Why could picture previews disappear on a poppy?

Question

System administration

Previously, everything worked fine, but recently 90% of the images were left without thumbnails in the finder.
Help step by step, by elimination to find the cause.
I am using 10.10.2

Answer 1

On the Internet they write that it is necessary to clean the finder's cache. See more details here File previews not showing in Finder

Answer 2

It is required to choose a mapping function whose integral on the segment [0,1] is equal to the integral on the segment [1,100]. Let it be a monotonically decreasing function. Let's take 1/(x+a), where a is a positive parameter.
Let us select the value of the parameter so that the above conditions for normalizing the integrals are satisfied.
The indefinite integral is equal to ln(x+a)-C.
Definite integral [0,1] = ln(a+1) - ln a = ln ( (a+1) / a)
Definite integral [1,100] = ln(a+100) - ln (a+1) = ln ( (a + 100) / (a ​​+ 1))
We equate them, removing the logarithms, we get the equation (a + 1) (a + 1) \u003d a (a + 100).
Solution: a=1/98
Desired mapping for the random number generator f(x) = 98/(98x+1)
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UPD: Damn. This will not be the arithmetic mean equal to 1, but the median. Let's finish the task now.
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UPD2: In order for the mathematical expectation to be equal to 1, it is necessary to equate to each other not just integrals, but integrals of the square of the display function.
In order not to recalculate, we can say that the 98/(98x+1) obtained above is not the mapping itself, but its square. Those. answer f(x) = sqrt ( 98/(98x+1) )
Maybe wrong, but too lazy to think. All sleep!