/sci/ - Science & Math

>>10527130
How many images of Remilia Scarlet are there?

why doesn't "chemical reactions of gases" have its own classes at university, or at least a chapter in a gen chem book. I've never heard of it in school that I remember and when I google I don't find a lot. I'm sure it exists and I'm sure it's out there, why is it considered by academic agenda-setters to be not worth any time? Are such reactions not economically valuable, or are they extremely uncommon in nature, or what?

I was given a project by my professor to test over-saturation in UV-Vis and Fluorescent spectroscopy using fluorescein. The lab paper said that fluorescien was water soluble. I found out the way that it slightly soluble and was absorbing all wavelengths. I know I need to use a solvent. But which give less overlap?
If I use PH=9 NaOH will that cause an over saturation of sodium ions? Will it affect my absorbance significantly?
Should I use ethanol?
Which solvent would be best for fluorescein?

>>10527252
Danbooru says at least 39k.
https://danbooru.donmai.us/posts?utf8=&tags=remilia_scarlet&ms=1

>>10527306

I did an internship in a lab that studied exacly that, and they were rolling in car industry money. Not sure how it is now.

>>10527377
that's neat. could you explain how it was relevant to the car industry? did their work help the cars to meet govt regulations on emissions? I can't think of another relevance

>>10527130
Well I was rejected admissions into the transfer program of my choice. They say I can't retake any of the critical tracking classes to boost GPA. Are summer terms more competitive than fall? Should I just suck it up and attend the rinky dink state university a few towns over? Any tips to weasel into program of choice?

>>10527338
I want to know how many there are total

An arbitrary union of a collection of sets is the set of elements that occur in at least one of the sets in that collection. An arbitrary intersection of a collection of sets is the set of elements that occur in all of the sets in that collection.

Is there some named generalization that would let me talk about e.g. a set of elements that appear in exactly two of the sets in a collection of sets, or between five and seven, or some specific proportion of sets?

>>10527338
danbooru is for plebians
I had a remilia folder on my old laptop that I built from a pixiv auto downloader and booru downloader
it bad over 200k images
once I deleted dupes it went down to about 150k
im sure there are many MANY more

>>10527494
>he just saves whatever trash shows up
Anon, that's... horrendously disgusting.

>>10527402

Basically yes, a small part of it was verifying that engines were respecting norms, but the major part was to test litteraly thousands of parameters such as combustion temperature, pressure, etc, to try and optimize engine programming and stuff.

Other teams were studying things like atmospheric pollution, hydrogen safety (aka in which particular conditions it will explode), and so on.

Pretty cool stuff all around, especially working with shock tubes (https://en.wikipedia.org/wiki/Shock_tube)), you can do it dozens of time it's still fun to push the button.

>>10527474
*Basically I'm a dumb CSfag and have a a function that takes in two integers (N and M) and a collection of sets and spits out a set that contains all elements that appear in between N and M of the provided sets. And I'm wondering what to call the function.

When N==1 and M==number of sets, the function is equivalent to an arbitrary union. When N==M==number of sets, it's equivalent to an arbitrary intersection. What is it for all settings in between, or in the general case?

>>10527503
Yes I save everything
I have two subfolders
SFW and NSFW
each of those folders is then split in subfolders A, B, C, D, E, F. Highest quality goes into A, lowest into F
If you loved Remilia you'd do the same, casual.

>>10527521
>I have two subfolders
I should say HAD, my precious thinkpad got yoinked

I'm having issues with the pictured problem. I think that the answer is no, since the Bhabha scattering has both an s-channel and t-channel diagram, whereas the muon production will only have one diagram.
Because of this, you'll have to sum the two amplitudes together for the Bhabha scattering in order to find the matrix element, which you won't have to do for the pair annihilation since there's only one diagram.
I think this means that the Bhabha scattering will have a far more complex equation to determine its cross-section than the pair annihilation, due to the greater number of terms, and so the answer is "no." However, I feel very uncertain that this is correct, and was having difficult trawling google to try and confirm my answer, so I figured I'd try asking here.

>>10527558
fucking forgot the picture

>>10527503
What a cop out answer, might as well be a booru mod justifying your lack of content by saying "m-muh quality over quantity" when you miss almost everything that gets on pixiv's top.

>>10527130
How do I get into gerontology? I'm a physicist.

I'm calculating torque specifications for an extracurricular project. One of the requirements is that all bolted connections include locknuts. I haven't been able to find data on the effective friction between bolt threads and a nylon locknut. Does anyone have a source for this that I can use?

I need to solve a non linear system with 4 equations, but I don't have numerical values for the "parameters" of my equations, I want to find a general solution. My problem is that Matlab, Python and the TI calc can't solve the system unless I give them numerical values for my parameters, what other program can I use to solve my system??

>>10528460
https://en.wikipedia.org/wiki/Cramer's_rule

>>10528465
there it says that it's for lineal equations :c

probably a very stupid question, but must H also be a cyclic group in this example?

>>10528460
> I need to solve a non linear system with 4 equations, but I don't have numerical values for the "parameters" of my equations, I want to find a general solution.
What makes you think such a solution exists? Most equations don't have a closed-form solution.

>>10528460
what are the equations

>>10528547
yes

given any of the 3 widely taught acid theories, is everything either an acid or a base in that system? So in Arhenius theory, is every chemical either an Arhenius acid or an Arhenius base? Would this depend on solvent and other thing too, so that something that's an Arhenius acid in water is not as a solid, or is not in pH5 water?

followup, now that I think about it, can water be ph5 without adding another substance, at STP?

>>10528547
No, but the image of G under the homomorphism is cyclic.

I have no higher education. If I wanted to gain a graduate level of understanding in both math and physics, what resources should I consult assuming I want to spend $0?
My timeframe is 30 years

What is the meaning of a phase in electrical distribution? Homes in the US have a split-phase system that's technically single phase power with the legs offset by some degrees. Two phase power seems to work the same way but there's obviously a difference between them as all split phase induction motors need auxiliary winding or some other measure in order to start while two-phase motors do not. I'm thinking it has something to do with phases being independent in some way but aren't both secondaries in a two phase transformer sharing the primary? Wouldn't that make them not independent?

>>10528917
> split phase induction motors need auxiliary winding or some other measure in order to start while two-phase motors do not.
Two-phase motors are quadrature: two phases offset by 90 degrees, which is effectively 4-phase (you can just flip either phase to get another phase: 0->180, 90->270). Split-phase power has the two phases offset by 180 degrees, i.e. it's just a single phase plus its inversion.

>>10527130
How can I look at path integrals intuitively? I just solved one (two singularities in a circle) and I got zero for the answer. I have no insight into whether this makes any sense or whether it means I made a mistake.

>How do I make the most of an honours year (Research)
So basically I'm placed at a lab and I'm helping do oncology

I have a literature review due that's worth 50% of my grade. I panicked and wasted heaps of time freaking out about it, and now I'm sure whatever I submit won't be very good but I'll pass.

So I won't get a first class honours, which means that I won't get paid a scholarship to do a PHD, and it seems a PHD is a dead end anyway. How tf am I supposed to network? I'm like an insect here. The other students are smarter than me despite me working what feels like twice as hard as them.

How do I make use of this opportunity other than just finishing it and passing? I'm super neurotic and lab work honestly stresses me the fuck out. I feel like a child missing his mommy in a kindergarden. I'm working my ass off but it just doesn't feel good enough. Everyone is miles ahead of me at this point.

>>10527130
you had to put an animu image didn't you

>>10529328
If its stressing u out this much. Have you thought about just taking a year off ? Get some mindless job with low hours and reevaluate what your doing.

Ok, I'm asked to prove that if [math]|x-x_0<\epsilon/2|[/math] and [math]|y-y_0|<\epsilon/2[/math] then [math]|(x+y)-(x_0+y_0)|<\epsilon[/math] and [math]|(x-y)-(x_0-y-y_0)|<\epsilon[/math].
I have successfully demonstrated #1 but I don't understand how to demonstrate #2.

>>10529328
I've recently learned that webisite called "reddit.com" uses such filenames for images. Do you happen to visit that website?

Ok, I'm asked to prove that if [math]|x-x_0|<\epsilon/2[/math] and [math]|y-y_0|<\epsilon/2[/math] then [math]|(x+y)-(x_0+y_0)|<\epsilon[/math] and [math]|(x-y)-(x_0-y-y_0)|<\epsilon[/math].
I have successfully demonstrated #1 but I don't understand how to demonstrate #2.

Question from last thread:
show that the mean square is always greater than the square of the mean

>>10529193
But they're different in more ways than just the offset aren't they, since two-phase uses two secondary windings in the transformer while split just uses two ends of one? If it was just a difference in offset, wouldn't you just be able to offset split-phase by 90 degrees instead?

>>10529417
nope

>>10529408
Literally just did that and it made me want to kill myself

>>10527130
How do you get relevant, scientifically accurate information out of /sci/?

I'm a physics undergrad taking a grad differential geometry class. What are some good ressources on Lie algebra ? I have a decent understanding of groups, but I'm having trouble understanding topologies and manifolds with the given material

>>10529421
>|(x-y)-(x_0-y-y_0)|
Typo? Mean |(x-y)-(x0-y0)|?
Use |a+b|<=|a|+|b|
>>10529319
In complex analysis or more generally?

