/sci/ - Science & Math

FUCK JANNIES

Were you not going to link unanswered stupid questions, anon~?
>>11082431
>when jannies give you a warning for posting anthro

>>11082500
>when jannies delete the two threads that you were posting in

>>11082506
My condolences. I'm sure they were quality threads.

>>11082509
one of them was terrible
but the other was just a uni thread
i suspect theres a janny on here who dropped out or something and is bitter about it

How do I explicitly show through math that position loses significance in Quantum Relativistic Mechanics while the momentum is still good to characterize particles.

Unsanswered questions from the previous thread:
Engineering questions:
>>11058903 (signals). >>11058969 replied, and the questioner followed up with >>11059022
>>11067640
>>11072077
>>11075028
>>11075917 followed by >>11075919

Maths questions:
>>11063456 followed up by >>11063461
>>11071184
>>11075014 [Huge mess of a background to this one, recommend not even trying to answer.]
>>11075516 [Ilegible, but if someone here is specialized in finite element methods you might know what the fuck he means.]
>>11077014

Chemistry questions:
>>11067263

/g/ questions:
>>11076975

Stupid questions:
>>11058654
>>11063472 (Because you aren't dead on your feet).
>>11064579
>>11065597 (Sort of, yeah.)
>>11069012 (No.)
>>11070574
>>11072172
>>11073721
>>11075746
>>11076447

Gold star answers:
>>11059917
>>11061663
>>11062102
>>11064335
>>11068613
>>11072252
>>11072298
>>11074730
>>11075657
>>11075838

Silver star answers:
>>11056810
>>11058442
>>11058619
>>11058697
>>11059008
>>11059089
>>11060678
>>11061263
>>11061820
>>11062315
>>11064237
>>11064933
>>11064961
>>11066012
>>11067868
>>11071450
>>11073148
>>11074560
>>11074593
>>11074643
>>11074831
>>11075179 [A for effort.]
>>11075640
>>11076429
>>11076912
>>11077684 followed up by >>11077694 [A for effort.]
>>11079644
>>11079645
>>11080475
>>11080530
>>11081236 followed up by >>11081261
>>11082234
>>11082237

Stars are a one time thing, don't expect them in the next thread.
>>11082500
This took a lot longer than I thought it would. Will not repeat.

>>11082569
Small mistake with >>11075917 , I didn't recognize the term and assumed it was something in engineering.
It's actually a stupid question.

I need some real world applications of hyperbolas for a school project, google couldn't really help me out.

>>11082590
This is easy, anon.

>>11082592
Yeah but why exactly a hyperbolic shape, some sites say it's for structural reasons but don't have any references to prove it even wikipedia doesn't

>>11082619
Structural reason:
Hyperboloids are a double ruled surface, meaning the apparent curved surface can be constructed only of straight lines or beams. They are also generally very stable shapes.

Thermodynamic reason:
The whole purpose of a cooling tower is to...cool. Usually by evaporation. The pic above is of natural draft, wet cooling towers. They are called natural draft because air is drawn in without the use of a fan, which has to do with the high relative humidity of the air in side, look up the stack effect. Somewhere around the middle of the tower there are a bunch of nozzles that spray a hot (liquid) water mist, usually from the condenser of some plant. The mist rains down, easily exchanging heat with air on account of the large surface area of all those mist droplets combined. The mist collects at a pool at the very bottom of the tower to be pumped out. Some water is lost in evaporation, and so there is a makeup water supply but that's neither here nor there.
In a nutshell: the first half of the tower relative to the air enters goes from fat to skinny, which acts like a nozzle and speeds up the dry air as it flows past hot mist from the condenser. The second half goes from skinny to fat, which acts like a diffuser, increasing the pressure of the wet air, and increasing the area at which it can then mix with the atmosphere.

Cooling towers are basically a venturi.

>>11082619
Structural reason:
Hyperboloids are a double ruled surface, meaning the apparent curved surface can be constructed only of straight lines or beams. They are also generally very stable shapes.

Thermodynamic reason:
The whole purpose of a cooling tower is to...cool. Usually by evaporation. The pic above is of natural draft, wet cooling towers. They are called natural draft because air is drawn in without the use of a fan, which has to do with the high relative humidity of the air inside (look up the stack effect). Somewhere around the middle of the tower there are a bunch of nozzles that spray a hot (liquid) water mist, usually from the condenser of some plant. The mist rains down, easily exchanging heat with air on account of the large surface area of all those mist droplets combined. The mist collects in a pool at the very bottom of the tower to be pumped out. Some water is lost in evaporation, and so there is a makeup water supply but that's neither here nor there.

In a nutshell: the first half of the tower relative to where the air enters goes from fat to skinny, which acts like a nozzle and speeds up the dry air as it flows past hot mist from the condenser. The second half goes from skinny to fat, which acts like a diffuser, increasing the pressure of the wet air, and increasing the area at which it can then mix with the atmosphere.

Cooling towers are basically a venturi.

>>11082430
>A penny is placed at the outer edge of a disk (radius = 0.150 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.80 s. (a) What, if anything, is producing the centripetal force that enables the penny to rotate along with the disk?

What does this mean? A penny is rolling along the edge? The penny is stationary but rotating while the disc rotates under it?

>>11082988
Presumably, the penny rotates around the disc like in the image.
I think the answer was gravity.

>>11082988
Did you draw that picture? I don't think that is what it is describing. Imagine laying a hula hoop flat on a surface. Now lay a penny flat on the ground inside the hoop. The penny rolls along the inside surface of the hoop.
The answer is normal force, by the way.

>>11082998
>>11082997
Ah okay, I drew the picture thinking that was what it's describing. Thanks

Am I being retarded?
I'm supposed to find field vectors for an electric field E and polarization vector P given the magnitude of an electric flux density D and relative permittivity of a material. I don't know if I drank a full barrel of stupid juice but I'm pretty sure it's not possible to find the field vectors with two scalar quantities. My book relates D, P, and E but the relations only work as vectors. and the only thing I can find from using them is more magnitudes

>>11083372
Perhaps you are assuming that P and D are parallel? Can you post the question?

>>11083389
That came across my head the moment I posted.
Can't post pictures from where I am but here's a near 1:1 phrasing
>in a dielectric media with relative permittivity 3.6 and strength D = 285 nC/m^2 find field vectors for E, P, and predict the value for electric susceptibility

>>11083420
[math]\mathbf{D}=\epsilon_0\mathbf{E}+\mathbf{P}=\epsilon_0(1+\chi)\mathbf{E}[/math]
assuming all vectors are parallel and plugging in

[math]285\ \frac{\text{nC}}{\text{m}^2}=\epsilon_0\cdot3.6\cdot E[/math]

so [math]E=8941\ \text{N/m}[/math] and [math]\chi=2.6[/math]

>>11083444
V/m***

>>11082569
get a fucking life

>>11083444
That's exactly what I did. I guess what threw me off was the orientation of the vectors since it probably flew over me in the book and lecture

>>11083459
rude :(

I'm doing a classical mechanics problem with constraints. A rod slides down a wall as shown and I need to find where it loses contact with the wall. I understand the gist of how to solve it but I keep getting complicated wrong answers. Is my setup ok?

[eqn]L = \frac{1}{2}m(\dot{x}^2 + \dot{y}^2) + \frac{1}{2}I\dot{\theta}^2 - mgy[/eqn]
[eqn]f_1: \frac{L}{2}\cos\theta - x = 0[/eqn]
[eqn]f_2: \frac{L}{2}\sin\theta - y = 0[/eqn]

>>11083473
But true.
Get a fucking life.

>>11083711
Where the fuck do you think we are?

>>11083733
Home

>>11083734
feels

>>11083733
>>11083734
ladies you're both pretty

>>11083734
>>11083738
>inb4 we all get banned for rp

>>11082430
When will we be able to create beings like the ones in OP’s image?

can a set of vectors be linearly independent if one of the vectors is the zero/null vector?

>>11083825

no, because the zero vector can be written as 0x where x is any other vector in the set.

>>11082569
I appreciate your brand of autism.

>>11083829
ty
>>11083459
kys

>>11083836
>ty

have a look at the definition of linear dependence on wikipedia too.

https://en.wikipedia.org/wiki/Linear_independence#Definition

clearly, it also includes the case where your set is just the zero vector.

>>11083844
i was confused because i knew that the set had a nontrivial solution to cv + cv + cv + ... = 0, but for some reason i got it backwards and thought that implied linear independence

>>11083459
Now that I think about it, I have been posting too much.
From now on, I'll only post after 10PM on my computer.

