/sqt/ - Stupid Questions Thread

[Anonymous No.10689474]

Ask and you shall recieve

[Anonymous No.10689648]

How effectively a punchbowl filled with plain water with a fan aimed at it directly filter the air? IDK I get the feeling that shorelines generally have better air quality.

[Anonymous No.10689655]

Can sodium form covalent bonds?

[Anonymous No.10689960]

Baryons have an odd (≥3) amount of quarks, mesons have an even (≥2) amount.

Why would this statement be false?

[Anonymous No.10689991]

Anyone know of a mobile browser that displays the math functions well? I've used clover for three years now but am getting tired of the equations not formatting.

[Anonymous No.10690098]

>>10689960
Mesons are 1 quark and 1 antiquark?

[Anonymous No.10690120]

So I have two points, A and B, in 3D space. I want to move and rotate them as like they are one thing. So if I move A in x I also move B in x and so on.
That's pretty simple for moving, but how do I do the rotation?
I mean if I rotate A around the y-axis, I have to move and rotate B. What would be the formula to calculate the new position of B after I rotated A by n degree?

[Anonymous No.10690206]

>>10690098
Which is two quarks.

[Anonymous No.10690539]

>https://www.quora.com/How-would-you-design-a-greedy-algorithm-which-connects-each-black-dot-with-a-white-dot-so-that-the-total-length-of-wires-used-to-form-such-connected-pairs-is-minimal
I don't understand what the fuck is happening here. Where does 2w_j-2b_0 etc come from? Can someone explain this argument for a dumbass? I can never understand why greedy algorithms work.

[Anonymous No.10690620]

>>10690120
The math works actually in 4D so you can actually move your points directly.

Usually you know your objects postion and the rotation operations applied to it in x, y and z direction.

For x y and z separately:
#1 objectA
#2 move rotation center of #1 to center
#3 apply rotation to #2
#4 move rotation center of #3 back to original location

Or something like that.

[Anonymous No.10690725]

>>10690539
He gave two equations:
[math] b_i - w_0 + \vert w_j - b_0 \vert [/math]
[math] b_0 - w_0 + \vert w_j - b_i \vert [/math]

We want to calculate the difference between these two equations:
[math] b_i - w_0 + \vert w_j - b_0 \vert - (b_0 - w_0 + \vert w_j - b_i \vert) = b_i + \vert w_j - b_0 \vert - b_0 - \vert w_j - b_i \vert [/math]

If [math] w_j < b_0 [/math] and [math] w_j < b_i [/math] , we can rewrite it as:
[math] b_i + (b_0 - w_j) - b_0 - (b_i - w_j) = 0 [/math]

If [math] w_j > b_0 [/math] and [math] w_j < b_i [/math] , we can rewrite it as:
[math] b_i + (w_j - b_0) - b_0 - (b_i - w_j) = 2w_j - 2b_0 [/math]

If [math] w_j > b_0 [/math] and [math] w_j > b_i [/math] , we can rewrite it as:
[math] b_i + (w_j - b_0) - b_0 - (w_j - b_i) = 2b_i - 2b_0 [/math]

[Anonymous No.10690760]

>making a new /sqt/ while the other one isn't anywhere close to 300 replies
truly a stupid [questions thread]

[Anonymous No.10690853]

>>10690539
This is not about a greedy algorithm.

He is trying to prove that the greedy approach chosen is optimal.

We know b0 < bi and w0 < wj and without loss of generality that w0 < b0 (because b0 < w0 would be proven the same way and w0 = b0 is impossible because a field can only be white or black)
I: c(w0,bi) + c(wj, b0) = abs(w0-bi) + abs(wj-b0) = w0-bi + abs(wj-b0)
II: c(w0,b0) + c(wj, b0) = abs(w0-b0) + abs(wj-bi) = w0-b0 + abs(wj-bi)

Case 1: wj < b0 and wj < bi results in order
w0 wj b0 bi
I: 3 + 1 (w0-wj-b0-bi + wj-b0)
II: 2 + 2 (w0-wj-b0 + wj-b0-bi)

Case 2: b0 < wj < bi results in order
w0 b0 wj bi
I: 3 + 1 (w0-b0-wj-bi + b0-wj)
II: 1 + 1 (w0-b0 + wj-bi)

2 * abs(wj-b0)
is basically the distance of the removed line segments between the first non-cross-pairing and second non-cross-pair
and removes the inner pair on it's own

Case 3: b0 < wj and bi < wj results in order
w0 b0 bi wj
I: 2 + 2 (w0-b0-bi + b0-bi-wj)
II: 1 + 1 (w0-b0 + bi-wj)

2 * abs(bi-b0) is the distance of the line segments that overlap and are superfluous.

Conclusion:
Strategy II seems to be better. Matching the leftmost free black node to the leftmost free white node (and vice-versa).

Since those nodes are practically taken out of the game, you start again with the leftmost unmatched node (white or black) and look for its opposite color leftmost and match that, taking out the remaining pairs consecutively. This is essentially w[i] matched with b[i], when both are sorted positions of the color-nodes.

Since any other node than the left-most-node-opposite-color-node has a higher or equal cost, this seems optimal.

[Anonymous No.10691024]

So it's almost time for me to choose my major and I can't choose between electronic and computer engineering. My main goal is to work on computer hardware, so judging from that CE could be my best bet. The thing is, though, robotics also interest me, and also electronic engineers have professional attributions in my country whereas computer engineers do not (I'm not sure if that's important).

What would be best?

[Anonymous No.10691045]

How do I find all the solutions to an equation in successive field extensions? For example, in R, x^8 equals 1 has solutions plus/minus 1. In C, this equation's solutions are the eighth roots of unity. What are the solutions in the quaternions? The Hamiltonions? So on and so forth?

[Anonymous No.10691090]

>>10691045
>quaternions
This is a division ring, not a field. There are infinitely many solutions to that particular equation.
>hamiltonions
Not a thing

[Anonymous No.10691117]

>>10691090
Then what are the solutions?
>hamiltonions
meant octonions

[Anonymous No.10691130]

>>10691117
>>10691090
>>10691045
also how do I generalize the procedure?

[Anonymous No.10691155]

>>10691024
what country?

[Anonymous No.10692382]

>>10690539
>>10690725
>>10690853
Would a greedy strategy reach at least a local optimum if the first and last node are connected in a circle?
Assuming we choose a random white node (without loss of generality a random black node) and apply the "closest node in opposite color" strategy in both directions, choosing the closest one every-time, then taking the next node of the starting color to the right of the starting node, continuing from there?

[Anonymous No.10692402]

whats the easiest way to get the sum of a range of f(x) where x is an integer using a graphing calculator like geogebra? I could just do it manually but surely there is a faster way to do this?

[Anonymous No.10692499]

>>10691045
In the quaternions, x^2=-1 has infinitely many solutions (every unit quaternion is a solution), all of which are solutions to x^4=1 and x^8=1.

