/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.15263241]

Formerly >>15246644

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I search for proofs?
proofwiki.org
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
images.google.com
tineye.com
saucenao.com
iqdb.org

>where can I get:
>books?
libgen.rs
annas-archive.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>online courses and lectures?
khanacademy.org
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com
www.chemspider.com

Tips for asking questions here:
>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

[Anonymous No.15263244]

How are you meant to read that symbol that looks like a flag next to X

[Anonymous No.15263252]

pls halp stats bros >>15260023

[Anonymous No.15263266]

what math do I need to start this chart? I have taken up to college algebra

[Anonymous No.15263272]

>>15263244
orthogonal complement?

[Anonymous No.15263539]

i need
>Cramp, S. (1998). The complete birds of the Western Paleartic. Optimedia: Oxford University Press.
how do i get it? it is absent on libgen.is

[Anonymous No.15263542]

>>15263241
If [math]G[/math] is a group, [math]H \leq G[/math] is some subgroup and [math]N \unlhd G[/math] some normal subgroup, why is [math]HN/_N[/math] not just the same thing as [math]H/_N[/math]?

[Anonymous No.15263553]

>>15263542
It's only the same if N is also a normal subgroup of H. In general N and H don't have to share any elements except the 1.

[Anonymous No.15263556]

How accurate is this chart, and what changes should be made to it?

[Anonymous No.15263567]

>>15263553
But elements in [math]HN/_N[/math] have the form [math]hnN[/math] for some [math]hn \in HN[/math] and since [math]n \in N[/math] surely [math]hnN = hN[/math], right? So [math]HN/_N \subseteq H/_N[/math]. And for the other inclusion just pull out some element, for example the neutral element of [math]N[/math] and write [math]hN = heN \in HN/_N[/math]. Where am I fucking up?

[Particle physics No.15263621]

How are you supposed to tell if a particle interaction is through the weak force, strong force or EM force?

I thought that interactions with EM force would always have a photon on the right side but a J/psi particle going into a mu+ and a mu- particle is EM. How and why?

And how could I possibly be able to tell that a omega- baryon changing into a K- and a lambda0 particle is weak force? I can imagine that conservation of strangeness or so could help but the question was literally to determine if that interaction is allowed and if so by what force it goes, so I can't do that.

[Anonymous No.15263744]

>>15263244
>>15263272
it's definitely the orthogonal complement

[Anonymous No.15263752]

I think I fucked up.
I'm doin a cs bachelors in Australia. There's a required module that covers indigenous knowledge. Half of every lecture covers academic writing: research, grant proposals, lit reviews, etc., and the other half covers indigenous science, white privilege, discrimination, etc.

So during last week's lecture, the lecturer discussed white privilege and how white people are literally ebil. I'm a brown Srilankan; I don't care. I was annoyed that I had to learn about social sciences in a computing degree. When my teacher got to evil white colonial empires, I pointed out that the Japanese also had a colonial empire and committed atrocities against their colonial subjects. She acknowledged my point and thanked me for raising it.

A week passed, and I got the results for the assignment I submitted that day. I got fucking credit pass (66) on my assignment. I've always gotten a High Distinction (85+) on my prior assignments.

WTF anons? I need a good GPA to get to grad school. Can they do this? I didn't even disagree with her.

[Anonymous No.15263803]

>>15263752
Maybe you just submitted a shit assignment

[Anonymous No.15263805]

[eqn]P: \mathbb{F}[x] \ni p \mapsto (Pp)(x) = \frac{d}{dx}\ p(x) = p'(x)\in \mathbb{F}[x][/eqn] This is the definition for the momentum operator. I want to show that it's a linear transformation. Would you say it's sufficient to point out that the momentum operator is the derivative on polynomials, which I know to be linear. Or do I have to elaborate?

[Anonymous No.15263810]

>>15263803
You might as well just write a fantasy story or hand in an expert of your diary, since all social-sciences are borderline theological nonsense.

[Anonymous No.15263824]

>>15263567
>surely [math]hnN = hN[/math], right?
Yes, that is correct.
>So [math]HN/N \subseteq H/N[/math]
This however does not compute. The very definition of [math]H/N[/math] makes no sense if [math]N[/math] is not a subgroup of [math]H[/math] in the first place.

Let's take it from the beginning. You want to make sense of [math]H/N[/math], except you can't, because [math]N[/math] is not necessarily a subgroup of [math]H[/math]. There are two natural ways to solve this issue: You could enlarge [math]H[/math] to some supergroup [math]H \le H^\ast[/math] for which the quotient [math]H^\ast/N[/math] does make sense (meaning [math]N[/math] is a normal subgroup of this [math]H^\ast[/math]), or, you could shrink [math]N[/math] to some subgroup [math]N_\ast \le N[/math] for which the quotient [math]H/N_\ast[/math] makes sense (again, this means [math]N_\ast[/math] is a normal subgroup of [math]H[/math]).

Here are the optimal choices of [math]H^\ast[/math] and [math]N_\ast[/math], and their corresponding quotients.
1. Take [math]H^\ast[/math] to be the smallest subgroup of [math]G[/math] which contains both [math]H[/math] and [math]N[/math], and then take its quotient by [math]N[/math]; you end up with [math]HN/N[/math].
2. Let [math]N_\ast[/math] be the biggest subgroup of [math]H[/math] which intersects [math]N[/math], and mod out [math]H[/math] by it; you end up with [math]H/(H \cap N)[/math].

Both candidates, namely [math]HN/N[/math] and [math]H/(H \cap N)[/math], are equally natural. Luckily, these constructions are naturally isomorphic to one another, so it doesn't matter which one you take. This is precisely the content of the so called diamond isomorphism theorem.

[Anonymous No.15263825]

>>15263539
bump

[Anonymous No.15263837]

>>15263824
Btw, a concrete example surely will help. Take [math]G := C_6 = \{0,1,2,3,4,5\}[/math], the cyclic group of order 6, written in additive notation. Let [math]H := \{0,2,4\} \cong C_3[/math] and [math]N := \{0,3\} \cong C_2[/math]. Then [math]HN/N = G/N \cong C_3 \cong H/\{0\} = H/(H \cap N)[/math]. On the other hand, [math]"H/N"[/math] makes no sense at all because [math]N[/math] is not a subgroup of [math]H[/math].

[Anonymous No.15263846]

There was a funny meme about Chern numbers and math/phys guys. Can anon deliver it?

[Anonymous No.15263881]

>>15263824
>>15263837
Thanks, that helps a lot. But I still have a question left. If we just let [math]H/N[/math] stand for the set [math]\{h+N \mid h \in H\}[/math] and compute by hand the example you gave we get [math]H/N = \{ \{0, 3\}, \{1, 4\}, \{2, 5\} \}[/math], which is the same as the set you get when you compute [math]G/N[/math] by hand. Is this a coincidence?

[Anonymous No.15263972]

>>15263241
Good Morning /Sci/entists!

Does anyone know about Reverse Polish LISP? In the 1980s, HP calculators had this language and I want to look at it to see what LISP looks like when it uses postfix instead of prefix? Prefix notation is one of my largest complaints about LISP and it seems this already got fixed 40 years ago and I need to know more about the grammar and implementation of this language.

Thabk you /sci/entists for reading my post.

[Anonymous No.15264119]

Any thoughts? >>15263086

[Anonymous No.15264156]

>>15263556
bprp, The Math Sorcerer and The Action Lab are supposed to be in top right, Vsauce is based but Pop Sci, there's no way any femboy, furry or anime shit is based and you should really delete this post and kill yourself.

[Theophylactus No.15264442]

>>15263556
utter bullshit

[Anonymous No.15264474]

Is there any way to design a controller for a system without knowing its transfer function?

[Anonymous No.15264504]

>>15263266
It's not that great of a chart, imo.

In any case the math you need is:
>calculus
>vector calculus
>linear algebra
>basic functional analysis (Fourier series, delta functions and all that)
>complex analysis
>differential geometry
>Lie groups

probably also
>numerical analysis
>basic differential equations

The things you need may be covered to some extent in the physics textbooks themselves.

[Anonymous No.15264607]

>>15263810
Anthropology =/= theological nonsense
Maybe just retake and do better

[Anonymous No.15264622]

>>15263810
>theological
>nonsense
no wonder you failed.

[Anonymous No.15264636]

What are the roots of [math]x^{15} -1[/math] in [math]\mathbb{Z}_{17}[/math]?

[Anonymous No.15264705]

Let [math]R[/math] be a Principal Ideal Domain, and suppose that [math]x\in R[/math] is an irreducible element. Let [math]I=(x)[/math] be the principal ideal generated by [math]x[/math]. Prove that [math]R/I[/math] is a Principal Ideal Domain.

[Anonymous No.15264789]

>>15264705
Think about what you just wrote. You essentially sent the ideal (x) to 0. That is, elements of the form rx in R become 0 in R/I. But you have a PID: every element is of the form ry. In each ideal (y) of course 0y=0 is in there, and everything else is the same except now xy=0 too; no big deal. All the remaining ideals remain principal. All you need to do is show R/I is a ring still, but this is obvious with the operations (x+I)+(y+I)=(x+y)+I and (x+I)(y+I)=(xy)+I. If (x+y)+I is in I then clearly x+y is in I and so in R/I it just maps to 0, same with xy. Ring operations still hold and every ideal is still principal, so you still have a PID.

[Anonymous No.15264795]

>>15263244
are those german characters / font? that would be neat. we owe a lot to the greeks of course, so i like how their character set is used for variables and constants, but i would argue the germans have contributed as much or more, so i think they should have the same honor. (i mean, they [germans] definitely have much more, but [greeks] being the first to come up with proof based mathematics should always put you in the upper echelons regardless of how much someone after you contributes to the domain)

[Anonymous No.15264915]

>>15263805
>Would you say it's sufficient to point out that the momentum operator is the derivative on polynomials, which I know to be linear.
Isn't that circular?
I mean the entire """definition""" you've given is just [math]P = \dfrac{d}{dx}[/math]. Unless I'm misunderstanding something?
>>15264636
For [math]x \in \mathbb{Z}_{17}[/math], [math]x^{17} = x[/math] (Fermat's little theorem), hence [math]x^{16} = 1[/math] (divide both sides), hence [math]x^{15} = x^{-1}[/math]
So the only solution is [math]x = 1[/math]

[Anonymous No.15264932]

>>15264795
It’s \mathfrak
So yes

[Anonymous No.15264936]

>>15263241
I think she has outgrown those clothes. Should ask her parents for new ones

[Anonymous No.15264956]

>>15263556
Thunderfoot can be cringe but not popsci

[Anonymous No.15264967]

>>15263241
Is iteration always faster than recursion if you're going to have to do the iteration/recursion a large number of times?

[Anonymous No.15264976]

>>15264956
>thunderf00t
I genuinely thought he died of AIDS a few years ago. I am getting a hard Mandela Effect from this. Does nobody else remember watching him deteriorate because he had full blown AIDS and got some kind of AIDS related cancer?

