Class groups of quadratic fields of 3-rank at least 2: Effective bounds

In this paper, we give parametric families of both real and complex quadratic number fields whose class group has 3-rank at least 2. As a consequence, we obtain that for all large positive real numbers x, the number of both real and complex quadratic fields whose class group has 3-rank at least 2 and absolute value of the discriminant ?x is >cx1/3, where c is some positive constant.     

A note on cycle spectra of line graphs

We show that line graphs G=L(H) with σ₂(G)≥7 contain cycles of all lengths k, 2rad(H)+1≤k≤c(G). This implies that every line graph of such a graph with 2rad(H)≥Δ(H) is subpancyclic, improving a recent result of Xiong and Li. The bound on σ₂(G) is best possible.     

Microstructure and Defect Characterization of Nanostructured Ni3Al

 Nanostructured Ni₃Al was produced by the inert gas condensation and in situ compaction technique and characterized by means of high-resolution transmission electron microscopy (HRTEM), X-ray diffraction, and density measurements. The defect structure was investigated using positron annihilation lifetime spectroscopy (PALS). It is shown that in some samples besides the cubic also the martensitic phase can be present. The defect structure can be divided into three major components: vacancy-like defects in the grain boundaries and nano-voids with a size of 1 nm as seen with PALS, and large pores with sizes up to 8 nm as seen with HRTEM. Furthermore, it is shown that an increasing compaction temperature leads to significantly smaller nano-voids.     

Claw‐free 3‐connected P11‐free graphs are hamiltonian

We show that every 3‐connected claw‐free graph which contains no induced copy of P₁₁ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of P₁₂ this result is, in a way, best possible. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 111–121, 2004     

Remarks on my paper: packing of incongruent circles on the sphere

The paper [3] contains an upper bound to the weighted density of a packing of circles on the unit sphere with radii from a given finite set. This bound is attained by many packings and has applications to problems of solidity. In the present note it is shown that a certain condition imposed on the set of admissible radii can be removed by modifying the original proof of the theorem.     

Material Discrimination in Nanoparticle Hetero-Aggregates by Analysis of Scanning Transmission Electron Microscopy Images

Hetero-contacts are interfaces between different materials at the nanoscale leading to novel functional properties. In hetero-aggregates, primary particles of at least two different materials are mixed at primary particle or cluster level. Double flame spray pyrolysis (DFSP) is a versatile technique for the controlled synthesis of such materials. Characterization of hetero-aggregates by scanning transmission electron microscopy (STEM) requires acquisition and evaluation of many aggregate images in order to derive statistically significant results. Usually, STEM energy dispersive X-ray spectroscopy (EDXS) is used to acquire elemental maps providing the material distribution of the primary particles within hetero-aggregates. However, the acquisition of a single EDXS map takes up to several minutes. For this reason, determination of material types of primary particles from the intensity in high-angle annular dark field STEM images alone is desirable. These images can be acquired within a couple of seconds. In the present work, a method is suggested which allows for achieving this objective. It can be applied to distinguish materials with a significant difference in their atomic number and hence sufficient material contrast in the STEM images.     

Covalent Protein Labeling by Enzymatic Phosphocholination

We present a new protein labeling method based on the covalent enzymatic phosphocholination of a specific octapeptide amino acid sequence in intact proteins. The bacterial enzyme AnkX from Legionella pneumophila has been established to transfer functional phosphocholine moieties from synthetically produced CDP‐choline derivatives to N‐termini, C‐termini, and internal loop regions in proteins of interest. Furthermore, the covalent modification can be hydrolytically removed by the action of the Legionella enzyme Lem3. Only a short peptide sequence (eight amino acids) is required for efficient protein labeling and a small linker group (PEG‐phosphocholine) is introduced to attach the conjugated cargo.     

Controlled Light‐Mediated Preparation of Gold Nanoparticles by a Norrish Type I Reaction of Photoactive Polymers

Gold nanoparticles (AuNPs) are subjects of broad interest in scientific community due to their promising physicochemical properties. Herein we report the facile and controlled light‐mediated preparation of gold nanoparticles through a Norrish type I reaction of photoactive polymers. These carefully designed polymers act as reagents for the photochemical reduction of gold ions, as well as stabilizers for the in situ generated AuNPs. Manipulating the length and composition of the photoactive polymers allows for control of AuNP size. Nanoparticle diameter can be controlled from 1.5 nm to 9.6 nm.     

Differentiation between Shallow and Deep Charge Trap States on Single Poly(3‐hexylthiophene) Chains through Fluorescence Photon Statistics

Blinking of the photoluminescence (PL) emitted from individual conjugated polymer chains is one of the central observations made by single‐molecule spectroscopy (SMS). Important information, for example regarding excitation energy transfer, can be extracted by evaluating dynamic quenching. However, the nature of trap states, which are responsible for PL quenching, often remains obscured. We present a detailed investigation of the photon statistics of single poly(3‐hexylthiophene) (P3HT) chains obtained by SMS. The photon statistics provide a measure of the number and brightness of independently emitting areas on a single chain. These observables can be followed during blinking. A decrease in PL intensity is shown to be correlated with either 1) a decrease in the average brightness of the emitting sites; or 2) a decrease in the number of emitting regions. We attribute these phenomena to the formation of 1) shallow charge traps, which can weakly affect all emitting areas of a single chain at once; and 2) deep traps, which have a strong effect on small regions within the single chains.