Haar wavelets of higher order on fractals and regularity of functions

Wavelets of Haar type of higher order m on self-similar fractals were introduced by the author in J. Fourier Anal. Appl. 4 (1998) 329-340. These are piecewise polynomials of degree m instead of piecewise constants. It was shown that for certain totally disconnected fractals, spaces of functions defined on the fractal may be characterized by means of the magnitude of the wavelet coefficients of the functions. In this paper, the study of these wavelets is continued. It is shown that also in the case when the fractals are not totally disconnected, the wavelets can be used to study regularity properties of functions. In particular, the self-similar sets considered can be, e.g., an interval in or a cube in . It turns out that it is natural to use Haar wavelets of higher order also in these classical cases, and many of the results in the paper are new also for these sets.     

Protein adsorption onto silica nanoparticles: conformational changes depend on the particles' curvature and the protein stability

We have analyzed the adsorption of protein to the surfaces of silica nanoparticles with diameters of 6, 9, and 15 nm. The effects upon adsorption on variants of human carbonic anhydrase with differing conformational stabilities have been monitored using methods that give complementary information, i.e., circular dichroism (CD), nuclear magnetic resonance (NMR), analytical ultracentrifugation (AUC), and gel permeation chromatography. Human carbonic anhydrase I (HCAI), which is the most stable of the protein variants, establishes a dynamic equilibrium between bound and unbound protein following mixture with silica particles. Gel permeation and AUC experiments indicate that the residence time of HCAI is on the order of approximately 10 min and slowly increases with time, which allows us to study the effects of the interaction with the solid surface on the protein structure in more detail than would be possible for a process with faster kinetics. The effects on the protein conformation from the interaction have been characterized using CD and NMR measurements. This study shows that differences in particle curvature strongly influence the amount of the protein's secondary structure that is perturbed. Particles with a longer diameter allow formation of larger particle-protein interaction surfaces and cause larger perturbations of the protein's secondary structure upon interaction. In contrast, the effects on the tertiary structure seem to be independent of the particles' curvature.     

Long-time-storage mechanism for Tm:YAG in a magnetic field

We obtained a long-time-storage mechanism for spectral features in thulium ions doped into YAG by applying a magnetic field that splits the electronic ground state. We show experimentally that the storage time can be more than 30 s, which is 3 orders of magnitude longer than that of the metastable state that normally is used for information storage in this material. Level splitting and storage lifetimes for various magnetic field strengths of as much as 5 T were investigated. This storage mechanism will be relevant in the many coherent transient-based signal-processing schemes in which Tm:YAG is being used, and we demonstrate long-time storage in a basic data storage application.     

Accelerating cosmologies from compactification

A solution of the (4+n)-dimensional vacuum Einstein equations is found for which spacetime is compactified on an n-dimensional compact hyperbolic manifold (n> or =2) of time-varying volume to a flat four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmology undergoing a period of accelerated expansion in the Einstein conformal frame. This shows that the "no-go" theorem forbidding acceleration in "standard" (time-independent) compactifications of string or M theory does not apply to "cosmological" (time-dependent) hyperbolic compactifications.     

Sorption of Pu(VI) onto TiO2

The sorption of Pu(VI) onto TiO(2) was studied as a function of pH (2-10) and Pu concentration (10(-8)-10(-4) M) under an N(2) atmosphere, in 0.016 and 0.1 M NaClO(4). A batch-wise method was used, in which pH was measured in separate experimental containers after removal of a sample to determine the amount of Pu that had been sorbed. As Pu is radioactive, it was used as a tracer and measured by liquid scintillation counting. No ionic strength dependence was discerned, which was taken as an indication of inner sphere complex formation. In the interval of pH 2-7 the system could be described by the formation of two positively charged surface complexes using a 1-pK Stern model. Sorption of the plutonyl ion (PuO(2)(2+)) and the first hydrolysis species (PuO(2)(OH)(+)) was estimated using FITEQL to logK(1)=6.9 and logK(2)=1.4, respectively.     

Obtaining the bidirectional transmittance distribution function of isotropically scattering materials using an integrating sphere

This paper demonstrates a method to determine the bidirectional transmittance distribution function (BTDF) using an integrating sphere. Information about the sample’s angle-dependent scattering is obtained by making transmittance measurements with the sample at different distances from the integrating sphere. Knowledge about the illuminated area of the sample and the geometry of the sphere port in combination with the measured data combines to a system of equations that includes the angle-dependent transmittance.The resulting system of equations is an ill-posed problem which rarely gives a physical solution. A solvable system is obtained by using Tikhonov regularization on the ill-posed problem. The solution to this system can then be used to obtain the BTDF.Four bulk-scattering samples were characterised using two goniophotometers and the described method to verify the validity of the new method. The agreement shown is excellent for the more diffuse samples. The solution to the low-scattering samples contains unphysical oscillations, but still gives the correct shape of the solution. The origin of the oscillations and why they are more prominent in low-scattering samples are discussed.     

Ornstein-Zernike theory for the planar random surface model

We prove that the two-loop function in the planar random surface (PRS) model has Ornstein-Zernike decay for all noncritical values of the temperature. A notion of breathing is introduced and it is shown that surfaces do not breathe at noncritical temperatures. With the aid of a simple assumption, supported by mean field theory and numerical calculations, we prove that the scaling limit of the PRS-model exists and equals that of a free field.     

Zur analytischen Chemie der Barbiturs?ureschlafmittel

Ohne Zusammenfassung     

Diffusion of Loops

We study a lattice model that is closely related to the Ising model and can be regarded as describing diffusion of loops in two dimensions. The time development is given by a transfer matrix for a random surface model on a three-dimensional lattice. The transfer matrix is indexed by loops and is invariant under a group of motions in the loop space. The eigenvalues of the transfer matrix are calculated in terms of the partition function and the correlation functions of the Ising model.