/sci/ - Science & Math

Stupid brainlet genetics question google can't answer for me: let's say I have the DNA strand
>AGGATTACGATCGCACAAGATCCT
Which translates as RNA to
>UCCUAAUGCUAGCGUGUUCUAGGA
Then the protein sequence starts at AUG and should stop at UAG. But if I do that, there's a pair number of bases in between them, which means there stop codon is shifted or something. Wtf do I do? does it not stop at UAG? or does it just somehow not translate the UC before UAG into proteins? how am I supossed to read this? I just want to know the number of codons and the number of aminoacids they make.

Is this correct?
[math]Let~\omega=a\cdot dx+b\cdot dy~and~v=c\cdot dx + e\cdot dy.\\
$Show that$~\omega\wedge v (V_1,V_2)$ is the area of the parallelogram spanned by $V_1~and~V_2$ times the area of the parallelogram spanned by $<\omega>~and~<v>$.\\
Because $~\omega\wedge v (V_1,V_2)=det\begin{vmatrix}
a\cdot V_1_x & c\cdot V_2_x\\
b\cdot V_1_y & d\cdot V_2_y
\end{vmatrix}\\$
and the parallelogram spanned by $V_1~and~V_2$ is $=det\begin{vmatrix}
V_1_x & V_2_x\\
V_1_y & V_2_y
\end{vmatrix}\\$ and the parallelogram spanned by $<\omega>~and~v=det\begin{vmatrix}
a & c\\
b & d
\end{vmatrix}\\$ the product of the latter two is equal to the first by the scalar multiplication property of the determinant.[/math]

Is this right?
[math]
Let~\omega=a\cdot dx+b\cdot dy~and~v=c\cdot dx + e\cdot dy.\\
$Show that$~\omega\wedge v (V_1,V_2)$ is the area of the parallelogram spanned by $V_1~and~V_2$ times the area of the parallelogram spanned by $<\omega>~and~<v>$.\\
Because $~\omega\wedge v (V_1,V_2)=det\begin{vmatrix}
a\cdot V_1_x & c\cdot V_2_x\\
b\cdot V_1_y & d\cdot V_2_y
\end{vmatrix}\\$
and the parallelogram spanned by $V_1~and~V_2$ is $=det\begin{vmatrix}
V_1_x & V_2_x\\
V_1_y & V_2_y
\end{vmatrix}\\$ and the parallelogram spanned by $<\omega>~and~v=det\begin{vmatrix}
a & c\\
b & d
\end{vmatrix}\\$ the product of the latter two is equal to the first by the scalar multiplication property of the determinant.
[/math]

Is this right?

Let [math]f[/math] be Lebesgue integrable on [math][a,b][/math]. Then for [math]c\in\mathbb{R}[/math], [math]cf[/math] is Lebesgue integrable.

The definition I'm working with for [math]f[/math] being LI is [math]\int_{a}^{b} = \underline{\int_{a}^{b} f} = \overline{\int_{a}^{b} f}[/math], where [math]\underline{\int_{a}^{b}f} =\sup\{U[f,P] : P\in \wp[a,b] \} [/math] and vice versa for the upper integral. I thought of just saying [math]\{ cE_{i} \}_{i=1}^{n}[/math] would be a measurable partition, but if [math]|c|<1[/math] there are problems.
Can anyone clean up this mess? I haven't a fucking clue. This isn't supposed to be hard.

>>10102634
There just isn't a stop codon. So just start codon and divide by three the number of nucleotides after it

I know what's an algebra in measure theory, but could someone arse themselves to explain the other definition?

What are the tests that can be made to the brain to detect emotions and other things? And how accurate are they? Can they detect if a person is feeling pain? Can they detect the amount of pain? Can they detect if the pain is physical or psychological?

>>10102706
Makes sense. Thanks man!

>>10102374
There are four equally likely outcomes:
1. You pick the first black ball from the bag with two black balls.
2. You pick the second black ball from the bag with two black balls.
3. You pick the black ball from the bag with one red and one black.
4. You pick the red ball from the bag with one red and one black.

Given that #4 is excluded, the probability that you picked the bag with two black balls is 2/3, versus 1/3 for the bag with a red ball.

>>10102691
Pls.

I've been wracking my brain over this for a good while now. I've done a) easily and I know it's necessary to apply it in b) but I'm not sure how to do b).

>>10102716
There are many things that are called 'algebras.' I'm guessing the first sense you mean is a sigma algebra? What's the second?

>>10102700
Can you explain the notation for the definition you are using please? I don't understand if it represents the standard definition or you are using something else, I understand the partition part but what is [math]U[f,P][/math] supposed to represent? Just the set of the integrals of simple functions that are smaller than f in that partition? At any rate, I also don't get why you are trying to prove that the partition is measurable. [math]cf[/math] just means that the image will be multiplied by the constant c. The function is still defined on the same interval as the original f, and since f is LI in on the whole interval (and for any partition you pick), cf will immediately be defined on the same measurable partition, because the partition itself doesn't change. And the simple function just needs to be multiplied by the same constant c, that isn't too hard to prove. But then again, maybe I'm misunderstanding your definition.

will it forever be impossible to observe an atom

>>10103058
Consider the case [math]a>1[/math] first. Then use the definition of [math]a^{1/n}[/math] you are given, and you will be able to apply the first inequality. With that you just need to proof that the constant x will be arbitrarily small.

The second case is immediate after you proof the first case. Just consider [math]b= \frac{1}{a}[/math].

>>10103058
[math](x+1)^n = \sum_{i=0}^{i=n} {n \choose i}x^i = 1 + nx + \sum_{i=2}^{i=n} {n \choose i}x^i > 1 + nx ~~\forall x\geq0 [/math]

assume a>1
1 < a -> 1 < a^1/n
so x_n>0
a = (1+x_n)^n > 1 + n*x_n
x_n < (a-1)/n

assume 0<a<1
let b=1/a
b^1/n converges to 1 so does it's reciprocal

>be me
>math major
>ace all "continuous" math classes up to complex analysis
>take baby's first "intro to number theory" course
>get utterly demolished in the first exam
Why is number theory so hard, guys? It's literally just checking if some numbers are multiples of another. I get everything the prof says but I just can't solve the damn exercises. It's so frustrating.

>>10102813
I'm a brainlet going through Gelfand's algebra book and I just hit my first wall when it came to the problems.
It was #42 c). I spent some time with it, and I think I ended up with a valid solution, but I've never done proofs before. I split it up into two cases:

Case 1: where [math]\frac{a}{b} < \frac{e}{f} < \frac{c}{d}[/math] and [math]\frac{e}{f} \leq \frac{a+c}{b+d}[/math]

So since they're neighbor fractions: [math]\frac{a+c}{b+d} - \frac{a}{b} = \frac{1}{b(b+d)}[/math] and [math]\frac{e}{f} - \frac{a}{b} = \frac{be - af}{bf}[/math] and we have [math]\frac{1}{b(b+d)} \geq \frac{be - af}{bf}[/math] recall that [math]f < b+d[/math] so it is impossible for them to be equal, so there's a contradiction there. (not sure how to actually prove this. the former can't be reduced since we have a numerator of 1, and you can't do anything to the right side of the inequality since f < b+d) On the other hand, the only way [math]\frac{1}{b(b+d)}[/math] can be greater is if [math]be \leq af[/math] which contradicts [math]\frac{e}{f} > \frac{a}{b}[/math] or [math]be > af[/math]
Case 2:
[math]\frac{e}{f} > \frac{a+c}{b+d}[/math] and we know that [math]cf > de[/math]. Proceeding like before: [math]\frac{c}{d} - \frac{a+c}{b+d} =
\frac{1}{d(b+d)}[/math] and [math]\frac{c}{d} - \frac{e}{f} = \frac{cf-de}{df}[/math] so we have [math]\frac{1}{d(b+d)} > \frac{cf-de}{df}[/math] but since [math]f < b+d[/math] the only way this can be true is if [math]cf \leq de[/math] which is a contradiction.

So, [math]\frac{e}{f}[/math] cannot be between these two neighbor fractions.

Did I at least solve it correctly?

>>10103400
whoops didn't mean to reply

>>10103345
Nigga I can't even tell what the fuck is a circle and radius and circumfrence.

nice humblebrag
try living with fucking 90 IQ

>>10103345
Number theory is for the turbo autists. I could solve a problem, come back to it months later, and spend hours struggling to solve it unsuccessfully unable to remember how to solve even though I remember all the material needed.

