/sci/ - Science & Math

By the way, sci-hub .tw is detected as spam.

~UNANSWERED~

Math
>>11559491 (you should be able to do this)
>>11560429 (definitely not)
>>11561536 (I think that works)
>>11562025
>>11563310
>>11564269
>>11564515
>>11565352
>>11565750

Physics
>>11558975
>>11561160
>>11561834
>>11564669
>>11565792

Electrical Engineering
>>11560692
>>11561628

Bio+Medicine
>>11554072

Stupid
>>11554939
>>11555815 (Yes)
>>11555835 (Yep. Have until May to decide. If you plan on going to grad school, maybe consider not opting in to pass/fail?)
>>11558316
>>11558761
>>11559536 (look up "decimal time," the autism brought to you by the french)
>>11560327
>>11564745
>>11565133

Is taleb a hack

>>11565804
Probably. Caring about him much at all indicates a hack tho.

How do I simulate/approximate probability distributions over an exponentially large state space?

To give some context, consider the set of all bit strings [math]\{ 0,1 \}^n[/math]. I have probability distribution [math]p[/math] over all possible bit strings [math]x \in \{ 0,1 \}^n[/math], and in fact I have a formula to efficiently compute each [math]p(x)[/math] *exactly* in linear time (requires some other problem-dependent parameters).

Now I want to sample from this distribution, say using whatever standard RNG protocols are built into numpy or scipy. Of course, I'm only interested in drawing some [math]\mathrm{poly}(n)[/math] number of samples. Clearly, I can't actually write down an array of all the [math]p(x)[/math]'s because that would be [math]2^n[/math] in space complexity, let alone computation time. I also know that it is not polynomially sparse, nor does it have some sort of "smooth" approximation. All I can do is, for a given instance of a bit string [math]\hat{x}[/math], "compute backwards" the corresponding [math]p(\hat{x})[/math].

How wide are your guys's hips? In terms of width. Im just trying to gauge whether my hips are really large or is it rather my waist and ribs are small. Also what are some exercises to expand ribcage and increase waist size?

>>11565779
Is the world gonna end due to the Coronavirus on June 28th?

>>11566268
no
>>11566181
34" waist

Idk if this is within the scope of this thread but can I be reasonably confident that https://www.amazon.com/gp/product/B002WKM6GM/ and https://www.amazon.com/product/dp/B017WWR2QS/ are the same chemical and/or function the same? The label looks identical but the "other ingredients" worries me a bit

How does it work?

How often do chemistry majors think about going walter white?

>>11565779

God bless all the autistic gay furries in the United States Military. I know that God doesn't want to do that but he doesn't have a choice in matter since I am better than God because I am real whereas he is not and so I tell God his business and make him bless who I please.

>>11566385
literally just grab the current amount of views and send YouTube a request to set the title to "This Video Has X Views", where X is the number that has been grabbed. AFAIK, YouTube just requires the auth key to change a title so it isn't that hard to do.

>>11566340
Both seem to be oxone. Either way, you'll have to use it in contaminated form, or find a way to repurify it.
Since pic related doesn't seem to encourage it, I'd pick the one with the least intrusive side products (surfactants are a major pain, but metal impurities can actually be dangerous, among other things)
Stay safe anon, oxidizers are real nasty stuff

thanks to corona I already have a passing grade in almost all my courses, so I don't even need to show up for finals, and I can just CR my classes at the end so they won't show up on my GPA.

What's the name of the claim that math proofs and computer programs are equivalent..? The something correspondence...?

Oh nice another furry general. Why cant OP keep his furry shit to himself?

>>11567209
Curry-Howard correspondence

>>11565779
What's the easiest way to make ethanol? Purification can be secondary. I'm sure you can convert something like vinegar or sugar even to ethanol CHEMICALLY. Any ideas?

Going to then concentrate to 70% and use as a disinfectant.

>>11567209
a script is basically magic auto calculating paper. of course you can write proofs as scripts. you couls just write the whole proof in #comments and then just have it spit out the numbers at the end with print.

Which field of study would enable the most lucrative schemes?

>>11567407
schemes? you'll have to elaborate. but id have to say on the face of it id have to say risk analysis.

scientifically speaking how much debt is too much debt? is there a ratio of debt vs expected income that becomes unbearable? obviously i will take as little as possible but besides that

Geology fellas pls halp
What's this pink rock I found?
>captcha related: select all hills and mountains

>>11567481
Any number greater than 0
Imagine being such a poor planning impulsive spending brainlet that you ever go into debt
Jesus Christ it really isn't that hard

Is there a name for "strong to weak" continuity?
[math] x_n \rightarrow x \Rightarrow f(x_n) \rightharpoonup f(x) [/math] where f is a not necessarily linear operator.

Can someone explain me how to swap the order of integration of this integral. I'm burning out

It's known that [math]\int_0^\infty x^n e^{-x} dx = n![/math]. While I can prove it analytically, I can't explain "why" it's true. I would absolutely love to see some (continuous analogue of) "combinatorial proof", if you will, of this identity; any intuitive explanation that could offer some insight.

It crossed my mind that this integral may be interpreted e.g. as the expected value of [math]X^n[/math], where [math]X[/math] is exponentially distributed with rate [math]\lambda = 1[/math]. Can anyone offer some insight on how to relate between these ideas? I googled properties of the Gamma function and even came across a thread on MSE that asked the exact same question, but the answers that were offered there were beyond my current level.

>>11567640
Personally I would just memorize the formula and not worry about it too much.

>>11567640
>muh intuition
You were able to prove the equality. What more could you possibly ask for?

>>11566497
Amen

>>11567676
Oh I'm not asking because this is HW or exam material or something. I'm just plain curious; it's a peculiar identity between a "fundamentally continuous" object and a "fundamentally discrete" one.

(Of course, a standard way to define the exponential in the first place relies on the factorial function, but that doesn't clear the mystery for me)

>>11567532
it is an investment, please kill yourself next time it will be a better answer

>>11567640
>>11567704
>integration by parts
>tabular method
It has to do with the fact that the mth derivative of x^n is (n!/(n-m)!)x^(n-m)

should i take the stipend + free tuition phd offer at decent school? or take the 50% tuition scholarship MS offer at a top 5 university and then hopefuly transfer into the phd there or maybe somewhere else. i like the city/environment of the good school much more but it is hard to pick against the fully funded offer

who the fuck said power was the easiest EE specialization, fucking lying piece of shit asshole.

Isnt a functor just a morphism in the category of (certain) categories?

>>11567850
An offer of an unfunded masters (only in America, graduate structure is very different in Europe and Canada) is generally the school's polite way of saying "we don't really want you here but we'll take your money if you want".
If the decent school is decent enough that you won't be locked out of a job later you're better off there.

>>11568006
Believe me, it is.

>>11565779
Why can't diseases ever be good for you?
For example, there are ticks that bite you and make you develop an allergy to meat, which is pretty ridiculous. Why isn't there a "disorder" you can get infected with that increases your testosterone production or lowers your myostatin or makes you immune to cyanide or something cool like that?

How I solve for x?

>>11568832
Do gut flora count? Technically they're an "infection"

Is this proof correct? I don't understand where they get "there are x,y such that c<x<a<y<b." Isn't this wrong? It's given that a<c.

stupid physics question but i need to sanity check:

if i have 100 ml of water at 80C and 300ml of water at 40C, will the mixture be 50C assuming ideal water and stuff?

>be Eastern European and can drink gallons of milk on end
>have French-American gf who is lactose intolerant
Will our kids be lactose tolerant or intolerant?

>>11565779
how do I argue with dumbass groupmates without sounding pretentious and calling them fucking idiots

>>11569321
you be as direct as you can in pointing out their flaws in arguments or beliefs without being condescending or personal

>>11569281
>http://www.vivo.colostate.edu/hbooks/pathphys/digestion/smallgut/lactose_intol.html
>Lactase persistence, and therefore lactose tolerance, is inherited as a dominant trait.
> In some circumstances, heterozygotes can manifest partial intolerance, indicating that this is an incompletely dominant gene.

tl;dr more than 50% odds your children will have tolerance

>>11565113
libgen

>>11567407
investing in crypto, obviously

>>11569182
No, it looks right. The idea of the IVT is that supposing [math] f(c)<f(a) [/math], then there must be an [math] x\in(a,c) [/math] such that [math] f(c)<f(x)<f(a) [/math], which means the function is decreasing. But the function was increasing by hypothesis. So either we have to accept [math] c<a [/math] or that f is decreasing. Either of these is a contradiction.
>>11569210
Water has specific heat capacity [math] c [/math], which you can assume is constant. The thermal energy lost by the 100 ml is the same energy gained by the 300 ml. [math]m_1c\Delta T_1=-m_2c\Delta T_2\implies \Delta T_1=-3\Delta T_2\implies T-80^\circ=-3(T-40^\circ) [/math]. So final temperature is 50 degrees. Yep.
>>11567586
What's the region you are integrating over?
>>11568944
Numerically
>>11567213
Did you have a question?

