An Erdős–Fuchs theorem for ordered representation functions

The Ramanujan Journal - Let $$k\ge 2$$ be a positive integer. We study concentration results for the ordered representation functions $$r^{{ \le }}_k({\mathcal {A}},n) = \# \big \{ (a_1 \le \dots...     

Wharton-fragmentation-based approach to the carbocyclic core of the phomoidrides

The carbocyclic core of the phomoidrides has been synthesized efficiently and in high yield. Key steps include a phenolic oxidation/intramolecular Diels-Alder sequence, tandem radical cyclization, and a late-stage Wharton fragmentation of a densely functionalized isotwistane skeleton.     

Layer thickness of hydrophobin films leads to oscillation in wettability

In nanobiotechnology, the properties of surfaces are often key to sensor applications. If analytes possess a low tolerance or affinity regarding the sensory substrate (surface), then the setup of mediators may be indicated. Hydrophobins enable biocompatible surface functionalization without significant restrictions of the physicochemical substrate properties. Because of the imperfect formation of hydrophobin films, a high variation in surface properties is observed. In this study, we report on the relation between the film thickness of hydrophobin-coated solid surfaces and their wettability. We found that the wettability of protein-coated surfaces strictly depends on the amount of adsorbed protein, as reflected in an oscillation of the contact angles of hydrophobin-coated silicon wafers. Fusion proteins of Ccg2 and HFBI, representatives of class I and II hydrophobins, document the influence of fused peptide tags on the wettability. The orientation of the first crystal nuclei plays a decisive role in the formation of the growing hydrophobin layers. Here, a simple method of deducing the film thickness of hydrophobin assemblies on solid surfaces is presented. The determination of the static contact angle allows the prediction of which part of the protein is exposed to possible analytes.     

Local Growth Envelopes of Triebel-Lizorkin Spaces of Generalized Smoothness

The concept of local growth envelope of the quasi-normed function space is applied to the Triebel-Lizorkin spaces of generalized smoothness In order to achieve this, a standardization result for these and corresponding Besov spaces is derived.     

Capillary electrophoresis of affinity complexes between subviral 80S particles of human rhinovirus and monoclonal antibody 2G2

Human rhinoviruses (HRVs), the main etiologic agents of the common cold, transform into subviral B- or 80S particles (they sediment at 80S upon sucrose density gradient centrifugation) during infection and, in vitro, upon exposure to a temperature between 50 and 56 degrees C. With respect to the native virion they lack the genomic RNA and the viral capsid protein VP4. 80S particles are unstable and easily disintegrate into their components, VP1, VP2, and VP3 in buffers containing SDS. However, this detergent was found to be a necessary constituent of the BGE for the analysis of these viruses and their complexes with receptors and antibodies by CE. We here demonstrate that dodecylpoly(ethyleneglycol ether) (D-PEG) a nonionic detergent, is suitable for analysis of subviral particles as it preserves their integrity, in contrast to SDS. Electrophoresis of the 80S particles in borate buffer (pH 8.3, 100 mM) containing 10 mM D-PEG resulted in a well-defined electrophoretic peak. The identity of the peak was confirmed, among other means, by complexation with mAb 2G2, which recognizes a structural epitope exclusively present on subviral particles but not on native virus. Upon incubation of the 80S particles with mAb 2G2 the peak disappeared, but a new peak, attributed to the antibody complex emerged. The separation system allowed following the time course of the transformation of intact HRV serotype 2 into 80S particles upon incubation at temperatures between 40 and 65 degrees C. We also demonstrate that subviral particles derived from HRV2 labeled with the fluorescence dyes FITC or Cy3.5 were stable in the separation system containing D-PEG. Dye-modified particles were still recognized by mAb 2G2, suggesting that the exposed lysines that are derivatized by the reagent do not form part of the epitope of the antibody.     

An oligomer-based approach to skeletal diversity in small-molecule synthesis

Access to small molecules of widely varying molecular shapes has been identified as an enabling step in the discovery of biologically active materials. In this communication we introduce an approach to the systematic development of architecturally distinct chemical compounds based upon the assembly of reactive monomers into linear oligomers, each of which encodes a unique molecular framework under a common set of reaction conditions. Certain products of the initial chemical transformation (Ru-catalyzed metathesis reaction) encode additional skeletons upon treatment with a second common set of reagents (Diels-Alder dienophiles). Application of this oligomerization approach has led to the discovery of a previously unreported tandem ene-yne-yne metathesis-6pi-electrocyclization-1,5-hydride migration that converts a linear substrate into a complex tricyclic 1,3-diene in a single step. Thus, the reported strategy might serve not only as a generator of skeletally diverse small molecules but also as a discovery platform for the identification of novel chemical transformations.     

Reconstruction of the density field using the Colored Background Oriented Schlieren Technique (CBOS)

In this paper the improved Background Oriented Schlieren technique called CBOS (Colored Background Oriented Schlieren) is described and used to reconstruct density fields of three-dimensional flows. The Background Oriented Schlieren technique (BOS) allows to measure the light deflection caused by density gradients in a compressible flow. For this purpose the local image displacements of the image of a background pattern observed through the flow is used. In order to increase the performance of the conventional Background Oriented Schlieren technique, the monochromatic background is replaced by a colored dot pattern. The different colors are treated separately using suitable correlation algorithms. Therefore, the accuracy and the spatial resolution can be increased. A tomographic reconstruction method is then used to reconstruct the density field in three-dimensional flows from CBOS measurements.     

Holographic and photoelectric characterization of a novel photorefractive organic glass

We present a detailed study of the photoelectric as well as the holographic properties of a novel organic photorefractive glass based on triphenylamine. We studied the quantum efficiency Φ of the photogeneration of charges by means of photoinduced discharge measurements. The photoconductivity σ and the charge carrier mobility μ were obtained via dc photoconduction and pulsed time-of-flight experiments, respectively. The holographic characterization was performed by two-wave and degenerate four-wave mixing experiments allowing for the determination of properties such as diffraction efficiency η, modulation of the refractive index Δn, gain coefficient Γ, and phase-shift φ_p of the investigated system. The experimental data for Φ could be successfully described by the Onsager formalism with a thermalization radius of r₀=24 ? and a primary quantum yield of Φ₀=40%. We evaluated the E field and temperature-dependent measurements of μ using the B?ssler formalism yielding a width of the density of states of σ=0.13 eV and a disorder parameter Σ=3.6. On this basis the lifetime and the average drift length of the charge carriers could be estimated from the dc photoconduction experiments. From the photoelectric measurements we also calculated the holographic response time that matched very well to the measured response time and described the E-field dependence satisfactorily. The presented photorefractive system shows outstanding optical properties and stability with respect to degradation. We measured a gain coefficient of Γ=90 cm^-1, and a diffraction efficiency of η=27% at a response time of 30 ms for only 40-μm-thick samples. Orientational enhancement was observed and evaluated quantitatively. To our knowledge, this work presents the first determination of each of the above quantities all in one single organic photorefractive material. Received: 16 November 1998 / Revised version: 4 January 1999 / Published online: 31 March 1999