>>10529319
Tbqhwyf the only way of really understanding it is reading up on algebraic topology and de Rham cohomology.

>>10529435
> But they're different in more ways than just the offset aren't they, since two-phase uses two secondary windings in the transformer while split just uses two ends of one?
Two-phase mains is a relic from the early 20th century. There are hardly any two-phase utility supplies still running. Modern two-phase motors are either low-voltage (where both phases are synthesised electronically from DC; e.g. PC fans) or (for mains power) use a run capacitor to generate the other phase.

You can't get two-phase just from two secondaries on the same core; you'd need two distinct primaries as well. The secondary voltage is in phase with the primary voltage (or opposite to it, if you make the connections the other way around).

> If it was just a difference in offset, wouldn't you just be able to offset split-phase by 90 degrees instead?
That's what a run capacitor does.

Split-phase isn't any different to single-phase when it comes to motors. Split-phase is used mainly as a way to provide a 240V supply in countries where 120V is standard.

Is it possible for somoene to learn to become a good Orator?

(dunno if this is the right board even, I mean it's the science board and I guess this is a question about Psychology?)

>>10529434
> show that the mean square is always greater than the square of the mean
Mean square:
[math]{1 \over n} \sum_{i=1}^n x_i^2[/math]
Squared mean:
[math]({1 \over n} \sum_{i=1}^n x_i)^2 = {1 \over n^2} (\sum_{i=1}^n x_i)^2[/math]
Note that
[math](\sum_{i=1}^n x_i)^2=\sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^n \sum_{j=1}^{i-1} x_i x_j[/math]
[/math]\sum_{i=1}^n \sum_{j=1}^{i-1} (x_i-x_j)^2 = (n-1) \sum_{i=1}^n x_i^2 - 2 \sum_{i=1}^n \sum_{j=1}^{i-1} x_i x_j[/math]
Thus
[math]((\sum_{i=1}^n x_i)^2+\sum_{i=1}^n \sum_{j=1}^{i-1} (x_i-x_j)^2 = n \sum_{i=1}^n x_i^2[math]
Divide both sides by n^2 to get
[math]{1 \over n} \sum_{i=1}^n x_i^2 = {1 \over n^2} (\sum_{i=1}^n x_i)^2+{1 \over n^2} \sum_{i=1}^n \sum_{j=1}^{i-1} (x_i-x_j)^2[/math]

>>10529434
> show that the mean square is always greater than the square of the mean
Mean square:
[math]{1 \over n} \sum_{i=1}^n x_i^2[/math]
Squared mean:
[math]({1 \over n} \sum_{i=1}^n x_i)^2 = {1 \over n^2} (\sum_{i=1}^n x_i)^2[/math]
Note that
[math](\sum_{i=1}^n x_i)^2=\sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^n \sum_{j=1}^{i-1} x_i x_j[/math]
[math]\sum_{i=1}^n \sum_{j=1}^{i-1} (x_i-x_j)^2 = (n-1) \sum_{i=1}^n x_i^2 - 2 \sum_{i=1}^n \sum_{j=1}^{i-1} x_i x_j[/math]
Thus
[math]((\sum_{i=1}^n x_i)^2+\sum_{i=1}^n \sum_{j=1}^{i-1} (x_i-x_j)^2 = n \sum_{i=1}^n x_i^2[/math]
Divide both sides by n^2 to get
[math]{1 \over n} \sum_{i=1}^n x_i^2 = {1 \over n^2} (\sum_{i=1}^n x_i)^2+{1 \over n^2} \sum_{i=1}^n \sum_{j=1}^{i-1} (x_i-x_j)^2[/math]

>>10529761
>or more generally?
Just in CA. I confirmed the answer with the cover up rule, but it's still a mystery why the path evaluates to zero. The function had two simple poles on the positive x-axis and the path was just a circle about zero that contained them both.
>>10529798
I'll keep that in mind for the future, I guess...

I need hel with this from probability: it has to do with random variable trasnformation and distributions I belive:
X is a random variable with probability density funcion given by:
[math]βx−^{(β+1)}I[1,∞)(x)
[/math]
Let W be random variable defined by W=Ln(X) Find the Density Function of W
b) Does W have a know density function

Aren't they all parallel?

>>10530047
Forgot to attach a pic lmao
And I meant to say in series, I'm high

>>10529434
>>10529976
An easier way to do this is to take the square root of both expressions
The mean square then becomes the norm of a vector x divided by sqrt(n). Squared mean then becomes the inner product of vector x and a vector of 1s, divided by n. This simplifies to the norm of x times the norm of the vector of 1s times cos(t) divided by n. The norm of the vector of 1s is sqrt(n), so the expression simplifies to the norm of x times cos(t) divided by sqrt(n). The magnitude of cos(t) is always 1 or less, so the squares of these expressions must show that Mean square is greater than or equal to Squared mean for all vectors x.

>>10529434
Jensen's inequality
>>10529688
lol

Is mathematics a creation or a discovery?

>>10530067
Only reason I ask is because of this post
>>457652491

>>10530074
Shit

>>10530038
F_W(w) = P(W <= w) = P(X <= exp(w))

= F_X(exp(w))

Find the CDF of X in terms of x, replace x with exp(w), then differentiate wrt w. Make sure you keep an eye on stuff like differentiability and whether the mapping is one to one. The function you get after differentiating with respect to w is the density function of W, assuming it exists. Looks to me like it might be the Weibull distribution.

p = np?

>>10529816
If your speaking problem stems from physical setbacks like speech impediment, then yes you can retrain yourself to speak and tighten muscles associated with speech with extensive practice.

If your problem stems from having cluttered thinking and incoherent thought processes, then probably not. The potentiality for any given person’s verbal competency is largely genetic and you won’t change it to a significant degree through practice.

Though, it’s important to remember that speaking unscripted with fluency to an audience is not a skill many people have. Most people who speak do numerous rehearsals and are heavily scripted. This includes most world leaders even, so leveling an expectation on yourself above that is not exactly reasonable.

Is the norm of each column in a unitary matrix equal to 1?

there's exists a master theorem equivalent for differential equations?

>>10530061
>>10530063
>>10529434
Here's my take:
say we have two equal values a=x and b=x and we take a little away from a and give it to b then the sum of the squares of a and b will increase because this is equivalent to being at x in the fucntion f(x)=x*x and moving a little left and right, the derivative on the right side is greater and the right side will then increase more than the left will decrease, and if we have any number of equal values and remove from some and give to other the mean square can only increase, and only at the beginning when all values are equal the mean square and square mean are equal otherwise the mean square is greater.

>>10530128
yes

>>10529812
>You can't get two-phase just from two secondaries on the same core; you'd need two distinct primaries as well. The secondary voltage is in phase with the primary voltage
I know, but those primaries/secondaries are on the same core and powered by the same magnetic flux are they not? Doesn't that mean they're synced in some way (even if offset from each other)? Which brings me back to my main question, what actually is a phase and am I wrong in that it relates in some way to independence? Also, how does that differ from a leg i.e. split phase( 1 phase 2 legs) and 3 phase 5 leg power.

Am I stupid?

>>10530272
...anyone?

>>10530843
Yes, a unitary matrix is basically a generalization of an orthogonal matrix for complex matrices. Just as an orthogonal matrix, it's columns are an orthonormal basis of the vector space they are defined in.

>>10530272
Fix a=(0, 0, 0, ...1, 0, 0....). It's image is the collumn. Since it's unitary, <Aa, Aa>=<a, a>=1.

>>10530943
i have no idea what this means

>>10530948
Ah, you're using the transpose definition, not the inner product definition.
It's suckier to prove from that one.

>BS in Physics
>Hate CS
>Want good money though

What should I do? Will an M.S. in engineering help my situation? Or should I keep aiming for an MS in physics with a focus on optics/lasers? Satan give me wisdom

CSfag who made this problem up for my friend in Calc I. I was planning to show at the end that integrating rotational frequency versus time would give me the number of rotations the same as if I had just multiplied the final position by the thread pitch. Apparently I'm a brainlet. Where did I fuck up?

>>10531016
Do the cool physics shit anon. Or do finance.

whats a good recoil dissipation mechanism if i want to fire a 5kg projectile downwards at nearly 1 km/s

>>10531023
Mostly where you decided to do notes in mspaint.exe using your mouse

>>10531114
I did it on a whiteboard at school and forgot to take a picture now help me you ass

>>10531023
Sign error lmao

I can't for the life of me figure out how to get to that last line. Any input ?

Say i have a function like:
z = 1/ (1/x +1/y)
x = {1 .. n}
y = {1 .. m}
x and y are integers


How would i find a set of x and y integer pairs that gives a linear (or closest to linear) set of z values over the lowest and highest possible z value range?

>>10531310
Do you guys think it could be a mistake ? Because

\frac{x}{x^2+y^2} = \frac{x}{1-z^2}=\frac{x}{(1-z)(1+z)}

But when I try to calculate it, I get
\frac{x(1+z)}{1-z}

Wich still has the properties needed (i.e. being continuous in a domain excluding z = +/-1)

Also, pretty sure that's not how you write equations on here so if anyone could also help me with that, it would be great

>>10527130
When we do dot product of A and B vector. Does it calculate the componet of A along B or component of B along A?

