/sci/ - Science & Math

>>12502293
Someone recc me a scientific field that I can practice asa hobby
NOW

>>12502296
Infinite Sums

A few years ago an anon posted a youtube video which contained a physics lecture in a early 2000s cgi enviroment with two babes as angels and demons. Everything was taught by these two in multiple 3D enviroments, it even had a paticular kind of music, I don't remember it well but I remember the essenece of it, so the music was distinct. Like I said the 3D enviroments were early 2000s looking, maybe late 90s? It was really mesmerising fellas, help me on my search, I need these online classes, I need to relearn it all through these angels and demons. They and they alone can truly teach teach physics. Pure, honest and sexy.

Does anyone have a link to that or even know what I'm talking about?

When it was discussing motion there were these 3D balls to demonstrate the motion. The babes were dressed like sluts I think. All 3D CGI.

I'm high sorry for my typing style right now. Very run on, I know.

is the indefinite integral a linear fucking image or not? answers on the internet are conflicting and wikipedia says that it maps to a quotient space (I understand this part) but it doesn't specify whether or why that prevents it from satisfying the definition of a linear image

>>12502296
electronics: buy your own pcb board and logic board
digital signals: learn some discrete mathematics and build some simulation filters that could be build with electronics
electrical motors and generators: you can buy yourself a battery and magnets and a conductive wire that you can bend and look up youtube videos on small motor models
aerospace: build yourself a hovercraft with a pizzabox, construction paper and a fan and battery, and calculate the moment of inertia of all items on the hover craft so it doesn't drag itself
there's a lot you can do.

>>12502798
[math]\frac{d}{dx}[aF(x)+bG(x)+c]=\frac{d}{dx}[aF(x)+c/2]+\frac{d}{dx}[bG(x)+c/2]=af(x)+bg(x) [/math]
I don't know brah looks linear to me. Maybe I misunderstood the question

we have this non-homogeneous ode
[math]\dot W\le -\frac{1}{2}[\frac{c_3}{c_2}-\frac{c_4}{c_1}\gamma(t)]W+\frac{c_4}{2\sqrt{c_1}}\delta(t)[/math]
its solution is
[math]W\le \phi(t,t_0)W(t_0)+\frac{c_4}{2\sqrt{c_1}}\int_{t_0}^t{\phi(t,\tau)\delta(\tau)d\tau}[/math]
where
[math]\phi(t,t_0)=\exp[-\frac{c_3}{2c_2}(t-t_0)+\frac{c_4}{2c_1}\int_{t_0}^t \gamma(\tau)d\tau][/math]
But when i try to solve it on my own with the integrating factor method for the particular solution
[math]f(D)W\le F(t)[/math]
where [math]f(D)W\le[D+\frac{1}{2}[\frac{c_3}{c_2}-\frac{c_4}{c_1}\gamma(t)]]W[/math] and [math]F(t)=\frac{c_4}{2\sqrt{c_1}}\delta(t)[/math]
so [math]W\le \frac{F(t)}{f(D)}\le\frac{\frac{c_4}{2\sqrt{c_1}}\delta(t)}{D+\frac{1}{2}[\frac{c_3}{c_2}-\frac{c_4}{c_1}\gamma(t)]}\le\phi(t,\tau)\frac{c_4}{2\sqrt{c_1}}\int\frac{1}{\phi(t,\tau)}\delta(\tau)d\tau[/math]
so i'm wondering why the [math]\frac{1}{\phi(t,\tau)}[/math] term disappeared in the particular solution?

>>12503092
[math]\frac{dW}{dt}=-\frac{1}{2}[\frac{c_3}{c_2}-\frac{c_4}{c_1}\gamma(t)]W+\frac{c_4}{2 \sqrt{c_1}}\delta(t)[/math]
[math]\frac{dW}{dt}=a(t)W+b(t)[/math]
[math]\frac{dW}{dt}-a(t)W=b(t)[/math]
[math]\frac{dW}{dt}e^{-\int_{t_0}^ta(s)ds}-a(t)We^{-\int_{t_0}^ta(s)ds}=b(t)e^{-\int_{t_0}^ta(s)ds}[/math]
[math]\frac{d}{dt}\left(We^{-\int_{t_0}^ta(s)ds}\right)=b(t)e^{-\int_{t_0}^t a(s)ds}[/math]
[math]W(t)e^{-\int_{t_0}^ta(s)ds}-W(t_0)=\int_{t_0}^tb(k)e^{-\int_{t_0}^ka(s)ds}dk[/math]
[math]W(t)=W(t_0)e^{\int_{t_0}^ta(s)ds}+\int_{t_0}^tb(k)e^{\int_{k}^ta(s)ds}dk [/math]
Which is the solution you were given if you use the inequality

>>12503138
[math]\frac{dW}{dt}=-\frac{1}{2}[\frac{c_3}{c_2}-\frac{c_4}{c_1}\gamma(t)]W+\frac{c_4}{2 \sqrt{c_1}}\delta(t)[/math]

[math]\frac{dW}{dt}=a(t)W+b(t)[/math]

[math]\frac{dW}{dt}-a(t)W=b(t)[/math]

[math]\frac{dW}{dt}e^{-\int_{t_0}^ta(s)ds}-a(t)We^{-\int_{t_0}^ta(s)ds}=b(t)e^{-\int_{t_0}^ta(s)ds}[/math]

[math]\frac{d}{dt}\left(We^{-\int_{t_0}^ta(s)ds}\right)=b(t)e^{-\int_{t_0}^t a(s)ds}[/math]

[math]W(t)e^{-\int_{t_0}^ta(s)ds}-W(t_0)=\int_{t_0}^tb(k)e^{-\int_{t_0}^ka(s)ds}dk[/math]

[math]W(t)=W(t_0)e^{\int_{t_0}^ta(s)ds}+\int_{t_0}^tb(k)e^{\int_{k}^ta(s)ds}dk [/math]

Which is the solution you were given

>>12503138
could you clean it up a bit

>>12503151
It's already quite bare bones imho

>>12503092
>>12503138
What do I do to understand this

>>12503157
i can't follow anything because the equal signs are misplaced plus the math tags are everywhere?

>>12503163
latex editor sucks bro. the procedure is a basic ODE trick. Write it down yourself equation by equation, the passages are crystal clear imho

>>12503176
oh i think i get it, but why is my method not suitable, especially for the particular integral?

>>12503138
In your last equation
[math]e^{\int_{t_0}^ta(s)d(s)}[/math]
is supposed to cancel the last term, where did you get the
[math]e^{\int_{k}^t(s)d(s)}[/math] term from?

>>12503138
[math]e^{\int_{t_0}^ta(s)d(s)}[/math]
is supposed to cancel the last term, where did you get the
[math]e^{\int_{k}^t(s)d(s)}[/math]
term from?

>>12503180
The inverse term actually appears also in my solution. thing is you have to manipulate the exponential directly into the right hand side integral to come up with the solution you were given.

>>12503228
in your last equation
[math]e^{\int_{t_0}^ta(s)d(s)}[/math]
is supposed to cancel the last term, where did you get the
[math]e^{\int_{k}^t(s)d(s)}[/math] term from?

