New methods to bound the critical probability in fractal percolation

We study the critical probability p_c(M) in two‐dimensional M‐adic fractal percolation. To find lower bounds, we compare fractal percolation with site percolation. Fundamentally new is the construction of a computable increasing sequence that converges to p_c(M). We prove that and . For the upper bounds, we introduce an iterative random process on a finite alphabet , which is easier to analyze than the original process. We show that and . © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 710–730, 2015     

Spin-asymmetry in elastic scattering of low-energy electrons from ultrathin Au films on W(110)

We present joint experimental and theoretical results on the elastic scattering of spin-polarized electrons from an epitaxial Au film on a W(110) substrate in the energy range from 8 eV to 27 eV. A time-of-flight technique with a position-sensitive detector is applied to measure secondary emission spectra for spin-up and spin-down primary electrons in a specular geometry. The spin-asymmetry of coherently scattered electrons is obtained by selecting the diffraction spot on the detector. Regions of large asymmetries – with a maximum of about ?60 % – are identified for electron energies of about 14 eV. Relativistic multiple-scattering calculations produce spin-orbit-induced asymmetries which are in agreement with their experimental counterparts. They further reveal that large asymmetries are associated with high intensities. This offers the possibility of an efficient new spin polarimeter with a figure of merit of about 1.5 · 10^?2.     

Linear fractional transformations of Stieltjes functions

Linear fractional transformations of Stieltjes (and inverse Stieljes) functions, which appear naturally in the extension theory of nonnegative symmetric operators with defect one in Hilbert spaces, are investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary Relations, Unitary Colligations, and Functional Models

Recently a new notion, the so-called boundary relation, has been introduced involving an analytic object, the so-called Weyl family. Weyl families and boundary relations establish a link between the class of Nevanlinna families and unitary relations acting from one Kreĭn space, a basic (state) space, to another Kreĭn space, a parameter space where the Nevanlinna family or Weyl family is acting. Nevanlinna families are a natural generalization of the class of operator-valued Nevanlinna functions and they are closely connected with the class of operator-valued Schur functions. This paper establishes the connection between boundary relations and their Weyl families on the one hand, and unitary colligations and their transfer functions on the other hand. From this connection there are various advances which will benefit the investigations on both sides, including operator theoretic as well as analytic aspects. As one of the main consequences a functional model for Nevanlinna families is obtained from a variant of the functional model of L. de Branges and J. Rovnyak for Schur functions. Here the model space is a reproducing kernel Hilbert space in which multiplication by the independent variable defines a closed simple symmetric operator. This operator gives rise to a boundary relation such that the given Nevanlinna family is realized as the corresponding Weyl family. Received: January 21, 2008., Revised: March 31, 2008.     

Adsorption free energy of variable-charge nanoparticles to a charged surface in relation to the change of the average chemical state of the particles

Variable-charge nanoparticles such as proteins and humics can adsorb strongly to charged macroscopic surfaces such as silica and iron oxide minerals. To model the adsorption of variable-charge particles to charged surfaces, one has to be able to calculate the adsorption free energy involved. It has been shown that the change in the free energy of variable-charge particles is related to the change in their average chemical state upon adsorption, which is commonly described using surface complexation models. In this work, expressions for the free-energy change in variable-charge particles due to changes in chemical binding are derived for three ion-binding models (i.e., the Langmuir, Langmuir-Freundlich, and NICA models) and for changes due to nonspecific binding for the Donnan model. The expressions for the adsorption free energy of the variable-charge particles to a charged surface are derived on the basis of the equality of the (electro)chemical potential of the particles in the bulk solution and adsorption phase. The expressions derived are general in the sense that they account for the competition between charge-determining ions that bind chemically to the particles, and they also apply in case of the formation of chemical bonds between particle ligands and surface sites. The derived expressions can be applied in the future to model the adsorption of variable-charge nanoparticles to charged surfaces. The results obtained for the NICA-Donnan model make it possible to apply this advanced surface complexation model to describe the adsorption of humics to minerals.     

Capillary electrophoresis fingerprinting, quantification and mass-identification of various 9-aminopyrene-1,4,6-trisulfonate-derivatized oligomers derived from plant polysaccharides

Various plant polysaccharide derived mono- and oligosaccharides were derivatized with the fluorescent 9-aminopyrene-1,4,6-trisulfonate (APTS) and subjected to capillary electrophoresis (CE) in combination with laser induced fluorescence (LIF) detection. CE-LIF was suitable for mol-based quantification of various APTS-monosaccharides. CE-LIF of APTS-oligosaccharides showed high resolutions, while analysis times were at maximum 15 min. The coupling of CE to electrospray-iontrap mass spectrometery (MS) with online UV detection showed to be a powerful technique in the identification of APTS-oligosaccharides. For the first time, various APTS-xylo-oligosaccharides, having either no, O-acetyl, arabinosyl or xylosyl substitutions at varying positions, were identified by using CE-LIF and CE-MS(n).     

Influence of frictional heating on temperature gradients in ultra-high-pressure liquid chromatography on 2.1mm I.D. columns

The effects of viscous heat dissipation on some important HPLC parameters, such as efficiency (N) and retention factors (k), using 2.1mm columns at pressures up to 1000 bar have been investigated from both a theoretical and experimental point of view. Two distinct experimental set-ups and their respective influences on non-homogenous temperature gradients within the column are described and discussed. In the first instance, a still-air column heater was used. This set-up leads to approximate 'adiabatic' conditions, and a longitudinal temperature gradient is predicted across the length of the column. The magnitude of this gradient is calculated, and its occurrence confirmed with experimental measurements also indicating that no appreciable loss in efficiency occurs. Secondly, when a water bath is used to thermostat the column, a radial temperature gradient is prevalent. The extent of this gradient is estimated, and the loss in efficiency associated with this gradient is predicted and demonstrated experimentally. It is also observed that approximate adiabatic conditions can lead to floating retention factors. The implications of temperature gradients for routine HPLC analysis at ultra-high pressure are discussed.     

Solid-phase synthesis of succinylhydroxamate peptides: functionalized matrix metalloproteinase inhibitors

[reaction: see text] A novel solid-phase synthesis strategy toward succinylhydroxamate peptides, using an appropriately protected hydroxamate building block, is described. Rapid and efficient access is gained to amine-functionalized peptides, which can be decorated with, for instance, a fluorescent label. In addition, we demonstrate an on-resin synthesis of a biotinylated photoactivatable hydroxamate peptide, which can be used as an activity-based probe for matrix metalloproteinases and ADAMs.