Is this really different? Can someone explain why?
>(-x/y) = -(x/y)
>this doesn't?

>>10531508
Draw the vector's A and B coming out from the same point O. From the ending of B, draw a line that hits vector A orthogonally, and mark this point C. Multiply OA by OC.

>>10531649
The - in front of the fraction is basically an implicit -1, while the whole numerator is just a single factor. Apply the distributive property to the numerator so you can see for yourself how you fucked up.

>>10531508
it is commutative...

>>10531649
>(-x+y)/z
>-(x+y)/z

>>10529688
it's a pretty good rule for the internet in general: confidently post some clearly wrong information about the subject you wish to know more of, then some smartass "akshually" type will come in and give you a free step by step lesson of the actual knowledge just to one-up the dumdum you seem to be

>>10531690
Oh
Yeah

If unpolarized light passes through a filter at 0°, is the resulting intensity unchanged? That seems kinda counter-intuitive to me.

>>10527403
>>>/adv/

>>10528460
>Julia
>total meme
Well at this point you have nothing to lose so I'd look into it anon

>>10530757
> but those primaries/secondaries are on the same core and powered by the same magnetic flux are they not?
With a poly-phase transformer, each secondary goes on the same edge/branch as the corresponding primary, so the primary and secondary for a given phase always share the same flux. Having all of the windings on a single physical core just reduces the size and mass compared to using three separate cores; the results are the same.

> Doesn't that mean they're synced in some way (even if offset from each other)? Which brings me back to my main question, what actually is a phase
See the first diagram in the wikipedia article for "three-phase". AC has a (roughly) sinusoidal waveform. Different phases of a supply are out of phase (offset) from each another. Motor windings for different phases need to be out of phase with each other in order for the net magnetic field to rotate, causing the motor to turn.

tbc (field too long)

>>10530757
Cont'd from
>>10531966
> and am I wrong in that it relates in some way to independence?
Not wrong. Two phases which are 180 degrees apart aren't independent; one is just the negation of the other. If you have two non-parallel vectors, you can construct any other vector in the same plane as a linear combination of the original two vectors. But if the two vectors are parallel, then any linear combination of them is also parallel. For a motor, this means there's no way to make a rotating magnetic field from a single phase (or split-phase). The direction will be fixed, and only the magnitude will vary. This may be enough once the motor is running, but the motor may not be able to start, or you may not be able to control the direction (CW or CCW). If a motor can run on a single phase, a start capacitor can be used to generate another phase just for starting.

> Also, how does that differ from a leg i.e. split phase( 1 phase 2 legs) and 3 phase 5 leg power.
A "leg" is just any supply terminal which isn't neutral. 1 phase 2 legs is has 2 phases of a 3-phase delta supply designated as legs with the centre tap of the winding between those phases designated neutral. 3 phase 5 leg is 3-phase delta with the 3 phases and 2 of the centre taps designated as legs (the other centre tap is neutral).

>>10531508
A·B = B·A = |A||B|cos(θ) where θ is the angle between them.

If you want the component of one in the direction of the other, the latter needs to be normalised (unit length). A·(B/|B|)=A·B/|B|=|A|cos(θ) is the component of A in the direction of B, (A/|A|)·B=A·B/|A|=|B|cos(θ) is the component of B in the direction of A.

Brainlet here, pls help me understand fourier transforms intuitively
From what I get, you take a function evaluated in t to another space where you get the frequencies (the values where there are peaks) which make up the fourier integral of that function.
Is this correct?

>>10532008
Don't know if this makes it more intuitive, but if you took differential equations first it's the same as a laplace transformations but with a real variable.

>>10532008
A Fourier transform of a function is similar to a matrix transform of a vector (in fact, a discrete Fourier transform is just a matrix transform). It just transforms one function to another. The transform is linear (F{f+g}=F{f}+F{g}, F{k.f}=k.F{f}) and invertible. The most important property is that it's a convolution transform: F{f∗g}=F{f}.F{g}.

The Fourier transform of a sine wave is a function which is zero everywhere except at the wave's frequency. The Fourier transform of any periodic function is zero everywhere except at multiples of the frequency (=1/T, where T is the period); this leads to the concept of a Fourier series: a periodic function is equal to the sum of sine waves whose frequencies are integer multiples of the function's frequency.

What causes changes in personality? recently I've noticed things I used to love I now have no interest in, it's a pretty drastic change since a lot of my interests and pastimes now just have no allure to me. I'm not depressed and am actually a lot happier, I still have things I like but seemingly overnight a ton of things I liked I just no longer care about, what could cause this?

>>10527511
>>10527474
Guise?

Simple gradient decent/stochastic gradient decent/deep learning question, and this might just take the brainlet-award:

How the fuck do i make a line from a set of points?? I think that's what I don't understand anyway. There's just something about the whole "make a line which fits the points"- ordeal which doesn't make any sense.

We have weights which approximate the actual result. So we have two dots: the approximation and the actual, the approximation - the actual = the error/the loss. But no we actually have a fuckton of pairs of dots. Because the weights approximate more than one case of the same categories of values, but with different result, and it does this in order to generalize so that it can predict something in the future, not just the current set of data (that's overfitting). The loss function is different depending on how hipster you are, but generally it's the mean squared error. This means the mean from each example squared, square it, add it all together, then divide by amount of examples to get the average loss.

The gradient decent part is where you magically make the weights become something which decreases this average loss. This is illustrated by making a line fit to dots. So you have a straight line, which you derive, and then this somehow creates a minimum? And here i thought derivating a straight line leaves only a constant, oh how i was wrong!

So where does this line come from? Nowhere did anyone mention a fucking line. They just say "now there's a line y = kx + m that we make point better towards the data". Yeah well, we have no line aswipe, we only have points. And these points aren't even sorted, so whatever line you think you may create wouldn't be very straight you fuck now would it?

And what do you even derive anyway? You have no fucking function to derive. Just data. Unless you think about it like f(x0, x1, x2, x3) = x0^2 + 8x1 + x2 * x3 = dependent variable or something, but we don't have that.

I'm pissed.

I was good at maths in high school all the way through calculus and I want to reacquaint myself. I work 80 hours a week and really just have like 30 minutes to an hour per day to do some drills. I just want to study algebra in depth again because that was how I got good at calculus, and maybe re-familiarize myself with geometry and trigonometry, so I'm looking for a book to study each day while I get financially prepared to gtfo my 80hr/wk kitchen job and get back to college

>>10532667
As it turns out, there's something called linear regression analysis which sort of ties it all together. I found that out myself without anyones help. Thanks a bunch, /sci/, i'm not angry, i'm disappointed.

what is a vector? I read the eli5, the wikipedia, a couple texts' chapters, still don't get it. I understand that velocity in a direction is an example of a vector, but I don't understand the general case. Who invented, them, for what purpose. Are they just ordered triplets if the third number is the amount of rotation?

I’m 90% of the way through my statistics degree. The only classes I have remaining are capstone, two math stats classes and Calc 3.

Here’s the fucking problem. I dropped Calc 3 my first attempt and am now 80% of the way through the class and it’s looking nearly impossible to get a C in the class. I don’t know what to fucking do at this point. I can’t take the math stats courses until I finish Calc 3 and who knows how fucking hard those math stats classes are going to be.

I’m spending 2 hours or so a day studying for this class, dominating the hw problems and fucking bombing the exams.

Please help me

>>10532406
Age and brain development

>>10532867
are there any books that cover what creates a personality and influences it etc, preferably brainlet friendly

>>10532740
> what is a vector?
An element of a vector space. See
https://en.wikipedia.org/wiki/Vector_space#Definition
That is literally what a vector "is"; no more and no less.

Specific types of vector space will add their own rules to that. E.g. for a coordinate space, vectors are fixed-size tuples whose elements are drawn from a field (commonly real or complex numbers, but can be any field), addition of vectors is defined as element-wise addition <x1,y1,z1>+<x2,y2,z2>=<x1+x2,y1+y2,z1+z2>, scalar multiplication is also element-wise k*<x,y,z>=<k*x,k*y,k*z>, the zero vector is <0,0,0>, etc.

Normed vector spaces include an operation which measures the length of a vector, inner product spaces include an operation which measures the angle between two vectors.

It's quite possible to make practical use of vectors without understanding most of the mathematical theory behind it. One downside of that is that a lot of "lay" writing on vector math (including a lot of useful stuff) is written by people with a fairly limited understanding of the underlying mathematical theory (particularly physicists and computer scientists, for whom practical applications are more important than the underlying theory).

how is this limit equal to 1/16?

>>10533058
nevermind im such a fucking retard

>>10532740
https://www.youtube.com/watch?v=fNk_zzaMoSs

>>10529434
the square function is convex.

QED

I’m an undergrad student and just found I’m eligible for an honors program through which I can get an MS in 5 years. Which is 3 years for me. So this means I took a year of tuition off my total cost.
My question is... should I get a PhD? This program makes it financially viable but I have no idea how this process even works. Is it like grad school but you apply as an graduate? Is it worthwhile to do it? I know I’ll have no life for my mid 20s, I’m ok with that. But if I don’t do this now I probably never will.
Redpill me on PhD studies
>inb4 /adv/
You know they have no experience with this

>>10531788
the resulting intensity is half.

it's the average of cos^2(t) where t goes from 0° to 360°

Could someone please explain vector fields in polar coordinates to me? Every explanation so far has used engineering notation, and I feel I don't grasp it well enough to change notation, which is a bad sign.

