Strong Nearness Frames Having Enough Cauchy Filters

We prove results establishing sufficient conditions for the sum of two nearness frames to have enough Cauchy filters. From these results and the fact that, in the category of strong nearness frames having enough Cauchy filters and uniform frame maps, complete spatial frames form a coreflective subcategory, follow a variety of results where the open-sets contravariant functor from topological spaces to frames transforms products into sums and inverse limits into direct limits.     

Shearlet coorbit spaces and associated Banach frames

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments.     

A note on equiangular tight frames

We settle a conjecture of Joseph Renes about the existence and construction of certain equiangular tight frames.     

喷水室典型空气处理过程中空气流速的实验研究

针对纺织厂空调系统的核心-喷水室,研究喷水室内处理空气的冷却减湿和等焓加湿两个典型热湿交换过程。提出Re准数对传热传质有显著作用,而Re数的大小取决于流体速度。通过实验研究当空气流速从3m/s提高到5m/s时对喷水室热湿交换性能的影响,从而确定空气流动速度因素对两个热湿交换效率的影响趋势。根据拟合的数学曲线,总结出当空气的流动速度提高后,热湿交换效率相应提高。从而推动高速喷水室在实际工程中的应用。     

Tight wavelet frames for irregular multiresolution analysis

An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourier-domain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of subdivision surfaces around irregular vertices, and nonstationary subdivision. We consider the case of nonnegative refinement coefficients and develop a fully local construction method for tight frames. Especially, in the shift-invariant setting, our construction produces the same tight frame generators as the Unitary Extension Principle.     

Uniform frames with block size four and index one or three

Abstact: In this article, we present a new construction to obtain uniform frames with block size four and index one. The known existence results for (4, 1)‐frames and (4, 3)‐frames are both improved with a small number of possible exceptions. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 28–39, 2001     

Performance Evaluation and Effectiveness of the Reverberation Room

This research presents a thorough evaluation of the reverberation room at Acoustics Laboratory in National Institute of Standards (NIS) according to the related international standards. The evaluation aims at examining the room performance and exploring its effectiveness in the frequency range from 125 Hz to 10000 Hz according to the international standard requirements. The room, which was designed and built several years ago, is an irregular rectangular shape free from diffusers. Its volume is about 158.84 m³, which meets the requirement of the ISO 354 standard L_max < 1.9V^1/3. Cut-off frequencies of one and one-third octave are 63 Hz and 100 Hz respectively; however Schroder frequency is 400 Hz. Calculations of cut-off frequency and modal density showed adequate modes that give acceptable uniformity starting comfortably from frequency of 125 Hz. The room has a reverberation time that is suitable for its size over the frequency range of interest. The room sound absorption surface area and its sound absorption coefficient satisfy the criteria given in ISO 3741 and ISO 354. There is an accepted diffuse sound field inside the room due to the standard deviation of measured sound level, which is less than 1.5 dB over all the frequency range. The only exception was 125 Hz which may be due to a lack of diffusivity of the sound field at this frequency. The evaluation proves that the NIS reverberation room is in full agreement with the international standards, which in turns qualifies the room to host measurements inside without concerns.     

A Hydrogen Peroxide Biosensor Based on Room Temperature Ionic Liquid Functionalized Graphene Modified Carbon Ceramic Electrode

A room temperature ionic liquid (IL) 1‐butyl‐3‐methylimidazolium hexafluorophosphate functionalized graphene (GE) was prepared and a hydrogen peroxide (H₂O₂) biosensor was fabricated by immobilizing hemoglobin (Hb) into the IL‐GE composite film. UV‐visible and Fourier transform infrared spectra of the composite film indicated that Hb retained its native structure in the film. Electrochemical investigation of the biosensor showed a pair of well‐defined, quasi‐reversible redox peaks with E_pa=?0.209 V and E_pc= ?0.302 V (vs. SCE) in pH 7.0 phosphate buffer solution at the scan rate of 100 mV/s. To the reduction of H₂O₂, the biosensor had a good linear range from 8.0×10^?7 to 1.8×10^?4 mol/L with a detection limit of 3.0×10^?7 mol/L. The apparent Michaelis‐Menten constant K^app_M was estimated to be 3.4×10^?5 mol/L.     

室温下合成纺锤形貌六方相NaLnF_4(Ln=Nd,Sm,Eu,Gd,Tb)纳米颗粒

室温下合成长250nm,宽100nm的纺锤形貌六方相的NaNdF4。NaEuF4,NaSmF4,NaGdF4和NaTbF4也用同样的方法获得。产物用XRD,TEM,HRTEM,FESEM和PL进行表征。PL光谱显示合成的NaEuF4的激发波长是394nm。NaEuF4有4个特征发射谱带,分别是591,615,650和681nm。