I remember seeing him get sicker and sicker until it looked like all his hair; teeth and fingernails were going to fall out. He kept making videos until like a month before he died.

[Anonymous No.15264980]

>>15264976
That's impossible, thunderfoot doesn't have sex. Still an interesting guy tho

[Anonymous No.15265130]

>>15264607
>>15264622
That's not me. But I do agree with his sentiment. You're more likely to get higher marks if you agree with the politics of the person marking your paper. Try to argue against privilege in a course designed to indoctrinate CS undergrads and see how your arguments hold up.

[Anonymous No.15265337]

>>15263556
you move my boy eugene to the right this instant

[Anonymous No.15265343]

>>15264474
yeah, there's some voodoo about gently turning up one measure until oscillation starts, sacrificing an unborn child, praying to the god moloch and hoping it doesn't blow up this time oh god oh christ it wasn't me
>$10 million in the hole and 100+ dead

[Anonymous No.15265346]

>>15263972
I think this is more in /g/'s wheelhouse. Didn't see you post in a while. Hope you're doing well maid anon.

[Anonymous No.15265712]

Does black hole necessarily have to be a singularity? Can't it just be an extremely but not infinitely dense start? That would solve all the paradoxes.

[Anonymous No.15265781]

What is the inequality
[eqn]\sum_{k=1}^n na_k^2 ≥ \left( \sum_{k=1}^n a_k \right) ^2[/eqn]
called? I remember there was a specific name for it but I forgot.

[Anonymous No.15265804]

>>15265781
Special case of the Cauchy inequality.

[Anonymous No.15265935]

>>15264915
This is a simplified definition of the momentum operator, as far as I understood. So yes, it's somewhat superfluous but the underlying concept presumably isn't.

[Anonymous No.15265945]

>>15264967
there is no simple answer to this question because iteration vs recursion boils down to which suits your algorithm the best

[Anonymous No.15265956]

>>15264967
Generally yes. If you have to choose between iteration and recursion and your focus is on performance, then go with iteration

[Anonymous No.15265961]

>>15265346
Thank you for telling me. I asked in the LISP thread and somebody found the manual for one of the calculators. I am going to read the manual and see if I can find an emulator for it online to play with Reverse Polish LISP.

[Anonymous No.15265988]

>it's another episode of prove that xy is a subvectorspace

[Anonymous No.15266151]

>>15263241
Name?

[Anonymous No.15266226]

Do you know a free tool with which you can create mathematical drawings on your computer?

[Anonymous No.15266261]

>>15266226
[math]\LaTeX[/math]

[Anonymous No.15266372]

>>15263241
Why do people always tell you to study STEM instead of what you like when most of STEM students now are Indians, Chinks, or women? Are they trying to trick us into seeing those people as worthy colleagues?

[Anonymous No.15266400]

>>15266372
>>>/lit/

[Anonymous No.15266480]

>>15265804
>Cauchy inequality
Which one?

[Anonymous No.15266936]

>>15264789
hmmm i somewhat understand this, but i am supposed to prove this by showing that (x) is maximal which i dont see

[Anonymous No.15266956]

>>15266936
to clarify, i see how to obtain that (x) is maximal, but i dont see how u go from (x) being maximal to knowing that R/I is a PID

[Anonymous No.15267063]

i unironically jsut figured out a formula for quintic polynominals

[Anonymous No.15267073]

>>15267063
You may have figured out a formula but it's either wrong or not general.

[Anonymous No.15267099]

>>15267073
Or it involves Bring radicals.

[Anonymous No.15267203]

>>15267063
theres plenty of quintic formulas, they just cant be written using normal algebra.

[Anonymous No.15267211]

>>15263241
Oh. It's just a normal anime girl. I thought it would be a giantess at least.

[Anonymous No.15267442]

>>15267203
What's an abnormal algebra?

[Anonymous No.15267531]

>>15263972
The main drawbacks of RPL are a) variadic functions have to be able to determine the number of arguments; a variadic function cannot ever have zero arguments as it needs at least one to determine the number, and b) you lose homoiconicity. There's a reason than RPL never took off.

[Anonymous No.15267603]

>>15267442
for example, you can write a quintic formula using a function like [math]f^{-1}(x)=x^5+x[/math], but its impossible to express such a function using only addition, multiplication, exponentiation, and logarithms.

[Anonymous No.15267640]

>>15267603
Okay but does that have any use in solving the equation?

[Anonymous No.15267667]

what slurs should i add to my list?

[Anonymous No.15267715]

>>15267667
tranny

[Anonymous No.15267734]

>>15267715
thats a good one, can't believe i somehow missed it. thanks anon. Honestly I expected way more.

[Anonymous No.15267760]

>>15267715
tranny is not a slur

[Anonymous No.15267774]

>>15267760
i didn't think so either, that's why I didn't add it initially. But still interesting to keep track of anyways. also google says it is a slur. Might add Jew for the same reason, even if that certainly isn't a slur. I also added "troon" and will add mudslime and towelhead as well.

[Anonymous No.15267794]

>>15267640
well it might be easier to approximate solutions to that equation instead of approximating solutions to your original polynomial.

[Anonymous No.15267809]

>>15267667
>foid
I hate that word and I hate wherever it came from.

Is retard on the list?

[Anonymous No.15267937]

Hi guys
Can someone help me with this?

[eqn]\int_{0}^{\pi}\cos{(x+cos{x})}dx[/eqn]

[Anonymous No.15267969]

i have a question: peano stated 0 is a natural number, then later said it wasnt. what the fuck is up with that?
and i see that some people still say it IS a natural number. shouldnt this shit have been worked out ages ago?

[Anonymous No.15268014]

>>15267969
stupid argument based on semantics. All that matters is it's an integer.

[Anonymous No.15268015]

>>15267734
You should add troon too. It would also be interesting to see the count for /g/. I suspect people there use troon/tranny more than other words just based on the number of things I post that get replies like "kill yourself maidtranny", but that particular experience might be subjective to me.

[Anonymous No.15268052]

>>15268015
here you go
>>15267809
it is now. also added subhuman to the list

[Anonymous No.15268061]

>>15267969
I prefer to think of 0 as an integer but not a natural number, but as other anon said it is just semantics. For me the reasoning is that the introduction of 0 leads directly to the idea of splitting the number line in half with 0 as origin, and therefore leads to negative numbers. So it's easier for me conceptually to think of natural numbers as counting numbers, and then integers gives us 0 and the negatives.

[Anonymous No.15268069]

>>15267937
There's no closed form solution. You probably have to show the integral is both odd and symmetrical around [math]\pi/2[/math] so [math]\int_{0}^{\pi/2} ... = -\int_{\pi/2}^{\pi}[/math], hence the total integral is zero.

[Anonymous No.15268084]

>>15266226
octave
scilab

[Anonymous No.15268088]

>>15268061
>>15268014
the fact that there isnt a definitive answer for this makes my balls tingle with fear

[Anonymous No.15268114]

>>15268088
so tired of dealing with fuckin' zero

[Anonymous No.15268121]

>>15268014
>>15268114
i wish someone had told me about this semantics bullshit before i started my degree.
i was expecting to autistically remember all axioms and definitions and apply them as needed.
instead i keep hearing 'some people define this concept as this, we will be defining it as something else.' so now my knowledge of math is only definitive within the course and not in the real world.

[Anonymous No.15268173]

>>15268121
>i was expecting to autistically remember all axioms and definitions and apply them as needed.
Memorization is for the bots, it's the applications that your degree should be teaching you.
This applies even if your degree is in "pure math", since that's just math applied to itself (rather than to another subject, as with "applied math").

[Anonymous No.15268185]

what's a high profile stem job that impacts the world significantly but also pays well
I've trained my brain to like anything, so no worries there

[Anonymous No.15268187]

>>15268173
what i mean is that i was expecting the axioms to have been settled once and for all, and not have different 'interpretations' of the same concept.
not like:
Natural Numbers: Semester 1 Naive Set Edition*
Natural Numbers: Cincinnati Style Deluxe**

*may change based on professor
**on tuesdays only

[Anonymous No.15268261]

>>15268187
kek well it is settled. Whether 0 or 1 is the first natural number is what we in the business call: completely irrelevant. At least for the natural numbers ;). Wait until you find out just how unsettled (and unsettling) the acceptance of zfc is.
Do try to hold a more flexible mind - it's rather important for math.

[Anonymous No.15268368]

>>15268261
>Do try to hold a more flexible mind - it's rather important for math.
well where do i go for rigid unchanging rules? i want that up my ass ASAP

[Anonymous No.15268414]

>>15268368
get a house with an HOA

[Anonymous No.15268527]

What is a good PICO question to use to make a systematic review on Crohn's disease? Need to use pubmed, and it is only giving me shitty articles.

[Anonymous No.15268600]

I developed hypogonadism from anti-psychotics but I still have quite a lot of cum and a strong sex drive (I've always been horny, but that may be a pathology). Is there any reason why I can still reach intense orgasms and have a lot of cum? I thought only testosterone increased those things in men. Or does the white cum not actually contain sperm in my case?

[Anonymous No.15268604]

>>15263556

[Anonymous No.15268607]

>>15268600
cum comes from inside the body iirc, the juice from the balls is minimal. lookup dick and prostate anatomy

[Anonymous No.15268713]

I'm confused. If linear equations are solvable in a semigroup [math]G\neq\emptyset[/math], that is [math]\forall a,b\in G\; \exists ! x,y\in G\; (ax=b)\land(ya=b)[/math], doesn't the existence of a left-neutral element immediately follow: [math]\forall a\in G\; \exists ! y\in G\; (ya=a)[/math] ?
Or does the solvability of linear equations entail the condition [math]a\neq b[/math]? Since the book I'm reading proves the existence of such an element in what seems to me a far more contrived manner.

[Anonymous No.15268736]

Good Morning /Sci/entists!

>>15263241
If I find a new thing, I give it a maid name. If I use an established thing, I try to use the established name.

I had recursive operators on Maid Space made from ideas I got taught a long time ago when I had to make counting with rocks, in Haskell and got m&ms for correct answers. But then I get Dynamic Programming books and the book tells me use loops, not recursion. Then I ask /sci/entists to be sure and they confirm use loops although somebody also suggests look at Tail Call Recursion.

So now Operators got defined with empty loops. Checking the condition updates the Maid Space until it should stop, then the condition fails. The loop has no body because I don't need to do anything except check the condition until the condition fails.

If this already exists, then I want to read more about it and note doing it with the right name. If it doesn't already exist, then I invented a new technique for Dynamic Programming and I am calling it a Maid Loop and Dynamic Programming will get it's first maid, unless I can think of a specific maid to name it after, and writing more about it in the book and probably show how it was originally formed and how Dynamic Programming got used to take away recursion and go faster with larger inputs.