So I was considering the problem of a basic keplerian telescope creating a flipped image and was wondering why not just move the ocular lens to a position forward of the objective's focal length to avoid flipping the image while preserving a generous eye relief.(concept illustrated to the best of my uneducated ability in the bottom section of attached image)

Any tips/solution for this problem? Not sure what to do

>>11569680
For any epsilon > 0, you can take N large enough such that for [math]n > N, b-\varepsilon < b_n < b+\varepsilon[/math]. This is just the definition, although maybe not written how you most commonly see it (it's just the expanded way of saying [math]|b-b_n| < \varepsilon[/math])
You can use these inequalities to compare b to a and c, because you know how to compare b_n to c.

based Tomcat edition, shame it didn’t have any success with the Phoenixes, at least in burger service
That aside, I’m a brainlet in first year physics struggling with special relativity. I managed to fraud a lot before just by visualizing, but it kinda breaks down now. So far, there are two basic questions I don’t understand.
The first one is about proper time. In class, they said proper time tau squared was t^2-x^2 (I guess setting c to 1), which is a hyperbola. They said that this was similar to say concentric distance circles from the origin in the xy plane. Unfortunately, my brain can only draw rough analogies to easier classical concepts, but it makes sense visually given the Minkowski diagrams are kinda bounded by the asymptotes of the hyperbolas. Then in order to get to the momentum four vector, they took a derivative with respect to proper time. Now the algebra and the chain rule makes sense, but what does it mean to take a derivative with respect to the hyperbolas? I’m just unable to visualize things anymore. I kinda just accepted it and went on, but it still bugs me. I feel like getting this will also help explain the energy momentum invariant thing, since that also involves something squared minus something squared.
The second one is about electric fields in different frames. In class, they said that E fields parallel to motion remain the same while those perpendicular to motion get scaled by gamma. They explained this using parallel plates of uniform charge, which makes sense because of length contraction. But I don’t see how this generalizes to all E fields from all charge distributions. How can I be sure that it isn’t just a transformation of the space and the charge distribution that then changes the E field? How (and why?) would this apply to say a point charge?
Thanks for putting up with my dumbass lmao

>>11569714
Ok, I have b - ε < c. How do you show from this that b <= c? If we have b - c < ε how do you get the equality part?

>>11569849
You have that [math]b - c < \varepsilon[/math] for ALL epsilon > 0.
That is, for every single positive number epsilon, (b-c) is less than that positive number. If a number is less than every positive number, it cannot be positive itself, so b-c <= 0.

How to test for klinefelters?

>>11569281
>marrying a mutt
dumbass

Function [math]g(x)=\dfrac{x+2}{3x-3}[/math] was created by moving the function [math]f(x)=\dfrac{1}{x+1}[/math] by a vector of [math][a,b][/math].

Then

[math]\dfrac{1}{x+1-a}+b=\dfrac{x+2}{3x-3}[/math]
[math]\dfrac{1}{x+1-a}+b=\dfrac{x}{3x-3}+\dfrac{2}{3x-3}[/math]

How do I read [math]a[/math] and [math]b[/math] from here?

They should be [math]a=2[/math] and [math]b=\dfrac{1}{3}[/math]

>>11570456
WHAT THE FUCKING FUK ARE YOU WRITING YOU FUCKING FUCK FUCKER WHAT THE FUCK ARE YOU TRYING TO FUCKING SAY, YOU FUCKING IMMENSE FUCK?

>>11570456

[math]\frac{1}{x+1-a}+b = \frac{b+xb -ba +1}{x+1-a}[/math]

i need a little help with my first thermodynamics class, specifically with this exercise:

water @ 300k, 2bar flows in a circular tube at a rate of 250kg/min with a speed of 0.5m/s. find at what state the water inside the tube is in

I guess I'd have to start from calculating the steam quality?

I have been chasing my tail for over an hour now with this stupid exercise, I don't have any of the books that I am supposed to have for this class and every other shitty online lecture there's a different person that teaches the class so shit's fucked.

>>11568635
why did I find all my other classes easier then?

Any AutoCHADS able to help me display this mesh as a elevation map, as pictured down to the left?

>>11570599
Just remember the state postulate of thermodynamics: you've got it that two intensive properties determine all the rest. This problem amounts to pretty much just reading a steam table.
>steam quality
I can tell you that water is a compressed liquid, so its quality is just 0. I know its compressed because saturated water @ 300 K is at a lot lower pressure that 2 bar, no matter what the quality is. So I know we've got compressed liquid water, quality=0 (a redundant thing to say), and looking at a steam table here, I would be able to read off the specific volume, density, internal energy, enthalpy and entropy with just a little interpolation. I can even tell you the internal diameter of the pipe. Did that help? What book do you need?

Did I do these right? Specifically that last one. Looking like there's no reaction, and since both reactants are in the aqueous state, I would not include water as a product, right?

can someone PLEASE for the love of god explain how to find the support reactions here?
I draw two separate beams by separating at the hinge like I always do but I the results I get don't add up
please

>>11565803
put >>11565792 Stupid

>>11565779
If you took genes from yourself and injext yourself with those same genes everyday would you stop to age?

Also how complex of a science is genetics?

Is getting a phd in chemistry worth it?

What in the hell are degrees of freedom? Wikipedia's definition doesn't make sense and my prof hasn't bothered explaining, he just gave us the Student T distribution....

>>11571280
Looks good. There's no unreacted H or O and no new water is produced, so no.
>>11571287
>I draw two separate beams by separating at the hinge like
What? Don't do that. What you can do is treat the distributed load as a point load acting at the geometric center of the whole beam. This gives 200*20=4000 pounds acting at 10 feet from the left end. Static equilibrium gives:
>moment about hinge
[math] 5\cdot700-4\cdot1500-5\cdot4000+15R_y=0 [/math]. Solve for the reaction at the roller. Then sum the vertical forces, equate to zero, and solve for the vertical reaction at the hinge. The horizontal and moment reactions are trivially zero.
>>11569463
Replace the right lens with something concave and you get a Galilean telescope. No image flipping involved.

>>11571246
i ended up figuring out this myself, and you guessed right, it gives us the speed of the water inside the tube to figure out the ID of the pipe.

i managed to find a pirated pdf of a thermodynamics book in my language.

correct me if I'm wrong:

the general thinking with problems like these is that they usually give you a known P, T or a property like H.

say they give you a known P and T. then you look up a table with one of these as an input, say P, and then compare the saturation temperature at that table with the current T and figure out the state of whatever is in there?

when would I want to use steam quality? in problems when you go from a semi-known state A to a unknown state B?

finally, for the pipe's ID, the only thing I have to look up is the density of the water at the given conditions?

>>11571359
If you have variables x,y, you have 2 degrees of freedom
If you have x,y,z, you have 3 degrees of freedom
Now apply that to reality

>>11571433
>say they give you a known P and T.
Then you find the entry in table at that P and T. If the fluid is saturated, then you need to determine the quality too. Like, saturated water at 100 kPa has a fixed temperature, but the density and internal energy and all that are functions of quality. If the fluid is saturated, you're going to need slightly more information.
>finally, for the pipe's ID
Yep. The compressed liquid state at that temperature and pressure uniquely determines the density of the water (something like 997 kg/m^3 IIRC). You are given mass flow rate and you are given average velocity. You've got [math] \dot{m}=\rho v A [/math]. Solve for the area A and then you get ID.

we're supposed to show that
[math]X=\begin{pmatrix}1\\ 2\end{pmatrix}e^{-5t}[/math]
is a solution to
[math]\frac{dx}{dt}=3x-4y[/math]
[math]\frac{dy}{dt}=4x-7y[/math]

However, when I try to compute it as shown in the textbook, I wind up with
[math]AX=\begin{pmatrix}-e^{-5t}\\ -6e^{-5t}\end{pmatrix}[/math]
which is definitely not what it says I should get
[math]AX=\begin{pmatrix}-5e^{-5t}\\ -10e^{-5t}\end{pmatrix}=X'[/math]

what am I fucking up here

>>11571508
The first equality in the last line is bad. [eqn] \begin{bmatrix} 3 & -4\\ 4 & -7\end{bmatrix}\begin{bmatrix}e^{-5t}\\ 2e^{-5t}\end{bmatrix}=\begin{bmatrix} 3\cdot e^{-5t}-4\cdot2e^{-5t}\\ 4\cdot e^{-5t}-7\cdot 2e^{-5t}\end{bmatrix}=\begin{bmatrix} -5e^{-5t}\\ -10e^{-5t} \end{bmatrix}
[/eqn]

>>11571537
shit, I see what I did now. Thanks.

Anyone know a website where I can pay an indian to solve calculus problems?

>>11571898
symbolab

>>11571898
Wolfram Alpha

How do you prove that the product of darboux-integrable functions is integrable?

Is there much value in turning a cold compost heap?

>>11572079
>>>/an/plant
>>>/out/homegrowmen

So I'm playing around with the generic 8-bit ADC on multisim and the numbers I'd expect to round up are actually rounding down at the output (-5V for the negative reference, 5V for the positive). I'd expect and input of -1.5V to output 5A in hex, but instead I get 59.

Is this because of a rounding error going from decimal 89.6? Since it is an ideal model, I'd expect the FSR/1LSB to be 89.6 which rounds to 90 decimal or 5A hex.

Seems like there's something wrong with the assumption that the full scale range is 10V, since obviously it isn't truly if it maxes at 9.961V. I am just going off of the formulas supplied by my telecommunications class but I'd appreciate any advice to help me understand the discrepancy.

>>11572074
If one function is bounded, simply bound the upper and lower sums by the upper and lower sums for the other function times the sup or inf of the bounded function.
It's not true in general if both functions are unbounded.

>>11572122
I'm pretty sure each function is bounded since it's integrable.

>>11571932
>>11571935
these are nice for integrals and derivatives but they suck for more advanced stuff
but I'm managing to check my answers using a mix of both, I'll hold off on the indian for now

>>11571502
do you have an easy way to remember definitions like subcooled liquid, superheated steam, etc?

what picture comes into mind when you hear something like a e.g. saturated liquid?

The answer is 0, right?
A part of me wants to say .5 for some reason

Is it correct if I write that the derivative of a function in point [math]x_0[/math] is [math]\dfrac{df(x_0)}{dx}[/math]?
Or should it be [math]\dfrac{df(x_0)}{dx_0}[/math]

For example [math]f(x)=1-x^2[/math], then is it correct to write
[math]\dfrac{df(1)}{dx}=-2[/math]

?

