A power series is the sum of an infinite number of terms. Each term is a power of x multiplied by a coefficient. The steps associated with finding the power series of ln(1 - x) include:Deriving the power series for a related function, 1 / (1 - x) Integrating to find the power ...
In a previous paper, we developed a power series representation and estimates for an effective action of the formln[∫ef(α1,…,αs;z,z)dμ(z,z)/∫ef(0,…,0;z,z)dμ(z,z)]. Here,f(α1,…,αs;z,z)is an analytic function of the complex fieldsα1(x),…,αs(x),z(x)...
powershell to the target foldersudo tar zxf /tmp/powershell.tar.gz -C /usr/local/microsoft/powershell/7# Set execute permissionssudo chmod +x /usr/local/microsoft/powershell/7/pwsh# Create the symbolic link that points to pwshsudo ln -s /usr/local/microsoft/powershell/7/pwsh /usr/local...
\int_{0}^{1}\frac{(\ln{x})^2}{1+x^2}dx=2(\frac{1}{1^3}-\frac{1}{3^3}+\frac{1}{5^3}-...) 后面是一个很well-known的级数,可以用Fourier series做出来,结果是 \frac{\pi^3}{32} ,所以: \int_{0}^{1}\frac{(\ln{x})^2}{1+x^2}dx=\frac{\pi^3}{16} 上次...
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applying either of the transfor mations xi=Ti(Xi)=XiQi, where Qi < 0, or xi = Ti(Xi) =exp(Xi) to any variables xi with positive powers in the term, as long as the inverse transformations Xi=Ti-1(xi)=xi1/Qi and Xi=Ti-1(xi)=ln(xi) respectively, are approximated by PLFs X...
$$\begin{aligned} C=\frac{1}{n} \sum _{x}^{} [yln(a)+(1-y)ln(1-a)] \end{aligned}$$ (16) In Eq. (16), y is the expected output and a is the actual output. Figure 4 SFE module disturbance image conversion. Full size image The confusion matrix is introduced to show ...
There is also zsh-theme-powerlevel10k community package. Historically, it has been breaking often and for extended periods of time. Do not use it.Alpine Linuxapk add zsh zsh-theme-powerlevel10k mkdir -p ~/.local/share/zsh/plugins ln -s /usr/share/zsh/plugins/powerlevel10k ~/.local/...
Let L and S denote generic random variables following the same distribution with initial loads L1,…, LN and free spaces S1,…, SN, respectively. Then, with x* denoting the smallest solution ofover the range x* ∈ (0, ∞), the final system size n∞(p) at attack size p is ...
of 2DSH crystals. We further measure three other systems, and all of theirdvalues lie on the lineard(X) as shown in Fig.3c. Therefore, we conclude that the soft deformable part governsd. A larger area fraction of the soft part can produce more nonuniform deformation under compression, t...