The Patterson–Sullivan Embedding and Minimal Volume Entropy for Outer Space

Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map from the Culler–Vogtmann outer space CV (F _k ) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding and thus obtain a new compactification of the outer space. We also prove that for every k ≥ 2 the minimum of the volume entropy of the universal covers of finite connected volume-one metric graphs with fundamental group of rank k and without degree-one vertices is equal to (3k − 3) log 2 and that this minimum is realized by trivalent graphs with all edges of equal lengths, and only by such graphs. Received: December 2005, Accepted: March 2006     

Enhanced coupling of subterahertz radiation with semiconductor periodic slot arrays

In this work, a theoretical study of the coupling of TM polarized subterahertz (THz) radiation with periodic semiconductor rectangular slot arrays was conducted, using InSb as an example. Simulation results showed that the structure with 4-12 microm thickness provides over a 20-30-fold increase in the electric field at slot edges in a nanosize region ( approximately 500 nm). The enhancement of the THz electromagnetic field extends across the slots and reaches peak values at the edges due to discontinuity effects. Because of the strong local electromagnetic field enhancement, the structure can potentially be used for the development of novel biophotonic sensors, leading to improved detection sensitivity.     

Copper‐Mediated Formation of Aryl,Heteroaryl, Vinyl and Alkynyl Difluoromethylphosphonates: A General Approach to Fluorinated Phosphate Mimics

A general and efficient access to aryl, heteroaryl, vinyl and alkynyl difluoromethylphosphonates is described. The developed methodology using TMSCF₂PO(OEt)₂, iodonium salts and a copper salt provided a straightforward manifold to reach these highly relevant products. The reaction proved to be highly functional group tolerant and proceeded under mild conditions, giving the corresponding products in good to excellent yields. This method represents the first general synthetic route to this important class of fluorinated scaffolds, which are well‐recognized as in vivo stable phosphate surrogates.     

Influence of Ag+ on the Magnetic Response of [2.2.2]Paracyclophane: NMR Properties of a Prototypical Organic Host for Cation Binding Based on DFT Calculations

The complexation of metal cations into a host–guest situation is particularly well exemplified by [2.2.2]paracyclophane and Ag^I, which leads to a strong cation–π interaction with a specific face of the host molecule. Through this study we sought a deeper understanding of the effects the metal center has on the NMR spectroscopic properties of the prototypical organic host, generating theoretical reasons for the observed experimental results with an aim to determine the role of the cation–π interaction in a host–guest scenario. From an analysis of certain components of the induced magnetic field and the ¹³C NMR shielding tensor under its own principal axis system (PAS), the local and overall magnetic behavior can be clearly described. Interestingly, the magnetic response of such a complex exhibits a large axis-dependent behavior, which leads to an overall shielding effect for the coordinating carbon atoms and a deshielding effect for the respective uncoordinated counterparts, evidence that complements previous experimental results. This proposed approach can be useful to gain further insight into the local and overall variation of NMR shifts for host–guest pairs involving both inorganic and organic hosts.     

Mechanism of proteolysis in matrix metalloproteinase‐2 revealed by QM/MM modeling

The mechanism of enzymatic peptide hydrolysis in matrix metalloproteinase‐2 (MMP‐2) was studied at atomic resolution through quantum mechanics/molecular mechanics (QM/MM) simulations. An all‐atom three‐dimensional molecular model was constructed on the basis of a crystal structure from the Protein Data Bank (ID: 1QIB), and the oligopeptide Ace‐Gln‐Gly～Ile‐Ala‐Gly‐Nme was considered as the substrate. Two QM/MM software packages and several computational protocols were employed to calculate QM/MM energy profiles for a four‐step mechanism involving an initial nucleophilic attack followed by hydrogen bond rearrangement, proton transfer, and C? N bond cleavage. These QM/MM calculations consistently yield rather low overall barriers for the chemical steps, in the range of 5–10 kcal/mol, for diverse QM treatments (PBE0, B3LYP, and BB1K density functionals as well as local coupled cluster treatments) and two MM force fields (CHARMM and AMBER). It, thus, seems likely that product release is the rate‐limiting step in MMP‐2 catalysis. This is supported by an exploration of various release channels through QM/MM reaction path calculations and steered molecular dynamics simulations. © 2015 Wiley Periodicals, Inc.     

Thermal analysis of heat-treated silver fir wood and larval frass

Glasses having composition 5Li₂O–5ZnO– xBi₂O₃ –(90 ? x) P₂O₅ (x = 5, 10, 15, 20 and 25 mol%) were prepared by the normal melt quenching technique. Nanocomposite glass containing bismuth phosphate BiPO₄ nanocrystals was obtained, which can be attributed to homogeneous nucleation process. The formation of BiPO₄ nanocrystals was confirmed and characterized by X-ray diffraction patterns (XRD), transmission electron microscopy (TEM), differential scanning calorimetry, optical absorption (UV–Vis) and micro-hardness studies. The morphological analysis by XRD and TEM microscopy showed the formation of hexagonal BiPO₄ nanocrystals, and its estimated nanocrystalline sizes were found to be varying from 5.35 to 11.53 nm depending on the Bi₂O₃ concentrations. The density (ρ) and molar volume (V _m) were also determined and found to be in compositional dependence. Glass transition temperature (T _g) and glass crystallization temperature (T _c) were obtained and found to be increased (from 240.0 to 337.2 °C) with increasing Bi₂O₃ up to 20 mol% and then decreased (from 337.2 to 331.8 °C) due to the structural changes in the glass network. Effect of BiPO₄ content on the optical properties had been investigated. From the UV–Vis spectra, it was observed that the fundamental absorption edge shifts toward lower wavelengths, i.e., blueshifts with increasing Bi₂O₃ mol% up to 20 mol%, and then shifts toward higher wavelengths, i.e., redshifts beyond 20 mol%. It was also observed that the obtained E _opt (for indirect and direct transitions) increases with gradual increase in Bi₂O₃ content up to 20 mol% and then decreases beyond 20 mol%. This may be due to the introduction of Bi cations into the glass network as a network former up to 20 mol% causing a decrease in ΔE values, beyond 20 mol%, the introduction of Bi ions into the glass network interstitially leads to increase the values of ΔE. The optical properties of the present nanocrystallized glasses showed a quantum size dependence, in which the optical band gap energy (E _opt) was changed as a function of BiPO₄ nanocrystalline sizes.