[Anonymous No.10692687]

>>10689474
How can I plot the solutions to the complex equations/inequalities such as [math]|z|=1[/math] or [math] z \bar z = 2 [/math] etc in Mathematica?

[Anonymous No.10692708]

The last time I took a practical exam nerves got the better of me, because to keep the exam fair the entire cohort was made to wait in a room without electronic devices and then taken out one at a time to test. So basically I was in a room for two hours getting more and more fucking wound up. What are some ways I can avoid the nerves getting to me this time? Was thinking of having a shot or two of vodka beforehand to loosen me up a bit, since the actual content of the exam is easy and I mainly fuck up because my hands won't stop shaking and my mind goes blank.

[Anonymous No.10692721]

>>10689648
You'd blow some airborne particulates into the water and blow water vapor around so have slightly cleaner, more humid air.
>>10689655
No, it'd be too unstable having additional electrons.

[Anonymous No.10692785]

>>10689474
How do I get laid using physics?

[Anonymous No.10692833]

>>10692785
What have you tried?

[Anonymous No.10692911]

Why does the current board culture hate mathematics and physics so much?

[Anonymous No.10692923]

>>10692785
use gravity and mechanics to incapacitate a person and violate them

[Anonymous No.10693250]

What is a good way to deal with anxiety? How can I overcome this shit mental genetics?

[Anonymous No.10693308]

>>10692499
but what about a general method for discovering such solutions?
>>10692785
Look up Richard Feynman pick up artist

[Anonymous No.10693496]

>>10693250
Bergen 4 day treatment.

[Anonymous No.10693535]

w-what would happen ???

[Anonymous No.10693568]

We can expand (1+Δx)3 to
1 + 3Δx + 3(Δx)2 + (Δx)3

Can someone explain to me how there is pow 2 and 3, and why ()2 has x3

[Anonymous No.10693698]

Why do posters here keep using the word "cybernetics" when that field has not only been dead for decades but it even never had a good definition in the first place? Are they mixing it up with AI and/or robotics?

[Anonymous No.10693702]

What's the "opposite" of P(A | B)?

e.g. P(A^c) is the "opposite" of P(A) because P(A^c) + P(A) = 1

[Anonymous No.10693715]

>>10689474
As a physics student who wants to learn programming, what languages should I take up and what interesting things can be done in regards to physics and programming. I have been learning how to solve ODEs with Mathematica this quarter.

[Anonymous No.10693716]

>>10693702
P(¬A | B)

[Anonymous No.10693724]

>>10693716
thanks nibba

[Anonymous No.10693778]

>>10693568
https://en.wikipedia.org/wiki/FOIL_method

[Anonymous No.10693818]

>>10693778
Thanks I'll have a look

[Anonymous No.10693864]

Uhhh, a homework question is: What are the 25th and 75th percentiles of the data x = {10, 14, 22}

How does that work when there's 3 values?

[Anonymous No.10693870]

>>10693568
>We can expand (1+Δx)3 to
>1 + 3Δx + 3(Δx)2 + (Δx)3

So, (1+Δx) (1+∆x) (1+∆x) but how do I do 3? Does Foil only work with 2 at a time?

[Anonymous No.10694055]

>>10693864
In geared if you have a distribution [math] f(x) [/math] of a random variable [math] X [/math], then

[math]
\text{Percential}(y) = \frac{\int_{-\infty }^{y} f(x)dx}{\int_{- \infty }^{\infty } f(x)dx}
[/math].

[Anonymous No.10694069]

>>10693864
10 is at at the [math] \frac{10}{10+14+22 \times 100 \text{percentile} [/math]
14 is at the [math] \frac{10 + 14}{10+14+22 \times 100 \text{percentile} [/math].
and..
22 is at the 100 percentile.

[Anonymous No.10694075]

>>10693864
10 is at at the [math] \frac{10}{10+14+22} \times 100 \text{percentile}[/math]

14 is at the [math]\frac{10 + 14}{10+14+22} \times 100 \text{percentile}[/math].

and..
22 is at the 100 percentile.

[Anonymous No.10694078]

Okay, our next big civilization ending crisis is automation. Politicians will ignore it because they are old rich and will die. You don't want to think about it but it is YOU, that will be affected. Even coding can be automated. What is the worse case scenario? Is the only way to avoid it is self sustain farming in the country? How the fuck can we sustain a market economy where product is in surplus but a large population of participant's that can't lawfully participate? Theft? Is government intervention nessisary? Socialism; communism? How will the companies profit off of a fiat tender whose only value is social?

Are we fucked?

[Anonymous No.10694091]

>>10693870
(1 + ∆x) (1 + ∆x) (1 + ∆x)

12 + ∆x + ∆x + ∆x2 (1 + ∆x)
12 + 2∆x + ∆x2 (1 + ∆x)
13 + ∆x + 2∆x + 3∆x + ∆x2 + ∆x3
13 + 6∆x + ∆x6(<<< power)

What I'm I doing wrong

[Anonymous No.10694095]

>>10693864
https://web.stanford.edu/class/archive/anthsci/anthsci192/anthsci192.1064/handouts/calculating%20percentiles.pdf

[Anonymous No.10694139]

Why can't virgin oxygen make these sweet chains like chad sulfur does with the disulfide bond in the middle of pic related?

[Anonymous No.10694261]

Which one of you anons have the evidence to prove that Rosalin Franklin didn't actually do shit for the discovery of DNA and she doesn't deserve the bullshit after hype that most faggots in genetics and biology give her?

[Anonymous No.10694267]

>>10694139
Oxygen isn't a dumb whore like sulfur or absolute HARLOT like carbon

[Anonymous No.10694291]

what the fuck was the point. anyone know an easy way to kill oneself? I don't a gun but I got a pretty big will and reason. How easy would it be to cut my jugular or carotid? and how fast would I die?
I am sick of this retarded shit, time to do what the philosophers are too pussy to do.

[Anonymous No.10694367]

>>10694139
Peroxide bonds are just higher in energy due to the electronegativity. The bond tends to split into radicals.

[Anonymous No.10694368]

>>10694267
Kek

[Anonymous No.10694387]

>>10693715
Choice of language doesn't matter much since they all have more or less the same function.
Pick one that's widely used or that you have access to resources for or can be used to extend Mathematica.
Maybe do simulations of chaotic systems?

[Anonymous No.10694440]

Why does my chest hurt so often? It comes and goes near everyday now, especially when I talk for a long time or lay my head on something elevated other than a pillow (like the arm of a couch). It can even happen when I'm standing still and not doing anything. I'm worried that this pain is in my head, but it feels too real for that to be the case which is even more worrying. What do you guys think?
>inb4 lose weight
I'm about 112 pounds and dropping. Soon I'll be 100

[Anonymous No.10694454]

what anime should I watch /sci/?

[Anonymous No.10694461]

If I were to learn a subject from just reading a text book, what would be the most optimal way of doing so?