How do I memorize chemical reactions and properties effectively?

>>10102628
Why mathematicians do this?
They're so smug

I am going to literally salt the earth. About 1 cup of table salt (iodized) per sq ft of my yard. about 2,000 sf. I have grass and fruit trees vegetable garden spaced around the property currently, so this isn't a weed killing idea. I believe salt works opposite to what contemporary science claims.

What will happen?

>>10103776
Or you could just salt the world.

>>10103776
did the Romans literally salt the earth? i mean i was told that did that with cartage so.... where did they get all that salt from? Literally hundreds of thousands of tons of salt would be needed for that. Wasn't salt like a currency or at least on par with gold at the time?

>>10103791
I researched that before deciding on my idea. Sounds like it would be more like millions of tons in order to make it infertile. Obviously there isn't growth on salt flats and hyper salinated areas, but I'm not shooting for that level. I've been experimenting already in small areas and 1lb 10oz of salt is only $0.50 so it's cheap. I've had unbelievable results, including reviving a dying orange tree.

I think I'll be buying salt pellets intended for use in water softeners. $5 for 40lbs

>>10103729
ANKI
> ANKI
ANKI
> ANKI

Finally a q. my 90IQ dog shit brain could answer

>>10103864
I've thought about that, but god damn, is there no way of knowing all this shit without memorizing it?

>>10103894
Sorry, this is where my IQ ends.

>>10103894
>doesn't want to memorize things
>studies chemistry
I honestly don't get it.

>>10103900
Mine too. I think this part is the brainlet filter.

>>10103904
I never implied that. Chemistry is fun but honestly sometimes I feel like I'm just memorizing complicated shit with no logic behind it.

So I really seem to learn from lecture videos.
Started with Feynman and Hammings.

What are some lecture series in YT about science (of really any kind, I'm a huge fucking brainlet) that you'd recommend?

>>10103345
I would suggest learning ring theory before number theory. Studying the properties of rings will allow you to see the speciality of the ring of integers. Number theory is all about the special properties of integers that allow us to develop arithmetical theorems. Some of them like the division algorithm exist outside of integers, while others like the fundamental theorem of arithmetic have an analogous version in other rings, but you find totally different structures. Being able to see integers as a special example of one of many rings tells you more about number theory than simply computing gcd and prime factorization 1000 times. You should of course have sharp arithmetic skills if you want to thrive in number theory. But if you want your analytical skills that you developed in your "continuous classes" to translate to success other branches of math, abstract algebra is a very powerful tool to help you do that.

>>10102628
How do I solve this? Without derivatives or integrals (we haven't learned them yet). I wanted to cancel out n^100 but I don't know what to do next.

>>10104163
Maybe there's some manipulation you can do if you replace stuff with the binomial formula.

>>10104169
yea, expanding it out gives
(n^100+400n^99+...-n^100-300n^99-...)/(n^100+200n^99+...-n^100)
from qhich you can then cancel n^99 and get a result

>>10104163
1/2

>>10104201
how?

>>10104210
Just keep the preponderant terms after expanding. Everything simplifies itself easily.

>>10104163
It goes to one.

why do maple procedures work this way? i can't understand it. i use A as my argument, assign A to two seperate variables, change one variable and then display the other and the other has changed aswell like they're linked somehow. if someone could help I'd be super appreciative because this is driving me crazy.

>>10104163
[math]\frac{(n+4)^{100}-(n+3)^{100}}{(n+2)^{100}-n^{100}} \sim \frac{n^{100} + 4n^{99}-n^{100}-3n^{99}}{n^{100}+2n^{99}-n^{100}} \sim \frac{n^{99}}{2n^{99}} \sim \frac{1}{2}[/math]

>>10104275
How do you get 4n^99?

>>10104281
Excuse me, it should be binomial(100, 1)*4*n^99.
And binomial(100, 1)*3*n^99 right after.
And also binomial(100, 1)*2^99 at the bottom.
Doesn't change the fact that the result is 1/2

>>10104261
Reference semantics. a:=b results in a and b referring to the same object. Use b:=Matrix(A) to make b refer to a new matrix initialised with the contents of A.

Most languages behave this way, at least with regard to container types.

Taking a stat phys course, can anybody tell me why we are not interested in a single microstate and instead take a little volume in phase space?

>>10104365
THANK YOU so much that makes sense, you're a lifesaver

>>10102628
I need some physics help, I'm a biologist but I wanna learn about lasers

how do I calculate the cavity modes of a laser?

Basically the question is whats the shortest distance between the lines, and also find a point on each line s.t. the distance between them = the shortest distance. I understand hoe to get the shortest distance, but I can’t figure out how to find the points I need

>>10104930
Nevermind I figured it out - I created a set of linear equations and solved for the two parameters that gave me the points whose vector equaled the one I found earlier for shortest distance

>>10103213
Here's a Strontium atom. Say hi to it, anon!

>>10102700
read the final paragraph of the OP

>>10103345
Number theory is literally the hardest branch of anything known to mankind

t. number theorist

if you want more proof: I am in one of the biggest and best NT department in the UK and there are literally 0 women. Even the algebraic geometry department has a couple women.

Doesn't the property underlined in red only hold for the finite field with two elements?
For instance, [math]\textbf{x} = (1,0,0) \in \mathbb{F}_{3}^{3}[/math] but [math] D(\textbf{x}, \textbf{x}) = 0 \neq W(\textbf{x} + \textbf{x}) = 1[/math].

Let f(x) = 1/(1-x). We make a 7th degree taylor polynomial at x = 0 to approximate f(x) on the interval [-0.7,0.7]
Use taylors formula to find the minimum constant C such that
|f(x) - P7(x)| < C

Can someone shed some light on this?

>>10105231
>Can someone shed some light on this?
What have you tried?

I'm trying to relate the physics with the math here. Ampere's circuital law gives a line integral of the magnetic field around a closed loop. But according to the fundamental theorem of calculus, the line integral around any closed loop such that start point = end point would be 0. Obviously [math]\mu_{0} * I \neq 0.[/math]
Where is my disconnect?

>>10105185
your book has a typo. replace wt(x+y) with wt(x-y)

>>10105238
I tried using this formula. I took the eight derivative and found when it was the largest (which was at the end point, 0.7), divided it by eight factorial, multiplied it by 0.7^8.
I don't think the other things I tried should be mentioned, at this point I just punch shit into the calculator and hope it flashes green so I can go to bed.
All the numbers I get are so large, and the approximation is really close desu.

>>10105251
>integral around closed loop is zero
Only if the function you are integrating is conservative. Hint: notice that the curl of B is non-zero.

>>10105238
Any input?

John has written five Valentine’s cards to his five friends, and put them in five addressed envelopes and sealed them. After doing this he realized that he forgot to ensure that the each envelope had the right card. What is the probability that at least one of the envelope has the right card inside?

I can't figure out how big the sample space would be for all 5 envelopes. I understand it'd be 25 for 1 of them, but once you open the first the sample space gets smaller for the next right? So the sample space for all five can't just be 25*5=125. Help

>>10105364
>but once you open the first the sample space gets smaller for the next right?
you are correct, every time you place a card you lose a possible envelope to choose from since you can't put two cards in the same envelope.

So there are 5 places to stick the first card, once the first one is fixed there are only 4 places left to stick the second one, and so on. Totaling 5*4*3*2*1 = 120 arrangements (or 5!, if you know what this is).

>>10105271
Oh shit, it all makes sense now. Thanks anon.

>>10103729
List down all the possible categories of chemical reactions starting from Combination/Synthesis. Do a fuckton of practices so your soul will remember how they work.
Then you start adding the properties. Do a fuckton of practices again.

How do I solve this?

>>10102700
Start with indicators, then simple, then no negative, then general measurable.

50% of all analysis proofs involving lebesgue integration work like this. You can even one line it by saying that each function has simple fn monotonically converging to it and just scale those fn

If emotions and feelings are brain signals and chemicals, couldn't you fabricate those chemicals? Couldn't you fabricate them in a form you can deliver to the human body? Besides ethics, what are some roadblocks to fabricating emotion eliciting chemicals? What's stopping those people from making something that makes people that imbibe it feel unfiltered pure rage, or lust, or something of that sort? Memes about the effects of THC triggering dopamine release, the myth of the aphrodisiac, and bone hurting juice that makes me wonder why people haven't been gearing toward bringing emotions out of people, from lust to rage to immense pain.

