Taylor公式在级数判敛中的应用

利用Taylor公式把一些级数的通项un近似表示成幂函数1/n^α和（-1）^n/n^β的线性组合，误差为高阶无穷小。根据级数∞∑n=1 1/n^α和∞∑n=1 （-1）^n/n^β的收敛情况比较容易地判别级数∞∑n=1 un的敛散性。     

The influence of air content in water on ultrasonic cavitation field

Cavitation is a complex physical phenomenon affected by many factors, one of which is the gas dissolved in the medium. Researchers have given some efforts to the influence of gas content on sonoluminescence or some specific chemical reactions in and around the bubble, but limited work has been reported about the influence on the ultrasonic cavitation field distribution. In this work, the intensity distribution of the ultrasound field in a cleaning tank has been measured with the hydrophone. After analysed and visualised by MATLAB software, it was found that the cavitation intensity distribution in degassed water was much better than that in tap water. And further study proved that degassing process can improve the cavitation effect dramatically both in intensity and scope. Finally, the cavitation fields in mediums with different gas content were measured and the specific influence of air content on cavitation field was discussed.     

Effects of ultrasound and temperature on copper electro reduction in Deep Eutectic Solvents (DES)

This paper concerns a preliminary study for a new copper recovery process from ionic solvent. The aim of this work is to study the reduction of copper in Deep Eutectic Solvent (choline chloride–ethylene glycol) and to compare the influence of temperature and the ultrasound effects on kinetic parameters. Solutions were prepared by dissolution of chloride copper salt CuCl₂ (to obtain Copper in oxidation degree II) or CuCl (to obtain Copper in oxidation degree I) and by leaching metallic copper directly in DES. The spectrophotometry UV–visible analysis of the leached solution showed that the copper soluble form obtained is at oxidation degree I (Copper I). Both cyclic voltammetry and linear voltammetry were performed in the three solutions at three temperatures (25, 50 and 80 °C) and under ultrasonic conditions (F = 20 kHz, PT = 5.8 W) to calculate the mass transfer diffusion coefficient kD and the standard rate coefficient k°. These parameters are used to determine that copper reduction is carried out via a mixed kinetic-diffusion control process. Temperature and ultrasound have the same effect on mass transfer for reduction of Cu^II/Cu^I. On the other hand, temperature is more beneficial than ultrasound for mass transfer of Cu^I/Cu. Standard rate constant improvement due to temperature increase is of the same order as that obtained with ultrasound. But, by combining higher temperature and ultrasound (F = 20 kHz, PT = 5.6 W at 50 °C), reduction limiting current is increased by a factor of 10 compared to initial conditions (T = 25 °C, silent), because ultrasonic stirring is more efficient in lower viscosity fluid. These values can be considered as key-parameters in the design of copper recovery in global processes using ultrasound.     

Fractal surface for calibration of an optical profiler

The surface profiler has become a basic metrology tool for the characterization of high-quality optical surfaces. The unknown effective resolution of the surface profiler is problematic in using the instrument, as it distorts the measured surface profile. In this paper, we suggest and describe the use of a fractal surface as a standard test surface with which to calibrate the effective resolution of a surface profiler. Fractal surfaces have the characteristics of irregularity, self-similarity and low correlation, with the correlation length being approximately equal to the length of the profile; therefore, a log-log plot of the power spectral density curve is a straight line. The power spectral density curves of fractal surfaces, which can be acquired through surface characterization techniques such as atomic force microscopy, are fitted to a straight line to act as a standard with which to calibrate an optical profiler in different ranges. Through calibration, we can obtain the effective resolution of the optical profiler, and the surface profiler is found to have good transmission capacity within the effective spatial frequency range.     