Also, if you're going to post on my behalf, at least attach a touhou.jpg.
>>11083832
It's not as autistic as it looks, usually takes ~15 minutes.
The time difference from the OP is large because I went home and had lunch in between.

>>11083945
thank you for your service

>>11083696
Update: after I did some cleaning up and trig substitutions I got the right answer.

Is there a specific medical term for when a foreign object from a wound can't be removed/is left in the body on purpose?

I have the option of getting a Bachelor of Nursing, or a Bachelor of Nursing (Honors). They're the same length, but the Honors one involves a year long research component during our clinical placements where we have to design and implement some rudimentary research in order to boost the uni's research rankings.

My question, would I be less favorable to employers if my degree is just a regular Bachelor's while most of the other candidates have the Honors version? I'm considering just doing the regular because I hate stats and research with a passion, hence the reason I chose a practical career rather than a research based one. Also planning to do med school afterwards anyway while doing part time nursing.

>>11084613
I'm pretty much just guessing here but I'd say honours will help you get into med school while non-honours will help you get a job.

>>11084622
In my country it wouldn't really help me with med school either way. My concern is that if I'm applying for a job and everyone has Honours but me I'll be dismissed as being lazy, when really I just want to enjoy my final year prac and get the extra time in the hospital rather than sitting at home hunched over a computer pushing numbers around. I looked at some of the current year's projects and they're fucking ridiculous, eg. Whether smiling at patients improves their care satisfaction etc. Our stats coordinator also has concentrated Asperger's and can't teach or help for shit.

>>11084625
Whats your long term goal? Do you want to specialize in something, like ER or Nurse Practitioner? Maybe ask around some people actually experienced in the medical industry and what hiring is really like

Real quick math question:
If I have a function x(n)=u(3-n) and I want (for convolution, but it doesn't matter what for) to calculate x(n-k), do I do x(n-k)=u(3-(n-k)) or x(n-k)=u(3-n-k)?

If it was n-3, it doesn't matter if I just plug it in "literally", or plug it in "properly", but I completely forgot what to do if it's the other way around, and I'm not sure how to even google it.

I guess this is a time invariance thing I should've learned by now.

>>11084685
The first one

>>11084701
Thank you very much anon

Since /g/ could not help me maybe /sci/ can. >>>/wsr/727001 and read replies for more information.

>>11084765
Not a hundred percent sure what you actually need but it sounds like you have a grammar that you can't parse but you can't figure out why.
Read this https://en.wikipedia.org/wiki/Context-free_grammar and https://en.wikipedia.org/wiki/Regular_grammar and see whether they apply to your problem. Rewrite your problem in the context of the appropriate grammar and then look into yacc and lex or whatever the modern tools in the language you use are.

This might be a bit of an undertaking but in general the problem is not easy.

>>11084804
>Not a hundred percent sure what you actually need but it sounds like you have a grammar that you can't parse but you can't figure out why.
Yep.
>Read this https://en.wikipedia.org/wiki/Context-free_grammar and https://en.wikipedia.org/wiki/Regular_grammar and see whether they apply to your problem. Rewrite your problem in the context of the appropriate grammar and then look into yacc and lex or whatever the modern tools in the language you use are.
Not really. This is context-sensitive grammar and I'm not even sure whether bison and flex can deal with it because of overlapping attributes. I'm writing everything by hand since it's easier that way (and I don't really know how to use flex and bison).
>This might be a bit of an undertaking but in general the problem is not easy.
Tbh. If you want I can elaborate the description if it's still not clear enough.

>>11084816
For attributes which don't have to nest (i.e. you don't have to end them in the reverse order to which they were started), don't try to parse it into a tree. Just treat the tags as on/off switches. Opening tag => turn the attribute on, closing tag => turn it off, run of text (without any tags) => text object having the attributes which are currently on. That turns a stream of (text OR start tag OR end tag) objects into a stream of text-with-attributes objects.

If you want to catch unmatched tags (although there's no particular reason to do so), check for a start tag when the attribute is already on, or an end tag when it's already off, or any attributes remaining on at the end of the input.

If you want to allow tags to nest (this may make copy/paste easier), replace the on/off flags with counters, so a start tag increments and an end tag decrements. An attribute is on if its counter is greater than zero. A counter less than zero indicates an error (an end tag without a matching start tag).

Note that if you use binary flags (rather than counters), the grammar is technically regular, but it will be simpler to treat it as a context-sensitive grammar (a regular grammar requires 2^n states where n is the number of attributes).

>>11084914
Hmm this may work. I'll see what I can do anon.

Silly question here. What's an example of a topological group whose fundamental group is itself, apart from the trivial case?

>>11084367
retained surgical instrument

help a retard out

[math](A \land B \iff A \land C) \implies (B \iff C)[/math]

is this true and if so why

>>11085621
yes
<=> basically means "equivalent"
set A to True: trivially seen
set A to False: true by implication truth table

So after reading about trans-cranial magnetic stimulation
https://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation
and how its able to dampen some subjects' brain areas and reduce their performance on cognitive tasks or temporarily abolish their belief in god (source: https://www.medicalnewstoday.com/articles/301117.php))

So I was wondering if it might ever be possible to create a wearable version of this device that is tuned to render the wearer slightly retarded for the purpose of my bimbo fetish. The effects are reversible and TMS has a good safety record, but the limiting factor might be the precision of the magnetic fields not doing so well with a device that you'd wear as you moved around, and the need for a substantial power source, since these things use magnetic fields on the order of 3-4 Teslas. What do you think?

>>11085636
can you elaborate anon I can't see it. I understand what an equivalence relation is.

>>11085621
why don't you just write the table

>>11085636
Retard here: in the case that A is false - shouldn't (A^B <-> (A^C)) equal (F <-> F) which is true? Then T --> (B <-> C) should be false if B and C are different?

first year of cs and it's horrible, why does discrete modeling exist when it's the same topics as discrete maths and when i search for discrete modeling on the net it's different that what i'm learning

>>11085667
you're right

>>11085680
so is >>11085621 false, generally?

>>11085691
25% of the time
https://www.wolframalpha.com/input/?i=%28%28A+and+B%29+%3C%3D%3E+%28A+and+C%29%29+%3D%3E+%28B+%3C%3D%3E+C%29

>>11085691
yes

>>11085701
>>11085746

thank you

>>11085363
Even if the object in question is not a surgical instrument, ie a bullet?

>>11085751
no problem anon, we're here to help and encourage

Normally I'd consider this a /mu/ question, but everyone there is a shitposting dumbass.

Is there anyone who can explain the absence of an E# or B# note, from a scientific perspective? Each note vibrates at a specific frequency, (IE A4 is at 440Hz), and then has a sharp or flat interval directly between it and the next lettered note, save E and B. The variance in frequencies seems pretty standard (As an example, the distance between E to F is approximately the same number of Hz as F to F sharp), so why are these specific notes not considered to have sharps or flats?

How were years known before it was known we revolved around the sun?

>>11085926
Seasons, movement of constellations, etc.

>>11085932
what did they interpret it as then?

>>11085953
The passage of time.

>>11085953
They thought the stars and sun moved around the earth

>>11085963
So its the period of the sun's epicycle then? I'm trying to think what exact element is supposed to be the year. Because the sun would move around the earth once every day by definition. Or did they just measure a star close to the north star and just measured the period of constellations returning to normal?

>>11085995
They still knew that the angle of the sun from the horizon changes with season

>>11085261
What you're essentially asking for is a space that is homeomorphic to the space of connected components of its loop space. The latter space is discrete, but discrete spaces have trivial pi_1. So the point space is the only example.

>>11085995
Yeah, I suppose so. Consider the fact that the Mayans measured the year so accurately that they even incorporated an extra day in their calendar every four years.

>>11085876
The reasons are entirely historical, the reason all of the base notes you know are considered naturals is simply because our (talking about western tradition in this case) music system has always been almost entirely based around diatonic scales, and the "most natural" scale that was considered to be used as the building block was C Major, so it just so happened that all of its notes became the natural notes in our music system.
Scientifically speaking nothing prevents you from using notes that are in between the 13 notes we normally use (outside of instrument-specific restrictions, of course), although at some point such a slight variation in frequencies would barely make a difference for our ears so giving them a different name wouldn't make much sense.

The reason E and B aren't considered to have sharps is because their sharps already exist as F and C which are naturals. Giving them additional "sharps" would mean introducing a half step between those half steps, and then we'd probably be asking why there are no quarter steps after F, F#, G, etc.
In other words, it's entirely a notation thing.

