/sci/ - Science & Math

What is the probability that I will live forever?

thank you based anon for the sophisticated OC

~UNANSWERED~

Physics
>>11403909
>>11405676

Math
>>11405061
>>11405068
>>11407710
>>11407916 (answered, I think)
>>11409497
>>11410597
>>11414205
>>11414831

Biology
>>11411726
>>11414393

Chemistry
>>11404206 (I believe this was answered in his thread)
>>11411363

Engineering
>>11403612

/g/
>>11404421
>>11404620

Stupid
>>11403705
>>11403745 (smartest = stupid = miscellaneous)
>>11404064
>>11406922 (don't wash your panties on hot, air dry them)
>>11410000
>>11410954
>>11412194
>>11413582
>>11413766
>>11414791
>>11414802 (desmos)

1/2
Okay, how come this converges to 1?
I'm using the Limit Comparison Test, with the original function on top (and 1/x^4 being the function compared to the original). When I plugged in infinity, it'd be infinity/infinity which would make it indeterminate right? How come the solutions managed to converge into 1?

Okay, so how come this converges to 1?
I'm using the Limit Comparison Test, with the original function on top (and 1/x^4 being the function compared to the original).
When I plugged in infinity, it'd infinity/infinity which would make it indeterminate right? How come the solutions managed to converge into 1?
Sorry if any of you got annoyed by my deleting my posts nonstop, first I messed up on Tex 3 time and then I posted the wrong images.

>>11414932
Also how come the bounds changed when they wanted to see whether or not the new integral being compared to the original converges or not?
I thought testing for the 'new compared one' doesn't matter when you do the Limit Comparison Test.

Again, I'm really sorry, I just can't seem to get shit right today.

>>11414933
>>11414932
Nvm a kind anon helped answer it on the previous thread after this was made.

>>11414956
Oh wait, can someone tell me why the bounds changed though? From 0 to infinity to 1 to infinity for the new integral?

>>11414854
0

>>11414993
Can't post a thread, fuck rangebans.
Thought of a quantum wine glass analogy, it's probably fucking stupid since I'm not a physicist but I wanted to know what /sci/ thinks.

Think of all the observable properties of a particle as like arbitrary partitions of the volume inside a wine glass.
Then the physical information that particle possesses is like wine.
There's wine in the glass, but not enough wine to fill the glass completely. Ergo, not enough wine to completely fill all the partitions of its volume at the same time.
When a partition is full of air, that property is uncertain, or wavelike. When a partition is full of wine, the corresponding property is collapsed.
Observing a property of the particle is like taking a drink from the glass (except no wine actually leaves the glass).
In the act of drinking from the glass, you tilt it toward you.
In so tilting it, you redistribute the wine across the volume partitions.
The partition close to your lips -- the property you're observing -- is filled with wine that flowed from the partitions farther from your lips.
Ergo, the property you're observing becomes more certain, at the expense of the certainty of other properties.
Simply because the particle does not contain sufficient information to fully describe itself. That is, the wine sloshes in the glass because the glass is not completely full.

Am I onto something here or is this just retarded

>>11414998
Didn't mean to reply to you >>11414993

Is there a short video/series that goes over basic ODE definitions and concepts, preferably with geometric connections, that doesn't worry about solving techniques?

Graph theory is destroying me.

Let k[math]\leq[/math]2. Suppose T is a tree with n vertices, k leaves and [math]\Delta[/math](T)=k.

Show that T decomposes into k paths with a common endpoint.

And find the minimum and maximum values of diam(T) in terms of n and k and draw representative examples attaining these values.

I've done so much math that I got a headache, did I make it bros?
Did I finally join the /sqt/ gang...

Is space even real?
I could be hanging around trad-caths too much but all I hear from them is that science is a myth and anything outside the Earth and the moon is fake and demonic.

Suppose you have two turbochargers spinning at 100k rpm, side to side. That's about 1700Hz each. My question is, will the volume of the sound produced by them in unison double, or will the Hz combine to 3400Hz? I don't know physics sorry. Intuitively the volume should double and the Hz (tone) stay the same, no?

>>11415502
Tradcath physics student here

They're morons

You're welcome anon

What's the best path for a career in robotics? Mechanical engineering with a master's in mechatronics? Or maybe electrical instead?

>>11414998
>Can't post a thread, fuck rangebans.
God bless rangebans and God bless America.
>>11415120
There's a unique path from each leaf to the vertex of maximal degree.
This is the decomposition.
>>11415123
You're thinking of the /mg/ gang, we just answer questions.
>>11415502
>top 10 things that didn't happen

>>11416278
Mechanical with a specialization in mechatronics, but a lot of people treat mechatronics as a meme. Either way, any of your choices would help in robotics.

>>11416307
hey anon, for the limit comparison test, how do we decide which one goes on top, F(x) [the original function] or bottom G(x) [the new one being compared to the original]? and which one goes on bottom?

>>11416423
or does it not matter?

>>11416416
I thought only undergrad degrees in mechatronics were bad

>>11416423
Usually, if you can show that [math]lim _{x \rightarrow \infty} \frac{f(x)}{g(x)} = L < \infty[/math], you can also show that [math]lim _{x \rightarrow \infty} \frac{g(x)}{f(x)} = 1/L < \infty[/math] (where showing is used in the practical sense), but the algebraic manipulation might turn out to be easier in one of the cases.

>>11416448
I forgot muh [math]0 < L[/math] and [math]0< 1/L[/math].

>>11416448
Alright so, we're going with the default that f(x) is always the original right?
And thank you, I get what you mean by flipping them.

>>11416463
>f(x) is the original
Yeah.

>>11416473
Thanks bro
This shit has me staying up all night unironically

>>11416479
I'll drop a proof just in case.
We have [math]h(x) = f(x)/g(x)[/math]. Then, for some [math] \epsilon[/math], we have that [math]h(x) > L/2 >0[/math], by the definition of the limit, which we'll use to guarantee [math]h(x)^{-1}[/math] exists.
The final property on this list gives [math]lim_{x \rightarrow \infty} g(x)/f(x) = lim_{x \rightarrow \infty} 1/h(x) = lim_{x \rightarrow \infty} 1 / lim_{x \rightarrow \infty} h(x) = 1/L[/math]

>>11416494
>this list
https://en.wikipedia.org/wiki/Limit_of_a_function#Properties

guys... how does ln(sqrt(x)) get simplified to lnx/2

>>11416514
log properties, ln(x^((1/2)) is the same as (1/2)lnx

>>11416496
>>11416494
thanks bro, give me a hug

I am stupid but my question is ?chemistry?
>>11410954
It is a liquid used in large quantities for some industrial processes. The weight reduction is not a result of boil off.

why is there no /pg/ (physics general)?

>>11416562
There are, sometimes.
Basically, schizos, cranks and some undergrads do two things in /sci/:
>they frighten away good, reasonable people who come here for the grand trinity of discussion, banter and shitposting
>they unreasonably speed up the board with inane generic posting
Some people do make /pg/ threads every now and then to check if the situation has changed enough to make them viable, tho.
Feel free to decorate the catalog with as many /pg/s as you want, tho.

>>11416753
Pretend I didn't write that second tho.

what happened to the /sci/ discord

I cannot wrap my head around group elements and generators in the context of quantum mechanics. I know that the Hamiltonian is merely the generator of time evolution, and to evolve a state you must apply [math]\exp{(i H t)}[/math]. But with this in mind, what does it mean to apply H directly to a state? Does this even make any practical sense? Spin is an even better example: the Pauli matrices are generators of complex rotations, so [math]\exp{(i \sigma_z t)}[/math] simply rotates around the z-axis but I don't understand what "happens" when you apply the Pauli matrix itself to a spin state.

Can this be understood logically in a differential-geometric picture?

>>11407916
Regular algebraic functions on [math]\mathbb{R}[/math] admit an analytic continuation to [math]\mathbb{C}[/math]. However, to do this we must leverage the holomorphicity (Laurent regularity) in a neighborhood, which requires us to consider them as [math]\mathbb{C}[/math]-valued. In other words, if you want to include complex parameters in your domain by analytic continuation, then you have to make your image [math]\mathbb{C}[/math] as well.
>>11404064
Consider "fruitfulness" as a map [math]f: X\rightarrow B\text{Fruits}[/math] then endow on each n-cobordism [math]M\in {\bf Bord}_n[/math] the tangent structure [math]f^*\xi[/math], where [math]\xi:E\text{Fruits}\rightarrow B\text{Fruits}[/math] is the classifying bundle. In this way we form [math]{\bf Bord}_n^{f}[/math] and we can gauge the theory [math]Z_f:{\bf Bord}_n^f \rightarrow {\bf Vect}_\mathbb{C}[/math] by averaging [math]Z(M) = \sum_{f\in [X,B\text{Fruits}]}\frac{1}{|\text{Fruits}|}Z_f(M)[/math].
>>11416800
Generators form the basis of the Lie algebra. Whenever you take [math]\exp[/math] you're moving to the (connected component) of the Lie group. By interpreting these Lie groups as "physical symmetries", the Lie algebra generators are the integrals of motion. The Hamiltonian [math]H[/math] is the total energy and [math]{\bf J}[/math] are the angular momenta.

>>11416815
I guess my idea is that the Lie group elements are the real actions on a state (like a vector rotating or otherwise being transformed), while a generator is, well, the thing that generates this element (it serves no purpose but to be put in an exponent, putting aside its algebraic qualities). This all makes perfect sense. My confusion comes when we are applying the generators on to the state and say that they "transform" the state, like the spin-flip operator Pauli-x matrix in the context of quantum computers. Can I still picture this like I can picture a rotation? And if this is indeed all abstraction, all preparatory algebra that must ultimately be put back into an exponent for a real, physical action, which I am led to believe, how come Pauli matrices physically exist, e.g. in quantum computers?

I feel like I'm glossing over something very important. I've heard some loose comments in the context of QFT that "physicists only care about local things", referring to generators (which are just derivatives), while the Lie group elements are in this sense global. I don't know if that makes any sense to you but I think it's relevant here.

Can someone explain the recursion formula to me?
is it (-1)^n * a(n)/5 ?
if that's the case wouldn't a(1) = (-1)^(1) * 10/5 = -2?

>>11416884
Your interpretation is correct. However, the second formula is defined for n > 1. If you meant a(2) instead of a(1) in that case that you were right, it is indeed -2.

