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7:34 AM
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Q: Solving for the General Leibniz rule index

Numoruvery simply put. $$(fg)^{(n)} = \sum_{k=0}^n {n\choose k}f^{(n-k)}g^{(k)},$$ where ${n\choose k} = \dfrac{n!}{k!(n-k)!}$ is the binomial coefficient and $f^{(j)}$ denotes the $j$th derivative of $f$ (and in particular $f^{(0)}=f$). Solve for n (integers only of course, not going to to play myself...

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Q: Using d'Alemberts formula to solve a non-homogeneous wave-equation

Luthier415HzI have the given problem : A string is at rest and at time t=0 it is exposed to a constant force-distribution perpendicular from the longitude of the string. This force distribution remains for all $t>0$. Determine the signal of the string $u=u(x,t)$ if it is fastened ($u=0$ at the ends) and has ...

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Q: What's the rationale behind the definitions of min- and max-entropies?

glSGoing for example with the notation used in (Renner 2006), min- and max-entropies of a source $X$ with probability distribution $P_X$ are defined as $$H_{\rm max}(X) \equiv \log|\{x : \,\, P_X(x)>0\}| = \log|\operatorname{supp}(P_X)|, \\ H_{\rm min}(X) \equiv \min_x \left(-\log\left(\frac{1}{P_X(...

In information theory, the Rényi entropy generalizes the Hartley entropy, the Shannon entropy, the collision entropy and the min-entropy. Entropies quantify the diversity, uncertainty, or randomness of a system. The entropy is named after Alfréd Rényi, who looked for the most general definition of information measures that preserve additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also...
 

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