[Anonymous No.10694475]

>>10694461
reading the book

[Anonymous No.10694486]

>>10694267
>I-I'm not very comfortable in crowds
>Oh s-sure you can dance with my hydrogen, that's cool hehe
>Don't get so close Oxygen bro, people are gonna think we're g-gay

[Anonymous No.10694610]

Let S be some well-ordered set.
Let M(S) denote the set of all ordinals α, such that there exists an injection f: α S.

It's easily provable that M(S) is an ordinal itself, and |S| ≤ |M(S)|. How can one prove, without using Choice, that |S| < |M(S)|? (In the sense that there is no injection f: M(S) S.)
It eludes me.

[Anonymous No.10694616]

Yeah I got a question. Why do mods allow shitposts on /sci/?

[Anonymous No.10694627]

Let S be some well-ordered set.
Let M(S) denote the set of all ordinals α, such that there exists an injection f: α -> S.

It's easily provable that M(S) is an ordinal itself, and |S| ≤ |M(S)|. How can one prove, without using Choice, that |S| < |M(S)|? (In the sense that there is no injection f: M(S) -> S.)
It eludes me.

[Anonymous No.10694632]

>>10694616
engineering and computer science threads don’t belong on the science and mathematics board sorry, also apu posts should be met with a one month ban minimum

[Anonymous No.10694674]

>>10694632
The thing is, /g/ is not interested in engineering and cs at all. All they talk about is browsers, OS and smartphones. Coding related stuff should not be here, but spaceflight is alright.

[Anonymous No.10694675]

>>10694632
>engineering and computer science threads don’t belong on the science and mathematics board sorry
I don't think you realize it but this is actually a containment board for all the sperglords, sorry.

[Anonymous No.10694766]

Now i know /sci/ isn't very hot on AI, but can someone explain softmax in word2vec?

Specifically: in order to get the probability of a word does it loop through every single word in the dictionary to get it's softmax value, and then chose the one with the highest probability? What is "V" in this case? The length of the dictionary?

>https://www.youtube.com/watch?v=ERibwqs9p38
Lecture if anyone would bother to look at it and see if you understand it better

[Anonymous No.10694807]

I want to know what subject is most befitting my interests. I love mechanics, geometry (I guess you could call it 'spatial mathematics'?) so I wonder if I should study mathematics or physics at uni? Or maybe even engineering, although the copious lab sessions and assignments just sounds like a chore. So which subject offers more of those things?

[Anonymous No.10694813]

Does potential energy have mass?

[Anonymous No.10694895]

How can I show
[math]
\frac{1}{L} \sum_{n} \frac{e^{i 2 \pi n x / L}}{ (2 \pi n / L)^2 + p^2} = \frac{1}{2 p} \frac{ \cosh p (\frac{1}{2} L - x }{ \sinh \frac{1}{2} p L }
[\math]
?
Any ideas?

>>10694813
Mass is a property of physical objects

[Anonymous No.10694927]

>>10694895
oops
[math]
\frac{1}{L} \sum_{n} \frac{e^{i 2 \pi n x / L}}{ (2 \pi n / L)^2 + p^2} = \frac{1}{2 p} \frac{ \cosh p (\frac{1}{2} L - x }{ \sinh \frac{1}{2} p L }
[\math]

[Anonymous No.10694930]

>>10694895
Oops
[math]
\frac{1}{L} \sum_{n} \frac{e^{i 2 \pi n x / L}}{ (2 \pi n / L)^2 + p^2} = \frac{1}{2 p} \frac{ \cosh p (\frac{1}{2} L - x }{ \sinh \frac{1}{2} p L }
[/math]

[Anonymous No.10695147]

What is the best notation to connect the steps to solve an equation? I don't want to go to a new line for every step, which connector should I use? The right arrow?

[Anonymous No.10695207]

what is the fourier transform of sin(x)?

i've looked at several tables of transformations and all of the give variations of a combination of delta functions, but I don't know how to get the right coefficients

for the example in the pic, what determines the pi/j?

[Anonymous No.10695254]

What's a (fast) fourier transform?

[Anonymous No.10695279]

>>10695147
If your equation is small enough, I would say use a double-lined arrow. However, new line is supremely easier to read and won't make your work look like a mess.

>>10695254
A regular fourier transform is a tedious sequence in which you decompose an equation into a sum of sinusoids, and is usually a pain in the ass to do by hand. The fast fourier transform is just a computer algorithm that very efficiently and quickly calculates the fourier transform.

[Anonymous No.10695377]

>>10695207
Normalization convention. There are many conventions with how the FT is normalized. Just plug your result back into the formula with your chosen convention and tack on a factor that makes the equality hold.

[Anonymous No.10695381]

>>10695254
http://lmgtfy.com/?q=fast+fourier+transform

[Anonymous No.10695385]

I'm looking to get a degree in physics. Which of the following schools would be the best for me to transfer to:
>Indiana
>Purdue
>Tennessee
>Utah
>Arizona
>Washington State

[Anonymous No.10695429]

>>10695279
> A regular fourier transform is a tedious sequence in which you decompose an equation into a sum of sinusoids, and is usually a pain in the ass to do by hand.
This describes a Fourier series, which isn't quite the same thing as a Fourier transform (although they're closely related).

A Fourier series is a decomposition of a periodic function into a sum of sinusoids. The Fourier transform does something similar but the result is a continuous function from frequency to (complex) amplitude, and isn't limited to periodic functions (if the function *is* periodic, then its Fourier transform is a sum of Dirac delta functions).

> The fast fourier transform is just a computer algorithm that very efficiently and quickly calculates the fourier transform.
The fast Fourier transform (FFT) is an efficient algorithm for computing a discrete Fourier transform (DFT). A DFT is basically a Fourier transform applied to a discrete array of values rather than a function. It's a linear transform, meaning that it could be implemented as matrix multiplication (the matrix has a[m,n]=e^-2πimn/N=(e^-2πi/N)^(mn) where N is the number of samples). But matrix multiplication is O(n^2), whereas the FFT is O(n.log n). From a theoretical perspective, the FFT uses symmetry and periodicity to decompose the matrix into O(log n) sparse matrices, each of which can be multiplied in O(n).

[Anonymous No.10695471]

>>10695385
WSU is not particularly well-known for its physics program. University of Washington is probably the best program in the state. However, UW doesn't offer undergrad research (as far as I know) while WSU does, and you'll get a lot more money from WSU while you probably won't get any from UW.

[Anonymous No.10695494]

>>10695471
WSU made the list, because they have a nuclear reactor on campus they not only allow students to work on, but also only gets like 20 people a year looking to do so.

[Anonymous No.10695534]

literally how

[Anonymous No.10695537]

>>10695534

[Anonymous No.10695543]

>>10695534
>Round your answer to two decimal places if needed

[Anonymous No.10695546]

>>10695543
already tried that

[Anonymous No.10695554]

>>10695546
do the calculation again, but this time round correctly

[Anonymous No.10695559]

>>10694895
Poisson Summation

[Anonymous No.10695570]

>>10695554
Is 93.915 rounded up to 93.92 an incorrect rounding to two decimal places? 93.9 doesn't work, and 94 doesn't work. On my ti-83+ sqrt((900)(9.8)) comes out to 93.91485505.
... Okay it just wanted all 8 decimal places.

