/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.11376745]

/wsr/ is the best edition.
Formerly >>11363090

>what is /sqt/ for
Questions relating to math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>pdfs?
libgen.is (Warn me if the link breaks.)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://mega.nz/#F!40U0zAja!cmRxsIoiLFZ_Mvu2QCWaZg
Shitty charts: https://mega.nz/#F!NoEHnIyT!rE8nWyhqGGO7cSOdad6fRQ (Post any that I've missed.)
Verbitsky: https://mega.nz/#F!80cWBKxC!ml8ll_vD2Gbw4I1hSLylCw
Graphing: https://www.desmos.com/
Calc problems: https://www.wolframalpha.com/

[Anonymous No.11376768]

The general quality of last thread's questions was abysmal.
There were also several boogaloos with anons asking questions, clarifying, trying to decipher other anons' explanations, and so on, which makes things harder to tally.

Unanswered questions from the previous thread:
Math questions:
>>11365784
>>11366878 [It isn't.]
>>11367356
>>11367818
>>11372775

Physics questions:
>>11365799
>>11365969
>>11366687
>>11368734
>>11373268

Chemistry questions:
>>11365203
>>11367329
>>11372075

Biology:
>>11363799 [IIRC it doesn't have enough anti-A to cause an issue.]

/g/ - questions
>>11369434
>>11371400

Stupid questions:
>>11363719
>>11369436
>>11370504 [Do an ARIMA or whatever.]
>>11372015
>>11374121
>>11376701

[Anonymous No.11376892]

I know this is supposed to be a stupid question thread but I wish I were at least half as smart as the anons explaining math and physics shit to each other.

[Anonymous No.11376922]

need some help deciding which professor

prof 1 4.7 on rate my professor
>4 tests no final, unlimited attempts on homework. review sheet each test. drops three lowest hw and lets you retake tests

prof 2 4.8 on rate my professor
>extra credit, practice tests, multiple attempts on quizzes, late work full credit if done soon after due date

[Anonymous No.11376998]

How does the top equation equal the partial derivative of theta? where
h(x) = theta_1 + theta_2(x)

pls explain. I am brainlet.

[Anonymous No.11377211]

how did they get to the equation

[Anonymous No.11377241]

>>11365799
No
>>11367329
>ingesting an acid to raise pH
I'm not sure if that makes sense. Nutrition is voodoo, tho.
>>11363719
No
>>11377211
Draw two FBDs and sum the forces to zero. Also, https://en.wikipedia.org/wiki/Capstan_equation

[Anonymous No.11377274]

>>11377241
What do I do with frictions

[Anonymous No.11377311]

>>11377274
Follow the load G up through the rope. The tension in the rope on the left side of the bollard is [math] T=G\exp(-\mu_2\beta) [/math] from the capstan equation. Now draw a FBD and set the net force to zero. You get [math]
\mu_1Q-\mu_1T\sin\alpha=T\cos\alpha [/math]. Combine these two equations and plug in values to get the weight in the solution.

[Anonymous No.11377314]

I want to calculate the Reynolds number for the flow of air at a pitot-static tube, but I can't use the general equation, Re = (dv)/v, because the tube is situated in a rectangular cross-section and not in a pipe. Is there any way to get the equation to work or is there another one that I can use?

[Anonymous No.11377345]

>>11377314
>>11377314
Is this is the sweetheart with the HVAC lab again? Just use the average airspeed and the hydraulic diameter of the duct. In general, the hydraulic diameter of a cross-section is [math] D_H=4A/P [/math] where [math] A [/math] is the area and [math] P [/math] is the perimeter. So for a rectangular duct with side lengths [math] a [/math] and [math] b [/math], you get [eqn] \text{Re}=\frac{D_Hv}{\nu}=\frac{(4ab)v}{2(a+b)\nu} [/eqn]

[Anonymous No.11377359]

>>11377345
Thanks, babe. Did you miss me?

[Anonymous No.11377362]

Please I need help, I'm getting desperate. I asked before but was ignored.

How do I get a 14 inch penis?

[Anonymous No.11377382]

>>11377359
yes, desu
>>11377362
kys

[Anonymous No.11377415]

>>11376785
Let [math](X, d_X)[/math] and [math](Y, d_Y)[/math] be two metric spaces.
We claim that [math](X \times Y, max(d_{X \times Y})[/math] is also a metric space, where [math]d_{X \times Y} ((a, b), (c, d)) = max (d_X(a, c); d_Y (b, d)[/math].
Indeed, we have that [math]d_{X \times Y} ((a, b), (e, f) = max( d_X (a, e); d_Y (b, f) ) \leq max (d_X (a, c) +d_X (c, e); d_Y (b, d) + d_Y (d, f) ) \leq max (d_X (a, c); d_Y (b, d)) + max (d_X (c, e) ; d_Y (d, f))[/math].
Proving the other parts of the definition of a metric is left as an exercise to the reader.
>>11377362
HONEY
CAN I LEND HIM MINE?
>>11376922
The one who looks smarter.

[Anonymous No.11377419]

>>11377382
Had to take a break from studying, so I've been out of the loop for 4 days, and I'm double checking all my work.
Is a Reynolds number of 248097 about right for a venturimeter, at the converging diameter?

[Anonymous No.11377420]

>>11377415
>local man forgets fifty parenthesis in a row
It was inevitable with this sort of problem, tho.

[Anonymous No.11377431]

>>11377419
Yup. For air in a duct I would expect Re to be huge.
>>11377415
>>11377420
ahaha how embarrassing~

[Anonymous No.11377444]

If we take the view of functions as sets of pairs, what's the name for the operation of forming the union of two functions?
I realize the result doesn't necessarily have to be a function btw.
Can I just say the union of f and g and people will understand?

[Anonymous No.11377469]

I'm trying to find an equation for the discharge coefficient. I want to calculate Cd at a venturimeter, pitot-static tube, and orifice plate. I have the diameters, mass flow rate, velocity, and differential pressure at each device for air.

[Anonymous No.11377516]

>>11377469
I used this one and it gave me a value higher than 1, 1.06 for the venturi. Any explanations?

[Anonymous No.11377518]

>>11377469
You'll find Cd from tables, not from those quantities you listed.
https://www.docdroid.net/4rD6JDS/copy-444-447.pdf
Ignore the shady link, it's fine I swear.

[Anonymous No.11377524]

>>11377469
Cd is found in tables. Here are some: https://www.docdroid.net/4rD6JDS/copy-444-447.pdf
The link is totally safe, I swear.
>pitot tube
No such thing as a Cd for a pitot tube.
>>11377516
The explanation is that you are using a mass flow rate that was determined from your velocity and differential pressure and all that, so you SHOULD be getting a Cd=1, exactly (you are seeing rounding errors, probably).

[Anonymous No.11377542]

>>11377524
>The explanation is that you are using a mass flow rate that was determined from your velocity and differential pressure and all that, so you SHOULD be getting a Cd=1, exactly (you are seeing rounding errors, probably).
Thanks for the tables.
Also, the proff gave us Cd values, for the venturi it's 0.97. So I'm quite close.

[Anonymous No.11377546]

>>11377518
>>11377524
There's no tables of Cd values in the pdf?

[Anonymous No.11377554]

>>11377542
When I said you "SHOULD" I meant that you would get a value of 1 from that (erroneous) application of the equation you used above. Obviously, discharge coeffs. are never equal to 1 in real life. Those tables are from Fluid Mechanics by White, btw. If you read, you will see that ASME actually has published some empirical formulas that spit out Cd as a function of diameter ratio and Reynolds number.
Based ASME.

[Anonymous No.11377555]

>>11376998
Define [math]J(\theta)[/math].
>>11376785
>got nowhere
Sorry to hear that anon, even though in that form literally every property you need for a norm follows directly from those of the absolute value in one line.

[Anonymous No.11377557]

>>11377546
I meant figures. Maybe there are more in that text, maybe some actual tables, but feel free to look.

[Anonymous No.11377564]

>>11377554
I used the same equation for the orifice plate and got 0.72, which is only a bit higher than the value I've been given.

[Anonymous No.11377578]

>>11377564
Good!

[Anonymous No.11377660]

I tried using the epsilon/delta method, but had no luck. Since it's a modified version of the dirichlet function: f(x)={ 1, if x is rational; 0, if x is irrational}, multiply this function by x and you get spivak's modified function. Now h(x)=x has a limit everywhere, and f has no limit. Just assume that x goes to nonzero a. Using rules of limits, sup lim f(x) does not exist (true), and suppose that lim h(x) does exist (true) and is equal to nonzero b (just for arguments sake). Now for the sake of contradiction, assume that lim f(x)h(x) exists and is equal to c. By the usual rules of limits, lim (1/h(x))= 1/b (for nonzero b), and so lim f(x)h(x)(1/h(x))=c/b, that is, lim f(x)=c/b, but this is clearly a contradiction, since f(x) has no limit. This is just a rough proof, but have I got the general idea right? Is there a way to do this with epsilon/delta?

[Anonymous No.11377712]

>>11377660
Your idea for the continuity of both [math]f,g[/math] being necessary for the continuity of [math]fg[/math] is correct. You essentially picked a random [math]a[/math] and applied the limit [math]x\rightarrow a[/math] (which you can pass into the function by continuity) to show that the multiple of the limit can exist only if both factors exist. The same can be done for the sum [math]f+g[/math].
Now just note that the indicator [math]\chi_W:X\rightarrow \mathbb{R}[/math] on any closed [math]W\subset X[/math] cannot be continuous. The reason is that the Hausdorffness of [math]\mathbb{R}[/math] guarantees the existence of an open [math]U\subset \mathbb{R}[/math] with [math]1\in U, 0\not\in U[/math], which has closed preimage [math]\chi_W^{-1}U = W[/math], contradicting the definition of continuity. With [math]\mathbb{Q}[/math] and [math]X=\mathbb{R}[/math] proves the discontinuity of [math]\chi_\mathbb{Q}[/math]

[Anonymous No.11377736]

>>11377712
Ok cool. However, I'm not at all familiar with what you mean by your note. I'm just gonna assume I'll run into that in analysis?

[Anonymous No.11377773]

>>11377712
I would like to interject for a second.
[math]\chi_{\mathbb{Q}}^{-1} ( \{0 \} )[/math] isn't closed, but [math]\{ 0 \}[/math] is closed, and thus the characteristic function isn't continuous (because pre-image of closed needs to be closed).

I'm sorry, but your proof was really weird.
>>11377444
Gluing, if the union is still a function (beyond the trivial case, you can also have f and g defined on subsets of a common X).
>>11377660
Your proof is really hard to read.
At least tell me what it is you want to prove at the start.

[Anonymous No.11377806]

>>11377773
Continuity is equivalent to both open preimages of open sets and closed preimages of closed sets; we can move between them with complements. The first definition in terms of open sets is, in fact, the standard one as it translates directly to [math]\epsilon-\delta[/math] balls. In fact (again) you need to prove the closure of [math]\mathbb{Q}[/math] with its density in [math]\mathbb{R}[/math] in order to surmise the openness of [math]\mathbb{R}\setminus\mathbb{Q}[/math], so I'd say your proof is really the weird one, if there really is such a thing as a "weird" proof in the first place. Good effort though.
Note that indicators are never continuous as long as the target is Frechet, since then you can find opens not containing certain points (in particular 0 and 1). We obviously do not need something as strong as this, however.