>>10102628
heeft xem een brein?

>>10105643
Mind-altering drugs already do that, sort of but the real limitation is that we lack a 100% accurate model on how these different chemicals affect emotions. We might have a rough idea but not accurate enough to start pumping drugs to change emotions. Just look at the entire state of anti-depressants and how they're usually prescribed. There's a lot of trial and error needed until someone gets the right medicine. We may have a rough idea on how lithium drugs affect depression but we don't have a 100% accurate working model on how it actually does affect depression.

>>10105643
"Fabrication" isn't really the word for what you want if I understood you correctly, its more of synthetically manufacturing emotions through drug usage, and those are already a thing. Drugs such as anti-depressants does things to your brain chemicals, which gives you effects like making you happier.

But since the brain is the most complex part of the human body, if not the most sensitive, shit like that doesn't work permanently. Drugs that affect the brain always gives some side-effects like making you even more of a retarded brainlet.

>>10105137
what do you think of mochizuki

Can a vector projection be described as the magnitude of one vector multiplied by the unit vector of another or am I misunderstanding it?

So I need to proof equivalence between A and B.
Can I do that by showing:
>not A => not B
>not B => not A
The only logical conclusion is:
>A => B
>B => A
or am i retarded?

I've been given some fancy formula for the water flow rate, based on about 10 variables. Each input variable has its lower and upper bounds given too. From this I went ahead and created a screening design using plackett burman and fractional factorials. After the screening design was made I could put the input variables in and work out the response (by putting everything through the fancy water flow formula). Then it was as simple as running an ANOVA to look at significance of the input variables - five of the ten variables were found to be statistically significant.

However, now I have to go through and create a D-Optimal model, and a space-filling model (using latin hypercubes), but we're limited to 50 runs. This is where I'm up to so far and am a little stuck.

I think I've managed to find some R packages which create the designs, but once I run the designs (with their input variable values) through the fancy flow rate formula and get my responses - how the fuck do I create my own model for flow rate from this?

If I knew what a 'good' response was then maybe I could go through and cherry pick the values of the coefficients which are most often producing these 'good responses.' But I have no way of knowing what's a 'good' or a 'bad' response - I just get a number.

In the assignment spec it talks about this process as "creating a meta model for water flow rate using D-Optimal and/or space-filling designs" and Google doesn't seem to yield much around any of those keywords.

Any ideas?

Is this book good for learning chemistry or should I read another book for the chemistry of today?
Reading as an introductory book.

Let's see how smart sci is, analyze this situation, basic sociolinguistics Rhetoric and all that

>>10105858
A vector projection is the vector from a linear operator (projection operator). I don't know how to format math equations on this website so I'll try my best (when I write "e1" I mean e subscript 1 and e^1 for e superscript 1).If e1, e2, ..., en forms a basis for an n-dimensional linear space R^n then for a vector x it can be represented as x = x1e1 + x2e2 + ... + xnen and the projection operator P sends x into Px,
such that Px = x1e1 + x2e2 + ... + xmem.
where m < n. P projects x into the vector Px on to the subspace R^m.
For example, for three dimensional space we can use the example of a projection operator P that sends it into the two dimensional subpace.
if x = (2,3,5) (x can be represented as x = 2e1 + 3e2 + 5e3 where e1 = (1,0,0), e2 = (0,1,0), and e3 = (0,0,1) then Px = (2,3) = 2e1 + 3e2
I tried to explain best I could. Just learned this so I could be completely wrong. Learning from Shilov's Introduction to the Theory of Linear Spaces

Please don't laugh. This is some elementary school tier shit :(

A company has grown from a worth of 35 to 44, so 25%.
When it is worth 44, sells item A, which is 70% of its products, and item B, which is 30% of its products.
How do I backtrack if I assume item A(the 70%) had a growth of 20%, find the growth of item B, and the percentages of the items

I've been getting pretty insecure with my methods of studying maths/sciences. What are your general takes on tackling exercises ? What are good situations for looking at resolutions that will not sabotage
me ?

>>10106198
>A company has grown from a worth of 35 to 44, so 25%.
No.

>>10106242
25.7%

>>10106238
yfw modern day maths is one of the worst taught subjects out of any subject
good luck mate

How do climate scientists determine the effect of volcanism on global warming when we have no idea how many active submarine volcanoes there are?

What percentage of anthropogenic global warming is due to direct heating from burning fossil fuels? What I mean is, excluding the greenhouse effect, would industrialization still cause warming?

>>10106238
Look up Polya on problem solving

>>10102628
I did the pre-algebra check on the Art of Problem Solving website, and I absolutely fucked up. I somehow passed college algebra, but after taking a break from college I don't even fucking understand the difference between the least common multiple and greatest common divisor.


It's like I cannot remember the most basic shit, but for some reason, a part of me wants to gravitate towards math and best my fear of it.

What type of book would help me blast the fuck out of even the most basic of math through rigorous exercises so that I will never forget the simplest of stuff ever again?

>>10106357
I know that the _______ for dummies series makes practice problem books with usually 1000 practice problems on the given subject. I found on amazon Algebra 1: 1,001 practice problems for dummies.
For other math Dover publications has some great books for learning math, and most if not all of them have practice problems with answers (except some which don't provide answers, though you can look up the book and find answers as some professors use their books and post homework answers online)
For Calculus I recommend The Calculus Primer by William L Schaaf, published by Dover. Book contains problems with answers. My 14 year old mind was able to comprehend it so I can imagine it is a good introduction book for calculus.
Before Calculus you should be familiar with trigonometry, limits, and geometry, after being confident with your algebra.
Not entirely sure if Algebra 1 for dummies would be a good book though apart from the practice problem book, so for a textbook I would recommend my high school's Algebra 2 book, Dugopolski's Intermediate Algebra 6th Edition (Which has plenty of practice problems with solutions).
To help memory I used to memorize 1 to 3 decks of playing cards in the sequence they were in, and the sequence of the cards backwards as well.

>>10106400
I've never heard of memorizing decks of cards to help with memory. I will try that out, and thanks for all of the book recommendations. I will definitely find a place to get that practice problem book on the internet. Thanks!

"If the strut has a thickness of 25 mm and the glue can withstand an average shear stress of 700 kPa, determine the maximum force P that can be applied to the strut.
Express your answer to three significant figures and include the appropriate units."

I had 3 attempts to get the right answer. I'm down to just the 1 last attempt and I just realized that I have been using 55mm as the width of the rod instead of the 50mm we're supposed. Hate when my mind spazzes out and just makes up numbers like that.

Anyone else want to have a crack at this one while I'm doing it over one last time to see if we get the same result?

/sci/, I want to teach myself physics. This is not for a career path, its merely in the pursuit of self improvement. I want to start with Classical physics then, if I decide I like it, branch out into the other fields

Mind you, I haven't taken any college bound math or science classes. I never took anything higher than algebra II in highschool and I've gotten quite rusty at it. However, my arithmetic has improved substantially over the past three years due to my job and I feel much more confident about my ability to learn mathematical disciplines

Can you recommend any books, apps or computer programs to help me master my algebra? and after I've gotten that down, can you recommend anything for geometry, trigonometry, and calculus

>>10106425
I got 2747.5 N but don't take my word for it, didn't do well in physics.

>>10106460
I used radius equal to 25 mm there

>>10106460
3500 N is my other guess if it's a square base, looked up strut and thought circle.

>>10106460
final guess 4041 N didn't account for area change because of tilt, as if it was a square. was playing vidya wasnt paying attention sorry anon

>>10106507

Damn, I got 2.02 kN by using

cos(60)Pmax / ((50mm/sin(60))*25mm) = 700 kPa

giving

Pmax = 700 kPa*50mm*25mm / (sin(60)*cos(60))

How did you arrive at 4041 N ?

>>10106579
followed same way but I was assuming it was 50 mm x 50 mm instead of 50 mm x 25 mm

I'm watching https://youtu.be/DclqE-9vFgY?list=WL&t=713 right now about Nofap and porn's effect on the brain, at the point I've linked, he mentions a study about video games, I don't get whether he's saying it's a positive or negative, but he mentions there's more brain activity because of playing video games, so... positive I guess?
Anyone mind explaining please?