>>11416884
It's a_n+1, not a_n. You’ve just worked out a_2

>>11416893
uhhh, so this formula only works under the condition that a(1) is given as it is only applicable to a(2) and future?

>>11416897
im so dumb i dont get it

I'm looking for this book:
Mark m. Benjamin water chemistry 2nd edition solution manual

it isn't on libgen, anyone know where else i could possibly find it?

>>11416900
Yes, a_1 is the initial condition. Since every value in the series of a is defined in terms of the one that precedes it, you have to start somewhere. Using a_1, you can find a_2 (you get this by putting n = 1 in the second formula in the image), and from a_2 you can get a_3 and so on.

>>11416911
>>11416897
>>11416893
Thank you bros I think I got it, I guess the a_n and a_n+1 is the thing tripping me up

A hunter and an invisible rabbit play a game in the Euclidean plane. The rabbit's starting point, A_0, and the hunter's starting point, B_0, are the same. After n-1 rounds of the game, the rabbit is at point A_{n-1} and the hunter is at point B_{n-1}. In the nth round of the game, three things occur in order.

(i) The rabbit moves invisibly to a point A_n such that the distance between A_{n-1} and A_n is exactly 1.

(ii) A tracking device reports a point P_n to the hunter. The only guarantee provided by the tracking device is that the distance between P_n and A_n is at most 1.

(iii) The hunter moves visibly to a point B_n such that the distance between B_{n-1} and B_n is exactly 1.

Is it always possible, no matter how the rabbit moves, and no matter what points are reported by the tracking device, for the hunter to choose her moves so that after 10^9 rounds she can ensure that the distance between her and the rabbit is at most 100?

Anybody worked in consulting before? I'm a ChemE considering applying for a position in the industry and I was wondering how's the work like? Is it true you're able to travel a lot? Can it be as comfy as it sounds?

Not big into math, but information theory seems really important so I'd like a fairly accessible book recommendation.

Is astrobiology a meme field?

>>11416857
>it serves no purpose
It serves EXACTLY every purpose. The Hamiltonian is fundamental in the sense that it determines everything in the system: we take its image as the Hilbert space [math]\mathcal{H}[/math] of states, and we require the observables, as a self-adjoint (SA) subalgebra in [math]\mathcal{B}(\mathcal{H})[/math], to contain it. To study properties of symmetries [math]G[/math] we must find a unitary irrep of it in [math]\mathcal{U}(\mathcal{H})[/math], which is a different space than the observables. This is why we use Stone's to consider their SA generators "[math]\operatorname{Lie}G[/math]" in order to have the commutation relations [math][H,\operatorname{Lie}G]=0[/math] well-defined. This wouldn't have made any sense if the domains of [math]H[/math] and [math]g\in G[/math] don't intersect, i.e. when the unitary rep of [math]g[/math] lies outside of the observable algebra.
This method also lets us consider discrete symmetries like PCT.
>Can I still picture this like I can picture a rotation?
Look up the Bloch sphere.
>I think it's relevant here
It is EXACTLY the opposite. If a symmetry is local then so are Lie algebras and their Lie groups. Gauging is fundamentally a distinct operation from taking [math]\exp[/math]. The reason why QFT people like the Lie algebra more is because the space of (associated) principal [math]G[/math]-connections is (locally) isomorphic to the affine space [math]\Omega^1_\text{aff}(M,\operatorname{Lie}G)[/math] of 1-forms, which lets them do minimal coupling very easily. In fact I have personally never encountered a case where the Lie group acts globally while the Lie algebra acts locally, or vice versa.

I think the problem here is your QM class focuses too much on computations and not nearly enough on the underlying theory. It'd be good for you to read Townsend or Cohen-Tannoudji.

>>11416965
I'm gonna have to get a little more into this. I don't know what B(H) is (except that it contains the generators of the observables), or U(H) (it's related to the irreps). I suppose [H, LieG]=0 is simply a tight way of defining a symmetry group. It's not quite clear to me how or under what conditions these three spaces come together, I will look into your recommendations, thanks for that.

>Look up the Bloch sphere
I know that a spin state can be viewed as a rotatable vector; my point is how to make sense of working with a generator on a vector instead of the Lie group element, which happens all the time inside a Hamiltonian. If a group element transforms a vector along a curve, then the generator transforms it along the tangent, I suppose, is how this works. The generator gives the instantaneous linear change along the respective transformation, no? Does it make sense to think like this when I'm thinking of a Pauli matrix acting on a spin state?

>Gauging is fundamentally a distinct operation from taking exp.
I'm gonna be honest, I still don't know what "gauging" means in this context, and it is making me anxious. I don't think it's that complicated of a concept, I've just never had it explained concretely before and the term is used everywhere.

Any tricks to remembering hyperbolics and their derivatives/integrals/identities?

>>11417104
[math]\mathcal{B}[/math] are the bounded linear operators and [math]\mathcal{U}[/math] are the unitaries. In fact if [math]\mathcal{H}[/math] is equipped with a sesquilinear form then they form [math]C^*[/math]-algebras, which is the backbone of QM. See Von Neumann's book on the mathematical foundations.
>>11417104
>Does it make sense to think like this when I'm thinking of a Pauli matrix acting on a spin state?
Yes, [math]\operatorname{Lie}G[/math] is by definition the tangent space of [math]G[/math] at the identity. If you think about [math]G[/math] as actually moving your state on the Bloch sphere then you [math]have[/math] to think about the generators as tangent fields.
>I still don't know what "gauging" means
Gauging makes global symmetries local. This is achieved by forcing parallel transport to have a horizonal lift, which can be done by minimal coupling to a connection. The entire point is that gauging makes local both the Lie group and the Lie algebra.
Don't worry about this for the moment. Focus on understanding elementary QM first.

>>11416761
Discord? What's a discord? Is it a platform geared towards math and science?
>>11416800
>But with this in mind, what does it mean to apply H directly to a state? Does this even make any practical sense?
IIRC the "infinitesimal" evolution of the system, or the "velocity vector" of the evolution.
You might want to just take the time to figure out Yukarifag's posts, tho.
>>11416931
https://math.stackexchange.com/questions/2363268/combinatorial-geometry-imo-2017-problem-3
>>11416957
Yes.

>>11417104
>simply a tight way
And no, that is THE way. It comes from the fact that integrals of motion have zero Poisson bracket with the Hamiltonian in a classical system.
Again, more books need to be read and leas posts need to be made.

How is the parallax angle found? I understand the earth rotating around the sun causing the star to appear to move but how is the angle found? My guess is it's the difference in angle of the telescope observing the star which is measured, but all the sources I read just hand wave it.

>>11417235
Alright, alright. I meant that it was the mathematical definition, and that it is very succinct.

I'm just perplexed by how the first lesson in any QM course is the application of Pauli matrices on spin states and even after years of having done quantum mechanics I still have no clue as to what that actually means in terms of real rotations. I'm going to look at the Bloch sphere until it makes sense that a tangent vector for z-rotation at the origin returns |0> unchanged and |1> with a minus sign.

If [math]f: \mathbb{R}^2 \rightarrow \mathbb{R}[/math], is of class [math]C^1[/math] and verifies:

I) [math]f( 1 , 2 ) < 0[/math]

II) [math](Q_n)_n[/math] is a sequence of [math]\mathbb{R}^2[/math] such that [math]\lim _{n\to \infty}f(Q_{n})=+\infty[/math]

Prove:

a) There is [math] P\in \mathbb {R} ^{2} [/math] such that [math] f(P)=0 [/math]

b) If there are two points [math] P,Q\in \mathbb{R}^2 [/math] such that [math] f(P)=f(Q)=0 [/math], then there is [math] R\in \mathbb {R} ^{2} [/math] such that [math] \nabla f(R) [/math] is orthogonal to the vector P-Q.

I managed to prove the first one, but I'm struggling with the b). It seems I want to prove that [math]\langle \nablaf(R),P−Q \rangle=0[/math], and it seems that there must be a R that satisfies this since f is C^1 but not really sure how to prove it.

>>11414845
What's a good book for learning formal logic?

>>11417325
Set [math]\gamma[/math] as the straight path from [math]P[/math] to [math]Q[/math], apply the gradient theorem, ingenuity and Bolzano's theorem.
In case you're using some other name, here's the statement https://en.wikipedia.org/wiki/Gradient_theorem

sorry for the blogpost but I think engineering-oriented Ordinary Differential Equations has got to be my least favorite mathematics class I've taken to date. The way it's being presented, I don't intuitively understand anything at all. The problems are extremely long and tedious, and worst of all, solving them isn't even gratifying.

some of the problems are so bad it literally just feels like shitposting with algebra. I can't imagine PDEs are any better, really.

what are some ODE applications to electrical engineering besides Maxwell's Equations (bonus points for DSP) so I can try and maintain a shred of motivation for this class

What can cause a particle to end up with an extremely uncertain position?

>>11417466
solving rlc circuits with ODEs is kinda cool. op amps n shit too. might look a little into control theory coz PID controllers are pretty baller. If you wanna go full turbo autismo and get heavy into neural nets, those are usually some form of PDE. heck if you've got some understanding of group theory, calculus of variations, and representations of lie algebras, you can model photons and stuff which is kinda cool.
>>11417473
a very precisely known momentum.

>>11414845
Help with proof pls.

>Let [math]E \in \mathbb{X}[/math] with [math]\mathbb{X}[/math] a metric space, define [math]E'[math] be the set of all limit points of [math]E[/math], define [math]\bar{E} = E \cup E'[/math] the closure of [math]E[/math]
>Prove that if [math]F \in \mathbb{X}[/math] , [math]F[/math] closed, and [math]E \in F[/math] then [math]\bar{E} \in F[/math]

Rudin's proof does a big leap, saying right of the bat that [math]F' \in F \implies E' \in F[/math] i don't get why.

>>11417492
Fuck me, by [math]\in[/math] I meant [math]\subseteq[/math]

>>11417477
So how do you nearly perfectly know the momentum of a particle?

>>11417492
Show that [math]E \subset F[/math] implies [math]\overline{E} \subset \overline{F}[/math] for arbitrary [math]E, F \subset X[/math] and then use [math]\overline{F} = F[/math].

>>11417500
you slam another particle into it which bounces off into your radiation detector. prolly calc its energy from the wavelength of the rad spike and use that to deduce momentum.
Mathematically, all you do is collapse the wavefunction in momentum space.