>>12503224
[math]e^{\int_{t_0}^ta(s)ds-\int_{t_0}^ka(s)ds}=e^{\int_{k}^ta(s)ds}[/math]
Because [math]t_0 \leq k \leq t[/math]

>>12503228
>>12503238
This is what I mean

>>12503238
oh i see my mistake, when you integrated the right hand side with respect to k, the varible of integration in the integrating factor changed from t to k, that's some neat trick on integrating an integral, i understand it, but i still can't wrap my head around when its allowed, i suppose you could make
[math]e^{\int_{t_0}^ta(s)d(s)}=g(t)[/math]
then since you are integrating with respect to k
[math]\int_{t_0}^tg(k)dk[/math]
where [math]g(k)=e^{\int_{t_0}^k a(s)d(s)}[/math]

>>12503160
study calculus and understand it well then go for odes

>>12502293
sex with frederica bernkastel

Should I go through MIT's OCW program? I took DiffEq this semester but not really happy with my understanding and thinking about "retaking" Calc III and DiffEq on MIT's cool site

Why can't i eat seafood ? Ever since my birth, before i could even speak according to my mother, i've not been able to stomach seafood. the best i can manage is nibbling on a fish finger, usually before violently throwing up. I don't like to consider myself a picky eater because i will eat almost everything else, even if i don't enjoy it. Yet, I get the urge to vomit as soon as i'm in close proximity to ANYTHING that lives in water fresh and saltwater fish, clams, seaweed, you name it...)
For all its worth, my father also hate seafood, but nowhere close to my level. the rest of my family enjoys seafood.
I've tried forcing myself, to learn how to enjoy it (or at least stand it) by buying nothing but seafood, and cooking some everyday for one full week but i ended up eating close to nothing (a few bites over a whole week, at best).

Why is that ? is it "fixable" ? I know i'm missing a lot. It makes travelling a pain, and i'm missing a bunch of delicious meals and fun activities : I can't camp for long because food supply is always a problem since fishing is useless, spearfishing and fishing disgusts me etc...

Is there any theory that defines zero as both an empty set and the concept of infinity?

This is retarded but aigth.
My ESL ass didn't understood what this said at all, but I'm trying to solve the Purple thing.
The Chemical Equation is Divided by half so [math]\Delta H[/math] should too.
Like this.
[math]2H\:_2+\:O_2\:\Rightarrow \:2H_2O\:\:\:\:\:\Delta H=-483.6kJ[/math]
[math]\frac{2H\:_2+\:O_2}{2}\:\Rightarrow \:\frac{2H_2O}{2}\:\:\:\:\:\Delta H=\frac{-483.6kJ}{2}[/math]
[math]H\:_2+\:\frac{1}{2}O_2\:\Rightarrow \:H_2O\:\:\:\:\:\Delta H=-241.8kJ[/math]
Am I right?

>>12505235
I didn't even Answered lol. No, I shouldn't expect the same value for ΔH

>>12504610
Try Strang's 18.085 course instead it's a 2 part course on applied DiffEq you don't need 18.03 or w/e. Try this too: https://mitmath.github.io/18337/

More sites like these? Any field other than humanities is acceptable.
https://organicchemistrydata.org/
https://roymech.org/
http://hyperphysics.phy-astr.gsu.edu/hbase/

I'm not sure if this is the right board for this sort of thing, but I'm trying to this out. I have never done anything cryptography related, but I think it's a substitution cipher because the symbols seem to correspond with latin characters.Unfortunately one of the clues is throwing a wrench into things for me because it's in chinese. I'll attach the clue to my next post.

This clue is a problem because I don't know chinese and have no way of verifying a machine TL. I am also assuming it is in chinese because it was made by chinese person.

I got the characters from OCR, they are 反噬
Google TL spits out "Fǎnshì" for chinese and "Hanzei" for japanese. I am assuming the chinese reading because the first three symbols
corresponded to "ihs" in the other clues, and were similarly written out right to left.

For reference, here's the first clue

The second clue

And here's the last clue I have. I'd appreciate any help in untangling this satanic wheel of fortune puzzle.

I'm currently an applied math major. The field of computational linguistics is interesting to me but I don't have time to minor or double major in Linguistics (I am taking an Introductory Linguistics class). How do I study linguistics to the point where my knowledge is relevant to being hired for projects/jobs involving computational linguistics?

I want to know how many photos a regular phone camera can take until it fails.
I'm not asking about hard drive space or battery... say I have petabytes of space for data (or the images upload to the internet) and I keep my battery charged. If I keep the battery charged and switch out microSD memory sticks is 10 million photos possible to take?
What are the first things that might break with a phone camera?

>>12505595
bumping

Why don't I die if i have mask on?

im trying to burn pieces of paper to create the most smoke possible.

why is it that if the paper caught on fire and has a flame going, no smoke is produced but smoke is produced if it's just glowing and ember-ing with no flame?

Scientifically speaking, how would one restore anal plasticity? Asking for a friend.

>>12506282
also can a smoking piece of cardboard ever reignite with flame on its own?

>>12506282
Smoke consists of carbon particles (soot); this indicates incomplete combustion. When a hydrocarbon burns with sufficient oxygen, the oxygen bonds with hydrogen to form H2O (water vapour) and with the carbon to form CO2 (carbon dioxide). If there's insufficient oxygen, bonding with hydrogen is preferred. Either the carbon bonds with only one oxygen to form CO (carbon monoxide) or with no oxygen resulting in carbon particles.

When a solid burns, the heat from the flame results in pyrolysis, causing solid material (e.g. long-chain hydrocarbons like cellulose) to decompose into more volatile chemicals which will be in gaseous form. When something is smouldering, the gases produced by pyrolysis don't move far from the surface of the solid material, limiting access to oxygen. The CO2 and H2O produced by combustion blanket the fire, choking the supply of oxygen.

Basically, a strong fire helps drive airflow (both by convection and by increasing pyrolysis increasing the pressure of the combustible gases), resulting in a stronger fire. I.e. the process perpetuates itself. This is why it's common to blow on a smouldering fire to light it; the added oxygen increases combustion to the point where the fire can sustain itself.

>>12506315
Plastic deformation is irreversible by definition. This is why gay sex is immoral in so many cultures.

>>12506218
Covid is most often found in droplets which are too big to go through a surgical mask. But you will still die because people are this retarded with their masks:

https://youtu.be/EBdB8AACBjU

And no mask will save you from that.

>>12506464
really feeling like a brainlet here haha.

i probably can't understand pyrolysis, incomplete combustion, what happens during smouldering, what convection is and how it can be used.... etc. News to me that H2O vapour is produced during combustion. weird imo

it seems simple but i can't quite wrap my head around all of this. thanks for exaplining a lot in your post though.

i don't even understand what smoke is anymore. are those carbon particles a gas now? durr what are elements even? i just discovered this "phase at STP" variable for elements.
do the carbon particles/soot have a chemical formula specific to what's burning or smouldering? is there CO being produced by burning cardboard/wood? what about smouldering cardboard?

so you can light a fire from smouldering material with like convection or what? that was a big part of your post i wanted to understand. how blowing on smouldering fire lights it. but i could probably find a video of it and be satisfied with my understanding. lol i just dont get any of this
you've helped a lot so don't feel obligated to waste your breath on responding to this confused post

What would be a good university to study Mathematics in Europe? I'm about to finish my compulsory education in Spain but I don't want to stay in this shithole.

>>12506616
ETH Zürich

Is there any legitimate reason to not agree with physicalism when it comes to human consciousness?

>>12506616
math is not to be taken lightly as there's a high dropout rate. Study math locally at a good uni, and if you're good enough get a masters from a top uni. Orherwise you can change fields without wasting too much money.

