ITT: QTDDTOT

Well, that's what happens when you rely too much on memorization.

Be glad that you learned the lesson you were bound to learn somewhere down the road in one of the easiest calc-track courses that you can easily pass regardless of one bad grade.

Is it me or is a pain in the ass to actually, completely, know the mechanism of a reaction? for example I am looking at the Heck reaction and the explanation of the reduction done by the phosphine is in 2 papers I can't access, there is no simple drawing of what to me should be the basis.

I admit I hate and I don't know well organic chemistry, but to me it seems like there should some place where every single mechanism is available.

Alright you fucks I'm currently looking at braid groups and links and how they relate to the quantum Hall effect and fractional statistics. I have currently a cylinder for the base manifold [math]M = \mathbb{R} \times S^1[/math] and in general [math]\langle \bar{\Psi}\Psi \rangle = N[/math] particles where [math]\Psi[/math] is the 8-component spinor of the Hartree-Fock Hamiltonian [math]H = \int_{M}\bar{\Psi}\left(i\gamma_0\gamma_i\partial_i + g_a A^a\right)\Psi[/math], where [math]A \in \Lambda^1(M) \otimes \operatorname{Lie}(U(4) \times SU(2) \times U(1))[/math]. This means that I have to find the configuration space [math]F_N(\mathbb{R} \times S^1) = \left((\mathbb{R} \times S^1)^N \setminus \Delta\right)/S_N[/math], where [math]\Delta[/math] is the set of diagonals and [math]S_N[/math] is the symmetry group on [math]N[/math] elements, and its braid group [math]B_N = \pi_q\left(F_N(\mathbb{R}\times S^1)\right)[/math].
I can probably find the generators of the braid group [math] B_N[/math] myself but I'm wondering how the gauge group [math]U(4) \times SU(2) \times U(1)[/math] affects the fractional statistics? In general the braid group [math]B_N[/math], and therefore the fractional statistics, can be found completely independent of the symmetries of the Hamiltonian but I'm thinking that maybe the symmetries might change how the generators of [math]B_N[/math] are defined so that the relevant braid group is some subgroup [math]\Omega_N \subset B_N[/math]? If this is the case then by Abelianizing [math]\Omega_N[/math] we can probably find a subset of [math]\left[-\pi,\pi\right)[/math] for the anyon statistical parameter that's relevant to the model at hand, and maybe the same formalization can explain the [math]\nu = \frac{5}{2}[/math] fractional QHE.

Let X be smooth,separated over R.

Let R[I] denote the ring of dual numbers associated to an R-Module I.

Show [math]{\operatorname{Def} _X}\left( {R\left[ I \right]} \right){ \cong _{{{\operatorname{Mod} }_R}}}{H^1}\left( {X,{\mathcal{T}_X} \otimes I} \right)[/math].

Starting an undergrad physics course, just starting non-bullshit error analysis, specifically error propagation and calculating error by quadrature.

I'm trying to find the error in acceleration calculated from pic related. I have the partial derivatives and the final equation for the error:
[eqn]
\sigma_{a} = \sqrt{( \frac{1 * \sigma_t}{t} ) ^{2} + ( \frac{-v \sigma_{v}}{t^{2}} ) ^{2}}
[/eqn]

But what confuses me is that, if I plug in the time of the measurement (t=1, 2, 3, etc.) into t when calculating the error, what that's going to do is make the error decrease as time goes on, which doesn't make any sense. So what do I use for t?

Im transferring next semester for engineering.
I've taken all my prereqs ( calculus, physics, diff eq) but I still don't know which discipline to major in. Any advice?
>Do you like machines? Pick mechanical.
Im interested equally in mechanical, electrical, civil, and computer science.
All I can say is I'd actually want to use most of what I learn after I graduate.

What do you want to do? So much of Veeky Forums is so focused on what they're learning rather on what they're going to do, it's ridiculous.

Excelfag here again. I don't use the program much so I'm back with another stupid question. I'll post the problem and perhaps someone can provide guidance on where to start. I really don't need it done for me but I need to learn how to do this myself.

>Create a line graph comparing small companies (with employees < 50) and big companies (with employees > 50) on their average morning, afternoon, and evening profits. This will be Figure 4. It should have 6 data points on it, and each data point should have error bars using the standard error

I'm assuming I would create the line graph using the "companies" and "# of employees" columns but 1) I'm not sure how to distinguish them by small and large companies (50 employees), and 2) I have no idea where to even begin applying the three profit columns to the overall line graph. I know how to do error bars so I'm good there.

