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Interpretation of Besov Space parameters
I've been reading about Besov spaces (my reference thus far has been "Mathematical foundations of infinite-dimensional statistical models" (Nickl &am...
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What is meant by domain of function to be "explicitly defined"?
In my maths books it's said that: "when the domain of f(x) is not explicitly defined then in this case domain will mean the set of values of x for wh...
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The law of the unconscious statistician
In Casella and Berger's Statistical Inference (2nd edition) it says at the start of section 2.2 (page 55) when defining expectations that If $ \mathr...
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Check equilibrium point for stability
$\dot x = -y^2$ $\dot y = x^3y$ The task is to draw global phase portrait (I guess I understand how to manage this using isoclines) and to check equilibri...
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The plane $ax+by+cz=1$ contains the line $L_2$ and perpendicular to $n$. Determine $a,b,c$.
Let $L_1$ and $L_2$ be two lines. $L_1:r(t)=\langle1,-2,4\rangle+t\langle4,-3,-1\rangle$ $L_2:s(t)=\langle1,1,0\rangle+t\langle2,3,-2\rangle$ The plane ve...
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Find a polynomial $p$ of degree $3$ if its value in $4$ points is given
Find a polynomial $p$ of degree $3$ such that \begin{align*} p(−4) &= −142, \\ p(1) &= −2, \\ p(−5) &= −242, \\ p(4) &= 10. \end{align*} T...
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What's the integral of a constant?
If the derivative of a constant is $0$ then what is the integral of a constant? What is the integral of $0$?
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What is the difference between the normal average and weighted average?
What is the difference?For what kind of purpose do we use the weighted average method?Why don't we instead always use the normal average method?and a...
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What are the dimensions of a 4D cube represented in 3D?
I'm hoping to construct a physical model of a 4D cube. However, I'm struggling to work out the proper size ratio between the inner and outer cub...
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Is there a list of common identities for principal branches of complex logarithms and roots?
Often I have a necessity to simplify some expressions involving roots or logarithms, where arguments appear to be imaginary or even more generally complex...
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