[Anonymous No.11377815]

>>11377773
Sorry, I assumed it was obvious from the image, I just want to show that the function shown in the image does not approach any number at a if a is nonzero. Precisely, [math]\lim_{x \rightarrow a} f(x) [/math] does not exist for [math] a \neq 0 [/math].

[Anonymous No.11377823]

what did i get wrong here

[Anonymous No.11377842]

>>11377823
If f is surjective, and not injective, why would k be unique such that f(k)=l?

[Anonymous No.11377844]

>>11377444
It's not gluing by the way, it's literally just the union of the graphs [math]\Gamma(f) \cup \Gamma(g)[/math]. To perform gluing you need the functions to agree on overlaps of their contractible domains [math]X,Y[/math]. The existence of a bona fide function [math]p[/math] such that [math]\Gamma(f)\cup\Gamma(g)=\Gamma(p)[/math] is obstructed by the first Cech cohomology of [math]X\cup Y[/math] (which can be non-contractible; see Meyer-Vietoris).
If one domain contains the other, then it's called an extension. Existence of extensions can be surmised from either Tietze or Hahn-Banach.
>>11377823
We do not have uniqueness, hence we do not have an inverse (only a right inverse). Surjections [math]\pi[/math] fit into the exact sequence [math]K\xrightarrow{\pi} L\rightarrow 0[/math], which admits a section [math]s:L\rightarrow K[/math] with [math]\pi s = \operatorname{id}_L[/math]. However without uniqueness it does not split, i.e. a morphism [math]\sigma[/math] with [math]\sigma\pi = \operatorname{id}_K[/math]. For [math]\pi[/math] to be invertible you need both left- and right-inverses and they have to be equal.
Please reread and understand the definitions first.

[Anonymous No.11377856]

>>11377815
The limit c either equals a, 0, or some other value.
I usually don't recommend exhaustion, but any of those takes one line.
>>11377806
>The first definition in terms of open sets is, in fact, the standard one as it translates directly to ϵ−δ balls.
The proof for the epsilon-delta definition is just "follows trivially from intermediate value."
>Note that indicators are never continuous as long as the target is Frechet, since then you can find opens not containing certain points (in particular 0 and 1).
I don't follow.
IIRC a characteristic function is continuous if and only if it's constant on the connected components.

[Anonymous No.11377862]

>>11377844
>To perform gluing you need the functions to agree on overlaps of their contractible domains X,Y.
If they don't agree on the intersection the union isn't a function.

[Anonymous No.11377865]

>>11377842
>>11377844
oh so it's 5 and 6 then

[Anonymous No.11377870]

>>11377865
It's three and six.

[Anonymous No.11377874]

>>11377856
>it's constant on the connected components
And? You do know that any connected open/closed has connected preimage, right?
>>11377862
>If they don't agree on the intersection the union isn't a function
No shit? The point is that even if that's the case it can [math]still[/math] not be a function. See monopole harmonics.

[Anonymous No.11377883]

>>11377870
what is the image then

[Anonymous No.11377887]

>>11377874
>And? You do know that any connected open/closed has connected preimage, right?
Yup, my bad, misread the earlier post.
>The point is that even if that's the case it can still not be a function.
A *continuous* function.
>>11377883
It's 5 and 3, I've forgotten counting.

[Anonymous No.11377891]

>>11377887
>It's 5 and 3, I've forgotten counting.

i realise i am the one that got it wrong but i disagree.

imo it's 3,5,6

[Anonymous No.11377915]

>>11377887
>A *continuous* function.
Well obviously there's no obstructions other than set-theoretic ones if you're just asking for maps in [math]{\bf Set}[/math]. It's also not interesting; the forgetful functor into [math]{\bf Set}[/math] is almost always faithful.

[Anonymous No.11377918]

>>11377891
6 is the literal definition of injective...

[Anonymous No.11377932]

>>11377915
Yeah, but anon was asking specifically for [math]Set[/math].
Also, where did you hear about characteristic functions with images different from [math]\{ 0, 1 \}[/math]?

[Anonymous No.11377962]

>>11377946
how good are the Feynman lecture books, really?

[Anonymous No.11378068]

>>11377962
why don't you read them and find out? They're free online

[Anonymous No.11378103]

>>11378068
well, the question is about how the gained knowledge compares to what a physics undergrad learns, which I won't know from reading the book.

[Anonymous No.11378288]

Consider [math]\{ 0, 1\}[/math]. If you place the trivial topology, all bijections are continuous, trivially. If you place the discrete topology, you get the same.
But with the Sierpinski topology, you have that the identity is continuous, but the "twist" bijection isn't.

So I was wondering what topology on a finite set has the most discontinuous bijections.
The solution is as follows:
For [math]\mathbb{Z} _n[/math], the open sets are [math]\mathcal{O}_j = \{ i \in \mathbb{Z}_n | i \leq j \}[/math] as [math]j[/math] runs through [math]\mathbb{Z} _n[/math].
And then the only continuous bijection is the identity (because it needs to send 0 to itself, and if it sends 0 to itself it also needs to send one to itself, and so on), so it maximizes a fortiori.
I was wondering if it still maximized the non-continuous maps if we lifted the restriction on bijections. Any ideas?

[Anonymous No.11378381]

can someone recommend a good resource to learn deep learning without going through machine learning first?
I'm looking for something well-written and concise, not too advanced with tons of mathematical equations but not too basic either (I have a good understanding of matrices from computer graphics)

[Anonymous No.11378618]

>>11378288
I'm going to assume there's a group structure on [math]\mathbb{Z}_n[/math]. Let [math]G=\mathbb{N}_n[/math] act on itself (as a [math]G[/math]-module [math]M=\mathbb{Z}_n[/math]) by translation [math]g\cdot n = g+m \mod n[/math]. Since [math]\operatorname{Hom}(G,M) \cong H^1(G,M)[/math] as objects in [math]{\bf AbGrp}[/math], this is independent of whatever topology you put on [math]G[/math] or [math]M[/math].
Now if we pick a topology, then we can find a correspondence [math]H^1(G,M) \cong H^2_G(\ast,M)[/math] between group cohomology and the [math]G[/math]-equivariant cohomology over a point [math]\ast[/math]; we must have a topology on [math]G[/math] in order to have the notion of "continuous action" on the fibre [math]V_\ast = V[/math], which in turn defines a similar notion on the [math]G[/math]-action on the module [math]M[/math]. If we pick the discrete topology for [math]G[/math], then [math]H^2_G(\ast,M) \cong H^1(BG,M)\cong H^1(S^1,\mathbb{Z}) \mod n = \mathbb{Z}_n[/math] by pulling back into the classifying space [math]BG= S^1[/math], the latter group of which is the [math]n[/math]-th roots of unity.
Now if we pick anything else, such as what you have in mind where open sets are [math]\mathbb{Z}_k\hookrightarrow\mathbb{Z}_n[/math] for [math]k\leq n[/math], then the continuous [math]G[/math]-actions on [math]V[/math] is changed: only certain rotations on [math]BG=S^1[/math] are continuous. This will in turn change the [math]G[/math]-equivariant cohomology [math]H^2_G(\ast,M)[/math]. If it is changed in such a way that [math]H^2_G(\ast,M) \not\cong H^1(BG,M)[/math], then you get discontinuous maps. Since the discrete topology is the finest topology we should expect [math]H^1(G,M) \cong H^2_G(\ast,M) \subset_\text{up to isomorphism} H^1(BG,M)[/math] so the discontinuous actions of [math]G[/math] on [math]M[/math] can be classified by [math]H^1(BG,M)/ H^2_G(\ast,M)[/math].

[Anonymous No.11378627]

>>11378618
Here's an exercise: find all typos I've made in this post.

[Anonymous No.11379289]

Is it possible to calculate the flow loss due to a sudden contraction, like in an orifice or venturi, using some basic equations?

[Anonymous No.11379396]

>>11376745
Dumb question, but can you use rat poison (warfarin) to quickly treat a stroke or heart attack at home?

[Anonymous No.11379423]

I'm going through Lang Math right now to bone up on my fundamentals after a break from learning. Is there a better way of solving pic related other than by induction or taking the right equation and multiplying by (x+1)/(x+1)?

[Anonymous No.11379437]

>>11379423
just multiply the RHS by [math]x+1[/math] and observe that all the terms [math]x^{n-1}, ..., x[/math] cancel

[Anonymous No.11379531]

is it possible that future humans may discover that there is nothing random?

[Anonymous No.11379535]

>>11379437
Literally said except that

[Anonymous No.11379536]

>>11379531
yeah, absolute determinism has not been ruled out

[Anonymous No.11379539]

>>11379531
No
https://www.youtube.com/watch?v=9rIy0xY99a0

[Anonymous No.11379549]

>>11379536
how about xn+1=rxn(1-xn)

[Anonymous No.11379551]

>>11379423
If you want the direct proof, do long division

[Anonymous No.11379563]

>>11379531
lol no because randomness is too hard to grasp

[Anonymous No.11379600]

anyone know any good results in divergent series?

i'd like to see an intuitive proof for something like 1 + 2 + 4 + 8 + 16 + ... = -1 in some system (obviously not the real line) if anyone knows any math like that...

[Anonymous No.11379605]

>>11379423
just use the formula for a geometric series.

[Anonymous No.11379609]

did particles evolve?

[Anonymous No.11379643]

>>11379609
no

[Anonymous No.11379648]

does this have a name?

[Anonymous No.11379671]

>>11376745
Why do serious physicists appear to entertain the idea that the universe could be infinite? Is it just because since we haven't discovered any boundaries, we can't ASSUME that it is finite? I think that's pretty cowardly.

[TBK No.11379673]

What kind of rapid exothermic reactions could l make out of 2-percent malk? Composting purposes? Something nitride-based?

[Anonymous No.11379708]

>>11379648
differentiation under the integral sign

[Anonymous No.11379716]

>>11379708
thanks

[Anonymous No.11379739]

>>11379648
chain rule

[Anonymous No.11379784]

>>11379289
>Is it possible to calculate the flow loss due to a sudden contraction
Yes.
>using some basic equations?
Not really. You better do some experiments. This kinda thing is always found empirically irl.

Let's assume a sudden contraction in a circular pipe from diameter [math] D_1 [/math] to [math]
D_2 [/math]. Assuming an incompressible fluid we have it that [math] v\pi D^2/4=Q=Q_1=Q_2 [/math]. From energy balance, you can show that [eqn] \frac{P}{\rho}+\frac{v^2}{2}=\text{const.}\implies \rho Q=\dot{m}=\sqrt{\frac{\rho\pi\Delta PD_1^4D_2^4}{8(D_1^4-D_2^4)}} [/eqn] Then, you directly measure the mass flow rate with a scale by measuring the time it takes to fill a container on a scale with so many kilograms of water (I coudln't find a pic of the exact apparatus I'm talking about), then [math] \dot{m}'=m/t [/math]. Now you have it that [eqn] C_d=\frac{\dot{m}'}{\dot{m}}=\frac{m}{t}\sqrt{\frac{8(D_1^4-D_2^4)}{\rho\pi\Delta PD_1^4D_2^4}} [/eqn] Once you have the experimentally determined the discharge coefficient, you could say that the flow lossed is [math] Q(1-C_d) [/math]. The percent loss would be [math] (1-C_d)\times100\% [/math].

[Anonymous No.11379798]

>>11379784
>>11379289
Oh, and you'd find that pressure drop using a monometer setup or something.

