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

KK-invariant cusp forms for reductive symmetric spaces of split rank one

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms coincides with the closure of the $K$-finite generalized matrix coefficients of discrete series representations if and only if there exist no $K$-spherical discrete series representations. Moreover, we prove that every $K$-spherical discrete series representation occurs with multiplicity $1$ in the Plancherel decomposition of $G/H$.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