Group 13 Lewis acid adducts of [PCl2N]3

Phosphazene polymers are classically synthesized by the high-temperature, ring-opening polymerization (ROP) of [PCl(2)N](3) to give [PCl(2)N](n), followed by functionalization of [PCl(2)N](n) with different side groups. We investigated the interactions of [PCl(2)N](3) with Lewis acids because Lewis acids have been used to induce the high-temperature ROP of [PCl(2)N](3). The reactions of [PCl(2)N](3) with MX(3) (M = group 13, X = halides), under strict anaerobic conditions gave adducts [PCl(2)N](3)·MX(3). Adducts were characterized by X-ray crystallography and multinuclear and variable-temperature NMR studies, and mechanistic understanding of their fluxional behavior in solution was achieved. The properties of the [PCl(2)N](3)·MX(3) adducts at or near room temperature strongly suggests that such adducts are not involved directly as intermediates in the high-temperature ROP of [PCl(2)N](3).     

Edge detection from truncated Fourier data using spectral mollifiers

Edge detection from a finite number of Fourier coefficients is challenging as it requires extracting local information from global data. The problem is exacerbated when the input data is noisy since accurate high frequency information is critical for detecting edges. The noise furthermore increases oscillations in the Fourier reconstruction of piecewise smooth functions, especially near the discontinuities. The edge detection method in Gelb and Tadmor (Appl Comput Harmon Anal 7:101–135, 1999, SIAM J Numer Anal 38(4):1389–1408, 2000) introduced the idea of “concentration kernels” as a way of converging to the singular support of a piecewise smooth function. The kernels used there, however, and subsequent modifications to reduce the impact of noise, were generally oscillatory, and as a result oscillations were always prevalent in the neighborhoods of the jump discontinuities. This paper revisits concentration kernels, but insists on uniform convergence to the “sharp peaks” of the function, that is, the edge detection method converges to zero away from the jumps without introducing new oscillations near them. We show that this is achievable via an admissible class of spectral mollifiers. Our method furthermore suppresses the oscillations caused by added noise.     

Phase-sensitive multimodal optical parametric amplifier for beam angle amplification

The single-mode phase-sensitive parametric amplifier has been proposed as an approximation to an ideal quantum phase amplifier. We demonstrate numerically that a real, multimode parametric amplifier operated in the spatial domain, and realized by the use of three-wave mixing in nonlinear media, behaves similar to a single-mode quantum phase amplifier, but exhibits smaller phase gain. Constraints for operation in this regime are found to be consistent with small departures of phase from the ideal deamplification condition.     

Consistency of Regularization for Free Scalar Fields

In two dimensional constructive quantum field theory for scalar fields, it is necessary to regularize both the action and the total (Gaussian) volume. In this paper we consider the compatibility of these regularizations.      

锂原子光电离过程中的弛豫效应

利用基于多组态Dirac-Fock方法的程序包GRASP92和RATIP以及在此基础上最新发展的RERR06程序,计算了锂原子1s²nl(n=2,3; l=s, p) 的内壳层和外壳层的光电离截面. 计算中详细考虑了光电离过程中的弛豫效应. 结果表明：在锂原子内壳层电子的光电离过程中弛豫效应较强,而在外壳层电子的光电离过程中弛豫效应较弱. 另外,相应于不同态的内壳层光电离过程,其弛豫效应的影响也不同,对激发态的影响比对基态的影响大,对高激发态 关键词： 多组态Dirac-Fock方法 光电离截面 弛豫效应     

Rational design of polymer colloids

Recent advances in understanding of the fundamental mechanistic events in emulsion polymerization give the potential for rational design of new materials based on polymer colloids. It is now possible to design a new industrial process from first principles, based on well‐understood mechanistic principles. An overview of recent developments in the fundamental science of emulsion polymerization is given, with examples of the application of this knowledge to topologically‐controlled synthesis of novel materials based on natural rubber and polybutadiene seed latexes.     

Designing A Reactor to Generate Hydrogen Bubbles

Hydrogen is produced by the reaction between zinc and hydrochloric acid. This reaction is used to illustrate the importance of considering thermodynamics when designing a chemical reactor. The gas released is collected in soap bubbles that rise in the air, indicating that a lighter than air gas has been produced. The bubbles can be lit to add a dramatic effect to the demonstration. The reaction is highly exothermic, raising the temperature of the reaction materials and the reactor. Batch operation of this reactor would require short cooling periods between reactions. Alternatively, a modification of the design is suggested to allow for continuous cooling of the vessel, which would allow semicontinuous operation of the reactor. (Zinc would have to be periodically replenished as it is consumed in the reaction.) The consequences associated with the cooling of the vessel are discussed.