>>11085876
> Is there anyone who can explain the absence of an E# or B# note
E=F, F=E
B=C, C=B
An octave has twelve semitones. A diatonic scale consists of seven notes which can be constructed as a chain of fifths (notes five semitones apart). E.g. C major is: CGDAEBF. Note that a fifth corresponds almost exactly to a 4:3 ratio (it's actually 2^(5/12)=1.33484, which off by around one part in a thousand); the small integer ratios are fundamental to chord harmony.

The seven notes which are part of this scale get distinct letters; the five which aren't are named as sharps or flats of the seven. As seven is more than five, two of the intervals (B-C and E-F) are only one semitone rather than two, so there's no B/C or E/F because the adjacent note is also part of the scale and has its own letter. Note that these are at the start and end of the CGDAEBF chain.

See also:
https://en.wikipedia.org/wiki/Scale_%28music%29
https://en.wikipedia.org/wiki/Diatonic_scale

>>11086078

> E=F, F=E
> B=C, C=B
E#=F, Fb=E
B#=C, Cb=B

> so there's no B/C or E/F
so there's no B#/Cb or E#/Fb

You'll just have to imagine that #=sharp and b=flat, as 4chan just eats those characters (does it with the squared and cubed also).

This question pertains to neutron stars.

I understand from a brief google that they're incredibly dense and incredibly hard to detect, and also there is apparently no known physical process that would result in their ceasing to exist.

This last part is what I'm confused by. A neutron star radiates energy in the form of light, hence why it's detectable. If this is the case, why would they not simply evaporate into heat energy much like other large bodies?

Even if it takes a fuck long time, won't they eventually fade away as they radiate their mass as energy?

Why are beta-blockers used to treat angina? Beta-blockers reduce the strength and rate of heart contraction. Angina is literally a block in the heart by plaque that can be stable/unstable. Anyways, it seems counterproductive to want to slow down the heart, as this could slow down the erosion process of the plaque - possibly a rate so slow that the plaque growth rate is higher, therefore increasing the plaque's size and leading to cardio-death. This is medicine? This is stupid I think.

>>11086158
beta-blockers do not reduce the risk of death from cardiovascular events
https://jamanetwork.com/journals/jama/fullarticle/1367524

Their treatment for angina is because that's what they were originally indicated for when the first beta blocker was discovered. The reduction in blood pressure is very important for severe hypertension, but honestly they do not improve the outcome of cardiovascular problems because all they do is like you said, reduce cardiac output.

Aspirin has better outcomes on the risk of cardiovascular events in cases of angina and actually lowers the risk of death: https://heart.bmj.com/content/88/1/11

>>11086231
wow thanks, i think beta blockers have fallen out of favor for angina though and they use ACE inhibitors now/ARBs -

Given a set D = C\{0}, I'm asked to find a local antiderivative in some neighborhood of z_0 for every z_0 in D.

What I've got so far is that for any z in the pi cut plane (C_pi), the antiderivative of 1/z is Logz. However, I'm having trouble trying to find an antiderivative for the points on the negative real axis (i.e. the cut part of the plane). I'm thinking it maybe has to do with Cauchy's Theorem but I'm not really sure.

Please help bros

Can cancer actually go dormant? Say chemo worked and you're living a normal life again, is it statistically more probable for that same patient to get cancer again at some point later in their lives than a normal person? I thought it's pure chance but I keep hearing that cancer goes dormant after being cured.

t. layman

>>11082430
How do I build muscle?

>>11086492
Dormancy is a stage in cancer progression where the cells cease dividing but survive in a quiescent state while waiting for appropriate environmental conditions to begin proliferation again. Quiescence is the state where cells are not dividing but at arrest in the cell cycle in G0-G1.

>>11082430
Yes, I would like to know; how do I Touhou?

>>11086494
eat alot while working out hard. its like 80% food 20% working out, make sure to keep your diet balanced or at least eat enough fiber and dont go overboard on the cholesterol

>>11086494
I WANT TO FUCKING STRANGLE YOU AND YOUR MUSCLES

>>11086512
B-But I don't have any.

Given an ice cold plastic water bottle, is it able to stay cooler longer in a desert with high temperature if the humidity is practically zero?

I heard a long time ago that condensation is what transfers the most heat, therefore without the humidity to transfer the heat, the water bottle can stay cooler longer in a paradoxically hot environment.

I am 27 and have been smoking pot since I was 14.
Have I fucked my brain? I plan on getting sober and going back to college, but I fear that my be pointless.

Let Y=SUM(X)/N
N is the number of number of elements, meaning Y is the average of all X.

Where X is an random variable with a PDF of 1/(2pi) from -pi to pi

Calculating the expected value of X E(X)=0 and E(X^2)=(pi^2)/3
Therefore Var(X)=(pi^2)/3-0=(pi^2)/3

Then E(Y)=E(X)=0
What is Var(Y)?

Please help me senpai

>>11086472
You can't give an antiderivative to 1/z defined in all of C\{0}.
The question asks for the antiderivative to be defined in some neighborhood around any point for a reason.
>>11086502
https://moriyashrine.org/
>>11086793
No, just pray every day for Jesus to unfuck your head.
>>11086798
I distantly recall there being a formula that gave you the variance of the sum of n independent distributions in terms of their variances, and another formula that gave you the new variance when you multiplied the old variance by a scalar. Something with a square in it, definitely.
I think you fucked up the calculation of that Var(X), tho.

>>11086828
E(X^2)=Integral[X^2/(2pi)]=X^3/(6PI)pi from -pi to pi
=(pi^3 +pi^3)/(6pi)=pi^2/3

All the documents i have look mention about variables being "independent" but they never mention what that means. All Xs have the same formula, are they independent?

>>11086836
>>11086828
Also do you mean:

Var(Y)=Var(SUM(X)/N)=Sum(Var(X))/N=
N/N*Var(X)=Var(X)=(pi^2)/3

Which seems intuitively wrong, Matlab code gives that Var(Y) approaches 0 as N increases

>>11086078
Okay, so basically this sounds like >>11086061, as in why bother counting whole tones and semitones if the interval distance is the same?

>>11086836
Jolly, the calculation seems alright.
The Xs are independent, yeah. It's hard to explain independence, wait until you see it in class.
>>11086838
>passing the N outside
I told you about the square, lad.
[math]Var( \lambda X)= \lambda ^2 Var(X)[/math].

>>11086901
B-b-but why?

I mean that would imply VAR(Y)=VAR(X)/N
which seems to be consistent with the simulation and my actuarian friend. I just don't get it

>>11086916
>why
Because it's a square minus a constant.
https://en.wikipedia.org/wiki/Variance#Basic_properties

>>11086924
This is why numpy.var is better, I don't need to worry about bs.

Thanks senpai UwU

Maybe this is just the best I can do.

when my gf turned on the stove today i had my ath-m50s on (headphones, but nothing was playing), and my headphones made a clicking sound in perfect synchronization with the stove's initial spark before the gas was ignited.

what the FUCK is this called and why is it happening?

>>11086828
I don't get why desu anon. Why are they asking for the antiderivative to be defined in the neighborhood of some point?

Is math the study of numbers or the study of variables?

>>11086962
Resonance, or Normal Modes. The frequency of the spark sound is one of the modes of vibration of some part inside the cups of your headphones.

>>11086962
A stove spark coincidentally is a spark gap generator, albeit a weak one. Generates electromagnetic radiation across a very wide frequency band. You're hearing the EMR burst of an electric spark.

Some speakers that are not good at filtering radio waves (unshielded cables) out will make 'wireless transmission' noises. I've usually kept a set of 2.1 speakers next to a cell phone, which would tip me off of an incoming call or text well before the phone would show a notification.

>>11087005
Cool

>>11086988
neither

>>11086995
>>11087005
thanks, I'm suprised I've never heard of this or experienced it yet. it feels like pure magic

>>11085642
>What do you think?
I think you should be ashamed.

>>11087005
>which would tip me off of an incoming call or text well before the phone would show a notification.
I remember that happening in '06 with cheap speakers and flip phones, I miss it so bad. What speakers should I get to replicate the effect?

Could anyone help me with my circuits/semiconductors assignment?
Any help is appreciated. Pic unrelated.

>>>/wsr/730079

Can someone please explain to me the universal property of free modules and how it is related to the usual, more elementary definition? I know that a free module is just a module with a basis (so a linearly independent generator).
I also know that the universal property of free modules states that if F is a (free) module, S is a non-empty set, and f a function from S to F, then for every arbitrary, non-empty module M with a function g from S to M, there is a unique homomorphism h from F to M such that the diagram commutes. Seems kinda convoluted at first but at least on paper I understand what it means. What I don't get is how that is supposed to be equivalent to the module F having a basis. I'm supposed to show the equivalence between those definitions.