[Anonymous No.11379878]

If [math]U\subseteq (X,\tau)[/math] where [math]X[/math] has base [math]\mathcal{B}[/math], how do I show that if [math]U[/math] is a union of finite intersections of [math]\mathcal{B}[/math], then [math]U[/math] is a union of elements of [math]\mathcal{B}[/math]? I thought it was obvious - the finite intersections are in [math]\mathcal{B}[/math] for all [math]i,j\in I,J[/math] and we're taking a union of them, hence a union of elements of [math]\mathcal{B}[/math]. Am I just retarded?

[Anonymous No.11379898]

>>11379878
do we know that finite intersections of gothic_B are in gothic_B ? looking at the definition now it says: for any element x in a finite intersection of A and B there exists another set C containing x which is a subset of A intersect B.

this doesn't immediately give finite intersections are in fancy B no?

[Anonymous No.11379901]

>>11379898
fucking retard

[Anonymous No.11379953]

>>11379784
How are you so smart, anon?
Wish I was like you.

[Anonymous No.11379956]

>>11379878
Seems correct to me.
>>11379898
Base is a finicky concept. If anon says it's closed under finite intersections, then it's closed under finite intersections.
I'm used to the "any open set is an union of elements of the base" definition. In that case, you'd just write down "[math]U[/math] is trivially an open set, and thus an union of elements of the base."

[Anonymous No.11379965]

>>11379784
>Q(1−Cd).
Is Q the volumetric flow rate?

[Anonymous No.11380010]

>>11379953
That's very sweet, but I'm nothing compared to the other smarty pants anons that answer stupid questions ITT. Don't do drugs.
>>11379965
Yes, specifically the value of Q that comes from naively applying Bernoulli's principle.

[Anonymous No.11380082]

I believe in Q

[Anonymous No.11380183]

Ok, i'm not very brainlet and i'm trying to learn basic calculus quickly, but i can't solve this thing using what I've learned. Maybe i'm missing something obvious, sorry for that.

[Anonymous No.11380239]

>>11380183
DUDE

[Anonymous No.11380283]

>>11380183
Ok my brain is rotten, i already solved it and it was so obvious that I tried to smash my face into the desk.

[Anonymous No.11380289]

Okay, guys, I'm a retard and you're geniuses, so I most humbly request your help and advices regarding a recent fluid dynamics lab. We used a device that contains 4 different flow measurement devices (see the image). We calculated the differential pressure, mass flow rate, and velocity at each device, based on H20 manometers. We got different data for each, which is expected. But now I’m really unsure as to what to talk about in my report. The way I’ve understood it, the experiment is basically a demonstration of differences between empirical results and theoretical results. For example, the mass flow rate for each device is slightly different, but the mass flow rate is a concept based on the law of conservation of mass. So theoretically, the mass flow rate at each device should be the same, but it isn’t. So I assume that means there has been some form of flow loss, either vicious or geometric or both. I’m not entirely sure of what I should talk about and would appreciate some advices and direction. P-p-please.

[Anonymous No.11380300]

>>11380289
I forgot to mention that we also did the experiment twice, with the damper at different positions (fully open and almost closed).

[Anonymous No.11380302]

>>11380283
Right?

[Anonymous No.11380347]

>>11378103
bůmp

[Anonymous No.11380373]

>>11380289
>>11380300
Is there not a specific prompt in your lab manual? Just report the results and discuss how they are different. At this rate, I demand to be credited as a co-author on your write-up. Or name me in your references section.

[Anonymous No.11380377]

okay /sci/entist, this retard here needs help with intermediate algebra and its pissing me off, I am about to throw a tantrum like a kid, kicking and screaming.

So I failed my first intermediate algebra last semester and now im retaking it, and to be honest whats the fucking point, my fucking retarded brain can't understand this shit.
ANWAYS lets get started with the kek'ing.

I am doing equations of lines, and this question pissed me off, and im annoyed.

passes through the points (-1,1) and (-5,-4)

So what I did was -4-1 and -5+1 which gave me -5/4.

so I put it in slope intercept form, and plugged in -1,1 to find the y intercept.

1=-5/4(-1) + b
1 = 5/4 + b

then I moved 5/4 to the other side
1 - 5/4 = b

and so we have the answers in the back of the unit, and the answer is y = 5/4x + 9/4

I am lost on how they got 9/4.

[Anonymous No.11380378]

How can I show that MN = AD?
How can I develop an understanding for solving these types of problems? I don't even have an idea where to begin and I stare at it for 30 minutes before giving up.

[Anonymous No.11380385]

refreshing my email every 5 minutes waiting for these fucking grad school results

[Anonymous No.11380387]

>>11380377
the slope is the ratio of change of y to x, for example slope 2 means that for every point of increase in x, y increases by 2 points
that means slope = y/x, not x/y
your slope should be (-4-1)/(-5+1) = 5/4
instead you got -5/4

[Anonymous No.11380392]

>>11380289
>>11380300
At this rate I request to be formally listed as a co-author, or at least in the references. The reason you are calculating different mass flow rates is because the density of air changes slightly throughout the duct as it encounters obstacles. Air is very much a compressible substance. I promise you, however, that real, true mass flow rate IS constant throughout the duct. The volume flowrate, however, definitely isn't constant (contrast this with how water typically behaves in a pipe).
>losses
Yep. There's energy losses due to viscous friction with the air against the duct (called major losses) and also losses due to interactions with changes in geometry (called minor losses). Once again, you find major and minor losses in tables.

[Anonymous No.11380393]

>>11380387

>your slope should be (-4-1)/(-5+1) = 5/4
Thats exactly what I did,

>So what I did was -4-1 and -5+1 which gave me -5/4.

Now suddenly you're making your 5/4 positive, how though? -4 - 1 is NEGATIVE -5
and -5 + 1 is still NEGATIVE -4

you don't indicate how you made your slope a positive, and if you're implying dividing, then what are you dividing?

[Anonymous No.11380397]

>>11380393
>-4 - 1 is NEGATIVE -5
>and -5 + 1 is still NEGATIVE -4
exactly, negative over negative is positive

[Anonymous No.11380398]

>>11380392
We didn't calculate the volume flow rate. And I will happily list you as a co-author, anon. If I could.

[Anonymous No.11380404]

>>11379956
>Seems correct to me
I guess I didn't show enough workings when I passed it in.

[Anonymous No.11380405]

>>11380398
>We didn't calculate volume flow rate
I thought you did with the pitot tubes? Anyway, my point stands. Do you have any questions in specific?
>If I could.
You can and you will. I require it. Find a way to explain to the boys in your group why you are listing Me as an author, I don't care.

[Anonymous No.11380431]

>>11380397
>exactly, negative over negative is positive

Just like that, without any help? I wanna call bullshit, ill apply this logic down the road, and the answer will be wrong.

Then how do you solve for b? It says its 9/4

[Anonymous No.11380435]

What is quantum chromodynamics actually used for? What task requires you to understand the intricacies of the strong nuclear force?

[Anonymous No.11380437]

>>11380431
you didn't know negative over negative was positive?
i'm pretty sure they explain that in primary school
>Then how do you solve for b? It says its 9/4
going back to your original comment but fixing the -5/4 slope for 5/4
1=5/4(-1) + b
1=-5/4 + b
1 + 5/4 = b
4/4 + 5/4 = b
9/4 = b

[Anonymous No.11380442]

>>11376745
Can someone scan this book and upload it to library genesis?

[Anonymous No.11380444]

>>11380431
There's no hope for you. Why do you even bother?

[Anonymous No.11380449]

>>11380183
I just happens sometimes

[Anonymous No.11380453]

>>11380283
It just happens sometimes

[Anonymous No.11380454]

>>11380431
negative * negative = positive
negative * positive = negative
positive * negative = negative
positive * positive = positive

we were all 10 years old at one point bro, don't take it personally.

[Anonymous No.11380467]

>>11380405
>I thought you did with the pitot tubes? Anyway, my point stands. Do you have any questions in specific?
No we only got the velocity and mass flow.
I need your name anon to reference you.
And I will have more questions to ask, but I have to go sleep now.

[Anonymous No.11380471]

>>11380467
>No we only got the velocity and mass flow
And an intermediate step was determining Q, no? I'll tell you my name, but not here. Sleep tight~

[Anonymous No.11380488]

>>11380437
>4/4
What did you do to get that? Cross multiplying doesn't seem right.

>>11380444
to be fair anon you made a point. I dropped the class.

Thanks for giving me clairvoyance that I have no hope.


>>11380454
Anon, my multiplication towards postive and negatives are just fine. AFAIK there wasn't any dividing on 5/4 to turn it into a positive, and if so, what were they dividing? -1?

[Anonymous No.11380490]

how do i restore .localstorage to sessionstorage on safari mac 10.8.5?

[Anonymous No.11380491]

>>11380488
>What did you do to get that? Cross multiplying doesn't seem right.
i turned the 1 into a 4/4
what do you get when you divide 4 by 4?

[Anonymous No.11380498]

>>11380491
anon 4/4 is 1, but what rule in math do you use to get 4/4 though? Is it because you want common denominators? How do you determine the numerator? Just say fuck it and have the num/denom be the same then add the num straight across?

[Anonymous No.11380504]

>>11380498
>but what ule in math do you use to get 4/4 though
Elementary school arithmetic
>Is it because you want common denominators?
Yes

[Anonymous No.11380508]

>>11380435
strong: you can transmutate small amounts of atoms in a neutrino factory. let me look at my chromo, i discarded it as usless

[Anonymous No.11380513]

>>11380508
anon, instead of chromodynamics pls get books such as p p- colliders & buid your own correctheory

[Anonymous No.11380518]

>>11380404
I'll double check to make sure, since the whole base/subbase/network thing always confuses me:
Does your definition of base directly imply it's closed under intersections?
And did the test actually tell you to the base generates some topology?
>>11380490
>>>/g/sqt

[Anonymous No.11380521]

>>11380488
division IS multiplication bro. just think about it.

[Anonymous No.11380531]

>>11376745
what books are accessible and good for learning about fungal intelligence? apparently mushrooms are big brained and fungus is fairly "smart" what should I read to find out more?

[Anonymous No.11380534]

>>11380518
Question premises with ' let [math]\mathcal{B}[/math] be the base of a topology on a set [math]X[/math]'. The definition we use for base is a collection [math]\mathcal{B}\subseteq \mathcal{P}(X)[/math] such that [math]\mathcal{B}[/math] is a subbase, i.e. a cover for [math]X[/math] and [math]\forall B_{1},B_{2}\in\mathcal{B}[/math] and each [math]p\in B_{1}\cap B_{2}[/math], there exists [math]B_{3}\in\mathcal{B}[/math] such that [math]p\in B_{3}\in B_{1}\cap B_{2}[/math]

[Anonymous No.11380547]

>>11380534
Then the proof you posted doesn't work.
Fix a function [math]f(U_1, U_2, p)[/math] on the base, where [math]p \in U_1 \cap U_2[/math] whose image is some [math]U_3[/math] in the base such that [math]U_3 \subset U_1 \cap U_2[/math] and [math]x \in U_3[/math] (note: we just used choice, but that's because it's faster).
You need to run the whole boogaloo of ordering [math]U_n[/math], setting [math]B_1 (p) = U_1[/math], [math]B_n (p) = f(B_{n+1}, U_n, p)[/math], and taking the union of the last (last in the iteration) [math]B_n (p)[/math] accross all p.

[Anonymous No.11380555]

>>11380547
>[math]x \in U_3[/math]
[math]p \in U_3[/math]
>ordering [math]U_n[/math]
Where [math]U_n[/math] are the elements in the base you want the intersection of.

Also, small mistake, you really just need choice.