[Anonymous No.10695575]

>>10695570
93.91485505 rounded to 2dp is 93.91, Anon

You don't round every number - so although it's 93.915 to 3dp, it's not rounded up to 93.92 as 148 rounds to 100, not 200

[Anonymous No.10695585]

>>10695575
Yes I see that now, the four wouldn't bump up the 1 in front of it. I just only bothered looking at the graphing software's estimation of 93.915 and assumed that it would be good enough for these online questions (as it has been all quarter long). Only after your suggestion did I actual calculate S(900) and tried entering the whole decimal, which did work. Thank you.

[Anonymous No.10695822]

>>10689474
Is there a nontoxic material(polymer) which is initially in liquid form, then after curing, becomes transparent gelatinous/rubbery?

[Anonymous No.10696079]

Ok, so I was doing my matter wave homework and it was all good until I checked the correct results.

Apparently this is the final formula I need and It corresponds to my formula almost perfectly, except the 'm' part:
How does one transform the left part of the equation into the right one? It just seems illogical.

[Anonymous No.10696103]

Why does every 2.4 GHz EM radiation detector detect a high amount of EM radiation from every microwave oven, even premium ones?

[Anonymous No.10696109]

>>10696103
*from outside, door completed closed

[Anonymous No.10696151]

>>10696079
Basically your question comes down to asking why [math] m \sqrt{\frac{1}{m}} = \sqrt{m} [/math]

Method 1:
[eqn] m \sqrt{\frac{1}{m}} = m \frac{\sqrt{1}}{\sqrt{m}} = \frac{m}{\sqrt{m}} = \sqrt{m} [/eqn]

Method 2: [eqn] m \sqrt{\frac{1}{m}} = m^1(m^{-1})^\frac{1}{2} = m^1m^{-\frac{1}{2}} = m^{\frac{1}{2}} = \sqrt{m} [/eqn]

[Anonymous No.10696315]

Am i retarded or what? i'm starting calc 3 and i noticed i don't know this basic shit:

[math]f(x)=x^{3/2}[/math] diff..:
[math]f(x)=[/math]
[math]f'(x)=\frac{3}{2}\sqrt{x}[/math] So far so good
[math]f'(0)=[/math] this is where i'm confused
the answer is "obviously" does not exists because several reasons like 1.limit doesn't exists so rip continuity then so it's not differentiable and we can't even draw a tangent line there so there's no value to the derivative
but my mind keeps telling me that [math]f'(x)[/math] is just a normal sqrt function so the value at 0 is 0. is my notation incorrect? maybe i have to add [math]f'(x)\in (0,\infty)[/math] idk it's surprisingly my first time seeing this, also my first time using LaTeX

>>10696151
i like

[math] m^{1}(m^{-1})^{1/2} = (m^{2})^{1/2}(m^{-1})^{1/2} = (m^{1})^{1/2}[/math]

looks kind of bad but that's because i didn't write it in a fraction form

[Anonymous No.10696511]

>>10689474
>why can't I compare a 1d thing to a 2d thing multiplied by a similar integer
>why can't I compare a 2d thing to a 3d thing multiplied by a similar integer

[Anonymous No.10696514]

>>10695822
I swear I read about such a thing.

[Anonymous No.10696734]

Hey guys, fucking precalc brainlet technician here, where did they get the 2?

[Anonymous No.10696766]

>>10696734
the point (0,2) is one of the given points, so they set all the x's equal to zero to solve for the constant knowing that y = f(x) = 2

[Anonymous No.10696810]

>>10689474
Is there an easy way to recall dreams over hours since sleep?

[Anonymous No.10696888]

>>10693702
what are we talkig about here? linear systems or logic?

[Anonymous No.10696919]

>>10695385
Try MIT, Caltech or Berkeley.

[Anonymous No.10697096]

>>10689474
I posted this in this >10696862 thread but anyway,
why is there a separate notation for partial derivatives? Why not just use the normal "d" with respect to various variables? Isn't it pretty much representing the same thing?

[Anonymous No.10697144]

>>10697096
nvm I figured it out

[Anonymous No.10697161]

>>10695385
What state do you live in?

[Anonymous No.10697181]

>>10696103
the microwave radiation leaks from microwaves as the screen doesnt block all of it, they are tested to make sure there isnt enough leakage to harm someone though

[Anonymous No.10697189]

>>10697161
Virginia

[Anonymous No.10697192]

Is there a chance I can slip into a PhD with only 1 semester of research experience? Probably won't have any publication, but it will still be better than nothing I guess. For the university im applying to my GPA and GRE are more than enough and my letters of recommendation will probably be decent. Area is electrical engineering in photonics. I think I will at least get into a masters if i dont make the cut for phd admissions

[Anonymous No.10697201]

>>10689474
so if i got 3 lithium cells in series and i dump the positive on a anode of 3 pin schottky thingy and use another lithium cell on the other anode then hook it up to a transformers center tap and the 2 primary wires go to the oscillator and off the oscillator i split the negative to go to the 3 in series AND the one by itself will i get the amperes of both the series group and the lone cell?

conventional wisdom is that batteries in parallel have to be perfectly matched (same age and type and same amount of usage) and if you have a series group you have to dump a identical group in parallel...

but whats the point of these things if i cant do as i stated i would? it has no switch function. there is no gate and no base. the data sheet shows them as 2 anode and 1 cathode. both face inwardly. i retrieved them from power supplies. it seems these mix what comes off of a transformer with some shit from a capacitor. so do i get the ampers of both with a minimal volt loss from the diodes?

[Anonymous No.10697230]

>>10697189
Well it also depends on your plans afterwards and what you think you want to specialize in later on, all of them are Research 1 universities so any should be fine, but maybe do some research on what each universities physics departments pros and cons are, maybe see if professors have room in labs to get you some undergrad research experience (assuming your plan is grad school) and just generally which might help you the most in taking the next step in your path.
Why not University of Virginia? It would probably be much cheaper, unless you already have financials taken care of

[Anonymous No.10697257]

Last question but I have no Idea on what the fuck to do. Can anyone tell me? Even just naming the exact topic so I can search for example questions and work-throughs will be helpful.

[Anonymous No.10697258]

If the world is apparently dying in thirty years then whats the point, whats the point of anything? Is there any hope that we, as a species can salvage our situation in any way shape or form? And do supplements for concentration and focus actually work or is that bullshit?

[Anonymous No.10697489]

>>10697257
What is 2*5? What is (2*5)^t ?