I'm pretty sure S is supposed to just be a set of indexes that get mapped to elements of F and the image f(S) is the basis of F? So far that seems fine, but then where the hell am I supposed to bring a random module M from, and how (in an intuitive way at least, if it's even possible) does that help define f(S) as a basis of F instead of a random linearly dependent or non-generating subset of F? I want to at least understand why we can define a module with a basis like this

How much harder is the workload jumping from CC to a 4 year university in equivalent classes? I'm transferring to a university next spring for EE and I'm worried my classes weren't rigorous enough. Or even if the material covered is identical, that perhaps the volume of work(which has been rather manageable) wouldn't prepare me for the grind of EE.

I'm in Calc 3 and Physics 2 and it's been rather easy to maintain an A in both, even while working full-time, and while I could accept that I'm just an outlier, most of my class didn't drop either whereas I heard these were weedout classes in Uni.

if i use the derivative of a graph from 0 to 2 seconds as part of my solution do i also need to use those as integration limits throughout the problem?

I have no idea how to do this and I can't find anything in the book that will help me

>>11087855
Wronskian

>>11087661

you'll be fine. half the reason they're considered "weedout" courses in uni is because they're so poorly organized, poorly taught, and so large that they feel very impersonal. it would make anyone feel lost. in fact, you've dodged a bullet. junior and senior level courses will be smaller and better organized.

What can you even do after college if you study biology? Work in a genetics lab? Anything else?

>>11087964
High school biology teacher

>>11087964
I studied biology. I work for a regulatory authority that monitors the local environment. It's pretty good. The government pays me to spend months collecting and analyzing data to write a report saying the local factory is polluting the water. Then they promptly ignore it.

Trying to show that [math]\mathbb{C}[/math] contains all its limit points. Suppose [math]z_{n}[/math] is a convergent seqeunce of complex numbers. Then [math]\lim z_{n} = L[/math] If [math]L[/math] was not in [math]\mathbb{C}[/math], then [math]L\in \mathbb{C}^{c}=\emptyset[/math] which is a contradiction. So [math]L\in\mathbb{C}[/math]. Is this reasoning sound?

>>11087840
Usually that would be the case, it depends on what your are integrating and wrt to what variable

>>11086988
tautological symbol manipulation

>>11088293
the graph im using is Transmission over time and i just found the slope of a short time frame when it goes from 0 to 100% transmission and use that as dT/dt.
from there i use some relations to find dH/dT and then multiply those two together to find dH/dt.
i then moved the dt over and then integrated both sides so i could find H as a function of time. for now i just did an indefinite integral and found the constant of integration later using given data

How did they go from left to right? I know the next step but I don't get this one.

Solve this and explain how.


You have object A which stands a distance of 2000m from objects B

Object B moves in the direction of object A at the velocity of 2.5 m/s

Every 5 seconds, object A emits a signal that travels at 150 m/s that B catches

After B catches the first signal, how long will it be until it gets the second signal?

Does it even make sense to talk about a group G acting on a set A if A is empty? It sounds fucking retarded to me, but I just wanted to make sure it's not me who's fucking retarded instead.

>>11088509
Multiply top and bottom by x^3, then you get one of those cubic identities which can be factored.
>>11088521
Since the signals all travel at the same speed and are emitted at constant intervals, there is a constant distance between them. When B catches the first signal, the second signal is exactly 150 m/s * 5s = 750 m behind it. Thus the time it takes for B to catch the second signal would be that distance divided by the combined velocity of B and the signal, which is 750 m / 152.5 m/s which is 4.918 s.

>>11088539
> Multiply top and bottom by x^3
By x^2. I.e. rationalise the numerator and denominator.

The numerator is (1+x^3)/x^2, the denominator is (x^3-1)/x^2; the x^2s cancel to give (1+x^3)/(x^3-1). By inspection, 1+x^3 has a root at x=-1 and thus a factor of (x+1), and x^3-1 has a root at x=1 and thus a factor of (x-1). Polynomial division gives you the other factors.

>>11088579
ye I meant x^2 mb, got ahead of myself there

>>11088539
>Multiply top and bottom by x^3
I really don't understand where the x^3 was taken from though.

The result is:
(x^3 +1) / (x^3 -1)

Could it be there is a method that allows to multiply the x^2 under the division line directly with the +x even though there is no multiplication path between them?

>>11088579
Oh alright, I was fiddling with wolframalpha trying to understand, thanks for clarifying.

>>11088534
>I just wanted to make sure it's not me who's fucking retarded instead.
I got bad news for you then

Hi /sci/
So I have a report to write about a physics experiment we did. We had to manually track the position of two objects on a video but first we had to find out the measurement uncertainty of the tracking. So we filmed the object with no movement for 10s or so and then tracked the position on 15 frames. We compiled the different positions in a table which automatically calculated the type A uncertainty of the position. It also displays a circle centered around the average value with a radius equal to [math]\Delta r[/math]. For the first object I found that 4 values were outside the circle and 6 for the other (out of 15 values in total). Now I'm being asked to write if this proportion seems correct and why. I'm kind of at a loss here how should I interpret it?

What is the evolutionary reason foe hair on our bodies stopping growth after a certain point, but hair on our heads not?

Also, what is the evolutionary purpose of beards

>>11088662
mustache rides

>>11088631
try posting in /sqtddtot/ (no offense, it's just the most likely to have folks interested in helping).
I wouldn't take my word for it, but that does seem to make sense if the radius is the average distance from the mean.

>>11085876
There is not an absence of E# or B#. Musical notation and theory is not at all based on science. The standard tuning system, 12TET, is a comprimise from just or pure intonation, which were derived a bit more from physics and may be worth looking into. 12TET offers loads of benefits to the composer, though.

>>11082988
Pretty sure the penny would roll off the end of the disk, but assuming it's somehow staying on, either the chemical bound of glue or gravity.

>>11086985
Set f(z)=1.
Then, using Cauchy's Integral formula we have that [math]1= f(0) = \frac{1}{2 \pi i} \oint _{\S} \frac{dz}{z} [/math], where S is the unit circle.
We can split the path into the part above the real axis [math]S+[/math] and the part below [math]S-[/math].
This gives that [math]\frac{1}{2 \pi i} \oint _{S+} \frac{dz}{z} = 1 + \frac{1}{2 \pi i} \oint _{-S-} \frac {dz}{z}[/math], where the minus before S- implies we've inverted the direction, which simply implies that [math] \oint _{S+} \frac{dz}{z} \neq \oint _{S-} \frac {dz}{z} [/math].
Since those are unequal, and both are smooth paths from 1 to -1, there isn't a global analytic antiderivative defined on some neighborhood of the unit circle.
>>11087473
I've tried for a while to explain how F "zeroes the least possible and this lets it lift morphisms", but a good explanation refused to come out.
Just show that if it satisfies the property we have an isomorphism from it to the classic construction of the free module, the intuition will eventually come to you.
>>11088709
>try posting in /sqtddtot/
What.
>>11083951
I'm not dead, lad, calm down.

>>11089189
Small mistake in [math] \oint _{S+} \frac{dz}{z} \neq \oint _{-S-} \frac {dz}{z} [/math].

I have problems controlling my focus. How do I know if it's ADHD or OCD?

can someone explain how this directional derivate isn't 7/13 ?
Apparently it's 21/13 and I honestly don't see how.

>>11089260
not only did I forget my pic but I also forgot a negative sign so nevermind, fuck me

>>11088509
hint:
x^3+1=(x+1)(x^2-x+1)
x^3-1=(x-1)(x^2+x+1)

Hey guys I've got to work out the average tidal propagation speed between two points. I know the distance between the two points, is it literally just

distance / average time period between high/low tide of point A and point B

any way to do this without just calculating it with all the terms?

>Prove for cardinals [math]a,b,c[/math] that [math]ac=bc \implies a=b[/math] is false.
Instead of showing a counter example could I instead do contradiction on the contrapositive: [math]a\neq b \implies ac\neq bc[/math] ?

i reading pages of textbooks and watching videos in my spare time like on public transport pointless?
will any of it stick or should i just save it for when i'm actually studying?

>>11090494
idk man, if you plan to formalize what you're reading/watching while commuting it's okay, otherwise is just a fancier mental masturbation.

>>11090694
granted, waaay better than reading normieshit or shitposting.

Please help with this question.
Using the knowledge of x^2n is congruent to 0 or 1 modulo 4, I need to prove that -1 + 4x +x^2 +8x^3 +x^4 = 0 has no integer solutions.