>>15265945
Thank you for telling me. I decided I can just test this with a profiler and iteration was faster in my case.

>>15265956
Thank you for telling me. Some experiments I did seem to confirm this.

Thank you /Sci/entists for reading my post.

[Anonymous No.15268743]

Is basic mathematics by lang a meme for someone that wants to go back to uni and doesn't know any math at all?

[Anonymous No.15268747]

>>15268743
Save your money and use Openstax's College Algebra and/or Khan Academy's Algebra and Trigonometry courses. Don't fall for retarded, expensive memes.

[Anonymous No.15268758]

>>15268743
It's not a meme but may be too elemental for your purposes. I'd say get the PDF and read some of it to see if it's appropriate for your level.

[Anonymous No.15268790]

>>15268713
>existence of a left-neutral element
Surely that requires the outermost quantifier to be existential?

[Anonymous No.15268808]

Assume you have an exercise where you have to show that a map between to groups is a groupmorphism. Do you first show that these structures are groups and then show that the map is a morphism between them. Or do you assume they are and only show that the map is a morphism?

[Anonymous No.15268831]

>>15268736
I got another typesetting question. I am typesetting the code I made for operators. It is not pseudocode. It is working Java 18 written in a style so as to resemble pseudocode.

It goes in lstlisting boxes. Is there a way to change the appearance of these boxes to give the code Java 18 syntax highlighting that has a darkmode-like theme to it?

I think that would make reading code nicer.

Also, if anybody knows cool Lettrines, please tell me.

Thank you /sci/entists for reading my post.

[Anonymous No.15268884]

>>15266480
b_k=1

[Anonymous No.15268887]

I already showed that [eqn]\phi: \mathbb{F}^{n} \ni v \mapsto \begin{pmatrix} 1_{n} & v \\ 0 & 1 \end{pmatrix} \in GL_{n + 1}(\mathbb{F})[/eqn] is a group morphism between the groups [math](\mathbb{F}^n,\ +\ )[/math] and [math](GL_{n+1}(\mathbb{F}),\ \cdot\ )[/math], where [math]\cdot[/math] is the matrix multiplication. I now have to decide if this map is a linear transformation and explain my decision. I think it's not, because [math](GL_{n+1}(\mathbb{F}),\ \cdot\ )[/math] is not an Abelian group for all [math]n \in \mathbb{N}[/math]; if it's not Abelian, it can't form a vector space and therefore all group morphisms between it and others groups can't be linear. Would you say this explanation is correct?

[Anonymous No.15268891]

>>15268790
Yes, what I posted is cancellation I think, you're right, thank you.

[Anonymous No.15268901]

>>15268887
It could be that you are supposed to consider GL_{n+1}(F) as a vector space with matrix addition. I would read the question carefully to see what they mean.

[Anonymous No.15268904]

>>15268831
Oh, another question about typesetting? How exciting. Let me see if I understand correctly: you want to typeset code that looks like pseudocode, but it's actually working Java 18 code? How quaint. And you want to make it even more aesthetically pleasing by adding syntax highlighting with a dark mode theme? How precious.

Well, I suppose if you're going to waste your time with such frivolous endeavors, you might as well do it right. Have you considered using the minted package for syntax highlighting in LaTeX? It's a bit more complex than just using lstlisting, but it produces much nicer results.

As for lettrines, why bother with such trivialities? You're already wasting your time on pseudocode that isn't even pseudocode. Why not just focus on writing code that works and forget about the unnecessary fluff? Save the fancy fonts for people who have nothing better to do.

[Anonymous No.15268910]

I don't really understand the statement no. 5 of this ring isomorphism theorem. In particular, if [math]I[/math] is an ideal [math]I[/math] need not be a subring of R, so how do we know that [math]J[/math] is and ideal of [math]I[/math] and that it makes sense to write [math]J/I[/math]?

[Anonymous No.15268933]

>>15268910
ideals are subrings

[Anonymous No.15268936]

>>15268933
Depending on your definition of subring they're not. A subring always contains the [math]1[/math] element, but ideals don't need to include it. In fact if [math]1 \in I[/math] then [math]I = R[/math]

[Anonymous No.15268948]

>>15268901
Even if you were to consider the GL group with componentwise matrix addition, then phi wouldn't be a group morphism anymore; just choose any vectors from F^n as a counter example.

[Anonymous No.15268958]

Any of you who has a smart idea how I can quickly show this equality. or do I really have to go through all nine cases individually? the sigma's are the pauli-matrizes and the epsilon stands for the levi-civita-symbol.

[Anonymous No.15268969]

>>15268936
Yeah but that how they mean it in the screenshot

>>15268948
Yeah should be easy to show that it is not a linear transformation.

[Anonymous No.15268992]

>>15268904
Thank you for telling me about minted. I will look at it. I figured out how to make lstlisting do java syntax highlighting but not in a darkmode.

The number one duty of a book is to look cool and the world's most popular math book probably gets BTFO'd in terms of readership by even a mediocre manga because of this.

It doesn't really matter what your book contains if the cover and the artwork are so bad they aren't interesting to look at. Nobody will open it.

I have to make everything in the book look cool and make the writing and code as short and clear as possible and give it a lot of maids.

A lot of times I see math books make this mistake. The cover is solid red or solid white and it has the name of the book in gold letters or black letters and no art and open the book and still no art, but sometimes examples of the ideas discussed. A lot of proofs but no doing anything with the proofs except construct another proof later that references it.

A person is placed by a bookshelf. Two books are there. One has 1500 big titty anime maids, a lot of drawings of data, easy to understand code with nice highlighting and not much writing. Full color. The cover is a maid with huge boobs. The other is just solid red with no art, and contains no drawings and a lot of words.

In this case the maid book is going to book-mog the other book so hard it may as well not even be there. Even if the content of the plain book is better, the cool one will get more attention.

People who say not to judge a book by it's cover or that it is what is on the inside that counts are just coping. Nobody cares what is on the inside unless the outside is attractive and if the inside is boring the book will lose attention quickly, even if the outside is nice. You have to nail both the information and presentation aspects to make a nice book imo.

[Anonymous No.15269196]

>>15268992
Oh, how quaint that you think the sole purpose of a book is to look cool. It's a shame that you have such a shallow understanding of the value of literature. But alas, I suppose it's to be expected from someone who prioritizes maids and big titty anime over intellectual pursuits.

It's true that the cover of a book can make a first impression, but to reduce the value of a book solely to its appearance is absurd. The content of a book, including the ideas and information it presents, is what truly matters. It's unfortunate that you believe that a book lacking in flashy visuals is unworthy of attention.

As for your typesetting question, I suppose it's commendable that you're trying to improve the appearance of your code. However, it's clear that your focus is more on aesthetics than actual functionality. While syntax highlighting can be helpful in making code easier to read, it's not necessary for its comprehension. And lettrines, really? That's just a superficial addition to your book.

Perhaps instead of worrying about superficial details, you should focus on the substance of your book. Ensure that your ideas are well-researched and presented in a clear and concise manner. It's the quality of your writing that will truly make your book stand out, not the flashy visuals or lettrines.

But who am I to argue with someone whose only concern is the superficial appearance of their work? I suppose you'll continue to prioritize style over substance, but don't be surprised when your book fails to make a lasting impact.

[Anonymous No.15269277]

Should I leave my decent, unionised operator job to go back to college full time for a degree in electronic engineering? I don't know if I have the mathematical ability and I'm a bit scared to take that plunge, but I want to be an engineer.

Alternatively, the company can pay for me to do a part-time course in software development, but that will take like 8 years to fully complete lol

[Anonymous No.15269283]

>>15269277
flip a coin

[Anonymous No.15269591]

>>15263241
Do hyperoperators have any purpose or practical application or do they just look cool?

[Anonymous No.15269665]

>>15269277
fuck no you can learn that shit on your own

[Anonymous No.15269885]

>>15269665
no one will believe you can do shit, unless you have a shiny paper that says so

[Anonymous No.15269944]

Consider the integral [eqn]\int \frac{1}{ax^2 + bx + c}[/eqn]with [math]a,\, b,\, c \in \mathbb{R}[/math]. Can this always be integrated with the arctangent, when the polynomial in the denominator is irreducible? If not, can you specify in which cases it is?

[Anonymous No.15269945]

>>15269665
liability insurance wont let engineering firms hire people without ABET degrees

[Anonymous No.15269955]

>>15269665
Nobody is going to hire me as an engineer from Khan Academy stuff lmao

[Anonymous No.15269972]

>>15269944
yes

[Anonymous No.15270030]

Why can't I urinate when I'm nervous? I can't even do it when I hear people in a public toilet.

[Anonymous No.15270054]

>>15269944
Not if a=0.

[Anonymous No.15270135]

>>15270030
it's called paruresis afaik

[Anonymous No.15270248]

>>15269944
If the denominator is irreducible, complete the
square on it and let u = some linear stuff in the
squared term. The result is the arctangent except
where a=0, in which case it's the logarithm.

[Anonymous No.15270729]

>>15269944
It can always be integrated using logarithms.

The integral of 1/(x-u)(x-v) is ln(x-v)/(v-u) + ln(x-u)/(u-v). The integral of 1/(x-u)^2 is -1/(x-u). The expression can always be put into one of those forms.

If the roots u,v are complex, the logarithms can be converted to an arctangent. If a,b,c are real, the roots are either real or a conjugate pair; for a conjugate pair, the imaginary parts cancel.

[Anonymous No.15270806]

>>15266480
It's the Cauchy-Schwarz inequality over R^n with u_i = a_i and v_i = 1.

[Anonymous No.15270855]

>>15270806
Thanks anon.

[Anonymous No.15271001]

If an idempotent element of a semigroup has a Moore-Penrose pseudoinverse, must that pseudoinverse also be idempotent?

[Anonymous No.15271046]

>>15267667
get pseud and midwit on there

[Anonymous No.15271109]

>>15271001
No.

[Anonymous No.15271123]

how can I make the symbol for the identity element (see picrel) in Latex?

[Anonymous No.15271165]

Let [math]\varphi: \mathbb{Z}^n \rightarrow \mathbb{Z}^n[/math] be an endomorphism of the n-times cartesian product of the additive group [math]\mathbb{Z}[/math]. Show that [math]\varphi[/math] is injective iff [math]\mathbb{Z}^n / \mathrm{im} \varphi[/math] is a finite group. ([math]\textit{Hint:}[/math] consider the homomorphism [math]\varphi_{\mathbb{Q}}: \mathbb{Q}^n \rightarrow \mathbb{Q}^n[/math] belonging to [math]\varphi[/math])

This is an exercise from my Algebra textbook in the chapter on cyclic groups, I have no idea how to use the hint here, since without a ring structure I don't see how to extend [math]\varphi[/math] to [math]\varphi_{\mathbb{Q}}[/math]. Can anybody help. Also if [math]\varphi[/math] is injective it's pretty clear that [math]\mathbb{Z}^n \cong \mathrm{im} \varphi[/math] but I don't really see how to go further after this.