If you're rich none of this applies obviously

Ever since GR (book by Carroll) I have been somewhat puzzled about the concept of tangent spaces, and I want this cleared up. I understand how tangent vectors can be generated by taking derivatives of curves through a point. But one thing that has always appeared strange to me is how tangent vectors can act on functions.

Perhaps addressing the following distiction will make things clear. When I think of a vector space, I think of the thing we studied at calculus. Consider a scalar field [math]\phi[/math], then one can define a vector field as [math]V = \nabla \phi[/math]. This construction already looks familiar, as the coordinate basis is given by [math]\partial_\mu[/math], and [math]\phi[/math] is like the trial function with which the definition of the tangent space is constructed. I would almost go so far as to say that [math]\nabla = (\partial_x, \partial_y, \partial_z)[/math] /is/ a vector field according the differential geometry definition. At least, it looks a lot like one.

The point I'm trying to make is that it seems that differential geometry says that [math]\nabla[/math] is a vector field, whereas calculus says [math]\nabla \phi[/math] is a vector field. Does this make sense? How is this explained? I would be extremely grateful if someone could clear this up as it would strongly improve my intuitive understand of GR.

>>12506832
>But one thing that has always appeared strange to me is how tangent vectors can act on functions.
let [math]\gamma(t)[/math] be a curve representing some tangent vector [math]X[/math]. then derivative of [math]f[/math] in the direction [math]X[/math] is [math]Xf = \frac{d}{dt}\mid_{t=0} (f \circ \gamma)(t)[/math]. note that this is a map [math]\mathbb{R} \to \mathbb{R}[/math] so it makes sense without going into local coordinates.

>>12506610
> i don't even understand what smoke is anymore. are those carbon particles a gas now?
No, just lots of really small solid particles. Like fine dust.

> do the carbon particles/soot have a chemical formula specific to what's burning or smouldering?
No, it's just carbon.

> is there CO being produced by burning cardboard/wood? what about smouldering cardboard?
Burning any hydrocarbon will produce CO if there isn't enough oxygen or the combustion isn't efficient. The main cause of death in house fires is CO poisoning (in an enclosed space, oxygen is extremely limited once a fire gets going).

> so you can light a fire from smouldering material with like convection or what? that was a big part of your post i wanted to understand. how blowing on smouldering fire lights it.
Blowing on something that's smouldering can cause it to catch fire. That's often necessary to start a fire with sparks and tinder; the sparks will only cause the tinder to smoulder, but blowing gently on it makes it catch fire.

Convection is airflow caused by the fact gases expand when hot, making them less dense, so hot air (or other gases, e.g. CO2) rises. In a fire, the gases produced by combustion rise and air is drawn in to fill the space. If something is only smouldering, there won't be enough convection to drive the airflow.

>>12507003
thank you so much anon. especially if you're same anon. clears up a lot of my confusion.

>The main cause of death in house fires is CO
mmm good to know

>but blowing gently on it makes it catch fire.
ohhhhh. the confusion came from my IRL experience of trying to blow on smouldering cardboard with no flames resulting but im kind of starting to see that theres a technique and more science involved with learning to start flames this way

>>12506869
I understand how a derivative along a curve is used to define a tangent vector. What I'm not seeing is what role [math]f[/math] plays in this. It looks to me as an analogue of a scalar potential. Just like [math]\nabla[/math] acts on a scalar potential and makes it into a vector field, [math]X[/math] (which is a linear combination of derivatives) acts on the function [math]f[/math]. Are those not analogous? And if not, how should I think about tangent vectors acting on functions?

>>12507147
(I assume you understand that this nabla is defined only when there's also a metric, otherwise we have only exterior derivative.) The nabla is a map which inputs a function and outputs a vector field. So it's a map [math]\nabla \colon C^{\infty}(M) \to \mathfrak{X}(M)[/math].

Every tangent vector acts on functions by directional derivative. A single vector acting on a function gives a single number. A vector field acting on a function gives another function. So every vector field [math]X[/math] can be understood as a map [math]X \colon C^{\infty}(M) \to C^{\infty}(M) [/math].

The analogy is that both are linear maps between infinite dimensional vector spaces.

Here's my stupid question:
Why does the /sqt/ have the highest quality questions on /sci/?

>>12507291
shitposters want attention so want to be an OP.

Explain differential and partial differential equations to me like I'm 5 years old.

would you watch a youtube channel that was just 24 hours of hololive karaoke archives on shuffling playlist?

How do I represent a ray extending from the origin outwards infinitely in the complex plane rotated by angle theta counter-clockwise from the positive reals in the form [math]f(x)*e^{i\pi *g(x)}[/math]?

>>12508107
f(x)=x
g(x)=theta
For x>=0 (otherwise the ray is a line, extending to infinity in both directions)

>>12507504
You can't explain PDEs to a 5yo. And you can't realistically "explain" the topic in the space of a post. Differential equations are equations involving variables and their derivatives. On the question of how to solve such equations, enough has been written to fill a library.

>>12508341
>>12508341

Can we take the alphabet as an axiom?

>>12508668
The alphabet no but alphabetic order yes.

Are there animals who can look at a picture of an object and understand that it's not the actual object?

Please help me make a fisher matrix

>>12502293
How do I write a function that has the curvature of y=x^2, but flips when x<0 like y=x^3?

>>12509644
f(x)=x^2 when x>=0, -x^2 when x<0

>>12509669
lmao analysts btfo

What is a set, mathematically speaking?

>>12509644
[math]\left[ \frac{x}{2} + \frac{\sqrt{x^2}}{2} \right]^2 + \left[ \frac{x}{2} - \frac{\sqrt{x^2}}{2}\right]^3[/math]

>>12509691
copy paste into preview, it works there

Ok bros analysis time

Assume [math]g_n(x),g(x) \leq M, \forall x \in [0,1], \forall n \in \mathbb{N} [/math] and all such functions are integrable.

Assume [math]g_n \to g[/math] uniformly on any [math][0,a],0<a<1[/math].

Prove that [math]\lim_{n \to \infty}\int_0^1g_n=\int_0^1g[/math]

I sketched this:

[math]\lim_{n \to \infty}\int_0^1g_n=\lim_{n \to \infty}\lim_{m \to \infty}\int_0^{1-1/m}g_n \stackrel{(1)}{=}\lim_{n \to \infty}\int_0^{1-1/m}g=\int_0^1g [/math]

where (1) is by the assumption of uniform convergence.

I went deeper and by using also the boundedness I also have

[math]\lim_{n \to \infty}\int_0^1g_n=\lim_{n \to \infty}\left[\int_0^ag_n+\int_a^1g_n\right]=\int_0^ag+\lim_{n \to \infty}\left[\int_a^1g_n\right]=\int_0^ag+\lim_{n \to \infty}\left[\int_a^{(a+1)/2}g_n+\int_{(a+1)/2}^1g_n\right]=\int_0^{(a+1)/2}g+\lim_{n \to \infty}\left[\int_{(a+1)/2}^1g_n\right][/math]

and so on by bisecting the remaining interval I get the result. Is it working as an argument?

anyone got good SQL textbook recs? I can't seem to find anything online besides shitty 30 IQ tutorials online

If I'm a biology researcher, is it worth learning programming/coding?

If it is, what's a free online resource I could use that could get me to be a decent coder in my spare time?

>>12509754
Oh I see that I assumed a big one, that is the integrals of type
[math]\lim_{n \to \infty}\int g_n[/math]
always exist in these arguments.
I won't avoid the epsilon delta arguments anymore.

