/sqt/ /qtddtot/ - stupid question thread

[Anonymous No.11329155]

The newest iteration of >>11314509

>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.11329164]

>>11329155
what proportion of posters on this board do you think can solve a calculus 1 exam question?

[Anonymous No.11329264]

>>11329164
unironically less than half. the state of this board is astounding at times

[Anonymous No.11329272]

~UNRESOLVED~

Physics:
>>11323749 (continuous because waves, discrete because existence of photons)
>>11328368 (possibly nonsense)
>>11328690

Chemistry:
>>11323512

Engineering:
>>11321134 (A transfer function is a complex function that relates the Laplace transform of the output of a system to its input. Bode plots are a visualization of the magnitude and phase of the transfer function. Frequency response is how a dynamic system reacts to a a purely oscillatory/purely imaginary input)
>>11322116

Biology and physiology:
>>11322743
>>11323412
>>11323703

Math:
>>11319497 (MATLAB)
>>11319555 (lots of practice, memorization)
>>11320591
>>11321153 (I feel like this has been asked many times before. FT is just Laplace transform with s=jω; frequency response)
>>11322036
>>11322297
>>11323890 (cs?)
>>11328112

Stupid:
>>11315193
>>11316103 (weebs need love, not bulli)
>>11317174
>>11320542 (STEM is bullshit, study music)
>>11320589
>>11320937
>>11321691 (getting a masters is part of grad school)
>>11322596
>>11322605
>>11324189
>>11325894
>>11326358
>>11327475
>>11329164 (<10%)

Probably typos and missed questions. Am phoneposting.

[Anonymous No.11329278]

>>11329272
***FT gives the frequency response, I meant to say

[Anonymous No.11330343]

>>11329164
35%

[Anonymous No.11330495]

Hi can you help me plz?
Is it valid to apply newtons law in a rigid body if the forces are not applies in the same spot. (IE: calculating the aceleraion of the center of mass using the sum of forces applied in the body despite not being applied in that point and the masss of the body)
Can you apply this law in a point that is not the ICR (Instantaneous centre of rotation):
sum of Torques=angular aceleration*moment of inertia

[Anonymous No.11330502]

>>11330343
potato

[Anonymous No.11330529]

>your ban will expire in 13 days and 17 hours from now
>mfw
>>11330495
>Is it valid to apply newtons law in a rigid body if the forces are not applies in the same spot
Yes. The sum of the forces on a rigid body is equal to the rate of change of linear momentum of the center of mass. [math]
\sum\mathbf{F}=m\mathbf{a}_{cm} [/math]. These forces can be applied to any point on the body.
>Can you apply this law in a point that is not the ICR (Instantaneous centre of rotation):
sum of Torques=angular aceleration*moment of inertia
You have to adjust for possible linear acceleration, but yes. The law becomes [math]
\sum\mathbf{T}=\mathbf{r}_{cm}\times\mathbf{a}_{cm}m+\mathbf{I\alpha} [/math] where the moment of inertia and ang. accel. are both about the center of mass. These torques must all computed from the same reference point, though this reference point doesn't matter.

[Anonymous No.11330538]

Guys can you please help.
I'm retarded.
I need to find the voltage across each resistor in an open circuit, using the supply voltage as the initial step

[Anonymous No.11330550]

>>11330538
Circuit

[Anonymous No.11330556]

How safe am I from coronavirus if I've ordered something from china in the past one month?
Is there also a need to disinfect the package? If so how should I go about doing it?

[Anonymous No.11330588]

>>11330538
>>11330550
Ohm's law and Kirchhoff's laws, sweetheart. This is a pretty simple circuit to solve. Refer to a circuits text if you are still confused.
>>11330556
Stop being a paranoid bitch. You're fine.

[Anonymous No.11330605]

>>11330538
>>11330550
Ohm's law and Kirchhoff's laws, sweetheart. This is a pretty simple circuit to solve. For each loop, assume there is a clockwise current i1, i2, i3. Because the sum of all currents into a node is zero, you know that the current thru the 3 kΩ is i1-i2, and the current thru the 3.93 kΩ is i2-i3. Now, sum the voltage drops around each loop and set to zero (because of conservation of energy). Recall that over a resistor, V=iR. So, you now have three equations for three unknown currents. Solve the system of equations. You now know the current at any point in the circuit and may find the voltage over whatever two points you like. Refer to a circuits text if you are still confused.
>>11330556
Stop being a paranoid bitch. You're fine.

[Anonymous No.11330666]

>>11330605
I've worked out i at the supply voltage by Rtotal for the first loop, but I'm not sure where to go from here.

[Anonymous No.11330671]

>>11330666
>Rtotal
No need to compute this. Just do what I said. The method I told you is the easiest and most straightforward way. I strongly suggest looking at your textbook.

[Anonymous No.11330712]

>>11330671
I'm looking at it, but it's not helping

[Anonymous No.11330716]

>>11330712
Please dont make me straight up solve this for you
https://courses.engr.illinois.edu/ece110/fa2019/content/courseNotes/files/?KirchhoffsCircuitLaws

[Anonymous No.11330734]

really stupid question
what decides whether an alcohol will oxidize to an aldehyde/ketone instead of co2+h2o?

[Anonymous No.11330784]

>>11330716
That link has only served to confuse me even more as it's different to what my textbook is saying.

[Anonymous No.11330789]

>>11330784
perhaps you should consider a different major

[Anonymous No.11330833]

>>11330789
My major isn't electronics.
I only have this for 2 semesters, thankfully.

[Anonymous No.11330866]

>>11330734
C-O bonds are easy to oxidize (pi bonds are easy to form and break)
C-C bonds are very hard to oxidiatively cleave (sigma bonds are usually harder to form/break) and require fire

[Anonymous No.11330878]

why do most of explosives have nitrogen?
why putting in fire some nitroglycerine will make it explode?

[Anonymous No.11330890]

>>11330878
nitrogen-nitrogen triple bonds have hilarious amount of energy

[Anonymous No.11330903]

>>11330890
so when those bonds break they release a ton of energy, ok. but why do these bonds break in the first place, if they are so strong?

[Anonymous No.11330920]

>>11330903
strong bonds do not correlate with high energy bonds, quite the opposite actually. The question you should be asking is why those bonds form and are relatively stable in the first place

[Anonymous No.11330975]

How do I show that [math]F:x\mapsto \int_0^{a(x)}f(t,x)dt[/math] is differentiable where [math]f[/math] and [math]a[/math] are both differentiable?

[Anonymous No.11330986]

>>11330975
Apply the fundamental theorem of calculus and differentiable functions being closed under composition.

[Anonymous No.11330997]

Has anyone used Stix2 with XeLaTeX? What commands have you added to your preamble to make it work?

[Anonymous No.11331022]

How much static electricity can one person hold?
And how can a person reach their maximum charge?

[Anonymous No.11331032]

>>11329155
I just started a chemistry class and my attention span is shit
Does anyone have any good resources for learning chemistry
I'm looking for passive, video game like apps or something to help me reinforce things

[Anonymous No.11331036]

>>11330529
>where the ang. accel. is about the center of mass.
How am i supposed to kwow this if the body is not spinning about the CM? should i divide a(about cm) projected in the tangent versor to the point of reference by the r(about cm)? wouldnt

[Anonymous No.11331094]

>>11331036
No matter the motion of a rigid body, you will be able to decompose its motion into the superposition (sum) of some purely rotational about the center of mass, and something purely translational. It's not easy in general. That's why you learn about instantaneous centers.
>should i divide a(about cm) projected in the tangent versor to the point of reference by the r(about cm)?
I think that works. You just have to be very careful about what frame your vectors are in. Remember that [math]\mathbf{a}=\alpha\times\mathbf{r}+\omega\times\omega\times\mathbf{r} [/math]
simple lol
>>11331022
Its complicated
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4241473/#s0005title
>>11331032
>I'm looking for passive
Not gonna make it

[Anonymous No.11331106]

>>11329155
My estimate was 1/3 for Calc 1, 1/5 Calc 2, 1/8 Calc 3, 1/10 Differential Equations.
>>11331032
You really really aren’t gonna make it. But, in the interest of preventing you from contributing to the student debt crisis Organic Chemistry Tutor on YouTube is quite servicable for Gen Chem and for O-chem.

[Anonymous No.11331120]

I'm given this, the only thing I know is that u_n is a positive sequence. I have to prove that u_n is convergent and its limit is 1. How would I do it? I know that from the inequality I get that it's bounded, but I'm not sure how to prove that u_n is increasing and find its limit

[Anonymous No.11331143]

>>11331106
I'm already aware of all the learning resources out there
I'm looking for something that will give me random problems to solve. Something I can mindlessly do for hours

[Anonymous No.11331149]

>>11331120
[math]u_n^2 - 2u_n +1 < \frac{1}{n} \iff (u_n-1)^2 < \frac{1}{n} \iff |u_n| < \frac{1}{\sqrt{n}}+1 \rightarrow 1[/math].

[Anonymous No.11331160]

>>11331120
Take limits to infinity on both sides of the inequality to get
[math]lim_{n \rightarrow \infty} u_n + \frac{1}{u_n} \leq 2[/math].
But [math]u_n + \frac{1}{u_n} \geq 2[/math] for [math]u_n \geq 0[/math]
>>11331149
Nice solution.

[Anonymous No.11331164]

>>11331120
[math]u_n = 1+d > 1, u_n + \frac{1}{u_n}= (1+d) + \frac{1}{1 + d} = \frac{d^2 + 2d + 2}{d+1}=2+\frac{d^2}{d+1}>2[/math]

[Anonymous No.11331168]

>>11331032
There's a shitload to learn. It helps to have an IRL example that's close to your heart, that you can draw inspiration from and brings context to your fundamentals.
Many chemists were either inspired by drugs, explosives, or pretty colors. Choose one.

[Anonymous No.11331183]

>>11331032
ngmi, but The Organic Chemistry Tutor saved my ass in both chemistry and physics

[Anonymous No.11331190]

>>11331168
I'm switching careers, I wanna study pharmacology

[Anonymous No.11331202]

>>11330975
Given [math]f[/math] AC in [math]x[/math] and [math]L^1[/math] in t, and [math]\alpha[/math] Lipschitz in [math]x[/math] and BV in [math]t[/math], the Riemann-Stieltjes integral [math]F: x\mapsto \int_E d\alpha_x(t) f(x,t)[/math] is differentiable in the weak sense on a Borel set [math]E\subset\mathbb{R}[/math]. This suffices to prove your statement.

