Mathematics - 2018-11-25 (page 2 of 2)

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Alessandro Codenotti

20:09

In the first case $X$ is a set whose elements are all taken from the family $F$, in the second case $X$ itself is an element of $F$

Liad

@BalarkaSen why can't there be $f,t$ s.t $f(t)^2 + g(t)^2 = 1$ ? is that involve your trick?

i squared - Keep it Real

that is what I was thinking. Thank you Alessandro

Balarka Sen

@Liad No, that's straightforward.

Think about it

Liad

is that involving f,g's roots?

Balarka Sen

too hard

Liad

20:19

ah.... they must be constants.

Balarka Sen

Correct; why?

Liad

degree zero

how did i miss this

Balarka Sen

That's right

Liad

thanks..

Jean-François Savard

Hello, anyone interested in helping me reach the ah-ah moment for a dynamic programming problem? I've been trying to figure out a recurrence for hours without any success.

ninja hatori

20:31

how one can show Surjection that Preserves Inner Product is Linear in hilbert spaces?

Liad

@BalarkaSen the contradiction would be that $(f,g) \subset k$ and the images in $k[x,y]/(x^2+y^2-1)$of f,g would generate everyting, correct?

Balarka Sen

@Liad $f, g$ are images of $x$ and $y$ in $k[t]$ by the isomorphism $k[x, y]/(x^2 + y^2 - 1) \to k[t]$.

You wrote it backwards

Liad

exactly

ah. ops ^^

Balarka Sen

If $f$ and $g$ are constants, then image of this isomorphism is strictly contained in $k$, but that's an oxymoron.

(As it's an isomorphism; it should surject onto $k[t]$).

Liad

yea, that is what i wrote just i reversed the spaces

thanks..

manooooh

20:42

Hey guys!

When you have a product of $n$ terms, how would you write that? For example:

$$a_0\cdot a_1\cdot\cdots\cdot a_n\qquad\text{or}\qquad a_0\cdot a_1\cdots a_n$$

I mean with a \cdot to the left and right of \cdots or not? I prefer the second option, and you?

Balarka Sen

I would write neither, as they are both products of $n+1$, not $n$, terms ;)

Liad

lol

Balarka Sen

But I prefer just \cdots. No \cdot to the right and left.

Astyx

$\cdot . \cdot$ ?

manooooh

@BalarkaSen LOL

@BalarkaSen that's enough for me $\dot\smile$, thanks!

Someone else?

Astyx

20:54

I prefer the other one. It doesn't really matter though I guess

manooooh

@Astyx the first one?

Balarka Sen

Don't believe the French on spacings and dots.

Astyx

Yes

We have a history of betrayal concerning that very subject

manooooh

@Astyx how can we access to that history?

I think it should be an aesthetic debate rather than formal

Astyx

Just write it as $$\prod_{i=0}^n a_i$$

manooooh

20:59

@Astyx I write rarely this kind of expression, so I do not need an operator that simplifies the expression

Astyx

What about $a_0a_1a_2\cdots a_n$ ?

manooooh

@Astyx that's another way

GFauxPas

I'm stuck on this sde problem. There's a particle moving right according to a drify p

Drift process u(x,t) so that del_t(u) = L^*u, the adjoint of the generator function

But i want to add a term that if the particle hits a boundary x=a then it sticks with rate lambda. Probability of sticking is v(t)

And if its stuck it's bounced back with rate mu

There aren't any examples in the source text >.<

Hint is that dv/dt and v only occur at x=a, which is obvious but I don't know how to implement that

Or if anyone can recommend a site, book, or video that explains sde's for simple drift processes

1 hour later…

Rithaniel

22:22

Hmmm, trying to find $a(n)$ where $a(1)=10$, $a(2)=9$, $a(3)=6$, and $a(4)=14$, where $a(n)$ is a function which uses only addition, subtraction, modulo, and multiplication by powers of two.

Trey

22:39

can someone explain me how do I transform $x + \frac{1}{2} \int\frac{\frac{1}{2}(u + 1) -1}{u^2+2}du$ into $x + \frac{1}{4} \int\frac{(u -1)}{u^2+2}du$ ?

mick

Q: About $ f(w,L) = \int_1^w \int_0^{2 L \pi} \frac{ \ln(\frac{\sin(x) +\ sin(vx)}{2} + \frac{5}{4})}{L(w - 1)} dx dv $

Consider $$ f(w,L) = \int_1^w \int_0^{2 L \pi} \frac{ \ln(\frac{sin(x) + sin(vx)}{2} + \frac{5}{4})}{L(w - 1)} dx dv $$ For real $w > 1 $ and integer $ L > 1$ Conjecture : $$ \lim_{L \to \infty} f(w + 1, L) - f(w,L) = 0. $$ How to decide if this is true ? Perhaps differentiation under the...