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31.
Li  Hanyu  Zhu  Yuanyang 《BIT Numerical Mathematics》2021,61(3):911-939
BIT Numerical Mathematics - We present randomized algorithms based on block Krylov subspace methods for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using...  相似文献   
32.
植物精油是从芳香植物提取的天然复杂化合物,作为芳香植物的次生代谢产物具有挥发性和浓郁香味,其特有的多样化生物活性广泛应用于医药和化妆品行业。植物精油具有高渗透性,能以活跃的分子态渗透皮肤组织,经淋巴腺吸收后进入血液,其所含的重金属元素也极易随植物精油进入人体对健康构成潜在威胁。采用硝酸-双氧水对植物精油进行微波消解,在多模式样品导入系统(MSIS)的双重模式下,采用电感耦合等离子体发射光谱(ICP-OES)测定其中可形成蒸气重金属元素As,Sn,Sb,Hg和不可形成蒸气重金属元素Cr,Ni,Cd和Pb的含量。选择盐酸对样品进行酸化并预还原氧化态元素,通过在线加入L-半胱氨酸/酒石酸提高可形成蒸气元素的蒸气发生效率,利用硼氢化钠/氢氧化钠在MSIS中将As,Sn,Sb和Hg转变为蒸气状态;针对分析过程中存在的多个或单个光谱重叠和背景干扰,分别对空白溶液、分析元素和预期干扰元素的纯溶液进行测定,根据获得的光谱响应数据解卷积构建快速自动曲线拟合技术(FACT)模型,将分析谱线从干扰谱线中分离出来,从而实现光谱重叠干扰和背景干扰的实时校正;采用加标回收并与电感耦合等离子体质谱(ICP-MS)进行对比分析评价方法的准确性。各元素方法的检出限(MDL)为0.38~11.2 μg·kg-1,加标回收率为95.4%~104%,相对标准偏差(RSD)为1.9%~4.9%,对比分析的相对误差(RE)在-2.1%~2.7%之间,表明方法准确可靠,精密度高。对8种植物精油中的重金属元素进行了分析,所有植物精油样品中重金属元素As,Hg和Pb的含量远低于GB/T 26516—2011制定的限量标准,植物精油中重金属元素Cr,Ni,Sn,Cd和Sb的含量虽然没有制定限量标准,但均处于极低水平。MSIS兼具传统雾化和蒸气发生双重功能,在分析可形成蒸气元素和不可形成蒸气元素时无需切换不同进样系统,能满足大批量植物精油中微量重金属元素的高通量分析需要。  相似文献   
33.
卓峻峭  夏爽 《化学教育》2022,43(1):115-117
介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。  相似文献   
34.

The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (U-PFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.

  相似文献   
35.
主要研究了两类近似凸集的关系和性质.首先,举例说明两类近似凸集没有相互包含关系.其次,在近似凸集(nearly convex)条件下,证明了在一定条件下函数上图是近似凸集与凸集的等价关系.同时,考虑了近似凸函数与函数上图是近似凸集的等价刻画、近似凸函数与函数水平集是近似凸集的必要性,并用例子说明近似凸函数与函数水平集是近似凸集的充分性不成立.最后,基于近似凸函数和拟凸函数的概念,给出了近似拟凸函数的概念并研究了近似拟凸函数与水平集是近似凸集的等价刻画.  相似文献   
36.
Wu  Zengyuan  Zhou  Caihong  Xu  Fei  Lou  Wengao 《Annals of Operations Research》2022,308(1-2):685-701

Quality inspection is essential in preventing defective products from entering the market. Due to the typically low percentage of defective products, it is generally challenging to detect them using algorithms that aim for the overall classification accuracy. To help solve this problem, we propose an ensemble learning classification model, where we employ adaptive boosting (AdaBoost) to cascade multiple backpropagation (BP) neural networks. Furthermore, cost-sensitive (CS) learning is introduced to adjust the loss function of the basic classifier of the BP neural network. For clarity, this model is called a CS-AdaBoost-BP model. To empirically verify its effectiveness, we use data from home appliance production lines from Bosch. We carry out tenfold cross-validation to evaluate and compare the performance between the CS-AdaBoost-BP model and three existing models: BP neural network, BP neural network based on sampling, and AdaBoost-BP. The results show that our proposed model not only performs better than the other models but also significantly improves the ability to identify defective products. Furthermore, based on the mean value of the Youden index, our proposed model has the highest stability.