I sent 1 to the RHS and then moduloed (?) 4x and 8x^3 which is 0 mod 4 and the other 2 is 1 mod 4. Its most likely wrong and I am just confused on how I should proceed.

>>11090219
> is it literally just
> distance / average time period
The mean speed is the mean of distance/time, which isn't the same as distance divided by the mean time. It is the same as distance divided by the harmonic mean (that's basically the point of the harmonic mean).

can someone explain the reasoning behind taking out the 2

>>11091410
It doesnt make any difference if you take it out or not

What's a free website with problems to practice trig identities, trig derivatives, trig integrals?

>>11091410
how the fuck do you get to the point of taking derivatives of quotients and not know the linearity properties of the derivative?

>>11090494
>is reading pages of textbooks in my spare time like on public transport pointless
Obviously not. Even if you don't understand anything, it'll still help you memorize definitions and identities.
>>11091593
https://www.wolframalpha.com/problem-generator/

>>11091410
At that point, factoring the integers out is just autism.

Curious mathlet here, is tgere a way to do pic related with a single equation?

Hey so i was wondering, how many brain cells would you lose if you held your breath till you passed out? There would be a brief hypoxia before you started to breathe again, would it be enough to kill some neurons?

How is [math] E [/math] not simply equal to [math] F\[x\]/\langle p(x)\rangle [/math]? Isn't this just like saying let [math] B = \{b \in B\} [/math] considering that the "factor field" (not sure if correct term, just using it analogously to the group term) of F[x] mod p(x) is simply defined as the set of equivalence classes in F[x] under congruence mod p(x). Basically I don't see how E and the factor field could be any different.
Wait lmao figured it out as I was typing it. Should have read the question a bit more clearly. Gonna hit post anyway in case it helps someone.
Basically it says [math] a \in F [/math] not [math] a \in F[x] [/math] so the set refers only to equivalence classes that differ from a multiple of p(x) by a constant, while the full factor field includes those that differ by any polynomial of degree less than p(x). So I guess if deg(p(x))=1 then the two are actually equivalent, but in general E is a subfield. Cool.

How do I get 7.4 from 20 * 0.37?

>>11092290
no you dolt it says a in F, read the problem you mor-
oh
well done

Do I need to analyse a continuous variable for normality if my sample size is greater than 30 for every group I'm splitting it into?

>>11092401
?
...you multiply them

Does the central limit theorem mean that I can ignore any normality tests for my data if n>30? Like if I have a group where n=4000 but my normality tests fail, can I still let it through normality assumptions because of the large sample size?

Why did I, as a brainlet, study chemistry and not business? Now I have to write thesis and its tedious and I am not smart enough to design the experiment.

>>11091763
nice it even has trig stuff in it, albeit not explicitly stated

>>11092630
you fell for the science meme. we all did, otherwise we wouldn't be in here.

>>11092672
At least it cannot be that bad right? I mean I will still get a job and some income eventually?

Is it possible to download the whole library genesis at once? I'd like to have it on my external drive...

imagine a spaceship that has an amount of rocket fuel available that's equivalent to the entire mass of the observable universe
what % of the speed of light could it achieve with all that fuel?

>>11092879
It would just collapse into a massive black hole.

>>11092433
lmao

>>11092888
yes, but let's imagine it doesn't and let's ignore all the other things that make such a scenario impossible
how fast could you go if you could use such an amount of fuel

>>11092895
Anything could happen given absurd premises.

>>11092901
I'm asking about maximum speed specifically, though
I don't know exactly how fast a rocket could get using say 10 tons of rocket fuel, but I imagine it's nothing compared to what it could do with 10^53 kg of fuel

>>11092879
>>11092908
gotta be practical

0 mph because of the time to collect it all
0 mph because of the weight

why is 3x2y - 3xy2 != x-y?
don't say im dumb cuz i dont care i am 11 years old and i play the mandolin beautifully

>>11092933
mandolin is for queers, learn a real fucking instrument

>>11092908
Your question is ill posed and has too many unknowns.
For instance, does the rocket has to propel the 10^53kg of fuel as well or does the fuel automatically spawn inside the tank? If the latter is the case what is the total weight of the rocket without fuel? What kind of fuel are we talking about?
Some question are nonsensical and don't have an answer. Even if they are interesting.

>>11092933
learn a new fag song while you enjoy your ban

>>11092941
>or does the fuel automatically spawn inside the tank?
let's say it does
>If the latter is the case what is the total weight of the rocket without fuel?
I don't know how much rockets usually weigh. 500 tons? I dunno. let's say 500 tons
>What kind of fuel are we talking about
whatever current rockets use

Is this 80-90degree weather with november approaching a sign of global warming?

4 years of studying physics, and just this week I've come to appreciate Newton's laws. Specifically how the First Law is not a specific case of the Second. It defines inertial frames—if an object is in constant motion when no forces act upon it, you are in an inertial frame. Then (and only then) the Second Law applies: any acceleration of an object in an inertial frame is caused by a force.

The latter statement can be seen as a definition of a force. However, this would be circular reasoning since the First Law defines inertial systems using the notion of force. What is the fallacy I'm committing? How do I state the First and Second Laws so as to consistently construct the system of Newtonian mechanics?

>>11092972
>if we suppose that the laws of physics do not apply what does physics predict will happen?

>>11093102
that's exactly it

>>11093103
Then the question posed has no answer. It's ridiculous.

Just making sure: the left Kan extension of a constant functor sending every object to some X is isomorphic to X, right?

>>11093131
I mean, isomorphic to a functor sending everything to X.

>>11093106
just give me the formula that gives you a rocket's top speed according to mass and fuel and whatnot and I'll punch the numbers in myself

I have to write my thesis on latex. My last one I had to write in word. I want to replicate the word format of 1.15 line spacing, 1.5 paragraph spacing and no indent.

I googled for over an hour and tried a ton of stuff and nothing seems to work. Maybe the thesis template fucks up the stuff that I try. How do I do it? Please help.

>\setlength{\parindent}{0em}
Worked, gets rid of the indent.
>\setlength{\parskip}{1em}
Does not work. Makes the spacing around chapters and sub chapters way too large.
>\renewcommand{\baselinestretch}{1.2}
Only changes the spacing for chapters, not for the actual lines themselves.
>\usepackage{setspace}
>\onehalfspacing
Seems to work although it seems a bit larger than 1.15. I can't use it in combination with \setlength{\parskip}{1em} though because the result is a HUGE gap.

The power of the current source is 54 W. How do I find the voltage of E? Using only Kirchhoff's laws. I've tried finding the current of the other branches but I don't think that's the way to go. Any pointers are appreciated.

>>11093401
I tried some more and for now settled with removing automatic paragraph space and manually inserting \vspace{0.5\baselineskip} in between paragraphs. Sadly that's the only thing that works so far.

>>11093371
[eqn]
v=\int_0^{m \over r} {F \over M+m-r \, t}\,dt \\
={F \over r} log\left({m \over M}+1\right)
[/eqn]
where F = force (thrust), r = rate of fuel consumption (kg/s), m = fuel mass, M = dry mass. This assumes Newtonian mechanics (negligible relativistic effects).

F/r is the rocket's specific impulse (Isp) in N.s/kg (= N/(kg/s)); multiply by 9.81 for Isp in seconds.

Note that this is logarithmic in fuel mass; as the total mass increases, adding more fuel has proportionally less effect upon the eventual speed due to the increase in mass reducing the acceleration.

I'm working on a binary relation problem:
aRb where a^2 = b^2 for all the reals, the goal is to determine if the relation has binary relation certain properties: reflexive,irreflexive,symmetric,antisymmetric,transitive

Is this relation transitive? The transitive relation is aRb and bRc implies aRc. So in this relation all numbers relate to themselves and their additive inverse. So 1R-1 and -1R1 implies 1R1. Is this correct?

>>11092451
Yeah, why wouldn't you need to?
>>11092608
No.
>>11092825
http://libgen.is/repository_torrent/
Please don't, tho.
Have mercy on those poor servers.
>>11094408
>is the relation transitive
a^2=b^2=c^2 implies a^2=c^2.
>1R-1 and -1R1 implies 1R1
Yes.
>>11093090
>circular reasoning
What do you mean? You don't need to define every word down to basic grunting noises, or take one word as an abstract thing and pull the remainder of the definitions out of it. That's just how axiomatic systems work.

>>11094575
>Yeah, why wouldn't you need to?
Because apparently the statistical test I need to use requires the data to be N>30 OR meets normality tests. There's no info on what I should do if that data is N>30 but fails normality tests.

