Carleson Measures for the Bloch Space

In this paper we study the positive Borel measures μ on the unit disc in for which the Bloch space is continuously included in , 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure μ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for μ being a p-Bloch-Carleson measure. We also give a complete characterization of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p > 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator , defined by , maps continuously into the Bergman space A ¹, . Furthermore, we prove that if p > 1, α >-1 and ω is a weight which satisfies the Bekollé-Bonami -condition, then the measure defined by is a p-Bloch-Carleson-measure. We also consider the Banach space of those functions f which are analytic in and satisfy , as . The Bloch space is contained in . We describe the p-Carleson measures for and study weighted composition operators and a class of integration operators acting in this space. We determine which of these operators map continuously to the weighted Bergman space and show that they are automatically compact. This research is partially supported by several grants from “the Ministerio de Educación y Ciencia, Spain” (MTM2005-07347, MTM2007-60854, MTM2006-26627-E, MTM2007-30904-E and Ingenio Mathematica (i-MATH) No. CSD2006-00032); from “La Junta de Andalucía” (FQM210 and P06-FQM01504); from “the Academy of Finland” (210245) and from the European Networking Programme “HCAA” of the European Science Foundation.     

Poly(methyl vinyl ether‐alt‐maleic acid)‐Functionalized Porous Silicon Nanoparticles for Enhanced Stability and Cellular Internalization

Currently, developing a stable nanocarrier with high cellular internalization and low toxicity is a key bottleneck in nanomedicine. Here, we have developed a successful method to covalently conjugate poly(methyl vinyl ether‐co‐maleic acid) (PMVE‐MA) copolymer on the surface of (3‐aminopropyl)triethoxysilane‐functionalized thermally carbonized porous silicon nanoparticles (APSTCPSi NPs), forming a surface negatively charged nanovehicle with unique properties. This polymer conjugated NPs could modify surface smoothness, charge, and hydrophilicity of the developed NPs, leading to considerable improvement in the colloidal and plasma stabilities via enhanced suspensibility and charge repulsion. Furthermore, despite the surface negative charge of the polymer‐conjugated NPs, the cellular internalization was increased in both MDA‐MB‐231 and MCF‐7 breast cancer cells. These results provide a proof‐of‐concept evidence that such polymer‐based PSi nanocomposite can be extensively used as a promising candidate for intracellular drug delivery.

     

The determination of certain major and minor elements in geological samples by inductively coupled plasma atomic emission spectrometry. Some interference problems with the analysis of geological standard reference materials and nutrition supplements

Direct ICP-AES measurements of the digested geological standard reference material samples yielded the wrong information about their composition. The differences between certified and measured concentrations of the samples were due to the complicated sample matrix. The measured concentrations can be successfully corrected by using a multiple linear regression technique. The correction is based on the multiple regression line calculated from the analytical results at synthetic mixtures of matrix elements, where concentrations varied on five levels. There were no significant (P = 0.05) differences between certified and measured concentrations in standard reference materials after the correction. The same method was used in the analysis of nutrition supplements. Received: 25 January 2000 / Revised: 15 March 2000 / Accepted: 31 March 2000     

Linear differential equations with coefficients in weighted Bergman and Hardy spaces

Complex linear differential equations of the form

with coefficients in weighted Bergman or Hardy spaces are studied. It is shown, for example, that if the coefficient of belongs to the weighted Bergman space , where , for all , then all solutions are of order of growth at most , measured according to the Nevanlinna characteristic. In the case when all solutions are shown to be not only of order of growth zero, but of bounded characteristic. Conversely, if all solutions are of order of growth at most , then the coefficient is shown to belong to for all and .

Analogous results, when the coefficients belong to certain weighted Hardy spaces, are obtained. The non-homogeneous equation associated to is also briefly discussed.

     

On Strictly Convex Subsets in Negatively Curved Manifolds

In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the ??-neighbourhood of some convex subset of X, in terms of the extrinsic curvatures of the boundary of C.     

An original approach for Raman spectroscopy analysis of radioactive materials and its application to americium‐containing samples

An approach for Raman measurements of highly radioactive samples is presented here. The innovative part of this approach lies in the fact that no single part of the Raman equipment is in direct contact with the radioactive sample, as the sample is sealed in an alpha‐tight capsule. Raman analysis is effectively performed through the optical‐grade quartz window closing the capsule. This allows performing micro‐Raman measurements on radioactive samples with no limitations on the laser source wavelength, polarisation mode, spectrometer mode and microscope mode (provided the focal length of the microscope objective is greater than the thickness of the quartz window and with sub mg samples). Some example results are shown and discussed. In particular, some spectral features of americium‐containing oxide nuclear fuel specimens are presented. Raman spectra clearly reveal in these specimens the presence of abundant oxygen defects induced in the fcc fluorite lattice by trivalent americium. In order to complete the analysis the Raman spectrum of pure americium dioxide was also measured with a lower energy excitation source compared with previous research. The current results seem to be consistent with the possible occurrence of a photolysis process induced by the Raman laser, resulting in the formation of hyperstoichiometric americium sesquioxide Am₂O_{3 + z}. Such a photolytic process is deemed to be unavoidable when visible lasers are used as excitation sources for the Raman analysis of americium dioxide. © 2015 The Authors Journal of Raman Spectroscopy Published by John Wiley & Sons, Ltd.     

Finite Degree Holomorphic Covers of Compact Riemann Surfaces

A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture.     

Intermittency of energy in rapid granular shear flows

Hard-disk simulations are used for two-dimensional rapid granular shear flows of circular disks between two rotating cylinders. The intermittency effects associated with the rate of the energy dissipation of collisions are studied. The statistics of intermittent signals of energy dissipation reveals that a power law governs the dynamics of rapid shear granular flows. A dynamical system approach based on the Gledzer-Ohkitani-Yamada shell model of turbulence is employed to reproduce signals for energy dissipation that are statistically consistent with those from simulations. The results suggest that rapid granular flows can be analyzed by appropriate turbulent models.