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32 votes

Can a real quartic polynomial in two variables have more than 4 isolated local minima?

Recent addition: Inspired by DimaPasechnik's and Matt F.'s comments about sum of squares decompositions, I tried the following very natural idea: Try to find $f$ of the form $f(x,y)=A(x,y)^2+B(x,y)^2$,...
1 vote

Roots of linear combination of $x \sin x$

The equation you wrote is $$\sum_{i,j}a_{i,j}(\theta_i-\theta_j)\sin((\theta_i-\theta_j)t)=0$$ for $t\in(0,1).$. Since sines are linearly independent, this is only possible either when $a_{i,j}(\...

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