>>12509754
>>12509991
Uniform convergence implies convergence of integrals.
For a close to 1, int_a^1 g_n is small for all n.

This will look a lot like a shitpost, but it's not. Please hear me out, some futa doujins seriously got me thinking.

How long could the average human survive on a diet consisting solely of semen and urine? Assume both resources are plentiful and the semen is healthy and rich in whatever nutrients normally found in semen. What kind of changes in health would you expect from someone on this diet, if any at all?
Bonus: What if you add faeces and/or sweat (kinda like how goats and hamsters have salt licks) to the diet? Would either increase lifespan and nutrition or decrease it?
I am but an autistic engineering senior who knows nothing about biology and if anyone is willing to respond I'd greatly appreciate it.

>>12510181
What kind of 3rd rate engineering are you learning. You should know about efficiency retard. If the body extracts such little nutrients from all the food we eat and produces a ton of shit, how much protein would you think is in the semen that you are feeding them. A better question is how much semen would you need to feed a donor to produce the same amount of semen without killing him from malnutrition. Your retarded idea is like the people who think they can produce free electricity because they don't understand efficiency.

>>12510201
Like I said, assume the semen is PLENTIFUL. The semen (and other resources) aren't coming from the person on the diet, I should've clarified that.
Assume that there's just an infinite amount of dickgirls ready to cum, piss and shit so that person X can eat and drink as much as they please.

What's some fun basic math things I could learn over break? I know only single variable calc and linear algebra.
Should I study more calculus? I kinda wanted to learn something like graph or number theory, maybe asbtract algebra

>>12510412
what happened to that boar?

>>12510181
>>12510222
How long could the average human survive on a diet consisting solely of semen and urine? Assume both resources are plentiful and the semen is healthy and rich in whatever nutrients normally found in semen. What kind of changes in health would you expect from someone on this diet, if any at all?
Bonus: What if you add faeces and/or sweat (kinda like how goats and hamsters have salt licks) to the diet? Would either increase lifespan and nutrition or decrease it?
I am but an autistic engineering senior who knows nothing about biology and if anyone is willing to respond I'd greatly appreciate it.
More likely to die of sepsis before starvation. I'd give it a month tops.

How the fuck does quantum mechanics have T symmetry if randomness is involved? Say you break a glass. OK, In newtonian mechanics you may unbreak it by reversing the momenta of every scattered piece. That makes sense. But if fundamental randomness is involved in motion of those pieces and you reverse the time, you depend on getting the same opposite random numbers to get. So glass isn't exactly like nuclear decay.

Think of it like this. You have a dice. A particle goes up, down, right, left, forwards, backwrads if you roll 1, 2, 3, 4, 5, 6 respectively. You do this a billion times. How is this process time reversible when you depend on rolling specific numbers? If you roll, 2, 2, 4, 4, 5, 1,... you have to roll 1, 1, 3, 3, 6, 2,.... Since what you'll roll is fundamentally random, it's likely you will not roll those numbers and you'll end up in a different universe. Therefore quantum mechanics can't be time reversible (for long periods of time).

>>12502296
Comparative genomics of Coronaviridae using bioinformatics

Baby measure theory. Let [math]M(X)[/math] be the space of all finite signed measures on [math]X[/math] endowed with the total variation norm [math]\lVert \mu \rVert = |\mu|(X)[/math]. Given a cauchy sequence [math](\mu_n)_n \subset M(X)[/math], we define [math]\mu(A) = \lim_n \mu_n (A)[/math] for all measurable [math]A[/math].

I've shown that [math]\mu[/math] defined as above constitutes a finite signed norm, but I'm struggling to show that [math]\lVert \mu_n - \mu \rVert \to 0[/math]. I'd appreciate any ideas that come to your mind

>>12506616
Karlsruhe

>>12509975
>If I'm a biology researcher, is it worth learning programming/coding?
Yes any python or R course will do.

>>12510680
Any suggestions?

I have two questions
1) why is everyone repeating the same narrative on covid-19. Who are the lefties parroting?

2) Which book should I use to learn lambda calculus and type theory.

>>12510425
2

>>12510425
thanks

>>12510181
The contents and nutritional value of semen itself probably depends on the diets of those who produce semen and how recently and often they ejaculate. Probably a detailed scientific study would need to be conducted or a nutritionist would have to look into it deeply to find the actual time length.

However, I think the time span would be surprisingly long (at least 1-2 months) without significant weight loss at all. Adding sweat, piss and shit to the diet (after it's been pasteurization) can extend this period by helping with hydration in which case drinking water could be obviated as well. Eventually though, some supplements would be needed since the diet is likely not diverse enough (even if those who produce semen and urine eat different things (and it's all mixed together) in order to diversify it)

I don't see how to turn it from the top equation to the bottom equation.
Could anyone show it with more steps?

>>12510950
I mean, if it's possible to do it at a glance
If one has to solve the equation to turn it into that form then I know how to do it, but I thought that there's some quick trick

>>12510950
>>12510964
There is no trick except lots of experience with expanding polynomials and spotting the pattern. Noticing that 12 = 7 + 5 is about it.

The square root maps the ray 0 to ±sqrt|x| and the ray pi to ±isqrt|x|, alternating for each pi rotation.

What is the analogous function that alternates like the above for each pi/3 rotation, mapping the rays 0, 2pi/3 and 4pi/3 to ±sqrt|x| and the rays pi/3, pi and 5pi/3 to ±isqrt|x|?

>>12511025
okay I see it now, thanks

>>12502293
Help a brainlet out, /sci/.
How is sin(θ) defined? And how is there even a ratio possible without a triangle? Is there some sort of base triangle used for this?

>>12511246

The speed of light in a "vacuum" is ~2.999 x10^8 m/s. Is this a "true" vacuum, or a vacuum that accounts for quantum fluctuations?

It's said that speed of light is the same in every reference frame and such, but how is this compatible with "speed of light through a dense medium is slower than through a vacuum"?

>>12511255
Thanks.

Does the universe 'know' what state two entangled electrons are or not until one of them breaks the entanglement?

Can experiments really find this potential-energy function? Is the author citing a famous paper or something?

>>12511256
the speed of light is defined to be that speed. if quantum fluctuations affect it then it has never been observed.

>>12511256
because it's not the original lightwave which leaves the material that entered it. the incoming lightwave interacts with the electrons in the material to create a lightwave with a slower group velocity.

>>12510950
The best is to guess. 1 is a root and also a root of its derivative, so it's a double root. So you guess f=gh with g(1)=h(1)=0 and the sum of their degrees = 12.

>>12510950
[math]x^{a+b}-x^a-x^b+1 [/math]
[math]x^{a+b}-1\cdot x^a- 1\cdot x^b+1\cdot 1 [/math]
[math]xy-zx-zy+zz [/math]
[math](x-z)(y-z)[/math]
[math](x^a-1)(x^b-1)[/math]

>>12510664
When people say there is time reversal symmetry they are referring to the unitary (coherent) dynamics of quantum mechanics, not the projective measurement aspect.

>>12510664
All time symmetry in QM means is that some final state can only be arrived at from one initial state. That is still true even with random measurement.

>two people want to flip a coin for some purpose
>they don't have any coins
>what do?
Are there any probability games for which there is a ~0.50 chance of winning or losing that can be done with only two people and without an object? Such as, pick a number 1 or 2. But whoever is initially thinking of the number can just lie.