I understand vector fields in Cartesian coordinates well enough, but the unit vectors depending on our angle seems strange to me, and I'm not even sure how you would express that without resorting to engineering notation, but of course it must be possible.

Can someone explain the term circled in red for this lagrangian of a charged particle in an EM field? Where does it come from and why is it like that

>>10533346
The lagrangian is designed so that it works when you derive the equations, it doesn't make any sense.

>>10533348
In the exercise i'm doing i was supposed to write the lagrangian of that system on my own, using the definition: kinetic energy - potential energy. How could i have done that if it doesn't make any sense?

When does the Limit Comparison Test not work, as in, when will I be forced to use the Direct Comparison Test?

Could anybody integrate this [math]\int _0^{\infty }\:\frac{c}{x}\cdot \:e^{-x^2\cdot \:y}dy[/math] and tell how the solution goes?

>>10533926

Don't overcomplicate - it's only an integral wrt y, so all of the x terms can be treated as constant. Then it's an integral of the form ae^(-by) which is simple enough.

Making a section view in solidworks, but the arrows look weird. How to a get the section arrow to point away from the cutting line?

>>10534022
You can change the direction in the side panel or buy clicking the arrows

>>10534044
That didn't work. Turns out I had to change the drafting standard from ISO to ANSI. Thanx anyway bby.

>>10533324

I'll put some words here about unit vectors first, in 2D. I'm not sure that I totally understand your ask.

Are you happy, with 2D polar coordinate systems, that we can specify every position on a plane with two coordinates: r and [math]\theta[/math]? So any point is some distance from the origin and in some direction - combining those two bits of data, we can specify any point (uniquely).

Now, back to Cartesian (xy) coordinates. If someone travels along the x axis, we talk about then moving the in [math]\hat{x}[/math] direction. And similar for y. When someone walks diagonally, they move in both [math]\hat{x}[/math] and [math]\hat{y}[/math] directions simultaneously. These unit vectors just give the direction.

In polars, we can similarly move in two specific ways. We can move closer or further from the origin. This is [math]\hat{r}[/math]. Alternatively, we can move in a circle (clockwise or anti-clockwise), maintaining radial distance from the origin. Now, if we do this, the value of [math]\theta[/math] changes, so we call this [math]\hat{\theta}[/math]. Our movement is changing [math]\theta[/math].

For example, when a force, say, rotates an object, it is moving that object in a [math]\hat{\theta}[/math] direction.

In general, if we move around a polar coordinate system, we are changing both r and [math]\theta[/math].

precalc brainlet reporting in.

On day 1 of Trigonometry. The others haven't arrived yet.

If I crush these books, how set will I be for calculus? And how long will it take to get through these? I have a lot of free time right now and I plan to use it wisely.

>>10534431
Precalc for me was nothing like calc 1. It's basically an algebra refresher course to teach skills for calculus but includes little actual calculus
Always aim to crush

I need an algebra book

Is geoengineering a viable way out of the coming global warming catastrophe? Or are we fucked

>>10534431
I felt calculus was only a smige harder than precalc. You'll do fine.

If I take the derivative of f(x') w.r.t. x', is the resulting function in terms of x'', or is it still x'?

Is it possible to solve multi variable functions using vectors?
If so
What are the best books to self-teach for a beginner?
(About Both multivariable calculus and vectors)

>>10527130
By age 12, the human eye attains its full size of about 24 mm in diameter (23.7 mm - 24.2 mm). There is little to no difference between sexes, ethnicity, ages, or even the size of the person's frame. - How then, do some people seem to have beady little eyes, and others seem to have very large eyes?

Reading about the EHT, and how they have to fly hard drives to wherever in order to compile the data.

What is the maximum throughput of a sneakernet, with current tech? And will sneakernet always have the highest throughput of any information transmission method?

>>10527130
Hey geeks, when my brain isn't busy, it thinks about Star Wars. How would Time work? I ain't a pro scientist but i am familiar with relativity. I don't know the numbers and measures or the scale of significance. They are pretty much running in or around one galaxy and we know that there are at least 12 parsecs to work with. Would this be enough to fuck things up when Luke is dicking with yoda and his friends are playing grabass on a gas giant, then they meet up later and everyone is still the same age and there is still time to do shit. Splain me?? The books never talk about this and it is hard to disregard parts that may be human construct. Like, I assume the republic threw time zones out and it is simply the same time everywhere but would that work??

Hi, I need to buy a calculator for a class and it needs to pass this restriction.

>Any calculators that can do symbolic mathematics such as TI-89 or HP-49 are NOT allowed on exams and quizzes.

Is the Casio fx-CG50 safe?

Right now is on discount. Same price as the Casio fx-9860GII on Amazon and it would be nice to get something a bit better for the same price.

>>10527130
what's an example of a square integrable function that's not a wavefunction?

Bit of an obscure question, but how the FUCK am I supposed to remember radiology positioning without actually doing it on a real patient?

For example, for one projection you need to have the patient's head at a certain angle to the x-ray tube, at a certain distance, with the light covering a certain area. Now multiply this by about 10 and insert a bunch of modifications depending on what bone/sinus you're looking at. I can attempt to categorize this shit in a spreadsheet, but how am I even meant to study it? I find anki usless when I have to remember so many rules of thumb and numbers for each projection.

The same shit happened to me when we learned extremities and I barely even knew what I was doing until my hospital rotation where I actually got to learn on people. Now I just sort of know that shit automatically because I got to practice it.

>have to make a facebook account to communicate with normie classmates in a group assignment
>make it and all goes well
>login today
>'we've noticed some suspicious activity, so fill out a captcha and give use your phone number goyim
What the fuck do I do now? We don't have google talk in my country and they're not getting my phone number, ever.

>>10535654
Get a vpn
Get a prepaid phone subscription (those are still around no?)

Does anyone have any hints to prove this?

Let [math]S(n)[/math] be the number of square free integers up to [math]n[/math]. Prove that

[math]S(n)=\sum\limits_{d=1}^{n}\mu(d)\lfloor\dfrac{n}{d^2}\rfloor[/math]

Where the mu is the Moebius Function

>>10532667
>>10532734
now do it with MCMC for better results.

I have a pretty stupid question but I was just (well, second time actually but first time it was in logic) introduced to mathematical induction. I think I have good understanding of the concept but I don't know how to prove this equality
[eqn]1^2+\dots+n^2=\frac{n(n+1)(2n+1)}{6}[/eqn]
using mathematical induction, ofc.
I've proven that when [math]n=1[/math] the equality holds so now I've only got left to prove that it holds for [math]n+1[/math] if it holds for [math]n[/math]. I tried doing it like this.
[eqn]1^2\dots+n^2+(n+1)^2=\frac{n(n+1)(2n+1)}{6}+(n+1)^2[/eqn] but I just can't seem to get [eqn]\frac{(n+1)(n+2)(2(n+1)+1)}{6}[/eqn]

>>10530067
Math is like a language, they are created symbols to represent an already existing reality, so I would most likely call it invented, cause it was produced by someone. As a way to understand something that already existed, but definitely created

>>10534688
bump

>>10534688
the skin is covering them

>>10536011
i could have got THAT answer on /b/ or /pol/.
came onto /sci/ for a reason.

>>10535978
Well, add the fractions together so that there's only one fraction then expand both polynomials out. If it's the same polynomial they're equal.

>>10536019
try making separate thread

>>10536020
That's what I did. I must be missing something here.
[eqn]\frac{n(n+1)(2n+1)}{6}+(n+1)^2[/eqn]
[eqn]\frac{n(n+1)(2n+1)}{6}+\frac{6(n+1)^2}{6}[/eqn]
[eqn]\frac{n(2n^2+3n+1)}{6}+\frac{6(n^2+2n+1)}{6}[/eqn]
[eqn]\frac{2n^3+3n^2+n}{6}+\frac{6n^2+12n+6}{6}[/eqn]
[eqn]\frac{2n^3+9n^2+13n+6}{6}[/eqn]
What now?

>>10532667
>We have weights which approximate the actual result. So we have two dots: the approximation and the actual, the approximation - the actual = the error/the loss. But no we actually have a fuckton of pairs of dots. Because the weights approximate more than one case of the same categories of values, but with different result, and it does this in order to generalize so that it can predict something in the future, not just the current set of data (that's overfitting). The loss function is different depending on how hipster you are, but generally it's the mean squared error. This means the mean from each example squared, square it, add it all together, then divide by amount of examples to get the average loss.


suppose your data points are generated by some function f(x,m,b) = mx + b + e, where e is random gaussian noise, and you want to find m and b. the important part here is the noise term. without it, your points would all be on the same line.

you want m and b that maximize p(m,b | data)

p(m,b | data) = p(data | m,b)p(m,b)/p(data).

p(data) is just a constant. if you just assume a uniform prior, a maximizer for the likelihood p(data | m,b) also maximizes p(m,b | data).

the density p( y | x,m,b, var) is N(y | mx+b, var), the normal distribution centered around mx+b.

assuming your y data were drawn independently, p(y1,y2, ...,yn | mx+b, var) = N(y1 | mx+b,var)*N(y2 | mx+b,var) * ... * N(yn | mx+b, var)

instead of maximizing this, you can equivalently minimize the negative logarithm. so the product becomes a sum, the logarithm undoes the exponential in the normal PDF, and the negative cancels so you have each term a(y-(mx+b))^2 where a is some positive constant.

so if you assume a linear relation between x and y, and that the only reason they don't all lie on the same line is because of normally distributed noise, then you can see how your loss function is justified.

