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Electronic Circuits
Published in Dale R. Patrick, Stephen W. Fardo, Electricity and Electronics Fundamentals, 2020
Dale R. Patrick, Stephen W. Fardo
A crystal by itself behaves like a series resonant circuit. It has inductance (L), capacitance (C), and resistance (R). Figure 4-74(a) shows an equivalent circuit. The L function is determined by the mass of the crystal. Capacitance deals with its ability to change mechanically. Resistance corresponds to the electrical equivalent of mechanical friction. The series resonant equivalent circuit changes a great deal when the crystal is placed in a holder. Capacitance due to the metal support plates is added in parallel with the crystal equivalent circuit. Figure 4-74(b) shows the equivalent circuit of a crystal placed in a holder. In a sense, a crystal can have either a series resonant or a parallel resonant characteristic.
Introduction to Fuzzy Sets: Basic Definitions and Relations
Published in Ali Zilouchian, Mo Jamshidi, Intelligent Control Systems Using Soft Computing Methodologies, 2001
Figure 8.7 illustrates some of the possible membership functions, we have: (a) the Γ-function: an increasing membership function with straight lines; (b) the L-function: a decreasing function with straight lines; (c) ∧-function: a triangular function with straight lines; (d) the singleton: a membership function with a membership function value 1 for only one value and the rest is zero. There are many other possible functions such as trapezoidal, Gaussian, sigmoidal or even arbitrary.
Dynamic lane changing trajectory planning for CAV: A multi-agent model with path preplanning
Published in Transportmetrica B: Transport Dynamics, 2022
Fang Zong, Zhengbing He, Meng Zeng, Yixuan Liu
In this paper, the cost function for energy-efficiency is denoted as the fuel consumption, which is calculated with velocity and corresponding acceleration (Ahn 1998) as follows: where denotes the fuel consumption (L) function of path candidate . The first part of is the fuel consumption of the SV, and the second the participants’. and are the velocity and acceleration of the SV in the Cartesian coordinate system, respectively, and and are that of the participant n, . c1 and c2 are the corresponding coefficient of velocity and acceleration power functions, respectively. is a constant coefficient.
Hybrid sampling method for autoregressive classification trees under density-weighted curvature distance
Published in Enterprise Information Systems, 2021
Hua Ye, Xilong Qu, Shengzong Liu, Guang Li
Because the result of the sampling method depends on the relationship between the sampling points and the overall data, the relative accuracy P of sampling can be used to evaluate the approximation degree of the algorithm to the data. Thus, a larger value indicates a better sampling performance of the algorithm (Kumar, Mohri and Talwalka 2009; Boming et al. 2018), with the maximum value being assumed as 1. Here, and represent the actual and sampling labels of the data points in the sampling algorithm, respectively. The function is a sampling function, map function is the optimal mapping, while L function represents quantisation level processing for the label. In the silhouette segmentation experiments proposed in this paper, the accuracy of the silhouette features obtained by segmentation is represented by the relative, accuracy of the sampling, and is the recall rate of silhouette features, TPR and FPR are defined as,
Inferring 3D ellipsoids based on cross-sectional images with applications to porosity control of additive manufacturing
Published in IISE Transactions, 2018
Jianguo Wu, Yuan Yuan, Haijun Gong, Tzu-Liang (Bill) Tseng
Under CSR, K(t) = πt2. Therefore, we can test the difference between the theoretically calculated K(t) curve under CSR and the estimated based on the observations. In practice, it is better to use the L function , as the estimated has an approximately constant variance. Under CSR, L(t) = t. To test whether L(t) = t, we use the test statistic . The p-values for the hypothesis testing are obtained through Monte Carlo simulations. Figure 10 shows the theoretical K function under CSR, the estimated , the histograms of the simulated , and observed test statistics for the three specimens. We can clearly see that the estimated function is very close to the theoretical K function. The p-values of the hypothesis testing are 0.466, 0.757, and 0.596, respectively, for the three specimens, all of which are not significant. Therefore, it is reasonable to assume that all of the voids are uniformly distributed.