>>10106598

Naisu, thanks.

>>10106625
This is the referenced study btw.
https://www.ncbi.nlm.nih.gov/pubmed/26252933
After having a look at it, I'm getting the feeling his point is that addiction can be effected by how much you do a dopamine-secreting activity like vidya.
Could be wrong, I'm a gaymer, science isn't my strong point.

>>10103400
bro is there a typo in question (b)? Because I can't show either of them. Should it be a+c / b+d?

can someone explain to me the process of determining the number of homomorphisms between cyclic groups? say, [math]C_{4}[/math] to [math]C_{2}[/math] for example?

>>10106689
yeah, it's a typo. it's a+c/b+d

>>10106723
I literally spent over an hour trying to show that shit, FUCK

How do I prove
[math](a_{1}a_{2}...a_{n})^{1/n} \leq \frac{1}{n}(a_{1}+a_{2}+...+a_{n})[/math] for [math]a_{i} \gt 0[/math] (the geometric-arithmetic means inequality) given that
[math]\frac{1}{n}(x_{1}+x_{2}+...+x_{n})\geq1[/math] when [math]x_{1}x_{2}...x_{n}=1[/math].
I was trying to think of a substitution for x in terms of a but I'm not getting anywhere.

>>10105597
its not true, since, for starters, one side will usually be an integer, and the other irrational...

>>10106824
induction?

>>10106855
I don't see how that would work using the given. Yeah, I could just prove it outright, but that's not the problem

>>10106866
are the n's from both statements linked somehow? Or can the statement you're given be true for any n?

>>10106824
Pass ^1/n to the other side, then 1/n to the other.

Does [math](\mathbb{R},+)[/math] form a group? I don't think so. There doesn't seem to be an identity.

is there a relatively simple circuit that can be made that does the following for n inputs and 20 outputs?
some examples with 6 inputs:
101010 -> 11110000001100000000
100110 -> 11100000001111111100
111100 -> 11111100000000000000
010000 -> 00000000001111111100


what's going on here is that the first 10 output bits represent the tens place in decimal, and the latter 10 output bits represent the ones place in decimal. the n inputs represent an n bit binary integer, which above is a 6 bit binary integer.
that fourth example with 010000 (8) returns ten zeros for the tens place and eight 1s for the ones place.

>>10106903
[math]\mathbb{R}^{+}[/math] I mean.

>>10106903
if you mean the real numbers bigger than 0, with multiplication they do form a group with identity 1

>>10106873
I mean they're not really linked, I just want to prove the G-A inequality by using the given inequality
>>10106877
so you get [math]n^{n}(a_{1}+...+a_{n}) \leq (a_{1}a_{2}...a_{n})^{n}[/math] ? I don't see how that helps.
Pic related 5.9 is the problem, I minimized the function on the constraint and found that its >= 1.I really don't think it's supposed to be a hard problem but I can't figure it out.

>>10106967
equation should say n^{n}(a_{1}a_{2}...a_{n}) \leq (a_{1}+a_{2}+...+a_{n})^{n}

>>10106971
fuck [math]n^{n}(a_{1}a_{2}...a_{n}) \leq (a_{1}+a_{2}+...+a_{n})^{n}[/math]

>>10106904
Obviously there's a circuit which does that. Whether that circuit is "relatively simple" is subjective.

There are 2 basic approaches. One is to design divide-by-10 and modulo-10 circuits then demultiplex the results. The other is to generate the truth table for each of the 20 output bits then optimise the minterms.

Can someone explain bra and ket notation to me in layman's terms?

>>10107004
>generate the truth table for each of the 20 output bits then optimise the minterms
and without doing this I'm sure the result would be too complex for what I want. I was hoping I guess that it was a common problem with a simple solution.
How about a circuit converting binary into BCD? what would that look like? what about twos complement into BCD (is there even such a thing as signed bcd?)

Is [math]\mathbb{Z}_{n}^{*}\cong Z_{m}^{*} \iff |Z_{m}^{*}| = |Z_{n}^{*}|[/math] true (where these are all the invertible elements?

>>10107073
No m=5 n=8

Is there a shortcut to simplifying the integral or ysqrt(4-y)^(3/2)?

How do I set up my integral for finding the mass of this lamina?

>>10105665
That's a comprehensive answer, thanks.
>>10105667
Yeah, I was incredibly tired when I wrote that post and my vocabulary was weird. Synthesizing is a much better term.
Anyhow, I don't imagine anything of the sort would work permanently, I imagine that it would work in highs and lows like alcohol or other inebriating drugs and substances do. Of course the main goal for a lot of people is feeling good so most of the thought when it comes to directly impacting someone's emotions might be combating depression, but I had to wonder if the similar treatments might be possible with anger, sadness, fear, lust, and the other plethoras of human emotions, or if there was a certain ease of access that we have to impacting euphoria over our other feelings. Obviously taking a medicine that makes you feel angry is far from desirable, I had just wondered if such a thing was possible.

>>10107115
what's wrong with integration by parts?

>>10107135
are you doing a line integral? or is that supposed to be y <= f(x)?

if the latter than you have to break it up into two double integrals or better yet convert to polar

>>10107135
a^2=x^2+y^2
It's a circle, so just use pi a^2.

>>10107196
Right, right, (pi a^2)/4

>>10105961
bump

To anyone that is in mechatronics or has some experience with line follower robots, why are races held? Why has nobody come and said "this is the fastest design that you can make" and made those competitions retarded?

PHYSICS QUESTION (banked anything always confuses me)

Suppose a car goes around a track with radius r, banked at an angle of 7 degrees. Suppose the coefficient of friction between the car and the track 0.70. Find the max speed around this track the car can go without slipping.

>>10107196
Wrong

>>10107345
Literally Google backed curve physics and you'll get a worked out example. Come back with a specific question or not at all.

>>10107345
I think you can make an fbd for a slice of the track but don't you need the cars mass?

>>10107317
Not in mech, but I think I can explain. Sure, you can mathematically determine the fastest iteration of a given design (a certain fuel, a certain material, a certain type of gyroscope, a certain type of propellor, a certain design for aerodynamics)
But these factors CONCEPTUALLY can be modified.
Take a (terribly designed) gas powered bot. It's not hard to maximize gas storage while minimizing weight to find the most efficient design in this regard.
But the whole game changes when you decide not to use gas at all. THAT is why competitions are held, and why the "fastest machine" won't ever really be determined (besides getting into relativity territory)

>>10107351
What do you mean by specific question? And i'll do that thanks
>>10107354
you'd think, but they basically never give me mass if they don't have to. it should cancel with something else, i assume

>>10103466
its not a humblebrag in these threads as this is all undergrad work which any brilliant student could handle without help from a tutor or professor, much less cynical sociopaths on a Natufian bone carving board

Say you had a car going at 21m/s. It is traveling over a hill that has an arc whose radius is 460m. The car's mass is 1200kg. It is traveling up the hill, and it 30 degrees from the vertical.

What is the normal force?

I figured:
sum(F) = m * a
Fc = m * ac

Fc = Fnet around a circle
Fc = Fg - N
Fg - N = m * ac

ac = v^2 / r
Fg - N = m * v^2 / r

Then plug and chug. But this found normal force at the TOP of the curve, not at 30 degrees from the vertical.

Help?

Suppose r red balls and b blues balls are arranged in a row at random. What is the probability that no two blue balls are next to each other?

No clue here? I know that the total way to arrange the balls is (r+b)! but I have no idea how many ways to arrange it so that no two blue balls are touching.

>>10107024
> How about a circuit converting binary into BCD? what would that look like?
A lot like divide-by-10/modulo-10.
> what about twos complement into BCD (is there even such a thing as signed bcd?)
Tens-complement (i.e. nines-complement plus one). If you had 4 digits, -x => 10000-x => 9999-x+1

>>10102628
I'm looking a book but I can't find it. I've already used all the links on the wiki but no luck. And no, I wont go to /wsr/ because is a dead board. Any of you guys can help me out?

I'm looking for "special functions of mathematics for engineers by larry c andrews"

>>10107536
>Any of you guys can help me out?
http://gen.lib.rus.ec

Show that j : [x]->[-x] defines an order 2 automorphism of Zn. Conclude that f: [1]_2 ->j determines a homomorphism of Z2 into Aut(Zn). Prove that Zn semidirect Z2 is isomorphic to Dn.