>>12511873
> Such as, pick a number 1 or 2
They write down, scratch in the dirt, whatever means available their answer first without the other person seeing. If both numbers are the same person 1 wins, if different the other.

>>12506832
Sounds like you're just confused about the language. A rough analogy I would give is that, in lower-level texts (and in physics), people say that [math]f(x)[/math] is a function. But obviously that's wrong, because [math]f : X \to Y[/math] is the function, and [math]f(x) \in Y[/math] is just a particular value of the function.
Likewise, you might imagine that when intro calc texts call [math]\nabla \phi[/math] a vector field, they're being imprecise (and borrowing language from the physicists). Once you get to differential geometry, the authors assume some level of maturity from the students and so they can teach you what these words really mean.
Of course this analogy kinda fails because your initial premise is also incorrect. [math]\nabla[/math] is not a vector field, because (in the precise definition), a vector field is linear map between the ring of smooth functions on the manifold to itself. [math]\nabla[/math] instead takes a smooth function to a tuple of smooth functions. So the vector field is really the "components" of [math]\nabla[/math], except that "components" is poorly defined because such language is chart-dependent. Of course, the whole reason differential geometry works is because at the end of the day, the object you're looking at (the affine connection) is indeed chart-independent. But it's messy to properly define things in terms of components etc (part of which I absolutely detest physicists' conventions with regards to differential geometry).

[Also, the affine connection itself is yet again NOT a vector field, but rather a map sending 2 vector fields to 1 vector fields. Therefore the image of the affine connection is a vector field, but this is not your "[math]\nabla[/math]" as defined from calculus III class.]

>>12510950
7+5=12
Let a=x^5, b=x^7
=> ab-a-b+1=0
=> a(b-1)-(b-1)=0
=> (a-1)(b-1)=0
=> (x^5-1)(x^7-1)=0

Hey guys. So my son (6 y.o.) heard about the Christmas star and now he's really into stars and planets. He asked me something kind of surprising the other day. What keeps planes from crashing into the moon? I wasn't sure how to respond in a way that he could understand. How would you explain it?

What's a good crash course/sampler course for statistical mechanics? Just to see what it's like, what it covers, common eqn's and applications
I really don't want to watch 40 hours of MIT lectures, or start another 700+ page textbook

>>12511954
what is the proper book for DG?

>>12511509
>>12511522
>>12511961
Thanks

>>12512210
Moon is very very far away, and planes don't fly that high.
You could show it to him with a globe and some other sphere for the moon

>>12512210
gravity is deformation of spacetime and planet is heavier than the moon, so if anything it would be the moon crashing on the planet

second, the mooon has too much angular velocity to leave earth's orbit, but it has enough to not be crashing on the moon.


it would be nice to see for instance if the sun gets twice as heavy all of a sudden, if the moon would crash on it (or at least leave earth's orbit)

or jsut find how heavy should the sun be to get the moon to leave earth.

>>12513135
a 6yr old would understand none of that but I still think they comprehend gravity better than you do.

>>12510419
>>12510412
Probably lived a cute and fulfilling life
But pls respond

How do I stop procrastinating
I’ve had one month to study for my finals and so far I have procrastinated two weeks away
I think studying at home is part of the issue but I cannot go to a library because libraries are closed
I keep telling myself I will not procrastinate but I find some way to procrastinate
I’m so fucked please help

>>12509929
I kind of like SQL Primer by Rahul Batra, but it doesn't cover all that much.

Got an Arduino kit for Christmas and I'm having a lot of fun with it. But if I want to make stuff a bit more advanced, I'll have to learn how to solder. What's the best way/kit/etc a brainlet like me can do this?

Scientifically speaking, why am I continuously degenerating? Why can't I do anything right?

>>12513887
Can any grads/postboomers help me with this? It's classified as a statement of purpose btw, can't remember if I mentioned in original post.

>>12514684
You'd probably be best off in >>12487940

>>12511339
this question is super incoherent, but I'm assuming you're asking "is the result of the measurement predetermined" and the answer to that is arguably unknown, although we are pretty sure we can't predict it with current theory.

>>12513655
If you're studying with notes and a textbook, shutdown and unplug the computer. If your studying requires a computer, only launch the applications which are needed, set a timer, close tabs that are unrelated. No opening random bullshit. You're on the clock.

>>12513142
yes it's normal for an undergrad like you to get filtered

>>12513809
cheap iron, at least 60W with temperature control knob (~$15). Many of these kits come with a small spool of solder and some tweezers.
Learn basic analog electronics: active/passive filters, opamps, cmos logic chips, RC timing/555 circuits, and get a breadboard

>>12505577
>>12505585
>>12505589
>>12505593
Its just a substitution cypher read right to left. Latin alphabet

>>12505589
except for this one is left to right
Check to see if text is boustrophedon

A state machine is just a mess of "if-then-else" statements, right?

>>12513655
>>>/adv/

>>12512663
Thanks for the idea. That was a fun little science experiment. I measured it all and showed him planes only fly a few millimeters off the globe while the moon is almost a meter away.

>>12514829
I fall under the latter case. Thanks for the advice I will try that
>>12515344
I have browsed /adv/ before deciding to ask here. It’s a board about relationship advice

>>12515304
No, it's a 2D array, with state and input as indices and states as values:

for input in ...:
....state = table[state][input]

You may have a switch(state) statement which is invoked on each iteration, or simply some test based upon the final state. E.g. a regex matches if the final state is an accepting state.

How many qubits to describe elementary particles like an electron??

Is this idea crazy: Couldn't the base level of space time just be an infinite net of planck length sized black holes, buttressing themselves against each other with their own hawking radiation, that we can't detect because the entire system is in perfect balance?

Dropout who only has classical physics knowledge going into electrical engineering in 2 months, what should I brush up on?

>>12515853
No. Apart from the fact that gives the 'vacuum' a fuck ton of energy any planck length scale black hole would evaporate almost instantly.

>>12515865

Yes. But what if it was constantly being hit by hawking radiation at the same rate it is losing it?

And isn't there supposed to be a fuck ton of energy in the vacuum that we don't see for some unknown reason?

>>12515885
Despite what you have read or seen in some pop-sci article or video Hawking radiation isn't to do with particle / anti-particle creation, it is thermal radiation, so your logic doesn't work.

To be more precise the energy in your scenario would be usable and hence measurable. That is not the case for the true vacuum.

>>12515891

Why does it matter what form the energy takes? Also, don't smaller black holes radiate at higher frequencies? They'd be hitting each other with like... maxGamma.

Like what i'm picturing here is not empty space with some black holes in it. I'm picturing WALL TO WALL black holes. They're on each others event horizons. All smashed as closely together as they can get. Constantly pushing each other away with radiation pressure, unable to fully evaporate because they absorb as much energy as they lose.

>>12515904
Sounds more like they'd just all collapse into a single large black hole.

>>12515913

They wouldn't have much mass. We're talking about planck scale. They have the MINIMUM amount of energy to form black holes. And they'd be hitting each other with as much radiation pressure as it is possible to make.

>>12515917
Bruh. They have enough mass to form a black hole no matter how small. That's all the requirement needed.

>>12515928

Okay? I mean you do know that black holes aren't necessarily strong outside their event horizon, right? Like they're strong enough at their event horizons to catch light, but beyond that, they're just as attractive as the same amount of mass. Which isn't a lot because it's the minimum.

>>12515934
You think all these micro-blackholes would remain stationary?