>>10536074
>p(y1,y2, ...,yn | mx+b, var) = N(y1 | mx+b,var)*N(y2 | mx+b,var) * ... * N(yn | mx+b, var)

p(y1,y2, ...,yn | x1,x2,...xn, var) = N(y1 | mx1+b,var)*N(y2 | mx2+b,var) * ... * N(yn | mxn+b, var).

also note that the variance is just a constant

>>10535506
anything that isn't differentiable

>>10536074
>p(data | m,b)

forgot p(data | m,b) = p(x,y | m,b) = p(y | x, m, b) p(x,m,b) and you get p(y | x,m,b) by assuming a uniform prior, and that y depends on x, and x is not random. correct me if i'm wrong

how the fuck does arctan(1/n) diverge? it doesn't make sense to me chief

>>10536072
> 2n^3+9n^2+13n+6
= (n+1)(n+2)(2n+3)
= (n+1)((n+1)+1)(2(n+1)+1)
= n'(n'+1)(2n'+1) where n'=n+1

The logical way to approach this is to expand both f(n+1) and f(n)+(n+1)^2 to the same form:

1. f(n) = n(n+1)(2n+1)/6
=> f(n+1) = (n+1)(n+2)(2(n+1)+1)/6
= (n+1)(n+2)(2n+3)/6
= (2n^3 + 3n^2+4n^2+2n^2 + 6n+3n+4n + 6)/6
= (2n^3+9n^2+13n+6)/6

2. f(n) = n(n+1)(2n+1)/6
=> f(n)+(n+1)^2 = n(n+1)(2n+1)/6 + (n+1)^2
= (2n^3 + n^2+2n^2 + n)/6 + (n^2+2n+1)
= (2n^3+3n^2+n)/6 + (6n^2+12n+6)/6
= (2n^3+9n^2+13n+6)/6

1,2 => f(n+1)=f(n)+(n+1)^2

>>10536072

You're correct so far.

You can either compare this with the expanded form of the expected answer - the last line from your post here (>>10535978).

Or you can do a division of polynomials.

E.g. you should find that (ignoring the factor of 6), that if you take a factor of (n+1) out:

[math](2n^3 + 9n^2 + 13n +6) = (n+1)(2n^2 + 7n + 6)[/math]

And then you'll find that the second bracket factorises neatly into [math](2n+3)(n+2)[/math] as required.

>>10534125
The issue I'm having is when we start doing stuff like setting [math]\hat{r} = (\cos(\theta), sin(\theta))[/math] and [math]\hat{\theta} = (-\sin(\theta), \cos(\theta))[/math], and all of a sudden we have these different coordinate systems whose unit vectors depend on our angle.

>>10536217

I'm not sure that I understand what you're getting at. Could you explain further or post some example materials?

>>10536217

are you confusing the standard basis with unit vectors in general?

>>10536294
>>10536315
Here's an example from the text we are required to use, I don't like it, but hey.

I don't think I'm confusing the standard basis with unit vectors, and I'm fine with regular change of basis from Cartesian to polar or spherical or whatever, but actually having my unit vectors depend on the angle seems strange to me. Furthermore, there doesn't seem to actually be a way to express this without using unit vectors, which seems fishy to me.

>>10536160
It's bounded above for n > 10 by 1/(nlogn), which diverges.

>>10536354
*bounded below, i mean.

My heat is broken, if I were to boil a big pot of water and set it in my room would it raise the air temperature by an appreciable amount?

>>10536328

Ah, I think I can see the first point of confusion. I'll try to give you some intuition for it, but it's going to be a little clumsy by the end. I suppose a more rigorous way would be to use matrices and all that shit.

Short answer is that they're a function of r and [math]\theta[/math], but the normalisation (because they're UNIT vectors) sets it to 1, so factors of r don't appear.

In general, when we transform coordinates, we end up with a function of the two previous coordinates. So, when we move from xy to r, [math]\theta[/math], we have that [math]r = r(x,y)[/math] and [math]\theta = \theta(x,y)[/math]. In this case, [math]r = \sqrt{x^2+y^2}[/math] and [math]\theta = \arctan (y/x)[/math].

In reverse, we can do a similar thing - [math]x = r \cos \theta[/math] and [math]y = r \sin \theta[/math]

Now, coming to my diagram. [math]\hat{r}[/math] is made of components in the i and j directions. If we forget hats and unit vectors for a moment and I asked you to break r into components, I am sure you'd give me [math]x = r \cos \theta[/math] and [math]y = r \sin \theta[/math].

So, in some sense, moving in the r direction is equivalent to moving in both x and y (or i and j if you prefer) directions.

[math]\vec{r} = r \cos \theta \vec{i} + r \sin \theta \vec{j}[/math]. Literally. And if we normalise that, i.e. convert it into a unit vector by dividing by the magnitude, you'll see that the factors of r drop out:

[math]\hat{r} = \cos \theta \vec{i} + \sin \theta \vec{j}[/math].

For [math]\hat{\theta}[/math], we can either straight away require that it be perpendicular and arrive at an answer. But, we can try some trigonometry in an analogous way.

If you treat [math]\hat{\theta}[/math] as a line perpendicular to r, use a bunch of right angled triangles, you'll be able to do something similar and get an expression like:

[math]\vec{\theta} = - |\theta| \sin \theta \vec{i} + |\theta| \cos \theta \vec{j}[/math]. And then you normalise again.

>>10536482
To continue, it might help if you try to do the reverse process first - try getting representations for i and j in terms of r and theta.

>>10535811
We'll be using induction, so we must find a way to compare the terms containing the floors. That is done by the following observation: [math] \displaystyle \Big \lfloor \frac{n}{d^2} \Big \rfloor + 1= \Big \lfloor \frac{n + 1}{d^2} \Big \rfloor [/math] iff [math] d^2 | (n + 1) [/math] (You can prove this by considering the remainder when d^2 divides n).

The n = 1 case is trivial. Now [math] \displaystyle S(n + 1) - S(n) = \sum_{1}^n \mu(d) \Big( \Big \lfloor \frac{n + 1}{d^2} \Big \rfloor - \Big \lfloor \frac{n}{d^2} \Big \rfloor \Big) [/math]. If [math] n + 1 [/math] is square free, by the above observation, [math] S(n + 1) - S(n) = 1 [/math] (only the d = 1 term survives).

If [math] n + 1 [/math] is not square free, then [math] n + 1 = a^2b [/math] for some square free [math] b [/math] and [math] a > 1 [/math] and also, [math] d^2 |(n + 1) \iff d | a [/math]

So [math] \displaystyle S(n + 1) - S(n) = \sum_{d | a} \mu(d) = 0[/math]. By induction, we are done.

>>10536482
>Short answer is that they're a function of r and θ,

pretty sure he's asking why this is the case. your unit vectors i and j are normally constant. i'm a bit puzzled by this too, why would you want this variable change of basis?

>>10536604

i and j are still the same. They still mean the same thing.

You may want to do this if you have derivatives with respect to certain variables. So you might have something in terms of i and j, but have a derivative w.r.t. r, for example. In that case, you either need to mess with the derivative, or rewrite your system in new coords.

>>10536482
Again, I feel like this is entirely dependent on having engineering notation. If we instead just use regular notation, i.e. (a,b,c) for the coordinates of some basis e_1, e_2, e_3, there is no good way of handling their dependency on the angle of our other basis.

Can someone help me derive the electric field at a point P, a distance r away from an infinite line of charge with linear charge density using Gauss’s Law?
So far, I've drawn a diagram resembling a cylinder but that's about it.

>>10536622

rotation matrix on your basis?

>>10536621
>i and j are still the same. They still mean the same thing.


that's what makes it confusing, there's no analogy in cartesian coordinates. i and j are not normally functions of the x or y in F(x,y)

If you lazy faggots don't start answering some questions in here, I'm going to. And I don't know shit.

>>10536817
Right, right. Point me to whatever pure math question you want, but I can't do physics or chemistry.

I'm trying to think of ways to plot coefficients of variation for multiple methods. Right now I'm using box-and-whisker blots just to visualize spread.

>>10536475
You can. But leaving a burner on can lead to carbon monoxide poisoning, so just wear a coat.

>>10534549
For grad algebra, Grillet.
>>10534598
Still x'.
>>10534629
How do you solve a function?
>>10536160
Because tan(0) explodes.
>>10536847
https://en.wikipedia.org/wiki/Box_plot#See_also

So heat is the result of energized particles giving off energy and cold is when particles slow down and dont give off as much right? And absolute zero is no energy in anything assuming.

So why does making something cold require heat or things that generate energy that gives off heat? Isnt that counter-intuitive? Like a refrigerator for instance, I am sure there are parts in there that are running that get a little hot in order to process whatever it does to keep things cool. Same with air conditioners and such. Shouldn't there be a method that sucks way the energy in a surrounding area and making it cold with little to no effort? Effort meaning expending more energy and making more heat from that effort. Some kind of device that not only makes things cold but you gain energy from it to power other stuff.