>>11572144
>>11571898
>>/sci/thread/S11487177#p11496062
>>11572188
>subcooled/compressed liquid
just think of regular ass liquid
>saturated
this is when the fluid is the middle of a phase change/on the verge of a phase change. saturated water at 1 atm will always be about 212 F (regardless of phase!). saturated water is what you cook pasta in. saturated water can be a solid or a liquid or a gas or in between.
>super heated
think hot, fully vaporized gas. it can get hotter than boiling.
>critical
Phase of a substance is determined by which saturation lines on the PT curve it falls between. At definite high T and P, the line become very ambiguous and so any distinct phase falls apart in the supercritical region.
>water coming from a hydrothermal vent at the bottom of the ocean
>really hot and wants to boil
>extreme pressure so its getting squeezed too hard to boil
>>11572255
[math] \beta(s)^{-1}\ [/math] or [math] \ -10\text{dB}\cdot\log\big(\beta(s)\big) [/math] i think
>>11572281
The second line is erroneous and bad notation. First and last are okay. Just write [math] f'(x_0) [/math]

>>11572144
>>11571898
>>>>/sci/thread/S11487177#p11496062
>>11572188
>subcooled/compressed liquid
just think of regular ass liquid
>saturated
this is when the fluid is the middle of a phase change/on the verge of a phase change. saturated water at 1 atm will always be about 212 F (regardless of phase!). saturated water is what you cook pasta in. saturated water can be a solid or a liquid or a gas or in between.
>super heated
think hot, fully vaporized gas. it can get hotter than boiling.
>critical
Phase of a substance is determined by which saturation lines on the PT curve it falls between. At a definite high T and P, the line become very ambiguous and so any distinction between phase falls apart in the supercritical region.
>water coming from a hydrothermal vent at the bottom of the ocean
>really hot and wants to boil
>extreme pressure so its getting squeezed too hard to boil
>>11572255
[math] \beta(s)^{-1}\ [/math] or [math] \ -10\text{dB}\cdot\log\big(\beta(s)\big) [/math] i think
>>11572281
The second line bad and totally misleading notation. First and last are okay. Just write [math] f'(x_0) [/math]

>>11565779
Does anyone understand what Eric Weinstein talks about?

A subset of a well ordered set is well ordered? Q is well ordered?

The sum of two orthogonal vectors' every components multiplied is zero. Why? Is there an intuitive explanation for this? Can't find anything on google, every source just accepts it as fact, which is pretty fucking dumb.

>>11572692
Do you understand why the dot product [math]a \cdot b = |a||b|\cos{\theta}[/math]?
This formula is the "reason" why that happens. The dot product is the sum of the components multiplied together, and two vectors are orthogonal to each other when they meet at a 90 degree angle, that is, whenever cosine of the angle between them equals zero.

>>11572684
>A subset of a well ordered set is well ordered?
Yes. If S is well-ordered, then if [math]W \subseteq S[/math], for any [math]A \subseteq W [/math] you also have [math]A \subseteq S[/math], so A has a least element because S is well-ordered.
>Q is well ordered?
It depends what you mean. With the usual way of comparing numbers a < b, Q is not well ordered (e.g. there is no least element of [math](0,1][/math]). But there is some different order on Q that makes it well-ordered. There exists a well-order on every set.
For Q, you can even build one explicitly if you want, since Q is countable and N is well-ordered.

>>11572723
>Do you understand why the dot product a⋅b=|a||b|cosθa⋅b=|a||b|cosθa \cdot b = |a||b|\cos{\theta}?
Yes, but I don't understand what that has to do with the sum of components to do in practice with proof. Is it related to the euclidian norm somehow? Can yourself provide a solid mathematical proof that |a||b|cosθ = the sum of multiplied components, without analogies?

>>11572741
https://math.stackexchange.com/questions/509719/proof-of-equivalence-of-algebraic-and-geometric-dot-product

>>11572115
Anyone? Should be any easy question for an electrical engineer but I'm an ET pleb

I don't understand the difference between bounded, closed and compact sets in R^n. I know compact sets are the ones both bounded and closed, but what's the difference between compact and closed sets? Wouldn't a closed set necessarily be bounded? I'm confused

>>11572752
>trigonometric identity fuckery
I'll buy it. Thanks.

>>11572797
>Wouldn't a closed set necessarily be bounded?
Not at all. For example, the entire space R^n is closed in itself; any convergent sequence in R^n converges to something in R^n.
If you want an example that's not the whole space, you can look at the spaces R^{n-k} inside of R^n, or slightly more complicated, you can picture something like an infinitely long cylinder (including the surface).
There's really no tight relation between bounded and closed sets in R^n. You can be bounded but not closed, or closed but not bounded, or you can be both, or neither.

a congruent to b mod m implies a^2 congruent to b^2 mod m? how to prove?

>>11565779
This is impossible right? 3 of the rooms have 5 entry points so there will always be 1 room with a door left over.

>>11572995
WAIT i think i got it. Because a^2 - b^2 = (a+b)(a-b) then because m|(a-b) then m|(a+b)(a-b). Is that right?

>>11572995
b-xm=a-ym and b^2-im=a^2-jm
b-xm-ym=a
(b-xm-ym)^2-jm=b^2-im
(b-xm-ym)(b-xm-ym)=
b^2-bxm-bym-bxm+x^2m^2+xym^2-bym+xym^2+y^2m^2
=b^2-2bxm-2bym+x^2m^2+2xym^2+y^2m^2
b^2-2bxm-2bym+x^2m^2+2xym^2+y^2m^2-jm=
b^2-im
therefore i = 2bx+2by-x^2m-2xym-y^2m+j which is a whole number so it's right


i think

>>11573066
clean way of doing it
>>11573069
severe autism

If I have |f(x)| <= M, how do I prove that sup(f)-inf(f) <= M? It's intuitively obvious but I'm not sure how to start. Can I just say that by definition sup(f) <= M and |inf(f)| <= M?

>>11573098
should say prove sup(f)-inf(f) <= 2M

>>11573098
>Can I just say that by definition sup(f) <= M and |inf(f)| <= M?
Pretty much, although you should probably explain why these hold "by definition" (e.g. M is upper bound of f, therefore M >= sup f)
Although you'll need that inf(f) >= -M to get the inequality you want.

>>11573108
>>Can I just say that by definition sup(f) <= M and |inf(f)| <= M?
>Pretty much, although you should probably explain why these hold "by definition" (e.g. M is upper bound of f, therefore M >= sup f)
>Although you'll need that inf(f) >= -M to get the inequality you want.

Is my proof correct? I forgot to mention that b<1 and because of that 1/a can't be bigger than 1.

>>11573111
?

>>11573196
Brainlet explanation

>>11573212
could you give a better one

>>11573232
>could you give a better one

so is developing a vaccine just trying to copy the protein "hook"s as accurately as possible, slap them accurately on a lump of fat then inject ourselves with it?

>>11573255
kys nigger

>>11573255
>>11573111
>Posts brainlet wojacks
>Dumbest person in the thread
Erry tiem

>>11565779
Can any anons help with this problem I am the big retard, got a question on Gas turbines where I am given T1 and P1 of air going from a compressor to a combustion chamber. the calorific value of the air fuel mixture within the CC. the CC outlet/turbine inlet temperature and pressure. the turbine outlet pressure. air fuel ratio, air feed rate. Cp for the compressor and turbine as well as their polytrophic indices. Given that I am told no dimension of inlets how am I supposed to calculate the mass flow rate of the fuel into the combustion chamber?

>>11565779
Anyone able to help me with pic related
I cannot find Vin - in any of the OP amps nor Iout and I cant solve R5 and R6

>>11573098
That's not true.
Take f(x)=x on the interval [-1,1]. M=1.
sup(f)-inf(f)=1 - (-1) = 2 is not smaller than 1.

I'm having a hard time describing this space. I tried with cartesian coordinates and it is too complicated since I just write that x goes from 0 to the solution of the equation when you substitute x by 2 and then the same with y. I get a really complicated equation.

When I try to to use spherical coordinates I just can't figure out the boundaries for phi and theta.

How should I do it?

do land wind turbines affect climate and are responsible for smaller than average rainfalls

>>11574072
Absolutely. Their effect is really small compared to coal but it's not negligible either either. If we want a chance at saving the planet the first step is to reduce our consumption of electricity first and foremost.

Not really a stupid question, but I am really behind my Non-Linear Programming (Optimization) class and my final is tomorrow. Any experts wanna help me out? Willing to pay

>>11574322
>Willing to pay
$50 an hour is good for you? Add me on skype or discord

>>11574345
Sounds good, what is your discord @?

>>11573986
>the calorific value
Enthalpy? Internal energy?

>>11574416
The
flow schematic diagram in Fig. 1b can be used to model the gas turbine.
Air is compressed from 1 b𝑎r at 15oC to 12.5 b𝑎r before entering the combustor
where a mixture of air and fuel with lower calorific value of 48 MJ/kg burns before
entering the gas turbine at 1100oC at a pressure of 13.4 b𝑎r. The turbine outlet
pressure is 1.02 b𝑎r. If the air feed rate is 15 kg/s and the polytropic efficiencies of
both the turbine and compressor is 0.92. For the purpose of cooling, 8% of the air
is bled from the compressor of which does not enter the combustor nor the turbine.
Use the following assumptions: cp for the compressor and turbines are respectively
1.002 and 1.155kJ/kgK, while the polytropic indices are also respectively 1.41 and
1.33. The mechanical losses from the gearbox as 2.5% of the gearbox input power.
The mechanical and electrical efficiency of the generator to be 95%. Take the fuel
to air ratio to be 1.5%.

