On zonoids whose polars are zonoids

Zonoids whose polars are zonoids cannot have proper faces other than vertices or facets. However, there exist non-smooth zonoids whose polars are zonoids. Examples in ℝ and ℝ are given. Supported in part by the United States-Israel Binational Science Foundation.     

The crystal structure of the inorganic surface films formed on Mg and Li intercalation compounds and the electrode performance

A crystallographic approach was applied to elucidate the influence of the nature of the surface films on the electrochemical behavior of Li and Mg intercalation compounds. This paper presents two examples: (1) protection of graphite electrodes by Li₂CO₃ surface films, and (2) the unique electrochemical behavior of Mg-containing Chevrel phases (MgCP) obtained by different synthetic routes. In the former case, the elucidation of the protection mechanism and the explanation of the high performance of such protected electrodes are based on the analysis of possible Li-ion motion in the carbonate crystal structure. In the latter case, a combination of synthesis, electrochemistry and XRD analysis was used to explain an unusual phenomenon: the difference between the excellent electrochemical behavior of the Chevrel phase (CP) based on Cu-leached Cu₂Mo₆S₈ (CuCP), and the poor electrochemical activity of the high-temperature synthesized MgCP, with the same phase composition. It is shown that this phenomenon is caused by MgO formation on the surface of the latter material. The different surface chemistry of the MgCPs obtained by the two different synthetic routes was substantiated by revealing the correlation between the electrochemical activity and the chemical stability of these materials under ambient atmosphere conditions. Dedicated to Prof. Mikhail A. Vorotyntsev on the occasion of his 60th birthday.     

Self-avoiding walks on random fractal environments

Self-avoiding random walks (SAWs) are studied on several hierarchical lattices in a randomly disordered environment. An analytical method to determine whether their fractal dimensionD _saw is affected by disorder is introduced. Using this method, it is found that for some lattices,D _saw is unaffected by weak disorder; while for othersD _saw changes even for infinitestimal disorder. A weak disorder exponent is defined and calculated analytically [ measures the dependence of the variance in the partition function (or in the effective fugacity per step)vL on the end-to-end distance of the SAW,L]. For lattices which are stable against weak disorder (<0) a phase transition exists at a critical valuev=v ^* which separates weak- and strong-disorder phases. The geometrical properties which contribute to the value of are discussed.     

Amplified DNA sensing and immunosensing by the rotation of functional magnetic particles

Amplified chemiluminescent detection of DNA-complementary DNA or of antigen-antibody interactions is accomplished in the presence of rotating functionalized magnetic particles.     

Growth of ZIF-8 MOF Films with Tunable Porosity by using Poly (1-vinylimidazole) Brushes as 3D Primers

This work reports on a novel and versatile approach to control the structure of metal–organic framework (MOFs) films by using polymeric brushes as 3D primers, suitable for triggering heterogeneous MOF nucleation. As a proof-of-concept, this work explores the use of poly(1-vinylimidazole) brushes primer obtained via surface-initiated atom transfer radical polymerization (SI-ATRP) for the synthesis of Zn-based ZIF-8 MOF films. By modifying the grafting density of the brushes, smooth porous films were obtained featuring inherently hydrophobic microporosity arising from ZIF-8 structure, and an additional constructional interparticle mesoporosity, which can be employed for differential adsorption of targeted adsorbates. It was found that the grafting density modulates the constructional porosity of the films obtained; higher grafting densities result in more compact structures, while lower grafting density generates increasingly inhomogeneous films with a higher proportion of interparticle constructional porosity.     

Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

${?}_{t}u?\mathrm{?}?({(u?z)}^{\alpha }|\mathrm{?}u{|}^{\gamma ?1}\mathrm{?}u)=f$

are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.     

Studies of the Synthesis of Diethyl Cyclopropylphosphonate and Its Thio and Seleno Analogs

Two methods for the synthesis of unsubstituted diethyl cyclopropylphosphonate are described. One method is a reaction between cyclopropylmagnesium bromide and diethyl chlorophosphite to give diethyl cyclopropylphosphonite, followed by oxidation with sodium periodate to the corresponding phosphonate. Alternatively, diethyl cyclopropylphosphonite was reacted with elemental sulfur or selenium to give the thio and seleno analogs, respectively. The second method involves exclusive 1,3‐elimination of HBr from diethyl 3‐bromopropylphosphonate. This method can be directed to either the 1,2‐ or the 1,3‐elimination reaction, leading to propenylphosphonate or cyclopropylphosphonate, depending on the solvent used.     

2D difference gel electrophoresis reference map of a Fusarium graminearum nivalenol producing strain

Fusarium graminearum is widely studied as a model for toxin production among plant pathogenic fungi. A 2D DIGE reference map for the nivalenol‐producing strain 453 was established. Based on a whole protein extract, all reproducible spots were systematically picked and analyzed by MALDI‐TOF/TOF, leading to the identification of 1102 protein species. The obtained map contributes to the annotation of the genome by identifying previously nondescribed hypothetical proteins and will serve as a reference for future studies aiming at deciphering F. graminearum biology and chemotype diversity.