Stupid Questions

I noticed my post got over the post limit so I'll re-post here:

>>7915753

>>7915823
[math]\sqrt{a \ast b} = \sqrt{a} \ast \sqrt{b}[/math]

You can't add 2 square roots unless a=b.

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How do I get the inequality in (56) ?

I suspect it involves the triangular inequality but I can't work out the details.

Do microglia activate only when a pathogen gets into the CNS or do they activate when pathogens enter the body?

My differential equations textbook recently introduced the notion of differential operator, but unfortunately didn't elaborate on any of the mathematical theory behind them.

My question is, what exactly is the difference between an operator and an operation? In my abstract algebra course, we learned that an operation is really just a function from the cartesian product of a set to the set itself; so considering addition on the integers we could write this function as +:ZxZ->Z. This makes sense to me.

I tried looking up the precise definition of an operator, but found some conflicting descriptions. Most say that an operator is a transformation (so a function?) that transforms a function into another function. I then looked up transformation, and several sources defined it as a function, lets say f, from a set to itself; lets say f:X->X

Am I correct in saying, operations and operators are both functions, however an operation maps the cartesian product of a set to itself, whereas an operator maps a set to itself? Must an operator only map sets of functions? Or is it really more general like operations? Thanks

>>7916069
The author wrote out P(z) used the triangle inequality distribute the absolute value over the addition and subtraction, distributed the absolute value over the multiplications, and factored out |z^n| = R^n from everything.

>>7916069
It is the triangle inequality for the given polynomial z^n+a_(n-1) z^(n-1)+...+a_0 with |z|=R

>>7916151
Math terminology is confusing because it's constantly being revised and not everything gets updated.

The most common definition of operator is that used in operator theory, a linear map from a vector space to itself. The easiest examples then are the linear (matrix) maps from a finite dimensional vector space to itself but if you're gonna use a fancy word like operator then you are probably the type to use an infinite dimensional vector space like a space of functions. The geometry of differential operators is pretty gnarly in comparison to the finite dimensional ones, unless the space of functions is carefully contrived to interact nicely with it. For example I can make a function small values but very big derivative and that would have to be disallowed.

>>7916157
>>7916169
The triangle inequality gives
[math]|P(z)| = |z^n + a_{n-1}z^{n-1} + \dots + a_0| \leq |z^n| + |a_{n-1}||z^{n-1}| + \dots + |a_0|[/math]

But this gives the upper bound and not the lower bound. How do I get the subtractions?

>>7916197
...
Wow, I actually can't tell what the author had in mind when writing that. Maybe a clever use of the factorization of z^n-1? But anyway, the only thing that it's needed for is to see that polynomials have their absolute value go to infinity for big inputs. Anyone would tell you that. Making a proof for that yourself should be doable by other means.

>>7916214
>>7916197
I think I figured out the intended thought process. Let [math] z > (|a_0| + |a_1| + ... + |a_n|) [/math] for big integers M, then by comparison |z^n| is bigger than the sum of all the other terms so that when you take the absolute value of bunch you actually get as a lower bound: [math](|z^n| - |a_{n-1}||z^{n-1}|+ ... + |a_0|. [/math]

>>7916238
Ignore the bit about M. I omitted the bit where you get epsilon delta-y.

Guys, if I stick out this semester with all these units, I'm gonna fail at least one class.

Which one should I drop? Linear algebra or intro to matlab?

I currently have an F in linear algebra, but the professor makes it so he makes the final 80% of the total grade for class. If I have more time to study, Im sure I can pass the class with a B at the lowest. I have a B in my matlab class, but I hear the midterm is an absolute killer and the midterm is past the drop date. So if I shit the bed in that class, then I'm fucked.

Only reason I ask is because I feel I don't have enough time to study. I'm already shit at managing my time and with 17 units it's just stressing me out everyday and I want to kill myself. Not only that, but my other classes are taking a hit as well. 17 units is much more than I can chew right now, but 14 is definitely something I can manage.

which one should I let go of?

>>7916250
>I currently have an F in linear algebra
Drop it

You tell yourself now that you'll magically have time to learn everything in the last week of class, but you won't. You'll get a 70% on the final and fail the class.

Spend your time concentrating on the matlab class since you seem to be caught up and doing fine in it.

>>7916214
>>7916238
Silly me, I should have seen this sooner.
[math]|P(z)| = |z^n + \dots + a_0| \geq |z^n|[/math]

Then, subtracting the absolute value terms on the RHS will give the desired inequality.

is the 'zero' value of a time series 1 or 0? or can it not be calculated?

say i have a correlation Et,Et-1 ; E1 = 8.

