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Why can't the Kernel in the Volterra integral equation ever be separable? My textbook says it's obvious due to K(x,s)=0 at s>x, but I don't see how that helps to prove it.
u(x) = f(x) + \int_a^x K(x,s)x(s)ds
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$u(x) = f(x) + \int_a^x K(x,s)x(s)ds$
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I tried to somehow use the fact that it can be rewritten as the Fredholm integral equation in a triangle area:
$\hat{K}(x,s)=\begin{cases} K(x,s) & a\leq s\leq x\\ 0 & x\leq s\leq b \end{cases}$

but so far no luck.
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>>7805285
Assume separability. For the zeroing condition to hold, the s-dependent functions in the expansion of the kernel need to also depend on x (or how else do you make them zero?). This clearly contradicts separability.

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So I found this paper online
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf

And found it to be very inspiring after carefully reading it and understanding it. It's actually revolutionary... Why is no one talking about it?
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>>7805268
>understanding it
I LOLed
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>>7805268
>understanding it

you oversold the troll, obviously nobody will believe you

>>
>>7805288
I'm sorry, you must be seriously limited mentally or cognitively. Consider visiting a psychologist for an intellectual quotient test.

I?m here to talk about something serious. I'll wait for the right person who wants to discuss the topic.

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So how does a guy kill his sex drive without decreasing his testosterone levels?
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self control
>>
Testosterone receptor antagonists.
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>>7805211
Through daily fapping. After a while you will not feel any pleasure anymore which will directly result in reduced sex drive.

Trust me. I know what I'm talking about.

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>>7805123
>I am saying that asians show to be objectively smarter
I think it's more of a factor of culture, population and selection. The majority of Asians who are smarter on average in my experience are the ones that are international students. The westernized ones I've met that were either born here or were heavily influenced by western way of life are more on par with everyone else. My experience on taking to these internationals were that it was very hard for...
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>>7805205
What Asians are they even talking about? Is it just East Asians? Or are they including Southeast Asians too? What about Indians, who are closer to Caucasians than anything?

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Why do razor blades dull and need to be replaced when they're much harder than the hair that they cut?
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>>7805192
Short answer that's only slightly correct, but correct enough for you:
lateral forces.
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Why is it called a hamburger when theres no ham in it
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>>7805192
same reason you can bend a clothes hanger by pressing it against a pillow.

The blade doesn't wear away, the edge just gets deformed and stops being as sharp.

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>these data
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>>7805174
?
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>>7805174
>not knowing data is the plural of datum
>>>/out/

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I'm trying to get into a physical therapist assistant program this fall.

I received a message from my anatomy/physiology instructor today inviting me to take part in an independent study for college credit/resume bragging rights. I have to let him know Monday if I want to do it. I'm interested but I have no idea how intensive it will end up being and I'm also unsure of what to do in relation to physical rehabilitation therapy. This is all stuff I'll talk with him about, but I'd like to know if anyone here has taken part in something like this...
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Any physical therapists in the house general?

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Can /sci/ recommend me a good, digestible textbook on Fourier Analysis? I know how it works but I want something that can give me stronger intuition.

In exchange I'll give a recommendation: I've reference-read about 30 different Abstract Algebra books and Pinter's "A Book of Abstract Algebra" is my favorite general purpose one. I don't think it's often assigned but it's great for building intuition.
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What do you think of Springers Algebra Chapter 0? And if you know any good books for Functional Analysis I'd appreciate a rec.
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>>7805115
Not OP, but
>What do you think of Springers Algebra Chapter 0?
I like it for the way it introduces categories and how they're intertwined with algebra.
>And if you know any good books for Functional Analysis I'd appreciate a rec.
I heard Kirillov, Gvishiani: 'Theorems and Problems in Functional Analysis' is p good.

What's the probability that a coin ends up on its side in a coin toss?
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depends on the thickness of the coin you fucking retard.
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>>7805084
Doesn't it depend on the relative position of the moon?
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>>7805084
Oh yeah? And what equation, theorem or peer-reviewed paper supports that?

Is it going to blow up soon?
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>>7805007
No, in distant future yes - maybe.
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>>7805007
Soon relative to what?
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yes

t god

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Halp /sci/. I constantly need some form of entertainment in the background while studying. I recently started listening to podcasts while studying and it slows down my progress greatly. Am I addicted? Is there some form of entertainment I can listen to in the background that won't distract me too much?
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Ambient music is the best. Ä±t gets you in the mood, it's not distracting, it's perfect.

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Where were you when economics became a real science by using computers to test their economy theories?
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Only works if the assumptions about the model's environment match those of the real world.
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>>7804948
sounds better than trying to use philosophy and expect models made by XIX century neets don't make millions of deaths.
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>>7804960
You can't simulate people.

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>tfw in college
>study environmental science/biology
>want to be wildlife biologist
>taking out shitload of student loans
>will have to go to grad school and take out more loans
>currently in environmental activism internship not extremely related to what i want to do
>will earn next to no money in target field

I will be a scientist on welfare checks
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>>7804913
>loans.

Stop. If your scholarship doesn't cover enough then don't fall for the college Jew, go find work.
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>>7804927
my scholarship covers about half. I want to become an RA so room/board is paid for, then I go for basically free. but some damage has already been done
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>will have to go to grad school and take out more loans

wut

could it be that planet 9s obit crosses the earths orbit every few million years in a way that it fucks with the earths gravitational field so that volcanoes explode and whole species like the dinosaurs get extinct?
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>>7804910
no
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>>7804910
No.
Next question.
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>>7804910
No, but in the 80's they theorized a planet 9 type object was responsible for sending shit from the Oort cloud toward earth.

https://en.wikipedia.org/wiki/Nemesis_(hypothetical_star)

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Hey guys, chemistry noob here. Can you help me with the questions in pic related and explain the answers to me, give me the basic idea of common ion effect on solubility?

Am I right for the first question?: The concentration of Pb2+ goes up, Cl- goes down and equilibrium shifts to the reactants and lowers the solubility.
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>>7804885
Yes, you are correct in your reasoning.

Ions which do not participate in the reaction (e.g. any of the other ones except Cl- in NaCl) do not affect the equilibrium.
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>>7804891
But am I correct to assume that adding H2O will increase solubility? Also what happens to the solubility when adding compounds that don't share a common ion?
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>>7804897
Since it's aqueous, and solubility product is determined by molarity, not absolute mole content, yes, adding more H2O will increase the amount of Pb2+ in the solution, but the concentration itself will not increase. Adding compounds that do not share a common ion will not affect concentration either, as the reaction quotient will not change.

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