[Anonymous No.15271287]

>>15271165
>I have no idea how to use the hint here, since without a ring structure I don't see how to extend φ to φQ
How would a ring structure change anything?
For [math]v \in \mathbb{Q}^n[/math], there's some [math]n[/math] such that [math]nv \in \mathbb{Z}^n[/math]. Define [math]\varphi_Q (v) = \dfrac{\varphi(nv)}{n}[/math]
Bada bing bada boom just works.

[Anonymous No.15271292]

Good Morning /Sci/entists!

I am working on the Maid Space book more. I was able to give lstlisting changes to make the code look like dark mode. I also changed the line numbers to be red. I have not figured out how to give the line numbers a background color so they look silly because they're red on white instead of red on black.

How can I change the background of the line numbers in an lstlisting?

>>15269591
I still need to know if these serve any purpose or more details about them.

Multiplication in Maid Space is not implemented as repeated addition. It uses a special operator for Maid Space I called Henshin (if you want an example of this process, look at the Henshin scenes from Kill La Kill) which changes the radix of the Maid Space, and then just use left-shift.

For example if I want 3*6 then rewrite 3 in radix 6 and shift left. So 3 is 3 in radix 6. Then shift it to get 30. Then change this back to radix 10 (if you want) and see it is 18.

If I want exponent then imagine 3^(3).

Write 3 in radix 3 and then shift left twice. 3 in radix 3 is 10. Shift twice and get 1000. Henshin back to radix 10 and see you got 27.

I think all hyperoperators can just be shifting more? But I need to study this topic to implement it correctly.

Please tell me about hyperoperators and also about fixing the background color of the numbers.

Thank you /sci/entists for reading my post.

[Anonymous No.15271309]

>>15263556
How is professor dave pop sci?

[Anonymous No.15271402]

Does anyone have any recommendations for good books to build physical understanding of particle or quantum physics?

[Anonymous No.15271413]

>>15271287
Thanks anon

[Anonymous No.15271482]

>>15271046
added.

[Anonymous No.15271493]

>>15271482
Throw in wanker and cunt, too.

[Anonymous No.15271494]

How does polynomial division change when working in [math]Z_{n}[/math]? For example, lets say were in [math]Z_{5}[/math] with a dividend of [math]x^3+2x[/math] and we want to divide it by [math](x-1)(x-2)(x-3)[/math] and we want to compute the remainder. Throwing it into a calculator gives a remainder of 1, but would this be the same for [math]Z_{5}[/math]? I have a feeling that I'm supposed to somehow use the divisor being in factored form to solve this, but I don't see how.

[Anonymous No.15271506]

>>15271482
Maybe add schizo, roastie, incel, virgin

[Anonymous No.15271525]

>>15267809
>t. seething foid
Cuntoids BTFO forever.

[Anonymous No.15271541]

>>15271493
>>15271506
very good suggestions and all added. Looks like schizo and retard are by far the most used on /sci/. on most boards i think nigger is usually by far the most frequent.

[Anonymous No.15271545]

>>15271482
monoid is an up and coming new zoomy meme insult, get it on there

[Anonymous No.15271553]

>>15271541
also it's important to note that the numbers are somewhat inflated for most of these, the way i wrote it it can not distinguish between someone posting and someone quoting a post. for example

anon1: you are a faggot
anon2: >you are a faggot
no, you are

would count as 2 instead of just 1. If anyone has any ideas for how to deal with quotes i'd be very grateful. All I can think is maybe after seeing an > maybe dont count any words again until after a newline? but then some quotes are multiple lines long.

[Anonymous No.15271569]

>>15271553
scrape some threads and calculate the percentage of quoted words to non-quoted words; then divide all statistical numbers by that constant. It's only an approximation ofc but should work fine enough

[Anonymous No.15271587]

>>15271292
Attached is an example of the current typesetting for code. I want to know how to make the background of the line numbers get a color.

[Anonymous No.15271639]

>>15271553
1. identify greentext.
2. check the reply to see if the exact same string appears. if so, dont count it.

[Anonymous No.15271652]

Let [math](W^{t}, X)[/math] be a continuous-time dynamical system and let [math](T, X)[/math] be its discrete time-1 map (i.e. [math]W^1x=Tx[/math]). Show that if [math](T, X)[/math] has a periodic point with a period of at least 2, then [math](T, X)[/math] has infinitely many points with the same period.

How do? I can see that it will somehow be dependent upon [math](W^t, X)[/math] being continuous, since this isnt true for an arbitrary discrete dynamical system, but I don't see how exactly.

[Anonymous No.15271663]

What do mathematicians mean when they say "a proof is conceptual"?

[Anonymous No.15271691]

I’m pretty sure this qualifies as a physics question and therefore a science question: Could you feasibly strangle somebody with Mardi Gras beads, or would they just snap under the force? What if you put, like, multiple rings of Mardi Gras beads around the victim’s neck, would that do anything to help or hinder the process?

[Anonymous No.15271704]

let R be a ring, is [math]M_n(M_m(R)) \simeq M_{nm}(R)[/math] as rings? I started computing away and it seems to be true, but now my head hurts and I don't want to suffer the pain of doubt any longer. PLEASE SET ME FREE ANON

[Anonymous No.15271814]

>>15271587
A dra/g/on is making some chapter header images for me, so I added one to an incomplete chapter to see what it looks like. I have two questions.

1. Why did it break my spacing and make big gaps between text?

2. How can I make the number on the lstlisting line up with the other text instead of sticking out?

Thank you /sci/entists for reading my post.

[Anonymous No.15272097]

should i use kcl to solve this or is there an easier way?

[Anonymous No.15272101]

>>15272097
forgot pic

[Anonymous No.15272140]

>>15272101
i ended up gettiing sqrt(10)* sin(2t-18.43)

[Anonymous No.15272360]

>>15251105
>>15251731
Closure if anyone cares about my mercury hysteria. I got my piss test results.
>0.6 µg/g creatinine
For reference 2.0 µg/g creatinine levels are considered normal, and around 10.0 µg/g causes poisoning symptoms to occur.

Bedroom confirmed as not a retard hotbox.

[Anonymous No.15272398]

>>15271704
Yes, classical freshman block matrices.

[Anonymous No.15272480]

Can irreducible polynomials of degree four and higher never be integrated? If no, then when can they be integrated?

[Anonymous No.15272520]

>>15272360
I'm the anon that gave you pertinent info on mercury.

I told you that you would be fine, didn't I?
>>15251521
>>15251823

[Anonymous No.15272539]

[eqn]\int \frac{dx}{x^2 \sqrt{x^2+1}} = \int \frac{\sec^2x}{\tan^2x \sqrt{\tan^2 + 1}}\, dx[/eqn]Is this legitimate, when I resubstitute with the arctangent in the end?

[Anonymous No.15272553]

>>15272539
the derivative of tan x is 2 tan x sec ^2 x. also, tan x might not be defined over your entire bounds of integration.

[Anonymous No.15272555]

>>15272520
True, but even thought I logically knew it to be true, I needed to see it on paper to feel at peace.

[Anonymous No.15272560]

>>15272480
There are no irreducible polynomials of a degree higher than 2 in [math]\mathbb{R}[x][/math]. Also all real polynomials can be integrated over any compact set.

[Anonymous No.15272580]

>>15272553
oops i fucked that up but the second part still stands.

[Anonymous No.15272586]

>>15272553
The derivative of the tangent is definitely sec^2(x); I think you're mistaking it for the derivative of the secant which is tan(x)sec(x). This is an indefinite integral.

>>15272560
What about p(x) = x^4+x^2+3? How could this polynominal be reduced?

[Anonymous No.15272601]

>>15272560
I'm sorry, I meant polynomials in the denominator with 1 in the numerator. I know that polynomials can be integrated, this is clear.

[Anonymous No.15272612]

>>15272555
>>15272520
Yeah, things are less scary if there is something
written down somewhere. Even if you're on a boat
without a paddle going over the waterfall, you'd
be like "ah...I know how this is...".

[Anonymous No.15272670]

in diffusion models, [math]\mathcal{N}(\mu_t = \sqrt{1 - \beta_t}x_{t-1}, \Sigma_t = \beta_t I)[/math]
what is the purpose of $\beta_t$? why not just set the mean to [math]x_{t-1}[/math] and the stddev to the identity?

[Anonymous No.15272764]

>>15263241
Theoretically speaking, could I use magnets to pull brain matter from other regions of my brain into my prefrontal cortex in order to improve cognition?

[Anonymous No.15273147]

>>15263621
>How are you supposed to tell if a particle interaction is through the weak force, strong force or EM force?
Learn how Feynman diagrams work.

>I thought that interactions with EM force would always have a photon on the right side but a J/psi particle going into a mu+ and a mu- particle is EM. How and why?
The charm and anti-charm quarks in the J/psi annihilate into a virtual photon which then 'decays' into muon and antimuon. You can't draw the same sort of diagram with gluons since the J/psi is a color singlet.

>And how could I possibly be able to tell that a omega- baryon changing into a K- and a lambda0 particle is weak force?
>I can imagine that conservation of strangeness or so could help
The strangeness in that decay is not conserved therefore it must decay by weak force

[Anonymous No.15273304]

Math subject question

I am currently trying to get through college and I'm in a Stats class. It's pretty basic and I understand most of it minus a few things that take me a minute to capture.
Next semester though, I have Business Calculus.
I wasn't too worried with Statistics because many told me it's not difficult to an extreme extent but how would Calculus compare?

For context, the highest math class I had was Algebra 2 over 6 years ago.
I don't "struggle" with math but I'd also like to know what I'm signing up for

[Anonymous No.15273309]

>>15273304
>Stats
is applied math, everyone likes it

>Calculus
is literally algebra, but with one added thing (the limit).
Downsides of algebra/calculus: lots of garbage identities/transformations to memorize. lots of grinding through tedious boring examples to prove you can do "hard" problems. No one agrees on notation and all the notations kinda suck

[Anonymous No.15273315]

>>15273309
I have faint memories of struggling with certain parts of Algebra so I'll have to think about it. Thanks for the detailed reply

[Anonymous No.15273680]

>>15271814
I tried using titlesec and titlespacing to fix it, but it kept breaking compilation. I am going to choose to ignore the bad spacing or incomplete lstlisting styling and focus on modifying Kurumi MaidHelper to draw operators being operated.

If you know about Symbolic Dynamics, drawing voxels or what can fix my latex problems, please tell me.

Attached is a drawing Stable Diffusion made while it was learning about maids. I might use it as a chapter header because it looks funny.

Thank you /sci/entists for reading my post.

