On a new class of dynamic Hardy-type inequalities and some related generalizations

Aequationes mathematicae - In this paper, we establish a new class of dynamic inequalities of Hardy’s type which generalize and improve some recent results given in the literature. More...     

Dual catalytic performance of arene-ruthenium amine complexes for norbornene ring-opening metathesis and methyl methacrylate atom-transfer radical polymerizations

Arene ruthenium(II) complexes bearing the cyclic amines RuCl₂(η⁶-p-cymene)(pyrrolidine)] ( 1 ), [RuCl₂(η⁶-p-cymene)(piperidine)] ( 2 ), and [RuCl₂(η⁶-p-cymene)(peridroazepine)] ( 3 ) were successfully synthesized. Complexes 1 – 3 were fully characterized by means of Fourier transform infrared, UV–visible, and NMR spectroscopy, elemental analysis, cyclic voltammetry, computational methods, and one of the complexes was further studied by single crystal X-ray crystallography. These compounds were evaluated as catalytic precursors for ring-opening metathesis polymerization (ROMP) of norbornene (NBE) and atom-transfer radical polymerization (ATRP) of methyl methacrylate (MMA). NBE polymerization via ROMP was evaluated using complexes 1 – 3 as precatalysts in the presence of ethyl diazoacetate (EDA) under different [NBE]/[EDA]/[Ru] ratios, temperatures (25 and 50°C), and reaction times (5–60 min). The highest yields of polyNBE were obtained with [NBE]/[EDA]/[Ru] = 5000/28/1 for 60 min at 50°C. MMA polymerization via ATRP was conducted using 1 – 3 as catalysts in the presence of ethyl-α-bromoisobutyrate (EBiB) as initiator. The catalytic tests were evaluated as a function of the reaction time using the initial molar ratio of [MMA]/[EBiB]/[Ru] = 1000/2/1 at 95°C. The increase in molecular weight as function of time indicates that complexes 1–3 were able to mediate the MMA polymerization with an acceptable rate and some level of control. Differences in the rate of polymerization were observed in the order 3 > 2 > 1 for the ROMP and ATRP.     

Erratum: The average degree of an edge-chromatic critical graph II

In the article “The average degree of an edge-chromatic critical graph II” by Douglas R. Woodall (J. Graph Theory 56 (2007), 194-218), it was claimed that the average degree of an edge-chromatic critical graph with maximum degree $\mathrm{\Delta }$ is at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+1\right)$ if $\mathrm{\Delta }⩾2$, at least $\text{◂+▸}\frac{2}{3}\mathrm{\Delta }+1$ if $\mathrm{\Delta }⩾8$, and at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+2\right)$ if $\mathrm{\Delta }⩾15$. Unfortunately there were mistakes in the proof of the last two of these results, which are now proved only if $\mathrm{\Delta }⩾18$ and $\mathrm{\Delta }⩾30$, respectively.     

Temperature Effects on the Fracture Dynamics and Elastic Properties of Popgraphene Membranes

Popgraphene (PopG) is a new 2D planar carbon allotrope which is composed of 5–8–5 carbon rings. PopG is intrinsically metallic and possesses excellent thermal and mechanical stability. In this work, we report a detailed study of the thermal effects on the mechanical properties of PopG membranes using fully-atomistic reactive (ReaxFF) molecular dynamics simulations. Our results showed that PopG presents very distinct fracture mechanisms depending on the temperature and direction of the applied stretching. The main fracture dynamics trends are temperature independent and exhibit an abrupt rupture followed by fast crack propagation. The reason for this anisotropy is due to the fact that y-direction stretching leads to a deformation in the shape of the rings that cause the breaking of bonds in the pentagon-octagon and pentagon-pentagon ring connections, which is not observed for the x-direction. PopG is less stiff than graphene membranes, but the Young's modulus value is only 15 % smaller.     

Kinetic model for Ostwald's rule of stages with applications to Boc-diphenylalanine self-assembly

A kinetic model which describes Ostwald's rule of stages, during the process of crystal growth from solution, is reported here. Reaction equations for stages are given where the stages convert from one to another. The final stage reacts to release a portion of solute back into solution, while the remainder converts to the final equilibrium form. Additionally, a remnant of the solute that was not consumed by any of the transitional stages, ultimately is converted into the final product. This particular model was motivated by a recent report for Boc-diphenylalanine self-assembly where the dissolved peptide was observed to go through two polymorphic stages before reaching the equilibrium supramolecular assembly [A. Levin et al., Nat. Commun. 5, 5219, (2014)]. Kinetic data for the concentration of solute present during the process are listed in the above-mentioned report. We show here how the model, for , describes the time-dependent behavior of the solute decay during the growth process. After comparing the model to the experimental data, we are able to report values for all of the rate constants and propose a rule whereby the relative magnitudes of these constants can be used to predict whether a supersaturated substance will noticeably pass through transitional stages or simply convert from solute to the equilibrium solid form.     

Aspartate‐Based CXCR4 Chemokine Receptor Binding of Cross‐Bridged Tetraazamacrocyclic Copper(II) and Zinc(II) Complexes

The CXCR4 chemokine receptor is implicated in a number of diseases including HIV infection and cancer development and metastasis. Previous studies have demonstrated that configurationally restricted bis‐tetraazamacrocyclic metal complexes are high‐affinity CXCR4 antagonists. Here, we present the synthesis of Cu²⁺ and Zn²⁺ acetate complexes of six cross‐bridged tetraazamacrocycles to mimic their coordination interaction with the aspartate side chains known to bind them to CXCR4. X‐ray crystal structures for three new Cu²⁺ acetate complexes and two new Zn²⁺ acetate complexes demonstrate metal‐ion‐dependent differences in the mode of binding the acetate ligand concomitantly with the requisite cis‐V‐configured cross‐bridged tetraazamacrocyle. Concurrent density functional theory molecular modelling studies produced an energetic rationale for the unexpected [Zn(OAc)(H₂O)]⁺ coordination motif present in all of the Zn²⁺ cross‐bridged tetraazamacrocycle crystal structures, which differs from the chelating acetate [Zn(OAc)]⁺ structures of known unbridged and side‐bridged tetraazamacrocyclic Zn²⁺‐containing CXCR4 antagonists.