[Anonymous No.11380561]

>>11380547
And that's [math]f(B_{n-1}, U_n, p)[/math]
Hopefully the typos are over.

[Anonymous No.11380580]

>>11380547
not only do I hardly follow, but I would have never thought to do this.

[Anonymous No.11380590]

>>11380580
It's an extremely simple argument, but the set theory and informality is making it harder to understand.
And general topology is one of those subjects that soaks into your bones in the long term, you shouldn't worry that much.

[Anonymous No.11380596]

>>11380590
i hope you're right. thanks for the help

[Anonymous No.11380653]

>>11380377

Think about it as 2 proportional segments

So you have the x segment and the y segment.

So a = (-4-1) /(-5-(-1)) = 5/4

Now, think about it. You have the proportion but you need to know where it began in y (if it haven't at 0)

So 5/4 * (-1) + b = 1
Then b = 1 + 5/4 = 9/4

[Anonymous No.11380677]

>>11380431
Why (-)/(-)=(-)(-)?

Because 1/(-1) = (-1)*1/(-1)*(-1) = -1/1 = -1

Why (-)(-)=(+)?

Because:

1 + (-1) = 0
(-1)*( 1 + (-1)) = (-1)*0
(-1)*1 + (-1)*(-1) = 0
-1 + (-1)*(-1) = 0
1 + (-1) + (-1)*(-1) = 1
0 + (-1)*(-1) = 1

(-1)*(-1) = 1

Why i can multiply by (-1) both sides?

Because:

a=a

Obviously -a=-a


but if a=b, replacing:

-a=-b

Exercise: Show that for a in a field:
(-1)a=-a where -a is the additive inverse of a.

This proof is valid for rational, real and complex numbers. For finite fields too, you can check which field axioms i used (exercise for the reader).

Is valid for integers too because the only number in this numeric structure with multiplicative inverse is 1.

What you need to accept is those axioms and the properties of equality (valid not only for numbers in a field but also for any mathematical object like sets, vectors, functions, etc).

You mention "logic", maybe you would like to read a book on mathematical logic. Seek recomendations.

[Anonymous No.11380696]

- legit stupid question trigger warning -
Physics exam coming up later today and I haven't studied as well as I should have by far; I'm pretty sure I'll have to repeat it in a month. Still, for the sake of the attempt, what should I absolutely write down in my formula sheet (we can have a sheet of paper with anything handwritten on it) to give me a (negligible) chance to wing it? Subjects are electrostatics-/dynamics, (electro-)magnetism, optics, pretty much. As for the Physics, if you would help me, I'm mostly just asking for the most obvious shit just in case I'd miss it somehow.
However, my mathematical fundamentals (area/volume integrals, dealing with spherical coordinates, some substitution stuff, etc.) are still very lacking as well. Since I won't have time to make a super comprehensive formula sheet anyway, what should I write in baby steps when it comes to mathematical operations (as in shit I'll have to be able to use)?

My sincerest thanks for any help (even if it probably won't amount to anything).

[Anonymous No.11380700]

>>11380521
division is reverse multiplication.
I was just confused on the part where it wasn't being worked on as in I wasnt actively dividing the -5 and -4 to make positive.

But there has to be cases where fraction stays negative. I figured it was one of those cases.

[Anonymous No.11380742]

>>11380378

P the point where BD touches the circle of center S

And call it T the center of the other circle.

By simmetry PT = SN

So both AD and MN are made of a diameter plus something

Since MDN is similar to PNY (where Y is the projection of P over the diameter of the circle of center S, we must have this something as proportional to this length

Therefore, they just be equal

[Anonymous No.11381329]

>>11378627
Guess no one was up to the task. I'll provide the solution
1. [math]\mathbb{N}_n \rightarrow\mathbb{Z}_n[/math]
2. [math]g\cdot n\rightarrowg\cdot m[/math]
Aaaand that's it.
>>11379878
First every element in [math]\mathcal{B}[/math] is open, hence [math]U[/math] is open if it's a finite intersection. Next, by definition of a basis for each point[math]x\in U[/math] there exists [math]B_x\in\mathcal{B}[/math] such that [math]x\in B_x \subset U[/math]. This means that we can take [math]U = \bigcup_{x\in U}B_x[/math].
>>11380435
>What task requires you to understand the intricacies of the strong nuclear force?
Understanding the intricacies of the strong nuclear force.
Some condensed matter systems also sometimes exhibit QCD-like [math]SU(3)[/math] symmetry in the low energy regime.

[Anonymous No.11381809]

For a non-ideal gas we have the correction for the ideal gas law given by the virial expansion [math] PV=nRT \left(1+\frac{B(T)}{V/n}+\frac{C(T)}{V/n}\right)[/math]. Than a good approximation is [math]PV=nRT\left(1+\frac{B(T)}{V/n}\right)[/math]. However if i solve for [math]V/n[/math] I find [math]V/n=\frac{RT\pm \sqrt{(RT)^2+4PRTB(T)}}{2P} [/math]. I would find this answer satisfying if the expression [math]RT - \sqrt{(RT)^2+4PRTB(T)} < 0[\math] so we may neglect the [math]\pm[/math] however this is not always the case since [math]B(T)[/math] is allowed to be negative. I don't understand how i'm able to get two different densities out of the same state wherefore the virial expansion holds.

[Anonymous No.11381817]

Can nanomachines cure my dedifferentiated chondrasarcoma? It has specific genetic markers and I want to become a senator

[Anonymous No.11381844]

>>11380471
>And an intermediate step was determining Q, no?
Nope. We put the data in a spreadsheet and got the values. I have done calculations to confirm our readings (such as for velocity and mass flow rate), but I haven't needed to calculate the volume flow.

[Anonymous No.11381850]

>>11381817
No because nanomachines are sci fi shit, faggot.

[Anonymous No.11381852]

>>11380405
>Do you have any questions in specific?
Well the general thing I'm after is something to talk about in the discussion.
Right now I will talk about the differences of measured mass flow rate (why they are different) and I've also worked out the dynamic viscosity, kinematic viscosity, and Reynolds numbers at each device, but I'm unsure as to how make that relavant in my discussion. I've also calculated the Cd value at each, though we were provided those and the values I got through calculation are slightly higher, like 1-3% higher, than the ones given by our prof.

[Anonymous No.11382118]

>Freshman relativity
pardon the brainletness but i have a small confusion

How does the writer decide to use the same a and b constants and negative b for x' frame?
Is this some kind of shear transform?
source pages, this is on the last page;
https://docdro.id/oK6KGkq

[Anonymous No.11382124]

the equations refer to this graph

[Anonymous No.11382126]

>>11382118
>>11382124
related posts

[Anonymous No.11382301]

A password consists of 8-12 characters and must begin with a letter, contain a capital as well as a number. How many total unique combinations are possible?
T = 52 * (11! - 8!)
T = 52 * (95^12 - 95^8)
T = 52 * (95^12)∩52 * (95^8)

[Anonymous No.11382314]

>>11381844
>We put the data in a spreadsheet and got the values
If the spreadsheet is multiplying velocity with area with density, you are calculating volume flux in the process.
>>11381852
So just report your observations and comment on your errors. It's not like anything unexpected happened during the experiment.

[Anonymous No.11382376]

Retard here.
If we have two values, such as two forces, where F1 = 150N and F2 = 130N,
where F1 15% greater than F2 (150/130 x 100), why can't that be called the percentage difference between the two values?

[Anonymous No.11382381]

>>11382376
150 is not 15% greater than 130. The %diff between 150 and 130 would be (150-130)/((150+130)/2)=14.3%

[Anonymous No.11382396]

>>11382381
So what's the value I calculated?

[Anonymous No.11382403]

>>11382396
I don't fucking know. Very little of what you wrote makes any sense.

[Anonymous No.11382407]

>>11382403
>(150/130 x 100)

[Anonymous No.11382473]

>>11382407
>115.4
???

[Anonymous No.11382475]

WEE WOO WEE WOO WEE WOO WEE WOO
NONCE ALARM NONCE ALARM NONCE ALARM
WEE WOO WEE WOO WEE WOO WEE WOO

[Anonymous No.11382476]

>>11382473
Yes I know that, what is it expressing?

[Anonymous No.11382477]

>>11382476
It isn't expressing any useful quantity that anybody cares about.

[Anonymous No.11382482]

>>11379708
>>11379716
not differentiation under the integral sign, although that is a very useful technique to know.
this anon is correct: >>11379739
Note that integration under the integral sign can be viewed as introducing a parameter into the integrand and looking at responses of the integrand and hence the integral w/r/t changing that parameter. This requires moving the derivative into the integral. You can't do that here (limits depend on x, nothing in the integrand actually varies with x)

[Anonymous No.11382485]

>>11380696
write the textbook

[Anonymous No.11382493]

>>11382118
>>11382124
Read, nigger, read:
>The symmetry implied by the relativity principle...

If one frame is moving relative to another, that other frame is moving in the opposite direction relative to the first frame.

[Anonymous No.11382496]

>>11382477
But why does it give an answer close the actual % difference?

[Anonymous No.11382503]

>>11382496
Because there are multiple ways to define %difference. Say you have values X and Y. One way is |X-Y|/X, which is shit. Another way is |X-Y|/Y, which is also shit. You are doing X/Y=|X-Y|/Y+1. The proper expression is |X-Y|/.5(X+Y).

[Anonymous No.11382509]

>>11382376
>>11382381
>>11382396
>>11382403
>>11382407
>>11382473
>>11382476
>>11382477
lol you guys are both brainlets.
The first post describes the percentage of 130 that 150 is, and the replies describe the stats percentage difference (ie difference/mean). So 150 is 115% of 130, or maybe you could say that 150 is 15% greater than 130. This would be used when F2 is the more "fundamental" of the two or is the baseline, and F1 were deviating from that baseline.
Meanwhile the percentage difference might be used in stats for example to compare two different means or things that don't have this sort of "baseline-deviation" relationship.

[Anonymous No.11382536]

>>11382503
>>11382509
The reason I am asking is because I want to make a chart with % differences between several velocities

[Anonymous No.11382541]

>>11382536
Alright. You now have the formula for %diff.

[Anonymous No.11382543]

>>11382536
Are these different velocities independent? Or are they coming from applying some intervention to a baseline (ie, lubing up some joints, applying more force, changing a moment arm, etc)? If you want to look at differences from one fundamental velocity use your original formula. If they are all independent and you just want to compare them to eachother then the other anon's formula is better but of seems to be of questionable worth here. Essentially what you do with the second formula is "least biased" and you treat the mean as the baseline rather than any one of the individual data points.
But saying that you are comparing multiple things isn't really context, obviously you are comparing things.

[Anonymous No.11382552]

>>11382543
They are independent in the sense that each velocity is being measured by a different device/method, but the object whose velocity the devices are measuring is the same object.

[Anonymous No.11382586]

>>11376745
Hello, what are the most based double major combinations?

[Anonymous No.11382608]

>>11382586
The ones that you will enjoy, be able to complete, and find work with.

[Anonymous No.11382648]

>>11382586
Based double majors:
>homology + cohomology double major
>economics + conmanship double major
>studying + employment double major
>one subject but you put 200% of yourself into it double major
>math + shitposting double major
>masters in math + phd in math double major
Anything else is decidedly unbased and possibly even cringe.

[Anonymous No.11382655]

>>11382118
>>11382124
>>11382126
They're almost the same because in each frame's perspective, it is at rest and the other is moving. The almost part comes from the sign of b. Suppose there was a particle at rest at the origin of the moving frame (x' = 0). It would go off in one direction in a stationary frame. Now suppose there was a particle at rest in the origin of the stationary frame (x = 0). In the moving frame, it would go off in the opposite direction.