[Anonymous No.15273699]

Trying to solve the functional equation
[math]f^3(x) + 3f(x) = x[/math] for x = 0. I know that this function is injective so there exists an inverse function. But I can't find the value. (it's probably 0 but I don't know how to get there)

[Anonymous No.15274132]

>>15263241
Is this okay?

[Anonymous No.15274147]

Either I'm having a brainlet moment or my professor got something wrong. If the sum of torques for any given point in space equals zero, does that imply that the sum of forces on a given object is zero? He states that if the sum of torques at the centre of gravity is zero, then that does not imply that the sum of forces is zero. Is there a derivation of the first statement?

[Anonymous No.15274183]

>>15274147
consider a nonrotating object in frictionless free-fall

[Anonymous No.15274192]

>>15273304
BUSINESS Calculus is very easy. All you will do is reduce the exponents in polynomials of at mos degree 3, and change their coefficients a bit. Then you will find their roots using the quadratic formula. That's it.

[Anonymous No.15274240]

anyone knows how to do this?

[Anonymous No.15274261]

>>15272586
[eqn]x^4 + x^2 + 3 = \left( x^2 - x \sqrt{2 \sqrt{3} - 1} + \sqrt{3} \right) \left( x^2 + x \sqrt{2 \sqrt{3} - 1} + \sqrt{3} \right)[/eqn]

[Anonymous No.15274459]

i took some higher math in uni ages ago. i sometimes mess with random math questions when playing with my kids.
so anyways, im trying to derive surface area and volume formulas or random 3d solids (cone, square pyramid, etc.). i used integration for all of those (deriving a formula for perimeter of a slice and then integrating for surface area; same with area of a slice and volume).
everything seemed to work, until i tried to derive the formula for spheres surface area.
basically, i took a quarter of a circle, derived the radius of slices in relation to radius:
r(x) = sqrt(R^2-x^2)
my logic is that i take slices along horizontal (x axis). the slices are all circles. the radius of the circle is the height (r axis), which is connected to x via circle equation:
x^2 + r^2 = R^2 (R being the radius of the sphere).
so i tried this approach for finding the volume:
V = 2*Pi*integrate(R^2-x^2, {x, 0, R}). everything seems fine, i get the correct formula:
(4/3)*Pi*R^3
i then tried the same for surface area:
S = 4*Pi*integrate(sqrt(R^2-x^2), {x, 0, R})
im too stupid to calculate this integral myself, so i used several different calculators. they all gave me the same result (i checked the solution, seemed good):
integrate(sqrt(R^2-x^2), {x, 0, R}) = (Pi*R^2)/4 (solution emitted)
this gives:
S = Pi^2*R^2
this is of course incorrect, it should be
S = 4*Pi*R^2

what am i doing wrong and why the same logic seemed to work for other solids and even spheres volume?

[Anonymous No.15274464]

does the fact that I went through my entire degree successfully without tutors/office hours mean I'm just retarded or smart

[Anonymous No.15274518]

>>15274464
Probably just means you avoid social interaction with strangers unless it's absolutely necessary (which is understandable)

[Anonymous No.15274539]

>>15274518
damn read like a book

[Anonymous No.15274996]

Self-teaching myself differential equations. Is it normal to consult a table of Laplace transforms for problem sets or do students usually work out the integral by hand?

[Anonymous No.15275018]

>>15274996
When I took it, prof gave us a table to consult, so I assume that it's normal. Of course, he also had a meltdown about how half of the class expanded (x+y)^2 as x^2+y^2 on a test, so maybe they weren't the best and brightest.

[Anonymous No.15275587]

>>15271123
I use \mathds{1} from the dsfont package

[Anonymous No.15275599]

>>15274464
95% of people never use office hours. That doesn't mean anything.

[Anonymous No.15275626]

>>15273680
I have more information about my typesetting problem. I am using a two-side mode in latex, so that if my book gets printed, the margin maids are always on the outside. This works fine, when margins are on the right. If a chapter starts with margins on the left, the chapter header image doesn't span the whole top of the page like it should. It leaves about a 2 inch gap.

Does anyone know why this happens? Worst case I will change it so a blank page keeps the first page of a chapter from ever having it's margins on the right, but I'd rather not have to keep track of that or insert blank pages. I can make the blank pages suck less by putting maids on them, but I don't want blank pages taking up space in the book. Is there something else that needs to be done to make \setchapterimage work when margins are on the left?

[Anonymous No.15275746]

>>15263241
Sorry for being late.

Unanswered questions:

Maths questions:
>>15247336
>>15247687
>>15247819
>>15247924
>>15252037
>>15253705
>>15255261
>>15260023
>>15262642 >>15262646

Physics questions:
>>15251787


Chemistry questions:
>>15246983
>>15260027

/g/ questions:
>>15249674

Stupid questions:
>>15247318
>>15248875
>>15250574
>>15250951
>>15251763
>>15252233
>>15254379
>>15257942
>>15260021
>>15260814
>>15260890
>>15260905
>>15261326

[Anonymous No.15275772]

>>15263968
>I need to know more good maid shows.
Somehow I have my doubts the best maids are from maid shows. Maids are at their best when they're in the background.

[Anonymous No.15276085]

>>15246983(Cross-thread)
Depends what exactly you mean.
- Benzyne is benzene with a triple bond in it, and useful as an aromatic precursor
- Cyclooctynes react with azides, and are famously involved in in-vivo click-chemistry reactions
- 1,5,9-Cyclododecatriene-3,7,11-triyne (C12H6) is a non-strained aromatic cycle made of dienes and trienes

[Anonymous No.15276312]

so i know the answer for this is an inductor and a resistor. But im kinda confused as how you would determine that. I know a inductor leads in voltage but lags in current. Capacitor is opposite where it leads in current but lags in voltage. But in this question both the current and voltage lead by 50 and 5 respectively. So im confused as to how you would determine if the components are either cap or inductor given this info

[Anonymous No.15276371]

Good Morning /Sci/entists!

I still have a problem with Latex as noted here >>15275626

Contingency procedeures are in effect, obviously a major malfunction. To keep from going insane, I am just going to force chapters to start with margins on the right. If it causes extra blank pages, then I will ask Stable Diffusion dra/g/on to make some full page maids for me and the page won't be blank anymore. I would prefer it just work properly on pages with left margins and not make extra pages to force alignment, but I refuse to let a minor stylistic problem slow me further and must continue creating the content.

>>15275772
Shows get boring when there isn't a maid. I used to watch western TV, because I live there and it is easy to get. It was nice until about 2010-ish, then it got ruined by the mass deployment of identity politics which made it boring and also made boredom inescapable which removed escapism from TV which until then had been TV's primary power and the draw to using it.

Then I found fanservice anime and that was immediately interesting, but got boring fast so I tried to see are there any fanservice animes with plots?

This caused me to watch isekai which also quickly got boring because Japanese World of Warcraft stories don't have a lot of variety.

I noticed that a lot of these shows had a maid as a minor character. It always made me laugh to see the maid because she is out of place. Why is there a maid in WoW world? Why is one of the most powerful spellcasters a maid? Why is there a robot maid punching a werewolf?

After a while I stopped asking "Why is there a maid?" and started asking "Where is the maid?" and stop watching the show if it doesn't have a maid.

Now I mostly just get books and use computers because TV got less interesting than Computer Science.

>tl;dr: Maids have to be central to the show because I didn't come to watch anime. I came to see maids and anime is the venue with the most maids.

Thank you /sci/entists for reading my post.

[Anonymous No.15276444]

>>15276312
Inductor: V=L.dI/dt
Capacitor: I=C.dV/dt
I=sin(ωt) => dI/dt=ω.cos(ωt)
Likewise for V.
cosine leads sine by 90°. The peak of cosine is at 0°, the peak of sine is at 90°, which is 90° later. So an inductor has V leading I, a capacitor has I leading V. The question has v(t) leading i(t) by 45°, so the circuit is a resistor and inductor of equal impedance at ω=10,000 rad/sec, i.e. R=10000L.

[Anonymous No.15276446]

>>15276312
>But in this question both the current and voltage lead by 50 and 5 respectively.

Voltage leads current by 45°. The extra 5° is just the phase of the current at t=0, which is an entirely arbitrary point.

[Anonymous No.15276452]

>>15276444
>>15276446
appreciate it thanks.

[Anonymous No.15276517]

>>15276446
so just to check my understanding with another problem, with this one the current is lagging by -30°, which means its an inductor

[Anonymous No.15276719]

I have a set of 20 projects with one performance metric. I need to make a visualization for how often each project is in the top 5 or bottom 5 on a monthly timescale. For example, Project A is in the top 5 25% of the time and bottom 5 10% of the time. Any suggestions on visualization? Tried grouped bar chart first, looks like shit. Dot plot looks like shit because there's too many projects.

[Anonymous No.15276817]

is there a name for the being able to convert an nth order differential equation into n+1 (or just n maybe, I can't remember) first order differential equations

[Anonymous No.15276820]

calc II student here, I just learned about the Feynmann integration technique. It's cool, but it seems it's only applicable under very specific circumstances. In how many cases can you actually use it from your experience, I mean in percentage terms?

[Anonymous No.15277235]

https://odysee.com/@standfortruth:f13/Barry-Trower-5G:7

[Anonymous No.15277274]

Unusual question here: I basically just got my boots filled with agar. Will I ever be able to wear them without turning my feet into a walking petri dish? Should I just trash them?

[Anonymous No.15277283]

>>15277274
Is agar water soluble?

[Anonymous No.15277290]

>>15277283
It's not actually agar. It's a dextrose mixture with some other minerals thrown in. It serves the same purpose - to make the perfect breeding ground for bacteria. I stepped in a massive puddle of it and my boots aren't waterproof.

[Anonymous No.15277770]

How do I solve y′′′ + 10y′′ + 25y′ = 0, y(0) = 0, y′(0) = 1, y′′(0) = −8?

[Anonymous No.15277778]

>>15276719
excel spreadsheet
20 rows
one column for each month
conditionally color each cell green or red (or leave it blank) according to the performance

[Anonymous No.15277797]

>>15263241
What is the answer to b)? I can't make any figure which matches this.
For context symetries of a square in a plane are the 4 rotations and 4 reflection lines.

[Anonymous No.15277844]

>>15277770
First integrate it and solve it like any other second-order differential equation.

[Anonymous No.15277910]

>>15277797
many such answers. just make a seven-pointed pinwheel or something

[Anonymous No.15277926]

>>15277797
The symmetry group has to be a group with 7 elements of which only one exist C7.

[Anonymous No.15277936]

>>15277844
>>15277770
I tried finding the the roots of the auxiliary(?) equation and got the solution to be of the form
y= c1 + c2e^(-5x) + c3xe^(-5x)
but I dont think this is correct

[Anonymous No.15277953]

>>15277936
Looks correct to me. You then use the boundary conditions to find the values of the constants.

[Anonymous No.15278024]

dont bugs still have a little poop in them when you eat them since their digestive track are still inside?