>>10537167
Particles giving off energy?

I thought it was when an electron was given off also in friction

>>10537211
Yeah that, what ever the basis is for creating heat.

>>10536648
bump

>>10537217
It's just friction. Rub your hands. That's heat generated from friction. Refrigerators use cyclopentane I think it uses a pump and runs a line so it cools down. Then there is a fan that blows the hot air. Idk I'm not an appliance expert.

>>10537167
The only thing making enough heat to be of any significance is the compressor, which produces comparably much less heat than the system is able to remove from the conditioned space.
AC, refrigeration, it all works the same way which is basically to take the heat from one place and put it somewhere else. So in a refrigerator for example, a substance running through copper coils absorbs heat from inside the fridge, then dumps it outside the fridge. It works as a cycle and has no clear start and end point, so it's hard to describe. Better shown
https://www.youtube.com/watch?v=mWVFXwhyn8g
Basically it exploits the second law of thermodynamics by putting a cold refrigerant inside a warmer space, the heat moves into the refrigerant which is made hot, then it moves outside and heat is released into the relatively cooler outdoor space.
>>10537294
134a, 401a, 410a are the most commonly used these days. They're just different hydro(chloro)fluorocarbons. Generally we refrain from using easily combustible chemicals for consumer applications, especially those which are more dense than air

Person 1 says that a 6" screen with a 16:9 aspect ratio has a bigger surface area than a 6" screen with a 21:9 aspect ratio.
Person 2 says they have the same surface area.
Which person is less retarded in this situation and how do they explain the other person that they're wrong?

>>10536822
Mine was the Star Wars time shit? Is there unpure math?

>>10537932
Star wars guy here. Use that pythageron shit. It ain't that hard. Fint hypotenuse or however its spelled. A squeared plus b squared equals c squared. Turn triangle into rectangle by doubling it. A x b equal area

>>10537993
Did that. Still can't convince the other person, so I'm looking for a second opinion in case not sleeping has made me retarded enough to mess up something that simple.

>>10538001
Your friends are dumb and /sci/ is full of lazy retards crying about global warming and the AI invasion. I concur that your method was correct.

>>10538011
It's not even a friend, just some retard online who keeps calling me stupid and "proving" his point by sending me random rectangles he made on some shitty app on his phone instead of using basic geometry. I guess I'll just stop arguing. Thanks for your time.

>>10528882
Thomas' Calculus Early Transcendentals, Published by Pearson
>Used for Calc 1, 2, 3

Differential Equations with Boundary Value Problems by Zill and Wright
>Used for Differential Equations

Thats the sum total of my undergraduate math needs in Aerospace Engineering.

>>10537932
16:9 is larger. If 6" is the diagonal measurement (which is how screens are usually measured), then 16:9 is 5.23"×2.94"=15.38"^2 while 21:9 is 5.51"×2.36"=13.03"^2.

Divide to confirm the aspect ratios, Pythagoras to confirm the diagonal size.

More generally, for an aspect ratio r=x/y and diagonal d, you have
x = d*r/sqrt(r^2+1), y = d/sqrt(r^2+1), area = d^2*r/(r^2+1).
Area is maximised when r=1 (i.e. a square) and decreases as it gets further from 1.

>>10537989
>is there unpure math
Yes, for eg. engineering math

>>10536536
Thanks mate

How do I go about solving such exercises?
Usually I just visualize a graph in my head and who grows to infinity faster but I can't think of graphs for some of these.

>>10540482
To check whether f grows more slowly than g, you might be interested to try evaluating [math]\lim_{n\rightarrow \infty} { f(n) \over g(n) }[/math]

Also memorize some basic facts after having proved them to yourself, for example "any logarithm grows slower than any polynomial", or "all logarithms differ only by a constant factor".

>>10534598
how are you defining [math] \frac{d f}{d 1} [/math]?

>>10540482
For the first one, log[a](b)=log(a)/log(b). So log[10](n)=(1/ln(10))*ln(n)
For the second:n!=1*2*3*...*(n-1)*n, 2^n=2*2*2*...*2*2, both having the same number of terms but with n! having terms which increase against 2^n having constant terms.
For the third, log(n) is barely larger than O(1), and grows more slowly than n^k for any positive k. n^k = (e^ln(n))^k = e^(ln(n)*k) = e^(k*ln(n)) = (e^k)^ln(n), so comparing n^k against ln(n) is comparing (e^k)^u against u where u=ln(n).

IOW: n! > k^n > n^k > n > n^(1/k) > log(n) > 1. (assuming k>1).

What pen do you guys use? Or pencil pen? My hand writing is shit and most pens I use don't help that. I like some Pilots but ink consistency is pretty bad from what I've used.

>>10541464
Not science or math

Brainlet with regards to astrophysics here, I've seen it written before that gravity propagates at the speed of light, in the context of hypothetical situations like the sun disappearing and stuff like that. But, if gravity can only travel at the speed of light, how is it that black holes exert gravity on objects outside the event horizon? Wouldn't the warping of space about the black hole prevent the gravity from the mass inside from exerting a force outside the point of no return?

I have pairs (i, j)

(0, n), (1, n-1), (2, n-2), ... (n-1, 1), (n, 0)

Is there a good word to use in a proof that describes the relationship between i and j? "Alternating" isn't descriptive enough. "Complimentary with respect to n" is too odd.

>>10541689
maybe you could call them 2-partitions of n.

>>10541689
Literally just the pairs (k,n-k) with 0<=k<=n.

>>10541907
>>10541954
2-partitions is a good one.
I was hoping for a good verb I could slip in like "note that i and j ___ with respect to n". "note that i and j are 2-partitions of n" is good

>>10541517
Because gravity =/= light.

Lads question. I’ve heard it said that If a person goes into a black hole they’ll come out of it (incredibly broken down) in the future when the black hole dissipates.

Is this true? Also wouldn’t this imply that when the black holes start dying off a MASSIVE amount of material is gonna explode into the universe? Like an incredible amount? What would happen to all of that matter? Would it condense into new stars?

>>10542158
Seconded this question.

I've looked it up, and the answer is always "You reach the singularity in a finite amount of time" and that makes sense. But I also know that time is massively dilated inside a black hole. Isn't it dilated more and more as you approach the singularity? Couldn't be dilated enough that the black hole evaporates before you reach it?

I want to learn the theory behind general and special relativity. I'm not a from a /sci/ background but I've always been fascinated by the concept. Can anyone recommend me any book or literature on the two theories, preferably without any (or at least not a lot) of math involved?

While I used to like math, it's been a while since I had a crack at it. But since math is kind of a prerequisite on this one, I'm willing to dredge through it as long as there's not too much of it.

>>10527130
Why are there so many touhoufags on this board?

>>10543591
Great stupid question

>>10543620
Great stupid answer.

>>10542903
Leonard Susskind has a series of very accessible, but not dumbed down, physics books called "The Theoretical Minimum." One of them focuses on special relativity and classical field theory, and I think the one after it is focused on general relativity.

Given how long it takes to reach postgraduate proficiency in mathematics
Will there come a day where cutting edge math is so specialized and abstract that it would take an infeasible amount of time to learn the prerequisite material to get there?

Who would win in a match of chess, Magnus Carlsen or Bobby Fischer?

>>10527558
Your intuition is correct, since the t-channel for [math]ee \rightarrow \mu\mu[/math] will involve electron-muon bilinears in the amplitude which vanish due to them being in different lepton families.
>>10531310
[math]x^2 + y^2 = 1 - z^2 = (1-z)(1+z)[/math]. You get the latter in the denominator when you compose the two charts.
>>10532008
By Parseval [math]\mathcal{F} \in U(L^2)[/math] preserves the Hermitian [math]L^2[/math] inner product. What this means is that, treating [math]f: X \rightarrow \mathbb{C}[/math] as a [math]L^2[/math] section of a Hilbert line bundle [math]\mathbb{C}\rightarrow X[/math], [math]\mathcal{F}[/math] descends to an automorphism on the space of unit-norm sections [math]f \in S^\infty[/math].
>>10533346
It's minimal coupling. The canonical momentum [math]p \mapsto p - qA[/math] under minimal coupling and when you do Legender transform back to [math]\dot{q}[/math] you get those terms in the Lagrangian. The reason why the canonical momentum acquires a term [math]-qA[/math] is because the [math]U(1)[/math]-principal gauge bundle defines a connection [math]\nabla -qA[/math] on the symplectic manifold [math](M,\omega)[/math] and the symplectic form [math]\omega[/math] needs to be covariantly closed or trajectories in the base space [math]X[/math] of the [math]U(1)[/math]-principal bundle won't lift to a Hamiltonian trajectory on [math]M[/math]. This condition leads to [math]\omega = dq \wedge d\tilde{p}[/math] where [math]\tilde{p} = p - qA[/math].
>>10535506
Any [math]L^2[/math] section of a prequantum bundle prior to doing holomorphic polarization.
>>10536648
Use Kirchoff's formula: [math]E(x) = \frac{1}{4\pi \epsilon_0}(P_x\ast \rho)[/math] where [math]P_x[/math] is the Poisson kernel and [math]\ast[/math] is the convolution operator.

if you were to jump in an artificial gravity cylinder (like in a sci-fi space station) is this what would happen? why or why not?