>>11093420
Loop analisis should do the trick here.
Setup your loop equations using kvl in each closed loop of the circuit in terms of the voltage drop across each lumped element.
For example, the loop equation for the loop with the 7v source (ill call it loop one) will be:
[math] I_1 [/math] is that loops current:
[eqn] 2(I_1 - I_2) + 1(I_1 - 3) = 7v [/eqn]

And so on.

>>11094593
First of all, look over the data for outliers. Removing them might fix the problem.
If it doesn't, what are you trying to estimate, specifically? Chebyshev's inequalities might do the job you need. Also, try taking squares (actually, the square times the sign, so negatives keep being negative), logarithms, exponentials, etc, and then checking if the deformed data passes normality.
Can you plot out the data and post a crop?

would it be better to go to a school with a bigger name like MIT or Stanford or with a lesser name but better program in the specialization im doing for grad school? i plan on going into industry research and not academia if that matters

>>11094859
The latter

>>11094575
Newtonian mechanics is an axiomatic system. Space, motion, inertial frames, mass, and forces all need to be rigoriously introduced, and then formulate predictions about our universe. I think the ambiguity reflects the fact that it's intrinsically impossible to be sure you are in a reference frame. A rotating observer, observing a rotating object only sees the centripetal force, but may save its claim of being an inertial frame by saying there exists a real centrifugal force he doesn't know the cause of. But up to here forces are rather undefined: they cause movement in some fashion, but it's not clear how this works. Only when you are in an inertial frame do you define forces as causes of acceleration, proportional to an object's property called mass.

>>11093131
>>11093136
This is false if you mean weak Kan extension. Consider an extension along a functor from a connected category to a disconnected one.

>>11095412
Fuck.

Why am I good with words and foreign languages, but absolutely terrible at math and science?

should i get my masters if i dont have any job experience? EE btw

>>11094612
I tried pic related but it's wrong. Help?

>>11096055
Never mind, ignore this, I just realized what it is. Thanks for the help, Anon!

>>11096016
if you need it for the positions your looking at sure, you could try getting into research at your university and internships during your masters too

Is there a sequence of transpositions ( permutations switching 2 elements) such that o_1, o_1 o_2, o_1 o_2 o_3, etc make up all the permutations of S_n, without repetition?

Let G=S4, permutation group order 4 and H=A4, subgroup of all even permutations of S4. Why is there no distinction between right and left cosets? The two right(left) cosets of G are generated by H and the subset of odd permutations of S4.

I don't get the 3.42 to 3.43 transition. Why does he make that change of variables?

http://web.mit.edu/fluids-modules/www/highspeed_flows/ver2/bl_Chap2.pdf

Apparently only 1.7 atm is required to induce supersonic flow.
Is it easy to make a /diy/ supersonic wind tunnel?

Partly a code question but /g/ is full of brainlets.
I'm modelling vectors in a rudimentary calculator, but I'm not sure on if it makes sense to have generic hierarchies of vectors (i.e. all vectors have a magnitude and dot product so have a base class/interface to derive) or to have separate logic for each dimension. What's the best way to do this?

>>11096318
In a planar wind tunnel, to have a throat of 20cm, you'd need an intake of 44cm. From that, you'd need about 30kg/s of air. With those dimensions, it'd need about 90kPa of pressure difference between the throat and the inlet. That's about 18kN per meter of tunnel width. Which represents 4.2MW of power per meter of tunnel width.

>>11096170
Dude, that's because A4 has index 2 in S4.

i have about 10 months between when i graduate from my bachelors and when i start grad school, i was thinking of going through some quantum, EM, and mathematics books when not working during that off time. I never really self studied before, but would it be better to just go through books and do the problems in the text or should i follow an MIT ocw course instead?

How can I find this limit? I can't use L'Hopital's rule

>>11096471
Plot it.

what's the deal with carnivores? is it possible humans are one or the other i.e
>either eat only meat or eat no meat
or are all carnivores retards who will die young?

>>11096471
Use the Maclaurin series for e^x, sin^(x) and log(1+x^2)

>>11096604
I meant [math] sin^2(x) [/math] of course

>>11096573
>is it possible humans are one or the other i.e
Every somewhat healthy human has the ability to consume both plants and other animals.

What is this asking? Sorry for brainlet question.

>>11097549
It's asking you to come up with a general formula for the sum in terms of n, and then to prove that formula holds for all n with a proof by induction.

>>11096151
We take the set [math]S_n[/math] and make a graph by associating to each vertex the edges given by composition with a transposition.
The essence of the problem is whether this graph admits a Hamiltonian path. Tackling this problem algebraically is most likely hopeless.
I've been looking through the wikipedia page if there aren't any theorems that can help, but I've come across nothing.
Hopefully some actual graphanon can help.
>>11096251
>which suggest
>why does he make that change of variables
Pure intuition.
>>11097549
It wants you to manually evaluate the sum for n=1, 2, ... etc and give a pretty formula for the general case.

Can someone give me an intuitional perspective of the pull-back and push-forward maps on some smooth manifolds [math]\mathcal{M}[/math] and [math] \mathcal{N}[/math]? I’m especially interested in how they come up in the definition of the Lie derivative.

>>11097710
>>11097734
>give a formula for the general case
How the fuck do I do that? I don't understand, there's never a clear step-by-step formula for providing the explicit formula.

>>11097774
Compute the values and try to see if any patterns show up.
>>11097751
>intuition
Literally just composition.
>how they come up in the Lie derivative
Tangent vectors were originally defined in terms of the "velocity of a curve". So a tangent vector determines a flow, which is locally a diffeomorphism of the manifold onto itself, which is essentially just the manifold "flowing" in the direction of the vector field. The physical intuition is outright unavoidable in this.
The Lie derivative is about how this flow changes the tensor field, or the function, or the whatever else.

>>11097831
>Compute the values and try to see if any patterns show up.
Isn't this basically an exhaustive method? I literally don't see how this is possible, I bring these problems to grad-students and it takes them like 20 minutes to figure them out after filling an entire sheet of paper with scribbles, I don't see why I'm being forced to do this for a junior level class.

>>11097947
>isn't this basically an exhaustive method?
Yeah.
>grad students take 20 minutes
This stuff doesn't get easier when you're a grad student, it's still absolute cancer.
In this case, tho, just try expanding the sum. Take a nice little least common multiple of the sum of fractions and see if the numerator gives any hints.

>>11086520
LMAO

Hi please respond quickly because my assignment is due in 1 hour and this is the last question. I have no idea how to go from the derivative in this form to the original function.

The limit below represents a derivative f(a). Find f(x) and a.
lim h->0 ((5+h)^4−625)/h

>>11097979
*represents a derivative f'(a). there should be a quotation mark symbolizing first derivative.

>>11097982
?
5^4=625
And if you are trying to solve that I'm guessing you know the definition of the derivative of a real function

>>11097979
>>11097982
Nevermind I am super retarded to not notice 625 =f(a)
a=5
f(a) = a^4

>>11097986
Thanks mate my bad

>>11096404
Oops that's a lot
Bye bye hopes and dreams

Can I get help with this question please? The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x)=F(x)G(x) and Q(x)=F(x)/G(x). Answer the following questions.

P'(1)=?
Q'(1)=?
P'(6)=?
Q(6)=?

>>11098047
There should be a quotation mark next to Q at Q(6).

I've done 7, how do I start 8? Could use some tips from analysts.

Can someone explain why shit wants to stay where it is in a frictionless environment without rhetorical tautology, e.g. "[thing] does it," e.g. calling "thing" "mass" or some particle ending with "-on"?

>>11096411
What is an index? Any examples?

Things conserve momentum because of symmetry preservation in spatial translation. therefore if you had no momentum to begin with, that translates to no momentum to end with. However it is near impossible to perfectly place an object over a frictionless surface because minute perturbations will eventually seep in and that will translate eventually into some motion.

>>11098262
basically the amount of cosets of a subgroup within the group that contains it. if the group is finite then it's just the quotient of the orders |G|/|H|
e.g. the order of <2> in [math] \mathbb{Z} [/math] is 2, since that's the order of the quotient [math] \frac{\mathbb{Z}}{\langle 2 \rangle} = \mathbb{Z}_{2}[/math]
it can be proved that all subgroups of index 2 are normal

>>11098300
>e.g. the order of <2>
meant the index of <2> here

>>11098300
Is there any example of how this would be true with permutation groups?

What exactly is Spin?