[Anonymous No.11331261]

>>11331149
I'm not sure I get what happens in the last part, why is u_n in absolute value? doesn't the +1 come from (u_n - 1)^2? And the final part, why does u_n being less than 1 when n goes to infinity let me conclude that that's its limit?, and, sorry if these are nonsensical questions

[Anonymous No.11331305]

Any chemist/bio bros who can translate this for me?

[Anonymous No.11331322]

I can't fucking understand any proof of the fundamental theorem of calculus I've read. I'm never going to make it. Please help me to understand it.

[Anonymous No.11331328]

>>11331305
The first one is trans-2-butene, the second one is cis-2-butene.
I think it's just a trans joke.

[Anonymous No.11331344]

How small is epsilon when doing a proof? I'm doing one that involves using the floor function, and it's pretty easy, but that is if I assume that epsilon is less than 1, otherwise I have no idea if I have to split the cases or what. As epsilon is usually described to be greater than 0, but with no specified upper bound I don't know if I can do that

[Anonymous No.11331502]

>>11331261
Three different people replied.
At least be confused with all three answers, you lazy cunt.
>>11331322
The velocity at which the area under a curve grows is proportional to the height of the curve.
This is the basic intuition for the fundamental theorem. It genuinely can't be simplified further.
>>11331344
As small as you want.
If [math] \delta[/math] works for [math] \epsilon _1[/math] and [math]\epsilon _1 \leq \epsilon _2[/math], then [math]\delta[/math] also works for [math]\epsilon _2[/math].
You can also always do something like [math]\delta = min (f( \epsilon), g( \epsilon)[/math].

[Anonymous No.11331522]

>>11330605
I solved it now, with two different methods. The one you recommended takes 10x as long.

[Anonymous No.11331552]

>>11329272
>>>11320589(You)(Cross-thread)
Please someone resolve

I'll try to condense my stupid question

>is math easy if you know what to do?
>Is there a philosophical reason to be good at it?
>are humans who are good at math, smarter than normal people?

[Anonymous No.11331562]

>>11331322

what part don't you understand?

[Anonymous No.11331589]

>>11331502
fucking excellent explanation, not him and not confused about it but this still made my day
>>11331143
bruh that’s a textbook, download a textbook from libgen and have at it

[Anonymous No.11331621]

If [math]O^p(G)[/math] is the [math]p[/math]-residual subgroup of [math]G[/math] and [math]H \le G[/math], does it hold in general that [math]O^p(H) = O^p(G)\cap H[/math]? That [math]O^p(H)[/math] is contained by the intersection is easy to show, but what about the other inclusion?

[Anonymous No.11331632]

>>11331621
I'm looking through the definitions in wikipedia.
Does it hold if [math]H = O^p (G)[/math]?

[Anonymous No.11331662]

>>11331632
Suppose that was the case. If [math]|G| = ap^n, |H| = bp^m[/math], (gcd = 1 in both cases) then I think that would force [math]a=b, m=0[/math] so that [math]|H| = a[/math]. Now, in order to make the quotient a [math]p[/math]-group, we would then need to have [math]O^p(H) = H = H\cap O^p(G)[/math].

[Anonymous No.11331679]

>>11331662
Actually, I think this can be generalised to the case where [math]O^p(G) \le H \le G[/math], and that I will check when I wake up (unless someone else does it for me while I'm asleep).

[Anonymous No.11331681]

Can I pay a lab to analyze the composition of material like cops do with drugs? Is this a common service or does it charge both arms and both legs like those research chemical labs?

[Anonymous No.11331701]

>>11331662
Actually, I've thought about it a bit further.
Your conjecture seems to be equivalent to [math]O^p[/math] containing all elements that don't have order [math]p^k[/math], and [math]G \ O^p[/math] containing all elements that do.
Specifically, assume [math]a[/math] doesn't have order divisible by p. Then [math]O^p ( \langle a \rangle) = \langle a \rangle = O^p(G) \cap \langle a \rangle[/math], which implies [math]a \in O^p(G)[/math]
Similarly, assume [math]a \in G[/math] has order [math]p^k[/math]. Then [math]O^p ( \langle a \rangle ) = \{ e \} = O^p (G) \cap \langle a \rangle[/math]. Then, [math]a \notin O^p (G)[/math].
This all seems insanely strong, so it's probably false.

[Anonymous No.11331777]

What prevents us from just building a Farnsworth fusor where the inner electrode is just a lithium ball with a heat transfer fluid run through? Why avoid ions hitting the cage when you can make it into fuel?

[Anonymous No.11332029]

>>11331681
send it to your university some will do it for free

[Anonymous No.11332031]

>>11331094
>you will be able to decompose its motion into the superposition (sum) of some purely rotational about the center of mass, and something purely translational. It's not easy in general. That's why you learn about instantaneous centers.
what?? that makes no sense. what if the cener of mass is NOT where the thing is spinnig around. For instance a planet that is orbiting. the angular speed wont be around the center of mass, but on other point.

[Anonymous No.11332113]

>>11322605
For the same reason it gets more difficult to distinguish between colors as ambient light decreases. Our eyes are more geared towards perceiving differences between colors rather than their absolute hues. Despite each cone cell belonging to one of 3 types, each of which captures certain chunks of the visible spectrum (usually simplified as being red-, green- and blue-perceiving), these 3 signals, plus one from rod cells, for light intensity, are encoded by neurons in terms of differences between them. Or so it seems, at least. This encoding still hasn't been figured out yet, so this difference system (opponent process theory) is the best model so far. At any rate, your rationale makes some sense because cone cells can perceive intensity too, but the factor which defines which cone type is activated to begin with is the light's frequency, and not its magnitude. By that metric, red is closer to black, so to speak, than to white, as red means activation of some cone cells while black means no activation of any of them, so red on black doesn't pop out as much as red on white.

[Anonymous No.11332131]

I have two questions. The first is back in the day did they run tv shows/ads on a set schedule for specific episodes/ads? Like a certain re-run will always be ran the first wednesday of every month for a year?

Secondly, I'm not sure of the exact name, but when you're having a paranoid episode except the thing you're being paranoid about is actually true does your brain fire faster/work better?

Some background on that is that I was in a relationship and I would have these freakouts over little things like noticing extremely small details. I'd freakout and connect a bunch of things together while being absolutely sick to my stomach and find out they were talking to someone else. I only let it happen twice. There's a couple other situations like that, but looking back I felt my brain was on a whole nother level with the things it was noticing and connecting. I'm generally very ditzy.

[Anonymous No.11332198]

>>11332113
Oh yeah, this kind of assumes the 3 color receptors each are responsible to equally "sized" bands of the spectrum, and that they generate signals on the same scale, and generally have no bias, which isn't true, but the explanation still holds.

[Anonymous No.11332300]

>>11332113
> For the same reason it gets more difficult to distinguish between colors as ambient light decreases
Uh, no. The main reason that colour perception gets worse in low light is that cones are far less sensitive than rods. In low light, most of our perception is due to rods which don't distinguish colour.

[Anonymous No.11332348]

How can I become more introspective on math?
Help me re learn algebra in the :best way"

[Anonymous No.11332388]

When an uranium atom splits and sprays out a bunch of neutrons, is it really jumping straight from being one atom, to two atoms and a bunch of neutrons? Or are there intermediate steps to that process?

[Anonymous No.11332401]

Why does pair production happen? What about passing a high energy photon across a heavy nucleus causes it split into an electron and positron? It's not because the nuclear "unfreezes" the photon in time, does it?

[Anonymous No.11332463]

>>11332031
>what if the cener of mass is NOT where the thing is spinnig around
This cannot happen unless the Casimir [math]L^2[/math] is not an integral. Given the configuration space [math]Q[/math] as a homogeneous space under the Euclidean group [math]\mathbb{E}(3)[/math] of rigid body motions, the phase space [math]T^*Q[/math] can be identified with the adjoint Lie algebra [math]\mathfrak{e}^*(3)[/math] with a natural adjoint action of [math]\mathfrak{e}(3)[/math]. The generators of moments [math]p[/math] and angular moments [math]L[/math] span [math]\mathfrak{e}(3)[/math] with integrals [math]p^2,L\cdot p[/math] spanning [math]TS^2 \cong \mathbb{R}^2\times S^2\subset T^*Q[/math], on which the action of [math]\mathbb{E}(3) \cong \mathbb{R}^3 \times_{p^2,L\cdot p \text{ const.}} SO(3)[/math] decomposes. By modding out the translations we have a projection [math]TS^2 \xrightarrow{\pi} S^2[/math] with a distinguished point [math]p_0 \in S^2[/math] fixed by the [math]SO(3)[/math] action. The canonical projection [math]T^*Q\rightarrow Q[/math] then maps [math]p_0[/math] to the CoM.
>>11332401
Pair production is described by the QED scattering amplitude [math]\mathcal{M} = \int_M \operatorname{tr}(\psi^\dagger\not A^{-1}\psi)^2[/math]. Now QED is a [math]U(1)[/math] gauge theory on a spin 4-manifold [math]M[/math], where the spin [math]\operatorname{Spin}(1,3)[/math] and charge [math]U(1)[/math] symmetries constitutes the internal symmetries; since fermion bilinears of the form [math]\psi^\dagger\psi[/math] is invariant under [math]\operatorname{Spin}(1,3)[/math], and [math]\gamma A[/math] is invariant under [math]U(1)[/math], the pair production amplitude is not forbidden by symmetry. [math]\operatorname{tr}\psi^\dagger \not A^{-1}\psi[/math] (or anything involving a trace over an odd number of [math]\gamma[/math]'s) is forbidden by Furry's theorem, however, but its square isn't, so there is nothing in the theory that forces [math]\mathcal{M}=0[/math].

[Anonymous No.11332478]

>>11332300
Yeah, but light bouncing off a green surface will always have the same frequency, regardless of luminosity. The cone cells are able to identify a color so long as they're being activated even if at the lowest intensity, yet the difficulty in telling colors apart starts mounting up far before the green-sensitive cones cease being activated. It's because that particular information gets lost in the encoding.

[Anonymous No.11332510]

>>11329155
I am using lgbm for a binary classification problem

The problem is that for some reason my predicted probability is inverted resulting in a low AUC score of 0.09

I know that if I transform the probability with:
"1 - target" then it will work fine.

Does somebody knows why is lgbm behaving like this?