>>11417507
Thanks, will try

>>11414854
almost 0

What would happen if you flew a bucket of and into outer space and poured the sand out of the bucket? Would the sand clump and form a ball?

>>11417466
>What are some applications of DEs for EE
Well literally everything we do is modeled by a DE, this is why we use the Laplace transform so much.
Moreover control is heavily reliant on DEs, we model systems using systems of DEs, this model is called the state space model.
On signal processing we use DEs to represent systems, when dealing with discrete time systems we use difference equations tho, not ordinary DEs.
Differential equations is literally the most important subject for EE along with complex analysis and linear algebra, to the point I would argue for more classes into the subject for the undergrad curriculum.

>>11417551
what is the laplace transform

>>11415770
bump

>>11415770
They won't be exactly at the same frequency and you'll hear a beat

>>11417552
You will see on your DEs class in detail, but basically is a transforms that takes the problem of solving a differential equation and turns it into a problem of elementary algebra on the complex field.
This is why its so insanely useful, instead of having to deal with Nth order DEs to solve a simple RLC circuit you just have to deal with simple algebra.
This is why we use complex numbers in the form of "phasors" so much.

In detail, if you have a function [math]f: t \in \mathbb{R} \rightarrow \mathbb{R}[/math] then the laplace transform turns it into a function [math]F: s \in \mathbb{C} \rightarrow \mathbb{C}[/math]
The transform is given by the general formula:
[eqn]F(s) = \mathcal{L} \{ f(t) \} (s)= \int_0^{\infty} f(t)e^{-st}dt[/eqn]

As you can see the kernel [math]e^{-st}[/math] turns [math]f(t)[/math] into a function of a complex number [math]s = \sigma + j \omega[/math]

>>11415770
>volume of the sound produced by them in unison double
Not really. The intensity of a sound's pressure wave itself is proportional to the square of the amplitude of the wave, so sound intensity will actually increase by factor of four. However, your ears perceive sound logarithmically. The acoustic gain would be [math]
10\log 4\ \text{dB}\approx 6\ \text{dB} [/math]
>or will the Hz combine to 3400Hz
No. You still have 1700 Hz.
>>11416761
They banned me.
>>11417127
Directly from Euler's formula you can get [math] \sin\theta=\frac{1}{2j}\big(e^{j\theta}-e^{-j\theta}\big) [/math] and [math] \cos\theta=\frac{1}{2}\big(e^{j\theta}+e^{-j\theta}\big) [/math]. Now just cover up all the j's to get the definitions of the associated hyperbolic functions. tanh=sinh/cosh just like tan=sin/cos. The derivative of sinh is cosh and the derivative of cosh is sinh. All other properties you should be able to derive from the definition that is now hopefully easier to remember.
>>11417466
>what are some ODE applications to electrical engineering besides Maxwell's Equations
You can't understand the transient or steady state response of a circuit without DEs and Laplace transforms are imperative to get the transfer function of a system.
>>11417547
>Would the sand clump and form a ball?
Probably not. There's lots of other forces in space. Even without them, it would take a very, very long time.

>>11417552
Look it up on wikipedia. Its most useful property is that L{df/dt}=sL{f}-f(0), meaning that a linear ODE becomes a polynomial in s and solving the ODE just requires finding the roots of the polynomial and converting to partial fractions. The Fourier transform is basically just the Laplace transform with s=jω.

Considering my goal is lucid dreams,or at least vivid dreams,and considering REM rebound;what will happen if I sleep one hour a night for a week?

>>11417335
Based usogui poster
I read part of the raws so I can tell you the final battle of current arc is awesome

why would someone decide to become a foot doctor? is it because they have a foot fetish?

>>11417551
You mention complex analysis and linear algebra being imperative for EE. I've known this for a while and it worries me because the curriculum for my uni's EE-S/SP specialization has neither of them. I'm not sure what that means for the program. Maybe I was expected to take them before hand and now I'm about to get fucked so hard that it'll be like god himself gave me 5 across the ass

>>11417596
Hi it's me again the guy you've been replying to for like 3 months now answering all of my inane questions about diffeq. Thanks as always.

Luckily we're learning Laplace Transforms just after spring break and I've been looking forward to them for a LONG time, so I've got that to keep me going. I at least have a 90% in the class.

>>11417654
Your curriculum seems convoluted as fuck Jesus christ.
Yeah it seems a bit lacking on the math part but dont worry too much about it, you'll probably learn a bit about those topics on your circuits classes.
Your curriculum seems fine nevertheless, pretty cool that you can "specialize" right away into comms and signal processing, they had me take a shit ton of power systems and electrical machinery shit that you didn't have to.

>>11417612
>I read part of the raws so I can tell you the final battle of current arc is awesome
Nice, thanks!

Yukariposter, any requests for the Yukari I'm dropping there?

>>11417803
Wot?
Also add Urs Schrieber to meh tier.

>>11417820
>creator of ncatlab
The absolute villainy of this lad. He's clearly just evil.
It was also easier to edit him in there and Ted didn't really make sense.

Not making my own thread for this, but why does this board attract so many pseuds? The amount of non-discussion and assinine claims about theoretical concepts is crazy.

>>11417942
everyone wants to be a scientist, man. Scientists preach the TRUTH

let's see if any of you can solve this.

Consider the variables X and Y, both independent and with a uniform distribution in the interval [0,1] and null outside said interval. Calculate the probability distribution of the new variable Z=ln(XY).

hey bros, so i know that he did an integration by part but why does the bounds change like that? why did he say "because integrand is EVEN"?

Err, if I draw a cube in [math]\mathbb{R}^3$[/math] is it a hypercube? Or do I make more edges? Images on google aren't all that helpful

Would a function with an empty domain and empty codomain be a valid function?

Why is the arcsin bounded between pi/2 and -pi/2? Shouldn't it be a part of quadrant 1 and 2 because that's where sin is positive rather than 1 and 4?

>>11418131
Yes, there's the identity.

>>11418150
identity would be \x -> x
so domain and codomain wouldnt be empty

>>11418164
Yikes...
https://en.wikipedia.org/wiki/Vacuous_truth
>definition of identity: [math]\forall x, f(x) = x[/math]
>no such [math]x[/math] exists
>hence [math]f(x) = x[/math] is vacuous

I'm currently in dynamics and absolutely stumped on a physics question. I just don't get how to relate momentum and power.

I have a mass flow rate that has a particular momentum which then falls onto a convayer belt that will change it's momentum into a different direction. I'm supposed to find the power needed to change it's momentum in the direction of the belt.

What I thought to do is use the kinetic energy equation like so:

m represents the mass flow rate.

(1/2)*mi*(vi^2) + Power = 1/2*mf*(vf^2)

My logic is that since power is energy over time and the mass flow rate is per time I could just find the energy needed to change the momentum and set it for the same time as the mass flow rate. I believe this would give me power.

>>11418059
if you graph the function being integrated, you will see that the GRAPH is even, meaning symmetric about the Y axis, from -pi to pi.
That being said, it is then possible to halve the bounds of integration and then double the integral by multiplying by 2

>>11418219
Energy per unit mass: [math] e=\frac{1}{2}v^2 [/math]
Energy per unit time into a control volume surrounding your machine via mass transfer: [math] \dot{E}=\dot{m}e [/math]
Energy in = energy out so [math] \dot{E}_i+P=\dot{E}_o [/math], where P is the power required. Looks to be exactly what you have.
>>11417654
EE babes are always welcome.

>>11418269
Thanks for the reply

When is coronavirus going to be over?

Drunk math dummy. Maybe I'm just thinking out loud. Collective Hungry Ratio. If we have negative 100 apples and 25 people. Average apple eating to people is 4:1 if there are 50 people, 2:1. So how can I see this kind of stuff at a glance and judge the amount of hunger of the situation? Like if 193 apples were eaten by 63 people or if 126 apples were eaten by 19 people. Can I see hunger amount on the fly? How? Would higher or lower number indicte more or less hungry?

What's this symbol I've underlined in yellow?

Also whats the answer?

>>11418544
Hat, for exponents? Im guessing

>>11418569
Correction, unsure cause the left e already has the thing. But i usually call that hat

How do pivot points work?
Say I use a wrench on a screw. The pivot point would therefore be the centre of the screw. But,for the screw to turn,wouldn't the pivot point have to rotate as well? I'm having a hard time grasping this concept.

>>11418569
>>11418571
Thank you

>>11415770
Why? Maybe i can help. Idk what you want to know.

>>11418544
It's a mistake in the anime. In the manga it's just a minus sign. They also wrote '-' instead of '+' on the right.

>>11418141
>>11418141
Keeping arcsine's codomain between -pi/2 and pi/2 ensures that it's single-valued, and covers negative values of its domain.
If you chose quadrants 1 and 2, a given value of sine would generally correspond to two different angles. Also, you wouldn't get an angle out of arcsine for negative values of sine.

>>11419014
I think I get what you're trying to say, if the domain was 0 to pi, it would cover two values of (1/2) which would be 5pi/6 and pi/6 so they chose 1 and 4 as it covers both (1/2) and (-1/2).
If that's the case, why not quadrants 2 and 3 but 1 and 4?

If two functions solve the same differential equation and share a common point where the derivative is the same a that point, is that enough to say the functions are equal? How would you show this with more rigor than just seeing it intuitively? I was writing a possible proof of Euler's formula and was able to show [math]f(x)=e^{ix}[/math] and [math]g(x)=cos(x)+isin(x)[/math] both solve [math]\frac{d^2 y}{dx^2}+y=0[/math] and that [math]f(0)=g(0) , f'(0)=g'(0)[/math] but is that enough to claim the identity?

>>11419023
You always want it defined for the first quadrant. Using the second or fourth for the other quadrant gives you a contiguous domain.

>>11419070
>Using the second or fourth for the other quadrant gives you a contiguous domain.
So like uhhh, Q1 and Q4 shares the domain of [0,1] and if I had used Q3 and Q1, the domain would've introduced conflicting results for sin^-1 (1/2) right?
I think I get it now, thank you so much anon

>>11419050
> If two functions solve the same differential equation and share a common point where the derivative is the same a that point, is that enough to say the functions are equal?
No.

>>11419050
1) Any nth order ordinary differential equation is going to have an n dimensional solution space
2) 2 functions from a given ODEs solution space are equal iff they share 2 boundary conditions
Can you prove these statements? Can you find pathological situations where they don't hold?
>>11418578
Rotation=/=translational motion. A point on the outside diameter of the screw translates while the point while the center of the screw does not. Look up "instant center"

>>11419087
Why not? Can DEs be used to prove identities in that manner at all?