>>12515936

I think they would roll around each other. If they are all planck length, then there would be holes in the network, through which any given bh might lose some energy to not exactly the next neighbor.

If they're not all planck length, then it might be possible for it to be like a fractal, with larger beads surrounding successively smaller beads.

I don't know the math for this, but there is probably an integral that could calculate how much mass is in "empty space" if this were true, based on knowledge of the energy in a planck scale black hole, and what size each next level down would be.

>>12515986
You mean something like Mass = Density x Volume ? No. Nothing like that exists.

>>12516000

Okay, but like dude, we're adding up an infinite number of things here.

>>12516006
No you're not. You would do it per unit-volume.

>>12516008

If each planck scale black hole is buttressed by smaller black holes, all the way down to infinity, we are adding up an infinite number of things. I don't know exactly how to figure out what size each level down would be. Perhaps there is some fundamental frequency, and each size down is smaller by a specific note.

Woops. Was trying to keep that off.

>>12516015
who's this absolute boomer

how do I compare
[math](2^6-1)^5[/math] and [math](2^5+1)^6[/math]

>>12516193

And after i went to the trouble to name myself something funny~

>>12516355
With a <

>>12515498
wholesome

>>12516355
https://www.wolframalpha.com/input/?i=%282%5E6+-+1%29%5E5+%3E+%282%5E5%2B1%29%5E6

>>12516355
[math](2^6 - 1) ^5 = \sum_{i = 0}^5 {5 \choose i}(-1)^i2^{6 + 5 - i}[/math]
while
[math](2^5 + 1)^6 = \sum_{i = 0}^6 {6 \choose i} 2^{5 + 6 - i}[/math]
Its pretty obvious which is the larger one.

>>12516355
[math](2^6-1)^5<2^{30}[/math]
[math](2^5+1)^6>2^{30}[/math]
Hence, [math](2^6-1)^5<(2^5+1)^6[/math]

>>12516355
Well we have that
[math](x^{n+1}-1)^n=(x-1)^n\left(\sum_{k=0}^n x^k\right)^n =_{n=2} \left(\sum_{k=0}^n x^k\right)^n[/math]
which further expands as a "relatively simple" multinomial expression (which have binomial coefficients with products of k! in the denominator, but all the x-terms are very basic)

and on the other hand the standard binomial expression
[math](x^n+1)^{n+1} = \sum_{k=0}^{n+1} {{n+1} \choose k} x^{n+(n+1-k)} [/math]
and you gotta e.g. argue that those binomial coefficients are each always smaller.

There's a chance that if you write down the multinomial expression explicitly, you can compare it to n+1 over k and find it's true on the nose.

There might also be a smarter way, I don't know..

>>12516355
Well we have that
[math](x^{n+1}-1)^n=(x-1)^n\left(\sum_{k=0}^{n+1} x^k\right)^n =_{n=2} \left(\sum_{k=0}^{n+1} x^k\right)^n[/math]
which further expands as a "relatively simple" multinomial expression (which have binomial coefficients with products of k! in the denominator)

and on the other hand the standard binomial expression
[math](x^n+1)^{n+1} = x^n \sum_{k=0}^{n+1} {{n+1} \choose k} x^{(n+1-k)} [/math]
and you gotta e.g. argue that those binomial coefficients are each always smaller.

There's a chance that if you write down the multinomial expression explicitly, you can compare it to n+1 over k and find it's true on the nose.

>>12516415
but this is actually the smart way

>>12516402
>>12516414
>>12516415
>>12516428
Have literally none of you heard what a log is?

Scientifically speaking, why does starraisin's art do the things it does to my dick?

>>12516625
your a weeaboo

>>12516612
How would logs help here? log((2^6-1)^5)=5*log(2^6-1) and log((2^5+1)^6)=6*log(2^5+1), but there are no further simplifications available. If you fudge the ±1, you can show that they are slightly below and slightly above 30*log(2) respectively, but >>12516415 does essentially the same thing but without introducing logs.

>>12516415
This is why I both love and hate maths. Unless you know the 'trick' to answering a question you score zero on the exam.

>>12516657
No idea what was he thinking.
You can slightly improve the estimates, I suppose.
[math]\displaystyle \log (2^6 - 1)^5 = 5 \log 2^6 - 1 = 5 \left[ \int_{1}^{2^6} \dfrac{dx}{x} - \int _{2^6 - 1}^{2^6} \dfrac{dx}{x} \right] \approx 30 \log 2 - \dfrac{1}{2^6}[/math] and [math]\displaystyle \log (2^5 + 1)^5 = 6 \log 2^5 + 1 = 6 \left[ \int_{1}^{2^5} \dfrac{dx}{x} + \int _{2^5}^{2^5 + 1} \dfrac{dx}{x} \right] \approx 30 \log 2 + \dfrac{1}{2^5 + 1}[/math]

>>12516742
Forgot to adjust the numerators.
[eqn]\displaystyle \log (2^6 - 1)^5 = 5 \log 2^6 - 1 = 5 \left[ \int_{1}^{2^6} \dfrac{dx}{x} - \int _{2^6 - 1}^{2^6} \dfrac{dx}{x} \right] \approx 30 \log 2 - \dfrac{5}{2^6}[/eqn] [eqn]\displaystyle \log (2^5 + 1)^5 = 6 \log 2^5 + 1 = 6 \left[ \int_{1}^{2^5} \dfrac{dx}{x} + \int _{2^5}^{2^5 + 1} \dfrac{dx}{x} \right] \approx 30 \log 2 + \dfrac{6}{2^5 + 1}[/eqn]

suppose [math]G[/math] is of order [math]pqr^2[/math] where [math]p,q,r[/math] are distinct primes, all [math]\ge 3[/math]. suppose also that [math]r > \frac{pq-1}{2}[/math]. how can I show [math]G[/math] is solvable?

I've been screwing around with the Sylow theorems, trying to extract some meaningful info about [math]G[/math]'s structure, but frankly it feels like strolling blindfolded in a forest. I don't see what I'm 'supposed' to do here. any hints would be appreciated

If I start off with a meromorphic function [math]f(z)[/math] and then Taylor expand it at some [math]a[/math] where [math]f[/math]'s holomorphic, I get a power series that's convergent in a disk [math]D = \{ z \in \mathbb{C} : |z - a| < r\}[/math].
Assuming [math]f[/math]'s domain contains [math]B - \partial D[/math] for some open set [math]B[/math] containing [math]D[/math], does [math]f[/math] necessarily have a singularity/pole in [math]\partial D[/math]?

>>12502293
I was born with a very severe concussion and I was clamped immediately after birth. I also abuse alcohol and have had a very unhealthy sleeping schedule for years. I started drinking as a teenager

Maybe I could have been a genius, lol

Do European schools offer stipends to graduate students like American ones do?

If a planet is one light-year away from the Earth, the time it would take for light to reach it would be a year, from the perspective of someone on Earth. However, what if it's a spaceship traveling at the speed of light, what time it would take for someone inside the ship? Using Lorenz transform we get zero, but that cannot be right.

>>12517784
Some of them do and you can often check at the university's website. Here's the pay for a PhD at the University of Antwerp, for instance: https://medialibrary.uantwerpen.be/oldcontent/container2377/files/Salaries/20201006_barema%20website_BAP_Engels.pdf

It's on the second page.

Fuck programming, statistics and quantshit, I just want to study geometry and microeconomics.

>>12518629
What is your question?