Elec and Civil are bread and butter of Engineering. Elec covers so much shit, power, electronics, radio, and not LEDs and solar panels and shit. Mechanical is making shit and calculating it's properties. Aerospace usually shares a lot with Mechanical. Honestly I like how easy Electrical has been for me, minus the shit teachers. Nothing like seeing the mechbros working til 5AM for like two weeks straight, while I wasn't doing much of anything.

Civil if you're into the outdoors or buildings I guess, architectural if your parents force you into it but you still want to be a faggot.

Computer Engineer is good, you can do a lot of programming with that.

If you're a girl you can go into Chemical or Biomedical Technology or whatever. There's also Environmental.

I guess I'm not sure career wise. I've shadowed in manufacturing with mechanical and industrial engineers and to me their office jobs look boring. I want to do technical work. That's very broad but I'm not picky. I guess a lab or shop would be cool.

Elec and Mech are the bread and butter REEEEEEEEEEEEEEEEE

One of the things I like to point out in terms of job prospects: EE covers like, so much shit, including, you know, ELECTRONICS, THE BASIS OF OUR FUCKING MODERN LIFE, while MechE is a lot more specialized (relatively speaking). Despite there being an estimate 0 job growth according to the Department of Labor, even after a decade of MechEs estimated growth, EE still will be ahead by like 10k+ jobs. It actually is really strange, that if you look it up, EEs are now being produced less than MechEs for like the first time ever.

Checking a quick article, seems a lot of MechEs can get into maintenance jobs, so like a solar installation would have a bunch of MEs as well as EEs, because infrastructure is just as important as the electrical system.

I know the descriptions for the disciplines, hence why Im equally attracted to them all. Thank you, but I need more info on what the day to day stuff is.
>Mechbros working till 5am
I've heard electrical was the hardest discipline.
.
Ive checked the BLS for every interesting job. 0% job growth isnt bad for 300,000 jobs.

I need to get up to speed in math for pic related in the next 1-2 months. I've pretty much forgotten everything from high school.

Am I totally fucked?

>(1R,4S)-2,3-bis(phenylsulfonyl)bicyclo[2.2.1]hepta-2,5-diene

How would you synthesise this? I can see it's a 4+2 dienophile + alkyne, but how do you get the bis phenylsulfonyl alkyne?
I know the phenylsulfonyl comes from its halide form, what I would assume is a 1,2 bis-ketone system that gets attacked by the phenylsulfoniyl, forming a vicinal diol that we can turn into an alkyne through dehydration..

Nevermind, I am looking around and sulfone synthesis seem a lot more complex than I expected.

Yeah, probably. If you just want to survive, review basic calc + trig and you'll make it.

Can someone give me a layman explanation of zero point energy?

Do you mean in general, or in cosmology, or string memery?
I'll assume in general: Every system as a ground state: this is the lowest energy state this system can have. If you consider an harmonic oscillator, you notice that the energy value of this ground state isn't 0, but some value higher than that. Which means it can't ever an energy lower than this value, the zero point energy.
Now sci-fi writers try to use it to mean "since such a system will always have energy so infinite energy yay". The reality is, since your system can't be in a lower energy state, it's impossible to extract this energy. And if you think "I'll just make an harmonic oscillator and have energy from nothing then!", you can't either because you would have to put this energy inside it yourself when building the oscillator.

Yeah, I've been watching videos about the possibility of harnessing vacuum energy in order to have "free energy." I just wanted to have a basic understanding of it.

Thank you, user.

dumbfag here. how do you find
[math]\lim_{x\rightarrow0} \frac{(1-\cos x)^2}{x}[/math]
without using lhopitals rule?

nevermind, its simple figured it out

Use Kramers-Kronig

Lagrange multipliers

Find the least and greatest distances from the origin to a point on the ellipsoid [math]9x^2+4y^2+z^2=36[/math].

System of equations I get:

[math]F=x^2+y^2+z^2+\lambda(9x^2+4y^2+z^2=36)[/math]
[math]F_x=2x+18\lambda x[/math]
[math]F_y=2y+8\lambda x[/math]
[math]F_z=2z+2\lambda x[/math]
[math]F_\lambda = 9x^2+4y^2+z^2=36[/math]

Each of the first equations cancel the variables and leave different values for lambda.

How'd you do it?