So j is order two since j(j([x]))=j([-x])=[x] which is true for all x in Zn.

How is f a homomorphism from Z2 to Aut(Zn)? I know j is an element of Aut(Zn) but am confused how to continue. Assuming this is true I am still lost on how to prove Zn semidirect Z2 isomorphic to Dn. Its only clear to me that they share order.

>>10107545
Fucking thanks anon you saved my shitty semester. How come this page isn't on the wiki tho? most of the wiki links don't even work.

How do I write an element of an automorphism? Since it's just the set of all mappings from G to G, is it literally just a function?
I think I may have answered my own question...

>>10107659
>How do I write an element of an automorphism?
An automorphism is a function, which is a set of ordered pairs.

is there a relatively easy way to solve the system of equations
6x+2z=b2x
2x+6z=b2z
x^2+z^2=25
I know the answer should be (x,z) = (+/-5sqrt(2), -/+5sqrt(2)) but I don't know how to get that

>>10107848
what is b2?

Is the answer B = 12 and A = -15?

I just did [math] -3 \leq f'(c) = \frac{f(b)-f(a)}{b-a} \leq 2 [/math]

Then I let [math] a = 0 [/math] and [math] b = x [/math] to get [math] -3 \leq \frac{f(x)}{x} \leq 2 [/math] then I just distributed the x for each case [math] -3x \leq f(x) [/math] or [math] f(x) \leq 2x [/math]

So picking the worst values for these in the interval [math] (-4, 5) [/math] I got B = 12 and A = -15

Is my logic here correct or am I just a huge brainlet who fucked up this problem?

Anyone here ever done Cluster Sampling in R and willing to help? I'm trying to do a sabermetrician project

>>10108089
I've made some histograms in R once a while ago

>>10108098
I'm trying to compute standard error for avg annual salary from a cluster of 8 baseball teams. Do you know what [math]M_i[/math] should be in this?

>>10107860
10 and -15 desu.
Ignore the minus four, only the five matters. How high and how low can it possibly go from 0 to 5?

>>10103058
Bernoulli's inequality holds for x >= -1, and I think that's necessary for (b) (since for x >= -1, (x+1) >= 0, and then it necessarily holds for a since a > 0)

Your prof probably forgot the "-"

>>10105279
f(x)=Pn(x)+Rn+1(x)
So set abs(R8(x))<C and solve

Apologies for phone posting

If I have 30 clusters and each cluster has 20 elements, if I randomly sample 5 elements from each cluster to use... Is that Two-Stage cluster sampling?

Since nothing can reach the speed of light but light, and because when the particles in matters move faster matter heats, the heat limit is when the particles reach 99% of the speed of light.

Ain't that so?

>>10108184
can you elaborate on why to ignore -4?

(we're just looking at 1-dimensional forces and movement here)
I was slightly confused at using different times for the force and velocity, but now I think I maybe got it.
Let me get it straight:
The principle of this is, through knowing the velocity and force at times t1 and t2, we can know the x coordinate at any given time t? And are t1 and t2 constants?

I'm considering joining the military if I fail this semester. How is it? Am I likely to get back problems or bullied (those are my two major concerns)?

>>10108432
>>>/k/

I've been told that a recursive function is from defining:
A basis
Recursive or reductive clause
Closure under the operations

I have no clue what any of this really means. Can someone explain, and also explain why addition is recursive?

I'm British, what're the admissions for MIT like? Is it like Cambridge/Oxford on steroids? I occasionally think about applying there in 10 years after I finish my degree and do a stint in the Army.

what does it mean for a predicate to be defined on the elements of a set?

>>10108527
?
A predicate is a boolean function, and for something to be defined on the elements of a set means that this function takes as arguments exactly those elements. Was that your question?

>>10107854
b*2 just a variable

>>10108628
If that is the case, the solution you posted can't be correct.

The first two equations are just lines through the origin, the third is a circle around the origin with radius 5.
So there can't be a point (x,z) that satisfies all three equations.

>>10108688
> The first two equations are just lines through the origin
They're lines; they aren't through the origin unless b=0. By symmetry, their intersection lies on x=z, which intersects the circle at x=z=±5/sqrt(2).

>>10108714
Are you seeing something I'm not seeing?

>>10107848
> 6x+2z=b2x
> (6-2b)x+2z = 0

Looks pretty line-through-the-origin to me, where's the constant? Or is this supposed to read "2b + x" on the right hand side?

How is the shadow of the lunar lander nearly hitting the horizon?

>>10108763
The moon is curvier than the Earth

>>10107570
f takes the generator of Z2 to the automorphism you just proved has order 2. So f is a homomorphism from Z2 to Aut(Zn). This means you have a group action of Z2 on Zn. From there, it's just verifying the semidirect product you get is actually isomorphic to Dn.

Is the answer E?
Can someone check my work. I converted y to rsin(theta)
When I integrate with respect to theta, I get cos(theta) and then cos(pi/2) -cos(0) = -512/3.
None of the answers are negative.

>>10108785
But how is the shadow nearly the same size as the moon?

>>10108800
Nevermind, I forgot to make cos negative.

>>10108811
You can also quite easily check your work by simply integrating without doing the conversion.

>>10108800
answer is D you dummy do your homework by yourself

>>10108800
>I have a fourth of a circle with radius 8 how do I calculate the area
You complete niggers I swear to God.

>>10108834
>how do I calculate the area
you dummy look again it doesnt ask for the area it integrates a function over an area

>>10108807
It's not?

>>10108834
64pi / 4 != 512/3

whoops I didnt realize this is a stupid question thread, I am sorry dummies

>>10108841
As in the length of the shadow nearly meets the horizon line, surely the moon's horizon should be much further away than that?

It's really misty or foggy tonight and I find the air quality really refreshing. It's nice and cool, makes me feel really alive.

How would you describe the air quality scientifically and why is it that I find so pleasant?

Also why is it that stars appear clearer on nights like tonight? Cold nights, often brought on by mist or fog.

>get midterm back
>91/100
>class avg was 70
>professor says we can turn in the midterm with corrections to recieve half of missing points back
I feel cheated. This isn't fair to me or others with higher grades. Should I email a strongly worded message about this?

>>10108922
Afaik, stars are always there, we just can't see them because of pollution.

>>10108925
No.

>>10108925
lmao get owned nerd

>>10108929
>afaik
thanks for the laugh

>>10108935
We both know you didn't laugh. Stop being insecure about abbreviations.

How did they get arcsinh?

>>10108938
It was not about the abbreviation, but more about how the statement implied that "stars are always there" is something people are unsure about.

>>10108947
The implication that people are unsure about stars not being there was never implied, but about pollution.

>>10108944
[math]\mathrm{arsinh} x = \ln(x+\sqrt{x^2+1})[/math]
substitute u=2x.

>>10108938
>>10108949
Why are you so mad about people enjoying the joke?

> afaik the sun always shines, but some people can't see it because their part of the earth points away from it

> iirc ice is water too but it its too cold to be liquid

Phrasing it like that is not funny to you?

>>10108963
How can you tell someone is mad over text? Nice head canon. Just like how you magically knew what someone was implying when you clearly didn't.

Can someone help me out? I'm trying to figure out what my boundary is for theta, but I'm having a little difficulty figuring it out.

Is there a name for something for something like a computer that get's smaller but more powerful? Like something with the same computing power but got more compact would be known as blank.

>>10109022
0 to pi/2, innit?

>>10109022
It is right in front of you: y=x means [math]\theta = \frac{\pi}{4} [/math]

>>10109034
Can you explain why? II would think that was right if there wasn't y = x cutting off the other function.

>>10109044
If you want to see it more clearly, remember x = r cos t, y=r sin t -- so x = y means t = pi/4 in the first quadrant.

>>10109026
Traditionally, the prefix "micro" was used; google for example "PDP-11" and "MicroPDP-11".

Hey, brainlet here. I was doing the exercises for chapter 1 of Spivak's Calculus and hit a wall. I did the first part very easily, but I don't even know how to start the second part, in which you prove the Schwarz inequality, and the answer manual I found just said that it follows immediately. Clearly I'm missing something. Any help would be appreciated.

>>10109135
Here's the answer key's solution.

I'm dressing up as a CIA nigger for Halloween. What can I inject or eat to make myself glow in the dark? Preferably the purchase shouldn't involve Libyan terrorists.