[Anonymous No.15278033]

>>15278024
Yes but most of them are vegetarian so it's fine. But it is why scavengers and bottom feeders like prawns are de-veined first.

[Anonymous No.15278071]

by definition atom in ground state can't release energy without external stimulus?

[Anonymous No.15278075]

>>15278071
it could decay yes

[Anonymous No.15278083]

>>15278071
Seems so unless proton decay will be observed
>>15278075
Radioactive atoms has radiactive nucleus which is not in ground state which means whole atom is not in ground state
https://physics.stackexchange.com/questions/274213/is-a-naturally-radioactive-elements-on-its-ground-state

[Anonymous No.15278102]

>>15278033
I don't know if I'd call that fine. Safe to consume maybe but it's still poop.

[Anonymous No.15278108]

>>15278083
>radiactive nucleus which is not in ground state which means whole atom is not in ground state
by this reasoning a hydrogen nucleus is not in its ground state, because fused with another it (now 1p of He) has less energy.

[Anonymous No.15278117]

>>15278108
As I understand decayable atoms can't be in ground state unless decayed in stable ones, but I'm not proficient at physics

[Anonymous No.15278121]

>>15278117
Not arguing with you, it just seems like that's a poor definition of "ground state." If picrel is how we distinguish 'meta'- from truly-stable states, seems like one proton as a hydrogen nucleus could make a similar over-the-hump transition to an even lower energy state, fusing with another into helium. That's a lower energy state for each proton individually, and the system as a whole

[Anonymous No.15278124]

>>15278121
fusing with another proton would be external stimulus
> by definition atom in ground state can't release energy without external stimulus?

[Anonymous No.15278137]

>>15278124
so is a system of two hydrogen atoms at its ground state?

[Anonymous No.15278183]

>>15278137
I don't know anon , I asked bing bot now and
> so is a system of two hydrogen atoms at its ground state?
=>
> The ground state energy depends on the distance between the atoms and their orientation

but I guess bingbot can be unreliable

[Anonymous No.15278198]

>>15278102
So are mushrooms but people still eat them.

[Anonymous No.15278368]

How can something like elementary charge be a defined value? So there's no point anymore in devising an experiment to measure it? What happens if you get a different value than what it's defined to be? You're just wrong?

[Anonymous No.15278402]

>>15278368
> How can something like elementary charge be a defined value?
That's what the quantum in quantum mechanics means. Certain fundamental properties of the universe have discrete values.

> So there's no point anymore in devising an experiment to measure it?
Not true. The unit of charge is an important quantity to know, improving the accuracy of experimental measurements is never a bad thing. Also there is also the chance better equipment might reveal something never seen before. For example that was how spin was discovered.

> What happens if you get a different value than what it's defined to be? You're just wrong?
That would certainly be you're first, second and third conclusion. How often do you think people discover new fundamental physics? It's like the time an experiment kept measuring neutrinos going faster than light. They eventually published a paper saying "we know this is wrong but we can't see why". Turns out they had faulty hardware: https://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly

[Anonymous No.15278429]

Good Morning /Sci/entists!
>typeset 90 page document
>leave out most math drawings
>leave out margin maids
>compiling it with Latex still takes half an hour
>make very minor spacing change
>want to see what something looks like with \medskip instead of \\
>30 minutes recompile time to see a header move up or down 4 pixels
>decide I don't like it
>change it back
>an hour of time consumed compiling a pdf
How can I make this process faster? Is there a more modern alternative to Latex that runs at a decent speed?

Waiting on compilation is slowing the speed at which I can iterate over the book to add more things or make things look nicer.

I like working on projects and making them nicer. I don't like waiting 30 minutes to see if a minor style tweak to my book looks good or not.

Thank you /sci/entists for reading my post.

[Anonymous No.15278432]

>>15278429
try LuaTex

[Anonymous No.15278434]

>>15278429
wtf are you doing that it takes 30 minutes?? longest document I've ever compiled took 30 seconds and that was a 300 page PhD thesis mostly filled with math and graphs.

[Anonymous No.15278443]

>>15278432
Thank you for telling me. I have never used this, but I think TexWorks has it, so I will try this and see what happens.

>>15278434
Making a book about Maid Space. With images it looks like the attached image. I removed the margin maids and began retypesetting it because header maids break my typesetting unless I force chapters to start on pages where margins are to the right. This causes some extra blank pages to make the count work, which is unfortunate. If I can fix that I would like to. If not, I will change the empty pages to full page maids.

Also my code has minor typesetting problems because I can't figure out how to make the background of the line numbers turn black.

You can see an example of the typesetting here >>15271814

[Anonymous No.15278448]

>>15278443
Fucking hell, I hope you're autistic because otherwise you're one sad, lonely manchild. Look at using the subfiles package or just cut out a single page to test a change.

[Anonymous No.15278506]

Help on this one ?
It feels true but i can't prove it, which makes me think it might be false.

(The norm that is mentionned is the euclidian one.)

[Anonymous No.15278535]

>>15278443
have you tried asking on https://tex.stackexchange.com/ ?

[Anonymous No.15278546]

>>15278448
One day you're going to go to a science meeting. They'll give you a swag bag with fun sized candy, an obsolete flash drive, and a stress ball shaped like a 3D shape 99% of humanity doesn't know the name of, a very low quality stylus-pen combo device made from happy meal toy plastic, and a small blank book probably with branding from a school or a bank or something that donates to whoever is hosting the meeting.

You will be fumbling with the obsolete flash drive you got at a previous science meeting to try to figure out how to get your slideshow about your niche inside a niche research topic on a projector. For a moment you'll wonder why the room is so empty? Last time you gave this talk, seven people came. Now you only have three? Then you'll see it.

A card table with a pile of nice, hardcover books with anime maids all over them. The table is being operated by maids with huge boobs. The maids are handing out copies of the book along with large warm cookies and bottles of various types of milk. There is a big crowd by the table. You realize that of the three people attending your talk, all of them have a copy of my book. One is reading it actively. The others are eating cookies and have it on the table in front of them.

At lunch the maid table will distribute free pizza and softdrinks alongside the book and remaining cookies.

Later at a closing speech you'll have to listen to a science donor who is probably a business boomer who funded the science meeting to virtue signal his company's commitment to science. He doesn't care about science. He is basically here for marketing reasons. So later he can say he went and donated and his company helps science. Somewhere in his speech he will mention or joke about the maids and the book.

A few years later you will discover nobody remembers anything from the meeting except the maids gave them a nice cookie and everyone was looking in the maid book.

At this point, you might understand the value of presentation.

[Anonymous No.15278573]

>>15278535
I read that site sometimes but I don't have an account. I don't like signing up to things or agreeing to a Terms of Service or making a login. I also don't like being subjected to the whims of internet janitors. I am not sure if the tex stack exchange has this problem or not, but on Stack Overflow a lot of times a Dunning-Kruger janny who doesn't understand the topic of discussion will shut down a useful discussion for no real reason, and mark it as a duplicate of an unrelated question from 2009. This is unappealable usually and the Dunning-Kruger janny has no accountability and can't be given useful feedback on how his jannying makes the site worse by stopping discussions he was not party to, for no reason. The only Terms of Service I will accept from a Computer Program are that I will dictate my terms to it, and it will service me the way I told it. There is no reason a place for discussion should require a login, user data of any kind, or host tracking javascript for targeted ads. This is why I mainly use 4Chan.

[Anonymous No.15278598]

>>15278573
Oh, how delightful it is to stumble upon the opinions of someone who clearly has a firm grasp on the intricacies of internet forums and the injustices of the world.
First, the mere notion of avoiding signing up for an account or agreeing to a Terms of Service is quite charming in its naivety. Surely, a person of your intellect must comprehend that these platforms are freely provided for our use, and as such, they require some basic rules and agreements to maintain order and security. Alas, I understand that such concepts might seem unreasonable to someone who prefers to roam maid porn sites.
Regarding the so-called "internet janitors": it's a shame that your keen insight and profound understanding of every subject ever discussed on Stack Overflow is not shared by these mere uneducated mortals, who are left to manage the vast ocean of content with the limited resources at their disposal.
As for the unappealing process of appealing a decision, I can only imagine that such an inconvenience must be unbearable for someone of your stature. It is truly a tragedy that the world cannot function more seamlessly to accommodate your preferences.
Now, let's move on to your insistence that a computer program should fully cater to your whims without any consideration for the needs and requirements of the platform or its users. A commendable position, indeed! How unfortunate it is that these services are not structured to revolve solely around your desires.
Lastly, I must applaud your dedication to 4Chan, a bastion of intellectual discourse and thoughtful contribution to the digital realm. It is a true testament to your discerning taste and exceptional ability to navigate the complexities of the online world.
Keep on being who you area, anon ;)

[Anonymous No.15278661]

I came up with this formula a long time ago for use in video game programming

CurrentValue += TargetValue - CurrentValue / 10

What happens is that the CurrentValue races to the TargetValue really quickly as this formula is repeated, but as CurrentValue gets close to the TargetValue then the amount of change eases to the TargetValue very slowly.

Could it be rewritten so the opposite happens? I'd like it if the CurrentValue eased to the TargetValue very slowly to begin with, but quickly ramped up to the TargetValue as the CurrentValue got closer to it.

[Anonymous No.15278679]

what would this circuit look like.

[Anonymous No.15278684]

>>15278573
Bullshit. You use 4chan because you get banned everywhere else.

[Anonymous No.15278696]

>>15278679
google "summing op amp topology" and figure it out

[Anonymous No.15278705]

>>15278598
People always say if you don't like how a platform is operated, don't use it or make your own platform.

Your wish is my command, I guess. I just follow this advice. For example, instead of using GitHub and making an account and giving them my email and a login and my phone number for 2FA and subjecting myself to their standards for jannying and agreeing to their TOS just to be able to distribute code, I made Kurumi MaidCard which gives me a way to distribute my code by sharing an image that used Maid-LZW to draw the code as a Maid Space on that image.

Now it doesn't matter how bad the deal Microsoft offered is, or how they unilaterally change it over time to squeeze more money and data out of people using their service, because I am not using it. I am using the alternative I made which doesn't involve entering into a long, very one-sided, incomprehensible legal agreement with a multinational company that hates me, just to put some Java classes on the internet for people to look at.

[Anonymous No.15278723]

>>15278684
This is also true. If I posted like this on Twitter or Facebook I would get literally get banned by the world's foremost experts on censoring the internet. People armed with the latest tech advances in censorship, paid by a billion dollar company for no reason but to censor speech and limit discussion on the internet. I don't care what people in San Francisco think about literally any topic and I refuse to use any platform that gives them editorial powers over what speech I am allowed to engage in.

4chan isn't perfect. Sometimes the janitors here are excessive too, but it is still about a million times better than dealing with the AI enabled janny squads big tech companies employ. I would rather 80% of my replies be people calling me a tranny and encouraging suicide than use a censored, sanitized platform that just removes my post and shadowbans me for any reason.