>>12518168
It is zero but something with mass can never travel at the speed of light. Also note that you would have to accelerate to some speed then decelerate to get there. That takes time.

>>12517041
The number n of r sylow groups divides pq, which is less than 2r+1. Hence, n is either 1 or r+1. Now pq, as a product of odd numbers, is not even, so neither is n which devides pq. Since r+1 is even, n=1.

Could I represent a path in a graph as a single node? Is there some convention for this?

>>12502351
Physics videos by eugene Khutoryansk
He's still doing videos, best place to learn shit

>>12519260
https://www.bing.com/videos/search?q=physics+videos+by+eugene&ru=%2fsearch%3fq%3dphysics%2bvideos%2bby%2beugene%26PC%3dU316%26FORM%3dCHROMN%26adlt%3dstrict&adlt=strict&view=detail&mid=B666822CEDED4D154EF2B666822CEDED4D154EF2&&mmscn=vwrc&FORM=VDRVSR

>>12518842
thanks anon, I feel so very stupid for not seeing this myself.

Suppose [math]G[/math] admits a Jordan-Holder series and [math]N\lhd G[/math]. Do any of [math]N, G/N[/math] necessarily admit a JH series as well? (Assume all groups are infinite, otherwise the claim is trivial.)

If one relaxes the normality assumption then the claim is false (i.e. there exists [math]G[/math] with JH series and [math]H \le G[/math] such that [math]H[/math] admits no JH series). But I'm struggling to prove/disprove the normal case. I realize that [math]\{1_G\} \lhd N \lhd G[/math] is a normal series for [math]G[/math], so if [math]\{G_i\}_{i=0}^{n}[/math] is a JH series for [math]G[/math], by Schreier's theorem the two have equivalent refinements. But I'm not sure whether this actually implies that [math]N[/math] has a JH series. Same for [math]G/N[/math].

if i soak my face mask with isopropyl alcohol will the alcohol damp air filter kill any airborne viruses like COVID-19 before they reach my respiratory system?

>>12515897
[math] \displaystyle
\begin{align*}
\text{Mass} && M \\
\text{Radius} && R &= M \cdot \frac{2G}{c^2} \\
\text{Surface area} && A &= M^2 \cdot \frac{16 \pi G^2}{c^4} \\
\text{Surface gravity} && \kappa &= \frac{1}{M} \cdot \frac{c^4}{4G} \\
\text{Surface tides} && d \kappa_R &= \frac{1}{M^2} \cdot \frac{c^6}{4G^2} \\
\text{Entropy} && S &= M^2 \cdot \frac{4 \pi G }{ \hbar c \; ln10} \\
\text{Temperature} && T &= \frac{1}{M} \cdot \frac{ \hbar c^3 }{8k \pi G} \\
\text{Luminosity} && L &= \frac{1}{M^2} \cdot \frac{ \hbar c^6}{15360 \pi G^2} \\
\text{Lifetime} && t &= M^3 \cdot \frac{5120 \pi G^2}{ \hbar c^4} \\
\end{align*}
[/math]


G https://en.wikipedia.org/wiki/Gravitational_constant
c https://en.wikipedia.org/wiki/Speed_of_light
ħ https://en.wikipedia.org/wiki/Planck_constant#Value
k https://en.wikipedia.org/wiki/Boltzmann_constant

>>12519262
https://www.youtube.com/user/EugeneKhutoryansky/videos

>>12519657
A refinement of a JH decomp has either trivial or simple quotients. N admits such a decomp, so removing duplicates gives a JH decomp.
For G/N just take GiN/N and iso theroem

>>12519809
nice TeX table bre

>>12502293
I'm asking this everywhere and I can never get a good answer.

Why haven't we come up with a better way to do neutron capture over the past 80 years?

>>12519809
observation before mathematical equations, that's what they are our observation and interpretation into numbers. what observation did they do to conclude the lifetime of a black hole?

>>12520100
that anon based his entire thought exercise on the fact hawking radiation is real, which both 100% defines its lifetime and it's dependency on size. so if you want to argue against that you need to disprove Hawkings maths.

Mathlet here, how do I figure out the probability of something happening within multiple attempts? For example, let's say I have a 33.33% chance of winning a prize, and I have 4 chances to win. What are the odds I win the prize 0, 1, 2, 3 and 4 times within these 4 attempts? Is there a name for this type of math? Please teach me how this works so I can stop being retarded, thanks

we say [math]f[/math] is differentiable at [math]x[/math] if the limit [math]\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/math] exists.

question: is this equivalent to saying that the one-sided limit [math]\lim_{h \searrow 0} \frac{f(x+h) - f(x-h)}{2h}[/math] exists? (i.e. [math]h \to 0^{+}[/math])
if not, could you please hint at an example that shows this?

>>12520752
Nope. Take the absolute value, the limit doesn't exist because because it jumps between 1 and -1.
But if both sided limits exist and are equal, then it's differentiable

>>12520752
The function f(x):=|x| is not differentiable, the finite h expression computing f'(0) being sign(h).
But f(0+h)-f(0-h) is zero for positive h.

>>12520794
In fact it's always zero even for negative h

>>12520790
>>12520794
I get it, makes sense. thank you!

I'm trying to discovering how to solve a diferential equation in R, but I'm a retard brainlet (and this is a gentle euphemism) I can't find out how to plot
[math]y' = y^2 [/math] with [math]y(1) = 1 [/math]

Like, I have not got a clue how to start from y(1), neither do I know how to make it work with a y2 apparently.
Pic related the code I've been told about using
[math]y' = y [/math] with [math]y(0) = 1 [/math]

Please welp, and sorry to be that braindead.

Please help! Taking calculus next semester, starting next week. I haven't taken a math class in 10 years. What are the most important concepts fundamental to calculus; trigonometry, polynomials ect??? What should I spend most of my time learning?

>>12520864
I'd say definitely NOT trig identities. Also don't you even think about memorizing differentiation and integration rules like they have you do in high school.

Intro to calculus classes tend to put a lot of emphasis on rigor and mathematical precision, very much unlike high school. To get a good feel of what that means, try reviewing proofs by mathematical induction. There's lots of reference material online.

>>12520913
Roger that, tyvm for the tip anon!

>>12520752

[math]\lim_{h \to 0}\left[\frac{f(x+h/2)-f(x-h/2)}{h}\right]=\lim_{h \to 0}\frac{1}{2}\left[\frac{f(x+h/2)-f(x)}{h/2}+\frac{f(x)-f(x-h/2)}{h/2}\right]=\frac{2}{2}\frac{df}{dt}=\frac{df}{dt} [/math]
This means that the central difference depends on both 'sides' of the derivative and cannot be taken as a definition of derivative. If the function is differentiable at x, then the central difference in the limit is the derivative, but not the other way around.

>>12520851
Nevermind. There was a mistake in the paper and it was y(1)=-1.

If a Chicxulub impactor size asteroid collided with the earth again (~6km diameter, 20km/s velocity), and you stood at the asteroid destination on the surface, would the heat radiation kill you before the impact happened? Did the dinos who were close to the impact site die before it collided with Earth?

>>12520021
Now that I think of it, the last part might be a bit misleading.
[math]H_i:=(G_iN/N)/(G_{i+1}N/N)\cong G_iN/G_{i+1}N \cong G_i/(G_{i+1}N\cap G_i)[/math].
[math]G_{i+1}N\cap G_i[/math] is normal in [math]G_i[/math] and contains [math]G_{i+1}[/math].
Hence, [math]H_i[/math] is either 1 or simple.
Now remove duplicates.

