# Tagged Questions

208 views

### Inequality involving the side lengths of a quadrilateral

If $a$, $b$, $c$ and $d$ are the four sides of a quadrilateral, the problem is to show that $ab^2(b-c)+bc^2(c-d)+cd^2(d-a)+da^2(a-b)\ge 0$. I've verified it to be true for quite a large number of ...
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### The fraction of the sphere a fixed distance from a subspace

The following problem has a beautiful geometric interpretation in terms of the proportion of points on the Euclidean sphere in $\mathbb{R}^d$ that lie at least a certain distance away from a ...
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### sobolev embedding theorem in the smooth metric measure space

we know the sobolev embedding theorem of Saloff-Coste $\Big(\int_B|F|^{2q}d\mu\Big)^{\frac1q}\le e^{C(1+\sqrt KR)}V^{-2/n}R^2\int_B\Big(|\nabla F|^2+R^{-2}F^2\Big)d\mu$ wtih $Ric\ge-(n-1)K$, for ...
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### Inequality involving probability measures [closed]

I have been working on a problem(alternate minimization) where I want to establish an inequality in which I am stuck. An $\alpha$- parameterized version of the divergence(Kullback-Leibler) takes the ...
5k views

### Is the Jaccard distance a distance?

Wikipedia defines the Jaccard distance between sets A and B as $$J_\delta(A,B)=1-\frac{|A\cap B|}{|A\cup B|}.$$ There's also a book claiming that this is a metric. However, I couldn't find any ...