Is there a way to get a better sense of how numbers translate to real world concepts? I've been interested in this because it's fascinating what we can use math for, and I just can't fathom how the people that came up with the formulae we take for granted came up with them. I've tried looking at proofs, but those just don't make much sense to me.

>>10544047
Not before we are either all dead from some 21st century catastrophe or we've extended the human lifespan and rearranged society in such a way that your problem goes away

what's a good linear algebra book for someone who hasn't done single variable calculus for a couple years and has never done very rigorous proofs?

>>10542158
>>10542196
Maybe you guys can take a crack at my star wars question. Wouldn't getting sucked into a black hole be the way to go? As long as you had some crossword puzzles or something, time would be nearly infinite.

>>10544247
Define "jump". At "rest", you'd have rotational inertia as well as linear inertia, so your jump would have to cancel that out in order to obtain the third picture.

As to what would happen in an experiment, this is essentially a question of cognitive psychology rather than physics. Someone who'd just arrived on the station would miscalculate movements due to the difference between artificial and real gravity, but eventually they'd learn to compensate (and probably need to re-adjust upon returning to earth).

>>10544247
You would fall down mutherfucker. Watch some old coney island videos.

How do I coast through college while putting in the bare minimum effort, WITHOUT constantly worrying? I did it in high school but now I just worry constantly even when I am putting in enough work to get perfect grades.

My free time should be MINE.

>>10543591

>>10542903
Einstein literally wrote the book on that shit. I check it out from the library when i was a high school dropout. It ain't difficult to read or understand. It is a regular ass book written by the man himself.

>>10545337
translated from german
I find it absolutely impossible to read

>>10544038
>The Theoretical Minimum by Leonard Susskind

Thank you, will give it a read! Much appreciated

Tomorrow I've got a seminar of 40 physics problems and I've still got 3 problems to solve! I can't get the right answer here, what am I doing wrong?

I'm supposed to calculate the magnitude of the force resisting the bullet's path alongside the pipe, with only knowing it's speed before and after the impact, mass and length of its path.

I tried doing this in a few different ways, always arriving at the wrong answer. Tried calculating the energies, energy before with and without an angle, compared to the kinetic energy after the bullet has slid against the pipe, again with and without taking angle into consideration, took a difference of those kinetic energies and compared it to the F*L=energy lost, divided by L, got F, still the wrong answer.

I get around 140kN, but it's wrong. Should be 9.46*10^7. Please someone just tell me how to solve it, you don't need to do it for me.

>>10545607
Do your own homework

>>10545655
if I knew how to do it correctly, I wouldn't be asking here for advice here, right?

Also, learn to read
>Please someone just tell me how to solve it, you don't need to do it for me.

how do I calculate the nominal current of a transformator?

>>10543591
most of the 2hu folk here have/are doing math PhDs. Yokari-poster sama is a postdoc I believe

I've got some test results and want to represent them in a graph. I want to do it based on "accuracy". i.e. how close a seeding was to the final result.
Essentially, it's a tournament bracket and I have:
>Player's seeding for that tournament
>My program's prediction for that seeding
>The actual player's result (1st, 2nd, ...)

Given this, how would I be able to represent this graphically?

No-one has been able to answer this question.

>>10545873
If I understand that correctly, you'll have a tuple of numbers that you want to quantify the accuracy of.
For this, you might use the inversion number of the permutation, i.e. the number of pairs of the sequence that are out of order. Say the correct tuple is (1,2,3,4), then (2,1,3,4) has inversion number 1; (3,1,2,4) has inversion number 2.

>>10545368
>impossible to read
You know how stupid that sounds?

Is this a proper notation to say "the slope of the tangent line at the point (4, 20)? Disregard my prime being an apostrophe.

>>10547601
also there should be an equal sign on the right, and y' was found with imp diff

>>10547601
>>10547616
"imp diff". very cool, very cool.

The slope of y at the point (4, y(4)) is: [math] y'(4) [/math].

A man is sitting in a chair, completely catatonic, his eyes glazed over, his body limp. He is alive but not for long; he's been cursed by a god to become the source of demise to his family - his wife and two children sitting in the next room.

The man is emitting high amplitude electromagnetic radiation of a specific wavelength - currently radio waves, strong enough to drown radio communication in the entire city - and the wavelength is getting progressively shorter and shorter. Within the next few minutes he will begin emitting microwaves, then ultraviolet, then x-rays, until eventually the intense gamma radiation spilling from a bubble around him will fatally injure any living organism within a 1km radius. He is completely and utterly unaware of the damage he causes, and will only awaken to find his ruined life once the screams have been silenced by merciful death.


My question is, at the point in time when he's transmitting electromagnetic radiation in the spectrum of visible light from a perfect sphere around his body, what would it look like to someone walking into that room? Will they actually see a bubble of light of a single color around him (depending on interference from other light sources in the room)?

Sorry for the silly question, haha.

>>10547739
I gave a approximate number for the slope. I'm trying to the slope of the tangent line to y at the point given is equal to that number.
>(4, y(4))
...you sure? The question is actually asking for the slope of the tangent line to ln(xy)=2 at the point (4, (e^2)/4).
So it would seem to me that if I came up with y'= -(y/x) that I can't just say y'(4)= because there's a necessary x value not accounted for. Should I not be plugging in the points into y'?
Asking srs here, don't be a cock

hello, total brainlet here, I don't understand what I'm doing wrong here, wouldn't it just be the sum of 0-10?

>>10548821
Just graph it.

>>10548849
I did?

>>10548821
Probably trapezoidal.

>>10548864
Then use the curve of the line between each point to calculate the distance for that segment then just add all those together.
Or just say infinity since the question failed to specify that it was talking about the detection of the obstacle as a beginning, it just asked how far the car travelled, which is unknown since he was already speeding down rt. 11 to begin with.

>>10548910
>Then use the curve of the line between each point to calculate the distance for that segment then just add all those together.
I did, it said it was wrong.

>>10544247
You would continue travelling in a straight line as the floor in front of you curved up. It would be like falling forward from your perspective.

Just how the fuck is an imaginary number a real number? Not real as in R, but real as in a legitimate thing.
Like how could you ever put i on a number line? It literally doesn't exist.
>but it's i m a g i n a r y you dip
I get that but it seems like it was just made up so we could fix the root of a negative problem? Does it even fix it? It doesn't really do shit. Am I just retarded?

Bit of help here. What is the highlighted phrase supposed to mean? I've tried it with De Morgan's law but the result is false. Am I supposed to flip the equal sign as well?

>>10549432
[math] (A \cup B) [/math] is considered as a single set, so taking it's complement means just [math] (A \cup B)^{c} [/math]. Applying the rest of the statement to what's inside of the parenthesis is just doing the process twice, you are just taking the complement of a complement so nothing changes on the left. That whole highlighted statement is basically just a loose generalization of the De Morgan's laws, when you think about it. The only difference is that it also tells you how to handle inclusions when applying it, and it also can be applied to a whole equation/inclusion at once.

>>10549415
>I get that but it seems like it was just made up so we could fix the root of a negative problem?
yes, that's how lots of things in maths are born

>Does it even fix it?
yes

>It doesn't really do shit. Am I just retarded?
yes

on a more serious note, you literally can't put i on the usual number line, that's why we extend the number line to a plane instead, where i and it's other imaginary partners reside without causing many issues, and in a whole different axis
they are extremely useful with the analysis of differential equations and also some functions in the complex plane behave really nicely, far better than what we can achieve with just the reals, so i'd say they do a pretty damn good job at dealing with the limitations that an undefined sqrt(-1) imposes

asking how it is a legitimate thing is also a pretty loose statement, the same thing was said about zero, the negative integers, irrationals, etc, and it's because they always caused different problems with the standard system that was used at the time
if we were to ask how a number is "real", we would probably still be stuck with the naturals

also just a pet peeve of mine (and basically anyone that studies maths)
>but it's i m a g i n a r y you dip
don't let anyone tell you that, the name imaginary is a shitty convention and only causes confusion like what you are having, there's nothing about them that makes them more imaginary than a lot of real numbers

I have a physics degree but I still can't retain the difference between diamagnetism and paramagnetism. Can anyone explain them such that even a brainlet could understand it?

Warning, there may be follow up questions.

>>10548280
ln(xy)=4 is unambiguously the function [math]y(x)={e^2 \over 4}[/math], meaning the tangent at x=4 is [math]t(x) = {e^2 \over 16}(x-4)+{e^2 \over 4}[/math].
Its slope is [math]\left({e \over 4} \right)^2[/math].

What's the difficulty?

>>10549415
> I get that but it seems like it was just made up so we could fix the root of a negative problem?
Well, it turns out that the square root of a negative isn't actually a problem. You can use √-x=√-1√x=ix where i=√-1. You can then manipulate the expression using the normal arithmetic operations, simplifying powers of i using i^2=-1. If a problem has a real solution, the terms involving i will ultimately cancel out.

Cardano discovered this while investigating the problem of finding the roots of a cubic polynomial. If the polynomial has three real roots (casus irreducibilis), then intermediate terms involve the square root of a negative number. However, it can be shown that the imaginary terms cancel leaving real solutions.