Freedom in communication has more value than anything offered by a big tech company.

[Anonymous No.15278727]

>>15278705
>>15278723
stop spamming /sqt/ you egotistical piece of shit. This is not your personal blog

[Anonymous No.15278754]

>>15278432
Retard.
>>15278429
No [math] \mathrm \LaTeX [/math] code should take 30 minutes to compile even if it has a lot of images. In fact, images shouldn't even affect compile time much unless you are rendering them using [math] \text{TikZ} [/math], which is a non-issue if you use [math] \texttt{standalone} [/math] to render them separately. Your code is messed up.

[Anonymous No.15278760]

>>15263241
I'm Probably going to off myself this weekend. What would be the best method to end myself? I was thinking of taking a train to a city then jumping off a sky scraper or just stabbing either the axial artery or the artery in the thigh( forget name)

[Anonymous No.15278771]

>>15278727
I have to keep posting until 4Chan changes into the world's most advanced Science Foundation. I can't leave until then.

>>15278754
I don't know if I am using tikZ, I will investigate more. I started with a template I found on a latex site somewhere called Kaobook. I modified it only really by adding Simpsons font, changing spacing in some areas so drawings like the attached one get rendered right and changing the kaobox color to pink and renaming it maidbox because I kept forgetting kaobox because what is a kao and what does it have to do with a maidbox?

[Anonymous No.15278789]

>>15264705
(x) irreducible in PID R iff (x) maximal iff R/(x) is a field and all fields are PIDs

[Anonymous No.15278886]

Can someone tell me what you would score the following questions from my geol exam? Don't worry you can't help me cheat, I already finished it (and did shit lol). Just feeling nervous.
> Why is the early rock record of the Precambrian rocks more difficult to interpret than the rock record of the Phanerozoic Eon?
The Precambrian era lasted for much, much longer than the Phanerozoic era and the usual methods of analyzing minerals aren't as present, due to the atmospheric makeup of earth at the Precambrian being far different than modern days and lack of fossils besides Cyanobacteria.

>Compare and contrast the Darwin-Wallace mechanisms of natural selection and evolution with Lamarck’s theory of inheritance of acquired characteristics. Explain how both of these concepts might apply to the development of long necks in giraffes.
Darwin-Wallance mechanism for natural selection and evolution involves each generation involves getting longer necks, by having parents of a fitter genetics (which in this case, longer necks) breed with each other. This makes evolution a gradual process, that happens over generations of a species time line
Lamarck's theory of inheritance of acquired characteristics says that the animal would get the needed trait. The giraffes in this case, would develop a longer neck over it's lifetime. This puts the change on the individual, and the giraffes gets a longer neck.
They both share the same principle of adapting to need, but they differ with how the change happens. Lamarck's is within the time scale of an animal's life, while Darwin-Wallaces timescale is within a species's timeline.

I asked chatGPT and it says "um, SWEATY, you didn't go enough detail", kinda stuff, for an intro to geol class. So here we are. ChatGPT says I would get 14/16 respectfully.

[Anonymous No.15278891]

how do I overcome linear algebra fatigue?

[Anonymous No.15279211]

>>15278771
>I started with a template
That's your problem. Templates suck always. I have always had better results customising the book class on my own. Besides, you shouldn't even be thinking of design until you have finished your manuscript.
Separating chapters into different .tex files and using \include also greatly improves compilation time.

>>15271814
>2. How can I make the number on the lstlisting line up with the other text instead of sticking out?
If you are asking about the numbers in the image, you have to scale it to \textwidth.
\includegraphics[width=\textwidth]{image.jpg}

[Anonymous No.15279268]

[math] \forall x \in \mathbb{R} f^3(x) + 3f(x) = x[/math]
How do I prove that f is differentiable? I've found that f(0) = 0 and that it's injective but I can't seem to do anything else.

[Anonymous No.15279322]

>>15279268
There's always only one real root to this equation, which is a continuous and differentiable function of [math] x [/math].

[Anonymous No.15279334]

>>15278137
No. It costs less overall energy if they are fused together

[Anonymous No.15279364]

>>15279268
Let [math] y = f(x) [/math]. Then:
[eqn] x = f^{-1} (y) = y^3 + 3y [/eqn]
The inverse function is differentiable, so should the actual function.

[Anonymous No.15279368]

>>15279322
I don't see how this implies that f is differentiable.
>>15279364
[math]f^{-1}(y) = f^2(y) + 3y[/math]

[Anonymous No.15279431]

>>15279368
not that anon but I'm pretty sure the differentiability of a function is equivalent to the differentiability of its inverse

[Anonymous No.15279435]

>>15263241
at what themparature can copper turn into plasma and gas?
its for /k/

[Anonymous No.15279447]

>>15278705
You can run git without github you know, on your own server.

[Anonymous No.15279597]

I'm struggling with basic integration should I give up and kill mhself

[Anonymous No.15279669]

>>15279597
no, instead you should be kind and loving to yourself - you'll find this helps you get better at integration

[Anonymous No.15279708]

would it be possible to build a machine that reverses or neutralizes oceanic and gravitational pressure in a bubble around itself for the purpose of exploring the deepest ocean depths

[Anonymous No.15279757]

>>15279708
Yes, it's called a submarine.

[Anonymous No.15279920]

>>15279211
Thank you for telling me. I meant the line numbers next to code.

>>15279447
I also don't want to do this. I don't want to have to buy a server or rent a virtual private server or something. I would literally rather invent a new software distribution system and use that than deal with hosting companies or Git (this is why partly Kurumi MaidCard exists).

[Anonymous No.15279959]

>>15279597
https://www.youtube.com/watch?v=dgm4-3-Iv3s
do all of these and if you can't, then watch their explanation videos on integration techniques

[Anonymous No.15280096]

>>15263556
>>15268604
>try checking out one of the top "based" and "informative" channels
>on his channel he's recommending channels that are at the bottom of "popsci" and "cringe"
yep, meme shart confirmed

[Anonymous No.15280216]

im trying to geometrically derive the arcsin function for an ellipse with major and minor axes a and b, respectively. right now i have
[eqn]
\arcsin(x)=\int_0^x \frac{(a^4-b^4)t^2 + b^4}{\sqrt{(b^2-a^4b^4)t^4 + (a^4 b^4 - 2b^8)t^2 +b^8}} dt
[/eqn]
if we set b to 1, it looks a little nicer
[eqn]
\arcsin(x)=\int_0^x \frac{(a^4-1)t^2 + 1}{\sqrt{(1-a^4)t^4 + (a^4 - 2)t^2 +1}} dt
[/eqn]
i would like the polynomial in the denominator to be degree 3, instead of degree 4. does anyone know some sort of change of variables i could do to get there?
(yes i know this function is non-elementary.)

[Anonymous No.15280281]

>>15279597
no, you should give up and learn numerical integration instead

[Anonymous No.15280373]

how do i find the fxy and fyx (mixed partial derivatives) of e^(x^2 y)-e^(xy^2 )

[Anonymous No.15280468]

>>15280373
Whats the problem? Just take the derivative wrt to x and y, and wrt y and x

[Anonymous No.15280476]

>>15280468
I keep on getting the wrong results for both of them in which I am missing expressions of 2x and 2y

[Anonymous No.15280479]

>>15280476
Forgot the chain rule?

[Anonymous No.15280490]

>>15280479
I have applied the chain rule and im still getting the wrong answer. I havent done maths in ages (3 years)

[Anonymous No.15280508]

>>15280216
heres my attempt:
we can rewrite the denominator like
[eqn]
\int_0^x \frac{(a^4-1)t^2 + 1}{\sqrt{-t^2((a^4-1)t^2+1)+(a^4-1)t^2+1}} dt
[/eqn]
then do a substitution like this, hopefully its all correct
[eqn]
u = (a^4-1)t^2+1 \\
t = \sqrt{\frac{u-1}{a^4-1}} \\
du = 2(a^4-1)t \; dt \\
dt = \frac{du}{2(a^4-1)t} = \frac{du}{2\sqrt{(a^4-1)(u-1)}} \\
\arcsin(x) = \int_0^{\sqrt{\frac{x-1}{a^4-1}}} \frac{u \; dt}{\sqrt{-t^2u+u}} = \int_0^{\sqrt{\frac{x-1}{a^4-1}}} \frac{u \; du}{\sqrt{-u^3+(a^4+1)u^2-a^4u}}
[/eqn]
which is soooo close, but theres no constant term.

[Anonymous No.15280521]

>>15280373
[math]\partial_{xy} (e^{x^2 y}-e^{xy^2})=\partial_{y} (2xye^{x^2 y}-y^2e^{xy^2})=2xe^{x^2 y}+2yx^3e^{x^2 y}-2ye^{xy^2}-2xy^3e^{xy^2}[/math]
Something like that

[Anonymous No.15280553]

>>15279597
No. Virtually all Derivatives are easy solvable by brute force, but Many integrals are bullshit dumb retarded like solving a diffeq, you have to work out the structure that its antiderivative fn could take, and then work backwards, catch all the coefficients and exponents etc. To the point that most people solve most integrals by memorizing a shitload of identities and common forms, or giving up and asking Daddy Worlfram right away

[Anonymous No.15280662]

Imagine that you have a function f(x) on an interval. If you split up that interval in different subintervals and compute the sum of f''(ξ_i) (the second derivative of f, with ξ_i being a single arbitrary x value on each subinterval) then why is that supposed to be equal to f''(ξ) with ξ a single arbitrary value somewhere on the whole interval?

[Anonymous No.15280700]

Let [math]K[/math] be a field and consider the factor ring [math]R = K[X, Y]/(XY^2)[/math]. How do I show that the elements [math]X + (XY^2), X+ XY + (XY^2) \in R[/math] are not associated in R (note that I can't use ideals as my argument since [math]R[/math] is not an integral domain, infact the principal ideals generated by those two elements do coincide). It is clear that [math]X + XY +(XY^2) = (X + (XY^2)) * (1+Y+(XY^2))[/math], but it doesn't suffice to show that [math]1+Y+(XY^2)[/math] is not a unit, does it? And even if it does, how would I go about showing that it is not a unit?

[Anonymous No.15280970]

>>15278723
Very based.

[Anonymous No.15280972]

Hi /sqt/. Consider [eqn]\text{rank} (\lambda \Phi + \lambda'\Phi) \leq \text{rank}\, \Phi + \text{rank}\, \Phi'[/eqn]with [math]\Phi,\, \Phi': V \to W[/math] being linear transformations and [math]\lambda,\, \lambda' \in \mathbb{F}[/math]. [math]V[/math] and [math]W[/math] are both vector spaces over the field [math]\mathbb{F}[/math].