[Anonymous No.10697743]

I have a problem with a particular type of exercises. I gotta show that H=<[2]_4, [4]_6> is normal to Z4 X Z6, and I can by showing it is a subgroup and Z4 X Z6 is abelian and all subgroups of abelian groups are normal, but then I gotta find to what known group is the quotient Z4 X Z6/H isomophic to. In the past on these exercises I dealt with quotient groups where the "nominator"(cant translate that, you get what I mean, the group on top of the quotient) is a direct sum of cyclic groups of coprime order thus cyclic, then it's easy showing that the quotient group of cyclic group is cyclic and there is only one cyclic group per order up to isomorphism. Now that "nominator" is not cyclic I'm stuck, please tell me I don't have to write out the whole quotient group to see what it's isomorphic to. What do I do?

[Anonymous No.10697870]

>>10697743
Bump

[Anonymous No.10698265]

>>10689474
>38. A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of 50.0 above the horizontal, positive x-axis. Another spacecraft is moving past with a velocity of 0.700c in the negative x direction. Determine the magnitude and direction of the velocity of the first spacecraft as measured by the pilot of the second spacecraft.
I used the Lorentz correction for the y component of v, and that leads to the answer the book supports, but everyone else just took the number and transplanted it. Why is the Lorentz transform being applied in the perpendicular direction?

[Anonymous No.10698340]

For the physicists:

if we'd load every earthling on a space ship, started our super engine with v_max = 0.98*c towards proxima centauri, would humanity get there in less than 4 years with respect to a clock on the space ship?

[Anonymous No.10698423]

>>10697192
I got accepted to 4 okay biochem programs (neither of my reach) with a 3.97 GPA (bio), 97th reading 85th quant 92 writing
I only had about a semester of research but i did a shitty poster and presented it at school a couple times.
Hope that helps.

[Anonymous No.10698455]

best precalculus book?

[Anonymous No.10698594]

I've been doing some topology and I need some help understanding the topological definition of a sphere (S^n). Of course the geometrical definition is the set of points with norm 1, but I have trouble intuitively capturing the idea of a stretchy shape that you can travel on and go around.

[Anonymous No.10698608]

>>10698340
They would. For earthbound observers, this would take roughly 4.3 years, but for observers on the space ship, the Lorentz factor cuts this time to 0.86 years.

[Anonymous No.10698808]

>>10689474
what does (y.dx)/dy equal to?

[Anonymous No.10698977]

Anyone good with fluid dynamics here?

[Anonymous No.10698980]

I already know that [math]\Xi_j=\sum_{i=1}^{n}\eta_i a_{ij}[/math], so I can write each ξ as a linear combination of all the ηs, but how to I write each η as a linear combination of all the ξs?

[Anonymous No.10698983]

All basic hashing methods I'm aware of are based on the assumption that the hashing algorithm is given a set of keys which may be hashed in its lifetime, and performs optimizations to select good hashing functions for the given set of keys.

Is there some similar algorithm/data structure that supports insertion and searching in O(1) time, such that it only knows beforehand the NUMBER of the keys rather than the keys themselves?

(Suppose for simplicity all keys are integers in some finite interval)

[Anonymous No.10698991]

>>10698980
Notice that your equation is equivalent to matrix multiplication. Invert the matrix and you're done

[Anonymous No.10698998]

what am I fucking up here

[Anonymous No.10699002]

>>10698977
>you are given the rate at which the sphere changes diameter
>from this you can figure the rate of change of volume
>from this you get the flow rate
>you are given the diameter (and thus area) of the exit
>knowing the flow rate, you can now figure out the velocity of the fluid at the exit
>use a basic kinematic equation to figure out the height of the jet assuming it is pointed vertical

[Anonymous No.10699014]

>>10698991
Sory but...what? This is like page 9 of a lin alg text, matrices and inverse matriceshavent even been mentioned yet. Be more specific?

[Anonymous No.10699015]

>>10694807
Physics
>>10695385
Go to UW or UCLA if you have the grades, otherwise grind comm college courses in your home state. Those schools are fucking terrible

[Anonymous No.10699026]

>>10698998
what's the question?

[Anonymous No.10699027]

>>10699014
>>10698991
I guess my question is how to show that the matrix of all those a values even has an inverse, let alone compute it.

[Anonymous No.10699036]

>>10699026
its irrelevant to the problem he is having which is not limited to just the inability to do a highschool chemistry problem from the first month of class.

[Anonymous No.10699045]

>>10699026
Here's the full question.

essentially, derive the empirical formula for whatever that CH compound is using the given information.

I have the molar quantity of C and H, I've divided them both by the smaller quantity (C, 14.7 mol) to get C1H1.5 . I multipled by 2 to get an integer answer for the both of them, but apparently C2H3 isn't right

it's a stupid simple question so I don't know why it's giving me such a hard time

>>10699036
go titrate your head into a toilet

[Anonymous No.10699087]

>>10699002
>>10699002

[Anonymous No.10699097]

>>10699087
I told you exactly what you need to do, you just need to plug in numbers and use a SUVAT eqtn. What more could you be confused about?

[Anonymous No.10699114]

>>10699045
Well the ratio isn't really 1.5 though. It's more like 1.6.
So maybe it's [math] C_5 H_8 [/math] ?
Not that I know anything about chemistry.

[Anonymous No.10699127]

Brainlet crossboarder here
Im sub high school tier in math ,like I cant even do equations,is there any website in which I can learn math?Like a mathematics duolingo,or what book should I read?

[Anonymous No.10699133]

>>10699127
khan academy

[Anonymous No.10699147]

/INTRO STATS/

I don't understand how mean/variance of a random variable X is difference than the mean/variance of the raw dataset. I get that the mean of X is weighted by the frequency of the values X takes on... but that doesn't matter if you have the raw dataset because values will just appear more than once?

[Anonymous No.10699155]

>>10699114
well shit I feel retarded now, my professor lead me astray. You were correct, thanks for the help.

[Cait !PROTIPqDn. No.10699165]

>>10699127
YouTube, KhanAcademy, really anything that will help visualize things. If you arrive to Calculus start using integral/derivative calculators to help check your answers. Wolfram Alpha may be worth it for you.

>>10698455
Reading maths is the worst way to actually learn maths. Sure understand a bit of a theory behind it but the best thing to do is use online resources aggregated from different sources and actually follow along. Passive learning will not develop mathematics skills.

[Anonymous No.10699175]

>>10699147
what?

[Anonymous No.10699180]

>>10699175
I meant "is different than" if that typo obscured the meaning

[Anonymous No.10699189]

>>10699180
still don't understand your question

[Anonymous No.10699194]

>>10699189
Oooookay... definition of mean with respect to random variables from my text:

"The mean of a discrete random variable X is a weighted average of the possible values of X, with weights equal to the probabilities"

How is this different from regular old mean we learned in 3rd grade

[Anonymous No.10699203]

how can I show that if R' is a subspace of R and that if R' has the same dimension as R, then we must have R'=R?

