局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

XANES/EPR Evidence of the Oxidation of Nickel(II) Quinolinylpropioamide and Its Application in Csp3−H Functionalization

An in situ generated oxidation species of nickel quinolinylpropioamide intermediate was produced. Characterization by X-ray absorption near edge structure (XANES) and EPR provides complementary insights into this oxidized nickel species. With aliphatic amides and isocyanides as substrates, a nickel-catalyzed facile synthesis of structurally diverse five-membered lactams could be achieved.     

Biosynthesis of Pd/MnO2 nanocomposite using Solanum melongena plant extract and its application for the one‐pot synthesis of 5‐substituted 1H‐tetrazoles from aryl halides

In this work, for the first time, Solanum melongena plant extract was used for the green synthesis of Pd/MnO₂ nanocomposite via reduction osf Pd(II) ions to Pd(0) and their immobilization on the surface of manganese dioxide (MnO₂) nanoparticles (NPs) as an effective support. The synthesized nanocomposite were characterized by various analytical techniques such as Fourier transform infrared (FT‐IR), X‐ray diffraction (XRD), transmission electron microscopy (TEM), field emission scanning electron microscopy (FESEM), energy dispersive X‐ray spectroscopy (EDS) and UV–Vis spectroscopy. The catalytic activity of Pd/MnO₂ nanocomposite was used as a heterogeneous catalyst for the one‐pot synthesis of 5‐substituted 1H‐tetrazoles from aryl halides containing various electron‐donating or electron‐withdrawing groups in the presence of K ₄ [Fe (CN) ₆ ] as non‐toxic cyanide source and sodium azide. The products were obtained in good yields via a simple methodology and easy work‐up. The nanocatalyst can be recycled and reused several times with no remarkable loss of activity.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Biological and catalytic evaluation of Ru(II)‐p‐cymene complexes of Schiff base ligands: Impact of ligand appended moiety on photo‐induced DNA and protein cleavage,cytotoxicity and C‐H activation

Two organometallic Ru(II)‐p‐cymene complexes of the type [Ru(η⁶‐p‐cymene)(L)Cl]PF₆ 1 and 2 , where L is N,N‐bis(4‐isopropylbenzylidene)ethane‐1,2‐diamine (bien, L1 ) or N,N‐bis (pyren‐2‐ylmethylene)ethane‐1,2‐diamine (bpen, L2 ) have been prepared and characterized well. Because of appended pyrenyl groups in coordinated bpen ligand, the complex 2 exhibits higher DNA and protein binding than complex 1 in which isopropylbenzyl groups are incorporated. Interestingly, the luminescent characteristic complex 2 is unique in displaying DNA cleavage after light activation by UVA light at 365 nm through oxygen dependent mechanism. AFM analysis attests the photo‐induced DNA fragmentation ability of complex 2 . Also, the complex 2 cleaves the protein after light exposure in a non‐specific manner suggesting that it can act as a protein photo cleaving agent. In contrast to the trend of DNA and protein interaction of complexes, the complex 1 exhibits cytotoxic activity against human breast carcinoma ( MCF‐7 ) and liver carcinoma ( HepG2 ) with potency higher than that of complex 2 due to enhanced hydrophobicity of isopropyl groups present in p‐cymene and bien ligands. Indeed, complex 2 is inactive against MCF‐7 and HepG2 cancer cell lines even up to 200 μM concentration. The AO/EB staining assay reveals that the complex 1 is able to induce late apoptotic mode of cell death in breast cancer cells, which is further confirmed by inter‐nucleosomal DNA cleavage. Furthermore, the complexes 1 and 2 are evaluated for their catalytic activities and found to be working well for the β‐carboline directed C–H arylation to afford the desired products in good yield (40–47%).     

Reversible Activation of Water by an Air- and Moisture-Stable Frustrated Rhodium Nitrogen Lewis Pair

[Cp*Rh(κ³N,N′,P- L )][SbF₆] (Cp*=C₅Me₅), bearing a guanidine-derived phosphano ligand L , behaves as a “dormant” frustrated Lewis pair and activates H₂ and H₂O in a reversible manner. When D₂O is employed, a facile H/D exchange at the Cp* ring takes place through sequential C(sp³)−H bond activation.     

Quaternary ammonium compounds in roots and leaves of Capparis spinosa L. from Saudi Arabia and Italy: investigation by HPLC-MS and 1H NMR

Capparis spinosa L. is a perennial plant typical of the Mediterranean flora and a multipurpose plant used for curing various human ailments. Quaternary ammonium compounds (QACs), as constituents of Capparaceae, play important roles in protecting against abiotic stress. Aim of this work was to determine QACs in root and leaves of caper from two proveniences. The presence of stachydrine, choline, glycine betaine and homo-stachydrine has been confirmed by high resolution MS, while ¹H NMR was applied to quantify the main QACs in the aqueous extracts. Stachydrine was quantified at 20.2 mg/g and 32.3 mg/g on dry leaves from South of Italy and Saudi Arabia, respectively, while a minor content was in dry roots (from 10.4 to 12.5 mg/g). Choline was considerably lower both in leaves and roots (from 0.3 to 1.2 mg/g). To our knowledge, this is the first report on the determination of QACs both in root and leaves of C. spinosa.