Is the correlation 8 or 0? or can we not calculate it?

How do I plot a plane on R3 in wolfram?

>>7916377
depends on the plane, for example:

http://www.wolframalpha.com/input/?i=plot+x%2By%2Bz%3D1

Given a linear Hermitian operator L in an N-dimensional vector space, how do I prove that there are N orthonormal eigenvectors of L s.t. any vector L produces can be expanded as a sum of these eigenvectors?

How do I express phase indifference of a state-vector in mathematical terms?

>>7916437
Let me guess, quantum mechanics?
For the first question, see https://en.wikipedia.org/wiki/Spectral_theorem

As for phase indifference, [math]||Ae^{i\phi}||^2 = A^2 [/math] which is independent of the phase.

Question about gromacs: does anyone know where the lennard jones parameter for the tip3p water model are? in the ffnonbonded.itp file in the force field folder I find the parameter for SPC and a bunch of tip4p models, not for tip3p.

Googling around I find only tables with the paramters listed and I know they have to be somewhere, but I can't find them.

>>7916596
Never mind, I just found them.

say I had a line segment at points (A,B) and (C,D)
and another one at points (E,F) and (G,H)
If I knew these line segments intersect, how would I find the point of intersection?

i really need help with this
>>7916638

>>7916471
Thanks for that link, yes I'm learning QM at the moment.

The text I'm using mentions that only two parameters are needed to construct the entirely of a spin state by constructing two pairs of basis vectors from an initial orthonormal basis vector pair, and the reason for this is the normalisation constraint (probabilities sum to 1) and the 'phase indifference of the state vector', the latter of which I am unsure of w.r.t how to represent it as am equation.

Context is that we're working with bra- and ket-vectors of 1x2 and 2x1 matrix form.

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I know this may seem simple but I can't figure out how the textbook gets the answer( the answer is 6). Pic related.

>>7916644
Look up the Fibonacci sequence.

>>7916701
From the 2 equations, we can see that the solid is bounded from x = 0 to 3.
The area of the cross section is [math](2y)^2[/math] for a particular value of x, so volume of the solid is [math]\int_0^3 (2y)^2 dx[/math].
However, the way y varies with x changes at the point x=1 where the 2 curves intersect.
So the volume is [math]\int_0^1 (2y_1)^2 dx + \int_1^3 (2y_2)^2 dx[/math] where [math]x = (y_1)^2[/math] and [math]x = 3 - 2(y_2)^2[/math].
Substituting y1 and y2 and computing the integration will give you your answer.

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Did I do this right? Is grounding as easy as always putting the minus sign of the voltage you want on the grounding node? Also, is simplifying the circuit to current source then going back to simplify to voltage source the only way to get V2 and i?

>>7916868

Interested in this topic; going to cover this after spring break.

TL;DR version: At what level of involvement is it generally expected (or even mandated) for a person's name to end up on an academic paper?

Long version: I'm an undergrad research assistant in a lab and my prof has been helping a post-doc write a paper. The paper is extremely behind schedule, the Air Force expects it in a week and it's not even half done, because the post-doc has pissed away the past year without making any real headway on it, so it's been a big priority in the lab and I've been given a lot of work on it. The idea initially was for the post-doc to provide me with the content and I would write the actual paper, but this week the post-doc apparently collapsed "due to stress" and is now in the hospital and can't keep working on the paper. This has led to the prof and I splitting up the remaining research, with me doing as much of the grunt work that I can and the prof doing the heavy lifting on the bits that are just completely above my paygrade.

The question is, can I expect this paper to end up with my name on it, or as a URA should I just expect to not get any mention and to just deal with it? I don't really know how these things work, so at this point I'm curious to see if this'll end up being the start of my C.V.. If so, I might actually have to start giving a fuck about its quality...

>Draw a circle centered at the origin, and connect points on this circle whose polar angles are
in the ratio 2 : 1.
I'm definitely retarded, but what is that supposed to mean?
I connect every one of the infinite number of pairs such as (1, 17°) and (1, 34°)?
That doesn't really make sense.

Anyone know if old school two pan analytical balances are still made? Or slide rulers?

I don't know why, but old style instruments made by modern methods to high tolerances interests me, but I'm having difficulty finding companies that would do such things.

So I want to get better at mathematics but Iv been away years and wasn't really decent at it without sheer practice but compared to others I was still lacking.Is it better to change my thinking of mathematics or just do math aimlessly till I "get it" because doing the later hasn't help me. Would a books on logic help me in anyway?What other books do you know would help me?