I have found the flow rate of the fuel to be mdotf = fuel to air ratio times air mass flow rate
now its a case of calculating the output ratio of the temperature of the turbine from the CC. Im thinking t1/t2=p1/p2 but i dont think that works for an isentropic process

>>11573986
Post a picture or screenshot of problem please

>>11574426
see
>>11574425

>>11574431
I would really like a picture so I dont have to guess what "gearbox" is

>>11574446
The gearbox addition is only to calculate the efficiency of the turbine at the end, there is no actual photo of turbine or gearbox

>>11574478
What is the prompt exactly?

>>11574478
Theres lots of things you could tell with the given information. What are you after in the end?

>>11574322
Bump
Really need help, anons

>>11574497
The temperature at the end of the turbine so I can calculate the outlet ratio of temp.
Work output of the gas turbine
electric power output
turbine cycle efficiency
electrical generation efficiency

>>11572473
thanks

>>11573030
yes
>>11574004
Baby, Vin- is just ground for all three. Recall that op-amps do everything in their power to keep V- = V+. There are only three unknown voltages in that circuit, each at the output of an op-amp. Sum the current into each node to zero.
>>11573986
>>11574523
>>11574425
Okay, so you know the pressure at inlet and outlet of the turbine. You know it's a polytropic process.
>t1/t2=p1/p2
Not quite. You've got [math] (T_{out}/T_{in}=(P_{out}/P_{in})^{(n-1)/n} [/math] with n being the polytropic index. This assumes ideal gas and comes straight from defn. of polytropic.

>>11573030
yes
>>11574004
Baby, Vin- is just ground for all three. Recall that op-amps do everything in their power to keep V- = V+. Also, IA2in and IA1in are trivially zero since ideal op-amps have infinite input impedance. There are only three unknown voltages in that circuit, each at the output of an op-amp. Sum the current into each node to zero.
>>11573986
>>11574523
>>11574425
Okay, so you know the pressure at inlet and outlet of the turbine. You know it's a polytropic process.
>t1/t2=p1/p2
Not quite. You've got [math] (T_{out}/T_{in}=(P_{out}/P_{in})^{(n-1)/n} [/math] with n being the polytropic index. This assumes ideal gas and comes straight from defn. of polytropic.

My friend is having an issue with the problem he's studying, and I'm a brainlet with chemistry

>>11573098
You mean to say sup(f) - inf(f) <= 2M.

Brainlet here.
Does a computer have an IQ? If it does, how much can a super computer have? 2000? Maybe more?
Also, why don't countries invest billions, instead of millions of dollars to the computers? Wouldn't it be better to just spend a 3-6 billion on one super computer and call it a day? Or would maintance be too expensive.
What's the purpose of a supercomputer and why do countries have more than one?
Thanks.

>>11574626
Cheers for that, from that I have gotten a Tout of the turbine of 724.68K.
looking at other examples and I have seen the to the power of (n-1/n) being multiplied by (1/Isentropic efficiency of the turbine) but we are not given this, nor are we given the ideal temperature to calculate ideal h4

Why does the immune system target implanted organs? Shouldn't the MHC inside them prevent that?

>>11574749
Just assume isotropic process then. [math]
n=\gamma=c_p/c_v=1+R/c_v [/math] with R being the gas constant of air.

How the fuck do I solve this?

>>11572115
Anyone?

>>11574978
>>11572781
You have to be patient.
>Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies

>>11574997
It doesn't hurt to try, there's plenty of posts from the start of the thread which have no replies and obviously Anons aren't rushing to answer them. Since my question should be conceptually easy to answer, I'd rather bring attention to it in the case that a knowledgeable Anon who may have missed it mid thread can share their insights. But thanks for sharing your thoughts.

>>11574907
tldr LOL

Pemdas, Pedmas, or Pedmsa?

>>11574907
Look up Bayes rule

What medications clear working memory in conditions such as OCD? If working memory is RAM how would you clear the cache memory?

Any mechanical/civil/aerospace grad students here? I'm about to go back to school after 5+ years of working and I wasn't a great student back in undergrad. I want to know how I should prepare? Re-do statics + strength of materials and vector calculus or go straight into continuum mechanics?

>>11575088
[math]PE {_d^m} {_s^a}[/math]

I'm a bit confused at this, because I'm not too sure how the 5 is used, and I dont know if this is the only thing to it.

Let [math]\alpha[/math] be a root of [math]x^2-5[/math], and suppose it is not already in the base field [math]\mathbb F_p[/math]. Since this polynomial is over the field [math]\mathbb F_p[/math] already, we have that [math][\mathbb F_p(\alpha):\mathbb F_p]=2[/math]. Since there is only one field up to isomorphism of each particular order, then [math]F=F_p(\alpha)[/math]. QED

The 5 could have been just about any number, even 0, and it would still work with my alleged proof. Also the form of the polynomial was irrelevant. Following from that, with virtually the same proof, would generalize the statement to let [math]f(x)[/math] be any polynomial over [math]\mathbb F_p[/math]. Then it has a root in any field [math]F[/math] with [math]|F|=p^{\deg f}[/math].

Is this even remotely correct?

>>11565779
Do sound waves change the density of water? If so how much?

I'm trying to prove the statement: "every element of a finite ring with unity is either a zero divisor or invertible". Here is what I have so far. List the elements as 0,1,a_1,...,a_n. Pick a_i. If a_i is a zero divisor, then it's really easy to show it can't be invertible. But if a_i is invertible, I'm not really sure how to show it can't be a zero divisor.

pls help.

>>11576234
suppose u is invertible. Then uv=1 for some v in the ring.

suppose xu=0 for some x. Then 0=xuv=x. So it isnt a zero divisor

>>11576234
Multiply the equation ab = 0 by a^(-1) on both sides. You get b = 0, so a cannot be a zerodivisor.

>>11576240
Ok, maybe I'm retarded then. It appears that I never used the finite condition then. Here is my proof for showing a_i can't be invertible if it is a zero divisor. Suppose a_i is a zero divisor. Suppose not, so suppose a_i is invertible. Then there exists a_k s.t. a_ka_i = 1 and a_ia_k = 1. So a_ia_k -a_ia_k = 1-0 => a_i(a_k-a_j) = 1. Since a_k is a unique inverse, a_k - a_j = a_k => a_k = 0 which is contradiction since a_k must be nonzero.

Where am I wrong here?

>>11576148
>Also the form of the polynomial was irrelevant.
This is the only part that's really not true. You are implicitly claiming that since f(x) does not have a root in F_p, then f(x) must be irreducible. This only sneaks through because the degree of f is small.
Once you patch that issue the rest is fine. IIRC you can even generalize a bit further if you want (if |F| = p^k, degf doesn't have to equal k, it just has to divide it in order to have a root in there)

>>11576262
Your proof is fine, you're wrong because you aren't proving what the question asks. You've shown that a zero divisor can't be invertible, and an invertible element can't be a zero divisor.
Can't an element be neither? It certainly can in e.g. the ring of integers. You need finiteness to show that "neither" isn't an option.

>>11576262
Let [math]x[/math] be an element that is not a zero divisor.

consider the function [math]R\to R[/math] defined by [math]r\mapsto rx[/math]. We show it's injective. Suppose [math]rx=sx[/math]. Then [math](r-s)x=0[/math]. Since [math]x[/math] is not a zero divisor, we must have that [math]r=s[/math]. Hence injectivity.

But then since [math]R[/math] is finite, it's also surjective, hence bijective. So there exists a unique element [math]u[/math] such that [math]ux=1[/math] by bijectivity. Hence it is a unit.

>>11576294
How would I go about using the finite condition then? I think I can use the fact that since 0,1,a_1,...,a_n are the elements of A, then then there must be n+2 distinct products a_i0, a_i1,a_ia_1,...,a_ia_n which would then imply that the products in my proof are distinct and unique. This would mean that the products in my proof are unique so they could only be a zero divisor or invertible. Right?

>>11576311
>>11576308

>>11576311
Suppose you have N elements in your ring. Pick some element a.
Look at the set a^0, a^1, a^2, a^3...a^N. There are N+1 elements in this list, but only N in your ring; therefore at least of them have to equal the same element. a^k = a^j for j=/=k will get you where you want to go.

This is a fairly common technique in abstract algebra, it's worth remembering once you've seen it.

This question is directed to STEM undergrads or higher:

How frequently do you drill """basic""" algebra problems? Do you find it beneficial to go over complex simplification/ factoring/ rationalizing expressions?

>>11576330
This is wrong. Let [math]R=\mathbb Z/2\mathbb Z\oplus \mathbb Z/2\mathbb Z[/math] and [math]a=(1,0)[/math].

>>11576334
(1,0) is a zero divisor, dude.

>>11576340
>Suppose you have N elements in your ring. Pick some element a.
you didnt specify which a

>>11576308
Ok. If I understand this proof correctly, if x IS a zero divisor, then it can't be invertible for the proof I gave above?

>>11576294
I also think I understand what you mean now. In the ring Z, 2 is neither a zero divisor nor invertible.

Let's say I have four pieces of pie, each the same size. If I add a fifth equal sized piece, would it be a 20% increase or a 25% increase?

>>11576346
Im not going to read that jumbled mess, this board has latex for a reason.

Suppose [math]a[/math] is a unit and [math]ax=0[/math]. Then [math]0=a^{-1}ax=x[/math]. So it's not a zero-divisor. Which would contradict [math]a[/math] being a zero divisor, if that were your assumption

>>11576332
Engineer here: absolutely never. Algebra aint that hard and if it is, pick up a symbolic math package of your liking and use that. Computers are way better at solving equations and finding roots; I'm not going to try and compete with them.

>>11576345
It doesn't matter which a you turbobrainlet. He's trying to prove "a is a zerodivisor OR a is invertible".
There's no work to do if you choose a to be a zerodivisor.