[Anonymous No.11332756]

>>11331701
Yeah, I think it is not true in general, not even if we take a subgroup between the residual subgroup and the whole group. However, it is sufficiently true for my purposes. Thanks!

[Anonymous No.11332978]

>>11329155

Why do my testicles smell so good?

[Anonymous No.11332985]

So, I'm a little lost on this one, I have to prove that g(x) is bounded. I can't use derivatives. I'm pretty certain that it's with the definition of limit to infinity and the boundedness theorem, but I'm not sure how to proceed.

[Anonymous No.11332986]

>>11332985
Did you figure out how small [math] f(x) [/math] might get?

[Anonymous No.11333000]

>>11332031
>what if the cener of mass is NOT where the thing is spinnig around
Then you need to use the method I briefly described. Read your textbook. I already got my A in rigid body dynamics.
>>11332978
that's nasty, babe. I don't doubt it though ;3

[Anonymous No.11333006]

>>11332986
I don't think so

[Anonymous No.11333015]

>>11332985
You're overcomplicating it. Look at the range of f, and think about how big e^x can be for numbers from that range.
You don't need any calculus concepts at all here.

[Anonymous No.11333035]

>>11332985
[math] -f(x) \leq 0 \implies e^{-f(x)} \leq e^0 [/math]

[Anonymous No.11333056]

>>11333035
Oh, didn't notice it was that simple. Thanks

[Anonymous No.11333561]

Is there a branch of mathematics that studies whether or not a function is invertible? Like whether an integral can be integrated, or a differential eq. solved for, or any log, root, quotient etc.?
Or whether a quintic equation has a solution - since we know some trivial quintics may have solutions - but not all?

[Anonymous No.11333627]

>>11333561
>Or whether a quintic equation has a solution - since we know some trivial quintics may have solutions - but not all?
Algebra, Galois theory.

[Anonymous No.11333632]

>>11332463
>>what if the cener of mass is NOT where the thing is spinnig around
>This cannot happen unless the Casimir L2 is not an integral. Given the configuration space Q as a homogeneous space under the Euclidean group E(3) of rigid body motions, the phase space T∗Q can be identified with the adjoint Lie algebra e∗(3) with a natural adjoint action of e(3). The generators of moments p and angular moments L span e(3) with integrals p2,L⋅p spanning TS2≅R2×S2⊂T∗Q, on which the action of E(3)≅R3×p2,L⋅p const.SO(3) decomposes. By modding out the translations we have a projection TS2πS2 with a distinguished point p0∈S2 fixed by the SO(3) action. The canonical projection T∗QQ then maps p0 to the CoM.
is that actually a thing or you are just schizo trolling? If the first what does it mean?

[Anonymous No.11333637]

>>11333627
Do those apply to logarithms, integrals, and inverse trig/hyperbolic functions?

[Anonymous No.11333659]

>>11333632
See http://www.mi-ras.ru/~snovikov/69.pdf..
I've shown in essence that if the rigid body rotates about any point other than its CoM then there will exist point masses with non-circular orbits. Constant [math]L^2[/math] defines a spherical space of orbits (e.g. on a great circle) so these point masses actually have changing [math]L^2[/math] whence it is not an integral of motion.

[Anonymous No.11333682]

>>11332463
> [math]TS^2 \cong R^2 \times S^2[/math]
In what sense?
[math]TS^2[/math] doesn't admit an everywhere non-zero section by the good ole hairy ball theorem.
[math]S^2 \times R^2[/math] admits the good ole constant [math](1, 0)[/math].

[Anonymous No.11333684]

>>11333659
yeah google search showed tha pdf as well.
> there will exist point masses with non-circular orbits
what does this even mean?
So what you are saying is that it is impossible to have a pure roatation of a rigid body around anything that is not its CoM or what?

[Anonymous No.11333690]

>>11332463
>>11333682
btw are you two physicists? that gibberish seems difficult and barely useful IRL

[Anonymous No.11333692]

>>11333682
>In what sense?
The local sense. The trivialization is constructed locally from the level sets of the integrals, I was just sloppy with notation.

[Anonymous No.11333699]

>>11333690
Nah.
>>11333692
Ah, thanks.
I can't really follow the physics, so I usually start getting concerned when I see weird stuff in the maths.

[Anonymous No.11333709]

holy FUCK I fucking hate chegg, studoc, coursehero and all these fucking websites

FUCK YOU AND FUCK CAPITALISM

[Anonymous No.11333719]

>>11333684
So what I have been saying, again and again, is that as soon as [math]L^2[/math] is an integral of motion, there exists a point, called the CoM, in the object such that every other point rotates about it under rigid body rotation. This will happen whenever the motion is free.

[Anonymous No.11333731]

>>11333719
>L2 is an integral of motion
what even is that? i am a freshman
>This will happen whenever the motion is free.
yes that was my point. if i make a solid body atached to a rope tied to a naild, the it wont rotate about the cm right?

[Anonymous No.11333738]

>>11333731
>the it wont rotate about the cm right
Yes, the point is that you HAVE to force the object to rotate about some other point, that's what being non-free means.

[Anonymous No.11333741]

>>11333738
well yes. that is pretty trivial man

[Anonymous No.11333750]

>>11333741
Except the "necessary" direction isn't, and it's this misunderstanding that led to you to ask your original question.

[Anonymous No.11333761]

Does printed version of Science magazine exist?

[Anonymous No.11333884]

>>11333750
>the "necessary" direction isn't,
what does this even mean again?

[Anonymous No.11333924]

>>11333709
A fool and his money are easily parted.
Let them feed the wolves in our stead.

[Anonymous No.11333933]

Which branch of physics is the most well funded?

[Anonymous No.11333965]

How big of a deal is a bad grade in an unimportant course for GPA reasons? I think I'm going to fail public speaking

[Anonymous No.11333968]

>>11333965
Obviously depends on its weight and so on.

[Anonymous No.11333973]

>>11333007
>>11333204
?

[Anonymous No.11334341]

No (You)s in /mg/ so here

I'm trying to parametrize the conic C:(XY+YZ+XZ=0) in the real projective plane by a change of coordinates which takes points from the real projective line (φ:P1(R)->C⊂P2(R)). I found projectivities for Y^2=XZ, and X^2+Y^2=Z^2, some of the other standard forms for nondegen conics, but I cant find a map for this one.

[Anonymous No.11334438]

>>11334341
[math]\phi (X, Y) = (P(X, Y), Q(X, Y), R(X, Y))[/math].
Assume P(X, Y), G(X, Y) and R(X, Y) are all homogenous of degree one, set up the system of equations associated to the coefficients of [math]PG
+GR+RP=0[/math], and you should be done.
>degree one?
Yeah.
If it doesn't work, try degree two or something. Just remember they all need to have the same degree or the equation has no solution.
>inb4 this solution is retarded
Definitely better than wild guessing.

[Anonymous No.11334456]

Is there any difference between mathematical physics done in the mathematics department and mathematical physics done in the physics department?

[Anonymous No.11334568]

>>11334438
Thanks that helps. I could probably use a 3x3 natrix then right?

[Anonymous No.11334570]

>>11334568
*matrix

[Anonymous No.11334573]

>>11334568
>3 by 3
I don't think so, no. There should be quite some liberty, because there are more variables than equations.

[Anonymous No.11334636]

>>11334456
Well, the former exists for one.

[Anonymous No.11334810]

>>11329155
How do I find the function for this series (pic)?
I tried integrating but the c value is not constant after the second integration
What am I doing wrong?

[Anonymous No.11334823]

what does freezing a hydrated substance look like on a molecular level? like a juicy fruit or a dessicant packet. does water freeze at the same temp or is it varied? how do the crystals form, do they take a different shape? what even defines a solid in that sense if the liquid water is immmoble and stationary within the substance anyway?

i left some mixed greens in the freezer and when i took them out the greens seemed flattened out, like ice crystals thrashed the cellulose structure and then it turned to goop when the crystals remelted

[Anonymous No.11334824]

i dont understand what a non orientable surface is, can someone explain? why is the mobius strip non orientable?

[Anonymous No.11334854]

[math]\sqrt{x^2-1}[/math]
[math]\sqrt{x^2+1}[/math]
What are these functions called, and why do they show up so often?
Physically, what do they represent?

[Anonymous No.11334884]

>>11334824
You need a globally-defined top-degree form, or a section of the normal bundle, that does not change sign for orientability. The Mobius strip isn't orientable because locally defined normal vectors must invert as you move (in a loop) once around the Mobius strip.
>>11334854
Try putting [math]x = \sin\theta[/math] in the first function and [math]x=\tan\theta[/math] in the second.

[Anonymous No.11334895]

>>11334884
So, [math]cos \theta[/math] and [math]sec \theta[/math], respecitively?
I'm familiar with cosine in nature, but where does secant appear?

[Anonymous No.11334909]

>>11334810
your reasoning is a bit off, the way I would do it:

[math]f(x) = c_2x^2 + c_1x + c_0[/math]

[math]f''(x) = 2[/math] so [math]c_2 = \frac{2}{2!} = 1[/math] (factorial is from successive integrations)

subtract [math]c_2x^2 = x^2[/math] from your terms to obtain [math]c_1x + c_0[/math]: [ 4, 6, 8, ... ] and you can now solve for [math]c_1[/math] in a similar manner. Ultimately you get [math]x^2 + 2x + 2[/math]

I wrote it this way to make it clear that this works for any size of polynomial (provided you have enough terms)

[Anonymous No.11334921]

>>11334895
I remember my little sister asked me this once.
Anyhow, this is for cosecant. It equals the inverse of the sine by triangle similarity (proof: stareat the drawing).
Secant is the same but sideways.