>>11419050 #
1) Any nth order ordinary differential equation is going to have an n dimensional solution space
2) 2 functions from a given second ODEs solution space are equal iff they share 2 boundary conditions
Can you prove or justify these statements? Can you find pathological situations where they don't hold? (Think about removable discontinuities)
>>11418578 #
Rotation=/=translational motion. A point on the outside diameter of the screw translates while the point while the center of the screw does not. Look up "instant center"

>>11419080
> if I had used Q3 and Q1, the domain would've introduced conflicting results for sin^-1 (1/2)
Q3 doesn't have a result for sin^-1 (1/2); sin is negative in Q3. For sin, you need (Q1 or Q2) and (Q3 or Q4), i.e. one positive quadrant and one negative. Q1 and Q3 would work (i.e. it would have an inverse) but means the domain is disjoint: [-π,-π/2)∪[0,π/2). Using Q1 and Q4 gives you a contiguous domain: [-π/2,π/2).

For cos you need (Q1 or Q4) and (Q2 or Q3), tan needs (Q1 or Q3) and (Q2 or Q4). The general rule is Q1 and whichever of the adjacent quadrants (Q2 or Q4) has the opposite sign to Q1. So Q1∪Q4 for sin and tan and Q1∪Q2 for cos.

>>11416278
>>11416416
I'd like to hear expertize of someone who works in this field.
What exact knowledge do they use?

>>11419098
According to your criteria, these two functions are the same since they pass through the same point and their derivatives are the same at the point.

If matter is neither created nor destroyed, and materialists believe that consciousness and awareness are just chemicals and the self is just an abstraction, why isn’t eternal existence/awareness possible simply by virtue that your compensate aren’t destroyed?

Yes this question is extra stupid

>>11417803
>>11417840
Wouldn't uncle Ted be hightier for trying to change society away from a technocracy?
>They may be seeking to change society as a whole

>>11419128
Cringed tbqh

>>11419114
I just want to thank you so much for dealing with my dumb questions.
>Q3 doesn't have a result for sin^-1 (1/2)
wouldn't it just be flipped (5pi/6)^(-1)?
>So Q1∪Q4 for sin and tan and Q1∪Q2 for cos.
this applies to their ^-1 (or arc) forms as well right?

>>11419122
*components, I’m dumber than I thought

Does the reduction formula for sin work for its hyperbolic counterpart?

I have 2 questions about the comprehension of this.

1) This is on the 2nd bullet point: if (c) is between 0 and infinity, then both a_n and b_n converges, and if (c) is less than 0, both a_n and b_n diverges right?

2) Does it matter what I choose for b_n? for example, if the original function a_n = (lny)/(y^3), then does b_n need to be something SIMILAR to a_n? my prof told me that it can be 'anything' which was extremely confusing for me.

can someone explain how you do this

>>11419247
What topic is this?

>>11419159
> wouldn't it just be flipped (5pi/6)^(-1)?
sin^-1(1/2)=π/6 (Q1) or 5π/6 (Q2). sin^-1(-1/2)=-π/6 (Q4) or -5π/6 (Q3).

> this applies to their ^-1 (or arc) forms as well right?
Well, it applies specifically to their inverses. sin /per se/ doesn't have an inverse, as it isn't injective (there are multiple arguments which map to the same value). What does have an inverse is sin restricted to a subset of its domain such that each value in that subset maps to a unique value in the codomain. Furthermore, you want the domain of the inverse to be as large as possible, i.e. equal to the codomain of sin = [-1,1].

The first requirement means that the restricted domain of sin must cover a range no larger than π (or it wouldn't be injective, some values would occur more than once), the latter that it must be no smaller than π (or it wouldn't be surjective; some values wouldn't occur at all). Ergo the restricted domain should cover a range of π, i.e. two quadrants.

Having so restricted the domain of sin, the domain of sin^-1 is the codomain of sin ([-1,1]) and the codomain of sin^-1 is the (restricted) domain of sin (typically [-π/2,π/2)).

The point is that a choice must be made as to the restricted domain. There are infinitely many "arcsin" functions satisfying sin(arcsin(x))=x and whose domain is [-1,1]. The one that's conventionally used has a codomain of [-π/2,π/2) because that results in the function being continuous and centred around zero. The same reasoning applies to the conventional definition of arctan. For arccos, similar logic would yield a choice between [-π,0) and [0,π); we choose the latter (i.e. arccos having a non-negative codomain).

>>11419247

>>11419253
just first year calculus. here's the full bit.

>>11419259
thank you, i've gotten used to the idea of multiplying by 1 (where 1 is some fractional term) or adding something that equates to 0 but this is the first time i've seen adding 1 to do something like that

>>11419247
(1+x^2)/(1-x^2)
=(x^2+1)/(1-x^2)
=(x^2-1+2)/(1-x^2)
=((x^2-1)+2)/(1-x^2)
=(x^2-1)/(1-x^2)+2/(1-x^2)
=-1+2/(1-x^2)

>>11419247
[eqn] \frac{1+x^2}{1-x^2}=\frac{1+x^2}{1-x^2}+\frac{1-x^2}{1-x^2}-1=-1+\frac{2}{1-x^2} [/eqn]

Does the existance of energy disproves materialism?

>>11419300
no

Any chance of Naproxen working against the coronavirus in a similar capacity? Would it mean anything substantial if it did?

[math]f(x)=2x + 2x^2 + 2x^3 + ...[/math]
How to solve it? I know it's an infinite sum [math]\sum_{n=1}^{\infty} 2x^n [/math]
Or a geometric series [math]f(x)=a_n \Leftrightarrow a_n=2x^n\Leftrightarrow r=x[/math]
But I don't know how to solve it. I know that the sum of first n terms of a geometric series is [math]a_1\cdot\frac{1-r^n}{1-r}[/math], for [math] r\neq1[/math]
But in my case [math]r=x[/math], so how do I know if it's convergent or divergent?
I also found the formula for sum of geometric series [math]S_\infty=\frac{a1}{1−r}[/math], for [math]|r|<1[/math]
But again, in my case [math]r=x[/math], so I don't know if it fulfills that requirement.
The task is to draw that function.

[math]f(x)=2x + 2x^2 + 2x^3 + ...[/math]
How to solve it? I know it's an infinite sum [math]\sum_{n=1}^{\infty} 2x^n [/math]
Or a geometric series [math]f(x)=a_n \Leftrightarrow a_n=2x^n\Leftrightarrow r=x[/math]
But I don't know how to solve it. I know that the sum of first n terms of a geometric series is [math]a_1\cdot\frac{1-r^n}{1-r}[/math] for [math] r\neq1[/math]
But in my case [math]r=x[/math], so how do I know if it's convergent or divergent?
I also found the formula for sum of geometric series [math]S_\infty=\frac{a1}{1−r}[/math] for [math]|r|<1[/math]
But again, in my case [math]r=x[/math], so I don't know if it fulfills that requirement.
The task is to draw that function.

>>11419350
Monolaurin is probably better since it has virtually zero side effects, but it's only been studied in vitro for antiviral effects so far.

[math]f(x)=2x + 2x^2 + 2x^3 + ...[/math]
How to solve it? I know it's an infinite sum [math]\sum_{n=1}^{\infty} 2x^n [/math]
Or a geometric series [math]f(x)=a_n \Leftrightarrow a_n=2x^n\Leftrightarrow r=x[/math]
But I don't know how to solve it. I know that the sum of first n terms of a geometric series is [eqn]a_1\cdot\frac{1-r^n}{1-r}[/eqn] for [math] r\neq1[/math]
But in my case [math]r=x[/math], so how do I know if it's convergent or divergent?
I also found the formula for sum of geometric series [eqn]S_\infty=\frac{a1}{1−r}[/eqn] for [math]|r|<1[/math]
But again, in my case [math]r=x[/math], so I don't know if it fulfills that requirement.
The task is to draw that function.

[math]f(x)=2x + 2x^2 + 2x^3 + ...[/math]
How to solve it? I know it's an infinite sum [math]\sum_{n=1}^{\infty} 2x^n [/math]
Or a geometric series [math]f(x)=a_n \Leftrightarrow a_n=2x^n\Leftrightarrow r=x[/math]
But I don't know how to solve it. I know that the sum of first n terms of a geometric series is [math]a_1\cdot\frac{1-r^n}{1-r} \Leftrightarrow r\neq1[/math]
But in my case [math]r=x[/math], so how do I know if it's convergent or divergent?
I also found the formula for sum of geometric series [math]S_\infty=\frac{a1}{1−r} \Leftrightarrow |r|<1[/math]
But again, in my case [math]r=x[/math], so I don't know if it fulfills that requirement.
The task is to draw that function.

>>11419373
[math]f(x) = 2x + 2x^2 + ... = \frac{2}{1 - x} - 2[/math] if x < 1. If x >= 1, then it's probably divergent (saucetation needed).

>>11419358
Well, it seems to me like you know what the function is, and you know the domain on which it is defined ( |x| < 1 ) and that it's undefined for all other x because the sum diverges. So draw it on that domain. Seems to me like you've answered your own question.

How do he get to (1) and (2)? I know that he skipped a lot of steps to get to (2) and is unconventional.

>>11419386
I don't know the domain. I have to state what the domain and the range is

>>11419257
Holy fuck, thank you so much dude. I really mean it, I hope you have a good day.

>>11419391
I see almost no skipped steps in this. (1) to (2) is just putting it back into the solved integral.

This probably is stupid as all fuck to chemists, but I'm a dumb babby still at the starting stages.

https://pubs.rsc.org/en/content/articlelanding/2016/ob/c5ob02034d

This is a reaction to hydrogenate a double bond while aminating one side and "ketonating"/"dioxidating" the other one, using pretty much just water and the aminating agent NBS. The mechanism seems pretty straightforward. Seeing as conditions are quite neutral and mild, it's just a matter of the water's oxygen, a nucleophile, attacking the most electrophilic side of the bromonium ion [4]. A benzylic carbon is much more electrophilic than a terminal carbon, so it receives the oxygen while the bromine settles on the other side.