In a computer science class on high school we shortly discussed the axiom that every smallest unit of a computer can only perform one task. Did I make this up, or is this actually a thing? What's this axiom called?

>>7915823
Look, we define [math]\sqrt x[/math] as a (let's say nonnegative) number [math]a[/math] such that [math]a^2 = x[/math]. So, if we let [math]b=\sqrt{y}[/math]:

[math]\sqrt{x}\sqrt{y}=ab[/math], and [math](ab)^2=a^2 b^2=xy[/math], so [math]\sqrt{x}\sqrt{y}=\sqrt{xy}[/math].

Hopefully this gives you an idea on *why* operations on square roots work.

>>7915787
To study physics, which one would I get the most out of?
-MIT OCW (with sex-offender walter lewin)
-Sears Zemansky University Physics (I've got the physical book)
-Halliday&Resnick Fundamentals of Physics (pdf)

what the fuck is up with the khan academy "mastery challenges"

they don't actually cover the subject I'm trying to learn

should I just re-do the excersize secitons every once in a while for retention instead even if it doesn't "level up" that skill in the eyes of kahnacademy? (I mean, obvioiusly yes I'm just worried that I'm in the wrong here somehow and not using the site right)

Is there a universal guide somewhere with procedures for simple organic reactions? Like, acid catalyzed esterifications and whatnot telling you what molarities to use.
I don't want to waste time optimizing a simple reaction when I have bigger issues to address, and I don't want to sift through proprietary heterogenous catalysts and/or poorly documented medchem papers to get a procedure

>>7917381
idk about the axiom but it sounds like a turing machine

Hey guys how would you have solved this problem I had in my first physics exam? I'll try my best to retell it here and what I did.

A car starts from at the origin and moves eastward with an acceleration of 2.04 m/s^2 . A motorcycle starts behind the car with an acceleration of 3.44m/s^2 and overtakes teh car at 38m. at what time did the motorcycle overtake the car?(just fyi, the accelerations aren't exactly the same as the ones on the test, I just remember the car had 2 something and the motorcycle 3 something)

To solve for time, I just solved at what time the car would arrive at 38 m, since the motorcycle would overtake the car at that exact distance....

I ended up getting t = 6.1 or something like that.

I didn't think it would be appropriate to use the motorcycles acceleration in the distance equation because it started behind the car and not at the origin.

and I wouldn't make xi be 0 becuase a different question at asked me at what distance did the motorcycle start from? It couldn't be zero...

Where can I learn about upper level math (specifically vector fields, the structure+scope of operators, and/or 3D topology) without having to read a 1000 page textbook? Are there any good overviews where I can delve into greater detail at a later time, while still getting a functional understanding of the topic?

>>7917931
You know that the car starts at x = 0 and presumably at rest so v = 0. You know that at x_car ( t_cross ) = x_bike ( t_cross ) = 38m. The function x_car ( t ) is fully defined, as you have initial position, velocity, and constant acceleration, so use x_car ( t_cross ) = 38m to find t_cross, then for x_bike the initial velocity and constant acceleration is known but not the initial position, so use x_bike ( t_cross ) = 38m to solve for the initial position of the bike.

Are we technically living in the 4th dimension considering we understand time?

What is a photon? does it have mass? is it released from a proton, electron or neutron? if so wouldn't that eventually degrade the element, neon lights for example release a photon when it goes down an energy level, so wouldnt that degrade?

How is it possible that sub atomic particles know when they are being observed. Does this have dramatic implications if it is true?

>>7917958
the general consensus is that time is not a 4th dimension.
major reason being that there's no relative space, but there is relative time.

How do magnets work?

>>7918033
Each subatomic particle has a little man with a little railroad cap inside. Whenever he sees scientists observing him he freaks out and starts trying to evade the watchers.

>>7918033
if you don't observe a particle, you don't know its state. You might know its possible states and the associated probabilities of those states, but that's all.

But once you look, well... you know and there is no superposition.

It's like tossing a coin and not looking. You know it's as much heads as tails. But once you look, it's either heads or tails.

>>7918053
what does "look" mean in the context of particles then

>>7916642
Please help

>>7916642
>>7919274
1. Find the equation of line 1
2. Find the equation of line 2
3. Calculate the intersection

To see that it's actually on both segments, you need to also check for the x and y values. But since you're assuming they already intersect you don't need to do that

>>7915787
more of a philosphical/theoretical physics question but: what is parity violation? CP violation? CPT violation? What does any of those things mean and how does it relate to physics?

>>7918033
Any disturbance can cause wavefunction collapse not just one that a human being observe it. That's why its so hard to build a quantum computer, because the particles are getting disturbed by everything.