[Anonymous No.11334922]

>>11334884
that doesnt make any sense you wacky anime poster. try again in normal speak

[Anonymous No.11334927]

>>11334922
That's actually normal speak, in this case.
The thing about normal vectors rotating is depicted in wikipedia with the crab gif.
https://en.wikipedia.org/wiki/Orientability

[Anonymous No.11334946]

>>11334909
I have no idea what you just said
Can you please provide a step by step solution for both f' and f'' or a link for integrating with your method?
thank you

[Anonymous No.11334947]

/sci/sqt/ + /mg/ and the other less popular but hard science generals deserve their own board

alternatively, move all psychology, IQ, climatology and human genetics stuff to another board and ban shitposters harder

[Anonymous No.11334956]

>>11334946
I forgot to add
Isn't the derivative of f'' supposed to be f' for the family of series?
Because the derivative of x2+2x+2 gives me 2x+2 which doesn't satisfy the series in f'

[Anonymous No.11334983]

>>11334927
thats confusing its requiring excess information about rotation. so the thing while moving flips eh? cant you just specify which run its on, like add 4 vectors instead of 2 normal vectors to give it flippy ideation

[Anonymous No.11335012]

>>11334946
>>11334956

It's not an integration method, it is simply inferring a polynomial from a discrete set of values, something firmly in the realm of just algebra, though you might use reasoning from calculus to accomplish it. Taking the successive differences does *not* immediately give you the values of the derivative, it may vary by a constant as you recognize. Your problem is that when you integrate [math]2[/math] and get [math]2x + C[/math], you try to infer C from [math]f'(1) = 5 = 2(1) + C[/math], but again, the successive differences of the original sequence [5, 7, 9, 11, ...] does not necessarily correspond to [f'(1), f'(2), ...].

What I tried to express was that the way to adjust the values by the necessary constant would be to instead take the [math]x^2[/math] term that you have already inferred and subtract it from the initial values. Comprehensive step by step:

[math]f''(x) = 2[/math] from the fact that the successive differences taken twice results in all 2s.
[math]f'(x) = 2x + c_1[/math] integrating above
[math]f(x) = x^2 + c_1x + c_0[/math] integrating above
let [math]g(x) = c_1x + c_0 = f(x) - x^2[/math]
[math]g(1) = f(1) - 1^2 = 4; g(2) = 6; g(3) = 8 ...[/math]
[math]g'(x) = 2[/math] from the fact that the successive differences take once results in all 2s (same as first step)
[math]g'(x) = 2x + c_0[/math] integrating above
[math]f(x) = x^2 + 2x + c_0[/math]
[math]f(x) = x^2 + 2x + 1[/math]

[Anonymous No.11335031]

>>11334983
Your reply is honestly unreadable.
Do you know what's an orientation in a vector space?
We can explain the rest if you know that much.

[Anonymous No.11335245]

>>11335012
Thank you, now I get it
>x2+2x+1
>the successive differences of the original sequence [5, 7, 9, 11, ...] does not necessarily correspond to [f'(1), f'(2), ...].
Does this mean the sequence of a series of that kind should be the same in every point (value) and the last "c" may change depending on the chosen set of numbers?

[Anonymous No.11335407]

Attractive forces between particles can be imagined in a simplified way, where it occurs as the result of virtual particles with negative mass causing a "pull" rather than a "push" to what they collide with. My question is, what situations does this simplification specifically fail to explain?

[Anonymous No.11335411]

>>11334895
sqrt(tan^2(x)+1)=sec(x)

[Anonymous No.11335431]

>>11329155

Why does my gf enjoy roleplaying as an underage little girl when we have sex?

[Anonymous No.11335436]

>>11335431
Because it brings balance to her psyche. Everything we perceive must evoke a reaction from us in some way, else causality is violated.

[Anonymous No.11335442]

>>11335436

I don't get it, how does that bring balance to her psyche?

[Anonymous No.11335471]

>>11335407
First of all that's not what "virtual particle" means. Virtual particles are just particles with off-shell momenta, which does [math]not[/math] at all imply negative mass.
Second of all that's one of the worst interpretations of an attractive potential I've ever seen. If [math]H[/math] is the Hamiltonian describing the dynamics of a particle with negative mass then it's no longer globally positive-definite and gapless points appear. These gapless/level-crossing points denote regions in parameter space where the spectral theorem fails, so you don't have a global Fock representation. Best you can do here is get a Fock space on each connected patch (i.e. local trivialization of the vector bundle of Fock states) with unitary transition functions between them. This introduces the possibility of the appearance of topological defects at the gapless points which were [math]not[/math] present in the original potential.
Of course if you ignore these considerations and just fractionalize the potential then you'll get the same effective interaction back. The problem here is the "multi-valuedness" of the vacuum sector due to the topological defects introduced. A globally-defined cyclic symmetric vacuum is an axiom of QFT that is necessary for the boundedness and definiteness of the number operator, so fractionalization may lead to you not being even able to (globally) count how many particles you have, which is stupid when the original potential isn't itself topological.

[Anonymous No.11335483]

is Beetlejuice okay?

[Anonymous No.11335543]

>>11334854
> why do they show up so often?
Pythagoras.

z^2=x^2+y^2
=> z = sqrt(x^2+y^2)
= sqrt(x^2+(y/x)^2*x^2)
= sqrt(x^2*(1+(y/x)^2))
= x*sqrt(1+(y/x)^2)
=> z/x = sqrt(1+(y/x)^2)
=> z' = sqrt(1+x'^2)
IOW, it's Pythagoras with the common scale factor cancelled out. z^2=x^2+y^2 => (k*z)^2=(k*x)^2+(k*y)^2.

The other one is the same but solving for one of the perpendicular edges rather than the hypotenuse.

They show up in trigonometry as:
sin = sqrt(1-cos^2)
cos = sqrt(1-sin^2)
sec = sqrt(1+tan^2)
csc = sqrt(1+cot^2)
https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Pythagorean_identities

[Anonymous No.11335628]

Does the vacuum inside of an extremely tiny box have extremely uncertain amount of energy?

[Anonymous No.11335698]

S = (1 2 3)(6 8 4)(9 5 7). Show that there is a cycle C and integer k such that S = C^k.

Not sure how to do this. I rewrote S as 2-cycles but this didn't help

[Anonymous No.11335800]

>>11333761
I still don't know. And how can I get it?

[Anonymous No.11336504]

Hello, anyone know any good problem books for organic chemistry?
Mainly undergraduate level.

[Anonymous No.11336505]

is this formula right? how can those be equal if ?

[Anonymous No.11336509]

>>11336505
[math](a-b)^2 = a^2 + b^2 - 2ab[/math]

[Anonymous No.11336514]

>>11336509
>>11336505
becacuse [math]\sum x_i\bar{x}=0 [/math]

[Anonymous No.11336540]

>>11329155
Is it correct if I say an intra-comparison is when I, for example see the difference of a variable for a single piece of tissue with or without treatment.

While an inter-comparison is when I see the difference with a control piece of tissue and a treated piece of tissue.

Can I use these two terms in this way? Regarding intra and inter?

[Anonymous No.11336554]

>>11336514
Wrong, retard. Think before you post.

[Anonymous No.11336588]

>>11331552
>6days and no reply
Are you guys scared because im questioning the Status quo?

[Anonymous No.11336755]

Hello I'm trying to get ready for a calculus 2 test. This is the first math class I've taken in almost 20 years

how are they finding c here?
finding y-average is easy, but how to solve for x when 4/pi = 2 sin x - sin 2x? my first instinct would to be to use my calculator's trace button on the graph, but I can't get it as exact as they did

[Anonymous No.11336845]

>>11334947
>/sci/sqt
You mean the homework thread?
>/mg/
You mean the homework and discuss Yukariposter thread?
>>11335698
C=(1 6 9 2 8 5 3 4 7), and C^3=S.
Understanding why this works is left to the reader as an exercise.
>>11336755
Probably Newton's method.

[Anonymous No.11336995]

/sci, help me with this basic probability problem. I roll a die three times and I want to know the probability of getting exactly a single one. The order doesn't matter. I thought it was (1/6)(5/6)(5/6) = 25/216. But according to the answers, it should be 75/216. What am I doing wrong?

[Anonymous No.11337008]

>>11336845
>Newton's method
perfect, thanks

[Anonymous No.11337035]

>>11336995
>(1/6)(5/6)(5/6) = 25/216
25/216 would be the odds of rolling a one on the first die only, hun. If you are looking for a single one, but it can be on any die, it would be 3*(1/6)(2/6)(3/6)=75/216.
>>11336588
>>11331552
>Are you guys scared because im questioning the Status quo?
No, it's probably more the fact that you come across as a sophmoronic tryhard. You aren't challenging anything or anyone. But here's a (You).
>is math easy if you know what to do?
Math is easier if you know what to do, just like fucking everything in existence.
>Is there a philosophical reason to be good at it?
There are many, many reasons to learn mathematics. I'm certain that at least one of those is a philosophical reason.
>are humans who are good at math, smarter than normal people?
People who are good at math are normal people, for the most part.

[Anonymous No.11337047]

>>11336995
its 25/72

[Anonymous No.11337056]

>>11337035
> 3*(1/6)(2/6)(3/6)=75/216
3*(1/6)*(5/6)*(5/6)=75/216

There's a (1/6)*(5/6)*(5/6)=25/216 chance of getting a one on the first die only (first=one, second=non-one, third=non-one), the same for the second die only, the same for the third die only. The three cases are mutually exclusive so add their individual probabilities to get 3*25/216=75/216.

[Anonymous No.11337059]

>>11337035
i was not trying to be a tryhard, i was just genuinely curious
but at last I had to write something provoking so that i get a reply

[Anonymous No.11337067]

>>11337059
I think science and math is more thought provoking than circlejerking about muh intelligence.
>>11337056
Thanks for helping confirm what I already typed.

[Anonymous No.11337135]

given two commutative linear maps A and B over the complex numbers, how do you show that they must have at least one common eigenvector and can you construct such a vector?

[Anonymous No.11337268]

How do I show that [math]h:(x,y)\mapsto \int_0^y\frac{\partial f}{\partial x}(x,t)dt[/math] is continuous when [math]f[/math] is of class [math]C^1[/math]?

[Anonymous No.11337299]

>>11337268
>when f is of class C1
Feels like this should be continuous in y even if the integrand isn't even continuous

Anyway, what's the point of considering ∂f/∂x instead of a general function?

[Anonymous No.11337326]

>>11337299
You are right, you can replace the partial derivative with any continuous function of x and t. I wrote that because i'm already deep inside an exercise wher h is already a partial derivative. Anyway, I think my statement is true but can't prove it.

[Anonymous No.11337359]

>>11337268
Consider some closed ball centered on zero that contains [math](x, y)[/math] and [math](x, y)+ \epsilon[/math]. This means it also contains the domain of the integral.
Since the derivative is continuous, it's uniformly continuous inside the closed ball, so you can do some simple comparisons on the two values of h(x, y).

[Anonymous No.11337687]

>>11335411
>>11335543
So if they're only physically relevant when you reduce them to [math]cos\theta[/math] and [math]sec\theta[/math], why not just write them like that?