My question is, to invert the regioselectivity, would it be simply a matter of making sure the benzylic carbon less electrophilic than the other side of the double bond? Would it work if the substrate's benzene ring had a strong EDG substituent or if the terminal carbon had a strong EWG substituent? For that matter, if that EWG were a hydroxyl, could this reaction turn it into an aldehyde?

>>11419373
Also, not to be a bother but I see this everywhere from people who are not native english speakers.
"How to solve it?" is not a proper English sentence, grammatically. This is because the sentence lacks a subject noun and instead contains a verb in infinitive form "to solve." The proper sentence would be "How do I solve it?" or better yet "How do I solve this problem?" because these contain a subject pronoun "I".
This second form is even better grammatically, because it is bad form to plop the pronoun "it" into a sentence without writing in English the pronoun's referrent.

>>11419394
You do know the domain, you just said it! When is |r| = |x| < 1? For values of x in which set?
The domain of a function is the set on which it's defined.

>>11419386
>>11419394
Oh, so for |x| >= 1 it diverges, so then it's undefined? Sorry for stupid question, but I thought that the graph would just change and not be continuous

>>11419391
What do you mean?
(1) is just the definition of sin. Look at the triangle on the right. Pythagorean theorem gives the vertical leg, and sin theta is opposite over hypotenuse.
(2) is literally just plugging in this formula for sin theta in the integral you got, because after you change variables for an integral you need to change them back afterwards.
>How would I think to do this?
If you see sin(sec^{-1}(x)) or any similar trig function of inverse trig function thing, always draw a triangle and go back to basic definitions. For trig substitutions it's very useful.

>>11419410
>>11419381
anyway, thank you!

One last thing I don't understand:
[math]\lim_{x \to +\infty} x^n = 0 \Leftrightarrow |x|<1[/math]?
But why isn't the result [math]\infty [/math] if |x|>=1? Is it undefined or do we not use infinity as a value?
If latter, then if something diverges, then can we say its value is undefined?

>>11419403
Whoops, pasted the machanism from a different study.

>>11419444
We don't use infinity as a value. This is kind of a strange, iffy topic, I wouldn't worry about it. Technically there are ways to make sense of these things as "converging to infinity" but these aren't things you need to worry about. It's just undefined (unless for some reason you're being asked for domain/range on the "extended real line")

>>11391341
>>11404206
Because of homophobia.

>>11419484
Lまo, thanks. I don't know chemistry but this looks promising.

>>11419246
1) No. Let a_n = n, b_n = n. Both sums diverge but lim a_n/b_n = 1. All you know is that they have the same behavior. Think of it this way, if lim a_n / b_n = c, then a_n "grows like" c*b_n. So they should have similar behaviors since c is just a constant.

2) You CAN use any sequence b_n, sure, but will any sequence be helpful? Certainly not. You could choose a sequence b_n which grows really fast, and even though a_n/b_n would go to zero it wouldn't matter because b_n doesn't converge so you cant use the second test.
Similarly, you could pick b_n 's which make the third test kind of stupid.
But think of it like this, if you want to show convergence of something, it's enough to find something which grows more than it yet also converges.

>>11419397
>>11419424
OH crap I just realized I went full retard, thank you bros

>>11417335
I have seen that theorem in physics but not in calculus, so I can't use it. My intuition tells me that the professor wants me to use Rolle (I have already used Bolzano's in a) ), but not really sure how to prove it using Rolle, I thought in a function [math]g=f(\alpha (t))[/math] but this just tells me that the derivative is 0 at some point. I though I could define this function such that [math]\alpha(0)=P,\alpha (1)=Q[/math], then for Rolle's I have that [math]0=\nabla f(\alpha (c)) \cdot \alpha '(c)[/math] and then define [math]\alpha '(c)=P-Q[/math] and call [math]R=\alpha (c)[/math] and then I would have prove b), but I defining [math]\alpha '(c)=P-Q[/math] seems wrong to me.

help

help

I might be better posting this in /diy/sqt/ but I heard Yukari is an EE. I got a bass with an internal active EQ chip in it (the "Phat" Equalizer). I want to bypass this EQ. The schematics online for this thing are SUPER shitty but this is what I've deduced is inside (haven't opened my bass yet so can't confirm). Pic related is my drawn schematic, blue squares are all connected to each other. My proposed changes are on the right and in orange. I just wanna make sure this will work and won't fry my amp. I might add a cap in the yellow wire between the switch and the jack too just to make sure no DC is going out (there's probably already one in the EQ chip but if im gonna bypass it, just wanna make sure) and maybe a high valued resistor connecting yellow to ground (also after the switch but before jack obviously). Not too well versed in audio electronics so I just wanna make sure this would work fine.

>>11419716
are you german

>>11419128
Ted absolutely isn't just evil, but I didn't have anyone to place there.
>>11419565
>can't use the gradient theorem
>has some n-dimensional version of Rolle's
Exactly what's the statement for it?
>>11419722
>but I heard Yukari is an EE
Kek.

>>11419565
>>11419737
Also, can't you just prove the gradient theorem for integrals along lines?

>>11419729
no

>>11419737
what? the rumours arent true?aren't both remilia and yuraki EE ?

What is the general term for numbers that are expressed as the difference between two sequential integers raised to the same power?
[math](n+1)^x-n^x[/math]

>>11419938
polynomials

>If this interaction is such that the total energy of the system is lowered, then the atoms bond
together to form a molecule
right so what does "energy" here actually mean? does it mean the electrons travel for a shorter distance or travel slower or have a different wavelength or what? what is it that is going up and down and what happens to an electron when it "gains" or "loses" "energy"?

>>11419975
It's generally referring to mass. When two atoms chemically bind together, the total mass decreases as it's converted into energy. Or the total energy decreases as it's converted into mass, in the case of molecules being used to trap energy rather than release it.

>>11419975
>right so what does "energy" here actually mean?
photons
>what is it that is going up and down
photons
>what happens to an electron when it "gains" or "loses" "energy"?
photons

>>11419983
>>11419987
photons are massless so there is obviously no agreement here

>>11419993
The mass gets converted into photons.

>photons are massless
what did he mean by this

i just wanna say
thank you all

>>11419996
yes, okay. so the mass of the electron decreases, the photons are emitted, the bond forms. the electron must now behave differently though?

>>11419975
electrons move between shells which are different distances from the nucleus. further away = more energy = it has to travel further around the atom.

when a bond forms then the electron is closer on average to the two nuclei than it was to the original nucleus, so it has to travel a shorter distance.

Say you're doing a projectile motion problem. What happens if you take the solution in negative time? Is this a real thing in physics?

>>11420113
it goes back in time bro

isn't -e^(infinity) -> -infinity? why did he write it so that it converges to 0?

doesnt -e^(infinity) converges to infinity?
or is that he forgot the -u from the middle line?

>>11420184
latter

Can someone check if I did the Limit Comparison Test correctly? It's always been something that fucks me up, I know that I could've done the Direct Comparison Test as well but just wanted to practice LCT

Sorry to ask, but what is this shape called? It's supposed to be a circular segment - a triangle with adjacent side < r, or a circular segment with a trapezoid added on.

>>11420281

is cos(-pi) the same as cos(pi) but the result is negative?

Sorry to ask, but what is this shape called? It's supposed to be a circular segment - a triangle with adjacent side < r, or a circular segment with a trapezoid added on.

>>11420288
Cos is an even function

>>11420292
>Cos is an even function
uhhh wut does that mean, sorry

>>11420293
https://en.wikipedia.org/wiki/Even_and_odd_functions
>though I'd advise you to look at what cosine and so on are supposed to represent in the unit circle

How much differential equation solving is there in your day-to-day EE/EE-DSP career job? Obviously there's a lot in college, but what about at work?

>>11414854
plz sign up for cryonics. it's only 30k and ill put you in my lake behind my house in winter.

can someone help me find a study and/or theorize? it basically went like this

give animal flavor and immune drug

later give animal only flavor

immune responds

------
either the study or theorizations on actual mechanism on neuron to immune and gut level helps. thx

my guess is something like: neurons associate increased immune with flavor, and it doesnt matter where increased immune comes from. but as long as the flavor neurons are active, the increased immune neurons are too, causing immune boost even without drug

>>11420326
ahh!new theory on neuron-othersystem interface

if something is active a neuron will note it
if neuron is active something will happen

the two are paired together. it doesnt matter which end starts it, whether somethng is forced into a neuron or neuron forces something to happen. one makes the other and when both are active content is content

Some effort has been expended in trying to understand the mechanism(s) behind conditioning of immune responses. Our group reported evidence favouring both an altered environment (in the conditioned animal), and some change in the responder cell pool which might explain these findings [6]; We predicted that at least some of the effects seen might reflect an alteration in recirculation of responder cells, and there is now also evidence to support this hypothesis [7]. Others have focused their attention on alterations in the molecular milieu which might contribute to conditioned immunoregulation. There is evidence that neuropeptides, neurohormones, conventional neurotransmitters and neurotrophins, growth factors which have been documented to regulate the development of nervous tissue cells, also participate in immune regulation [8–12], though their role(s) in conditioning of immunity remains to be explored in detail.

Following an interest in taste aversion conditioning paradigms and oral immunization [13], my laboratory has explored cytokine production (TNFα, IL-1) following conditioned oral exposure to LPS. Conditioned induction of cytokines occurred in parallel with augmented local (in the gut) and distal (in the brain) expression of mRNAs for substance P (SP) and somatostatin (SOM). Antagonists of the latter molecules blocked the increased brain mRNA cytokine expression in conditioned mice, while systemic administration of anti-cytokine antibodies did not produce inhibition. We conclude that neuropeptides, rather than the cytokines per se, are of key importance in the regulatory loop producing altered expression of mRNAs for certain cytokines in the CNS.


WHAT DOES THIS MEAN

Is it true my ballsack can taste sweet things? Because if so, I think I might wanna try this...

>>11419108
So it means that there's no moment/turning force at the pivot point,right?
That's the concept I didn't get. Since moment equals force times perpendicular distance, and moment is equal throughout the whole length,I thought that the force exerted at the pivot point would be moment over 0(distance),which would be... I'm not sure. Undefined,I guess.

>>11418483
It makes a little more sense when I'm a little less drunk. I'm good.

in this formula, is x the number of trials _including_ the success? i think its worded incorrectly here

>>11420221
It's done right, but it could be done simpler without using l'hospital :
Write [math]\sqrt{5x+2} =\sqrt{5x}\sqrt{1+\frac{2}{5x}}[/math] and then take the limit of the ratio.
I don't know why people always wanna use l'hospital when it's enough to just factor the term of highest degree.