>>11082568
You don't, because what you've said is nonsense.
>>11082569
Thank you again for the hard work.
>>11085261
For a discrete group [math]G[/math] we have [math]BG \cong K(G,1)[/math]. So if [math]\pi_1 G \cong G[/math] then [math]G \simeq BG[/math] weakly. In addition, as all higher homotopy groups are trivial for both, their suspension spectra are equivalent in [math]+{\bf hSpec}[/math]. As [math]G[/math] is CW, this implies by Whitehead's theorem that [math]G \simeq BG[/math], which is impossible unless [math]G[/math] is trivial.
>>11086472
Weird question because, as you've said, [math]\ln z[/math] has a branch-cut on [math]\mathbb{R}_{<0}[/math]. This puts you on different branches of [math]\ln z[/math] whenever the neighborhood intersects [math]\mathbb{R}_{<0}[/math].
If you notice that [math]\ln z[/math] is a conformal map taking the punctured plane to the cylinder, however, you can define the Cauchy principal value by [math]forcing[/math] the "regularized" [math]\ln z[/math] to cancel the [math]2\pi[/math] jump across [math]\mathbb{R}_{<0}[/math] whenever it changes the branch.
>>11087473
Try understanding this for free groups first. The unique homomorphism basically tells you that there is essentially only one way [math]F[/math] is "embedded" in [math]M[/math].
>>11088534
A group action is a map [math]G\times A\rightarrow A[/math], so for [math]A = \emptyset[/math] we have the action is a map [math]G\times \emptyset = \emptyset \rightarrow \emptyset[/math], which actually exists (at least if you accept that the category [math]{\bf Set}[/math] has an initial object).
>>11098363
Spins are irreps of [math]SU(2)[/math].

>>11098398
But what exactly IS Spin?

>>11098412
Irreps of [math]SU(2)[/math].

How would I produce:

1/i+2/(i-1)+3/(i-2)+…+(i-1)/2+i/1

In java where i equals an integer?

>>11098651
you need 3 variables

>>11097947
> I don't see why I'm being forced to do this for a junior level class.
Because it's a junior-level problem. Do what the question says and evaluate the sum for n=1..5; the pattern is obvious. Once you have conjectured a closed-form expression for s(n), show that s(n)-s(n-1)=x(n) and s(1)=x(1).

>>11098662
Are the defined numbers(i.e. 1, 2, 3....) determined by the value of i?

>>11098398
>Spins are irreps of SU(2).
While this is technically true, spin comes from the projective unitary representations of SO(3,1), which can be related to the tensor product of two SU(2) unitary representations.

>>11098330
Bump for help

>>11098413
Yeah, but what does that mean on a physical level?

>>11098230
>why shit wants to stay where it is in a frictionless environment
It doesn't.

Proof: space is a frictionless environment. The moon is moving around the earth since forever.

>>11082430
Is there any universally approved textbook for the study of fluid mechanics and thermodynamics? Have been studying through textbooks but with so many being outdated or laid out in a way that makes fact recital + recollection difficult I've been looking for something that could perhaps give great depth whilst giving great means of practice.

Wesa gonna die?

How do I make latex work on firefox?

Also is Σ cos(ωn + θ), for n=0 -> N-1, zero?

Anyone know where I could find some modeling or can explain what would happen if a large heated object (think a spaceship reentering atmosphere) passed through fog?
Would it just stir it up? Create more? Clear it away?

Where is

1471.5SGx = 962 coming from? The 962.

>>11099236
Fuck, nevermind, found it,

>>11082430
Am I the only one that fines bilear algebra hard as fuck ?

>>11099375
*finds*

>>11099375
Only because you read it in french....
Jokes aside, Schmidt method is really simple when you think about it:
1. You have a set of vectors that are neither orthogonal nor have unit length. What can you do?
2. Well, choose one of them and divide it by its norm. Now you have your first unit vector.
3. Take now a second vector. But it is not orthogonal to your first vector, what can you do? Well, you subtract from it its projection over your first vector, thus the resulting one has to be orthogonal to it. And normalize the result. Now you have two orthogonal unit vectors.
4. Take the third one, subtract its projection over the first and second vector and normalize the resulting one.
5. Repeat ad eternum.

In another thread, I got the impression that squareroots of positive numbers are always positive, since they're assumed to have rotation [math]e^{i0}[/math]. In order to take squareroots deterministically, and avoid headaches like {1, -1}, we just assume the rotation is zero. Negative and complex numbers, however, can't have a rotation of [math]e^{i0}[/math].
1. Is the purpose of complex conjugates to render their effective rotation to zero, i.e., to give a real number?
2. Aren't you losing information by doing this?
3. Another anon mentioned that when differentiating |x| using [math]lim_{x->\infty}|x|=\frac{f(x)-f(x+a)}{x-(x+a)}[/math], you get a derivative of 0 at x=0. Isn't this essentially the same phenomenon - getting zero instead of an indeterminate/inconvenient solution it should be?

>>11099375
just draw a picture man

>>11099432
I have legit no idea what are you asking or even talking about

>>11099446
The squareroot of one can either be 1 or -1. In order to stay sane, we say it's just 1.
The dumb answer is, we choose it arbitrarily.
The smartest answer I've found is that phasors, which are necessary to understand complex roots, create a branch point at the origin. Essentially, [math]e^{i0}\neq e^{i2\pi}\neq e^{i4\pi}[/math]. The real number line is defined as the branch cut where [math]e^{i0}[/math]. That way, when we take the squareroot, we get [math]1^{\frac{1}{2}}=(e^{i0})^{\frac{1}{2}}=e^{i0} = 1[/math].
My question is, isn't that essentially the goal of complex conjugates? To average the phasors out to zero, and produce a real number? And using the analagous example of d/dx |x|, doesn't that destroy information?

>>11099479
>The squareroot of one can either be 1 or -1
No it isn't. The square root of 1 is strictly positive 1.

>>11099488
The squareroot of one is, strictly, the inverse of the function [math]x^2=1[/math]. There are two solutions to this.

>>11099479
>phasors, which are necessary to understand complex roots
no
>Essentially, ei0≠ei2π≠ei4π
no
>The real number line is defined as the branch cut where ei0ei0
erm, no?
>isn't that essentially the goal of complex conjugates?
no

learn some complex analysis and read about covering spaces. these issues have been adressed and solved a century ago.

>>11099503
>these issues have been adressed and solved a century ago.
Enlighten me. All I'm seeing is some topological crap.
And while you're at it, solve for the following:
>[math]\sqrt{e^{i2\pi}}[/math]
>[math]\sqrt{e^{i4\pi}}[/math]
And then tell me that they are equal

>>11098999
> How do I make latex work on firefox?
Disable whatever script blocker you're using. As well as 4chan, you need to allow mathjax.org and cloudflare.com.

> Also is Σ cos(ωn + θ), for n=0 -> N-1, zero?
Only if ω=2kπ/N, for k not a multiple of N.

>>11099496
The principal nth root is the one with the smallest absolute argument, ties going to the one with the positive argument (i.e. positive imaginary part). This is why e.g.√a√b=√(ab) doesn't necessarily hold for complex numbers. A radical sign (√, ∛, etc) denotes the principal root, not some unspecified or arbitrarily-chosen root.

>>11099521
>Enlighten me. All I'm seeing is some topological crap.
this "topological crap" would unironically answer all questions about the ambiguity or "loss of information" regarding square roots.

>And while you're at it, solve for the following:
>>ei2π−−−√ei2π
>>ei4π−−−√
depends on how you define the √ symbol. if it's the principal root, then 1. if it's supposed to denote all solutions to the equation, then {1,-1}.

>>11099560
Then is it fair to say [math]\sqrt{x}\neq x^{\frac{1}{2}}[/math]?
I'm getting the impression that roots are "open," and ambiguous. Short of writing everything in phasors, how do you distinguish between the principal root and any other roots? Verbally?

>>11099567
Topology's all fine and good, but does it lend itself to computation?
>if it's the principal root, then 1. if it's supposed to denote all solutions to the equation, then {1,-1}.
The first is arbitrary, and the second is ambiguous. How does that not create open, unsolvable problems in complex analysis?

>>11099432
>Is the purpose of complex conjugates to render their effective rotation to zero, i.e., to give a real number?
No, it's a mirroring.

>Aren't you losing information by doing this?
Why would you?

>3
No. The limes to zero of the difference quotient does not exist, it is dependent of the sequence.
|x| is not differentiable.

>>11099588
>How does that not create open, unsolvable problems in complex analysis?
Because mathematicians aren't idiots and understand that a symbol might have separate meanings in different contexts?

