Rational Development of Remote C−H Functionalization of Biphenyl: Experimental and Computational Studies

A simple and efficient nitrile-directed meta-C−H olefination, acetoxylation, and iodination of biaryl compounds is reported. Compared to the previous approach of installing a complex U-shaped template to achieve a molecular U-turn and assemble the large-sized cyclophane transition state for the remote C−H activation, a synthetically useful phenyl nitrile functional group could also direct remote meta-C−H activation. This reaction provides a useful method for the modification of biaryl compounds because the nitrile group can be readily converted to amines, acids, amides, or other heterocycles. Notably, the remote meta-selectivity of biphenylnitriles could not be expected from previous results with a macrocyclophane nitrile template. DFT computational studies show that a ligand-containing Pd–Ag heterodimeric transition state (TS) favors the desired remote meta-selectivity. Control experiments demonstrate the directing effect of the nitrile group and exclude the possibility of non-directed meta-C−H activation. Substituted 2-pyridone ligands were found to be key in assisting the cleavage of the meta-C−H bond in the concerted metalation–deprotonation (CMD) process.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

制作高密度衍射光栅的光电式刻划控制的研究

高精度的光电式刻划控制系统是制作高密度母光栅的关键技术,以光栅干涉仪为控制核心,设计了光电式的光栅刻划控制系统,并对可能产生的加工误差进行了初步的分析;采用该控制系统的光栅刻划实践表明,所设计的光电式刻划控制系统已完全达到了高密度衍射光栅的亚微米栅距分度要求。     

A Faster Deterministic Maximum Flow Algorithm

Cheriyan and Hagerup developed a randomized algorithm to compute the maximum flow in a graph with n nodes and m edges in O(mn + n² log²n) expected time. The randomization is used to efficiently play a certain combinatorial game that arises during the computation. We give a version of their algorithm where a general version of their game arises. Then we give a strategy for the game that yields a deterministic algorithm for computing the maximum flow in a directed graph with n nodes and m edges that runs in time O(mn(log_{m/n log n}n)). Our algorithm gives an O(mn) deterministic algorithm for all m/n = Ω(n^ε) for any positive constant ε, and is currently the fastest deterministic algorithm for computing maximum flow as long as m/n = ω(log n).     

Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

TiN/Al2O3纳米多层膜的共格外延生长及超硬效应

采用多靶磁控溅射法制备了一系列具有不同Al2O3调制层厚度的TiN/Al2O3纳米多层膜.利用X射线能量色散谱、X射线衍射、扫描电子显微镜、高分辨透射电子显微镜和微力学探针表征了多层膜的成分、微结构和力学性能.研究结果表明,在TiN/Al2O3纳米多层膜中,单层膜时以非晶态存在的Al2O3层在厚度小于1.5 nm时因TiN晶体层的模板效应而晶化,并与TiN层形成共格外延生长,相应地,多层膜产生硬度明显升高的超硬效应,最高硬度可达37.9 GPa.进一步增加多层膜中Al2O3调制层的层厚度,Al2O3层逐渐形成非晶结构并破坏了多层膜的共格外延生长,使得多层膜的硬度逐步降低.     

Systematic Errors Associated with the CPMG Pulse Sequence and Their Effect on Motional Analysis of Biomolecules

A theoretical approach to calculate the time evolution of magnetization during a CPMG pulse sequence of arbitrary parameter settings is developed and verified by experiment. The analysis reveals that off-resonance effects can cause systematic reductions in measured peak amplitudes that commonly lie in the range 5–25%, reaching 50% in unfavorable circumstances. These errors, which are finely dependent upon frequency offset and CPMG parameter settings, are subsequently transferred into erroneousT₂values obtained by curve fitting, where they are reduced or amplified depending upon the magnitude of the relaxation time. Subsequent transfer to Lipari–Szabo model analysis can produce significant errors in derived motional parameters, with τ_einternal correlation times being affected somewhat more thanS²order parameters. A hazard of this off-resonance phenomenon is its oscillatory nature, so that strongly affected and unaffected signals can be found at various frequencies within a CPMG spectrum. Methods for the reduction of the systematic error are discussed. Relaxation studies on biomolecules, especially at high field strengths, should take account of potential off-resonance contributions.