>>11420221
It's correct but it would be elegant to avoid using l'hospital :

[math] \sqrt{5x+2} = \sqrt{5x} \sqrt{1+ \frac{2}{5x}} [/math]
so you can just get the limit of the ratio from this.

>>11420667
Replace 5x by x^5 in my post of course.

>>11420667
Avoiding L'Hospital is probably the single stupidest meme known to man.
But if you wanna insist,
[math]lim_{x \rightarrow \infty } \frac{ \sqrt{x^5 + 2} }{\sqrt{x^5}}= \sqrt{ lim_{ x \rightarrow \infty} \frac{x^5+2}{x^5} }[/math].

le hospital

>>11420681
Because the degree is the same, it converges to the ratio which is 1 because the ratio is 1:1 right? I never looked at it in the way of taking the radical all the way out... Thank you.
>>11420667
>>11420658
Using that, wouldn't it converge to infinity? Sorry if I'm missing something, (infinity)^(5/2) would just be infinity so the other 1+2/x^5 doesn't matter in the end right? Sorry, I'm not really good at factoring, but thank you, I'll pay more attention to factoring and seeing whether or not I could avoid using the rule.

>>11414845
Maybe this should go on advice but that board is shit so fuck it.

>Im a senior year EE undergrad
>Taking final class into power systems
>Absolutely despise the subject
>Maybe because the prof. Is utter shit but damn I fucking hate this shit
>Not even doing bad, in fact one of the best performers in our small classroom
>At a point where I simply can't get myself to study this shit, still need to pass the class

What do?

The professor is simply garbage, sure she's a damn PhD with over 20 years of industry experience but I she can't teach for shit and is always doing annoying arbitrary stuff, to top it off she's head of the department, so there's no one to complain about.

I cant even begin to describe how much of a fucking douchebag she is and she has literally 0 self awareness

>Handing grades for last exam
>The whole classroom did horribly, I got a fucking 50% and I was literally the best grade
>Someone tells her she should curve the grades
>"Well, you guys curved yourselves lmao"

We did so bad because she explicitly told us a bunch of shit were not going to be asked but ended up accounting for 40% of the grade, we spent over 90% of the time leading up to the test studying a subject that wasn't even asked about on the damn thing and she changed what material you could use for the test as we walked in the classroom to take it.

Moreover there's some brilliant students on the class that took the previous power systems class with her and did remarkably well, including myself.
How in the world doesn't she see she is the one that fucked up?

Ive got a ton more stories of her douchebaggery if anyone is interested.

The material itself is also stale as fuck and built upon shaky at best mathematical grounds, whichs annoys the shit out of me as im a math double major.
I dont have any sense of why im doing what Im doing, and it all seems like pointless theorical masturbation that unlike math its just a bunch of annoying number crushing bs.

How long in modern day 2020 does it take a disease "cure"/treatment, into a "complete" human cure, and that human cure into every dr office/hospital?
I would think years and years. But it could happen faster now a days right? I mean tech is better, faster and stuff.
Might need someone who knows about modern day lab research or something.

How long in modern day 2020 does it take a disease "cure"/treatment tested on animals/mice first, into a "complete" human cure, and that human cure into every dr office/hospital?
I would think years and years. But it could happen faster now a days right? I mean tech is better, faster and stuff.
Might need someone who knows about modern day lab research or something.

What is the index of H = <(1, 3)> inside [math]\mathbb{Z}_4 \times
\mathbb{Z}_6[/math]?
(Explain what formula you use to compute this.)
I understand what happens for a single element in Z/mZ, but I have no idea what's going on here. Any help is appreciated.

>>11420842
>What do?
try your best
theres not a whole lot of options
hang in there, bud, we're all gonna make it
t. EE undergrad, currently shitposting instead of studying for circuits II exam tomorrow

>>11419050
Yes. In general the non-linear Cauchy problem [eqn]\begin{cases} \Delta u = f(u,\cdot); & \text{in }\Omega \\ au+ b(n\cdot \nabla u) = 0; & \text{on } \partial\Omega\end{cases}[/eqn] is well-posed for [math]u\in H^1(\Omega)[/math] for [math]C^1[/math] boundary [math]\partial\Omega[/math], meaning that it has the usual Chauchy criterion for existence and uniqueness of solutions, at least for sufficiently small times (depending on how nice [math]f[/math] is; being Caratheodory is enough), as long as you propagate your boundary value from somewhere other than a hyperbolic critical point of the submanifold [math]N\subset H^1(\Omega)[/math] of functions satisfying the Cauchy boundary conditions.
Now "unique" here means that the tangent space has codimension one: this is a [math]functional[/math] condition, not a numerical one, in the sense that if you find two solutions [math]u,v[/math] solving the same problem then you have [math]v \in \operatorname{Span}_{H^1}u[/math], not [math]u=v[/math]. In the case of the harmonics, notice that the general solution [math]e^{ix} + e^{-ix}[/math] is a linear combination of [math]\sin x[/math] and [math]\cos x[/math].
>>11419118
[math]\sin(3x)[/math] satisfies [math]y'' + 9y = 0[/math] sweetie.
>>11419975
Energy is an eigenvalue of the Hamiltonian [math]H[/math]. Typically [math]H = K+V[/math] where [math]K[/math] is the kinetic energy and [math]V[/math] is the interaction; if you look at [math]fixed~V[/math]-slices of the energy landscape and find a local minimum at some slice, then that means the kinetic energy [math]K[/math] is minimized. [math]K[/math] is typically a symmetric bilinear form in the momenta [math]q[/math] (if there is [math]\operatorname{Isom}(X)[/math] symmetry on [math]H[/math]) so it means slower objects, but this is a classical description that is not exactly accurate. Better way is to think about the dispersion relation and the "group velocity" [math]\nabla_q K[/math].

>>11420932
You inspire me~

Is quantum entanglement a consequence of conservation laws applying within stochastic systems? Or was it first derived for a completely different reason?

>>11421012
Let's start here: do you know the meaning of the words you're using?

>>11421020
Two systems are entangled if the properties of one system are dependent on the properties of the other.
Conservation laws state that any gain or loss of energy, charge, or momentum must be balanced out elsewhere.
Stochastic means that something can be described in terms of probability but not have a precise outcome predicted.
Derive means to deduce information based on other information that is assumed to be true.

>>11421029
>Two systems are entangled if the properties of one system are dependent on the properties of the other.
No. [math]States[/math] are entangled, not the system. A quantum state is said to be entangled, or mixed, if it is a convex sum of two states. There is no entanglement in classical systems.
>Conservation laws state that any gain or loss of energy, charge, or momentum must be balanced out elsewhere.
No. Conservation of the dynamical variable/observable [math]A[/math] means [math]\dot{A} = i[A,H] = 0[/math] by the Heisenberg equation. There is no "balancing out elsewhere".
>Stochastic means that something can be described in terms of probability but not have a precise outcome predicted.
No. Stochastic means the process is generated by a measure-preserving ergodic map. The expectations is perfectly deterministic.
>Derive means to deduce information based on other information that is assumed to be true.
Yes, but we do not assume incorrect terminology or misunderstandings to be true.

>>11421012
>>11421029
>>11421044
Now back to your question. Quantum processes can be thought of as being stochastic because of the Hamiltonian/energy is promoted to an operator generating the time-evolution [math]U(t)[/math], which is a measure-preserving ergodic map on the Hilbert space [math]L^2(\Omega)[/math]. Integrals of motion/conservation laws, generated by SA operators, cannot disentangle the ground state of [math]H[/math] since they preserve the ground state eigenspace, the trace [math]\operatorname{tr}\rho \leq 1[/math] of the density matrix [math]\rho[/math] defining said entangled state, and every measurement [math]\operatorname{tr}(\rho O)[/math] done on it; they are distinct objects and have no intrinsic relationship. What integrals of motions do is that it reduces trajectories to lie on the leaves of the foliation [math]X\rightarrow X/G[/math] on the symplectic space [math]X[/math], hence if the ground state is mixed then it is mixed on the orbits [math]X/G[/math]. KAM theorem even states that trajectories lie [math]\epsilon[/math]-close to [math]X/G[/math] when an [math]\epsilon[/math]-small perturbation breaking some symmetry/conservation law is added to the Hamiltonian. Starting with an entangled ground state [math]\rho[/math] to the unperturbed Hamiltonian, using adiabatic theorem we can prove that the ground state of the perturbed Hamiltonian is also [math]\epsilon[/math]-close to the unperturbed, entangled ground state, hence even in this case the ground state remains mixed.
The only way to disentangle a mixed state is to couple it to a huge heat bath, which breaks every quantum order you originally had; this is the thermalization hypothesis.

When was pipolar disorder invented?

>>11421150
When God took a rib from Adam.

>>11420681
I did my undergrad in France. Never used it, never even learned the theorem in school, I only saw it online talking with foreigners.
The theorem is completely useless and can be replaced by much more explicit arguments.

>>11421012
Entanglement is a consequence of [math] \otimes [/math] being a richer structure than [math] \oplus [/math].

>>11420890
[eqn](1, 3)^1=(1, 3)[/eqn]
[eqn](1, 3)^2=(2, 0)[/eqn]
[eqn](1, 3)^3= (3, 3)[/eqn]
[eqn](1, 3)^4 = (0, 0)[/eqn]
Then H has order four, and computing the order of G is left as an exercise for the reader.
Alternatively, the order of [math](a, b) \in A \osum B[/math] was the least common multiple of a and b's orders. You prove it using [math](a, b)^n =(a^n, b^n)[/math]
>>11420738
Nah.
I spun it upside down because we then have [math]lim_{x \rightarrow \infty } \frac{x^5 + 2}{x^5} => lim_{x \rightarrow \infty } \frac{x^5}{x^5} + lim_{x \rightarrow \infty } \frac {2}{x^5}[/math].

>>11420738
You forgot to take the ratio.
You're looking for [math]\lim \frac{ \sqrt{x^5}} {\sqrt{x^5 + 2}} [/math].
With what I said it becomes [math] \lim \frac {\sqrt{x^5}} {\sqrt{x^5} \sqrt{1 + \frac{2}{\sqrt{5}}} [/math]
And then, you just have [math] \lim \frac{1}{\sqrt{1+\frac{2}{x^5}}}[/math] which gets you to the right answer.