[Anonymous No.10699210]

>>10689474
What matlab library can I use to make conductor cross section area requirement calculations? Obviously for power systems

[Anonymous No.10699224]

>>10699203
Thats definitely not true. For example take [math] \mathbb{R}^3 [/math] and [math] \mathbb{R}'^3 [/math] such that [math] (x,y,z) > 0 \forall (x,y,z) \in mathbb{R}'^3 [/math] then both R^3 and R'^3 have the same dimension and R'^3 is clearly a subspace of R^3 but not the same set

[Anonymous No.10699256]

>>10699224
How can a vector be greater than 0?

[Anonymous No.10699259]

>>10698983
Most hash tables don't know the keys (or even how many keys) until items are added. If the keys *are* known in advance, that enables construction of a perfect hash function which maps each key to a distinct integer (no collisions). But that's a special case, not the typical case.

Most hash table libraries (or languages which have hash tables in the standard library) allow a hash to be generated for a value without regard to a particular table, which wouldn't be possible if the set of keys had to be known in advance.

[Anonymous No.10699304]

How do you prove pic related for non integers?

[Anonymous No.10699386]

>>10699256
You know what I mean, x > 0 , y > 0 and z > 0

[Anonymous No.10699434]

>>10699386
But the zero vector is necessarily an element of (sub)spaces, so that isnt a counterexample

[Anonymous No.10699470]

Is a quadratic equation said to grow exponentially, or is this a misunderstanding cum colloquialism?

[Anonymous No.10699474]

>>10699470
That's a misunderstanding. How fast a quadratic function grows depends on its degree, but no quadratic function grows exponentially.

[Anonymous No.10699491]

>>10699474
Neat. Also a quadratic function has a degree of two, but I think you read "polynomial" instead

[Anonymous No.10699495]

>>10699491
didn't know if you knew the difference so I figured I wouldn't church it up too much

[Anonymous No.10699549]

>>10693715
JavaScript, Ruby, and Snap.

[Anonymous No.10699566]

I got a question, would all of the material concerning computer science exist if we didn't have computers? Did the science itself exist before computers were made? I know the math required by CS and other skills like logic existed beforehand but would we still be discussing things like data structures, machine learning, and that kind of thing?

[Anonymous No.10699567]

>>10698423
that helps a little, my gpa isnt quite as good, my gre is about the same except high quant and lower reading
Not even sure if I'll be able to do a poster as i dont know what the professor is going to do yet kek
i'll just apply and hope i get in and if not just slug through the masters first

[Anonymous No.10699580]

>>10699495
Fair enough. I think I might keep saying "exponential" in casual conversation because the last time I said "quadratic" I got a blank look

[Anonymous No.10699698]

Is it possible to teach math without using a language other than numbers? As in no English or any other world language?

[Anonymous No.10699730]

Is it true that going for pure math for a bachelors is only worth it if you are thinking of academia or research?

[Anonymous No.10699847]

>>10698608
This blows my mind. Thanks. I think i just learned how to compute relativistic times

[Anonymous No.10699876]

Why does my tongue feel "dry" when I drink any kind of tea-related beverage?

[Anonymous No.10699915]

>>10699194
According to the definition in your text the mean of a discrete random variable is equivalent to the arithmetic mean only when X is uniformly distributed. The mean of a random variable is also referred to as the expected value https://wikipedia.org/wiki/Expected_value..

If X is not uniformly distributed you'll likely see a difference between the expected value of X and the sample mean (arithmetic average of raw dataset).

[Anonymous No.10699937]

>>10699876
It might be cancer, you should look that up, anon..

[Anonymous No.10699966]

apparently socializing is very important for physical and mental health, does this still apply to people with autism who have no desire to socialize?

[Anonymous No.10699996]

>>10689474
Can someone tell me how they got to 9/10 x 3/5? Considering that alpha was a constant that clearly was not defined in any situation it seems like they just said 'lol stick any number in, that'll work' and went with it. God I fucking hate this so much, keep going through these textbooks but can barely answer a question let alone get it right, I read the methods, the examples, numerous times very CLEARLY and it doesn't fucking work - I apply what they teach me and each question is completely different from the examples and make you apply shit that is from fucking anywhere in the spec. Like wholly shit I need practice with the basics of a new concept BEFORE I start throwing god-knows-what into it. I cannot grasp stuff, yes I'm a retarded fucking failure and I want to throw myself off a bridge, I'm 20 and still cannot grasp what bed-shitting toddlers can do, its fucking pathetic.

[Anonymous No.10700029]

>>10699996
You can find sine if you know tan. Just draw a right angle triangle with 3 and 4 as the side lengths of the legs. Then the hypotenuse is sqrt(3^2 + 4^2) = 5 by Pythagoras. So sine = opposite side/ hypotenuse = 3/5

[Anonymous No.10700162]

>>10699698
probably

[Anonymous No.10700268]

>>10699996
> Considering that alpha was a constant that clearly was not defined in any situation
You should see an optician. It clearly says tan(α)=3/4. Twice.

[Anonymous No.10700615]

why are there so many pajeets on quora

[Anonymous No.10700625]

>>10699966
I just have in-depth conversations with imaginary people instead

[Anonymous No.10700745]

>>10699876
the tannins in the tea are whats known as "astringents", they're what do that
https://en.wikipedia.org/wiki/Astringent

[Anonymous No.10700909]

I'm asked to do some computation that require the cumulative of the normal distribution. Do I just use a table? I haven't been told what way to use.

[Anonymous No.10700953]

What's the verdict, /sci/? E for energy, E for potential, or E for field?

[Anonymous No.10700981]

>>10700953
E for euler's constant, but yelled

[Anonymous No.10700993]

>>10700909
You can use a table. You may need to convert if you're not working with standard normal https://wikipedia.org/wiki/Standard_normal_table#Conversion

[Anonymous No.10701010]

>>10700909
Check whether the language/library has an erf() function. It's present in C99, C++11 and Python (and probably anything else with a comprehensive math library). Also, the wikipedia page for "error function" gives various methods for computation.

[Anonymous No.10701037]

>>10700953
>>10700953
XD

[Anonymous No.10701054]

What are some good resources for learning how to learn faster/better?

[Anonymous No.10701064]

I have two signals modeled as Gaussian random variables, with equal variance but different means. How do I prove that the best classifier(that determines which of the two signals has been recieved) is the one that has a floor that is between the two means?

See pic rel, two poorly drawn Gaussians with mean 0 and 10, the best classifier would be 5 in this case?

[Anonymous No.10701962]

Could the inverse square law tell us anything about the nature of spacetime?

[Anonymous No.10701975]

how is babby formed?

[Anonymous No.10702306]

>>10701064
show that it minimises error rate, which will be areas under curves on the wrong side of 5.

