Hilbert空间中非扩张映象的最近的公共不动点的逼近问题

本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．     

由数列定义的函数

We construct real valued functions from infinite sequences. We also consider some properties of such functions and null sequences.     

Quantitative characterization of hydroxyl radicals produced by various photocatalysts

Hydroxyl radicals ((·)OH) have been deemed to be the major active species during the photocatalytic oxidation reaction. In this study, (·)OH produced on various semiconductor photocatalysts in aqueous solution under Xenon lamp irradiation was quantitatively investigated by the photoluminescence (PL) technique using coumarin (COU) as a probe molecule. The results indicated that the formation rate of (·)OH on the surface of irradiated commercial Degussa P25 (P25) was much higher than that of other semiconductor. The pH values of the solution and phase structure of TiO(2) significantly influenced the production rate of (·)OH. The acidic pH environment of the solutions and bi-phase structure (anatase and rutile) of TiO(2) were beneficial to enhancing the formation rate of (·)OH. In addition, the formation rate of (·)OH on anatase TiO(2) and P25 was much faster than that of (·)OH on the other semiconductors (such as rutile TiO(2), ZnO, WO(3), CdS, Bi(2)WO(4) and BiOCl, etc.). A new concept "OH-index" was first proposed to compare photocatalytic activity of photocatalysts, which would provide new insight into the investigation of semiconductor photocatalysts.     

Bacteria-based AND logic gate: a decision-making and self-powered biosensor

We developed a bacteria-based AND logic gate using a Pseudomonas aeruginosa lasI/rhlI double mutant with two quorum-sensing signaling molecules as the input signals. We showed a distinct electrical output signal, despite the complexity and continuous regulation of metabolic reactions of living cells.     

A versatile palladium catalyst system for Suzuki-Miyaura coupling of alkenyl tosylates and mesylates

A general and effective palladium system for Suzuki-Miyaura coupling of alkenyl electrophiles under mild reaction conditions is reported. With the Pd(OAc)(2)/CM-phos system, a variety of alkenyl tosylates are coupled well with ArB(OH)(2). Moreover, the first successful examples of using alkenyl mesylates in alkenylation are also described.     

Gold(I)‐Catalyzed Enantioselective Intermolecular Hydroarylation of Allenes with Indoles and Reaction Mechanism by Density Functional Theory Calculations

Chiral binuclear gold(I) phosphine complexes catalyze enantioselective intermolecular hydroarylation of allenes with indoles in high product yields (up to 90 %) and with moderate enantioselectivities (up to 63 % ee). Among the gold(I) complexes examined, better ee values were obtained with binuclear gold(I) complexes, which displayed intramolecular Au^I Au^I interactions. The binuclear gold(I) complex 4c [(AuCl)₂( L3 )] with chiral biaryl phosphine ligand (S)‐(−)‐MeO‐biphep ( L3 ) is the most efficient catalyst and gives the best ee value of up to 63 %. Substituents on the allene reactants have a slight effect on the enantioselectivity of the reaction. Electron‐withdrawing groups on the indole substrates decrease the enantioselectivity of the reaction. The relative reaction rates of the hydroarylation of 4‐X‐substituted 1,3‐diarylallenes with N‐methylindole in the presence of catalyst 4c [(AuCl)₂( L3 )] / AgOTf [ L3 =(S)‐(−)‐MeO‐biphep], determined through competition experiments, correlate (r²=0.996) with the substituent constants σ. The slope value is −2.30, revealing both the build‐up of positive charge at the allene and electrophilic nature of the reactive Au^I species. Two plausible reaction pathways were investigated by density functional theory calculations, one pathway involving intermolecular nucleophilic addition of free indole to aurated allene intermediate and another pathway involving intramolecular nucleophilic addition of aurated indole to allene via diaurated intermediate E2 . Calculated results revealed that the reaction likely proceeds via the first pathway with a lower activation energy. The role of Au^I Au^I interactions in affecting the enantioselectivity is discussed.     

Long-Period Gratings in Planar Optical Waveguides

Our progress in the study of long-period gratings (LPGs) in planar optical waveguides is reviewed. In particular,experimental LPGs in glass and polymer waveguides are presented to demonstrate the potential of LPG-based waveguide devices.     

关于3连通图的容错直径和宽直径

容错直径和宽直径是度量网络可靠性和有效性的重要参数．对任意k连通图，它的容错直径Dk不超过宽直径dk,本证明：当D2=2时，d3≤max{D， l，2D3-2}；当D2≥3时，d3≤(D2-1)[2(D2-1)(D3-1)-D2-2] 1．