[Anonymous No.11382711]

>>11379648
Leibniz integral rule
https://en.m.wikipedia.org/wiki/Leibniz_integral_rule

[Anonymous No.11382891]

can anyone help me out with this initial value problem? how am I supposed to find the coefficients if they cancel out when I substitute?

[Anonymous No.11382904]

>>11382891
just a glance, did you do product rule for y'?

[Anonymous No.11382907]

>>11382904
fuck

[Anonymous No.11382923]

What is the yearly outline of a PhD in science/engineering? For example, in my country PhDs are generally 4-year programs that go more or less like this:

1st year: coursework + research
2nd year: coursework + research (with mid-term exam by the end of second year)
3rd year: 6 months to 1 year abroad doing research
4th year: finishing projects, thesis writing and post-doc hunting

I'm specifically asking about programs in theoretical physics or/and theoretical electrical engineering (stuff that does not require experiments).

[Anonymous No.11382927]

>>11382923
BTW I'm asking about American universities.

[Anonymous No.11382930]

>>11382904
thanks I had a brainfart

[Anonymous No.11383065]

>>11382711
nope, or at least a trivial application. Note that the variable t is completely bound, the differentiation is w/r/t x, and the integrand is independent of x. You could use the liebniz integral rule but its total overkill.

[Anonymous No.11383569]

>>11376745
Suppose I have a vector [math]x \in \mathbb{R}^d[/math]. Let [math]x \vert_{A} \in \mathbb{R}^{|A|}[/math] denote the restriction of [math]x[/math] onto the support of indices [math]A \subseteq \{ 1, \ldots, d \}[/math]. I am interested in the quantity [eqn]S = \sum_{k=1}^m || x\vert_{A_k} ||_2 = \sum_{k=1}^m \sqrt{\sum_{j \in A_k} x_j^2}, [/eqn] where I have partitioned [math]\{ 1, \ldots, d \} = \bigsqcup_{k=1}^m A_k [/math], i.e. [math]A_k \cap A_{k'} = \varnothing[/math] for [math]k \neq k'[/math], and to avoid trivial partitions, suppose all [math]|A_k| > 0[/math]. Note that I have chosen a "standard basis" in which to express my vector elements, i.e. [math]x = (x_1, \ldots, x_d)[/math].

I have two questions, one of which should be trivial but I'm too brainlet to formally prove right now, and the other being a bit more conceptual.

1) What is the minimum value of this quantity, minimized over all possible partitions? This means that I allow [math]m[/math], the number of sets in my partition, to vary, as well as the actual choice of partitioning the indices. I suspect that it's just [math]m=1[/math] due to the concavity of [math]\sqrt{\ \cdot \ }[/math], but I'm not 100% sure.

2) Suppose I have some constraints on what partitions are allowable, and I want to minimize over these constraints. For instance, this may be some esoteric constraint on the indices which may be grouped together (e.g. each [math]A_k[/math] can only contain all odd or all even indices, or the sum of all indices in [math]A_k[/math] must be less than some constant (these are not the actual constraints I'm looking at, they're just examples of what I mean)). How would I go about implementing such a minimization procedure? I often see terms like "semi-definite program" and "linear program" thrown around, but I don't really know how to determine whether my problem (including constraints) falls into one of these nice, tractable settings.

[Anonymous No.11383637]

>>11383569
>minimum at m=1
Yes, the trivial partition minimizes.
We have [math](\sqrt{a^2 + b^2})^2 = a^2 + b^2 \leq a^2 + b^2 + 2ab = (a+b)^2[/math], and thus [math] \sqrt{a^2 + b^2} \leq \sqrt{a^2} + \sqrt{b^2}[/math].
>For instance, this may be some esoteric constraint on the indices which may be grouped together (e.g. each Ak can only contain all odd or all even indices, or the sum of all indices in Ak must be less than some constant (these are not the actual constraints I'm looking at, they're just examples of what I mean)). How would I go about implementing such a minimization procedure?
If k is small, it's actually easier with really weird and strong constraints, because you can and havce an excuse to just exhaust manually.
But, in the example you gave:
You have an overarching partition (evens and odds), and any subpartition needs to be more refined than that one. So in essence, you have to choose a subpartition of the odds, and another one for evens. Plus, both minimization problems are essentially independent, so you're golden.

[Anonymous No.11383793]

>amino acids are acids
>the amino group is basic
???

[Anonymous No.11383889]

>>11383569
First note that projections [math]p_A:V\rightarrow V/A[/math] preserves the norm on a normed linear space [math]V[/math] for each [math]A\subset V[/math]. If [math]V[/math] is in addition Hilbert, then each projection is orthogonal whence [math]V = \bigoplus_{A\in\mathcal{A}} \operatorname{im}p_A[/math] and [math]|x|^2 = |p_A x|^2 + |p_{A^\perp} x|^2[/math] by the polarization identity for any mutually orthogonal collection [math]\mathcal{A}[/math] of subsets [math]A[/math]. If [math]V[/math] is in addition separable then we may fix a complete ONB for which we have a one-to-one correspondence between [math]\mathcal{A}[/math] and partitions [math]\mathfrak{A}[/math] of [math][\infty] = \{1,\dots,\infty\}[/math]. Denote this correspondence by [math]\pi:(\mathcal{A},\bigoplus)\rightarrow (\mathfrak{A},\coprod)[/math], which sends [math]0\mapsto \emptyset[/math].
Now for any collection of partitions [math]\mathfrak{a} = \{a_\alpha\}_\alpha[/math] put [math]P_\mathfrak{a}(x,|x|)^2 = \sum_\alpha |p_{\pi^{-1}a_\alpha}x|^2= |p_{\bigoplus_\alpha \pi^{-1}a_\alpha}x|^2[/math] by the polarization identity, hence [math]P_\mathfrak{a}(x,|x|)[/math] is merely the norm-squared [math]|p_A x|^2[/math] of [math]x \in V[/math] on the subset [math]A = \bigoplus_\alpha \pi^{-1}a_\alpha[/math]. In other words, [math]P[/math] is your quantity [math]S[/math] with the sum passed into the square root.
Now since [math]\sqrt{\cdot}[/math] is convex on [math][0,1)[/math] and concave on [math](1,\infty)[/math], we have the inequalities [eqn]S_\mathfrak{a}(x,|x|) \begin{cases} \geq |p_A x| &; |x|<1 \\ \leq |p_A x| &; |x|>1\end{cases}.[/eqn]
Hence for [math]|x|<1[/math] the minimization occurs for [math]\mathfrak{a} = [\infty][/math] while for [math]|x|>1[/math] the minimization occurs for [math]\mathfrak{a} = a[/math]. Constraints the partitions can be simply encoded by a map [math]b:\alpha\mapsto \beta_\alpha[/math] and taking [math]b^*\mathfrak{A} = \{a_{\beta_\alpha}\}_\alpha[/math].

[Anonymous No.11383893]

>>11383889
I had convex and concave switched. [math]\sqrt{\cdot}[/math] is concave on [math][0,1)[/math] and convex on [math](1,\infty)[/math].

[Anonymous No.11383899]

>>11383889
>hence [math]P_\mathfrak{a}(x,|x|)[/math] is merely the norm-squared
FUCK I meant the norm itself ugh.

[Anonymous No.11383910]

how do i improve my work ethic and ability to study effectively before august? barely got into a few phd programs despite slacking through my bachelors and i want to change my habits and try my best for once

[Anonymous No.11383916]

god fuck this fucking calculus shit

[Anonymous No.11383919]

fucking bullshit

[Anonymous No.11383974]

friendly asian youtubeman helped me..
I thought it seemed ridiculous that you end up with it coming to another integral where it's the same damn thing [(e^2x)(sin3x)] but that's actually what you want because you've then got an equation that you can simplify

plus I just learned the tabular method and now I'm feeling pumped

[Anonymous No.11384005]

Do neutrons and protons remain distinct from each other within atomic nuclei, or would it be more accurate to describe atomic nuclei as wriggling masses of quarks?

[Anonymous No.11384039]

Where should I start researching how to cure aging?

[Anonymous No.11384046]

How much boiling water would I have to add to a bathtub of average size (maybe 2 feet across, 4 feet long) filled halfway with 40 F water for it to heat to maybe 90 F? And, no, this isn’t homework. My water heater broke. Now, the water is so cold that my weiner actually turns blue when I try to take a shower :(
I was thinking of heating some rocks in the oven to use, but they can apparently explode from that

[Anonymous No.11384051]

Is there a reason why it's so hard to find a video of the double slit experiment actually being performed? Does setting up a detector for the slits involve a lot of complicated equipment or something? A quick google search tells me that you can just used differently-polarized filters, unless that technique fails to demonstrate quantum mechanics for some reason. Do lights of different polarization still interfere with each other?

[Anonymous No.11384179]

Can you resolve the event horizon information paradox by saying that the information gets transported to its entangled components? That is, if an electron-positron pair has the positron cross an event horizon, then the electron will spontaneously transform into a photon as it reabsorbs the positron's information.

[Anonymous No.11384200]

>>11381809
>PV=nRT
Yuck.
[eqn] \frac{P\nu}{RT}=1+\frac{B}{\nu}\implies\nu=\frac{RT}{2P}+\sqrt{\Bigg(\frac{RT}{2P}\Bigg)^2+\frac{RTB}{P}} [/eqn] The discriminant is going to be positive so we have [math]-B<RT/4P[/math]. You should know that the second virial coefficient is actually always negative so we are just saying that a positive number is less than a big positive number. As far as the plus/minus goes, only the plus will give you the proper specific volume.
>>11384046
I will assume the specific heat of water is a constant 1 BTU/lbm-R. You want to heat water from 40 F (500 Rankine) to 90 F (550 Rankine). At 1 atm, water boils at 671 Rankine. By basic energy balance,
[math] c_pm_c(550-500)=-c_pm_h(550-671) [/math]. So [math] m_h/m_c\approx0.4. [/math] Therefore, for every gallon of cold water in your tub, you need about 0.4 gallons of boiling water to bring it from 40 to 90 F (and it needs to be well mixed).
>>11383916
>>11383919
embarrassing desu

[Anonymous No.11384213]

>>11381809
>PV=nRT
Yuck.
[eqn] \frac{P\nu}{RT}=1+\frac{B}{\nu}\implies\nu=\frac{RT}{2P}+\sqrt{\Bigg(\frac{RT}{2P}\Bigg)^2+\frac{RTB}{P}} [/eqn] The discriminant is going to be positive so we have [math]-B<RT/4P[/math]. You should know that the second virial coefficient is actually always negative so we are just saying that a positive number is less than a big positive number. As far as the plus/minus goes, only the plus will give you the proper specific volume.
>>11384046
I will assume that the specific heat of water is a constant 1 BTU/lbm-R. You want to heat water from 40 F (500 Rankine) to 90 F (550 Rankine). At 1 atm, water boils at 671 Rankine. By basic energy balance,
[math] c_pm_c(550-500)=-c_pm_h(550-671) [/math]. So [math] m_h/m_c\approx0.4. [/math] Therefore, for every gallon of cold water in your tub, you need about 0.4 gallons of boiling water to bring it from 40 to 90 F (and it needs to be well mixed).
>>11384051
>"khan academy young's double slit"
>first result
>section: kindergarten thru grade 12 physics
>video
*<3~Use Your Brain <3~*
>>11383916
>>11383919
embarrassing desu

[Anonymous No.11384227]

woah never been on this board
you guys talking about all this advanced stuff and I didn't pass first grade

[Anonymous No.11384269]

>>11384227
There's always pol

[Anonymous No.11384290]

>>11384269
/pol/ is a more scientific board than /sci/ retards here unironically believe in crap like climate change

[Anonymous No.11384391]

>>11383889
>>11383893
>[math] \sqrt{x}[/math] is concave on [math
[0, 1)[/math] and convex on [math](1, \infty)[/math]
I get the impression I actually said that months ago. Is this some form of harassment?
https://en.wikipedia.org/wiki/Concave_function#Examples
https://math.stackexchange.com/questions/834862/is-sqrtx-concave
https://www.quora.com/Is-square-root-convex

Also, set [math]P_{A_k}[/math] as the orthogonal projection for the indices [math]A_k[/math].
We then have that [math]\sqrt{\Sigma_{j \in A_k} x_j^2}=||P_{A_k}x||[/math], and then [math]||x||= || \Sigma_k P_{A_k}x || \leq \Sigma_k ||P_{A_k} x||[/math], by the norm inequality.