My book wants me to show this identity, which I did. But I suspect that the author might have misspelled it and it was supposed to be [eqn]\text{rank} (\lambda \Phi + \lambda'\Phi') \leq \text{rank}\, \Phi + \text{rank}\, \Phi'.[/eqn]What do you think of this?

[Anonymous No.15280981]

>>15280972
Probably.

[Anonymous No.15281002]

>>15280972
I think worthless trash, kys

[Anonymous No.15281309]

how can I make this look less ugly

[Anonymous No.15281330]

Just to check:
When setting up the Riemann zeta function (before analytic continuation) with a definition like [math] \zeta(s) = \sum_{n=1}^{\infty} n^{-s} [/math] , do authors specifically mean [math] n^{-s} = \exp(-s\ln(n)) [/math] where the natural log is the usual one that's real-valued on the positive reals?

[Anonymous No.15281356]

>>15281309
Align it to the left, for one. What are you, arabic?

[Anonymous No.15281501]

>>15281356
right looks better desu

[Anonymous No.15281561]

>>15280700
First, to show [math] 1+Y \text{ mod } XY^2 [/math] is not a unit in [math] R[/math] :
Note [math] (1+Y , X) [/math] is a prime ideal of [math] K[X,Y] [/math] containing XY^2 ,
hence (by 3rd Iso Thm with prime ideals), [math] ((1+Y) \text{ mod } XY^2 , X \text{ mod } XY^2 ) [/math] is a prime ideal in [math] R[/math];
in particular [math] (1+Y) \text{ mod } XY2[/math] is contained in a proper ideal of [math] R[/math], hence it cannot be a unit in [math] R[/math].

[Anonymous No.15281577]

I've a question about the mathjax. Does it just not render if posted in a thread past the bump limit? It works on everything I've tried including the tex previewer, but not in a non-bumping thread. Also tried different browsers and other services/software and it renders correctly just not in threads past the bump limit. Is there some trick to it or am I just stupid?

[Anonymous No.15281668]

>>15280700
>>15281561
Also is [math] K [/math] algebraically closed? I think we can find a counter-example for e.g. [math] K = \mathbb{R} [/math] .

[Anonymous No.15281790]

If gene A is dominant over gene B and gene B is dominant over gene C, will gene A always be dominant over gene C?

[Anonymous No.15281815]

Hello friends. Attempting to integrate via partial fractions... still pretty new. What is wrong in my solution?

[Anonymous No.15281844]

>>15281815
Why sqrt(x) +- 2?

[Anonymous No.15281873]

>>15281844
IDK, maybe I'm retarded. How else would one integrate this via partial fractions without factoring x-4 to sqrtx +- 2?

[Anonymous No.15281917]

I'm trying to understand Lewis diagrams. I have to represent HNO2. What I did is 1), the solution is 2). Why is what I did wrong?

[Anonymous No.15281931]

>>15281917
single bonded oxygen bonds more readily to hydrogen than the double bonded oxygen because that's a lower overall energy

[Anonymous No.15281937]

>>15281931
Okay thank you

[Anonymous No.15281941]

>>15281873
I don't think you would, or even could use it.

[Anonymous No.15281952]

>>15281815
The actual integral step is wrong. [eqn]\int \dfrac{1}{\sqrt{x} \pm 2} \neq \ln(|\sqrt{x} \pm 2|)[/eqn]

[Anonymous No.15282339]

if a obese person (e.g 5'9 & 180lbs) fell on top of a skinny person (e.g 5'3 100lbs) would they crush their bones or at least badly injure them.

[Anonymous No.15282379]

>>15281815
Don't use partial fractions. Use u-substitution to get rid of the sqrt(x), then do polynominal division. After that remember the derivative for the hyperbolic tangent.

[Anonymous No.15282403]

I'm trying to review for my test using the text book instead of youtube videos and I don't understand what the fuck its talking about. why would I subtarct L from a n. what question am I trying to answer and what is it trying to teach me

[Anonymous No.15282413]

>>15282403
you subtract L from a_n and take the absolute value because you want the difference to be arbitrarily small. essentially, if you pick literally any positive number at all, it's greater than the difference between your limit and any term sufficiently far in the series.
so you want the series to get closer to the limit than a difference of 1, 0.1, 0.001, 0.00001, 0.000000001, etc.

[Anonymous No.15282442]

>>15282413
I can't conceptualize this. what makes a term sufficiently far. and when would I use this in a problem

Is it just saying increase n until there's a very small difference between a_n and L

[Anonymous No.15282450]

>>15282413
>>15282442
Also what exactly does corresponding interger N mean

[Anonymous No.15282463]

>>15282442
>Is it just saying increase n until there's a very small difference between a_n and L
Yes.
>Also what exactly does corresponding interger N mean
We label the terms in our sequence a_1, a_2, a_3, a_4, etc.
The "corresponding integer N" just means that we can pick any positive number, which we call ε, and there is some a_N such that no term in the sequence beyond it differs from L by more than ε.
As an example, if we consider the sequence 3, 3.1, 3.14, 3.141, 3.1415, 3.14159, etc., then if we pick, say, ε=0.0001, then we consider a_3=3.1415, since |3.1415-π|<0.0001.
It should be pretty clear that every term after 3.1415 is also off from π by less than 0.0001. The definition of a limit there is basically applying this over and over again.

[Anonymous No.15282508]

>>15282442
Think of a practical example. Let's try to prove this
[math]
\lim_{n\to\infty} \frac{1}{n} = 0
[/math]

Intuitively, you know the limit is 0 because if you take a really large n, it's pretty close to 0. But to argue this formally, you need to show that you can get arbitrarily close to 0. You also need to show that the function stays arbitrarily close to 0 when you get there. A function which gets very close to 0, then oscillates up to 1, does not have a limit of 0. So what you really want to say is "I can find some number N such that, for all terms in the sequence after N, the difference between 0 and a term is arbitrarily small. That's where the subtraction from L comes from

[Anonymous No.15282711]

>>15281941
>>15281952
>>15282379
Got it, thank you all for your help :)

[Anonymous No.15282839]

>>15281577
let's see: [math]t^e + st\mu[/math]

[Anonymous No.15282847]

>>15282839
werks on my machine ;)

[Anonymous No.15282860]

>>15282839
Well I'm fuckin confused then. I've used mathjax plenty and just in one particular thread it refused to work. Everything was right, worked on every piece of software I have locally and example websites, and in the tex preview. Just sometimes, in some threads, it doesn't in that thread. Not my browser either.

[Anonymous No.15283008]

>>15282508
>A function which gets very close to 0, then oscillates up to 1, does not have a limit of 0.
what the fuck are you talking about

[Anonymous No.15283221]

When A and B are matrices, then this identity [eqn](AB)_{ij} = A_{i}B_{j}[/eqn] is true, right? i and j are indices ofc and the product is defined.

[Anonymous No.15283239]

>>15283221
No. Matrix multiplication doesn't work like that.
You can pick almost any matrix as a counterexample, e.g. multiplying two 2x2 matrices filled with 2s gives you a matrix that never has this property.

[Anonymous No.15283279]

>>15283239
Maybe I should clarify what I mean by i and j. It is i the index of the i-th row and j is the index of the j-th column. So it would satisfy your example: You're multiplying the (2 2) and (2 2)^T matrices for e.g. the 1st row and 1 column, which is 8, and that is also the entry at i = 1 and j = 1 of the 2x2 matrix product.

[Anonymous No.15283325]

>https://en.wikipedia.org/wiki/Dual_space
what do you actually need this autismfest for?

[Anonymous No.15283387]

>>15283325
This is what happens when you study theoretical nonsense before the motivating application behind it.

[Anonymous No.15283726]

What's the importance of proofs to a non-mathematician? Practically all proofs I've seen in uni are just a bunch of algebraic manipulations which are supposed to "prove" something.

[Anonymous No.15283750]

Consider [eqn]\alpha: W \ni w \mapsto \begin{cases} v_{b}& : w \in W \backslash \text{im}\, \Phi \\ 0& : w \in \text{im}\, \Phi \end{cases} \in \mathbb{F},[/eqn]with [math]W[/math] being a vector space, [math]\Phi[/math] being a linear transformation and [math]W \backslash \text{im}\, \Phi[/math] being the complimentary vector subspace of [math]\text{im}\, \Phi[/math] in [math]W[/math].

Is this well-defined or do I have to include vectors [math]w \in W[/math] into the direct sum of [math]\text{im}\, \Phi \oplus W \backslash \text{im}\, \Phi[/math] before applying [math]\alpha[/math]?

[Anonymous No.15283755]

>>15283726
>What's the importance of proofs to a non-mathematician?
They exists so that the mathematical tools that engineers or physicists use are reliable.

[Anonymous No.15283956]

How to prove that linear function is the only function in R that satisfies f(x + y) = f(x) + f(y) ?

[Anonymous No.15283957]

>>15283726
Is the ice maid smart?

[Anonymous No.15283974]

>>15283956
it's not if you accept the axiom of choice
but it is the only continuous one.
observe initially that f(0)=f(0+0)=f(0)+f(0)=2f(0), implying f(0)=0.
then begin playing around a bit and see what patterns you can find. a couple more observations to help:
0=f(0)=f(-x+x)=f(-x)+f(x) -> f(-x)=-f(x), so f is an odd function
f(2)=f(1+1)=f(1)+f(1)=2f(1), f(3)=f(2+1)=f(2)+f(1)=3f(1), etc.

[Anonymous No.15284066]

>>15283974
Could you plot this, if you chose a fixed set of values for all numbers in ]0, 1]. What would the plot look like?

[Anonymous No.15284071]

>>15283974
how many functions of this kind exist?

[Anonymous No.15284159]

>>15269944
Assuming a is nonzero then yes

[Anonymous No.15284171]

>>15283957
Why cirno is being called “ice maid” is the real question xd

[Anonymous No.15284214]

>>15283387
iirc it actually is used in engineering somehow

[Anonymous No.15284396]

[eqn]\lim_{x\ \to\ \infty} (2^x + 3^x)^{\frac{1}{x}} = 3[/eqn]How would you show this?

[Anonymous No.15284572]

>>15284396
[eqn]
\frac{d (2^x + 3^x)}{dx} = 2^x \ln 2 + 3^x \ln 3 \\

\lim_{x \to \infty} (2^x + 3^x)^{\frac{1}{x}}
= \lim_{x \to \infty} e^{ \frac{1}{x} \ln (2^x + 3^x) }
= \lim_{x \to \infty} e^{ \frac{ \ln (2^x + 3^x)}{x} }
= \lim_{x \to \infty} e^{ \frac{\frac{2^x \ln 2 + 3^x \ln 3}{2^x + 3^x}}{1} }
= \lim_{x \to \infty} e^{ \frac{2^x \ln 2 + 3^x \ln 3}{2^x + 3^x} }
= e^{ \ln 3} = 3
[/eqn]

[Anonymous No.15284573]

>>15284396
>>15284572
Forgot to add, use L'Hôpital's rule.