An $$H^1$$-Galerkin mixed finite element method for time fractional reaction–diffusion equation

In this article, an \(H^1\)-Galerkin mixed finite element (MFE) method for solving time fractional reaction–diffusion equation is presented. The optimal time convergence order \(O(\varDelta t^{2-\alpha })\) and the optimal spatial rate of convergence in \(H^1\) and \(L^2\)-norms for variable \(u\) and its gradient \(\sigma \) are derived. Moreover, some numerical results are shown to support our theoretical analysis.     

Notes on Automorphisms of Prime Rings

Let R be a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of R such that usσ(u)ut= 0 for all u ∈ L, where s, t are fixed non-negative integers. If either char R s + t or char R = 0, then R satisfies s4, the standard identity in four variables. We also examine the identity(σ([x, y])-[x, y])n=0 for all x, y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. If either char R n or char R = 0, then R is commutative.     

The Wigner–Yanase information can increase under phase sensitive incoherent operations

We found that the Wigner-Yanase skew information, which has been recently proposed as a measure of coherence in Girolami (2014), can increase under a class of operations which may be interpreted as incoherent following the framework of Baumgratz et al., while being phase sensitive.     

Nondestructive rare earth element imaging of fish teeth from deep‐sea sediments

X‐ray fluorescence computed tomography is an emerging imaging modality that allows for the nondestructive reconstruction of the internal distribution of elements within a sample. The common use of X‐ray excitation energy (up to approximately 20 keV) has necessitated the use of l ‐shell fluorescence for heavy elements. In this study, based on high energy X‐ray at BL13W1 of the Shanghai Synchrotron Radiation Facility, we employed high‐energy excitation for tomographic imaging of the heavy metals (rare earth elements) in fish teeth from deep‐sea sediments on the micrometer scale using K‐shell X‐ray fluorescence. The virtual cross‐sectional distribution of La, Ce, Pm, Pr, Nd, and Sm were obtained, thereby providing a feasible approach for analyzing the enrichment mechanism of rare earth elements. Copyright © 2015 John Wiley & Sons, Ltd.     

Preparation of polyaniline grafted multiwalled carbon nanotubes and conductive application in polyetherimide

A methodology for improving antistatic property of polyetherimide (PEI) composite using polyaniline (PANI) grafted multi‐walled carbon nanotubes (MWNTs) as conductive medium was proposed. First, the MWNTs grafted with PANI (PANI‐g‐MWNTs) were prepared by in‐situ polymerization in an emulsion system. Subsequently, PANI‐g‐MWNTs were blended with PEI using N‐methyl‐2‐pyrrolidone as solvent. After removing the solvent, the PEI/PANI‐g‐MWNT composite was prepared. As assisted conductive medium, the grafted PANI molecular chains on MWNT surface were dispersed in the PEI matrix to decrease the percolation value of the antistatic composites. The structure and morphology of PANI‐g‐MWNTs were characterized by Fourier transform infrared spectroscopy, transmission electron microscope, thermogravimetric analysis, and X‐ray powder diffraction, respectively. The dispersion of PANI‐g‐MWNTs in PEI matrix was studied by scanning electron microscope. The electrical performance was characterized by highly resistant meter. The volume resistivity of the conductivity percolation threshold was 1.781 × 10^?8 S/cm when the loading of PANI‐g‐MWNTs was 1.0 wt%. The conductivity of PANI‐g‐MWNTs/PEI composites was found to be higher than that of pristine MWNTs/PEI composite. Copyright © 2012 John Wiley & Sons, Ltd.     

Mechanical and anti‐stabbing properties of modified thermoplastic polymers impregnated multiaxial p‐aramid fabrics

New forms of hybrid multiaxial nanocomposites with enhanced mechanical and stab resisting properties are presented. This study is motivated by the lack of knowledge in the study of the multiaxial fabric nanocomposites with two modified thermoplastic matrices for antiballistic protection. Introduction of 5 wt.% silica nanoparticles in the composite of polyurethane/p‐aramid/poly (vinyl butyral) leads to significant improvement in mechanical properties, and the addition of silane as a coupling agents and glutaraldehyde as a crosslinking agents yielded maximal values of storage modulus, tensile modulus and anti‐stabbing properties for hybrid nanocomposites. Ballistic resistance testing and penetration depth of the hybrid nanocomposites were visualized using image analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis and Properties of pH-Responsive Polymers with Cadaverine Side Groups

A water-soluble monomer N¹-(4-vinylbenzyl)-pentane-1,5-diamine dihydrochloride (VBPDA) with cadaverine (1,5-pentanediamine) group was synthesized. pH-responsive polymer with cadaverine group was obtained by free radical polymerization of VBPDA using 4,4-azobis(4-cyanovaleric acid) (ACVA) as the initiator. The structure and molecular weight of the polymer were characterized by FTIR, ¹H-NMR and GPC-MALLS. Aggregation behavior of the polymer in aqueous solution was investigated by dynamic light scattering (DLS), UV-Vis and fluorescence measurements. The experimental results show that the fluorescence intensity of the aggregates decreases and the size of the aggregates increases with increasing pH due to the continuous dehydration of the cadaverine side groups.     

NMR studies of conformations and molecular recognition of pyridinio-appended and nicotinamide-appended β-cyclodextrin

Abstract

The conformations of pyridinio-appended β-cyclodextrin (CDP⁺) and nicotinamide-appended β-cyclodextrin (CDNA⁺) were studied by NMR spectroscopy. The orientations of the pyridine residue of CDP⁺ and the nicotinamide residue of CDNA⁺ were determined by using a combination of NMR spectroscopic techniques. NMR spectra indicate that the shapes of the cavities of CDP⁺ and CDNA⁺ were changed after forming complexes. This change depended on the shape of the guest. CDNA⁺ could separate the ¹H resonances at the Cβ position of racemic tryptophan into two sets of resonances for each enantiomer.