  相似文献   
37.
Considering the random impulses of mechanical noise and the limitations involved while identifying mechanical fault impulse signals via traditional measurement indices of signal-to-noise ratio, which require the characteristic frequency to be known in advance, this study proposes an adaptive unsaturated stochastic resonance method employing maximum cross-correlated kurtosis as the signal detection index. The proposed method combines the features of a cross-correlated coefficient to indicate periodic fault transients and those of spectrum kurtosis to locate these transients in the frequency domain. Actual vibration signals collected from motor and gear bearings subjected to heavy noise are used to demonstrate the effectiveness of the proposed method. Through a coarse tree-based machine learning method, the proposed method is verified to be more suitable for explaining the periodic impulse components of bearing signals, as compared to the ensemble empirical mode decomposition denoising method and unsaturated stochastic resonance using the kurtosis-intercorrelation index.  相似文献   
38.
Josephson junction is an active electric component and its channel current can be adjusted by external magnetic field, which can trigger additive phase error along the junction. From physical viewpoint, the Josephson junction can capture and release field energy when it is exposed to a magnetic field, and this time-varying current can be used to excite neural circuit for generating target firing patterns. In this paper, a Josephson junction is connected to a simple neural circuit, which is made of a capacitor, induction coil, a nonlinear resistor, two linear resistors and one constant voltage source in the branch, and the improved neural circuit is adjusted to percept external magnetic field and estimate the potential application of Josephson junction in nonlinear circuits. Bifurcation analysis is applied to explore the mode selection and dynamics dependence on parameters setting in the biophysical neural circuits. Furthermore, the neural circuit is exposed to external magnetic field and its physical effect is estimated by applying scale transformation on the variables and parameters in the neural circuit. It is confirmed that the neural circuit can be controlled and the neural activity shows distinct mode transition by taming the intensity (or angular frequency in periodic field) of external magnetic field. This kind of neural circuit can be further used as smart sensor for detecting weak magnetic field.  相似文献   
39.
Stochastic resonance (SR) has been extensively utilized in the field of weak fault signal detection for its characteristic of enhancing weak signals by transferring the noise energy. Aiming at solving the output saturation problem of the classical bistable stochastic resonance (CBSR) system, a double Gaussian potential stochastic resonance (DGSR) system is proposed. Moreover, the output signal-to-noise ratio (SNR) of the DGSR method is derived based on the adiabatic approximation theory to analyze the effect of system parameters on the DGSR method. At the same time, for the purpose of overcoming the drawback that the traditional SNR index needs to know the fault characteristic frequency (FCF), the weighted local signal-to-noise ratio (WLSNR) index is constructed. The DGSR with WLSNR can obtain optimal parameters adaptively, thereby establishing the DGSR system. Ultimately, a DGSR method is proposed and applied in centrifugal fan blade crack detection. Through simulations and experiments, the effectiveness and superiority of the DGSR method are verified.  相似文献   
40.
秦杰  李佳  李军 《化学物理学报》2021,34(6):649-658
H+SO2→OH+SO反应在燃烧、大气和星际化学中都扮演着重要角色. 它还是具有深势阱中间体形成的典型反应,是检验速率理论和提供有趣反应动力学现象的理想候选反应. 基于之前构建的全维高精度势能面,本文对该反应进行了准经典动力学研究. 在1400 K≤T≤2200 K的温度范围内,计算值重现了实验速率常数. 当反应物SO2处于振-转基态,在31.0∽40.0 kcal/mol的碰撞能范围内,计算得到的积分反应截面随碰撞能增加;在40∽55 kcal/mol的碰撞能范围内,积分反应截面几乎不受碰撞能影响. 产物角度分布呈现对称的前后向双峰结构. 本文还分析了产物OH和SO的振动态分布.  相似文献   
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