>>10109139
(x1^2+x2^2)(y1^2+y2^2)>=(x1y1+x2y2)^2
Is the Schwarz inequality. Look at the first picture. The left side is the same, and right one also has the element of the second picture, which is >=0.

Where does the negative come from? I get the rest but I think my professor made an error

>>10109181
D(u^n)=nu^(n-1)
D(v^1)=-v^-2

>>10109181
the derivative of 1/x is -1/x^2

>>10109181
Chain rule, (1/v)' = (-1/v^2) v'

>>10109187
Fockn hell D(v-1)

>>10109181
1/V = V^(-1)

>>10109160
Thank you so much. It makes much more sense when you write the Schwarz inequality that way(both sides squared). It was given as pic rel, which confused me. Cheers!

>>10108423
>The principle of this is, through knowing the velocity and force at times t1 and t2, we can know the x coordinate at any given time t? And are t1 and t2 constants?
No. You need to know the force function F, which I suppose is a given, as in a given information to solve the problem, since it appears in the original differential equation. t1 and t2 are just integration constant so the integration result gets a different variable when it's solved. You can see in the forth line he just renamed t=t1, dt = dt1, it doesn't matter what it's called, once you solve the integration limits, there's t again. In the final equation the constants are v(0) and x(0), F(t) is a function that describes the force acting on the system at any given time.

Don't bully too hard for this one.
How exactly does GPA work?
Does each class just give an integer dependent on the letter-grade received? Or is it more specific, based on the percentage?
For example, would an 81% hold the same weight as an 89%?

Why can't you graft cancer cells from a human into a horse then harvest the horse's antibodies to create a cure for the cancer? Does the immune response of the horse not use antibodies in this scenario, or are the antibodies too nonspecific?

A stupid question: Consider a circle with center O of radius 1 and a point X inside of the circle. Let A be any point on the circle, does there exist a point B on the circle such that |AX||BX|=|0X|^2?

>>10109512
Consider |OX| < 1/2, A chosen so it lies on the line OX. |AX| > 1/2, |BX| >= |AX|, so |AX||BX| > |OX|^2

>>10109474
At least everywhere I've been, an A is an A, regardless of percentage. A 92.5% and 100% both show up in the gradebook as a 4.0, assuming the A range is 92-100.

>>10109531
Ugh, what about |AX||BX|=|OX|?

>>10109563
of course X=/=0

>>10109563
For the same reason as above, that won't have a general solution.
What is this about? Why are you doing this.

>>10106719
Use prime decomposition and look at where the identity goes.
>>10107011
Let [math]\mathcal{H}[/math] denote a (reflexive) separable Hilbert space equipped with a non-degenerate sesquilinear form [math]\langle\cdot,\cdot\rangle: \mathcal{H}^2 \rightarrow \mathbb{C}[/math], then kets [math]|\psi\rangle \in \mathcal{H}[/math] are elements of [math]\mathcal{H}[/math] and bras [math]\langle \psi|[/math] are elements of the dual [math]\mathcal{H}^*[/math] given by the sesquilinear form such that the natural non-degenerate bilinear pairing [math]\mathcal{H}\times\mathcal{H}^*\rightarrow \mathbb{C}[/math] is equal to the sesquilinear form under the isomorphism [math]\mathcal{H}^*\cong\mathcal{H}[/math].
>>10104382
Because stat mech systems are not integrable, and asymplectically-invariant Liouville measure isn't always globally defined over the entire stochastic phase space. This means that the trajectories of a microstate does not necessarily stay in the leaves of an integrable foliation, only its expectation value does.
>>10105251
Because an enclosed current leads to a divergence (singularity) in the magnetic field on the manifold, hence [math]{\bf B}[/math] as a differential one-form [math]\omega = {\bf B}\cdot d{\bf x}[/math], though closed, need not be globally exact (locally they are described by the vector potential [math]A = {\bf A}\cdot d{\bf x}[/math]). The loop integral is exactly the pairing in de Rham duality [math]H_1(\mathbb{R}\setminus \ast,\mathbb{R}) \times H^1(\mathbb{R}\setminus \ast,\mathbb{R}): ([\gamma],[\omega]) \mapsto \int_\gamma \omega \in \mathbb{R}[/math].
Incidentally, the induction of a current in a loop [math]\gamma_1[/math] by a magnetic field generated by another [math]\gamma_2[/math] is proportional to the linking number [math]\int_{\gamma_1\times\gamma_2} A\wedge dA[/math].

>>10109571
Oh its really stupid, I 'm trying to directly (by definition) compute the line integral of log(|x-y|)dS(y) (by log i mean the natural logarithm here) over the unit circle ( so y is on the unit circle ie |y|=1). If you would divide the circle in to two 2N arcs of length pi/N, the the idea would be to pair the arcs and for each of the pairs find a point y_i in one element of the pair and Y_i in the other such that |x-y_i||x-Y_i|= |x|, then the riemann sum would always be equal to pi/2 log(|x|). Then you pass with N to infinity and get the value of the integral.

Could I please get some help with this? I really have no idea how to answer it and can't seem to find any information within or outside of my course about it.

>>10108625
Yes, thanks.

>>10109710
All I can think about off the top of my head is that they want you to relate convection currents to the viscosity of the environment, in other words, the more liquid it is the more "heat rises".

Remember that for any point inside the earth, the amount of mass that acts as gravitationally relevant is basically that of the sphere with radius below that point (everything else -- the spherical shell above that point -- cancels out). So the liquid inside the outer core, for example, experiences less gravity than that in the mantle. This to me means that heat radiates more homogeneously in deeper regions, and more directionally upward the more outward you go.

Dumb physics question. Let's say you've got two different cylindrical bars. They're both the same weight, the same length, and made of the same metal. One is solid, while the other is hollow. The hollow one has a thicker diameter so that they're still the same weight and length. Which one is stiffer?

>>10109768
https://physics.stackexchange.com/questions/12913/hollow-tube-stronger-than-solid-bar-of-same-outside-diameter-o-d

Same mass: hollow cylinder wins. Read link related.

>>10102628
A long time ago a /sci/ anon recommended a math textbook authored by Russian authors that taught the concepts in a story-like way. Does anyone know the title of the book?

>>10109778
Thanks anon

Let p_1(x) and p_2(x) be two Newton Polynomials approximating f(x) on [a,b] with deg(p_1)<deg(p_2). Is it possible that [math]max(|f(x)-p_2(x)|)-max(|f(x)-p_1(x)|)[/math]?

i.e. can a higher degree interpolating polynomial result in a higher maximum absolute error in it's approximation

>>10109592
>asymplectically-invariant Liouville meassure
can you please elaborate? I haven't taken a measure theory course yet, although i understood that we defined a measure [math]d\vec{\mu}[/math] in phase space from the characteristic function (probability density) [math]\rho(\vec{\mu},t)[/math] which is constant if [math]\vec{\mu} \in \Omega (t) [/math] and zero else. What is a Liouville measure? How can i express Liouvilles theorem of volume conservation through this measure? What does "asymplectically-invariant" mean? We saw in the last lecture that the rate of change of the microstate [math]\vec{\mu}[/math] was given by the multiplication of a symplectic matrix with the gradient of the Hamiltonian.

sorry for all these questions and thank you for your time.

I am starting trigonomitry

Can someone explain why the exact value of arctangent (-1) is equal to -pi/4


I really know fuck all about these kind of problems..
Explain it like i am 10 years old

>>10110074
Because tan(-π/4)=-1

>>10110082
Yes but how do i find -pi/4 when the range is between -pi/2 and pi/2

>>10110089
-pi/2<-pi/4<pi/2

>>10105070
Is that actually a single strontinum atom. Why is it so large compared to all the material around it?

I have to split a bulk sale of three properties among each other and dictate which lots hold what area of acreage. I'm boned, I'm gonna be here all fuarking day doing this. I can't isolate regular shapes out of the smaller section at the top for the life of me, and the surveyor left NO angles for any of these calls.

>>10110146
Oh my god I'm a fucking idiot. There's an angle on EVERY call

Could I make my own moisture absorber using a plastic ice block in a bowl? Like, the water from the air would condensate right?

>>10110140
stront means shit in dutch

>>10110138
Ok thanks but suppose the awnser -pi/4 was not given in this question,

How do you get the awnser?

