2 votes
Accepted

Is it possible to split the optimization problem into multiple sub problem if the objective function are product of univariate function?

Without restrictions on the functions $g_1,g_2,g_3$ the general answer is no, you cannot separately optimize the variables. For example, For a concrete example consider $g_1 = g_2 = g_3 = f_1 = f_2 = ...
Matt Werenski's user avatar
1 vote
Accepted

What it means by Modulo $1$ in a self-transformation

It is a way of saying "Take the decimal part". Clearly multiplying by $10$ easily brings you out of the interval $[0,1)$, so this solves the problem. In this way $T(0.31)=0.1$. A correct way ...
SilvioM's user avatar
  • 1,233
1 vote

Impact of Basis Transition on Vector Magnitudes

Basis change doesn't change length ratios. If $M$ is the matrix for basis change from $B$ to $C$, i.e. $[v]_C=M[v]_B$, then we have: $$[v_1]_C = M[v_1]_B = M\cdot 3[v_2]_B = 3\cdot M[v_2]_B=3[v_2]_C \ ...
SilvioM's user avatar
  • 1,233
1 vote
Accepted

What function looks like the edge of a paper book sideways?

This appears similar to the probability density function of the F-distribution from statistics. You will likely need to make a few tweaks to the d1 and d2 numbers from the formula for the F-...
Jonah Pandarinath's user avatar
1 vote
Accepted

How to deduce the new distance function of a manifold after a transformation of coordinates?

As for a formula for a change of a distance function, it is the following. Suppose that $𝑓:𝑀\to (𝑁,𝑑)$ is a homeomorphism, where $d=𝑑_𝑁$ is a distance function. Then the corresponding distance ...
Moishe Kohan's user avatar
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