Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Catalytic carbon dioxide hydrogenation to methane: A review of recent studies

Recently,various efforts have been put forward on the development of technologies for the synthesis of methane from CO₂ and H₂,since it can offer a solution for renewable H₂ storage and transportation.In parallel,this reaction is considered to be a critical step in reclaiming oxygen within a closed cycle.Over the years,extensive fundamental research works on CO₂ methanation have been investigated and reported in the literatures.In this updated review,we present a comprehensive overview of recent publications during the last 3 years.Various aspects on this reaction system are described in detail,such as thermodynamic considerations,catalyst innovations,the influence of reaction conditions,overall catalytic performance,and reaction mechanism.Finally,the future development of CO₂ methanation is discussed.     

Two new terpenes from Tripterygium wilfordii

<正>Two new terpenes,wilfornine H(1) and triptobenzene Q(2) were isolated from Tripterygium wilfordii,as well as 11 terpenes. Their structures were elucidated by spectroscopic methods.Compounds 5,9-13 showed significant immunosuppressive activities.     

Reduced field-of-view diffusion-weighted imaging of the brain at 7 T

Ventral and rostral regions of the brain are of emerging importance for the MRI characterization of early dementia, traumatic brain injury and epilepsy. Unfortunately, standard single-shot echo planar diffusion-weighted imaging of these regions at high fields is contaminated by severe imaging artifacts in the vicinity of air–tissue interfaces. To mitigate these artifacts and improve visualization of the temporal and frontal lobes at 7 T, we applied a reduced field-of-view strategy, enabled by outer volume suppression (OVS) with novel quadratic phase radiofrequency (RF) pulses, combined with partial Fourier and parallel imaging methods. The new acquisition greatly reduced the level of artifacts in six human subjects (including four patients with early symptoms of dementia).     

Three coordination polymers of 5-aminoisophthalic acid with similar benzimidazole derivative ligands: synthesis,structure and DNA-binding studies

Three novel coordination polymers, [Co(NH₂-Aip)(H₂Bibim)] _n (1), [Co(NH₂-Aip)(HBibimop)] _n  √ nH₂O (2) and [Mn(NH₂-Aip) √ H₂O] _n  √ 2nH₂O (3) with NH₂-Aip and similar benzimidazole derivative ligands (NH₂-Aip = 5-aminoisophthalic acid, H₂Bibim = 2,2′-bibenzimidazole and HBibimop = 1,3-bis(benzimidazol-2-yl)-2-oxapropane), have been synthesised under hydrothermal conditions and structurally characterised by single-crystal X-ray diffraction analysis, elemental analysis and IR spectroscopy. 5-Aminoisophthalic acid ligand adopts μ₂-, μ₃- and μ₄-bridge coordination fashion and benzimidazole derivatives exist as terminal- and bridge-mode in complexes 1–3. The intricate hydrogen bonds and π–π stacking interactions in supramolecular framework are discussed. Using the combination of ultraviolet–visible absorption titration and fluorescence spectra, the experimental results show that complexes 1 and 2 bind to DNA in an intercalative mode and their DNA-binding constants (K _b ) are also found.     

An approach to the Paal–Knorr pyrroles synthesis in the presence of β-cyclodextrin in aqueous media

An efficient and facile method for the synthesis of N-substituted pyrroles in moderate to good yields by the Paal–Knorr reaction of γ-diketones with amines in the presence of β-cyclodextrin in aqueous media has been developed.Moreover,this process tolerated diamines(e.g.,para-,meta- or orthophenylenediamine)to construct bis-pyrrole or mono-pyrrole derivates.β-Cyclodextrin can be recovered easily after the reactions and reused without evident loss in activity.