In 2SAT problems, are they always of the form:
(x v y) ^ (q v p) ^ ...
That is, are they always OR in the clauses connected by AND?

Or could you have one like:
(x^y) v (q^p) ?

>>10110228
Calculating arctan, arcsin, etc is a huge pain in the ass. In this case, you should've just remembered that tan(-pi/4)-=-1.

>>10110237
Care explaining how this calculation is done?
I would like some huge pain in my ass

>>10110269
https://math.stackexchange.com/questions/128514/solving-the-arctan-of-an-angle-radians-by-hand

>>10110059
That’s a typo, it’s supposed to be “a symplectically invariant Liouville measure”. What this means is that it is invariant under the action of the symplectic group Symp(M), of which a Hamiltonian vector field X_f is a member. What this means is precisely what Liouville’s theorem guarantees: phase space volume (the fibre integration of the Liouville measure over a leaf of an integrable polarization) is preserved by time evolution, and this is no longer the case in stochastic process. If your measure samples phase space points from a probabilistic distribution, the sampled microstate might not stay within the phase space volume. Things “leak out/in” due to random noise.
I’ll answer the other questions later today, I’m at work rn

I don't get it.

Suppose there was a set.
And in this set there was an element
And that element was a positive integer e.g. 200
Isn't that element a set which contains any number less than 200?
Surely 200 contains 100 and 1/2 and .000000001

And if it contains 1/2, couldn't it contain 400 as well, the two being factors of 200?

Is this math?

>>10110407
Numbers aren't sets that contain smaller numbers unless you're working with reals, and even then they contain rationals.

>>10110410
Isn't a positive integer real? What do you mean by rationals?

>>10110407
Not quite.
1. The set theoretic definitions of numbers as sets are really just methods of 'encoding' numbers and creating definitions so that you can emulate arithmetic within set theory (because technically speaking, numbers aren't a part of set theory). When dealing with things like this it's important to keep in mind a few things.
1a. There's more than one way to encode the same set of numbers.
1b. Different sets of numbers are encoded in completely different ways and the arithmetic systems for them function entirely differently. That is to say that the natural 200 is completely different from the integer 200, the rational 200, and the real 200.
1c. Technically speaking it's incorrect to say that the naturals are a subset of the integers, integers a subset of the rationals, etc...
2. If you're working with natural numbers as sets then the set only contains natural numbers smaller than it.
https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
If you're working with reals as dedekind cuts then 200 would contain all rationals smaller than 200 (but no reals, see 1b and 1c). So, the real 200 contains the rational 1/2 which contains the integer 400; but not the real 1/2 or the real 400.

according to the Pareto principle, 20% of people do 80% of the work in a given group, say a company.

Say you have a company of 100 people, so 20 people do 80% of the work. Does the pareto principle also apply to the remaining 20%? So does 1 person do just over 65% of the work?

>>10110431
It's a meme.

>>10110231
The name is DNF, or disjunctive normal form, for your first example, the regular case.

If terms of the kind of your second example occur, you can see that every pair of parentheses is a solution for those variables; so usually you would split up the expression into as many duplicates as you have distinct conjunctive expressions, set those variables accordingly, and solve the remaining free variables in DNF as usual.

>>10110431
No. Pareto principle assumes a Pareto distribution. If you chop off the lowest part of a Pareto and look at it in isolation it no longer belongs to that family, so you can't apply the heuristic again.

>>10110436
You have it backwards.
CNF: [math](x\lor y)\land (q\lor p)[/math]
DNF: [math](x\land y)\lor (q\land p)[/math]
https://en.wikipedia.org/wiki/Conjunctive_normal_form
https://en.wikipedia.org/wiki/Disjunctive_normal_form

DNF is nice because it tells you exactly how the truth table looks (each conjunct denotes a true entry in the truth table). So it's trivial to convert back and forth from DNF to truth table.

>>10110231
2-Satisfiability typically uses 2-CNF statements (CNF statements with 2 terms).
https://en.wikipedia.org/wiki/2-satisfiability

Kinda simple question regarding probability theory
I have a task where a bag contains 12 balls where 7 are white and 5 are black. I am tasked to find the probability on getting 2 white and one black when picking 3. This is unordered with no replacement.

Now, I've already found the answers but it's done in a very time-requiring process, where I have to make a tree with all possible outcomes and the probability of getting each of them as there become fewer and fewer balls in the bags
Is there any other way to do this which is much less time demanding?

>>10110342
Thanks man. One last thing, do you have book/notes recommendations for statphys? I’m okay with the math (at most parts) but this is my first touch with the subject. Currently reading Kardar.

>>10110470
>Now, I've already found the answers but it's done in a very time-requiring process, where I have to make a tree with all possible outcomes and the probability of getting each of them as there become fewer and fewer balls in the bags
And this is pretty much an obsolete thing to do if the amount of possible outcomes reach 100 or even thousands

>>10110398
the sum of the exterior angles of any polygon (ie: one that doesnt cross its own sides) is 360. So divide your object into two polygons and apply that

>>10110431
If you're talking about real life stuff, my father is a big time consultant and says that you don't actually need at least 50% of the workforce in any normal company. Anyone competent and motivated can do the work of at least 3-5 people, more so in the lower rungs of the ladder of intelligence required to complete a task.

The reasons why there's so much people even if it's dumb are:
>incompetent management
>size of a company matters a lot sometimes, showcases their stability, reliability, etc
>it's very expensive to fire some people that have worked very long there (more often the case in Europe I guess)
>workers don't actually work as much as they could (a lot of people just get there and mingle, have cig breaks, coffee breaks, stupid meetings, or just browse the internet all day)

>go to professor's office hours to talk about their paper
>h-hi professor
>hello
>...
>Do you want to talk about your grade?
>n-no no I just want to talk about a paper you wrote
>Oh okay. Ah, I remember now, but I have to teach a class in 15 minutes so I need to get going.
>...oh okay
>Maybe another day, not at this time though
>...
>...
>...is Monday okay?
>Tuesday would be best. Just not at this time.
>...oh okay.
>...
>...
>...
>...okay... I should go now to let you get to your class.
>Bye
How do I stop myself from sperging out again? I swear I'm not like this with other people. It's only around professors do I get nervous and run out of things to say.

>>10102628
how do i prove that 2^55+1 is divided by 11?

>>10110522
by Fermat's Little Theorem,
(2^5)^11 + 1 = 2^5 + 1 (mod 11) Since 11 is prime.
2^5 + 1 = 0 (mod 11)

Or you could just calculate it out.

>>10110520
think that somewhere in the past year they shit and while cleaning their ass they got poo in their hand so they spent a little longer rubbing that spot when washing their hands

>>10110455
whoops. I aporogize. Thanks for fixing my mistake.

>>10110532
ok, i'll try it, thanks a lot.

>>10109495
You can. But nobody uses horses for that.

>>10110470
you might notice that [math] \frac{5}{12} \cdot \frac{4}{11} \cdot \frac{7}{10} = \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{4}{10} [/math] since multiplication is commutative.
Therefor instead of adding all of the probabilities up you just need to calculate one leg of the tree and multiply it by the number of ways that you can order them (keeping in mind that 4 must follow 5 etc.) which is easily found with the combination function in this case [math] _3C_2 [/math]

we can generalize this method into what is known as the hypergeometric probability.

>>10110295
Oh man nevermind.
Thanks dude

>>10110570
Then what do they use?

Lottery players pick five different numbers from 1 to 47, and also a MEGA number from 1 to 27 on a ticket. The player can choose any number between 1 and 27 (including the 5 numbers that have been chosen) as the MEGA number.

What is the probability of matching exactly 3 of the 5 winning numbers
and also matching the MEGA number?

I know the total number of ways to draw 5 numbers is 47C5. So the probability of getting all 5 right is 1/(47C5). But how do I know the probability of getting exactly 3 right?

I am taking this exam right now
Help me

I am preparing for an exam tomorrow and this is one of the practice problems that we were given. I don't understand how to calculate the tension. The horizontal component of Tension is responsible for the centripetal acceleration but when you draw the FBD, both gravity and the vertical component of tension are in the same direction. Doesn't this mean that the ball will accelerate downwards? I know this isn't right tho because I can put a ball on a string and swing it above my head in a circle and it will not accelerate downwards. Any help?