If we're taking Similarity Transformation of a plane, is it gonna be it's own invariant regardless of the similarity coefficient?

separate to lim (1-cosx)/x and lim 1-cosx
(1-cosx)/x tends to 0 (easy to prove) and 1-cosx is just 0 when plugged in so its 0 * 0

Anyone with access to this paper? Care to share it?

Green Chlorination of Organic Compounds Using Trichloroisocyanuric Acid (TCCA)
Gabriela F. Mendonca and Marcio C.S. de Mattos
Current Organic Synthesis vol. 10, iss. 6 (2013) pp. 820-836

dx.doi.org/10.2174/157017941006140206102255

>is there a field whose additive group is isomorphic to its multiplicative group?
No. Let [math]F[/math] be a field and suppose for a contradiction there exists an isomorphism of groups [math]\phi:F^+\mathrel{\tilde\longrightarrow}F^*[/math].

Then the equation [math]2x=0[/math] must have as many solutions as [math]y^2=1[/math]. If the characteristic is not two, [math]2x=0[/math] has one solution, but [math]y^2=1[/math] has two. If the characteristic is two, then everything in [math]F[/math] is a solution to [math]2x=0[/math], while [math]y^2=1[/math] has only one solution.

These numbers do not agree for any field, so no such isomorphism can exist.

>are there any pairs of (infinite) fields where the additive group of one is isomorphic to the multiplicative of the other?
I don't know, but we can shed some light on where to look by examining what we did above.

Suppose [math]E[/math] and [math]F[/math] are fields, and we have [math]\phi:E^+\mathrel{\tilde\longrightarrow}F^*[/math]. Again, count the solutions to [math]2x=0[/math], [math]x\in E[/math] and [math]y^2=1[/math], [math]y\in F[/math].

If [math]E[/math] has characteristic two, then [math]|E|=2[/math], so [math]E=\mathbb F_2[/math] and [math]F=\mathbb F_3[/math], which work, but aren't infinite.

The other case is that [math]F[/math] has characteristic two but [math]E[/math] doesn't. If [math]\mathrm{char}\,E=c\ne0[/math], then every element of [math]E[/math] is sent to a [math]c[/math]-th root of unity. We know that there are at most [math]c[/math] such roots in [math]F[/math], so [math]|E|\le c < \infty[/math].

So suppose [math]E[/math] has characteristic 0, WLOG an extension of [math]\mathbb Q[/math]. At this point I'm stuck. However, observe that no nonzero element of [math]E^+[/math] has finite order, so everything not equal to 1 in [math]F[/math] has infinite multiplicative order---there are no roots of unity besides 1 itself. That's gotta be pretty weird if it exists.

Why does 16^1/2 equal 4? I mean, I get it, if you do the reciprocal of 1/2 its 2/1 which is 16^2, but *why*?

[eqn] \sqrt [n] { a } := a^{ \frac { 1 } { n } } [/eqn]

Yeah I get it but why the one half? Like I get its just a square root and that you can think of as:

16*1/2 = 8
16* 2 = 32
16^1/2 = 4
16^2/1 = 4

That makes sense. I just don't get it. What's special about the exponant? If you have 16*1/2 you're asking "what multiplied by 2 is 16". If you do 16^1/2 you're asking "what squared equals 16?"

I just want to see it in mechanics, like 8*2 = 16. I can get that.

But 4*4*4*4 = 16^1/2? Where does the "2" come in?

I think I'm thinking too deeply into this.

Never mind I get it now after lloking at what I wrote (which was wrong btw). When you ask "16^1/2", the denominator is representing the the number that it is being raised to 2. The 1 = what that number is multiplied by one.

H E L P
E
L
P

This shit aint googlable

Sorry if this isnt the right place to post this but having problem with a homework question in Discrete structures.

Represent the following quote using propositional logic. "Do or do not, there is no try."

Appreciate it if anyone could help. Thanks

Can somebody tell me why v ( -dx) and u (dy) represent a ''volumetric flow rate'' ?

I know we are talking about flow and all here, but all I get from those expressions is:

v = velocity component in y
dx = changes in x
v ( - dx) = changes of v in the x axis? I dont get the significance of the '' - '' either.

In other words, why does this mean ''volumetric flow rate per unit depth''?

post more context

Shit man I dont even know myself, all I know is that this is the Stream function and that its basically derived from the continuity equation.

According to what I found, continuity equation, when satisfied, also means that the volumetric dilatation rate is equal to 0.

Here again they relate it to volume, when all they have in the equation are the velocity components of x, y, z. I dont understand.

how to prove that the weierstrass function is differentiable nowhere?

sci-hub.cc/

is tan y/x or sin(y)/cos(x)?