[Anonymous No.11384453]

>>11382586
Psychology and gender studies

[Anonymous No.11384659]

Isn't science actually a delusional mental illness?
It factually has a great deal in common with autism, borderline personality disorder, etc:

- Inflexible adherence to rules
- Mindless repetition
- Lack of compromise
- Black and white thinking
- Brings people into conflict with tradition and populism
- Disregards societal norms and obedience to authority

I think that Soft Sciences like psychiatry and psychology have finally surpassed the "hard sciences", and in fact disprove the theory of them being rational or even healthy.
I'm glad the DSM is constantly expanding to catch all of these behaviors before they start to influence thinking.
What's ridiculous is that if you disagree then you also probably don't believe in rationality, evolution, etc... and probably are a mental illness denialist.

[Anonymous No.11384683]

>>11378103
Bump 2. Has noone read the Feynman lectures?

[Anonymous No.11384818]

>>11384683
My perception of the Feynman Lectures is that he breezes through topics as if you are already at least somewhat familiar with them. I wouldn't reccomend if you don't already have undergrad knowledge, or else you won't learn much in depth.
t. only read bits and pieces

[Anonymous No.11384829]

>>11365784
This has been SOLVED (original asker).

>>11366878
This has NOT. Proof in question is pic related (trying to prove the discriminant > 0 without substituting x = -b/2a. Only reason I'm asking is I found this reply:
>NOOOOO
>what did you do...
>this should be an easy proof by contraposition
>First consider the discriminant to be zero or gfreater, then you can plug this into the Quadratic equation and you get an Solution where ax^2+bx+c=0 and you got your contradiction


And the OP ITT says my proof isn't good, but why? It's perfectly valid, right? Though the contrapositive proof outlined above is probably better, my proof is essentially the same thing, just fleshed out with algebra, isn't it?

[Anonymous No.11384839]

>>11384829
>discriminant > 0
*< 0

[Anonymous No.11384874]

>>11384659
>Inflexible adherence to rules
>Disregards obedience to authority
So which is it? Why are you even here?
>populism
I wonder where you come from. Hmm...
>>11384829
>>11384839
>degree 2 polynomial is always greater than zero
>so it never crosses the x axis
>so there are no real roots
>by the fundamental theorem of algebra, there are two complex (conjugate) roots
>complex roots have form a+jb
>you can only get that imaginary part if the discriminant is negative
done. it has been shown. this problem is incredibly boring.

[Anonymous No.11384880]

>>11384874
I know it's boring, but I wanted to see the varying proofs, and when someone told me my proof was bad I was curious as to what made it so. You didn't really prove anything, just stated facts, wasted time..

[Anonymous No.11384882]

>>11384880
>just stated facts
What do you think a proof is besides a list of facts that argue for the truth of some statement

[Anonymous No.11384888]

>>11384882
It's PROOF of said facts, obviously. Incrementally supplying facts that build up to the desired fact. You know this, and if you're "bored" I don't know why you're wasting our time; I didn't ask for a proof, or if it was true, or for anything else: I asked WHY MINE IS BAD, which is inherently less boring and more constructive than this, imo.

[Anonymous No.11384955]

>>11383637
Cool, thanks, that's the inequality I needed. Much appreciated.

As for the minimization stuff, well I do have relatively strong constraints, but the search space is still intractably large, even if discrete. (This minimization be a subroutine for a larger problem, where [math]d = \mathrm{poly}(n)[/math] for the actual input size [math]n[/math].) So I suppose I was looking for a way to use ideas from optimization techniques over continuous parameter spaces as a way to find an approximate minimal solution. But anyway I should properly learn this stuff, so don't worry about trying to spoonfeed me.

>>11383889
Thanks too, although not to be rude, the notation is a bit tough to parse and some of the techniques seem like overkill.

[Anonymous No.11385066]

>>11384829
It starts from an asspull and finishes with algebra.
Now, an asspull proof can still be good, as long as its sufficiently slick and shorter than properly intuitive proofs.
But literally just substituting x=-b/2a has clear geometry behind it, and is the exact same length.
Thus, the proof is bad.
Note: substituting x=-b/2a isn't good either. It's half decent at best.

[Anonymous No.11385081]

>>11385066
>asspull
? it starts from a quadratic, already factored into a multiple of square + the discriminant, and yes it finishes it with algebra.

>just substituting x=-b/2a has clear geometry behind it, and is the exact same length.
the point of the proof was proving it WITHOUT making that substitution, as stated.. There was one other person giving feedback:
>NOOOOO
>what did you do...
>this should be an easy proof by contraposition
>First consider the discriminant to be zero or gfreater, then you can plug this into the Quadratic equation and you get an Solution where ax^2+bx+c=0 and you got your contradiction

but the thing is, I basically did exactly what he said, just showed it with algebra instead of contraposition, so I don't get why I'm being my proof is 'bad', and I like my proofs to be good, so naturally I'm curious if there's something substantial behind the criticism, I just want to know.

While I appreciate the feedback, I don't feel it's been very instructive (yet).

[Anonymous No.11385086]

>>11385066
And if sub'ing x=-b/2a isn't good, what is? This is what started the whole thing, I didn't like making that sub and wanted to prove it otherwise, and the screenshot was my attempt. What else ya got?

[Anonymous No.11385090]

>>11385081
>literally starts swapping in [math]x \rightarrow x-b/2a[/math] with no explanation given
>not an asspull

>the point of the proof was proving it WITHOUT making that substitution, as stated..
That's irrelevant. Not being some other proof or not using some result on purpose doesn't make it a better proof.
>>11385086
Not everything has a good proof, anon.
For example, [math]A \subset B \subset C \rightarrow A \subset C[/math] is literally too simple for any proof to be called good.

[Anonymous No.11385091]

>>11385090
My bad, x+b/2a.

[Anonymous No.11385096]

>>11385090
>literally starts swapping in xx−b/2a with no explanation given
Yes, this is the factored form of a quadratic, I would not call that an asspull, especially in the context of solving a problem involving quadratics and discriminants. In the original thread, the context was even more apparent, so it would've felt silly to start with ax^2+bx+ on line 1 yet again.

>That's irrelevant. Not being some other proof or not using some result on purpose doesn't make it a better proof.
It's not irrelevant, because it's part of the original constraints of the problem.

>Not everything has a good proof, anon.
Everything is relative. Why call it bad if it's not relatively bad, then? That's retarded, and so is everything else you said in this post.

[Anonymous No.11385179]

>>11382923
Anyone?

[Anonymous No.11385241]

How is this true?
I keep getting -60 degrees
arctan(imag/real) = -60, not 120

[Anonymous No.11385254]

>>11385241
It's true all right. Look at the coordinates and think about what quadrant they would be in the complex plane. Then recall that arctan(...) only returns values between -90 and 90. To be less ambiguous, I recommend the atan2 function.

[Anonymous No.11385300]

>>11385254
So should I always use arctan(2*imag/real)?

[Anonymous No.11385326]

>>11385300
No, no, that's not what I meant. Do not do that. You can keep using the regular inverse tangent function, just keep in mind what coordinate you are in. This is what I was talking about. https://en.wikipedia.org/wiki/Atan2

[Anonymous No.11385416]

How do I solve this integral again?
[math]\int_{-\infty}^{\infty} e^{-a |\vec{p}|}d\vec{p}[/math]
In both 3 and n dimensions where a is just a constant.
Wolfram cant solve it (or I cant ask it properly) and I dont know how to find the solution by myself. Im sure Ive learned it a bunch of times by now but I always forget after I dont need it for a few months...

[Anonymous No.11385509]

>>11385416
>three dimensions
Polar coordinates.
>n dimensions
Polar coordinates but shittier.
IIRC you had a result like [math]\partial _r \int _{B_r} f(x) d \mu (x) = \int _{S_r} f(x) d \lambda (x)[/math], where [math]d \mu [/math] is n-dimensional Lebesgue measure and [math]d \lambda [/math] is the usual n-1 dimensional measure. I'd recommend googling the formula for the volume of the n-dimensional sphere and checking if there are any adjustment factors I forgot.
But in your case, [math]f(x)[/math] is constant on the sphere, so the integral on the right is simple enough to evaluate.

[Anonymous No.11385516]

>>11385509
I actually just googled the formula for volume of the ball and the formula I gave checks out, so you shouldn't worry.

[Anonymous No.11385708]

Why does a high growth rate diminishes the carrying capacity?

I'm plotting the simple function [math]\frac{\mathrm{d}x}{\mathrm{d}t} = rx(1-x)[/math], with initial condition of 0<x<1. Why does my asymptote gets lower and lower as my growth rates gets higher than 2.74?

Also, why doesn't bifurcation happen on continuous time domain?

[Anonymous No.11385747]

I'm reading Zee's book on Group Theory, and I'm a little confused by his assertion (given without proof) that
[eqn]
\chi(c) = \chi(\bar{c})^*
[/eqn]
where [math]c[/math] is an equivalence class, and [math]\bar{c}[/math] is the equivalence class consisting of the inverse elements of [math]c[/math].

I can only see that this works for a unitary representation, since in a unitary representation [eqn]\chi(\bar(c)) = \mathrm{tr} (D(g^{-1})) = \mathrm{tr}(D(g)^\dagger =\mathrm{tr}(D(g))^* = \chi(c)^*,[/eqn] but not every irreducible representation is unitary, so why does this hold?

[Anonymous No.11385763]

>>11385747
It's kinda obvious, but the last line was meant to be
[eqn]\chi(\bar{c}) = \mathrm{tr} (D(g^{-1})) = \mathrm{tr}(D(g)^\dagger) =\mathrm{tr}(D(g))^* = \chi(c)^*[\eqn]

[Anonymous No.11385809]

can someone please help me with this thermodynamics question? i used the first law (change in internal energy = heat supplied - work done) (sorry i cant into tex) to solve part c in pic related, but when i try using it in part d to express the change in internal energy (seems pretty straight forward) it doesnt seem to work. what am i not getting? was there a different (easier?) way to get the heat absorbed that i shouldve used?

[Anonymous No.11385879]

>>11385747
I don't really know, but I have an idea.
[math]A^* A[/math] has some nice properties.
Assume it has norm less than one. Then, it either equals the identity, or it isn't a root of the identity. Proof:
Either there is some [math]u[/math] such that [math]||A^* A u||<1[/math] or there isn't. If there is, we're done. Thus, assume there isn't.
Then [math]1 = \langle Au, Au \rangle = \langle A^* Au, u \rangle \leq ||A^* A u|| ||u|| =1[/math]. But equality only occurs in Cauchy-Schwarz if they're multiples of each other, and thus it's the identity.