I'm trying to calculate the exponential of a self-adjoint operator by using it's spectral decomposition but get only rubbish

>>10110847
If you don't know, you don't deserve to get it right.
Either that or acknowledge that the educational system has failed you, and/or that you have failed it.

>>10110848
Imagine the moon spinning around the earth. Gravity is constantly pulling it to fall over our heads, but here's the thing, it doesn't. As the moon accelerates, it moves, and the new velocity ends up once again parallel to the earth, so it doesn't fall.
To put it really simply, the ball has a force towards Lancelot's hand that spins as the ball spins. The tension is the force the ball makes on Lancelot's hand.

Yo yo my niggas. An easy question for yall.

I have a problemo: I am trying to solve this using the quadratic formulur but I am stuck trying to convert it to the standard form.

When I do try to get it to standard form, it turns out as: 0=r^2+3r-8 but when I plug the a, b, and c values into the quadratic formula, the answers are wrong.

What's the step I'm missing?

>>10110955
that should be -10 not -8

>>10110955
Sup familia.
First I'll pass the one third to the other side. Then, it's least common multipl, so we'll have
4/(r^2-1)=(3+r-1)/(3r-3)
Decomposing
4/(r-1)(r+1)=(3+r-1)/3(r-1)
So we'll cut r-1 on both sides.
Pass the r+1 to the other side, and you should have a normal second degree polynomial.

>>10110520
why would you go to office hours 15 minutes before they end
you're really making things harder on yourself here spergo

If spit has white blood cells in it, can it cause allergic reactions?

guys what do. im playing white...

>>10111019
>guys what do. im playing white...
not science or math

>>10111019
After going King b1 black would need to go Bishop f7 or move his rook (a,b,c)8 to prevent checkmate or a bishop-rook trade, to which you can maybe do something like bishop b2 to get a tempo on black's queen? Responses after that would depend on where black moves his queen, like f3 to wipe up your last pawns

>>10111019
b2 to b1

>>10111019
knight to b5

>>10111037
Didnt work i ended up rage quiting

>>10111041
What knight?

>>10111044
Was my suggestion retarded or did I respond too late? If the former, what did black do? I'm still a learning chess player

>>10111048
nvm now I see the bishop to f5 move, you were fucked from the start friendo

>>10111048
no it was a good plan, it was just that the other player saw it coming so he defended his rook with a pawn and then bla bla and i just rage quit

what

>>10111061
huh

>>10111061
where

What is the evolutionary benefit to producing children that starve to death?

>>10110059
>What is a Liouville measure?
On the symplectic vector space[math](\mathbb{R}^{2n},\omega_0)[/math], the Liouville measure is just the symplectic form [math]\omega_0 = dq_i \wedge dp_i[/math] itself. If such symplectic coordiantes [math](p,q)[/math] can be found such that the 2-form [math]dq_i \wedge dp_i[/math] can be globally defined, then we say that the symplectic manifold [math](M,\omega)[/math] admits a Liouville measure.
>How can i express Liouvilles theorem of volume conservation through this measure?
Let [math]M[/math] be orientable and let [math]\gamma: t \mapsto (p(t),q(t))[/math] be a trajectory generated by a Hamiltonian vector field [math]X_H[/math], then [math]\operatorname{vol}(t) = \int dp_i(t)\wedge dq_i(t)[/math] satisfies [math]\frac{d}{dt}\operatorname{vol}(t) = 0[/math]. Suppose a Liouville measure exists on [math]M[/math], and suppose we have second class constraints given by some integrable polarization [math]P \subset TM[/math], it is desirable that the Liouville measure restricts also to another Liouville measure on the leaves of the foliation given by the polarization [math]P[/math]. If this is the case then we have conservation laws.
>>10110473
Stat mech in general has no rigirous mathematical treatment since it involves informal functional integrals. However there is a differential geometric treatment of thermodynamics that might give you some ideas towards a diff geo approach to physics.

>>10110852
Your second line is incorrect. You cannot factor exponentials of operators unless they commute. You need to follow the Baker-Campbell-Hausdorff formula.

>>10111149
I know, but the operators commute since they are orthogonal projections
i.e. |a><a||b><b| = |a> <a|b> <b| = 0 = |b> <b|a> <a| = |b><b||a><a|
see third line

>>10111164
No. They are orthogonal on their respective eigenspaces. You're trying to prove a general operator identity for everything in the Hilbert space. There are obviously vectors that overlap.

>>10111149
>>10111164
where |a> = (1,0) and |b> = (0,1) are orthonormal

>>10111170
in this particular case you can simply prove that the operators commute by choosing a basis and explicitly calculating the commutator

>>10111200
Seriously?

>>10111218
Am I doing something extremely stupid here? I don't know, it's late and I might not see a glaring error.

>>10111227
Operator identities are basis independent mate.

>>10111149
Based Touhouposter, should I go for functional analysis or linear analysis first?
I know my multilinear, if that makes a difference.

>>10111232
Uh yes, commutation relations are basis independent that however gives us the freedom to choose a basis to calculate them

>>10111235
>should I go for functional analysis or linear analysis first?
What do you mean by "linear analysis"? Harmonic/wavelets?

Can someone help me find alpha?
I've tried S1 = -alpha -+ sqrt(alpha^2 -wo^2)
wo^2 = sqrt(LC)
Couldn't find alpha that way, unless I'm doing my arithmetic wrong and that's the correct way. I should be getting 200 rad/s

>>10111243
>be me
>huh what does he mean what is linear analysis
>google linear analysis
>it isn't a subject in english
Ah, sorry. Either way, having finished up with essential Analysis on R^n (Stokes, etc) I go straight to functional or is there anything I should go for first?

>>10111261
You meant vector anal then? Do measure theory first before fun anal

>>10111272
I know measure. Topology too.

>>10111273
Then go ahead

>>10111279
Thanks b.

>>10110852
Why that notation? Does it make it easier?

>>10111283

>>10111290
what, bra-ket notation?
Because I'm studying physics, but else you could just use the usual notation for tensors instead

Can some one explain what the fuck is going on here.

Did I do this problem right lads? I don't know if my assumptions are correct

>>10111434
step 1: use trig to find an equation relating theta to x
step 2: take the derivative of both sides of the equation (product rule, chain rule, and basic trig derivatives)
step 3: isolate dx/dt then plug and chug

it would probably be much more straightforward to isolate x first before you take the derivative, my only thought as to why they did it this way is that sin = cos at the particular theta given so all the trig functions will cancel out nicely

>>>/g/68321023
>>>/g/68321023
>>>/g/68321023

plesse respond to this
pkesde

>>10111481
How can I solve it if theres that x by it self.

>>10111639
you have an equation relating theta to x and you are given theta, so simply solve for x and plug it in

so theres essential oils and shit that are 'anti-oxidant' ie they discourage(?) oxidation.. my question is, would essential oils exist that promote oxidation? what would that property be called? and what are some examples if possible? googling doesn't yield me anything but health articles about oxidation

What's the quickest way of solving e^At matrix by hand? I've been doing it by diagonalizing but it takes forever

>>10111136
>integrable polarization I have no idea what polarization means here (same goes for leaves of the foliation).

[math] M[/math] is taken to be the configuration space for all the positions [math]\{x_i \}[/math] right? So it’s a 3N-dimensional manifold? Sorry for all the questions, we haven’t analyzed the proper mathematical formalism.

ok i wasn't sure the best place to post this on 4chan but i think this is most suitable, i have had schizo-affective for nearly 10 years i was just reading and realised i have had all the diagnostic tests besides mri/ct what stood out to me is this test is done to rule out lesions, i dont know much about lesions just that dextromethorphan can cause them, 6months before my psylocybin triggered schizo-affective i heavily used dxm i did mention this in my drug histroy questions 10 years ago but i havn't used since and have felt no need to mention to current psychs, is it possible that i did a lesion? should i bring this up with psych get a scan and find out for sure? would recovery be different then anti-psych meds? am i just being schizophrenic over a wiki article i read?

Is this still cluster sampling?

A market research firm randomly selects 5 cities in a certain state and then randomly selects stores in those cities to test a product. However, due to budget they did not send the product to all of the stores, because it would've been to expensive.

My gut tells me that this is two-stage clustering because they eventually pick stores within their cluster to sample to. However, it doesn't state whether or not it is randomly selected or not.

>>10111444
f(x) is bounded for all x implies f(g(x)) is bounded for all x since any single value of g(x) is bounded, and hence is in R