Encapsulated Neutral Ruthenium Catalyst for Substrate-Selective Oxidation of Alcohols

The neutral complex dichloro-{diethyl[(5-phenyl-1,3,4-oxadiazol-2-ylamino)-(4-trifluoro-methylphenyl)methyl]phosphonate} (p-cymene)-ruthenium(II) was encapsulated inside a self-assembled hexameric host obtained upon reaction of 2,8,14,20-tetra-undecyl-resorcin[4]arene and water. The formation of an inclusion complex was inferred from a combination of spectral measurements (MS, UV/Vis spectroscopy, ¹H and DOSY NMR). The ³¹P and ¹⁹F NMR spectra are consistent with motions of the ruthenium complex inside the self-assembled capsule. Molecular dynamics simulations carried out on the inclusion complex confirmed these intra-cavity movements and highlighted possible supramolecular interactions between the ruthenium first coordination sphere ligands and the inner part (aromatic rings) of the capsule. The embedded ruthenium complex was assessed in the catalytic oxidation (using NaIO₄ as oxidant) of mixtures of three arylmethyl alcohols into the corresponding aldehydes. The reaction kinetics were shown to vary as a function of the substrates’ size, with the oxidation rate varying in the order benzylalcohol >4-phenyl-benzylalcohol >9-anthracenemethanol. Control experiments realized in the absence of hexameric capsule did not allow any discrimination between the substrates.     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Composite host lattices of 4,4′‐sulfonyldibenzoate water/boric acid in two tetrapropylammonium inclusion compounds

Two novel inclusion compounds of 4,4′‐sulfonyldibenzoate anions and tetrapropylammonium cations with different ancillary molecules of water and boric acid, namely bis(tetrapropylammonium) 4,4′‐sulfonyldibenzoate dihydrate, 2C₁₂H₂₈N⁺·C₁₄H₈O₆S²⁻·H₂O ( 1 ), and bis(tetrapropylammonium) 4,4′‐sulfonyldibenzoate bis(boric acid), 2C₁₂H₂₈N⁺·C₁₄H₈O₆S²⁻·2H₃BO₃ ( 2 ), were prepared and characterized using single‐crystal X‐ray diffraction. In the two salts, the host 4,4′‐sulfonyldibenzoic acid molecules, which are converted to the corresponding anions under basic conditions, can be regarded as proton acceptors which link different proton donors of the ancillary molecules of water or boric acid. In this way, an isolated hydrogen‐bonded tetramer is constructed in salt 1 and a ribbon is constructed in salt 2 . The tetramers and ribbons are then packed in a repeating manner to generate various host frameworks, and the tetrapropylammonium guest counter‐ions are contained in the cavities of the host lattices to give the final stable crystal structures. In these two salts, although the host anion and guest cation are the same, the difference in the ancillary small molecules results in different structures, indicating the significance of ancillary molecules in the formation of crystal structures.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.