[Anonymous No.11385883]

>>11385879
>*less or equal to one

[Anonymous No.11385910]

>>11385879
>>11385747
Ah, I'm dumb, I think it's possibly just that every irreducible representation can be made unitary with a similarity transformation (i.e. Weyl's unitary trick), which obviously doesn't affect the character of the group due to cyclicity of the trace.

Not sure if that's correct, I don't think I entirely understand Weyl's unitary trick, but it would allow one to prove general statements about characters based on unitary representations.

[Anonymous No.11385920]

>>11385708
Well, fuck. Apparently, my integrator is a piece of shit. I've got no idea what the fuck is going on, I'm using a RK4. Using default ode45 integrator gives me the actual result.

[Anonymous No.11385943]

>>11385809
First law of thermodynamics:
[eqn]
\delta U = \delta Q + \delta W
[/eqn]
[math]\delta Q[/math] = heat absorbed BY the gas, [math]\delta W[/math] = work done ON the gas, (signs differ depending on conventions)
You've already worked out the work done on the gas and the heat absorbed by the gas in parts (b) and (c).

[Anonymous No.11385947]

>>11385920
Use Euler on a paper spreadsheet with a mechanical calculator like a real man.

[Anonymous No.11385950]

>>11385943
right, but its asking for an expression in terms of the volumes and pressures and i dont understand why what i put isnt correct

[Anonymous No.11385964]

>>11385950
Have you tried inputting [math]Q_1 - W_1[/math]?

[Anonymous No.11385975]

>>11385964
i can only use [math]P_0[/math], [math]V_0[/math], and [math]V_1[/math]

[Anonymous No.11385976]

>>11379396
How is warfarin administered in hospital? I imagine eating rat poison would take too long for any pharmacological effects to occur during the heart attack

[Anonymous No.11385987]

>>11385975
Okay.
I worked through the problem and got a similar answer, but I think you're using the wrong value for specific heat capacity for a monoatomic gas. It should be 5/2, not 3/2. Also go ahead and simplify that.

[Anonymous No.11385988]

>>11385987
*I should clarify: specific heat at constant pressure for monoatomic gas = 5/2

[Anonymous No.11385990]

Fuck. This was supposed to be a straight-forward RK4 application, wtf. How do I save this, lads?

>>11385947
But that would take a fucking long time for me to do some cool population dynamics graphs!

[Anonymous No.11385995]

>>11385990
I'll kill the next person that tells me that jpeg is good enough, by the way.

[Anonymous No.11385997]

>>11385987
>It should be 5/2, not 3/2.
yeah, that did it
hmm, guess my algebra needs some work, tyvm
>>11385988
i was using
[eqn]E_{int}=\frac{3}{2}nRT=\frac{3}{2}PV[/eqn]

[Anonymous No.11386000]

>>11385997
>hmm, guess my algebra needs some work, tyvm
Your algebra is fine, your expression is correct if [math]C_P = 3/2[/math], but it doesn't. I assume you confused it with the specific heat at constant volume, [math]C_V[/math] which is 3/2 for a monoatomic gas. You should read up on calculating specific heats from degrees of freedom and the thermodynamic definitions of specific heat.

[Anonymous No.11386006]

>>11385995
Maybe you fucked up your code or maybe the equation is very sensitive to error. Do the solutions start out the same and diverge at some point?

[Anonymous No.11386011]

>>11386000
so is [math]E_{int}=\frac{3}{2}nRT[/math] really [math]E_{int}=C_pnRT[/math] ? i should probably read equations before just mindlessly memorizing them

[Anonymous No.11386014]

>>11386006
Yes, I forgot to fix the axis of the image and spent the last 10 minutes debugging why the fuck did they start from different points.

[Anonymous No.11386081]

>>11386011
Not really, no.
The internal energy of a constant molar volume of a system is [math] C_V T[/math], but the derivation of that expression assumes volume stays constant which it doesn't here.
Here's my working:
Take the differential of the ideal gas law [math]pV = nT[/math] with [math]p[/math] and [math]n[/math] constant. Then
[eqn]
p dV = n dT.
[/eqn]
Hence the work done by the gas is
[eqn]
W = \int p dV = p \int dV = p (V_1 - V_0) = \int n dT = n (T_1 - T_0).
[/eqn]
the second equality holds because pressure is constant.
Heat absorbed by the gas at constant pressure is
[eqn]
Q = n \int C_P dT = C_P n (T_1 - T_0) = C_P p (V_1 - V_0)
[/eqn]
(you might want to look up the definition of heat capacity for the first equality one)
Then using the first law, we get
[eqn]
\delta U = Q - W = C_P p (V_1 - V_0) - p (V_1 - V_0) = (C_P - 1 ) p (V_1 - V_0)
[/eqn]

[Anonymous No.11386098]

>>11386081
ah, i see now, thanks for the breakdown, ive just been using cookie cutter equations for [math]Q[/math] and [math]W[/math] without regard to any context

[Anonymous No.11386103]

Why doesn't the Casimir effect cause a tiny tube with one closed off end to experience in a net force in one direction?

[Anonymous No.11386106]

>>11386081
>>11386011
Hang on, I'm wrong you can use that formula for the energy. It doesn't require that volume remains constant, but in that case you're just subtracting the internal energy from the initial state from the final state, which is just
[eqn]
\delta U = E_1 - E_0 = C_V n T_1 - C_V n T_0 = C_V p (V_1 - V_0)
[/eqn]
Notice that we get the same result because for an ideal gas C_V = C_P - 1

[Anonymous No.11386426]

>>11384179
The entire paradox is that everything past the horizon goes off to past infinity, hence no information regarding the prior entanglement can exit without violating locality. Anything inside the horizon is quite literally not part of the universe.
Incidentally the information paradox can be resolved with string theory
https://arxiv.org/abs/0810.4525
Please read up before making another post.
>>11384955
>some of the techniques seem like overkill
You [math]were[/math] looking for a rigorous proof after all. It's either that or I do variational calculus on the path space [math]P\mathfrak{A}[/math] to get the minimizers.
>>11385747
Here's the idea: for any irrep [math]\rho[/math] there's a conjugate irrep [math]\overline{\rho}[/math] with [math]\chi_\rho(c) = \chi_{\overline{\rho}}(c^{-1})[/math]. This arises because [math]\rho(c)\rho(c^{-1})[/math] lies in the conjugacy class of the centre of [math]{GL}_\mathbb{C}(V)[/math] so by Schur it must be similar to a multiple of the identity. The similarity transform then induces [math]\rho\mapsto \overline{\rho}[/math] with [math]\rho(c)\overline{\rho}(c) \sim \lambda\mathbb{C}[/math]. Hence [math]\chi_\rho(c) = \chi_{\overline{\rho}}(c^{-1}) = \overline{\chi_\rho(c^{-1})}[/math].

[Anonymous No.11386612]

I have a fun question today I thought up of based on something with a potentially real application. Let's say you're playing minecraft and want to build a base. However, you happen to be playing on 2b2t and don't want anyone to find your base. Assuming spawn is at (0,0) and nether highways stretch horizontally, vertically, and diagonally with respect to spawn and for generality, the world only goes to the edges plus or minus 1 (i.e. can't go farther than (-1,1)). Say a griefer starts at a random point along any nether highway and then travels in the overworld in a straight line at a random angle until they meet the next nether highway. The question is, can you pick a base location that is less likely to be found than other locations as the number of griefers increases (or if the griefer once again picks another random angle and travels in a straight line until they meet the next nether highway)? There's probably a cleaner way to actually write this as a maths problem but I thought it'd be funny in minecraft terms.

Pic related is an example of a random path I drew.

[Anonymous No.11386705]

so for real, how high a chance is it that the books on libgen have been modified to have minor errors in them?

[Anonymous No.11386744]

>>11386705
if youre smart enough, you can simply spot them for yourself anon.

[Anonymous No.11386751]

>>11386612
After some pondering I think I may have solved my own question. Realizing that given a starting point on some highway, there are "forbidden" areas a griefer wouldn't search because he would never intersect another nether highway. I constructed a small red circle wherein I call the "willing to start search" circle. A griefer would start on a point within this circle and then proceed like normal. The light gray lines are those lines the griefer would not travel across (would never intersect a highway) on the farthest points of said circle. You can realize that there are certain areas (dark grey) that a griefer would NEVER travel across for ANY starting highway, as long as they never start their search beyond the red circle. Therefore you'd construct your base in any dark grey area. As the sphere grows in size (aka the griefers are willing to broaden their search), the grey areas shrink to a point (w/o loss of generality there are 8 of these points) for a finite map. tl;dr build away from spawn, what a no brainer lol.

So I want to append my question - can you still pick a point that is still more unlikely to be hit than other points if there are now nether highways bordering a finite map? (aka highways on the lines x = 1, x = -1, y = 1, and y = -1) given all else is still the same?

[Anonymous No.11386781]

When proving NP-hardness of some problem X, do I have to reduce X *to* or *from* a known NP-complete problem? Does it not matter which one I start with and construct a polynomial-time reduction algorithm, or do I have to do both (sorta like proving necessary and sufficient conditions)?

[Anonymous No.11386857]

>always came on the wall, floor and basically anywhere (i have a fetish for flailing my cock around as i cum)
>always clean every drop afterwards
>never thought of it
>buy one of those black light led strips
>it shows spots everywhere, walls, floor, bed, carpet, sofa, every fucking where
>try to clean it
>it doesn't go away
how do i remove it? can it cause me any problems with my landlord?

[Anonymous No.11386949]

uneducated retard here - are there any well established methods how to study some subject? I mean something that will help me to organize information in some way so I can easily go back to it. Also I would prefer paper over some kind of wiki system. T-thanks pals

[Anonymous No.11386955]

>>11386857
>it shows spots everywhere, walls, floor, bed, carpet, sofa, every fucking where
Just fill in the gaps between spots with more cum so it just looks like a uniform glow with no spots visible

[Anonymous No.11386958]

>>11386949
have you tried books?

[Anonymous No.11387000]

Can a droplet of semen impregnate a female if it came from outside the vagina first?
e.g. there's cum left in your hands and you then proceed to finger a girl

[Anonymous No.11387034]

>>11386958
I did, but my problem is that I need to capture information I learn from the books in some structured way so I can get back to it later.

[Anonymous No.11387051]

>>11386705
Near zero percent.
I don't actually have the data, but I'm fairly sure most of the libgen library was methodically scraped with institutional access, compressed, cleaned of metadata and uploaded.
My evidence for it is how you'll sometimes find stuff like this: http://libgen.is/book/index.php?md5=14E74E50C4438D29CC486FB051FABB49
,how just about every single book in libgen has duplicates, which would be weird if they were human uploaded, and how I can't ever find books on libgen that I also can't find available for download on the publisher's website, i.e. Geometry of Vector Sheaves Volume One (but the second volume is in both springer's website and in libgen.)

[Anonymous No.11387101]

>>11387000
yes, those fuckers are quite determined

[Anonymous No.11387145]

How the fuck am I supposed to reduce the steady state error for my ramp response PID controller to 1%?

