富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Ultra high performance liquid chromatography with ion‐trap TOF‐MS for the fast characterization of flavonoids in Citrus bergamia juice

We have developed a fast ultra HPLC with ion‐trap TOF‐MS method for the analysis of flavonoids in Citrus bergamia juice. With respect to the typical methods for the analysis of these matrices based on conventional HPLC techniques, a tenfold faster separation was attained. The use of a core–shell particle column ensured high resolution within the fast analysis time of only 5 min. Unambiguous determination of flavonoid identity was obtained by the employment of a hybrid ion‐trap TOF mass spectrometer with high mass accuracy (average error 1.69 ppm). The system showed good retention time and peak area repeatability, with maximum RSD% values of 0.36 and 3.86, respectively, as well as good linearity (R² ≥ 0.99). Our results show that ultra HPLC can be a useful tool for ultra fast qualitative/quantitative analysis of flavonoid compounds in citrus fruit juices.     

FIPSDock: A new molecular docking technique driven by fully informed swarm optimization algorithm

The accurate prediction of protein–ligand binding is of great importance for rational drug design. We present herein a novel docking algorithm called as FIPSDock, which implements a variant of the Fully Informed Particle Swarm (FIPS) optimization method and adopts the newly developed energy function of AutoDock 4.20 suite for solving flexible protein–ligand docking problems. The search ability and docking accuracy of FIPSDock were first evaluated by multiple cognate docking experiments. In a benchmarking test for 77 protein/ligand complex structures derived from GOLD benchmark set, FIPSDock has obtained a successful predicting rate of 93.5% and outperformed a few docking programs including particle swarm optimization (PSO)@AutoDock, SODOCK, AutoDock, DOCK, Glide, GOLD, FlexX, Surflex, and MolDock. More importantly, FIPSDock was evaluated against PSO@AutoDock, SODOCK, and AutoDock 4.20 suite by cross‐docking experiments of 74 protein–ligand complexes among eight protein targets (CDK2, ESR1, F2, MAPK14, MMP8, MMP13, PDE4B, and PDE5A) derived from Sutherland‐crossdock‐set. Remarkably, FIPSDock is superior to PSO@AutoDock, SODOCK, and AutoDock in seven out of eight cross‐docking experiments. The results reveal that FIPS algorithm might be more suitable than the conventional genetic algorithm‐based algorithms in dealing with highly flexible docking problems. © 2012 Wiley Periodicals, Inc.     

基于改进免疫遗传算法的近红外光谱变量选择方法

该文在免疫遗传算法（IGA）的基础上,提出一种改进免疫遗传算法（iIGA）用于近红外光谱波长变量的选择。该算法舍去了原算法中固定抗体相似度阈值的思想,取而代之的是抗体相似度阈值自适应,同时引入精英保留策略和贪心算法思想,使得算法朝着正确的方向进行局部性探优。将该算法在玉米的淀粉和蛋白质含量数据集上进行实验测试,建立偏最小二乘（PLS）分析模型,并与IGA、遗传算法（GA）以及全谱方法进行了对比。结果表明,在玉米淀粉含量的预测上,iIGA相较于原IGA算法,预测集均方根误差（RMSEP）从0.312 0降至0.298 0,预测集预测精度提升4.5%;在玉米蛋白质含量的预测上,RMSEP从0.124 4降至0.110 3,预测集预测精度提升11.3%。分别对预测淀粉和蛋白质模型的RMSEP值进行显著性检验,F值分别为165.22和182.05,P值分别为9.5 × 10－23和4.5 × 10－24,P值均小于0.05,因此,iIGA能显著提升模型预测精度。     

基于联合分步APIT定位算法的改进

本文研究了无线传感网络( Wireless Sensor Network,WSNs)的节点定位问题,并针对APIT由于锚节点在低密度环境下的节点误判和节点失效等问题给出了改进,在APICT定位算法的基础提出了联合分步定位算法UNION-APICT(Union Approximate Point-In-Circumcircle Test),该算法是结合连通性的测距技术,RSSI测距技术以及质心定位和APICT等技术,来联合解决对未知节点定位问题。通过仿真实验结果表明,改进后的UNION-APICT在APICT算法的基础之上平均定位误差减少了10%-25%,定位性能有了明显的提升;随着通信半径R和最大探测距离rmax的增加,定位误差也在逐渐减小,该算法较APIT和APICT定位算法在锚节点密度、节点覆盖率和定位精度上都有所提高。     