[Anonymous No.11337692]

>>11337687
Because of the small angle approximation

[Anonymous No.11337703]

>>11336504
Pick your favorite pharmaceutical, propose a synthesis, then go on WIPO/patent search and see how the industry does it.

[Anonymous No.11337711]

When an antenna is physically too short or long, compared to the target frequency's wavelength, it's considered "capacitive" and "inductive," respectively. If you don't match the complex impedences to your reciever, screwy things happen.

When a wavefunction is observed, is any effort made to match the probe's impedence to that of the wavefunction?

[Anonymous No.11337719]

Hey guys. I'm currently working on how to separate p points in n dimensionsional space into n groups. Say, i have 1000 points in 3D space, so each group should have 333 points (the last one 334) and i'm using a hyperplane represented by a normal vector (set in Origin) to do the separation(as the dot product is computationally cheap).

My problem now is how to update the normal vector in a way, which is usable in every dimension. I more or less use perceptron learning rule to do this, but maybe there is a better way, as this is for now not reliable enough.

[Anonymous No.11338042]

If 8! = 8*7*6*5*4*3*2*1
what would be the sign for
8+7+6+5+4+3+2+1
?

[Anonymous No.11338062]

>>11338042
sum, retard

[Anonymous No.11338139]

>>11338042
I'm going to suggest a new notation.
[eqn] \displaystyle\sum_{k=1}^8 k [/eqn]
It's out-there, but I'm sure if you explain it before, then you shouldn't have any problems.

[Anonymous No.11338196]

>>11338139

>not also cluing him in that there's a capital letter pi which is used for certain things

>not cluing him in on the sign (8(8+1))/2

rude tbqh

[Anonymous No.11338227]

>>11329155
Ya'll are familiar with GDB I'm guessing right?

I'm used to debugging in a general sense, but am relatively new to gdb. HOW THE FUCK DO YOU GET IT TO ACTUALLY DEBUG?

It just keeps printing the fucking hex value at each breakpoint. If I set breakpoint to main, hex. Next line? Hex. It doesn't trace the code at all.

How can I get this piece of shit to actually display the line of code it is tracing? The hex is neat and all but I'm trying to practice some hacking challenges and need to know the context with what I'm working with.

On an additional note, any reason why setting the breakpoint to buffer would trigger a segmentation fault? The buffer is clearly called in the code correctly (as I can execute the program okay, and do various means of testing what is in the buffer). I figure this is probably related to the issue of GDB not tracing the code, so it has no idea when buffer is called.

I already made sure that the directory of both the c code and compiled code are included in GDB. I compiled both in the same directory with the same name, so have no idea wtf is causing this weirdness.

[Anonymous No.11338236]

>>11338227
Think I might've just figured it out.

The absolute numbskull who created this tutorial didn't include the -g flag. Every other tutorial for this challenge has it. That explains a lot.

[Anonymous No.11338255]

>>11338227
>any reason why setting the breakpoint to buffer would trigger a segmentation fault?

Did you redirect code execution to the buffer? If you did so successfully (eip points to location of the buffer on the stack) but there isn't valid code in the buffer, you'll get a segfault. Also, check out phoenix challenges from https://exploit.education/

[Anonymous No.11338301]

Have the figured out what is up with Lithium 7 yet?

[Anonymous No.11338323]

>>11338255
I'm not sure. I'm pretty new to this.

I'm working on a Buffer Overflow challenge. I have gotten the address where ebp is read into, the return address, and can compile everything without error and run without seg fault.

However...my program is returning normally. I'm obviously trying to return as root. Clearly something is up with my entry point to the malicious code. Any idea what I could be fucking up, or how to find it?

[Anonymous No.11338328]

>>11338323
To help clarify what I mean, here are a few examples of people doing similar problems online.

In both cases, they do not explain where the underlined values are coming from. Clearly that's where the issue lies, because I can inject the code without issue now. My attack command is the issue.

[Anonymous No.11338405]

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 92 students in the school. There are 36 in the Spanish class, 33 in the French class, and 22 in the German class. There are 12 students that in both Spanish and French, 5 are in both Spanish and German, and 8 are in both French and German. In addition, there are 2 students taking all 3 classes.
If one student is chosen randomly, what is the probability that he or she is taking at least one language class?

I got the answer for this .739

Now for this question: If two students are chosen randomly, what is the probability that neither of them is taking a language class?

Why is the answer not 1-.739 * 1-.739

help me

[Anonymous No.11338413]

>>11338405
wait nvm i got it, i forgot to subtract 1 after doing the first one

24/92 * 23/91 not 24/92 * 24/92 oops

[Anonymous No.11338426]

>>11337135
help anons i suck at linear algebra

[Anonymous No.11338597]

I ask again. Does a printed version of Scicence magazine exist? And how to get it?

[Anonymous No.11338888]

[math]e^x^2-x-1=0[/math]
How do I find these roots? I know 0 but Wolfram doesn't help for the second one.

[Anonymous No.11338936]

>Assume that x is an int variable. Write a statement that assigns the value 24 to x.
Teacher never told me. Book doesn't tell me. Only resources don't tell me. How the fuck do I do this? It's an Intro to C++ class and I know nothing about programming.

[Anonymous No.11338939]

>>11338936
>Only resources
online resources

[Anonymous No.11338949]

>>11338936
x=24;

I hope you are trolling.

[Anonymous No.11338956]

>>11338949
Ah, thank you. I wasn't trolling.

[Anonymous No.11338966]

>>11338597
>>11333761
>For a print issue of Science, please visit the Single Issue Online Store
https://www.sciencemag.org/members/order-article-or-issue
>>11338888
With a numerical method like Newton's. Use Desmos.
>>11338936
x=24

[Anonymous No.11338976]

>>11338888
>>11338966
Ok I clarify my question. Is there a way to know how many roots I would have to expect from it even without computing them? It's something from a test so I can't use Desmos.

[Anonymous No.11339257]

Are there any good videos/apps where I can practice and relearn basic elementary math?I've been a math brainlet my whole life and I want to make a change.

[Anonymous No.11339289]

>>11339257
khan academy

[Anonymous No.11339384]

>>11338328
Bump
Anyone? Figure at least someone on 4chan of all places has done Buffer Overflow attacks.

[Anonymous No.11339611]

>>11337719
Elaborate.
Are you doing something like chosing a vector [math]v[/math] and separating your points between the half-spaces [math]\langle v, x \rangle \geq \alpha[/math] and [math]\langle v, x \rangle < \alpha[/math]?
>>11338227
>>11338323
>>11339384
Try >>>/g/sqt or >>>/wsr/
>>11338976
No, unless it's a polynomial.
What you can do, tho, is give upper and lower bounds on the number of zeroes.
If you find a point whose value is zero, then for any other point to also have the value zero, the derivative needs to zero in between them (this is Rolle's theorem.) You can also take derivatives and consider where the function is increasing or decreasing to obtain these upper bounds (i.e. if the function is positive at a, and the derivative is everywhere positivo on a's right, then there are no derivatives there, etc).
For lower bounds, you're basically stuck with Bolzano.

[Anonymous No.11339622]

What kinda math is required for mathematical physics. Is it just algebraic/differential geometry/topology?

[Anonymous No.11339659]

>>11339622
Required for what in mathematical physics?
If you just ask like that I'll hardly be able to resist shitposting you into learning quantum topos theory and abstract differential geometry (with applications to gauge theory).

[Anonymous No.11339672]

>>11339659
I was just hoping for some general advice, I'm not sure what I want to specialise in.

[Anonymous No.11339689]

>>11339672
Study PDEs, differential geometry and functional analysis.

[Anonymous No.11339726]

>>11338966
$15 for a magazine? Where I can find these magazines of past years cheaper?

[Anonymous No.11339730]

>>11339689
Is that all? I thought there was more to it.

[Anonymous No.11339731]

>>11339726
nigger, just pirate it like a normal person.

[Anonymous No.11339741]

>>11339730
>is that all
PDEs and DG are gargantuan subjects, anon.

[Anonymous No.11339750]

>>11337135
posting a new yomu to bump the question one last time

[Anonymous No.11339792]

>>11339741
I know, I've just seen other anons mentioning other subjects. Do you recommend any math textbooks for those subjects, I've only seen the Tenebaum Dover book recommended, but that's ODEs not PDEs. As for DG, I'll maybe get Do Carmo's book.

[Anonymous No.11339810]

>>11339792
>PDEs
Craig is extremely comfy. Evans is good too.
You'll eventually have to start just reading random books about elliptic equations, parabolic equations, finite difference methods, finite difference for elliptic equations, the transport equation, the heat kernel on manifolds, etc.
>DG
You can just pick it up from any graduate text in classical mechanics.
Alternatively, read Tu.
>functional analysis
Reed and Simon is recommended a lot for physicists.
Lax is also good.

[Anonymous No.11340439]

Has anyone literally tried Schroedinger’s cat experiment? What would happen if you tried it with a human?

[Anonymous No.11340441]

This isn't exactly math, it's more related to latex syntax. In pic related, how would I align the term "a" in the first equation with the "a" in the second equation. Here is the code i used:
\begin{align*}
S&=1+a+a^2+a^3+\dotsc+a^n\\
aS&=a+a^2+a^3+\dotsc+a^n+a^{n+1}\\
\end{align*}

[Anonymous No.11340446]

>>11340439
>Has anyone literally tried Schroedinger’s cat experiment
probably not
>What would happen if you tried it with a human?
potentially murder. I'm not sure what you think would happen.

[Anonymous No.11340459]

>>11340441
Like this?
[eqn]S = 1 + a[/eqn]
[eqn]\quad ~ aS = a + a^2[/eqn]

[Anonymous No.11340462]

>>11340459
Forgot eqn added half a kilometer in between them outside the Tex display.
[math]S = 1 + a[/math]
[math]\quad ~ aS = a + a^2[/math]

[Anonymous No.11340465]

>>11340441
I don't know how to use the align bullshit, but you can always use \ , \quad, \qquad, etc. for spaces

[Anonymous No.11340472]

>>11340459
No, I wanted both = aligned at the same time, with only the right-hand side of the bottom equation shifted to align. Something like pic related.

[Anonymous No.11340484]

>>11340472
[math]S ~ ~ = 1 + a[/math]
[math]aS = \quad ~ a + a^2[/math]
?

[Anonymous No.11340489]

>>11340484
Fuck, broke the other one.
[math]S ~ ~ = 1 + a[/math]
[math]aS = ~ ~ \quad ~ a + a^2[/math]

[Anonymous No.11340491]

>>11340484
Oh, how do you add the spaces there?