>>11576377
What I'm telling you you're wrong in is the fact that you're claiming that [math]a^0,a^n[/math] constitutes [math]n+1[/math] different elements, which is absolutely and utterly wrong, as my example proves

>>11576384
[math]a^0,...,a^n[/math] I meant*

>>11576384
>>11576377
Not only do you not achieve the "0" in this way, you're actually assuming the multiplicative part of a ring forms a cyclic group in every finite ring

>>11576384
Are you retarded or trolling?

You posted a zero divisor with a^2 = a. This implies a(a-1) = 0. Either a = 1 (a unit) or a divides 0. The second holds. Where is your problem?

>>11576406
>every ring is a domain

>>11576416
The classic "damage control being wrong by shitposting furiously" technique.

>>11576364
what about when you simplify derivatives etc?
some of the results can get pretty hairy, no? You don't think it's beneficial for these sorts of simplification purposes?

What is math?

How's this proof:

It is reflexive because y1/x1 = y1/x1.
It is symmetric because y1/x1 = y2/x2 implies y2/x2 = y1/x1.
It is transitive because y1/x1 = y2/x2 and y2/x2 = y3/x3 implies y1/x1 = y3/x3.

Just seems to easy, but this is right and in proper form, right?

>>11576533
oh, i forgot the equivalnce classes... they would just be sets of equivelant fractions, right? like {(-2, 1), (2, -1), (-6, 3), (6, -3) .....}, right? for all equivelant fractions barring (0, 0)

>>11574978
This dogshit board only answers math questions

>>11572115
I'd ask this on /ohm/ in diy desu, or maybe the tarduino general

>>11576570
I know where to ask if I get stuck with a calculation I suppose, was just hopeful someone experienced with multisim or ADCs could explain the discrepancy.

I don't know any good books on DSP theory, but "Think DSP" is pretty good if you want some hands on practice using Python. I picked up this book and read it along side a theory heavy DSP class I had. If you have a basic understanding of Signals & Systems you could probably learn DSP with this book.

>>11574642
E2 elimination, then a syn-dihydroxylation of your chosing. The exact mechanism/reagents are up to him/you
>>11576332
>How frequently do you drill """basic""" algebra problems?
whenever I need them, and am sick of staring at screens
>>11576175
yes. my fluid mech is shit, but I'd look up the compressability of water and sound pressure/sound energy density
>>11572115
>>11575025
post schematics or fuck off. Wait for the unanswered q's scraper post next thread, your chances are better then

>>11566268
June 28th is my birthday man, that’s when the world STARTED. I’ll be 32, where does the time go lads?

>>11572473
>>11571246
I am having trouble understanding when to use what table to find the properties of a fluid for the given conditions.

Since water at 300k, 2 bar is a subcooled/compressed liquid, why would you look up its properties at a steam table?

Shouldn't its properties be on a subcooled/compressed liquid table?

I tried looking up a subcooled/compressed liquid table but the table at the book I found only has small table on subcooled/compressed liquid state.

>>11577435
>>11572473
>>11571246
Why would you put the properties of a subcooled liquid at a superheated steam table? Is the pair of properties I circled the correct one?

This is exactly the thing that I don't get, how are these tables organized.

>>11577279

Thanks a lot man

>>11573030
this is a solved problem, google graphos theory

>>11577435
>why would you look up its properties at a steam table
Steam table is just a generic term for a booklet of thermodynamic properties at different states. Subcooled liquid is by no means "steam."
> tried looking up a subcooled/compressed liquid table but the table at the book I found only has small table on subcooled/compressed liquid state
That's because density doesn't change a whole lot with pressure in a subcooled liquid (they are often called "incompressible"). Constant volume and pressure heat capacities for liquid water for example are basically identical and each constant over temperature. Therefore to find things like dU and dH is just a matter of multiplies cv=c or cp=c times change in temperature. Printing these tables for as many values as for saturated fluids, for example, isn't practically justified. They are usually scant compared to the other ones.

>>11576175
~DERIVATION OF THE SPEED OF SOUND IN A FLUID~

Picture a vertical wave moving with constant speed [math]c[/math] and area [math] A [/math]. From the reference frame of the wave, the fluid ahead of the wave has density [math] \rho [/math], pressure [math] p [/math] and fluid velocity [math] c [/math]. Behind the wave there is density [math] \rho+\delta\rho [/math], pressure [math] p+\delta p [/math] and velocity [math] c-\delta v [/math]. Under steady state conditions, the net mass transfer into a region enclosed by a control surface is governed by [math] \int_{CS} \rho\mathbf{v}\cdot\hat{\mathbf{n}}\text{ d}A=0 [/math] (basically, if the mass inside is constant, then the sum of all mass flow rates into the region is zero). Now pick a control surface around the wave and apply consv. of mass. You find [math] (\rho+\delta\rho)(c-\delta v)A-\rho c A=0 [/math]. Area and higher order terms cancel to get [eqn] c=\rho\frac{\delta v}{\delta \rho} [/eqn] The force on a control surface is again given by Reynold's transport theorem: [eqn] \sum\mathbf{F}=\int_{CS}\mathbf{v}\rho\mathbf{v}\cdot\hat{\mathbf{n}}\text{ d}A=(c-\delta v)^2(\rho+\delta\rho)A-c^2\rho A=pA-(p+\delta p)A [/eqn] Once again area cancels out. It takes a little bit of playing around, but you can rearrange and substitute the first equation and neglect higher order terms to get [eqn]
c^2=\frac{\delta p}{\delta \rho } [/eqn] Next, realize that a sound wave moving across a point in space is an adiabatic process, so we can treat it as isentropic. This means [math] p/\rho^k [/math] is constant. Applying the ideal gas law and doing a little more playing around you get [math] \partial p/\partial\rho=pk/\rho=RTk [/math] with R being the gas constant and k the polytropic index. Define "bulk modulus" to be [math] K=\text{d}p/(\text{d}\rho/\rho)=\rho\cdot\partial p/\partial\rho [/math]. Finally: [eqn] c=\sqrt{\bigg(\frac{\partial p}{\partial\rho}\bigg)_s}=\sqrt{K/\rho}=\sqrt{RTk} [/eqn]

>>11576175
~DERIVATION OF THE SPEED OF SOUND IN A FLUID~

Picture a vertical wave moving with constant speed [math]c[/math] and area [math] A [/math]. From the reference frame of the wave, the fluid ahead of the wave has density [math] \rho [/math], pressure [math] p [/math] and fluid velocity [math] c [/math]. Behind the wave there is density [math] \rho+\delta\rho [/math], pressure [math] p+\delta p [/math] and velocity [math] c-\delta v [/math]. Under steady state conditions, the net mass transfer into a region enclosed by a control surface is governed by [math] \int_{CS} \rho\mathbf{v}\cdot\hat{\mathbf{n}}\text{ d}A=0 [/math] (basically, if the mass inside is constant, then the sum of all mass flow rates into the region is zero). Now pick a control surface around the wave and apply consv. of mass. You find [math] (\rho+\delta\rho)(c-\delta v)A-\rho c A=0 [/math]. Area and higher order terms cancel to get [eqn] c=\rho\frac{\delta v}{\delta \rho} [/eqn] The force on a control surface is again given by Reynold's transport theorem: [eqn] \sum\mathbf{F}=\int_{CS}\mathbf{v}\rho\mathbf{v}\cdot\hat{\mathbf{n}}\text{ d}A=(c-\delta v)^2(\rho+\delta\rho)A-c^2\rho A=pA-(p+\delta p)A [/eqn] Once again area cancels out. It takes a little bit of playing around, but you can rearrange and substitute the first equation and neglect higher order terms to get [eqn]
c^2=\frac{\delta p}{\delta \rho } [/eqn] Next, realize that a sound wave moving across a point in space is an adiabatic process, so we can treat it as isentropic. This means [math] p/\rho^k [/math] is constant. Applying the ideal gas law and doing a little more playing around you get [math] \partial p/\partial\rho=pk/\rho=RTk [/math] with R being the gas constant and k the ratio of specific heat capacities. Define "bulk modulus" to be [math] K=\text{d}p/(\text{d}\rho/\rho)=\rho\cdot\partial p/\partial\rho [/math]. Finally: [eqn] c=\sqrt{\bigg(\frac{\partial p}{\partial\rho}\bigg)_s}=\sqrt{K/\rho}=\sqrt{RTk} [/eqn]

>>11576175
>>11577881
So basically, the density change in water is like [math] \text{amplitude of pressure wave}}/\text{speed of sound}^2 [/math] which turns out to be a tiny number

>>11577279
It is a fucking bipolar ADC on multisim, how complicated do you think it is? Two power supplies, +5V and -5V, Vin as -1.5V and a 10kHz clock pulse. It isn't rocket science bro, I explained the question in more than enough detail, it is an ideal model and I just want to know why it isn't rolling over to the hex value I would expect.

>>11577881
>>11576175
So basically the change in density of water is like (Amplitude of pressure wave)/(Speed of sound in water)^2 which is a very small number.

I dont understand how to prove a function is always greater than some given value. DESU I dont understand how proofs about real valued functions make sense.

Like, if I want to show a function is monotonically increasing on some interval, I take the derivative and show that on that interval the derivative is positive. That makes sense to me because of what the derivative is. But what I dont get is how do you show that the derivative is always positive on that interval. I can't just go "Here's the graph, see! it's always positive" that's fucking stupid, but if I try to do it algebraically it would involve taking an uncountable amount of inputs and showing that they are all positive valued on the output. So there must be a way to do it, because non-algebraic "proofs" are not real and not worth any degree of consideration.

So what is the algebraic way to show that some function f(x) is always greater than some value v, or to show on some interval (a,b) some function g(x) is monotonically increasing, and such?