Because wolfram says the latter but mathematica exchange says the former.

mathworld.wolfram.com/Tangent.html
math.stackexchange.com/questions/434795/finding-functions-for-an-angle-whose-terminal-side-passes-through-x-y

one is linear and one is polar, it depends in which system you're working on

For any x, you construct a certain sequence of [math]h_{n}[/math] such that
[math]\lim_{n \to +\infty} \left|\frac{f(x+h_n) - f(x)}{h_n}\right| = + \infty[/math]

I have a babby question about rule of natural logs.

I got marked down for [eqn]log(x)-log(y)-log(z) = log(\frac{\frac{x}{y}}{z})=log(\frac{x}{yz}) [/eqn]. Why is it incorrect? Doesn't [math]log(x)-log(y)=log(\frac{x}{y})[/math] which would mean that any subsequent subtractions would basically stack under the preceding fraction?

Fucking christ, I meant [math]ln[/math] instead of logs.

Log(X/yz) = log(X) - log(yz) = log(X) - (logy - logx)= logx - logy + logz

This is infuriating me. Am I supposed to combine all natural logs at the same time or something, then? How am I supposed to handle multiple chains of these guys?

Distribute your negatives properly, nigga.
[eqn]ln(\frac{x}{yz}) = ln(x)-ln(yz) = ln(x)-(ln(y)+ln(z))=ln(x)-ln(y)-ln(z) [/eqn]

What method does one use to solve for y (or x) in these types of equations?

Plugged it in wolfram but the solution didnt make much sense to me.

What are you 12?

Complete the square. You're not finding a single solution, but a family of solutions. It's a hyperbola.

>complete the square

Thats what I was looking for. I completely forgot about that, thank you for reminding me user.

Rest assured I tried. Several times.
>! Oшибкa: нe yдaлocь oткpыть cтpaницy
>! Error: unable to access the page

I got a tonne of various math textbooks across lots of different topics especially lots on stochastic processes and probability type stuff.
How should I organize my folders?

No problem friend

I'm studying digital design, right now sequential logic and I'm wondering how I should deal with previous unknown states. For instance with a d flip flop, if both outputs are unknown, which pair of inputs cause a definite output and what is that output?

I've got problems with Thevenin' theorem, how do i calculate the equivalent voltage? R2 boggles me because it's outside the mesh

R2 doesn't have any effect upon the Thevenin-equivalent voltage.

So the voltage is just f*R1/(R1+r) (i.e. r and R1 form a voltage divider).

The point about Thevenin's theorem is that for any linear network (resistors, voltage sources, current sources), the relationship between output voltage and current drawn is linear. And any linear voltage-current relationship can be obtained with a voltage source in series with a resistor, or a current source in parallel with a resistor.

So you can always derive a solution from first principles using the fact that the voltage-current relationships for the original and simplified networks are equivalent.

If black holes can bend the path of light a la gravitational lensing, can it ever trap light in an orbit?

And, since I have a feeling that the answer is no, and the reason is probably interesting: why not?

anyone remember the name of that site where you could find a ton of books? it was library of somethng i think, dont remember

Should I go into ECE or Double Degree of Math and Business Management at Waterloo?

>can it ever trap light in an orbit?
Yes. Look up photon spheres.

If we're taking Similarity Transformation of a plane, is it gonna be it's own invariant regardless of the similarity coefficient?

Libgen.io

What am I doing wrong here guys. The website says that answer C. is the correct answer.

Mistake on their part. Unless you're a primary school student you should be confident enough to conclude that.

If we define [math] d(A,B)=inf \{ |a-b| : a \in A, b \in B \} [/math] how can we prove that if A and B are nonempty disjoint sets with b>a for all b and a [math] d (A,B)=|inf (B)-sup (A)| [/math]
I'm trying to prove this lemma to help solve another problem and I'm so shit at this real analysis stuff it hurts.

Thanks buddy.

I'll try and push you in the right direction.

First, your result can be strengthened a bit. [math]|\inf(B) - \sup(A)| = \inf(B) - \sup(A)[/math] under your assumptions. To show this, fix b in B. Then b is an upper bound of A, so [math]\sup A \leq b[/math]. Then because every b in B satisfies this inequality, [math]\sup A[/math] is a lower bound for B, so [math]\sup A \leq inf B[/math].

