一类Neumann-型特征值问题的Kr¨oger-型估计*

本文考虑了紧致带边的光滑度量测度空间上同加权Laplace算子有关的一类Neumann-型特征值问题,利用Fourier变换, 给出了该问题的低阶特征值和的Kr¨oger-型估计.     

On−off−on gold nanocluster-based near infrared fluorescent probe for recognition of Cu(II) and vitamin C

The authors described gold nanoclusters (AuNCs) for use on an “on ? off ? on” NIR fluorescent probe for the determination of citrate and Cu(II) ion. The AuNCs were prepared by a microwave-assisted method using BSA as both the stabilizing and reducing agent. The resulting BSA-capped AuNCs display NIR fluorescence peaking at 680 nm under 500 nm excitation, a quantum yield of ~6.0%, an average size of 2.8 ± 0.5 nm, water-dispersibility, stability and biocompatibility. The on?off probe for Cu(II) is based on the interaction between Cu(II) and BSA which causes the fluorescence of the BSA?AuNCs to be quenched. The quenched fluorescence is recovered on addition of vitamin C (VC), obviously due to complexation of Cu(II) by citrate. The probe was employed to image Cu(II) and citrate in HeLa cells and in aqueous solutions. The method works in the 20 nM to 0.1 mM concentration range for Cu(II), and in the 8 nM to 120 μM concentration range for VC.

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Graphical abstract Schematic presentation of the gold nanocluster based probe whose fluorescence is quenched by Cu(II) ions and then restored by addition of vitamin C. This is demonstrated for both aqueous solutions and living cells.

     

Boundedness and Asymptotic Behaviour of Solutions of a Second-Order Nonlinear System

Consider the second-order nonlinear system where a is a positive and continuous function onR:(– , ), b, c and h are continuous functions on R, ande is a continuous function on I:[0, ). We obtain a sufficientcondition for all solutions of (*) to be bounded, and obtaina sufficient condition for all solutions of (*) to tend to zero.Our results can be applied to the well-known equation which substantially improves and extendsseveral known results in the literature.     

差分浓度调制激光光谱技术

报道了在近红外波段的差分浓度调制激光光谱技术的研究工作,以N2^ 的浓度调制光谱为例,研究了浓度调制制激光光谱技术的特性。将浓度调制光谱与速度调制光谱相结合得到了速度调制光谱调制度与各因素的关系。同时展示的Ar激光发态的差分浓度调制光谱表明,差分浓度调制光谱技术在探测中性自由基分子和分子离子方面具有很大的应用潜力。     

THE SURFACE AREA PRESERVING MEAN CURVATURE FLOW IN QUASI-FUCHSIAN MANIFOLDS

In this paper,we consider the surface area preserving mean curvature flow in quasi-Fuchsian 3-manifolds.We show that the flow exists for all times and converges exponentially to a smooth surface of constant mean curvature with the same surface area as the initial surface.     

A Numerical Calibration Approach to Obtain Cutting Fluid Droplet Sizes in a Turning Process via an Imaging System

Airborne inhalable particulate in the workplace can represent a significant health hazard, and one of the primary sources of particles is mist produced through the application of cutting fluids in machining operations. The atomization process is one of the principal mechanisms associated with cutting fluid mist formation and generates droplets from fifty to a few thousand micrometers in size. These particles subsequently undergo vaporization and settling effects resulting in an aerosol to which workers may be exposed. While a variety of equipment is available to characterize the fine particulate in the breathing zone, standard equipment to measure the size of the atomized droplets is not available. In this paper, an imaging system is employed to characterize the large droplets produced by atomization in turning. One of the drawbacks of such a system is the time‐consuming experimental calibration procedure that is required to improve the accuracy of the droplet size measurements and extend the depth of field of the imaging system. With this in mind, an approach is introduced to predict droplet diameter based on measurement data without physical system calibration. The relationship between the actual diameter and the measured diameter is established based on an imaging system simulation model that includes a three dimensional point spread function and an image formation relationship grounded in the principles of geometric optics. These two components are combined using convolution integral theory to derive an image intensity profile. The introduction of halo width into the simulation greatly extends the image depth of field, which is a critical factor in capturing more droplets in one image and also minimizing particle size distribution bias towards larger droplets. The model predicts droplet diameter as a function of measured diameter and halo width. Model behavior of predicted diameters from the simulation compares well with those from a physical calibration of the system. The numerical calibration model is then used in the study of cutting fluid atomization in a turning process, and the measured droplet size distribution compares favorably with droplet sizes predicted by a mechanistic atomization model.