When you have a ratio of polynomials, or in general sums of powers of x, you can directly find the limit in 0 of infinity by factoring of highest or lowest degree (depending if you're checking in 0 or in infinity) from both sums and compare them. The rest of the functions will be irrelevant as you see in that example.

what's the speed of sound in vaccuum

How do you prove that d and b are equivalent metrics?
d(x,y)=b(x,y)/(1+b(x,y))

I have shown that d(x,y)<=Kb(x,y), for K>=1, but i don't know how to show b(x,y)<=Md(x,y) for some M? I know i can write b(x,y)<=M-1, but i dont know if b(x,y) is bounded. Can anyone help?

Quick question.
How I can halve the uncertainty of a measurement, such as time taken for x to occur?

>>11421425
Forgot to mention, WITHOUT changing the equipment that was used in the first experiment.

This is a very basic question but I really don't know. What is the best way to find scientific papers and studies?

>>11421425
>>11421429
Bump. Obviously omitting the obvious answer like increasing the number of measurements.

I think I actually have some kind of attention defecit disorder. Is there any value to diagnosis as an adult?

>study 1st year math
>equations
>learn different ways of solving them
>do well in the exercises of each method
>reach the end of the chapter
>"here's a final exercise for you"
>"various equations"
>"you decide which method is best"
>get absolutely lost
>don't know where to start

Is there any tricks to find which method is best? Suddenly I feel like I can't solve any equations while before I was doing 10/10 on the exercises..

Made a thread but I'm retarded since my question belong in here.
In quantum field theory the professor claims in his notes about the relation between klein Gordon and Dirac that
[/eqn](-\gamma^{\mu}\gamma^{\nu}\partial_{\mu}\partial_{\nu}-m^{2})\psi=0[eqn/]
and the he says that since both derivatives commute only the symmetric part of the product between the gamma matrices survives. wtf? ive tried all i could remember and the antisymmetric part doesnt disappear. whats happening here?

>>11421711
just fucking guess

>>11421716
Sorry but I forgot how to post latex in /sci/

>>11421717
It's a trial and error process then?

Does anyone know how to solve part b in this thermodynamics question? I assume we are supposed to use the steady-flow energy equation though I'm not quite sure how to use it (as I do not know what the values of Z nor C are), I could be wrong in thinking this as perhaps there is another related equation better suited. What do you think?

can you guys check my work

"division by 0" is an operator. division is an operator class that takes a quantity as its modulator. division by 0 as an operator does not exist; division is the grouping of pieces, so youre applying "no groupings" to a number. youre not making "no groups" of a number which would be 0, youre simply.. not grouping it at all. if you dont partition a number into groups, you cant know how many numbers per group there are; its a nonsensical statement. division by 0, or any R/0 is a non meaningful statement, aka, it doesnt have a perturbation in reality. so it does not exist

further note - 0 is actually intimately related to DNE. 0 is the statement of "object DNE". in a sense "/0" means division DNE (with division being the object in question)

>>11421720
yes but try in your head the easy ones first before pen on paper

Is my answer (top box) the equivalent of wolframalpha's (bottom box)? I think I might've done something wrong because I have an extra term while wolframalpha only has 2.

>>11420019
Do you have any questions?
>>11420639
If x=1, then we have that f(1)=p, which is the probability of you getting a success on the first shot, i.e. without failures.
>>11421379
We trivially have that [math]1+b(x, y) >0[/math] everywhere, and thus [math]b(x, y) = d(x, y)[1+b(x, y)][/math]. If [math]b(x, y) \leq 1[/math], we have [math]b(x, y) = d(x, y)[1+b(x, y)] \leq 2d(x, y)[/math].
>can I really not find a K for all [math]b(x, y)[/math]?
Not really. [math]b(x, y)=[1+ b(x, y)]d(x, y)[/math], so [math]K \geq 1 + b(x, y)[/math]. If the right is unbounded, you're fucked. If it's bounded, you have finite diameter, and then you can use that.
>>11421719
Ahem.
[eqn](-\gamma^{\mu}\gamma^{\nu}\partial_{\mu}\partial_{\nu}-m^{2})\psi=0[/eqn]
There's a guide somewhere in the OP.
>>11421734
This is too advanced for me, I'll have to ask the Bogdanovs.

why the fuck do neural network materials always note theta i,j with i being the number of unit in the current layer and j the number from the previous layer? this always confuses me

>>11421720
No, you figure out which ones are easy to solve which way as you try them and you can recognize the patterns.
Assuming you're doing quadratics, what I recommend is:
If you don't see a constant term, just fact the x out.
If you don't see an x term, just solve via square roots.
Otherwise, look quickly for a possible factorization but give up almost immediately and just use either quadratic formula or completing the square. They're the same thing.

>>11421257
L'Hospital is one of, if not the single most convenient theorem in calculus, it's extremely intuitive, and I don't care if autists in France don't learn about it and proceed to do disgusting algebraic arguments.

>>11421843
my math test is today, can i have ur blessings

>>11421855
Sure thing.

how is [math]xy''+y'=0[/math] considered Cauchy-Euler if the leading coefficient is degree 1, but the derivative is of order 2?

>>11421425
>>11421429
>>11421655
G-G-GUYS

>>11421425
>>11421877
just calculate better lol

>>11421808
You were very close. When subbing [math]u=tan(x)[/math] back in on the last step you went from [math]\frac{u^{4}}{4}[/math] to [math]\frac{2tan^{4}}{4}[/math}. Other than that, nothing is wrong.

Simply by looking at it, f(x) diverges because it fails the P-test right? Which means I wouldn't have to do 8b? Or does the bounds of 1->3 change the result?

>>11421881
Oh crap, thank you, I always make stupid little mistakes.

>>11421879
So there's no other way except increasing the data set?

>>11421883
>it fails the P-test
The P-test shows it converges though. The integral is in the form [math]\int_{a}^{b}\frac{dx}{(x-a)^{p}}[/math] which implies it will converge iff [math]p<1[/math] which it is.

>>11421729
>a
[math]\Delta h\approx c_p\Delta T[/math]
>b
The heat transferred to the air IS its change in enthalpy
>c
[math] \dot{Q}=\dot{m}\Delta h [/math]
>d
[math] \nu=RT/P [/math]
>e
[math] A=\frac{\dot{m}}{\rho v}=\frac{\dot{m} \nu}{v} [/math]
>>11421877
What are you timing? You really have to be more specific.
>>11421871
>an Euler-Cauchy equation is a linear, homogeneous, ordinary differential equation with variable coefficients
[math] xy''+y'=0 [/math] satisfies all that.

>>11421920
Oh fuck, can you elaborate a bit more on that form or where I can get it? I know that if the bounds is from 1 to infinity, then p>1 = converges, does p<1=converge only work if its a -> finite number?

is it true that graphite is more permanent than ink?

>>11421729
>a
[math] \Delta h\approx c_p\Delta T [/math]
>b
The heat transferred at constant pressure IS the change in enthalpy, by definition.
>c
[math] \dot{Q}=\dot{m}\Delta h [/math]
>d
[math] \nu=RT/P [/math]
>e
[math] A=\dot{m}/\rho v =\dot{m}\nu/v [/math]
>>11421871
I don't think it is, is it?
>>11421877
>>11421901
You really have to be more specific. What are you measuring, exactly?

>>11421935
The standard P-test with which you are probably familiar is for improper integrals in the form [math]int_{0}^{b}\frac{dx}{x^{p}}[/math] right? To get to the from I used, either consider a translation of the function or use a substitution [math]u=x-a[/math] to get back to familiarity.

>>11421969
Sorry for bad formatting, do you need me to rewrite or can you understand?

>>11414845
I want a /sci/ perspective on this question. There is no inherent meaning to life, so is a life without meaning a life worth living?

>>11421972
Yeah if possible, sorry, I'm just having a bad time visualizing it. So originally, from the bound 0->1, 1/x^p would converge if p<1, and to get to 1->3, we're essentially translating the function over?

>>11421974
>is a life without meaning a life worth living?
No. Look to Nature or make your own meaning.

>>11421978
I've tried looking into what making your own meaning means. What I find as results is a bunch of self-help uppity bullshit from pricks trying to sell their books.

>>11421986
What do you like about life? What brings you pleasure? Are there any people you love or places you want to be? This is your meaning.

>>11421965
>You really have to be more specific. What are you measuring, exactly?
Oscillation period, T, for a trifilar pendulum (which was then used to get its moment of inertia). We took the time taken for 20 oscilations, ten times, and then worked out the time for 1 oscillation.

Is there a fast, reliable and easy way to solve polynomial equations of degree 3 and 4? I've been reading to some pages on google but nothings seems easy or reliable. Why is the quadratic formula so easy but everything beyond degree 2 absolute aids

>>11421992
Thanks for proving his point and also demonstrating what it means to be a true, born and bred, NPC.

>>11422017
You're still working on that? If you have already taken the measurements, then there is obviously nothing you can do to "improve them". What you could do is determine the mean time and standard deviation. If you can measure again but don't have access to more precise equipment, just measure more oscillations per trial.
>>11422021
In general, no. Numerical methods.

>>11422029
k

>>11421986
the only thing that makes life worth living is your family and other humans you like
it's really that simple and I understand that a lot of 20-30 year olds with very impersonal family relationships and a shitty job struggle with this

>>11421975
There are two changes to be made to your formula. First I need to argue that changing 1 to b is justified, then I need to explain the use of a.
1) Consider where the divergence in the integral could arise. It is from the lower bound not the upper. We can rewrite [math]\int_{0}^{1}\frac{dx}{x^p}[/math] as [math]\int_{0}^{b}\frac{dx}{x^p}+\int_{b}^{1}\frac{dx}{x^p}[/math]. I hope you can see [math]\int_{b}^{1}\frac{dx}{x^p}[/math] will be convergent so if [math]\int_{0}^{1}\frac{dx}{x^p}[/math] is divergent, [math]\int_{0}^{b}\frac{dx}{x^p}[/math] will be too and vice versa.
2) In regard to using a, the translating was just a way of thinking about it. You can say [math]u=x-a[/math] which then means [math]\int_{a}^{b}\frac{dx}{(x-a)^p}=\int_{0}^{c}\frac{du}{u^p}[/math] which is the form you know. Hopefully my formatting will work this time.

>>11422129
Damn. Maybe just try to justify it yourself.
Could a Latex person explain what's going wrong, I'm pretty new to it?