Dimensional considerations on the mechanical properties of 3D printed polymer parts

Additive manufacturing offers a useful and accessible tool for prototyping and manufacturing small volume functional parts. Polylactic acid (PLA) and thermoplastic polyurethane (TPU) are amongst the most commonly used materials. Characterising 3D printed PLA and TPU is potentially important for both designing and finite element modelling of functional parts. This work explores the mechanical properties of additively manufactured PLA/TPU specimens with consideration to design parameters including size, and infill percentage. PLA/TPU specimens are 3D-printed in selected ISO standard geometries with 20%, 60%, 100% infill percentage. Tensile and compression test results suggest that traditional ISO testing standards might be insufficient in characterising 3D printed materials for finite element modelling or application purposes. Infill percentage in combination to design size, may significantly affect the mechanical performance of 3D printed parts. Dimensional variation may cause inhomogeneity in mechanical properties between large and small cross section areas of the same part. The effect was reduced in small cross section parts where reducing the nominal infill had less effect on the resulting specimens. The results suggest that for 3D printed functional parts with significant dimensional differences between sections, the material properties are not necessarily homogeneous. This consideration may be significant for designers using 3D printing for applications, which include mechanical loading.     

Effect of Gaussian size distribution width on minimum fluidization velocity in tapered gas–solid fluidized beds

This paper investigated the effect of Gaussian distribution width, average particle diameter, particle loading, and the tapered angle on minimum fluidization velocity (U_mf) by conducting extensive experiments in tapered fluidized beds. Three powders with Gaussian size distribution and different distribution widths were used in the experiments. An increase in U_mf with increasing the average particle diameter, particle loading, and the tapered angle was observed. There was also a nonmonotonic behavior of U_mf as the Gaussian distribution width increased. An empirical correlation including dimensionless groups for predicting U_mf in tapered beds was developed in which the effect of distribution width was considered. The proposed correlation predictions were in good agreement with the experimental data, with a maximum deviation of 16.5% and average and standard deviations of, respectively, 6.4% and 7.4%. The proposed correlation was also compared with three earlier models, and their accuracy was discussed.     

HIGH-ORDER-ACCURATE DISCRETIZATION STENCIL FOR AN ELLIPTIC EQUATION

The coefficients for a nine-point high-order-accurate discretization scheme for an elliptic equation ∇²u− γ²u=r₀ (∇² is the two-dimensional Laplacian operator) are derived. Examples with Dirichlet and Neumann boundary condtions are considered. In order to demonstrate the high-order accuracy of the method, numerical results are compared with exact solutions.     

仪器定量分析中几个问题的探讨

详细介绍了分析方法的评价指标,包括检出限、测定限、灵敏度、精密度、准确度、动态范围和线性范围、抗干扰能力等,单因素优化方法与加标回收实验评定测定结果准确度的可靠性,并就分析工作中遇到的一些实际问题进行了讨论.     

Preparation and Properties of Poly（ether ether ketone）/Carbon Nanotube Modified Polypropylene Janus Composite Separator北大核心CSCD

Lithium-ion batteries （LIBs）have attracted wide attention because of their broad prospects in electric vehicles. However,the safety problems and low multiplier performance of the commercial polyolefin separator limit their further development,due to the poor dimensional thermal stability and low electrolyte absorption rate. Poly（ether ether ketone）（PEEK）and carbon nanotube（CNT）are compounded to coat on polypropylene （PP） to prepare Janus composite separator （PP@C） through the phase inversion method. PP@C composite separator does not deform at 180 ℃ for 0. 5 h（only slight deformation）,illustrating excellent thermal stability. The electrolyte absorption rate of PP@C2 is 193. 8%. The electrolyte uptake rate of the PP@C2 composite membrane was 193. 8%,which was 64. 5% higher than the PP membrane,showing a superduper electrolyte permeability. As a result,the specific discharge capacity of LIBs assembled with PP@C2 composite separator is 157. 6 mA·h/g at 0. 2 C and 129. 8 mA·h/g at 2 C,showing good rate performance with the capacity recovery rate of more than 99%. This might be attributed to the ultra-high thermal stability of PEEK,the good affinity of the electrolyte,the high conductivity of CNT,as well as the uniform dispersion of Li+ ,so that the separator can have excellent electrochemical performance while improving safety. © 2022, Science Press (China). All rights reserved.