Zero sequences,factorization and sampling measures for weighted Bergman spaces

The zero sets of the Bergman space \(A^p_\omega \) induced by either a radial weight \(\omega \) admitting a certain doubling property or a non-radial Bekollé-Bonami type weight are characterized in the spirit of Luecking’s results from 1996. Accurate results obtained en route to this characterization are used to generalize Horowitz’s factorization result from 1977 for functions in \(A^p_\omega \). The utility of the obtained factorization is illustrated by applications to integration and composition operators as well as to small Hankel operator induced by a conjugate analytic symbol. Dominating sets and sampling measures for the weighted Bergman space \(A^p_\omega \) induced by a doubling weight are also studied. Several open problems related to the scheme of the paper are posed.

     

The influence of shear on the dewatering of high consistency nanofibrillated cellulose furnishes

This paper demonstrates a way to utilize the rheological properties of high consistency microfibrillated and nanofibrillated cellulose (MFC and NFC) based furnishes for improved dewatering. This is relevant to a new manufacturing platform that is being developed to form composite webs from suitable mixtures of MFC or NFC, traditional pulp fibres and pigments. The studied furnishes were evaluated in the consistencies range of 5–15 % with an MCR 300 rheometer and an immobilization cell. This setup enables us to characterize the rheology of the samples before and during the dewatering process. Classical rheological methods are used to characterise MFC and NFC furnishes. Yield stress as an indicator of the flocculated network strength was found to increase with the consistencies, following the increase in elastic moduli, which indicated a gel-like strongly flocculated matrix. The shear thinning properties of furnishes are observed to follow the Oswald’s rheological model on a wide range of shear rates. It was found that when the MFC and NFC furnishes were dewatered under vacuum conditions, the final solids content was increased with application of shear. This behaviour is more pronounced for furnishes which contained the more swollen NFC (higher WRV, i.e. higher zeta potential). This effect is further exemplified by the change of the complex and dynamic viscosities during the dewatering. The shear rate, the fibre content, and the furnish consistencies were also found to influence the dewatering rate.     

Bi-Lipschitz concordance implies bi-Lipschitz isotopy

We modify the proof of an earlier result of ours to deforming topological, bi-Lipschitz, and quasiconformal embeddings of an open subsetU ofR ⁿ which now are of small uniform distance from the inclusion map. As an application we show that two bi-Lipschitz homeomorphismsf ₀,f ₁:R ⁿRⁿ are bi-Lipschitz isotopic if and only ifd(f ₀,f ₁)<.Research supported in part by a grant from the Institut Mittag-Leffler.     

Spectral control in anisotropic resonance-domain metamaterials

We introduce a concept to control the spectral and dichroic properties of metamaterials. The approach is based on anisotropic metal nanoparticles and on varying their mutual orientation in a periodic lattice. Even seemingly inconsequential changes in particle ordering strongly modify the dichroic properties of the arrays and result in either very narrow resonances or ultrabroad extinction ranges. The results arise from long-range diffractive coupling between the particles, as determined by the dependence of the array unit cell size on particle ordering.