[Anonymous No.11387185]

Why is this wrong
Why is photomath telling me that the answer to this is (x-2)^2
I am losing my mind over this shit

[Anonymous No.11387199]

>>11387185
>that cheeky -3x+2 on the extreme right

[Anonymous No.11387221]

>>11386781
How is that a question, fren? Just fucking think about it.
NP-hardness means that all problems in NP are reducible to it, so obviously you have to find a polynomial reduction of a known NP-hard problem to yours.
By doing the reverse, you just show the problem is in NP and obviously, it might very well not be NP-hard.

[Anonymous No.11387323]

>>11387185
you forgot to change negatives and positives in the negative parenthesis. never forget to flip the negatives and the positives when remove a negative parenthesis, bro.
it should be
[math]-x^2+3x-2[/math]
the answer is
[math]2x^2-4x-3x+6-x^2+3x-2[/math]
[math]x^2-4x+4[/math]
if you can't see it, quadratic formula that bitch and it would be
[math](x-2)^2[/math]

[Anonymous No.11387436]

>>11387199
>>11387323
Thanks anons. God I feel like a retard sometimes doing more complicated math and then getting lost at elementary shit like this.

[Anonymous No.11387471]

why does stopping stopping the wheels on just one side of the car make it start turning around it's axis?

[Anonymous No.11387595]

Is there a correlation between looking at the mirror too much and delaying the aging process through the placebo effect? I've noted that when I used to look at the mirror many times per day I end up does not have to make a plastic surgery but when I used to stop being a narcissist for 3 years I've aged horribly!!
does that have anything to with men live shorter that women???

[Anonymous No.11387874]

>>11387221
Oh okay, guess I just didn't fully understand what it meant to be NP-hard. Thanks.

[Anonymous No.11387886]

What is the answer to this

[Anonymous No.11388005]

>>11387886
First of all the problem is asking about the ring structure of [math]H^\ast(\mathbb{R}P^n,\mathbb{Z})[/math]. The stuff aout pizza's and bananas is about [math]{\bf Ext}[/math] and [math]{\bf Hom}[/math], which isn't useful here since they're for computing the spectral sequences for the stable cohomotopy theory.
Let us consider [math]H^\ast(\mathbb{R}P^n,\mathbb{Z}) \cong H_\ast(\mathbb{R}P^n,\mathbb{Z})[/math] as a polynomial ring over [math]\mathbb{Z}[/math]. We are done if we can find all generators and their relations. Toward this end we write [math]\mathbb{R}P^n \cong S^n\mathbb{Z}_2[/math] where the antipode map [math]\mathbb{Z}_2[/math] acts transitively. This means that we pick up
1. a free generator [math]e_0,e_n[/math] at degree [math]0,n[/math]
from the sphere [math]S^n[/math], and
2. a 2-torsor [math]e_1\in \mathbb{Z}_2[/math] at degree 1 since paths linking antipodal points descend to a non-contractible loop, hence [math]\pi_1(\mathbb{R}P^n)\cong\mathbb{Z}_2[/math] and [math][\pi_1]_{\operatorname{ab}} \cong H_1[/math] by Hurewicz.
To understand what happens at other degrees we decompose [math]\mathbb{R}P^n[/math] into a finite CW complex, whose [math]k>0[/math]-skeletons are endowed with a monodromy action by [math]\pi_1[/math]. Due to the CW structure, a map [math]f:S^k \rightarrow \mathbb{R}P^n[/math] is determined by its value on the [math]k[/math]-skeleton, and hence by its degree [math]\operatorname{deg}f[/math]. Due to the monodromy action this degree is again 2-torsion.
From basic algebraic topology the degree is only non-trivial for [math]k[/math] odd, hence we get 2-torsors at each odd degree, while anything at all even degrees (except 0) are killed off. Hence [math]H^\ast(\mathbb{R}P^n,\mathbb{Z}) = \mathbb{Z}[e_0,\dots,e_n]/\prod_{m \text{ odd}\leq n}\langle e_m^2-1\rangle[/math].

[Anonymous No.11388010]

>>11387886
the answer is getting laid

[Anonymous No.11388080]

>>11388005
>everything at even degree except 0 is killed off
Doesn't that mean we have [math]\mathbb
{Z}[e_0, \cdots , e_n]/ \Pi_{m ~ odd \leq n} \langle e^2 _m \rangle[/math], since the squares of odd-degree elements have even degree?

[Anonymous No.11388152]

>>11386949
bumping for this

[Anonymous No.11388273]

>>11388080
Sorry I wrote the relations multiplicatively since I was thinking about the about the homotopies. It should be 2e - 1 for odd degrees in the relation.

[Anonymous No.11388278]

>>11388273
FUCK it’s 2e not 2e - 1

[Anonymous No.11388290]

>>11388152
>read a book
>with a pen and paper, summarize the most important concepts of each chapter once you get done reading them
This is extremely simple.

[Anonymous No.11388413]

>>11386949
If you want to get a strong grasp of something, my best recommendation is:
>read a book on the subject
>restudy the pre-requisites for the subject
>study some application of the subject
So for example, if you want to really know your functional analysis, you could:
>read up on functional analysis
>restudy linear algebra, general topology and measure theory
>study integral operators/inverse problems

[Anonymous No.11388428]

>>11387886
kek.
moar like this?

[Anonymous No.11388472]

[math]$\forall$[/math]x

[Anonymous No.11388476]

>>11388472
[math]\forall x[/math]

[Anonymous No.11388479]

>>11388290
> Implying there is not hundred books about the topic all covering different aspects of it
I'm not asking about how to write down notes you retard, but how to organise them. Learn to read before giving any sort of advice. Also kys. But thanks for responding anyhow

>>11388413
Thanks

[Anonymous No.11388481]

>>11388476
[math]\forallx, \thereis[/math]

[Anonymous No.11388482]

>>11388481
[math]\forall x, \exists y such that [/math]

[Anonymous No.11388488]

>>11388482
[math]\forall x, \exists y such that x<y[/math]

[Anonymous No.11388490]

>>11388488
>>11388482
>>11388481
>>11388476
>>11388472

[Anonymous No.11388494]

>>11388490
Can't I practice here? The thread is already dying anyway.

[Anonymous No.11388495]

>>11388488
Use ~ for spaces.

[Anonymous No.11388497]

>>11388488
[math]\forall x \ \exists y \ such that[/math]

[Anonymous No.11388499]

>>11388495
Thank you, that what I wanted to figure out so I should write

Such~that
Or
Such ~ that?

[Anonymous No.11388500]

>>11388497
If your keyboard doesn't have that key, use \, or \space.
>>11388499
Either works.
You can also use the TeX button on the reply box to preview the Latex instead of posting.

[Anonymous No.11388501]

>>11388494
>>11388499
You can practice by clicking the TeX icon in the top left corner of the reply window. Actually, keep posting so I can make the next thread.

[Anonymous No.11388502]

>>11388500
>preview the Latex instead of posting.
That's not available on mobile though, thanks anyways

[Anonymous No.11388508]

>>11388502

[Anonymous No.11388511]

>>11388499
Don't write text in regular mathmode. TeX doesn't care about spaces in mathmode. Use text{}
[math] \forall x, \exists y\ \text{such that } [/math]
\forall x, \exists y\ \text{such that}

[Anonymous No.11388512]

>>11388511
Sugoi, nice tip thanks

Btw you guys have any books recommendations for learning LaTeX or should I learn from practice?

[Anonymous No.11388519]

>>11376745
Whats up.
Should I do a masters and then phd or go straight for PhD? (EE, systems and signals)
I would need funding for both.
In looking at sweden, were I meet the requirements for a phd position and would really appreciate the stipend.

[Anonymous No.11388521]

>>11388512
there's no reason to read a book on LaTeX lol. Just learn from practice. It's insanely easy. God Bless Donald Knuth.

[Anonymous No.11388522]

>>11388519
Only you can answer that question. Do you feel prepared for escaping masters? If you do, then do it, but if you're not sure then don't

[Anonymous No.11388531]

>family is complaining that I'm a NEET who do nothing all day
>i work all day on my proof of one of the millenium problems in my room
>they're too stupid to understand that though so they want me to slave myself in some underemployment

So I decided to live alone, but in order for me to sustain myself I'll need some money, then I decided I would teach math to those in need for just $50 an hour. The real question is, how the fuck do I get students? I don't use social networks and I'm too shy to go to schools and market myself there. Should I make cards or something and give them to people in the street?

[Anonymous No.11388534]

>family is complaining that I'm a NEET who do nothing all day
>i work all day on my proof of one of the millenium problems in my room
>they're too stupid to understand that though so they want me to slave myself in some underemployment

So I decided to live alone, but in order for me to sustain myself I'll need some money, then I decided I would teach math to those in need for just $50 an hour. The real question is, how the fuck do I get students? I don't use social networks and I'm too shy to go to schools and market myself there. Should I make cards or something and give them to people in the street?

[Anonymous No.11388542]

what should I specialize in as an EE in 4th year? What's the most demanding?

[Anonymous No.11388544]

>>11376745
c[x] = floor[x] -floor[x/2] -floor[x/3] +floor[x/6]
Notice how there are alternating steps of two widths: a shorter one with a width of 2, and a wider one with a width of 4.

I would like to create a similar function d[x] with some property of steps going up by 1, and with the shorter steps having the same width of 2. However, I would like the longer step to have a width of 6.

How do I achieve this?

[Anonymous No.11388548]

>>11388534
>I cut myself off from people and have never worked in my life and also I have no education credentials and am delusional about my abilities, how can I get a high paying job pls?

[Anonymous No.11388550]

>>11388544
*a similar function d[x] with the same property of steps going up by 1

[Anonymous No.11388577]

>>11388548
Not high paying no, I just want to earn enough in order to survive living alone, I almost doesn't buy anything, just books and only do math these days

[Anonymous No.11388641]

>>11385509
Ah yeah of course now I remember. I think we learned it as something like a transformation [math]d^np = r^{n-1} dr d\Omega_{n-1}[/math] where the n-1 surface differential had some whacky gamma functions and the likes in it but could be easily computed.
Im afraid Ill probably forget it in a few months but maybe I can keep the n-sphere in mind...

[Anonymous No.11388692]

How do I write logically this sentence:

>Nobody in the calculus class is smarter than everybody in the discrete math class
My answer is:
[math] \forall x \ (C(x) \ \rightarrow \ \exists y \ \lnot (D(x,y))) [/math]

Where C(x) stands for 'x is in the calculus class' and D(x,y) stands for x is smarter than y
What's wrong with it?

[Anonymous No.11388716]

>>11388692
y isn't necessarily in the discrete maths class.

>logic
Let A be the set of people in the calculus class, and let B be the set of people smarter than everyone in the discrete math class.
Then [math]A \cap B = \emptyset[/math].

[Anonymous No.11388754]

>>11388716
Hey, is my answer right in letter c?

m=Mary

[Anonymous No.11388768]

>>11388754
Nah, because for x=m you have both L(m) and not L(m).
Gotta go with for all x we have that x not equal to m if and only if L(x).

[Anonymous No.11388773]

>>11388768
Am I a brainlet or is logic just too damn hard?

[Anonymous No.11388776]

>>11388773
Practice, anon.
By the way, good night. Someone else will have to answer your next questions.

[Anonymous No.11388786]

>>11388776
Ok, good night, rest in peace sweet prince

[Anonymous No.11389203]

>>11388511
[math]\text{for all }\forall x \text{ there exists } \exists y \text{ such that s.t.}: \dots[/math]

[Anonymous No.11390047]

silly question but doesnt anyone here know how to use tex in a word document? im sick of microsofts shitty equation thing

[Anonymous No.11390130]

>>11390047
nvm i found it