3,012 research outputs found
Normalizations of Eisenstein integrals for reductive symmetric spaces
We construct minimal Eisenstein integrals for a reductive symmetric space G/H
as matrix coefficients of the minimal principal series of G. The Eisenstein
integrals thus obtained include those from the \sigma-minimal principal series.
In addition, we obtain related Eisenstein integrals, but with different
normalizations. Specialized to the case of the group, this wider class includes
Harish-Chandra's minimal Eisenstein integrals.Comment: 66 pages. Minor revisions. To be published in Journal of Functional
Analysi
-invariant cusp forms for reductive symmetric spaces of split rank one
Let be a reductive symmetric space of split rank and let be a
maximal compact subgroup of . In a previous article the first two authors
introduced a notion of cusp forms for . We show that the space of cusp
forms coincides with the closure of the -finite generalized matrix
coefficients of discrete series representations if and only if there exist no
-spherical discrete series representations. Moreover, we prove that every
-spherical discrete series representation occurs with multiplicity in
the Plancherel decomposition of .Comment: 12 page
Gas phase polymerization of ethylene with a silica-supported metallocene catalyst: influence of temperature on deactivation
Ethylene was polymerized at 5 bar in a stirred powder bed reactor with silica supported rac-Me2Si[Ind]2ZrCl2/methylaluminoxane (MAO) at temperatures between 40°C and 80°C using NaCl as support bed and triethylaluminium (TEA) as a scavenger for impurities. For this fixed recipe and a given charge of catalyst. the average catalyst activity is reproducible within 10% for low temperatures. The polymerization rate and the rate of deactivation increase with increasing temperature. The deactivation could be modeled using a first order dependence with respect to the polymerization rate
Discrete Breathers in One-Dimensional Diatomic Granular Crystals
We report the experimental observation of discrete breathers in a
one-dimensional diatomic granular crystal composed of compressed elastic beads
that interact via Hertzian contact. We first characterize their effective
linear spectrum both theoretically and experimentally. We then illustrate
theoretically and numerically the modulational instability of the lower edge of
the optical band. This leads to the dynamical formation of long-lived breather
structures, whose families of solutions we compute throughout the linear
spectral gap. Finally, we observe experimentally such localized breathing modes
with quantitative characteristics that agree with our numerical results.Comment: 5 pages, 4 figure
Correction of blink artifacts using independent component analysis and empirical mode decomposition.
Blink-related ocular activity is a major source of artifacts in electroencephalogram (EEG) data. Independent component analysis (ICA) is a well-known technique for the correction of such ocular artifacts, but one of the limitations of ICA is that the ICs selected for removal contain not only ocular activity but also some EEG activity. Straightforward removal of these ICs might, therefore, lead to a loss of EEG data. In this article a method is proposed to separate blink-related ocular activity from actual EEG by combining ICA with a novel technique, empirical mode decomposition. This combination of two techniques allows for maximizing the retention of EEG data and the selective removal of the eyeblink artifact. The performance of the proposed method is demonstrated with simulated and real data
Emulsification in binary liquids containing colloidal particles: a structure-factor analysis
We present a quantitative confocal-microscopy study of the transient and
final microstructure of particle-stabilised emulsions formed via demixing in a
binary liquid. To this end, we have developed an image-analysis method that
relies on structure factors obtained from discrete Fourier transforms of
individual frames in confocal image sequences. Radially averaging the squared
modulus of these Fourier transforms before peak fitting allows extraction of
dominant length scales over the entire temperature range of the quench. Our
procedure even yields information just after droplet nucleation, when the
(fluorescence) contrast between the two separating phases is scarcely
discernable in the images. We find that our emulsions are stabilised on
experimental time scales by interfacial particles and that they are likely to
have bimodal droplet-size distributions. We attribute the latter to coalescence
together with creaming being the main coarsening mechanism during the late
stages of emulsification and we support this claim with (direct)
confocal-microscopy observations. In addition, our results imply that the
observed droplets emerge from particle-promoted nucleation, possibly followed
by a free-growth regime. Finally, we argue that creaming strongly affects
droplet growth during the early stages of emulsification. Future investigations
could clarify the link between quench conditions and resulting microstructure,
paving the way for tailor-made particle-stabilised emulsions from binary
liquids.Comment: http://iopscience.iop.org/0953-8984/22/45/455102
Sorting with Teams
We fully solve a sorting problem with heterogeneous firms and multiple
heterogeneous workers whose skills are imperfect substitutes. We show that
optimal sorting, which we call mixed and countermonotonic, is comprised of two
regions. In the first region, mediocre firms sort with mediocre workers and
coworkers such that the output losses are equal across all these teams
(mixing). In the second region, a high skill worker sorts with low skill
coworkers and a high productivity firm (countermonotonicity). We characterize
the equilibrium wages and firm values. Quantitatively, our model can generate
the dispersion of earnings within and across US firms
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