements. The measured peak
magnitude and propagation velocity of the electric field is found to match
those of the Hall electric field, inferred from the magnetic-field front
propagation measured previously.Comment: 13 pages, 13 figures, submitted to PR
Cross-frequency coupling of brain oscillations in studying motivation and emotion
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in unraveling the workings of the human brain and its functions. In this review we provide evidence that studying interdependencies between brain oscillations may be a valuable approach to study the electrophysiological processes associated with motivation and emotional states. Studies will be presented showing that amplitude-amplitude coupling between delta-alpha and delta-beta oscillations varies as a function of state anxiety and approach-avoidance-related motivation, and that changes in the association between delta-beta oscillations can be observed following successful psychotherapy. Together these studies suggest that cross-frequency coupling of brain oscillations may contribute to expanding our understanding of the neural processes underlying motivation and emotion
Investigation of spherical and cylindrical Luneburg lens antennas by Green's function method
Luneburg lens antenna radiation fields are calculated with Green's functions of spherical and cylindrical layered structures. Electric field components for Luneburg lenses excited by a linear and circular polarized antenna are analyzed. Co-polarized and cross-polarized field radiation patterns are shown. Reflection from the lens, losses in the lens material, spillover and polarization loss are taken into account for antenna gain calculation. The proposed method significantly reduces computing time for multilayered lens in comparison with the most commonly used in antenna design. © 2015 Radio Society (Mauritius)
Spin-splitting in the quantum Hall effect of disordered GaAs layers with strong overlap of the spin subbands
With minima in the diagonal conductance G_{xx} and in the absolute value of
the derivative |dG_{xy}/dB| at the Hall conductance value G_{xy}=e^{2}/h,
spin-splitting is observed in the quantum Hall effect of heavily Si-doped GaAs
layers with low electron mobility 2000 cm^2/Vs in spite of the fact that the
spin-splitting is much smaller than the level broadening. Experimental results
can be explained in the frame of the scaling theory of the quantum Hall effect,
applied independently to each of the two spin subbands.Comment: 4 pages, 4 figure
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