[Anonymous No.11340494]

>>11340491
Tip:
>rick click
>Show Math As...
>TeX Commands

[Anonymous No.11340503]

>>11340491
I'll be honest anon.
I've been helping you, but you just shouldn't do this.
It looks really stupid.

[Anonymous No.11340504]

>>11340494
Ok, thanks anons, I managed to align my stuff how I wanted!

[Anonymous No.11340537]

>>11340504
i'm probably being pedantic, but you can get a better alignment with

\begin{align*}
S & = 1+a+a^2+a^3+\dotsc+a^n \\
aS & = \hphantom{{} 1 {} + {}}a+a^2+a^3+\dotsc+a^n+a^{n+1}
\end{align*}

[Anonymous No.11340605]

Is this accurate?

[Anonymous No.11340608]

>>11340605
Yes, I'm 100% certain.

[Anonymous No.11340620]

>>11340608
How long have you been here?

[Anonymous No.11340624]

>>11340620
For like 9 years

[Anonymous No.11340631]

>>11340624
Ah, thanks.

[Anonymous No.11340955]

When throwed, a special coin has 40% chance of turning head and 60% of turning tails. How many times do you need to throw this coin so that the probability of getting head at least one time is 90% or higher?
Also how do I approach problems like this?

[Anonymous No.11340961]

I'm learning about lagrangian multipliers to solve constrained equality optimizations, like: [math]f(x, y) = -(x^2 + y^2)[/math] subject to [math]g(x, y) = x - y = 0[\math].

So, the answer is the set of points that satisfy both [math]\nabla f = \lambda \nabla g[\math] and the equality constraint. However, we also need to consider the critical points of [math]f[\math] that just so happen to fall into the constraint, right?

The things is, these points actually belong to [math]\nabla f = \lambda \nabla g[\math], since we can just take [math]\nabla = 0[\math]. So really, we are including them after all. But they wouldn't be considered at all if our equation was [math]\lambda \nabla f = \nabla g[\math]! So that's surprising to me, since it means that the fact that the lambda is on the RHS is somewhat important, since it sweeps under the rug a few corner cases.

Does that make sense? I haven't actually read this anywhere, so I'm looking for a little validation

[Anonymous No.11340979]

I'm learning about lagrangian multipliers to solve constrained equality optimizations, like: [math]f(x,y)=−(x^2+y^2)[/math] subject to [math]g(x, y) = x - y = 0[/math].

So, the answer is the set of points that satisfy both [math]\nabla f = \lambda \nabla g[/math] and the equality constraint. However, we also need to consider the critical points of [math]f[/math] that just so happen to fall into the constraint, right?

The things is, these points actually belong to [math]\nabla f = \lambda \nabla g[/math], since we can just take [math]\lambda= 0[/math]. So really, we are including them after all. But they wouldn't be considered at all if our equation was [math]\lambda \nabla f = \nabla g[/math]! So that's surprising to me, since it means that the fact that the lambda is on the RHS is somewhat important, since it sweeps under the rug a few corner cases.

Does that make sense? I haven't actually read this anywhere, so I'm looking for a little validation

[Anonymous No.11341034]

>>11340955
Look up geometry distributions, they should be useful.

I'll try to reason it out though.

A first step to make the problem easier is fixing the number of throws (which sounds random, but fixing variables can often be useful). So, ask yourself, what's the probability of getting heads at least once in K throws? That's way easier, right? Since it's one minus the probability of getting tails K times in a row.

So, you can start at K=1, calculate the probability of getting heads at least once, and then keep going with higher valued Ks until you hit 90%.

Maybe there's a more compact solution, but that's what I got.

[Anonymous No.11341057]

Do particle-antiparticle pairs arise from different quantum fields? For example, is there a "positron field" separate from the electron field, or do positrons come from excitations in the good old electron field? If the latter, what makes a positron excitation different from an electron excitation?

[Anonymous No.11341086]

>>11340979
>However, we also need to consider the critical points of [math]f[/math] that just so happen to fall into the constraint, right?
No, the intuition is backwards.
There is a function f, and it has a restriction to the constraint set. When the constraint set is nice, we can compute the critical points of the restriction of the function inside the constraint set, and some of these won't be critical points of the entire set.
Of course, if it's a critical point of the "entire" set where the function is originally defined, it's also a critical point of the constraint set.
The condition on the gradients basically translates to critical point inside the constraint, but the full explanation is long.
>>11340955
If the probability of getting at least one head is higher than 90%, the probability of getting no heads is smaller than 10%.

[Anonymous No.11341137]

>>11331552
>is math easy if you know what to do?
Things are hard until you learn them. Go figure. Also, "inventing new math" is just hard, you have to be smart, period.

>>are humans who are good at math, smarter than normal people?
Yes. At math.

>>11341086
I see. My confusion arised from the explanation that [math]\nabla f = \lambda \nabla g[/math] were the points where a contour line of f was tangent to a contour line of g. But I suppose that that was just a simplified intuition.

Thanks for answering!

[Anonymous No.11341156]

>>11341137
>Things are hard until you learn them. Go figure. Also, "inventing new math" is just hard, you have to be smart, period.
are you learning math anon? if yes for what job?

[Anonymous No.11341178]

>>11341057
No. Classical fermions are sections of a spinor bundle whose spin structure is inherited from irreps of the central extensions of [math]SO(1,3)[/math], which contains two copies of the conventional "spin" group [math]SU(2)[/math]. One copy is the "usual spin"/helicity sector, while the other is the "fictitious spin"/charge sector. The -1 eigenspace of the latter of which is spanned by precisely the antiparticles. Fermion fields as a section into the associated vector bundle automatically takes into account the two sectors.
In fact, if the fermion is in addition massless then we have a chiral operator [math]\gamma_5[/math] decomposing the charge sector; this is where Weyl fermions come from. This decoupling between the charge and spin sectors allows us to move spins around independently of its charge copy, which is why Weyl fermions are the ones responsible for the chiral anomaly.

[Anonymous No.11341202]

you guys know how to access encyclopedia Britannica for free? They have a nice article I want to read but I wont pay for only one use.

[Anonymous No.11341368]

>>11341202
>paying for snooty wikipedia

[Anonymous No.11341639]

is there an element w in *R s.t. 10^(-w)=0?
If so, is there an element a in *R satisfies 10^(-w-a)=-1? Is it a=1? If not, is it finite or infinite?

[Anonymous No.11342049]

I'm struggling hard with some brainlet analysis.
[math]\text{Let } f:\mathbb{R} \longrightarrow
\mathbb{R} \text{ be a function such that } f(x)\longrightarrow +\infty \text{ as } x \longrightarrow +\infty.\text{ show that }\frac{1}{f(x)} \longrightarrow 0 \text{ as } x \longrightarrow +\infty [/math]

[Anonymous No.11342152]

>>11342049
I think I have found a proof to this:
[math]\forall K \in \mathbb{R} \text{ and } \forall \epsilon > 0, \exists L \in \mathbb{R} \text{ such that } x > L \implies f(x) > K \text{ choosing K positive and manipulating gives } \frac{1}{K} > \frac{1}{f(x)} > 0 [/math]

[Anonymous No.11342712]

>>11329155
Can anyone advise what order I should study the different subjects of mathematics in?
I've been looking at the /sci/ wiki for book recommendations and whilst it has been quite helpful it doesn't seem to suggest an order you should approach the topics in.
For context, I didn't study mathematics at university and I want to expand my knowledge of it. I'm most interested in learning the "core" subjects (subjects which many other subjects depend on) and then potentially build from there in the future.

[Anonymous No.11342721]

>>11342712
Learn linear algebra and basic calculus first, then learn ODEs. From there you can do whatever you want.

[Anonymous No.11342731]

>>11342721
Perfect, thanks!

[Anonymous No.11342738]

>>11342049
Let e be an arbitrarily small real greater than 0

Let y = smallest natural in the image of f greater than e (one must exists because f goes to infinity)

Let x = f inverse (y)

y > 1/e
1/y < e
1/f(x) < e

Therefore 1/f(x) can be made arbitrarily small (hence it goes to 0)

[Anonymous No.11342819]

How does one get the abelianization of a monoid? There is no guarantee that the inverses exist, so what can one use as a replacement of the commutator subgroup?

[Anonymous No.11342990]

>>11342152
It's correct.
>>11342819
Remember that quotients aren't constructed with subgroups, they're constructed with relations.
So take the smallest equivalence relation such that [math]\Pi a_i \cong \Pi a_{ \sigma (i)}[/math] for [math] \sigma \in S^n[/math] , define multiplication on the equivalence classes, and check that it's well defined.

[Anonymous No.11343196]

I'm taking Ordinary Differential Equations. I'm confused over exact equations and homogeneous equations.
In my book they're both represented in differential form, [math]M\left(x,y\right)dx+N\left(x,y\right)dy=0[/math]

However, they have two very different methods of solution (proving exactness, integrating vs. using a substitution to yield a separable equation). So, being unable to correctly identify which is which is a death sentence.
What do I look for in an actual DE to tell the difference between the two?

[Anonymous No.11343267]

is this a legit proof of the angle bisector theorem?

[Anonymous No.11343366]

Hey guys could you please provide some guidance/direction. I'm writing up a lab for an electronics experiment. Created several circuits (open, short, loaded) and measured the voltage at all the resistors with a multimeter and then did separate calculations (using nodal analysis, Thevenin's, superposition, etc) to work out the voltage at the same resistors. The voltages are slightly different. Is there any good reading material out there that I can use to write up a good conclusion for exactly why this happened? Something that goes into good detail that I can reference.

[Anonymous No.11343379]

>>11343366
It could be related to loading on the power supply itself. Remember how a battery can be modeled as if it had an internal resistance? What are the effects of this internal resistance. If you did an absolute short, there is some other factors as well.

[Anonymous No.11343433]

What does this author mean? If we ignore y', none of the terms have any degrees in common

[Anonymous No.11343444]

>>11343196
Exact DEs can be homogeneous and vice versa, they aren't mutually exclusive. I typed up another post a while back that explains why we bother studying exact DEs. >>/sci/thread/S11250238#p11260811
>>11343267
>using calculus to prove elementary geometry
wat
just use law of sines https://en.wikipedia.org/wiki/Angle_bisector_theorem#Proof_1
>>11343366
>the voltages are slightly different
The theoretical voltage predicted by Kirchhoff, Thevin, superposition, etc. should all be exactly the same unless you are doing something wrong. If the experimental value is differing from that unique theoretical value, it's likely related to what this anon >>11343379 said. Also, remember that the resistors have pretty wide tolerances on them, usually like 5-10%, sometimes even up to 15% error from the color code value printed on their side. Lastly, it's a pretty tiny effect for what you are doing, but the resistance of a single resistor will definitely change with temperature and mechanical stress and all that.