>>11577747
talk about missing the forest for the trees

>Therefore to find things like dU and dH is just a matter of multiplies cv=c or cp=c times change in temperature.

..and I didn't understand a single word from this. so far, we've barely broken into the 1st thermodynamic law.

I've been studying all day today, and although I've learnt the basic definitions and all that that my class has covered so far, I just can't put everything together and see the bigger picture.

>>11577989
The answer to your main question was essentially "because it isn't that useful of a thing to waste time printing out." Try asking a better question or think of what exactly it is you don't get. Id like to help you.

>>11567487
is this quartz?

I have a question about radars. So say a ship is moving and emitting RF and the RF hits a target 200 nautical miles out. How does the return RF come back to the receiver when the ship moved say 5 feet since it emitted? I know RF travels at the speed of light or near it but still how does it return directly back to the receiver? Is it simply cause it moves at the speed of light or is there some trick radars use to intercept return RF near them?

>>11565779
There are 6 factories that produce .84 of a product every second and a new factory comes online every 48 seconds what would a formula where x is in seconds and the y is in products look like?

>>11572088
You don't know? I was right that this board is fake smart artists whi only know hard algebra. You don't know anything useful in the real world. You just masturbate all day to your imaginary numbers and science fiction.

There is loads of science you just ignore. That question was so easy you should be ashamed you couldn't answer.

>>11579124
lol

>>11579126
The answer was yes btw.

In general, if I have a set S and an algebraic object A, does the set of all functions from S to A form an algebraic object of the same type as A, where the operations are defined pointwise?

How do I find the limit as x - > infinity of
(3x^2 -5x +7)/ ((3 +2x^3 +13x^4)^(1/2))

I know the answer is 3/ (13^(1/2)) I just don't know how to get there.

I tried l'hôpital rule but that didn't help, so I'm guessing I have to do something alegbraical but I don't know what.

>>11578744
Draw a diagram, it should be a triangle with one side being the ship's path and the other two being the radars path to and from the object. The radar is hitting a surface of the target that is at an angle that causes the returning radar to meet the ship at its new location. Its the fact the target has a surface that is at the right angle of orientation that allows the radar to work. That's how I understand it anyway.

>>11579424
Multiply both the numerator and denominator by [math]\frac{1}{\sqrt{x^4}}[/math] :~)

How do i search for ++ like "c++" on libgen?
It seems to be a special character and I tried \\ escaping it but that didn't work.

Why is Taleb so obsessed with fat tails?
I get the gist, the probability of catastrophic events is not gaussian so they are more likely than one might think. But still I don't get what this current situation has to do with fat tails if everyone knew it was gonna happen but nobody gave a shit.

>>11579508
I thought about that, but it's there that I get stuck. What good is root(x^4).u?

How do you prove some congruence class a(modn) is a subset of some other congruence class b(modk)?

Maybe one day I'll become a quackademic, it would be better than being NEET.

>>11579508
Ignore my reply here >>11579544 I figured it out thanks to you help. :)

Is there a name for that technique? I've never come across it before

>>11579611
First off, this can only be possible if a=b (mod k) (if a isn't even in the congruence class of b, then the congruence class of a definitely isn't).

So then you're down to asking
>when does n | (x-a) imply that k | (x-a)?
Which happens exactly when k | n.

test

[math]2^{b}[\math]

im feeling like complete retard because this is basic analysis and i cant solve this

Im given [math]|\int_{x}^{x+h}f(t)dt|\leq h^{2}[/math] for all [math]x,h \in R[/math], from this i have to show that [math]f(x)=0[/math] for all[math]\ x \in R [/math]

i think im supposed to apply mean value theorem but i dont understand how to to use the inequality after that

>>11580019
do you have that the function is continuous or something?

>>11580025
yes

>>11580019
>>11580025
assuming continuity (it's false otherwise) for any epsilon > 0 and any x in R, take delta < epsilon such that |x - y| < delta implies |f(x) - f(y)| < epsilon. Then, by the mean value theorem for integrals, there exists a point c in the interval [x, x+delta] for which [math] |f(c)| = \mathfrac{1}{\delta}\left|\int_x^{x + \delta} f(x) dx\right| \leq \delta [/math]. Then, [math]|f(x)| \leq |f(c)| + |f(x) - f(c)| \leq \delta + \epsilon \leq 2\epsilon[/math].
Then |f(x)| is arbitrarily small, as we can take epsilon to 0. So f(x) = 0.

>>11580043
Shoot. I meant [math]|f(c)| = \frac{1}{\delta}\left|\int_x^{x + \delta} f(x) dx\right| \leq \delta [/math]

Let f,g be elements of some group, and suppose that g does not have finite order.
Is it true that [math]fg^k = g^kf[/math] for some k > 0 implies that [math]fg = gk[/math]?
I feel like the answer is probably no, but I can't think of a counterexample off the top of my head.

Fixing serious typo.

Let f,g be elements of some group, and suppose that g does not have finite order.
Is it true that [math]fg^k=g^kf [/math]for some k > 0 implies that fg=gf?
I feel like the answer is probably no, but I can't think of a counterexample off the top of my head.

>>11580100
The answer is no. Take G to be the group of bijections N->N (symmetries of natural numbers).
Let g be the bijection represented in cycle notation as (123)(4567)(8 9 10 11 12)....
, i.e. a product of infinitely many cycles each increasing in length by 1, starting with 3. g does not have a finite order (because it's made up of arbitrarily large cycles)
Take f to be (12).
Now g^3 f = f g^3 because g^3 leaves {1,2,3} fixed.
But g f g^-1 = (23) != f

>>11580143
Simple enough. Thanks

>>11580156
Even simpler:
Just take G to be S^3 x Z (direct product).
take f to be ((12), 0) and g to be ((123), 1)

>>11579611
This happens if and only if
k|n
and
a=b mod k

Can someone download and upload this to docdroid or somewhere else so I can access it, please?

https://pubs.acs.org/doi/pdf/10.1021/es4014807

>>11581019
Why aren't you using scihub?
I can't post the link, because the system thinks it is spam...

>>11581099
Thanks, I got it using scihub now.

Are there any bandwidth saving proxies/addons for firefox? As in, redirect images to another server, then compress it, and send the compressed image to user. Or download css/js files, compress it, send it to users. I know I could probably set one myself on my computer locally with bit of work, but I need one that's hosted remotely cause can't use home desktop for proxy.

>>11581135
NVM found a perfect addon LMAO. Bandwidth hero exists.

How to stop a ten year addiction? Is it even possible? I lost so much

>>11581178
Find new hobby. Be straight/honest with yourself. DO IT.

How I stopped my world of warcraft addiction.

>uninstall/delete all characters/install file cold turkey
>I reinstalled it multiple times since, but since I deleted all my characters, cant put myself to level up again
This coldturkey nuclear option cutdown my 8-10 hour daily game time to few hours every few months or so

The Laplace Transform of the product of two functions is NOT the product of the Laplace Transform of the two functions.
Likewise, the integral/derivative of the product of two functions is NOT the product of the individual integrals/derivatives.

What is this property called?

my bad I made a thread but i should have posted it here.


If a magazine contains an average of 1 error per page, then if N is the number of misprints per page, what is the distribution of N?

How do i separate ammonium formate and ammonium bicarbonate in a industry scale process?

>>11581569
not enough information

>>11581608
my bad.

I have another question

I have a random variable Y that has expectation 10 and standard deviation 5.

What is the smallest upper bound on P(X >= 15)?

i'm not sure exactly

>>11581677
i mean P(Y >= 15) **

>>11581677
It's unbounded, but you would expect roughly 16% of population to be greater than 15 because 15 is 1 std more than 10. Use something called a z table.

hello, homework helping service?
I'm stuck and have no idea what this question is asking of me. Using matlab, I kind of know how I would filter a signal with a "standard" butterworth filter with n-th order (butter(n,Wc)) and some cutoff frequency, but how do you also account for the epsilon and regular w? anyone wanna point me in the right direction :)

>>11581690
thanks man

>>11581353
non-multiplicative:
https://en.wikipedia.org/wiki/Multiplicative_function

retarded algebra question
x - 0.6x = 0.4x ?

>>11581838
True for all x in the real numbers.

What is the name for this concept, I want to read more about it :
Evolution of the living is a special case of a more general concept. That concept, which is mathematical in essence is applied to everything including language, religion, countries, everything that is subject to change and/or reproduction with or without alterations.
It is in a lesser extent applied to actually everything.
For instance a grain of sand, which is non-living, when blown in the wind, allows to facilitate just a tiny bit the creation of more grains of sand by the wind compared to just the wind hitting a rock with 0 grains of sand around.
It's not only about making more copies of oneself, but also about affecting its surroundings in a way that eventually may enhance the chances of its reproduction.
I was thinking of "positive feedback loop" but even though positive feedback loops are involved, I'm thinking this term wouldn't apply to stuff that is barely (but still) subject to [the concept].
Some sort of pseudo-randomized optimisation process "guided" by entropy.

>>11565779
Not really a science question but wtf is the purpose of this van parked near my house?

Is Electrical/Computer Engineering a better choice than Computer Science?
Which is more challenging, more valuable?

I heard a conspiracy theory that COVID-19 is a genetically engineered bio-weapon created by taking an existing animal virus and evolving it to attack humans. Is this true?

>>11581971
>Is Electrical/Computer Engineering a better choice than Computer Science?
Depends.

>Which is more challenging
EE requires more analysis and I would say that in general it is harder.

>more valuable?
CS often is a glorified "programmer" degree, at least in the US. But programmers aren't badly paid, so again, it depends...

>>11579371
If you mean variety of algebras, then yes this is Birkhoff's theorem. If you mean "something an algebraicist might study", then no; e.g. [math]\mathbb{Q}[/math] is a field but [math]\mathbb{Q}^2[/math] is not.

