However, again, I would only say yes to $\frac{150}{24}h^2\max\limits_x\left\|f^{(4)}(x)\right\|$

So it is not $\leq |-\frac{22}{24}h^2| ||f^{(4)}||_{\infty}= \frac{22}{24}h^2 ||f^{(4)}||_{\infty}$ ? @robjohn

@MaryStar that is true, but not what you wrote before.

You could have $f^{(4)}(x_1)=f^{(4)}(x_3)=-f^{(4)}(x_2)$

which would reinforce, not cancel

hii

@Lepidopterist How does $A$ vary with $p$?

@robjohn say that A tends toward a certain empirical spectral density in the limit

@Lepidopterist I am not exactly sure what that means, so I won't try to comment.

that's just to say that A is converging in the sense that its eigenvalues are all converging

the eigenvalues of A_p converge to something

@Lepidopterist converging to one value?

one set of values, or one measure, if you like

the eigenvalues need not be the same

Then the trace of $A$ would tend to $\infty$ unless the eigenvalues tend to $0$.

ok, actually that's a good point. let me include the condition that $A$ always be normalized to have trace 1

Ap=Ap/trace(Ap)

yo guys

Hi @LucasHenrique

How'ya doing?

I have simple question: There is no such thing as centrifugal acceleration (nor force, this way), right?

Say I have a vector space $V$ over a field $L$ with a subfield $K$ (so that it's a field extension $L/K$), it's not hard to see that the dimension of $V$ over $K$ can be larger than over $L$ (for instance, take a tower of three fields, consider the top as a vector space over the bottom 2, the degrees multiply, etc.) -- but can the dimension ever decrease when you restrict the scalars to a subfield? Is that possible? (I can't find an example.)

@LucasHenrique it's inertia in disguise, from a different frame of reference, google "fictitious force"

@AndrewG $\dim_K(V)=[L:K]\dim_L(V)$

@anon Really, that doesn't just apply to field extensions? it's more general like that? cool.

degrees of field extensions are just dimensions of vector spaces

The problem was: A car is at 10m/s made a full circular rotation. Then the $a_x$ was like 3m/s² and $a_z$ was like 4m/s². But I still don't know if these were influenced by centripetal or centrifugal forces. It moves only in z and x (because of gravity)

If $V=\bigoplus vL$ and $L=\bigoplus \ell K$ then $V=\bigoplus v\left(\bigoplus \ell K\right)=\bigoplus v\ell K$

ok, ya, i guess there's nothing necessarily field-y about this

Anyone into physics? ^^^

@anon thnx

@AndrewG can it be calculated then? I got that centripetal force is how hard is to move from some point to another point

(Given the circular motion)