It's not like there is only one "=" or one "+" either, these symbols are totally ambiguous.
Not him by the way.

>>11099605
>who needs standards lmao
>>11099601
>it's a mirroring.
|x| is a mirroring, and because of that it's undifferentiable at x=0.
In a way, couldn't you say that [math](a+ib)(a-ib)[/math] is just [math](a+|ib|)^2[/math]? And wouldn't you expect complex conjugation to be undifferentiable, or otherwise cause problems, in the same way?

>>11099588
>The first is arbitrary
yes

>the second is ambiguous
yes

>How does that not create open, unsolvable problems in complex analysis?
because solution to a problem is not always just a highlited formula. the solution to "can we choose a non-arbitrary, unambiguous continuous inverse for z^n?" is "no, we cannot." the mapping z -> z^n is just not injective, but we understand perfectly in what way it fails to be so: each non-zero value has a discrete set of preimages (there's precisely n of them and they are evenly spaced on a circle), none of them is distinguished in any way, and the inverse exists locally around a small neighborhood of any of them, but it cannot be chosen globally in a continuous manner. I mean what else do you want?

>>11099694

>>11099694
>the mapping z -> z^n is just not injective, but we understand perfectly in what way it fails to be so: each non-zero value has a discrete set of preimages ... none of them is distinguished in any way,
That sounds a lot like multiplying things by zero desu. Like yeah, we all understand exactly what's being lost there, and we can stroke our beards all we want - but you cannot expect to perform reversible computations like that.
>none of them is distinguished in any way
>what else do you want?
Well, you/someone claimed earlier that phasors weren't necessary. However, if you take the 4th-root of 1 in phasors, you can easily distinguish the roots.
>[math]\sqrt[4]{e^{i0}}=1[/math]
>[math]\sqrt[4]{e^{i2\pi}}=i[/math]
>[math]\sqrt[4]{e^{i4\pi}}=-1[/math]
>[math]\sqrt[4]{e^{i6\pi}}=-i[/math]
And in reverse, you'll always know that:
>[math]i^4=e^{i2(4n+1)\pi}[/math]
>[math](-i)^4=e^{i2(4n+3)\pi}[/math]
And the modulus of 1 or 3 would give insight into how, say, capacitors (-i) and inductors (+i) work on a dimensional level. I forget the term for it, a double sphere? triple sphere? a three-loop? Basically, what >>11099719 posted: It would imply that capacitors work like a three-loop at the top, and that inductors work like a 1-loop on the bottom. Along those lines.

How are you supposed to reverse engineer reality when your calculations only work one way?

>>11099640
>>who needs standards lmao
Again. "=" is an ambiguous symbol.

>|x| is a mirroring
Nope, it isn't even a mapping to the same space, how can it be a mirroring?
Are you thinking of an even function, that is unrelated.

>and because of that it's undifferentiable at x=0.
Plenty of mirrorings are differentiable at zero.
Take a linear mapping if you don't believe me.

>And wouldn't you expect complex conjugation to be undifferentiable, or otherwise cause problems, in the same way?
Nope. There is no reason for that expectation.
The complex conjugate seems very differentiable to me. Among other things it is linear.

>In a way, couldn't you say that (a+ib)(a−ib) is just (a+|ib|)2
No.
It's a^2 + b^2, also |ib|=|b|

>>11099762
Not him, but you thinking in EE terms is highly counter productive.

>How are you supposed to reverse engineer reality when your calculations only work one way?
Just because a function isn't bijective doesn't mean represent something physically meaningful.
The mapping of your room to it's average temperature isn't bijective.
Is mathematics at fault? Or is the description of reality reductive?

>>11099800
>The mapping of your room to it's average temperature isn't bijective.
Temperature is a spook
>Is mathematics at fault? Or is the description of reality reductive?
I'm talking about systems where dimensionality is preserved. I'm also talking about things like Planck's [math]e^{\frac{a}{\lambda T}}[/math]addendum to the blackbody radiation equations, which is mentioned in every quantum mechanics course as direct evidence for quantized mechanics.

>>11099823
Thinking about complex numbers in terms of physics is highly counter productive.
The real world isn't the same as it's mathematical description. The map isn't the territory.

Something being arbitrarily defined in mathematics is totally inconsequential for mathematical descriptions, as long as the definitions are consistent, which they are in your case.

>>11099762
>That sounds a lot like multiplying things by zero desu
that sounds nothing like multiplying by zero

>you cannot expect to perform reversible computations like that.
I don't and nobody else does either, only you do. but belive it or not, there actually do exist functions which are not injective.

>>ei0−−√4=1ei04=1
>>ei2π−−−√4=iei2π4=i
>>[math]\sqrt[4]{e^{i4\pi}}=-1[/math]
>>[math]\sqrt[4]{e^{i6\pi}}=-i[/math]
>And in reverse, you'll always know that:
>>i4=ei2(4n+1)πi4=ei2(4n+1)π
>>[math](-i)^4=e^{i2(4n+3)\pi}[/math]
this is completely arbitrary. why not [math]\sqrt[4]{e^{-i4\pi}} = i, \sqrt[4]{e^{-i2\pi}} = i, \sqrt[4]{e^{i0}} = -1, \sqrt[4]{e^{i2\pi}} = -i[/math] or anything else ?

>>11099868
>why not e−i4π−−−−√4=i,
Maybe I should clarify. I don't get how this "principle root" is worth any more than a conversation piece, so for this post, [math]\sqrt[4]{x}=x^{\frac{1}{4}}[/math]
It should be obvious that
>[math]\sqrt[4]{e^{-i4\pi}}=(e^{-i4\pi})^{\frac{1}{4}}=e^{-i\pi}=-1[/math]
>[math]\sqrt[4]{e^{-i2\pi}}=(e^{-i2\pi})^{\frac{1}{4}}=e^{-i\frac{\pi}{2}}=-i[/math]
and etc.

>>11099924
>I don't get how this "principle root" is worth any more than a conversation piece
It's unique and well defined. Something which is an essential property for any "function".
It is the only meaningful way (up to some essentially equivalent definitions maybe) to talk about the square root of a complex number as a function onto the complex numbers.

Where is your actual issue, what does it mean that something is a "conversation piece" it is a well defined mathematical function.
You do not manage to actually justify why there is any issue except for very vague physics analogies which simply fall flat for far too many reasons, not him btw.

>>11098698
Actually in relativity it's better to treat spins as irreps of the homogeneous subgroup [math]SO(1,3)_+[/math]. This way you can use the action of time-reversal [math]T[/math] to distinguish between bosons and fermions using spin-statistics. [math]T[/math] is of course still an antiunitary automorphism between each spin-irrep but fermions and bosons correspond to the two different pull-backs of [math]SO(1,3)[/math] to [math]\text{Spin}_{1,3}[/math], so they will transform differently under [math]T[/math].

>>11099956
>Where is your actual issue
Whether or not complex conjugation caused a loss of information >>11099432
It's been a long day

>>11099970
>Whether or not complex conjugation caused a loss of information
no, it's a bijection

>>11098194
please help

>>11100200
what have you tried ?

>>11098194
looks like cauchy-schwartz anon-kun

>>11100240
It's Holder, proven with Young's inequality.

Didn't want to create a new thread so asking here, is neet catalog dead for everyone or just me?

>>11100273
ty yukarifag

>>11100240
We haven't learned it yet, but I'll look into what it is
>>11100219
I've finished problem 7, so I tried using that inequality for the summand but I don't know how to proceed

what does it mean to find a matrix transformation with respect to a basis or bases?

>>11100664
Consider a linear map [math]f \colon V \to W[/math]. Let [math]\alpha = (u_i)[/math] be a basis of [math]V[/math] and [math]\beta = (v_j)[/math] a basis of [math]W[/math]. A vector [math]u\in V[/math] can be written as [math]\sum_i x_i u_i[/math] for some scalars [math]x = (x_1,\dots,x_m)[/math]. Similarly the vector [math]f(u) \in W[/math] can be written as [math]f(u) = \sum_j y_j v_j[/math] for some [math]y = (y_1,\dots,y_n)[/math]. The matrix [math]A[/math] of [math]f[/math] in [math]\alpha[/math] and [math]\beta[/math] is the unique matrix satisfying [math]Ax = y[/math] in this scenario for EVERY vector [math]u \in V[/math], resp [math]f(u)\in W[/math].

>>11100690
tyvm anon

>>11100273
>Holder
Learn to spell.

>>11099992
it lost information on the starter of this little debacle, that bit is true

What does this mean?

D given ab implies d given a? I don't understand.

>>11102605

a = 3, b = 4, d = 6