[Anonymous No.11343453]

>>11343444
>>>/sci/thread/S11250238#p11260811

lol that was me too. I'm about a month into the course now so re-reading that post will offer a lot more insight.

[Anonymous No.11343454]

>>11343444
>just use law of sines https://en.wikipedia.org/wiki/Angle_bisector_theorem#Proof_1
i know there's simpler and more elegant ways, i'm trying to make my own proof for various theorems

[Anonymous No.11343480]

>>11343433
Yes they are. Tip: [math] x^2y [/math] would be degree 3, and so on. That is a terrible definition of homogeneous, though. A better one would be. "A DE is homogeneous if we can write it in the form [math] y'=f(y/x) [/math]."
>>11343453
Awh, hope you're doin good~ Did I asnwer your current question, though? Generally, the idea with homogeneous DEs is to get them in a form so that you can separate variables. With exact DEs that are also homogeneous, you can do the same.
>>11343454
I'm going to have to say "no, it's not a good proof." Using calculus to prove a result from very basic geometry is absurd. Also, the jump from the second to last line to the last does not follow at all.

[Anonymous No.11343483]

>>11343444
>The theoretical voltage predicted by Kirchhoff, Thevin, superposition, etc. should all be exactly the same unless you are doing something wrong. If the experimental value is differing from that unique theoretical value, it's likely related to what this anon
I mean that there are differences between the experimental and calculated results. We had to use different calculations methods for each circuit configuration. I'd really like some sources or reading, something I could reference rather than just blather my opinion.

[Anonymous No.11343490]

Should a lab report have both an abstract and introduction? Seems like they're both the same thing.

[Anonymous No.11343499]

>>11343366
>>11343379
>>11343444
I probably should have been more specific about my data, the voltage readings from the multimeter are all higher than the calculated results. By very small amounts like 0.04.

[Anonymous No.11343522]

>>11343483
>I'd really like some sources or reading
I'm not sure what kind of source you want for the part I said about tolerances. The tolerances are usually printed right on the resistor. You know the gold/silver band to the far right? That's what's there to tell you that there is a lot of wiggle room in the ohm'age.
>temperature
https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1049&context=ameslab_iscreports
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html
Also I know there's a bit about it in University Physics by Young
>stress
https://link.springer.com/content/pdf/10.1007%2FBF00866867.pdf
There's something called a gauge factor that relates the mechanical strain of the material to its resistivity.
But these two effects are small.
>internal resistance of battery/power source
Literally just your circuits textbook.

[Anonymous No.11343524]

>>11343480
>the jump from the second to last line to the last does not follow at all
the idea was that as long as i take the derivative of the new angle (θ + dθ) since i start with equilateral triangle at the bottom of recursion it will always be a = b, so i can always take the derivative of the new angle as long as the slope does not become parallel to any of the sides

[Anonymous No.11343527]

>>11343499
What's the percent error? If less than ~5% just call it a day. Resistors aren't precisely made. You are definitely going to have a least some small error. It's normal. Welcome to engineering.
>>11343490
Yes you should. They are different. Abstracts are much shorter and contain no background info.

[Anonymous No.11343529]

>>11343480
>>11343524
also it's a good way to exercise the principles in calculus by trying to apply it to things i already know, you don't have to bust my balls

[Anonymous No.11343537]

>>11343529
>you don't have to bust my balls
sorry~ but it still doesnt follow. A/B=C/D does NOT imply A=C, B=D

[Anonymous No.11343542]

>>11343537
yes, but i've chosen to start with isosceles triangle

[Anonymous No.11343553]

>>11343542
then you haven't proven anything

[Anonymous No.11343559]

>>11343553
but if the ratio remains unchanged for as many times the derivative as we want doesn't that prove it?

[Anonymous No.11343567]

>>11343559
What are you taking the derivative with respect to?

[Anonymous No.11343577]

>>11343527
>What's the percent error? If less than ~5% just call it a day. Resistors aren't precisely made. You are definitely going to have a least some small error. It's normal. Welcome to engineering
But how do I explain the discrepancy?

[Anonymous No.11343583]

>>11343577
Did you manually measure all the resistances of the resistors to find exact values first? If not, "My error is X%. This is an acceptable error because it is smaller than tolerance of the resistor as given by the manufacturer."

[Anonymous No.11343592]

>>11343583
Yes. Manually measured the voltage at each resistor using a multimeter. Afterwards, with the same supply voltage, used network theorems to calculate the voltage at the same resistors.

[Anonymous No.11343611]

>>11343567
i realize by my logic a=b after the derivation, which is wrong. i'm gonna have to think on this a little more.

[Anonymous No.11343615]

>>11343522
Thanks anon.

[Anonymous No.11343617]

>>11343592
>Manually measured the voltage at each resistor using a multimeter
No no no, did you manually measure the resistance? I dont think you did. There isnt much to explain.

[Anonymous No.11343624]

>>11343617
Oh no, we didn't measure resistance. Just used standard resistors of a certain rating. Sorry I'm half asleep.

[Anonymous No.11343627]

>>11343624
Yup. The rating is slightly wrong. That's the explanation. You have a trash prof if he didnt go over this.
>>11343615
You are so very welcome~

[Anonymous No.11343642]

>>11343627
>Yup. The rating is slightly wrong. That's the explanation. You have a trash prof if he didnt go over this.
The guy who did our labs isn't the same guy giving our electronics lectures. I'm studying mechanical engineering and we have to do 2 semesters of electronics, so I don't think they really care that much about us since they won't see us again.

[Anonymous No.11343656]

>>11343480
>Awh, hope you're doin good~
I'm a bit worried for diffeq. Usually unclear concepts just "made sense" when we went over them in other classes. It feels almost completely opaque, as much so as on the first day of the semester.
As far as answering my question, it's a bit of a "symptom, not the cause" kind of thing. I'm having a lot of trouble ascertaining what kind of ODE a given equation is, when it's just presented in a vacuum.
It's one thing to be able to identify a linear equation in the "Linear Equations" section of the textbook, but another when it's presented in all of its ugly algebraic glory with no guidance on an exam.

[Anonymous No.11343765]

>>11343656
DEs is hard because it is presented as a math class, but at the same time, there is no explicit, unambiguous way to even start the process of solving a DE, not to mention the fact that for an arbitrary ODE there is no such thing as an analytic solution. Just focus on the numerical part of the class (if they touch on that), because that's what actually matters. Solving a DE analytically is glorified guesswork, but teachers rarely want to admit it. Good luck, anon! Im here for help.

[Anonymous No.11343894]

>>11332510
help

[Anonymous No.11343931]

why do a polynomial of degree M be the unique polynomial to hit some list of M+1 points? aka why do two polynomials of degree M never intersect at more than more than M points?

[Anonymous No.11343936]

>>11343656
git gud at algebra and rearranging then, there are some archetypes and just learn what forms the archetypes may take

[Anonymous No.11343970]

>>11341639
No.
There's no real number, but there is a complex one.
>>11342152
Works.
>>11342819
Remember that quotients aren't constructed from subgroups. They're constructed from a relation built on top of the subgroup.
>>11343931
A polynomial of degree n has at most n roots, and the difference of any two polynomials of degree n has degree smaller or equal to n.

[Anonymous No.11343984]

>>11343970
>the difference of any two polynomials of degree n has degree smaller or equal to n.
ohhh
i fogot subtraction was a thing
fuufufufufufu

[Anonymous No.11344095]

>>11343970
>Remember that quotients aren't constructed from subgroups. They're constructed from a relation built on top of the subgroup.
Yes, and?

[Anonymous No.11344161]

>>11344095
I dunno.
Did you try setting up the relation [math]ab \cong ba [/math] or [math]\Pi a_i \cong \Pi a_{ \sigma (i )} [/math] for [math]\sigma \in S^n[/math] , taking the smallest equivalence relation containing either and checking if you can define the group operation on the equivalence classes?
Do I have to hold your hand throughout the entire construction?

[Anonymous No.11344291]

has/does anyone else feel like their masters thesis is complete shit? like - ive spent quite a few months now doing coarse graining and my models not even working yet and the eventual data analysis im going to do is very basic. spent most of the time asking phd students what the fuck errors mean

[Anonymous No.11344351]

Does the uncertainty principle mean that the energy of the vacuum will appear higher on average based on how closely it's measured?

[Anonymous No.11344419]

>>11329155
Hey im kinda stuck on an exercise from the first chapter of Rudin's analysis.

If im not mistaken its exercise 6 part b, in part a you do a small proof and define:

[eqn]b^r = (b^m)^{1/n}[/eqn]

For [math]r \in \mathbb{Q}[/math]

Then, the exercise im stuck with consists of proving that for any positive real number [math]b[/math] then:

[eqn]b^{r+s} = b^rb^s[/eqn]

With [math]r,s \in \mathbb{Q}[/math]

I've been doing a shit ton of proofs today and at this point im toast, some pointers would be very much appreciated.

[Anonymous No.11344430]

>>11344419
Im thinking that rudin is asking for a proof so it cant be as simple as saying:

Let [math]r = m/n[/math] and [math]s = p/q[/math]

So:

[eqn]b^{r+s} = b^{\frac{mq + np}{nq}} \\
= (b^{mq + np})^{1/nq} \\
= (b^{mq}b^{np})^{1/nq} \\
= (b^{mq})^{1/nq}(b^{np})^{1/nq} \\
= b^rb^s[/eqn]

If its just this ill an hero for sure.

[Anonymous No.11344535]

How does the weak nuclear force cause alpha decay and neutron decay?