[Anonymous No.10702501]

>>10689991
firefox probably has extensions for that

[Anonymous No.10702510]

>>10692785
people assume you will make a lot of money if you do physics

[Anonymous No.10702895]

Easy physics question. Let's say I measure the longitudinal stress and corresponding strain of some material for different values of force stretching the sample. Then I want to estimate the Young's modulus of the material. Hooke's law is
[math] \tau = \frac{F}{A} = K \varepsilon = K \frac{\Delta L}{L_0} [/math],
where [math] \tau [/math] is the stress, [math] K [/math] is the Young's modulus and [math] \varepsilon [/math] is the strain.
I want to estimate [math] K [/math] by a least squares fit to the measured stress and strain data. Is it wrong to do this by assuming the cross-sectional area stays constant? Should I modify Hooke's law so that the area is expressed in terms of Poisson's ratio and then estimate both [math] K [/math] and Poisson's ratio instead?

[Anonymous No.10703348]

Organic chem question:

What happens to the claisen product if you treat it with a strong base afterwards (NaOH) while heating?

[Anonymous No.10703553]

Could someone rewrite what's supposed to be written here? I bet it's obvious to someone who understands probability, but I have no idea what's supposed to be in the smudged bit.

[Anonymous No.10703576]

>>10703553
Sorry for bothering you, found it elsewhere.

[Anonymous No.10703633]

>>10689991
I just browse in Clover until I come across a [math]\LaTeX[/math] post, at which point I open that specific post in Chrome, read it, then go back to Clover, and so on.
Though I just yesterday made the switch from Chrome to Firefox on my desktop, so I'll probably do the same on mobile.

[Anonymous No.10703636]

>>10690120
Sounds like your boy Hamilton has you covered:
https://en.wikipedia.org/wiki/Quaternion

[Anonymous No.10703650]

What field do you feel a slighty above average intelligence person can do the most good for the world in?

[Anonymous No.10703722]

>Taking intermediate algebra online class in college
>low level math
>doing well
>im starting to understand it
>oh gotta break down fractions into whole numbers
>read example in text book to understand it better
>learning about isolating variables, and solving an equation with one variable
>Do about 3-4 questions where I have to eliminate the fractions and have my answer be whole numbers.
>Get to pic related.
>ah no problem just have to convert to whole numbers
>plug in my answer
>incorrect
>hmm lets go over it again and see what I did wrong..
>oh I see the problem
>incorrect
>wdf, I guess I will say there is no solution
>incorrect, answer is 50 over 17
>what the fuck? I am learning how to eliminate fractions, and have my answer be whole answers
>fucking go in autism REEEEE for about 5 minutes on why even try for computer science/software engineering degree

Seriously guys how am I suppose to know when the answer is a fraction? Do I keep the whole equation in fraction form, then simplify the fraction to see if I can get a whole number out of it??

I literally just want to cry, this is basic shit I can't understand.

btw as a brainlet my original answers were
>2.8, I thought it was weird I got a decimal but obviously I realized my mistake
which I corrected to
>2 which I thought was the right answer...

[Anonymous No.10703858]

>>10703722
(4/5)b-4 = -(9/10)b+1
=> 8b-40 = -9b+10
=> 17b = 50
=> b=50/17
If the answer is a fraction, then it's a fraction. In general, if a and b are integers the solution to a*x+b=0 => x=-b/a will be a fraction unless b happens to be an integer multiple of a.

Multiplying through by the least common multiple of the denominators (in the above case, 10) may help simplify the intermediate steps, but you should assume that the end result will be a fraction.

[Anonymous No.10703994]

>>10703722
>Do I keep the whole equation in fraction form, then simplify the fraction to see if I can get a whole number out of it??

pretty much yeah. Dont know why the question gave you trouble though, it's pretty simple, just multiply everything by 5 to get rid of the fractions, collect terms and solve

[Anonymous No.10704248]

>>10703994
Okay so I was talking to a friend, she also got the same answer of
50/17
It may be simple to you, but wasn't for me, Math has always been a troubling subject for me, and would give up on it. But now that I know I hope it still holds true down the line when doing equations.

>>10703858
The part that confused me was, how did you determine that its a fraction? After some frustrating moments I asked her, well if you can't divide into it, and get a whole number, would you use the divisble number (17 in this case) as a denominator? She said yes, so IDK if thats always true.

>If the answer is a fraction, then it's a fraction. In general, if a and b are integers the solution to a*x+b=0 => x=-b/a will be a fraction unless b happens to be an integer multiple of a.

What I mentioned earlier?

[Anonymous No.10704544]

>>10699567
you could always ask the PI to do a poster in advance of applying. They aren't really published so a poster doesn't really reflect on his quality as a PI.
desu i don't think you need to worry about /getting in to A/ program, I don't think PhD programs in general are super selective, just the good ones. I applied to U nebraska lincoln and the students there told me its basically a safety school. That being said I had no interest in going there once i visited so "schools in shitholes will accept you no matter what, dude" is probably not that helpful. Don't worry about getting accepted, worry about writing an excellent statement of purpose.

[Anonymous No.10704630]

How do I show that every entry of row [math]2^k-1[/math] of Pascal's Triangle is odd?

Induction doesn't seem nice since there is no easy relationship between rows [math]2^k-1[/math] and [math]2^{k+1}-1[/math]. I've tried looking at row [math]2^k/math] instead, since I can count the number of 2:s in [math]2^k![/math], but counting the 2:s in the denominator is much harder.

The book claims this can be done (somewhat easily) using either direct proof or contrapositive, but I'm stumped. Any ideas?

[Anonymous No.10704636]

How do I show that every entry of row [math]2^k−1[/math] of Pascal's Triangle is odd?

Induction doesn't seem nice since there is no easy relationship between rows [math]2^k−1[/math] and [math]2^{k+1}−1[/math]. I've tried looking at row [math]2k[/math] instead, since I can count the number of 2:s in [math]2k![/math], but counting the 2:s in the denominator is much harder.

The book claims this can be done (somewhat easily) using either direct proof or contrapositive, but I'm stumped. Any ideas?

Repost to fix latex.

[Anonymous No.10704641]

How do I show that every entry of row [math]2^k−1[/math] of Pascal's Triangle is odd?

Induction doesn't seem nice since there is no easy relationship between rows [math]2^k−1[/math] and [math]2^{k+1}−1[/math]. I've tried looking at row [math]2^k[/math] instead, since I can count the number of 2:s in [math]2^k![/math], but counting the 2:s in the denominator is much harder.

The book claims this can be done (somewhat easily) using either direct proof or contrapositive, but I'm stumped. Any ideas?

Repost to fix latex.

[Anonymous No.10704825]

does mmHg get less accurate the larger it is, because the pressure of the Mercury has to fight gravity?

[Anonymous No.10705140]

>>10699224
Baffling post

[Anonymous No.10705185]

>>10689474
Is the difference between a P-series and the Riemann Zeta function the idea that Riemann zeta is used with complex numbers as well or am I being a fucking first year brainlet?

