Measurement interpretation and information measures in general probabilistic theory

The incompatibility of dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has recently been solved by Zurek from an information transfer perspective. Luo gave his derivation by relaxing the repeatability postulate. In this paper, we reconsider Luo’s derivation in the setting of general probabilistic theory (GPT). We also introduce the concept of sub- and super-fidelity in GPT and discuss their properties.     

Preparation and photocatalytic activity of bicrystal phase TiO2 nanotubes containing TiO2-B and anatase

Bicrystal phase TiO₂ nanotubes (NTS) containing monoclinic TiO₂-B and anatase were prepared by the hydrothermal reaction of anatase nanoparticles with NaOH aqueous solution and a heat treatment. Their structure was characterized by XRD, TEM and Raman spectra. The results showed that the bicrystal phase TiO₂ NTS were formed after calcining H₂Ti₄O₉·H₂O NTS at 573 K. The bicrystal phase TiO₂ NTS exhibit significantly higher photocatalytic activity than the single phase anatase NTS and Dessuga P-25 nanoparticles in the degradation of Methyl Orange aqueous solution under ultraviolet light irradiation, which is attributed to the large surface and interface areas of the bicrystal phase TiO₂ NTS.     

Metal Nanoclusters–Based Ratiometric Fluorescent Probes from Design to Sensing Applications

Ratiometric fluorescent probes have many advantages including improved sensitivity, high reliability and accuracy, visualization sensing, etc. Herein, the development of metal nanoclusters (NCs)‐based ratiometric fluorescent probes in the recent years is summarized. NCs, an emerging new class of fluorescent nanomaterials, have demonstrated excellent optical properties, good biocompatibility, great aqueous solubility, low cost, and simple synthesis, and NCs‐based ratiometric fluorescent probes have attracted much attention. In this progress report, the preparation and properties of NCs and the design of ratiometric fluorescent probes are summarized. Sensing of a broad range of analytes including cations, gas, small molecules, macromolecules, temperature, and pH is discussed. In addition, the challenges and future directions for NCs‐based ratiometric fluorescent probes are also presented.     

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

In this paper, the authors consider the boundary value problem

and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.

     

基于有限条带的厚/薄板矩形通用单元

基于两广义位移梁理论，利用解析试函数来建立厚／薄梁单元的横向位移、转角位移、曲率、剪应变等位移模式，构造出厚／薄梁通用单元．应用有限条带，将厚／薄梁单元的位移模式应用于厚／薄板矩形弯曲单元，直接构造出单元的横向位移、转角、曲率、剪应变，导出了单元的刚度矩阵和结点等效力，编制了计算程序，进行了数值计算和比较，结果表明，所研究的单元不出现剪切闭锁且精度较好．     

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.     

带权Paneitz算子和带权圆盘振动问题的特征值不等式

本文研究光滑度量测度空间上带权Paneitz算子的闭特征值问题和带权圆盘振动问题,给出Euclid空间、单位球面、射影空间和一般Riemann流形的n维紧子流形的权重Paneitz箅子和带权圆盘振动问题的前n个特征值上界估计.进一步地,本文给出带权Ricci曲率有界的紧致度量测度空间上带权圆盘振动问题的第一特征值的下界...     

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.     

Facile fabrication of freestanding through-hole ZrO2 nanotube membranes via two-step anodization methods

Highly ordered freestanding tubular zirconia (ZrO₂) membrane was prepared via an electrochemical anodization of zirconium (Zr) substrate in non-aqueous electrolytes (mixture of formamide and glycerol (weight ratio = 1:1) containing 1 wt% NH₄F and 3 wt% H₂O). Two methods were used to fabricate the two-end opened ZrO₂ membranes, one is a potential shock method and another is a reducing potential method. The two-end opened ZrO₂ membrane was produced through the detachment of the existing self-organized ZrO₂ tubular layer from Zr substrate or sub tubular layer. The microstructures and morphologies of the samples were studied by scanning electron microscopy and the growth mechanisms of the two-end opened ZrO₂ nanotube arrays were investigated.