>>11582109
Ah, didn't consider the specific case of fields. Was just messing around with it, seemed to work for groups, modules, and rings. Thanks for name-dropping the theorem, I'll go check it out.

>>11581971
Computer science is harder. Double major in Mathematics & CS

>>11565779
this question is a bit nsfw but i don't think there's a better place to ask it. it is a scientific question, afterall.

a friend of mine is trying to understand what it'd be like to have a penis. they aren't a tranny.
now, i thought that would be like the communication between a blind person and a deaf person about what it'd be like to see and hear. But come to think of it, in the early developmental stages of the baby, they both start out the same, develop into either the penis or the vagina.

Now, my question, is that given you look at the path of development, would it be reasonable or unreasonable to think that a part of both of the genitalia, if they have the same "root"(That is, they come from the same part of the original, singular undeveloped genitalia), they would feel the same?

>>11582603
(sorry if the 'tranny' language isn't welcomed here. I'm used to less civilized boards, and have unconsciously taken their vocabulary)

>>11581971
CompEng you learn about computer architecture, design, embedded systems etc. instead of analog circuits, drives, power systems, antennas etc.

brainlet here, if im given a function that is real, continuous and differentiable on [a,b], and also:

[math]f(a)=f(b)=0 [/math] and [math]\int_a^bf^2(x)dx=1[/math]
i have to prove that:
[math]\int_a^b(f^{\prime}(x))^2dx\cdot\int_a^bx^2f^2(x)dx\geq\frac{1}{4}[/math]

as far as i know this should be solvable with only integration by parts and cauchy schwarz inequality but im lost in how to even start

>>11582788
There's no trick. Literally start with Cauchy Schwarz:

[eqn]
LHS \geq \left( \int_a^b x f'(x) f(x) dx \right)^2
[/eqn]

Let dv = f'(x)f(x) and u = x and take it from there. That expression equals 1/4.

I need to find a power series for [math]f(x)=\frac{2x}{(1-x)^2}[/math]
I start with [math]\frac{1}{1-x} = \sum_{n = 0}^{\infty}x^n[/math], because [math]\frac{d}{dx}[\frac{1}{1-x}] = \frac{1}{(1-x)^2} = \sum_{n =0}^{\infty}\frac{d[x^n]}{dx} = \sum_{n = 1}^{\infty} nx^{n-1}[/math].

Then from here getting my answer is... as simple as multiplying by [math]2x[/math] (from the numerator of f(x))? So:
[math]2x \cdot \frac{2x}{(1-x)^2} = 2x \cdot \sum_{n = 1}^{\infty} nx^{n-1} = \sum_{n = 1}^{\infty} 2nx^{n} [/math].

Therefore the interval of convergence is [math]|2x|<1 \rightarrow -2<x<2 [/math]


Notice the index change after the derivative in the summation (due to the first term being a constant and therefore going to zero after differentiaton).

Did I do it right? Kinda struggling with this shit rn desu

Can anyone help me with a machine learning problem? With boosting (e.g. AdaBoost), why do we use decision stumps? Why wouldn't we just use the weighted majority class of the data points as our classification?

Help.

I'm trying to learn more about complex systems & complexity theory. I've ran through the wiki tree (which needs editing) but I haven't found any good books to start my journey.

>>11582978
Bump, and I could also use some tips for finding the power series representation of [math] f(x) = x^2[ln(8+x^3)][/math]

>>11583437
this is where I'm at on this one:
[math] = x^3[ln(8) + ln(1 + \frac{x^3}{8})[/math]

>>11583474
ok,using [math]ln(1+\frac{x^3}{8})[/math], set [math]u = \frac{x^3}{8}[/math], then we can use the power series for ln(1+u):
[math]\sum_{n=1}^{infty}\frac{-1^{n-1}u^n}{n}[/math], so we can sub that into f(x):
[math]f(x) = x^3[ln(8) + \sum_{n=1}^{\infty}\frac{-1^{n-1}u^n}{n}][/math]


wat do next? or am I done?
[math]\sum_{n=1}^{infty}\frac{-1^{n-1}u^n}{n}, so we can sub that into f(x):
[math]f(x) = x^3[ln(8) + \sum_{n=1}^{infty}\frac{-1^{n-1}u^n}{n}][/math]

>>11583487
Am I on the right track? it feels very wrong. after I distribute the x^3 into [ln...] (which is actually supposed to be x^2), I'm not sure how to do with ln(8)*x^3 + sum, I feel like my whole approach is way off the mark

>>11583360
http://greenteapress.com/complexity2/thinkcomplexity2.pdf
https://textbooks.opensuny.org/introduction-to-the-modeling-and-analysis-of-complex-systems/

I gotta big brained question here.
There were 2,813,503 deaths in the US in one year.
The life expectancy was 78.6 years.
So a randomly chosen person has a 1 in 78.6 probability of dying on a given year, right? So for every death there should be 77.6 people that don't die, right?
But if you figure it out, the US population would only be around 221 million. I'm off by 50% which is a lot.

>>11583866
>So a randomly chosen person has a 1 in 78.6 probability of dying on a given year, right?
No.

>So for every death there should be 77.6 people that don't die, right?
No.

So the thing is, as is, I don't think this works.
You can take
[eqn]a = \begin{array}{cc} 0 & 1 \\ 0 & 0 \\ \end{array} [/eqn]
[eqn]b = \begin{array}{cc} 0 & 0 \\ 1 & 0 \\ \end{array} [/eqn]
And then it's easy to see that [math]a^2 = b^2 = 0[/math], and finally we can take [math]m = 3[/math] or whatever other odd integer larger than two.
I essentially just want someone to confirm I'm not going insane.

>>11584409
I think it works. Use Euclidean division in the exponent.

>>11584428
additional comment: you may have to require that a and b are not divisors of 0. In an integral domain, the result is true.

>>11584428
It does work if you assume [math]a[/math] and [math]b[/math] aren't zero divisors.
Then, there are [math]l, k \in \mathbb{N}[/math] such that [math]ln=km+1[/math] and then [math]a^{km}a = a^{ln} = b^{ln} = b^{km} b = a^{km} b[/math], so [math]a = b[/math].

Is there some mistake in the couterexample? I forgot to mention it, but it's supposed to 2 by 2 matrices valued in the reals.

>lim f(x) = 1.999999
>but also
>lim f(x) = 2.1111111
>so practically we'll just write 2

So atheists can't even prove that the 'pure' and 'perfect' math are not objectively %100 accurate. Kek.

>>11584444
No, I went a bit fast and did not consider zero divisors on a first thought. Indeed, two distinct nilpotent matrices of the same nilpotency order give endless counter-examples. Are you sure there isn't a line in the book somewhere in that chapter that adds properties on R?

>>11584445
>2.1111

>>11584510
2.000000000001
But you know what I meant.

>>11568541
https://en.wikipedia.org/wiki/Category_of_small_categories
>>11569182
It should be [math]a<x<c<y<b[/math], yes. On both cases.
The proof is otherwise correct.
>>11573098
Recalling that [math]sup ~ f \leq M[/math] and [math]inf ~ f \geq - M \rightarrow M \geq -inf ~ f[/math] we get [math]sup ~ f - inf ~ f \leq M + M = 2M[/math].
>>11576357
You now have [math]\frac{5}{4}[/math] times what you had earlier, so it's a 25% increase.
>>11576521
Baby don't hurt me.
>>11576533
The equivalence part is definitely correct.
The issue is the "relation" part, since even if you exclude [math](0, 0)[/math], you still have issues with division by zero.
Unless you go and consider undefined equal to undefined or similar finicky stuff.
Was it supposed to be [math](x_1, y_1) R (x_2, y_2)[/math] whenever [math]y_1 x_2 = y_2 x_1[/math] or something similar?
>>11576539
Yeah, seems about right.
>>11582978
The computation seems overall correct, but the interval of convergence looks wonky.
Consider that [math]\frac{1}{(1-x)^2} = ( \sum _{n=0}^{\infty} x^n )^2[/math], which tells you that the radius of convergence includes that of [math]\sum _{n=0}^{\infty} x^n[/math] and that this sum dominates [math]\sum _{n=0}^{\infty} x^n[/math] term-wise for [math]x> 1[/math].
>>11583487
Seems correct.
Just sub in u in terms of x.

>>11584477
I didn't find anything.
It's "Basic Exercises in Ring Theory", if you wanna look.
BTW, I've just noticed that any nilpotent gives a counterexample.
Suppose [math]a^n = 0^n = 0[/math]. There's a prime [math]m>n[/math], and then [math]a^m = 0^m = 0[/math], but [math]gcd(n, m) = 1[/math] trivially.

>>11584445
You should look into the formal definition of a limit. It makes perfect sense and captures exactly what you want it to capture.

What is the easiest explanation for Gauss's law?

>electric field mode
>integral form: "The flux through a closed surface is directly proportional to the charge contained inside"
>differential form: "The divergence of E is proportional to local change density"
So charges generate electric field lines around them, right? Well the more field lines there are in a region, the stronger E is. If you imagine you have a chunk of charge and you draw a number of field lines radiating from it, then you draw an imaginary surface around it, you'll find that the number of field lines that exit the surface increases if you add more charge. Divergence is the spacial "explosiveness" of a vector field. The explosiveness is proportional to charge density. The integral and differential forms are equivalent because [math] \int_{\partial R}\mathbf{E}\cdot\hat{\mathbf{n}}\ \text{d}A=\int_R\nabla\cdot\mathbf{E}\ \text{d}V=Q_{enc}/\epsilon_0 [/math] by the divergence theorem, but [math] Q_{enc}=\int_R\rho\ \text{d}V [/math] which means they say the same thing.
>magnetic mode
>integral form: "Flux through a closed surface is always zero"
>differential form: "Divergence is zero"
It just so happens that whenever you draw a surface around a magnet, you get the same number of field lines entering as there are leaving the surface. It also turns out that you can write magnetic field as the curl of a vector potential: [math] \mathbf{B}=\nabla\times\mathbf{A} [/math]. Recall from basic vector calculus that the divergence of a curl is identically zero. Equivalence follows from divergence theorem. The "explosiveness" of a magnetic field is zero.
>>11584514
>2 point 000...0001 = 2
Yes.

