On the hyperbolic order

We define the hyperbolic order of any locally injective holomorphic function between arbitrary hyperbolic domains of the complex plane and study the relation between the hyperbolic order and the Schwarzian derivative for locally injective holomorphic functions from the unit disk into itself.     

Invariance for stochastic differential systems with time-dependent constraining sets

The first part of this article presents invariance criteria for a stochastic differential equation whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.     

A new size extensive multireference perturbation theory

A new multireference perturbation series is derived based on the Rayleigh–Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller–Plesset perturbation theory. It is demonstrated numerically that the present multireference second‐ and third‐order energies are size extensive by two types of supermolecules composed of H₂ and BH monomers. Spectroscopic constants of as well as the ground state energies of H₂O, NH₂, and CH₂ at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH₄ and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances. © 2013 Wiley Periodicals, Inc.     

Raman spectroscopy of CaM2+Ge2O6 (M2+ = Mg,Mn, Fe,Co, Ni,Zn) clinopyroxenes

The Raman spectra of Ge‐clinopyroxenes CaM²⁺Ge₂O₆ (M²⁺ = Mg, Mn, Fe, Co, Ni, Zn), general formula M2M1T₂O₆, are reported for the first time. Their spectral features are discussed in comparison with corresponding Si‐pyroxenes. The vibrational wavenumbers of germanates may be roughly obtained by a scale factor of about ~0.8 by those of the corresponding silicates, due to the Ge‐Si mass difference. The main peaks in the germanate Raman spectra at ~850 and ~540 cm⁻¹ may be related to Ge‐O tetrahedral stretching and chain bending, respectively; minor peaks between 200 and 400 cm⁻¹ are ascribed to bending and stretching of the non‐tetrahedral cations. Within Ge‐pyroxenes, possible correlations between crystallographic parameters and the vibrational wavenumbers are investigated. The main stretching mode at ~850 cm⁻¹ shows wavenumber changes with M²⁺ substitutions, but no simple correlation can be found with M²⁺ cation mass or size. On the other hand, the chain bending wavenumber linearly decreases with increasing ionic radius of the M²⁺ cation: the expansion of the M1 polyhedron reduces the chain kinking angle and the Ge‐Ge distances correspondingly increase. Copyright © 2015 John Wiley & Sons, Ltd.     

Tailoring 3,3′‐Dihydroxyisorenieratene to Hydroxystilbene: Finding a Resveratrol Analogue with Increased Antiproliferation Activity and Cell Selectivity

Four novel compounds were designed by “tailoring” 3,3′‐dihydroxyisorenieratene (a natural carotenoid) based on an isoprene unit retention truncation strategy. Among them, the smallest molecule 1 (2,3,6,2′,3′,6′‐hexamethyl‐4,4′‐dihydroxy‐trans‐stilbene) was concisely synthesized in a one‐pot Stille–Heck tandem sequence, and surfaced as a promising lead molecule in terms of its selective antiproliferative activity mediated by blocking the NCI‐H460 cell cycle in G1 phase. Additionally, theoretical calculations and cell uptake experiments indicate that the unique polymethylation pattern of compound 1 significantly induces a conformational change shift out of planarity and increases its cell uptake and metabolic stability. The observation should be helpful to rationally design resveratrol‐inspired antiproliferative agents.     

Construction of mixed carboxylate and pyrogallate building units for luminescent metal-organic frameworks

A metal-organic framework,Ce-FDM-50,was constructed by employing gallic acid featuring both carboxylate and pyrogallate as the coordinating sites and Ce(Ⅲ).The co-assembly of the carboxylates and pyrogallates with two metal ions have achieved a new type of paddle wheel secondary building unit.These building units were further joined by organic struts to obtain frameworks in sql topology.This synthetic approach could be expanded to five different lanthanide metals(Nd,Eu,Gd,Tb,Yb)for the construction of a series of isoreticular MOFs based on FDM-50,and even MTV-MOFs in which mixed lanthanide metals with specific ratios were distributed.In addition,featuring the lanthanide metals as the inorganic nodes in the network,Tb-FDM-50 showed distinct luminescence properties that could be furtherly tuned for variable applications.     

Thermal stability and dynamic mechanical thermal analysis of epoxy thermosets possessing N,N′-disubstituted pyromellitimide units

Abstract

In this work, three epoxy resins including diglycidyl ethers of N,N′-bis(2-hydroxyethyl)pyromellitimide (DIDGE), bisphenol-A (BADGE), and polyethylene glycol (PEDGE) were isothermally cured by an amine curing agent possessing N,N′-disubstituted pyromellitimide units (denoted by DIDAM). DIDGE resin was synthesized from the reaction of N,N′-bis(2-hydroxyethyl)pyromellitimide with an excess of epichlorohydrin. Also, DIDAM curing agent was prepared from the reaction of pyromellitic dianhydride with an excess of ethylene diamine. Completion of the isothermal curing processes was approved by both Fourier transform-infrared spectroscopy and non-isothermal differential scanning calorimetry (DSC). The DSC traces showed only the phase transitions related to the thermal degradation of the resulting thermosets. According to the thermogravimetric analyses, the DIDGE/DIDAM thermoset showed higher thermal stability at temperatures above 425?°C than the other two thermosets. While BADGE/DIDAM and PEDGE/DIDAM thermosets showed about 70% weight loss in the thermal range of 400–850?°C, DIDGE/DIDAM thermoset was encountered with only about 40% weight loss. The glass transition temperatures (T_g ) of the resulting thermosets were determined using tan δ vs temperature plots obtained from dynamic mechanical thermal analysis. The T_g values of BADGE/DIDAM, DIDGE/DIDAM, and PEDGE/DIDAM thermosets were found to be 211?°C, 189?°C, and 81?°C, respectively.     

Three‐dimensional Octameric Assembly of Icosahedral M13 Units in [Au8Ag57(Dppp)4(C6H11S)32Cl2]Cl and its [Au8Ag55(Dppp)4(C6H11S)34][BPh4]2 Derivative

The high‐dimensional (that is, three‐dimensional (3D)) assembly of nanomaterials is an effective means of improving their properties; however, achieving this assembly at the atomic level remains challenging. Herein, we obtained a novel nanocluster, [Au₈Ag₅₇(Dppp)₄(C₆H₁₁S)₃₂C_l2]Cl (Dppp=1,3‐bis(diphenylphosphino)propane) showing a 3D octameric assembly mode involving the kernel penetration of eight complete icosahedral Au@Ag₁₀Au₂ units for the first time. The atomically precise structure was determined by single‐crystal X‐ray diffraction, and further confirmed by thermogravimetric analysis, X‐ray photoelectron spectroscopy, and electrospray ionization mass spectrometry measurements. Furthermore, ligand‐induced transformation prompted the conversion of [Au₈Ag₅₇(Dppp)₄(C₆H₁₁S)₃₂Cl₂]Cl, with complete octameric fusion into [Au₈Ag₅₅(Dppp)₄(C₆H₁₁S)₃₄][BPh₄]₂, with incomplete octameric fusion. These observations will hopefully facilitate further research on the assembly of M₁₃ nanobuilding blocks.