[Anonymous No.11344648]

>>11343196
Let [math]y:x\mapsto y(x)\in \Omega[/math] describe a certain curve in a normed measure space [math](\Omega,\mu)[/math], the strongly continuous one-parameter unitary [math]U(x)\in\mathcal{U}(C^1(\Omega,\mathbb{R}))[/math] of translations along which is locally generated by a vector field [math]V_x\in T\Omega[/math] by Stone's. The equation [math]\frac{dy}{dx} = V_x(y)[/math] is the DE in question. Or, more generally, if [math]W\in T\mathbb{R}[/math] generates "time evolution" [math]V(x)\in\mathcal{U}(C^1(\mathbb{R}))[/math] then the DE can be written locally as [math]W(x) + V_x(y) = 0[/math], which interprets the curve as the zero locus of a certain vector field in [math]T(\Omega\times\mathbb{R})[/math].
Now when the 1-form [math]\omega_x \in T^*M[/math] dual to [math]V_x[/math] is exact for all [math]x\in \mathbb{R}[/math], the DE is said to be exact. Similarly, given the scaling operator [math]D_\lambda: y\mapsto \lambda y[/math], the DE is homogeneous if [math]D^*_\lambda V_x = \lambda^\alpha \cdot V_x[/math] for all [math]\lambda\in\mathbb{R}[/math] and some [math]\alpha \in \mathbb{Z}[/math]. In particular, if [math]\alpha = -1[/math] then [math]V_x[/math] descends to the projective space [math]P\Omega[/math] and we can consider the projection [math]\Omega \rightarrow P\Omega[/math] and solve the DE there.
>>11344291
Yes. My masters felt like pure grunt work. Was glad I got it published and the defense over with as soon as possible.
>>11344351
No.

[Anonymous No.11344771]

>>11344161
No.

[Anonymous No.11344904]

Ive used 3 different brands of sleep trackers for a month each now and each reports an average of 30 minutes deep sleep over 8 hours sleep, what kind of issues could this cause and how to fix it? Internet said you need 60-90 per night

[Anonymous No.11345178]

what does the random variable notation X = x translate to if you want to be 100% formal ?

[Anonymous No.11345510]

>>11329155
Could someone explain to me how this question works? When I saw the du/dy part of the formula I immediately went to integrating the τ though it doesn't appear to have had the result I was anticipating. Of course I know now that the objective is to find U (which I have no real unerstanding of how to do, there's the formula F = τA which I'm sure is relevant in some way). How do I progress? Do you know anywhere where I could find similar questions as there's only one question of this type on our learning board and I haven't had luck in finding others outside of the textbook which doesn't give answers.

[Anonymous No.11345660]

>>11345510
>assume the velocity varies linearly
This tells you that the fluid is Newtonian. What Newton noticed is that many fluids (at low Reynold's numbers, at least) satisfy the property that [math] \tau=\mu\frac{\partial u}{\partial y} [/math]. Now, we have a no-slip boundary condition. This means that the relative velocity between the water and the plates wherever they interface is zero. We can now say that
[eqn] \frac{\partial u}{\partial y}=\frac{\Delta u}{\Delta y}=\frac{u}{t} [/eqn]
where t is the thickness of the water between plates. [math]F=\tau A[/math] is correct. The middle plate isn't accelerating so the force applied to it is equal to the viscous force that opposes motion (keep in mind there are two interfaces with the viscous fluid). So:
[eqn] F=2F_{visc}=2\tau A=2\mu\frac{u}{t}A [/eqn]
Rearrange and plug in:
[eqn] u=\frac{Ft}{2\mu A}=\frac{0.02\times0.02}{2\times8\cdot10^{-4}\times0.2\times0.3}=4.167\ \text{ m/s} [/eqn]

>similar questions
Fluid Mechanics by White, 7th Ed. (2007):
>Ch. 1, ex. 1.7, pg. 29
>Ch. 1, prob. P1.38 through P1.61, starting on pg. 52

[Anonymous No.11345680]

>>11344904
Sleep trackers are often unreliable. If you don't feel like you're rotting from within, you're getting plenty of deep sleep.
IIRC in cases of sleep deprivation, deep sleep is vastly prioritized over REM, so if you're short on anything it should be REM.

[Anonymous No.11345828]

>>11344419
>i've been doing a shit ton of proofs today
>exercise 6
lol

[Anonymous No.11345903]

I don't get why q has to divide p^n, or how this is a contradiction.

[Anonymous No.11345914]

>>11344430
>>11344419
why u readin rudin if ur stuck on elem alg? are you in uni?

[Anonymous No.11345947]

>>11345903
[math] - p^n = a_{n-1} p^{n-1} q + \cdots + a_o q^n[/math]
q divides the right side, so it also divides the left side.
Filling in the gaps is left as an exercise to the reader's little sister, little brother or pet dog.

[Anonymous No.11345991]

>>11345828
>There is only 1 analysis book you can do proofs from
Retard

>>11345914
Did you read my post?

[Anonymous No.11345996]

>>11344430
It's literally just that.

[Anonymous No.11346273]

>>11345996
Thats a relief, i just thought "its too simple, no way its this easy"

[Anonymous No.11346769]

I have the stupidest question in this thread. It's literally for grade 5s.

[Anonymous No.11346848]

>>11346769
3.95, -1.45, -1.55, 4.15

[Anonymous No.11346865]

>>11345660
Whaaaa!!? That's how they did it!! I was wondering why the only worked solution in the book went to u/t, it was making me cry unironically (inb4 I was revising that section 2 hours a day for the past two weeks and other parts of the book but could never wrap my head around how they got to u/t despite the notation, it makes so much sense now. I love you anon!! Seriously, I kinda rage-quitted that class, just got back from work thinking it was going to be an hour of mulling it over. Thank-you so much!! Will do the questions now!~

[Anonymous No.11346895]

>>11346848
What about the 2.8?

[Anonymous No.11346903]

I have to approximate this equation using eulers method. I wanted to find the proper solution before approximating so that I know what I should be working to
I got y = -1 - x
so y(0) = -1
but apparently its 1?
even online calculators are saying itd be -1
is this an error in print or am I stupid?

[Anonymous No.11346960]

>>11346769
11, 12, 13, 15. Figure out the smallest(12+12), then the largest (13+15), and tweak the #'s until you can solve the middle ones.

[Anonymous No.11346991]

>>11346903
>is this an error in print
No. The analytical solution to [math] y'-y=x [/math] is [math] y=ke^x-x-1 [/math] where [math] k [/math] is an arbitrary constant that is determined by whatever your initial condition is. The initial condition can be anything. If [math] y(0)=1 [/math] then [math] k=2 [/math]. So the function you are approximating by Euler
s method is actually [math] y=2e^x-x-1 [/math]. (The exponential part of y is called the homogeneous portion of the solution, and the rest is called the particular part of the solution, for what it's worth.) Of course, you don't actually need to know this to use Euler, but it helps if you are trying to double-check your work.
>>11346865
I love you too and yw~ and all that, but
>making me cry unironically
Get a grip, anon.

[Anonymous No.11346998]

>>11346903
>is this an error in print
No. The analytical solution to [math] y'-y=x [/math] is [math] y=ke^x-x-1 [/math] where [math] k [/math] is an arbitrary constant that is determined by whatever your initial condition is. The initial condition can be anything. If [math] y(0)=1 [/math] then [math] k=2 [/math]. So the function you are approximating by Euler's method is actually [math] y=2e^x-x-1 [/math]. Of course, you don't actually need to know this to use Euler, but it helps if you are trying to double-check your work. (The exponential part of y is called the homogeneous portion of the solution, and the rest is called the particular part of the solution, for what it's worth.)
>>11346865
I love you too and yw~ and all that, but
>making me cry unironically
Get a grip, anon.

[Anonymous No.11347110]

>>11346895
shit

[Anonymous No.11347334]

1. What term means the inverse of entropy? That is, something where saying it's "higher" is the same thing as saying that entropy is "lower".

2. Is it accurate to say that all particle interactions are determined by many different equilibriums that all have priority at different energy levels?

[Anonymous No.11347367]

Is there any way to fuck with someone's sleep cycle, like some inaudible sound wave? Want to get revenge on my sister somehow.

[Anonymous No.11347448]

Is it necessarily true that an invariant subspace S of a linear operator T is also an invariant subspace of its adjoint T*? I know it holds for finite dimensions by looking at the matrix of T.

[Anonymous No.11347470]

>>11346769

I just worked it out with pen and paper in a couple of minutes:

>1.1
>1.2
>1.3
>1.5

These allow for all the answers while also allowing for a possible 2.3, which did not appear in his sample.

If we need to find numbers which ONLY give the results listed though.. pls help.

[Anonymous No.11347479]

What bottlenecks how much energy the brain can use in a day? Is there a general "pool" of energy that all of the body can use, and the brain draws from the same place as, for example, the muscles?

[Anonymous No.11347481]

>>11346848
This doesn't allow you to get answer 2.8 and I'm genuinely curious how the f*** you came up with such retarded numbers please tell me what method you used, I MUST KNOW.

[Anonymous No.11347728]

Why do you guys enjoy science and math so much?

[Anonymous No.11347733]

>>11347728
Nobody here actually enjoys science and math, just like nobody on /tv/ actually enjoys television and film.

[Anonymous No.11347735]

>>11347728
Interesting, challenging, suppresses mental health problems. Those would be my reasons.

[Anonymous No.11347747]

>>11347728
For me its the prospect of creating my own business empire.

[Anonymous No.11347748]

So I am walking downtown lost in my thoughts and I notice the pebbles at my feet look like I am losing framerates and lagging, then I raise my eyes and I can the roads stretching out and feel like I am further away while the vision in my peripheral is waving.

What the fuck just happened?

[Anonymous No.11347868]

Hey guys, idiot question here.

Does fast moving air actually cause the air there to be lower pressure? Like if i get air moving real fast in some spot, could i get it down to like 0.5 atmospheres of pressure?

[Anonymous No.11347932]

>>11347868
Do you mean in reference to flight?

[Anonymous No.11347936]

>>11347932

No i mean in reference to like forcing air through a chamber at high speed.

[Anonymous No.11348427]

>>11347481
basic system of equations, I wasn't trying too hard and I goofed the algebra somewhere along the way

[Anonymous No.11348441]

>>11347936
yes, this is why cavitation happens. The drop in pressure allows fluids like water to instantly boil

[Anonymous No.11348514]

>>11348441

Okay, so imagine a solar updraft tower that is designed to make air moving through its base to be moving as fast as it possibly can, then you put that over sea water, then you use metal "sails" to be heated by the sun and then channeled down into the water, and at the top of the solar updraft tower we put nets to catch the air as it rides past and then drips down into a reservoir. The point of passing air over the surface of the salt water as fast as possible is to lower the air pressure and allow evaporation at a lower water temperature. The entire system uses no electricity, just heat from sunlight. The purpose is desalination.

Is this a stupid idea?