超声波促进手性双酰基氧化膦的合成

以L-薄荷醇为原料,经3步反应制备得到中间体薄荷基二氯化膦.该中间体首先通过与超声波辐射制备的微米级钠粒反应形成薄荷基膦二钠盐,然后依次经过偶联及氧化反应合成了目标产物(-)-双(薄荷基甲酰基)薄荷基氧化膦(BMMPO),并经过1 H NMR、13 C NMR、31P NMR和元素分析进行了表征.     

Six‐wave mixing induced by free‐carrier plasma in silicon nanowire waveguides

Nonlinear wave mixing in mesoscopic silicon structures is a fundamental nonlinear process with broad impact and applications. Silicon nanowire waveguides, in particular, have large third‐order Kerr nonlinearity, enabling salient and abundant four‐wave‐mixing dynamics and functionalities. Besides the Kerr effect, in silicon waveguides two‐photon absorption generates high free‐carrier densities, with corresponding fifth‐order nonlinearity in the forms of free‐carrier dispersion and free‐carrier absorption. However, whether these fifth‐order free‐carrier nonlinear effects can lead to six‐wave‐mixing dynamics still remains an open question until now. Here we report the demonstration of free‐carrier‐induced six‐wave mixing in silicon nanowires. Unique features, including inverse detuning dependence of six‐wave‐mixing efficiency and its higher sensitivity to pump power, are originally observed and verified by analytical prediction and numerical modeling. Additionally, asymmetric sideband generation is observed for different laser detunings, resulting from the phase‐sensitive interactions between free‐carrier six‐wave‐mixing and Kerr four‐wave‐mixing dynamics. These discoveries provide a new path for nonlinear multi‐wave interactions in nanoscale platforms.

     

Simultaneous and Sensitive Detection of Cd(II) and Pb(II) Using a Novel Bismuth Film/Ordered Mesoporous Carbon‐molecular Wire Modified Graphite Carbon Paste Electrode

An electrochemical sensor for the simultaneous and sensitive detection of Cd(II) and Pb(II) is proposed on the basis of square‐wave anodic stripping voltammetry (SWASV) experiments using a novel bismuth film/ordered mesoporous carbon‐molecular wire modified graphite carbon paste electrode (Bi/OMC‐MW/GCPE). Ordered mesoporous carbon (OMC) and molecular wire (MW) (diphenylacetylene) were used as the modifier and binder, respectively. The Bi/OMC‐MW/GCPE was prepared with the addition of graphite powder, OMC and DPA at the ratio of 2 : 1 : 1. The electrochemical properties and morphology of the electrode were characterized by electrochemical impedance spectroscopy (EIS), cyclic voltammetry (CV), SWASV and scanning electron microscopy (SEM). The parameters affecting the stripping current response were investigated and optimized. The experimental results show that the prepared electrode exhibited excellent electrochemical performance, good electrical conductivity and a high stripping voltammetric response. Under optimized conditions, a linear range was achieved over a concentration range from 1.0 to 70.0 μg/L for both Cd(II) and Pb(II) metal ions, with detection limits of 0.07 μg/L for Cd(II) and 0.08 μg/L for Pb(II) (S/N=3) with the deposition time 150 s. Moreover, the sensor exhibited improved sensitivity and reproducibility compared to traditional CPEs. The fabricated electrode was then successfully used to satisfactorily detect Cd(II) and Pb(II) in real soil samples.     

Hyperbolic Yamabe problem

In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the(1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Solitons and other solutions to a new coupled nonlinear Schrodinger type equation

In this paper, the first integral method combined with Liu's theorem is applied to integrate a new coupled nonlinear Schrodinger type equation. Using this combination, more new exact traveling wave solutions are obtained for the considered equation using ideas from the theory of commutative algebra. In addition, more solutions are also obtained via the application of semi-inverse variational principle due to Ji-Huan He. The used approaches with the help of symbolic computations via Mathematica 9, may provide a straightforward effective and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics.     

Solitary wave solution of the generalized Hirota–Satsuma coupled KdV system

In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.     

The global weak solution for the shallow water wave model of moderate amplitude

In this paper, we firstly establish the existence theorem of the global weak solutions of the Cauchy problem for the shallow water wave model of moderate amplitude, then following the idea in Xin and Zhang’s work (see Xin and Zhang, 2002), we prove the uniqueness of global weak solutions using the localization analysis in the transport equation theory. Finally, several travelling wave solutions are derived.     

Computation of waveguide scattering matrix near thresholds

A waveguide occupies infinite strip with one or several narrows on a two-dimensional (2D) plane and is governed by the Helmholtz equation with Dirichlet boundary condition. On the waveguide continuous spectrum, which coincides with a half-axis, a scattering matrix is defined. At each point of the continuous spectrum this matrix has finite size, which changes at thresholds. The thresholds form a sequence of positive numbers increasing to infinity. Approximate calculation of the scattering matrix in a threshold vicinity requires special treatment. We discuss and compare two methods of numerical approximation to the scattering matrix near a threshold.