In this lesson, we find the power series for ln(1 - x) by deriving a simpler series and then integrating it. This lesson includes how to find the...
Find the power series for f(x)=lnx centered at x=2 by using term-by-term integration or differentiation. f(x)=ln2+∑n=0∞There are 3 steps to solve this one. Solution Share Step 1 Find the power series for f(x)=lnx...
Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the ro
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Transient prompt makes it much easier to copy-paste series of commands from the terminal scrollback.Tip: If you enable transient prompt, take advantage of two-line prompt. You'll get the benefit of extra space for typing commands without the usual drawback of reduced scrollback density. Sparse...
(9)varY∝{E(Y)}2(1−λ), Taylor series expansion shows that the variance is approximately stabilized by using as the response yλλ≠0log yλ=0. So, for λ = 1, the variance is independent of the mean and no transformation is necessary. When λ = 0.5, the variance is propor...
Using cross entropy as the loss function, the mathematical formula for the function is shown in Eq. (16). $$\begin{aligned} C=\frac{1}{n} \sum _{x}^{} [yln(a)+(1-y)ln(1-a)] \end{aligned}$$ (16) In Eq. (16), y is the expected output and a is the actual output....
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In the next subsection, we will present the general PI-PBC design for bilinear systems. 3.1. Bilinear Representation To develop a controller based on the PI-PBC approach, let us make the following definition. Definition 1. An admissible equilibrium point ( x ★ ) exists for non-linear ...
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