>>11584779
>>11584702

>>11584786
Thank you!

Math and CS double degree student here. About to apply for my masters degree. I am at a loss if I should pick applied mathematics or computer science as my masters.
I wish to work as a machine learning researcher in industry, preferably avoiding a Phd.

>>11584832
Clearly you shouldn't go for applied maths, since you'll fall in love and give up on machine learning.

>>11584832
If you want to mainly do research without being a code monkey, I would say do AMS, because you can always switch to finance or something else later in case ML dies (It probably won't in a decade).

>>11584832
how much time did the double degree add? I'm a math major CS minor right now, but I might tack on a few extra classes for the double. Is it worth it?

Why would you take a magnitude in order to integrate? I need justification

>>11585052
because they added an extra sign change for some reason. it doesn't matter. [math] W=\int F\ dx=-k\int x\ dx [/math]

howdy pardners! anything y'all got in store for elementary problem books? ya know, just elemntary geometry, number theory, combinatorics, calculus n such n such. no teachins, just problems preferred

>>11585052
More or less no time because of the autonomy in Bsc programs in my country. I was afforded a really high degree of freedom in the selection of courses and I enrolled in math courses which only had a written examination without taking the original exam, instead studying them over the summer break and taking the exam during a retake opportunity right after the summer.

Tbh I'm not sure that it's worth it. I had to take some courses which were not that interesting or relevant to me, just to get the piece of paper which tells me I've been a good boy.
As it is my plan to go into industry I'm guessing the good boy points I've collected in academia probably won't be worth that much. In hindsight that time might have been better spent on side projects or Kaggle competitions, rather then stroking my ego.

>>11585284
hindsight current year my friend. at least your uni process was comfy, i wish I could take exams like that, instead we're bossed around like toddlers.

what industry are you entering? probably something more related to CS? the only reason i don't wanna full major cs is the non-math classes are a bit more boring to me, i don't care as mch about the details of OS implementation for example.

>>11585298
I was actually pleasantly surprised by our OS class, they paired it really well with concurrent programming which was interesting. But I get what you are saying.
I want to do research in industry for ML. I think a math degree gives me more credibility for that, but I could have just taken the master in AMS.

At least it's better to go the way you are. It's easier to prove some proficiency in CS related stuff with hobby projects. If I had to pay extra to get a double degree I would not do it.

Extremely basic calculus question.
[math]\int{} dx = x + c[/math]. In fact, if I pop that into wolframalpha, it just assumes I meant to write [math]\int{1} dx[/math] and corrects it without comment.
So an "empty" integrand- an integrand with no terms- "defaults" to 1. Is this just convention? If not, can you justify it in a way my mathlet brain can understand?
In particular, why isn't it zero?

does this look right? obv the interval on the bottom was intended to be (-infty, 2), not (-infty, 1)

>>11585571
You've somehow turned a [math](\frac{x}{2})^3[/math] into a [math]\frac{x^2}{2}[/math] going from lines 3 -> 4 in your limit. That doesn't look like it's supposed to happen.

>>11585605
you are correct, it was not intentional. I've since corrected it so my interval of convergence comes out to |(x/2)^3| < 1 -> -2 < x < 2, correct?

>>11585385
Warning: the last time I studied this was in AP Calc four years ago so my explanation is very rough and intuitive. It’s my personal understanding of it, not anything mathematically rigorous

>is this convention?
No, it follows from what an integral fundamentally is.

Think about an integral as representing the area under the curve f(x). You write it as Sf(x)dx because it’s a sum [S] of *products* [f(x) * dx], where each product is the area of basically an infinitesimally thin rectangular “slice” under the curve with width dx (infinitesimal change in x) and height f(x) for some x-value.

>why isn’t it zero?
The stuff to the right of the S-symbol can be looked at as a product, so if it’s just Sdx, then the f(x) factor must be 1. If f(x) were zero then the whole thing would simplify to just S0, which would just be c.

There’s no notion of an “empty” integral without any f(x) component. You have to be taking the integral of some function. Either you write f(x) explicitly, or it’s implicitly 1.

Another (more abstract and less intuitive imo) way to look at it is that the integral Sf(x)dx simply gives the function g(x) whose derivative g’(x) equals f(x). So if you have Sdx, and f(x) is this implicitly 1, then g(x) is x + c because taking the derivative of x+ any constant gives you 1.

Alternatively if you had S0dx -> S0 you’d get c because taking the derivative of a constant c with respect to any variable gives you 0

>>11585385
Sorry, rereading your post I think most of what I wrote was superfluous.

Basically, you can’t have “no integrand”. Any integral is the integral of SOME function. So Sdx is implicitly S1dx because 1*dx = dx. &int;

>>11585385
A=1*A
dx = 1*dx
it's literally that simple

>>11585668
You've got the correct radius of convergence.
There's just the technical issue that you need to remember to check the endpoints. Remember that when the ratio test gives you exactly 1, then you don't get any information, it could diverge or converge. To make sure it doesn't converge at x = -2 or 2 you have to check them manually.

I dunno if it's allowed in whatever class you're using, but since you're getting this series by trying expanding log, it would be easier to say that the series for log(1+x) converges exactly for -1 < x < 1, so by replacing the variable, the series of log(1+x^3/8) converges exactly when -1 < x^3/8 < 1.

How would I convert peak to peak wattage for an AB push-pull amp into RMS watts?

>>11578007
okay, so there's a table that I have to fill for water. we know that the temperature is 120C and the enthalpy is 1525 kj/kg, which means that it's a compressed liquid.

how am I going to find the pressure, the specific volume, the internal energy, its entropy and steam quality (which I guess is 0?)?

guys i dont know how to use order statistics, any help?

Consider a group homomorphism [math]\varphi : G \to H[/math] between two unitary groups. Homomorphisms preserve inverses between the groups, [math]\varphi(g^{-1}) = \varphi(g)^{-1}[/math]. But for unitary operators, the whole point is that [math]g^{-1} = g^*[/math]. Thus does it make sense to talk about [math]\varphi[/math] as a *-homomorphism? My problem is that this language of * usually refers to algebras (i.e. a *-algebra), but I don't see how unitary groups have an algebra structure.

>>11585385

[math]\sum_n 1 = 1 + 1 + \cdots \neq 0.[/math]

[math]\sum_n 0 = 0 + 0 + \cdots = 0.[/math]

>>11565779
Why is it that for a linear ODE with indicial root of degree two that a second solution can be found via:

[math] y_2 = y_1 + \frac{\partial y_1}{\partial r [/math]

Given the first series solution solution "y" sub one and where "r" represents the indicial root for the general series solution (before plugging in the root of degree two)?

I know that a second solution can be found using integrating factors, but that way sucks.

>>11585859
That's not a compressed liquid, it is saturated.
>saturated steam table
>find 120 C
>read off pressure
>compute quality = (1525-s_f)/(s_g - s_f)
>find everything else

Is there a periodicity to the wavelengths emitted by most obects/materials? We see approximately one octave of visible light, from 380 to 760ish nm, I'm wondering if that's because the emission ratios repeat so it'd be unecessary to see outside one octave

>>11586197
They don't have an algebra structure, but they have a canonical inclusion into an algebra.
So essentially, people might assume that the homomorphism extends to the entire algebra.
I'm not sure if it did, actually. I remember that it didn't necessarily for the Clifford groups, but fuck me about U(n).

>>11585723
is dx a thing that can be multiplied though?

>>11585385
ye its a convention

>>11586254
I see, interesting. I'll have to look into this canonical inclusion.
By Clifford group do you mean the quantum info notion of preserving Paulis?

>>11586258
(Local) differential forms are simply elements of a cotangent space, which is a vector space. Thus they inherit all the usual features of a vector space, such as scalar multiplication.

>>11586264
I just mean the ususal [math]U(n) \hookrightarrow M_n( \mathbb{C})[/math].
Also, I mean Pin and Spin. You had to require that stuff extended to the whole Clifford algebra sometimes.

>>11586320
oh okay

I'm asked to find the third degree taylor approximation of [math](1+x)^{\frac{1}{4}}[/math], centered at 2.
I recognize this is a binomial,
and know that binomials can be represented as [math](1+x)^k = \sum_{n=0}^{\infty} {k \choose n} [/math]x^n

I have found the first three derivatives, and computer their value at f(2), but I'm not sure what to do next. Do I plug in f'''(2) into the formula for a taylor series? like [math]\sum_{n = 0}^{\infty}\frac{f'''(2)}{n!}(x-2)[/math]?

>>11586722
the last math was supposed to be:
[math]\sum_{n = 0}^{\infty}\frac{f'''(2)}{n!}(x-2)[/math]

I don't know why it didn't work, it worked in tex

>http://mathb.in/41402
does it look good? is it rihgt?

>>11583937
why not? shouldn't it at least be close?

how's this look? I'm the mathb.in fag from above, so ignore that post now.

>halp.png[1/2]

so how do you solve this

>>11586960
this one I'm less sure about.. also, based off how the question is phrased (i closely rephrased it in the answer), it doesn't sound like I need a series, just a 'taylor approximiation of degree 3,' so hopefull i answered right

i also just realized I'm supposed to have a macluarin for above as well
>halp.png[2/2]

>>11586960
I forgot my n!'s in the denominators here