>>11422129
Press the tex button on the top left of the message box

>>11420312
I am signed up for cryonics. Also relevant:
https://www.cryonicscalculator.com/

>>11422159
>I am signed up for cryonics
yikes, dude

>>11421379
All metrics on finite dimensional normed linear spaces are equivalent.
>>11421716
Subtract the two equations you get from permuting the indices. [eqn]0=\gamma_\mu\gamma_\nu\partial_\mu\partial_\nu \phi - \gamma_\nu \gamma_\mu\partial_\nu\partial_\mu\phi = (\gamma_\mu\gamma_\nu - \gamma_\nu\gamma_\mu)\partial_\mu\partial_\nu \phi. \qquad \ast[/eqn]
which states that the antisymmetric part vanishes. Generally, tensors satisfy the graded commutation relation [math]A\otimes B = (-1)^{ab}B\otimes A[/math] where [math]a,b[/math] are the degrees of [math]A,B[/math], respectively. Now since [math]\{\gamma_\mu,\gamma_\nu\} = 2\delta_{\mu\nu}[/math], [math]\gamma_\mu\gamma_\nu[/math] is antisymmetric while [math]\partial_\mu\partial_\nu[/math] is symmetric, so [math]\gamma_\mu\gamma_\nu\partial_\mu\partial_\nu[/math] is antisymmetric. Klein-Gordon then implies (*) on the spinors [math]\phi[/math].
>>11421871
Consider [math]z = y'[/math].

>>11422033
>f you can measure again but don't have access to more precise equipment, just measure more oscillations per trial.
That's what I've wrote, just wanted to ask in case there was something else I could use, a different equation or whatever. I took a break and I'm finishing the final part of the write up now.

>>11422173
What's wrong with cryonics?

>>11422217
No. You can't magically increase the resolution or decrease the uncertainty of a measurement with different equations.
>>11422223
How much did they scam you out of?

>>11422129
There are two changes to be made to your formula. First I need to argue that changing 1 to b is justified, then I need to explain the use of a.
1) Consider where the divergence in the integral could arise. It is from the lower bound not the upper. We can rewrite [math]\int_{0}^{1}\frac{dx}{x^p}[/math] as [math] \int_{0}^{b}\frac{dx}{x^p}+\int_{b}^{1}\frac{dx}{x^p}[/math]. I hope you can see [math]\int_{b}^{1}\frac{dx}{x^p}[/math] will be convergent, so if [math]\int_{0}^{1}\frac{dx}{x^p}[/math] is divergent, [math]\int_{0}^{b}\frac{dx}{x^p}[/math] will be too and vice versa. This means if the P-test is valid between 0 and 1 it will be valid between 0 and b.
2) In regard to using a, the translating was just a way of thinking about it. You can say [math]u=x-a[/math] which then means [math]\int_{a}^{b}\frac{dx}{(x-a)^p}=\int_{0}^{c}\frac{du}{u^p}[/math] which is the form you know.
>>11422154
Thanks.

>>11422244
I no longer know what is going on. It was formatted correctly in the TEX preview but broke when I posted.

>>11422249
put spaces between the TeX and the tags, hunny

>>11422244
It sometimes fucks up, even if it works in the "TeX" thing in the top left
>>11422252
even without them it bugs if you have two [math]s in paragraph

>>11422244
>>>11422252
There are two changes to be made to your formula. First I need to argue that changing 1 to b is justified, then I need to explain the use of a.
1) Consider where the divergence in the integral could arise. It is from the lower bound not the upper. We can rewrite [math] \int_{0}^{1}\frac{dx}{x^p} [/math] as [math] \int_{0}^{b}\frac{dx}{x^p}+\int_{b}^{1}\frac{dx}{x^p} [/math]. I hope you can see [math] \int_{b}^{1}\frac{dx}{x^p} [/math] will be convergent, so if [math] \int_{0}^{1}\frac{dx}{x^p} [/math] is divergent, [math] \int_{0}^{b}\frac{dx}{x^p} [/math] will be too and vice versa. This means if the P-test is valid between 0 and 1 it will be valid between 0 and b.
2) In regard to using a, the translating was just a way of thinking about it. You can say [math] u=x-a [/math] which then means [math] \int_{a}^{b}\frac{dx}{(x-a)^p}=\int_{0}^{c}\frac{du}{u^p} [/math] which is the form you know.

What would be a likely underlying cause of pervasive suicidal ideation in the absence of any stressors or other psychiatric symptoms?

I'm bored, should I ask questions for myself to samefag answer?

When was Bipolar Disorder invented?

>>11422267
C in that case would be infinity and B a finite number right? Sorry for having you rewrite it three times, I really appreciate it.

>>11422516
Finite number between 0 and 1 I mean

>>11422492
2009

>>11422516
>>11422530
b is any finite number. c=b-a

>>11422364
You could do that.
Alternatively, you could read Usogui.
You can also work through something like https://link.springer.com/book/10.1007/978-94-017-1514-0
Also, wouldn't it be embarassing if someone else gave a better answer than yours?

>>11419716
When multiplying an inequality throughout by a a negative, the inequality must be flipped. x can be negative so you have to consider that case.

i just don't understand what happens to the numerator in this substitution... I probably missed something in the chapter but idk what

>>11422841
It's split as [math] x \cdot x^2 [/math]. The [math] x [/math] is then canceled by subbing [math] \frac{-du}{2x} [/math]. So, we are left with [math] - x^2 [/math] with the [math] \frac{1}{2} [/math] moving outside the integral. [math] u=16-x^2 \implies x^2=16-u \implies -x^2=u-16
[/math]

>>11422910
thanks, I didn't know you had to put back in the u

>>11422649
Not really, I'd be glad to know someone else here is familiar with my field. We could maybe even have a discussion here.

Bros I think I definitely got above an 80 this math exam because of /sqt/, thank you all so much, I really mean it.

Is phlegm a symptom of coronavirus?
I feel tired, weird sensation in my throath, got mucus on my nose I think, so is it the cold or the coronavirus? I've got chest pain but I don't think it's from that and more like bad posture, btw my mucus is very liquid.

>>11422549
This may be when it was perfected but, I remember my aunt contracting this strange, new, mysterious illness. Just after, she recalled that grandpa was drinking and raping her around the clock, while still finding the time to perform his duties as the county sheriff. By the time of this experimental diagnosis, grandfather had raised to the office of judge on a state level and was instrumental in bringing Bob Dole to senate. Grandma sent him packing, he fell from his position in disgrace and was found dead in a pile of his own vomit within a fortnight. This somg was on Mtv when I heard the news:

https://m.youtube.com/watch?v=UtvmTu4zAMg

Aunt (despite her illness) and grandmother live happily ever after to this day.

>>11423090
you do not have corona virus

>>11421992
Not that anon, but I like to bake bread. Kneading dough and rolling it in my hands is very comforting and therapeutic. If I could just bake bread and solve differential equations all day, that would be the life for me man. Heck, I should solve differential equations about bread now that I think about it.

A-are there any diffeq about breads?

>>11421965
Ah, I see! Thank you very much. What I fool I am for not recognising that. Hope you sleep well and enjoy your night!~

>>11421974
>there is no inherent meaning to life
My opinion is that analysing your thoughts and judgements from a pseudo-third-person perspective is dishonest and impedes you from fully experiencing your own humanity, and furthermore that you should fully take responsibility for your opinions and desires as an individual.
>>11423008
What field?

What is the most effective way of studying a subject? No anecdotes, the method to max brain mode and concentration.

>>11423214
Baking is an excellent hobby. I am not an expert, but the DEs associated with baking would be related to heat transfer into the dough, the leavening and rise of the dough, and the kinetics of browning reactions. Someone who knows more than me will hopefully show up.
>>11423237
Thank you, love

Is Industrial Engineering a good degree if I really like mathematics but dislike physics and can't study mathematics as a degree in itself? Or should I go EE and just push through al the physics?

>>11423292
hmm, that all sounds fairly complicated. I understand simple heat transfer just fine, but come to think about it, I've never used a DE that models heat transfer of a mass that actually increases its volume when heated (i.e. most actual heat transfers in existence). There a resource for this I can look up?

>>11423207
why? explain

>>11423279
give a shit

>>11418059
even function: f(x) = f(-x)
odd function: f(x) = -f(-x)

>>11423313
*shits in your mouth*

>>11423090
add watery eyes and runny nose

>>11419565
If f is identically zero along the line between P and Q, then the directional derivative is zero and so the gradient is perpendicular. If f is positive somewhere on the line between P and Q then it attains a maximum somewhere on the line strictly between P and Q. At that maximum the directional derivative is again zero so the gradient is perpendicular. Similarly if f is negative.

>>11423303
The way you do math in engineering classes is different than in math classes. If you just like math and want to make money you should do some sort of data science or statistics major. ChemE might be a good option tho because the physics is mostly thermo/fluids stuff, which is just differential equations and shit.

>>11419722
You're probably going to have better luck in >>>/diy/ohm/ . This is despite remilia and yakarianon's unparalleled EE skills.

>>11423734
so the rumours are true then? has their EE past finally caught up to them?

>>11423728
Actually I had heard data science and statistics were a heavy part of the IE course, and that was why I was considering it. Will check out ChemE though

>>11423789
No lol. Neither of them are EEs.

>>11423734
mmm, i posted to /diy/ already but i think im fine to go through with my plans anyways. I can't imagine how any of my changes royally fuck anything up since it's all passive components at that point.

I am curious about Khan academy. I plan on starting from their preschool math and just going through their entire catalog of courses till I run out. I know I shouldn't care but thoughts and opinions on this approach to practice math? Is there another site I could do this with as well? Anyone tried that "Brilliant" site that I keep seeing in popsci videos?

>>11424990
>starting from their preschool math
cant you at least start from highschool?

>>11424994
I can start from a mid level college course. As for why I am starting all the way down there, I just kinda want to recap everything I've gone through since I was a bab.

>>11425072
but if you start that low, it'll mostly just be arithmetic
you should probably start at elementary algebra

>>11425086
You certainly aren't wrong. I'll think on it for a bit. Thanks all the same.

http://www.ms.uky.edu/~droyster/courses/fall98/math4080/classnotes/implfuncthm.pdf

If [math]f:\mathbb{R}^{n+1} \rightarrow \mathbb{R} [\math], why did he differentiated it n times instead of n+1 times?