>>10549934
Typo: those e^2/16 should be -e^2/16

Anyone with experience able to give me a clear idea on alternative ways to fight cancer? Also, does anyone have a good scientific reason to believe that cancer could at least in part be the result of psychology?

>>10549979
Ask on /x/. Look up the Gerson diet and yeah, your physiology reacts to the hormones your mind causes your glands to produce.

For a local maximum of a function, must the fourth derivative be negative?

>>10550081
No, first and second are the only ones that matter.

>>10550095
I mean in the case that it is fourth order differentiable.

>>10550098
Still no.

>>10550081
>>10550095
>>10550098
>>10550103
If the second derivative is zero at the point of interest, you may need to check further derivatives to make a determination.
Try [math] y = -x^n [/math], with [math]n \leq 4[/math]. You'll see that you can't use the second derivative to conclude whether x=0 is a maximum.
So no, the fourth derivative does not need to be negative in all cases, but there are those where looking only at two derivatives down doesn't suffice.

>>10550149
>≤
That should say [math]\geq[/math] of course.
As an example, [math]y=x^6[/math] has a local minimum at x=0 obviously, but the second derivative is 30x^4, with value 0 at x=0.

>>10549979
I mix "myrrh" with jagermeister. Myrrh has actually been used in medicine as an alternative but i do not know the pro method. I've read of a mushroom (one of the names is "jew's ear") it is more for tumor stuff. Haven't tried. But these are a couple of real deals among snake oils. There is a book called "Anti Cancer" written by a cancer research doctor who got cancer and i find it hard to read (for psychological reasons) but it seems that your psychology plays a role according to what I've flipped through. I've been hanging around with my tumor for ten years and have done better than statistics so.. maybe the Myrrh?? I eat poppies whenever i get a chance but there's better research on weed. I know I'm not very/sci/ but hope you can do something with it.

>>10550164

Thanks very much. I'm trying to help a friend with Peritoneal Cancer which is extremely fast moving.

Is there a mathematical term for the operation of going from the square of a number to the cube of it? Or I guess multiplying a number by its root, same thing

>>10550214
[math] x \mapsto x^{3/2} [/math]?

Why does 5G have shorter range than 4G?

I get it operates on higher frequencies resulting in shorter wavelengths but what is it about short wavelengths that decrease it's width?

just got locked out of my appartment and the nearest person with a spare key is 1,000miles away.
What the most scientific way of breaking into my own apartment ?
PS sitting at my uni typing away like a retard while watching new Jojo, also: no phone, in flipflops and no money

>>10550342
Lockpicking is a nerd pastime, if your lock is not too complicated, look for a lockpicking group at your university. Maybe you're lucky. Good luck.

>>10550573
>nigga literally telling me to find the thieves guild in my uni

>>10550342
What kind of housing are you in?

>>10550573
Unless he knows where he can get a bump key, he's not gonna be picking locks any time soon.

Any programmers around? I've been tasked with making a recursive function in C that takes two integers as input (say, X and Y) and then removes Y even digits from X, starting at the lowest order of magnitude. For example, an input of 1234567 2 would return 12357. Any ideas?
>inb4 fuck off of to /wsr/
I will, it's just slow as shit, giving it a go here first.

What actually happens to the atoms that fall into a black hole? Is there a tiny solid sphere at the centre made up of everything that ever fell into it?

>>10550720
i live in an apartment, my neighbors are retards so cant ask them for favors

>>10550720
>Unless he knows where he can get a bump key, he's not gonna be picking locks any time soon.
He might not, but people who pick locks for fun might, and do it for cheaper than a locksmith.
https://www.youtube.com/watch?v=c0a5OyqEfmA
I know it is a stretch, but come on, the question was asked on 4channel.

>>10550720
int remove(int X, int Y)
{
....if (X==0) return X;
....if (Y==0) return X;
....if (X%2==0) return remove(X/10,Y-1);
....return remove(X/10,Y)*10+(X%10);
}

If we see a galalxy in the sky that 1 million lightyears away for example, how do we even know that galaxy even exists anymore if we're looking at an image of it 1 million years ago. Doesn't this kind of make lighyear travel impossible? You're going to say send people on a generation+ long spacefligt to an object you don't know exists anymore or not

>>10550720
int ans = X/(10^Y)

>>10551262
Damn, anon, that worked like a charm. I'm still wrapping my head around it. Thanks a bunch.

maths are for retards

prove me wrong

Any advice on how to derive closed-form formulas from recursive ones and those that involve "..."? I'm stuck for hours on a brainlet-tier problem.

>>10551433
Then why aren't you doing "maths"

>>10551456
cause it's for retards

Is getting a BSc at 29 a retarded decision? Office wqgie drone with absolutely no meaningful career to speak of ready to commit suicide. Have always wanted to study Physics.

>>10551433
Enlighten me, wise sir, what isn't for retards? What do intelligent partisans do?

>>10551262
that's really cool, where did you learn recursion like that? Any particular book or did you go to uni?

How do I go about solving these?

>>10551729
You decompose the exponential into smaller parts and recompose the remainders.
For example, [math]2^{100} \mod 3
= (2^2)^{50} \mod 3 \\ = ((2^2)^2)^{25} \mod 3
\\ = 2 \cdot (((2^2)^2)^2)^{12} \mod 3 \\ = 2^4 \cdot (((2^2) \mod 3)^2)^2)^{12} \mod 3
\\ = 1 \cdot (1^2)^2)^{12} \mod 3
\\ = 1[/math]

>>10551450
There are some standard techniques. Start by understanding how arithmetic and geometric series are derived. The method used for arithmetic series can be extended to polynomials of any degree; if f(n) is a polynomial of degree n, then f(n+1)-f(n) is a polynomial of degree n-1. Telescoping is another technique; if you can express f(n) as g(n)-g(n-1) for some g, then f(a)+f(a+1)+...+f(b-1)+f(b)=(g(b)-g(a-1)) as all of the intermediate g() terms cancel out. If you're looking for the limit of a sequence, then note that x[n+1]=x[n] at the limit; you may be able to solve that algebraically. Other than that, just try evaluating a few terms and see if you can find a pattern.

>>10551729
for fractional q = 1/d mod n it is a simple matter of finding q such that q * d = 1 mod n. 1/4 mod 7 = 2, 2 * 4 mod 7 = 1. 3/4 mod 7 = 3 * 1/4 = 3 * 2 = 6. Note that if d and n are not coprime no such solution exists.

I've been told that oxygen lines should not be checked for leaks using soapy water, on the grounds that it is a fire hazard. I have also been told that it can only be a fire hazard if there is an ignition source. Which is true? Will soap spontaneously combust when exposed to pure oxygen?

>>10527130
Why'd you post one of the worsthu?

>>10552812
No but true and safe are different.

If I'm trying to learn technical skills like welding, sewing, or gunsmithing, is there any way to accelerate learning to reduce the amount of practice needed to get to a certain skill level? I have so much I want to learn and so little time.

Why are orgasms purple?

>>10552993
>needing to do something manual more than once to learn it

>>10550293
shorter wavelengths penetrate less most media.until you get to much higher energies

>>10550233
Well sure but I meant more as a word in English

>>10547879
What.

Any idea how to disprove
sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1
I was thinking about explaining on how the value of sqrt(1) can be either 1 or -1. Any other ideas?

>>10553824
Shit, I meant 1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1

>>10553824
Wait, i1 x i1 = 1?

>>10553824
Anon [math]\sqrt{1}=-1[/math] is correct, since (-1)^2=1.
>>10552830
Shut up.
>>10552993
>>>/diy/sqt

>>10553847
>>10553827

>>10527130
Know how to calculate eigenvectors/values and change of basis well, but this type of question fucks me.

>>10553873
That just happens because the root function isn't single valued.
You might as well just write [math]1= \sqrt{1} = -1[/math].
>>10553876
Hard to help when I don't know what the question asks.

>>10553876
For reference, the actual question is to calculate [T(e1)] basis B

>>10550573
>>10550720
im >>10550342 in ))

>>10553881
Just substitute (x_1, x_2, x_3) = (1, 0, 0)

>>10553963
Holy fucking shit I've been trying to figure this out for an hour why the fuck am I so retarded fuck

what will I be able to do once I learn all of this?

>>10553882
How did you accomplish this?

>>10554083
You'll be able to trick people into believing you finished a physics bachelors a few years ago and have forgotten some stuff.

Someone start a new thread

>>10554314
I did it for you.

>>10553824
√(ab)=√a√b doesn't necessarily hold if the roots aren't real.

√x denotes the principal square root of x. If x is a positive real number, then this is the positive real number y such that y^2=x (-y also satisfies this). If x is negative or complex, the principal square root is the root whose argument (angle) lies between -π/2 (exclusive) and π/2 (inclusive), i.e. the one closest to the positive real axis. For negative real numbers (with an imaginary root), the principal square root is the one with an argument of π/2.

When multiplying complex numbers, arg(a*b)=arg(a)+arg(b). Even though arg(√a), arg(√b) and arg(√(ab)) always lie in (-π/2,π/2] (by the definition of the principal square root), arg(√a√b)=arg(√a)+arg(√b) may lie outside of that range, in which case √(ab)=/=√a√b, i.e. the principal square root of the product isn't equal to the product of the principal square roots.

IOW, in the disputed "proof", the third term isn't necessarily equal to the second.