[Anonymous No.10705610]

>>10705185
Well yes, the name p-series is usually used only for real values, although that can be easily extended to complex numbers with arbitrary imaginary parts as long as the real parts still converge. The main difference between the p-series and the Zeta function is that the p-series only describes a specific case of the Dirichlet series (the series you usually see when there's talk about the RZF) that represents the Zeta function for all complex numbers with real part larger than 1.
The RZF is defined for almost the entirety of the complex plane, so when you need to evaluate it for complex numbers with a negative real part or maybe somewhere between 0 and 1, you can no longer use that series to evaluate it. That's when the analytic continuation of the function kicks in, but at that point the p-series is no longer relevant for the discussion, since the function turns into a whole different beast.

[Anonymous No.10706159]

>>10704641
Note that if you take a Pascal's triangle of size 2^k and just consider the parity, you get a Sierpinski triangle.

[Anonymous No.10706532]

>>10706159
Already considered that. It didn't really help though, since it's just restating the original problem.

I eventually found a proof by induction on the entry given a fixed row of that form. If there's a simpler direct proof I do not know, but honestly I doubt it.

[Anonymous No.10706917]

Question from >>>/qa/2779622

[Anonymous No.10707012]

Anyone here into relativistic quantum fluid electromagnetic thermodynamics?

[Anonymous No.10707166]

I am looking for a site for a niche need.

To out it simply, say I have an apple. And each apple needs 4 bananas. So to get 5 apples, I need to do 4*5=20 bananas. Simple. But also need 3 pears, that requires 6 grapes and 3 nuts.

So something that lets me input multiple entries, and shows what that each of those entries needs as well, like showing:

4 apples
____16 bananas
4 pears
____20 grapes + 12 nuts

[Anonymous No.10707208]

I posted this in the other /sqt/ thread I didn't realize this one was still up.

>>10707177

[Anonymous No.10707933]

>Get stuck on a problem
>Move on to other problems
>Get stuck on those too
What do?

[Anonymous No.10707943]

Does anyone know the persons in this chart? I know John von Neumann, Grothendieck and Kaczynski but who ist the last guy in this chart?

[Anonymous No.10708084]

>>10694440
I think you should go to a doctor not ask 4chan about your cancer.
My diagnosis is lung cancer by the way

[Anonymous No.10708158]

>>10707208
your answer is correct

>>10706917
it weighs the same, all the matter is already in the ipod, it just gets rearranged.

[Anonymous No.10708311]

Let T : V W and L : W W be two linear tranformations.
Prove that: Nu(L ◦ T) = Nu(T) Im(T) ∩ Nu(L) = {0}.
How THE FUCK do i do this?

[Anonymous No.10708316]

Let T: VW and L: WW be two linear tranformations.
Prove that: Nu(L ◦ T) = Nu(T) Im(T) ∩ Nu(L) = {0}.
How THE FUCK do i do this?

[Anonymous No.10708326]

>>10708316
fuck ASCII

[Anonymous No.10708348]

>>10708326
[math] x \in \text{Nu}(L \circ T) \Longleftrightarrow L(T(x)) = 0 \Longleftrightarrow T(x) \in \text{Nu}(L) \cap \text{Im}(T) \Longleftrightarrow T(x) = 0 \Longleftrightarrow x \in \text{Nu}(T) [/math].

[Anonymous No.10708382]

>>10708348
is this a troll? i dont see how are you proving the tesis nor how did you conclude step 2 and 3 (i dont see a tautology only a one sided implication)

[Anonymous No.10708400]

>>10708084
Damn, I hope that's not the case. I hope that it's just an angina, but thanks anon.

[Anonymous No.10708403]

>>10708382
Obviously it's only the proof of the 'if' part of your question. The converse is very similar and you should be able to do it by yourself.

[Anonymous No.10708415]

>>10708403
but you are not proving what you are supposed to. read the exercise again.

[Anonymous No.10708425]

>>10708415
What are you talking about? I proved that Nu(LT) = Nu(T) if the condition holds

[Anonymous No.10708461]

>>10708425
If he has trouble with this kind of question, he can't properly understand your answer

>>10708415
As always, you should rewrite the terms of the questions in terms you understand (it will also help you with learning the definition of the basic object you manipulate).
For the implication the other anon didn't prove you can start by :
Writing what does it mean for an element to belongs to Im(T) and Nu(L)
After that you can see what does it mean for x to belong to Nu(LT)
Now naturally combining the two above things you should see that x is in Nu(T)

The other inclusion is trivial but if you don't see it. Again : write does it mean to be in Nu(T). Then what happens if you apply L to Tx = 0

[Anonymous No.10708489]

>>10708461
I am not retarded but the anon is worse than i. I finally proved it using the dimention theorem. and the otherway was trivial.
the thing is i am not completely sure if one step of my procedure is OK. See:
<math>Nu(L\circ T)= Nu(t) \Leftrightarrow Nu(L)=0</math>

[Anonymous No.10708493]

>>10708489
oops
[math]Nu(L\circ T)= Nu(t) \Leftrightarrow Nu(L)=0 [/math]
also
[math]Dim (Nu(L\circ T))= Dim(Nu(t)) \Leftrightarrow Nu(L)=0[/math]

[Anonymous No.10708508]

>>10699304
For [math] \Re{s} > 1 [/math], [eqn] \Gamma(s) = \int_0^\infty e^{-x} x^{s-1} dx, \ \zeta(s) = \sum_1^\infty \frac{1}{n^s} [/eqn][eqn] \Gamma(s) \zeta(s) = \sum_1^\infty\int_0^\infty e^{-x} \left( \frac{x}{n} \right)^s \frac{dx}{x} [/eqn]Make a change of variables from x to nx and interchange the summation and integral sign (by the dominated convergence theorem, say) [eqn] \Gamma(s) \zeta(s) = \int_0^\infty \left( \sum_1^\infty e^{-nx} \right) x^s \frac{dx}{x} = \int_0^\infty \frac{1}{e^x - 1} x^s \frac{dx}{x} [/eqn]

[Anonymous No.10708560]

>>10708493
Could you present your full proof?
There should be no need of using the "dimension theorem" and thus fear you did some mistakes

For your equivalence to be true, you would need additional hypothesis. For instance think about what happens if T is not a surjective map onto W. Then there may be elements belonging to Nu(L) but not belonging to Im(T)

Really, if you listened to going back to definitions you would not get into those issues.
Let x in (Im(T) and Nu(L)) = 0
Then Let x in Nu(T), it means that Tx = 0
Thus LTx = L0 = 0
Thus x is in Nu(LT)
Thus Nu(T) is included in Nu(LT)

Now the otherway :
Let x in Nu(LT)
Then LTx = 0
But (Im(T) and Nu(L)) = 0
We have Tx in Im(T) and Tx in Nu(L) from two lines above
Thus Tx = 0
Thus x is in Nu(T)
Thus Nu(LT) included in Nu(T)
Thus under the problem hypothesis Nu(LT) = Nu(T)

Please I know it's long and boring but it's the only way you will not do errors. Later, you can be sure that the propositions are right and you can now use them to prove more complex propositions

Moreover, if there is some step you didn't understand, go back to the underlying definition of the written operations till you understand what happens or prove it wrong