Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

Plasmon Coupling-Induced Hot Electrons for Photocatalytic Hydrogen Generation

We present the fabrication of core-shell-satellite Au@SiO₂-Pt nanostructures and demonstrate that LSPR excitation of the core Au nanoparticle can induce plasmon coupling effect to initiate photocatalytic hydrogen generation from decomposition of formic acid. Further studies suggest that the plasmon coupling effect induces a strong local electric field between the Au core and Pt nanoparticles on the SiO₂ shell, which enables creation of hot electrons on the non-plasmonic-active Pt nanoparticles to participate hydrogen evolution reaction on the Pt surface. In addition, small SiO₂ shell thickness is required in order to obtain a strong plamon coupling effect and achieve efficient photocatalytic activities for hydrogen generation.     

The Effect of the Spacer of Bis(biurea) Ligands on the Structure of A2L3‐type (A=anion) Phosphate Complexes

By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A₂L₃ complexes (A represents anion, here orthophosphate PO₄^3?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes.     

Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

Eco‐friendly ionic liquid assisted capillary electrophoresis and α‐acid glycoprotein‐assisted liquid chromatography for simultaneous determination of anticancer drugs in human fluids

In the current work, two eco‐friendly analytical methods based on capillary electrophoresis (CE) and reversed phase liquid chromatography (RPLC) were developed for simultaneous determination of the most commonly used anticancer drugs for Hodgkin's disease: methotrexate (MTX), vinblastine, chlorambucil and dacarbazine. A background electrolyte (BGE) of 12.5 mmol/L phosphate buffer at pH 7.4 and 0.1 µmol/L 1‐butyl‐3‐methyl imidazolium bromide (BMImBr) ionic liquid (IL) was used for CE measurements at 250 nm detection wavelength, 20 kV applied voltage and 25 °C. The rinsing protocol was significantly improved to reduce the adsorption of IL on the interior surface of capillary. Moreover, RPLC method was developed on α‐1‐acid glycoprotein (AGP) column. Mobile phase was 10 mmol/L phosphate buffer at pH 6.0 (100% v/v) and flow rate at 0.1 mL/min. As AGP is a chiral column, it was successfully separated l ‐MTX from its enantiomer impurity d ‐MTX. Good linearity of quantitative analysis was achieved with coefficients of determinations (r²) >0.995. The stability of drugs measurements was investigated with adequate recoveries up to 24 h storage time under ambient temperature. The limits of detection were <50 and 90 ng/mL by CE and RPLC, respectively. The using of short‐chain IL as an additive in BGE achieved 600‐fold sensitivity enhancement compared with conventional Capillary Zone Electrophoresis (CZE). Therefore, for the first time, the proposed methods were successfully applied to determine simultaneously the analytes in human plasma and urine samples at clinically relevant concentrations with fast and simple pretreatments. Developed IL‐assisted CE and RPLC methods were also applied to measure MTX levels in patients’ samples over time. Copyright © 2014 John Wiley & Sons, Ltd.     

Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.