Measurement of the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame by means of a laser-based interferometer technique

With a view to measuring the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame, a thin laser beam is sent into the flame perpendicular to the flow direction. The laser beam generally undergoes fluctuations of direction, phase, and amplitude. Only the random deflections of the laser beam may be taken into account. After having traversed the flame, the perturbed laser beam enters into an interferometric system. Materials and experimental procedure are described. In the unperturbed interference pattern, the zones only sensitive to fluctuations of the angle-of-arrival of the laser beam are detected. From the random displacements of the central bright fringe, the structure coefficient of refractive index fluctuations in the flame is measured. To prove that the method of measurement is satisfactory, the result obtained is applied for computing the power spectral density of the angle-of-arrival of the laser beam from the formula of correlations of the laser beam deflection angles which we have demonstrated in previous works. This computed power spectral density is compared to that measured from the effective position of the detector. A good agreement is observed between the two results.     

Harmful effects on organism induced by light of different wavelength and power

Although a variety of experiments on light exposure stress to animals significantly affect the retina and circulation system, it is still unknown the relationship between the different extent of harmful effect on organism and light with different wavelengths and power. This study is aimed to investigate the changes to microblood vessel and the variations in serum absorption spectrum. LED light of different wavelength and power were used. The results show that power has a relatively larger impact on physiological indexes than wavelength. The extents of these variations are relatively different according to the regression equations. All of these stimulations cause damage to mice physiological conditions, producing some extent of light pollution. The research findings supply the guideline for the effective prevention of the harmful effect on organism by light pollution from the view of science of optical life science.     

蓝青铜单晶Rb_(0.3)MoO_3和Rb_(0.15)K_(0.15)MoO_3的热电势特性

在 90～ 2 90 K范围内对蓝青铜单晶 Rb0 .3 Mo O3和 Rb0 .1 5 K0 .1 5 Mo O3的热电势与温度的关系进行了比较研究 ,发现 :1)在 180 K附近 ,两种蓝青铜导体的热电势出现突变是这两种物质存在 Peierls相变的的又一例证并分别分析了 A位元素的完全替代和部分替代对 Peierls相变的影响 ;2 )在相变点 TP以上和以下 ,两者的热电势有相似的变化 ,由高温区较小的正值变为低温区较大的负值 ,并可以用经验关系式 S=AT B/ T来描述     

Closed-form analysis for indirect learning digital pre-distorter for wideband wireless systems

Indirect learning architecture (ILA) for digital pre-distortion (DPD) is commonly used to linearize power amplifiers (PA). To the author’s best knowledge, most of the DPD results in the literature obtain the matrix form of the least-square solution in order to get the DPD coefficients numerically. There exists no explicit closed-form for these coefficients that can be used as plug-and-play in simulations, or used for further closed-form analysis of important measures such as signal-to-noise ratio (SNR) and mean square error (MSE), bit-error rate (BER), …etc. In this paper, we analyze the ILA-DPD system for general memory-polynomial PA models. We provide a closed-form solution for the DPD coefficients. We first present the analytical methodology for deriving the mathematical expressions for each DPD coefficient and then introduce an open-access code that generates the DPD coefficients in symbolic form that is used to mathematically model the DPD. We consider case studies for PA and show that the analytical DPD solution matches the Monte Carlo simulations. Moreover, we also provide a closed-form solution for the iterative adaptive ILA-DPD. Our analysis shows that in the case of a large training block length the non-iterative DPD achieves approximately the same performance as an iterative DPD with a shorter training block length. System impairments are also considered, e.g. the thermal noise and the quantization noise in analog–digital conversion (ADC). We derive the normalized mean square error (NMSE) for the transmit chain in the presence of these impairments. The NMSE expression is verified through numerical simulations.     

超导低电阻接头衰减法测试过程中的拟合偏差控制

超导技术在许多高新技术领域有着广泛而深远的应用前景,其中超导导体接头技术是超导发展过程中必不可少的关键环节之一,快速而又准确地评估低电阻接头显得尤为重要.本文在考虑超导体的E-J特性后,针对目前低电阻接头采用的衰减法测量,计算得出感应电流完整的衰减曲线方程-幂函数方程.对比目前广泛采用的指数方程拟合与采用幂函数方程拟合的偏差,指出采用指数方程代替幂函数方程拟合的必要条件,为接头电阻衰减法测试,尤其是低电阻接头情况下的测量提供参考.