Now on to the main problem. Here's an outline:
1) Set [math]\alpha = \sup A[/math], [math]\beta = \inf B[/math]. Show that for every a in A, b in B, [math]b - a < \beta - \alpha[/math]. Use this to conclude [math]d(A,B) \geq \beta - \alpha[/math].
2) Suppose for contradiction [math]d(A,B) > \beta - \alpha[/math]. Then [math]\beta < d(A,B) + \alpha[/math], so there is a [math]b \in B[/math] such that [math]\beta \leq b < d(A,B) + \alpha[/math]. Use a similar trick to find an element of [math]A[/math], and use this to contradict the definition of [math]d(A,B)[/math].

Dang user big thanks man. I did like 8 hours of hw yesterday and at the end I was just fried. I'm gonna try to fix my schedule and hopefully that doesn't happen again.

...

Lads I've been stuck on a question for quite some time now, and I'm hoping one of you can figure it out. It's my first time posting here and the question is simple to formulate, so I won't type it in latex (I'd just mess it up).
Here goes: Given a bounded hyperplane, how to determine if it contains any points where all of the coordinates are integer.
So basically, the plane is given by an equation a_1x_1 + a_2x_2 + ... + a_nx_n = g, and it is bounded by several equations b_1x_1 + .. + b_nx_n

shit nigger that actually sounds pretty hard

for A) and B) what you're looking for is called solving diophantine equations. You can probably find some material in your language on it.

C) looks tricky, try to read up about diophantine geometry to see if there's a general solution to that

Are the a_i integers, rational or arbitrary reals?

If the a_i are integers or rationals, then it's basically about modular arithmetic. If there's a single integer solution to the plane equation, there are infinitely many, forming an (n-1)-dimensional grid.

I'm trying to pay for a parking permit at my college and they are asking for plate type. It's just a regular car.

I believe i asked this in the past but I dont recall getting an answer.

Light can bend around the gravity well of a large star or black hole correct? Which is why we can see objects that are directly behind a large mass that really should be obfuscated from our view.

Does this not occur on both sides of the gravity well? Are many of the stars and galaxies in the sky duplicated?

All coefficients are arbitrary real numbers
Thanks! I'll look into that

Forgot pic

Maybe i dont understand but I feel like that just doesnt make sense. log8 and log5 are really just arbitrary decimals. The simplest form would be log5*a/a which I mean if you needlessly expanded out you could write as log13/a.

Nevermind, figured it out.

i believe we would see a single star - the light would bend around all 'sides' of the gravity well. showing light as a single thin line like in that pic doesnt help at all m8, its more like a massive broad beam of photons eminating from the source which would envelope the whole sun and we would only see the one star

Use Mendeley

Then how does it choose which side of the star to bend around? If the gravity well is uniformly radial, I feel like there should be a path on all sides of the star, and we should really see a ring around the sun.

>The other case is that F has characteristic two but E doesn't.

Why does F still have to have characteristic two? All we know about it is that there is only one solution to y^2 = 1, namely y = 1.

So let's say the coefficients are integer as well. How does this make things different? Would it be possible to answer A,B and C?

I was watching a stream of the ISS the other day when I noticed these things on the station at the bottom of the screencap, wondering if there's someone here who can tell me what these things are for.

> So let's say the coefficients are integer as well. How does this make things different?
Bézout's identity.

Let d be the greatest common divisor of the a_i. sum_i(a_i*x_i) must be a multiple of d. So if g is a multiple of d, then the equation sum_i(a_i*x_i)=g has infinitely many solutions, otherwise it has none.

And if solutions exist, they form a regular grid. I.e. there exist n-1 n-dimensional axis vectors (y_1,...y_n) such that if sum_i(a_i*x_i)=g, then sum_i(a_i*(x_i+y_i))=g.

Note that the axis vectors don't depend upon g, only upon the a_i. Also note that these vectors are all perpendicular to the plane normal (a_1,...a_i), i.e. sum_i(a_i*y_i)=0.

How about solve the integer solutions, then for the greatest distance argue that there exists a greater distance, e.g. plot a sphere against it and find out whether there is a solution or not. Same goes for the minimum.

Also as far as I know you got your lambda applied to the wrong function, try again.

That's correct! This tells you that at least two of the x,y and z must be zero.

You know that already. It's a sphere centered on the origin with axis in the coordinate directions.

Alright thats already some really helpful information, thanks, but there's still the problem of the linear inequality constraints. If n is large, the gcd will be 1 and any integer value g will ensure integer solutions to exist, but what guarantees there will/will not be one that satisfies the constraints?