Math brainlet here. I've trying to derive this Voltage Divider Formula, however I don't quite understand the ending.

Does this mean that

<math>\mathrm{E}_{n}^{} = \frac{\mathrm{E}_{Total}^{}}{\mathrm{R}_{Total}^{}} * \mathrm{R}_{n}^{} </math>

Is equal to

<math>\mathrm{E}_{n}^{} = \mathrm{E}_{Total}^{} * \frac{\mathrm{R}_{n}^{}}{\mathrm{R}_{Total}^{}}</math>

If that's the case how is that derived? Any clues?
Thanks

Math brainlet here. Having a bit of trouble figuring how to correctly derive the equation in pic related. It would seem to me that this says:

[math]\mathrm{E}_{n}^{} = \frac{\mathrm{E}_{Total}^{}}{\mathrm{R}_{Total}^{}} * \mathrm{R}_{n}^{}[/math]

is equivalent to

[math]\mathrm{E}_{n}^{} = \mathrm{E}_{Total}^{} * \frac{\mathrm{R}_{n}^{}}{\mathrm{R}_{Total}^{}}[/math]

However this does not make much sense. What I’m missing?

>emailed professor asking for recommendation letter last week
>completely ignored
>he probably missed it because grades were due that week and he was really busy
how do I remind him without sounding rude?

>>12521633
this has to be a shitpost

>>12521694
Make up an excuse to e-mail him (like asking a question about a subject he's specialized in, if you really can't think of anything flip through his articles until something confuses you) and off-handedly ask him if he received the email while apologizing for the hurry.

>>12521694
fwd email and ask again. However, I can assure you that he ignored you on purpose. So he probably doesn't know you enough to give you attention. If you manage to get it, the letter will SEVERELY lack quality. Look for another prof.

Guys, how do I git gud at these type of questions?

>>12515759
Depends on what your model of an electron is.

>>12521737
Write out the equations. You know that C is at [e*cos(θ), e*sin(θ)], P at [0,y], and |P-C|=R => |P-C|^2=R^2.
=> P-C = [e*cos(θ), y-e*sin(θ)]
=> |P-C|^2 = (e*cos(θ))^2+(y-e*sin(θ))^2
= e^2*cos^2(θ)+e^2*sin^2(θ)-2*y*e*sin(θ)+y^2
= e^2+y^2-2*y*e*sin(θ)
=> R^2 = e^2+y^2-2*y*e*sin(θ)
=> y^2-(2*e*sin(θ))*y+e^2-R^2 = 0
=> y = (2*e*sin(θ)±√(4*e^2*sin^2(θ)-4*(e^2-R^2)))/2
= e*sin(θ)±√(R^2+e^2*sin^2(θ)-e^2)
= e*sin(θ)±√(R^2-e^2*cos^2(θ))
Clearly, we want the positive root, so
y = e*sin(θ)+√(R^2-e^2*cos^2(θ))
The velocity is dy/dt = dy/dθ*dθ/dt = ω*dy/dθ
dy/dθ = e^2*cos(θ)*sin(θ)/√(R^2-e^2*cos^2(θ)) + e*cos(θ)
=> dy/dt = ω*(e^2*cos(θ)*sin(θ)/√(R^2-e^2*cos^2(θ)) + e*cos(θ))

Given a matrix that represents a linear transformation in a different basis, and the vectors that constitute that basis, if I wanted to find a base for its kernel and image, do I have to make it so the transformation is in the canonical basis?

What is a cheap way to prevent fluids from leaking from a chamber but allow gas to pass through? Most membranes I can find are decently expensive.

>>12521633
Commutative Property of Multiplication.

I'm a giga brainlet. Would pic related be correct?

>>12522654
No. Distance is not energy, never will be.

Can I get an example of a supergroup of the integers under addition?

Do people who die from the flu basically just kill themselves? Is it only the body’s immune response that’s dangerous about it? What would happen if the virus was allowed to grow uncontrollably, but the body made no effort to fight it off?

>>12522878
The virus would spread uncontrollably and take over every cell in the body stopping all other cell production.

>>12522654
Even if the positions are in [math]\mathbb{R}^3[/math], the question cannot be answered if the distance function is not defined

>>12522899
How far away from that point are the people who die? It seems like everyone who dies, dies due to the body’s response (fever or sepsis) way before the virus itself has affected organs to a significant degree. Would that be more or less accurate to say, or is there some damage the virus itself causes that also commonly leads to death?

I am a hapless tit who is trying slowly to self-study on digital signal processing in order to write software synthesizers.

Right now I am experiencing paralysis of choice in determining if I should use a BLIT, BLEP or minBLEP in order to to handle creating a buffer library where I set a clock and output rate and then log the times amplitude changes in a given waveform so it can be generated efficiently later at the output rate with minimal aliasing. I am aware there's other libraries for this, but I'm looking to both learn how this properly functions and have the freedom to release things under an extremely liberal license.

I've already written a pulse-wave generator, but ultimately my goal is to do a 4-operator FM synthesizer with selectable waveforms and an 8-bit wavetable synthesizer. Hard sync would not be a requirement. Given these goals, does anyone here have a favored approach? Right now I'm thinking BLIT.

>>12523058
Ever virus causes random side effects some more severe than others, some intentional, some accidental. Even if they lead to death as long as the virus can transmit itself before that occurs then it doesn't matter.

bros, how do you memorize Formulas?
I've tried anki but I always miss a sign and/or the units in wich they should be written.
Is there kind of a table that has all Fundamental Constants, Formulas and Units (With it's definition.)?
I just want the basic bros but It's so hard to memorize.

>>12523303
>bros, how do you memorize Formulas?
Cheat.
I always wear pic related.
Slip little strips of papers with the formulas on them up there and cycle as needed.

The idea that people should have to remember formulas in the current year of our lord is as retarded as making students do calculus by hand without a calculator to make sure they know how to multiply.

>>12523368
Nah bro, believe me they will catch me and they will ban me from the only test that matters in my county.

>12502293
>help with calculus?
Spivak
>too hard
Go slower
>still too hard
Apostol
>still too hard
>>>/g/

>>12523368
You will never make it.

>>12523413
I already did.

>Hey guy's it's ok I memorized the MSDS, I don't need to look at it
Gets you an A in the classroom and gets you killed IRL. We have the internet now. You should be focusing on how to use formulas, not memorizing the entire thing hoping you don't accidentally transpose something.

>>12523303
Just switch to math
no memorization necessary

>>12523427
I don't like math in general, it's just that I need it for the MCAT.

Does a good notebook actually matter?
I've never been a person who's taken good notes and would use it scarcely when doing homework.
Now that I'm graduating, I'm looking to buy another notebook for my new job, wondering if I should invest in one of the more expensive ones or just get a $2 one.

why did my asthma er visit bill my insurance $6000+? I got a chest xray which was billed at $100, an ekg, covid test, basic doctor services (listening to my lungs and taking history), a rescue inhaler and prednisone.

the $6000+ part was for outpatient services or some general thing. My insurance paid ~$4000 and i was billed nothing.

What the fuck is going on?

>>12523134
That’s not really relevant to my question...I guess in its most basic form, my question is what part of this, if any, is false:
The flu seems to be unique in that it’s relatively harmless by itself (besides stealing resources) but immune responses are 100% responsible for severe cases.

>>12521477
Thank you very much!

>>12523551
The point is that some symptoms are intentionally (evolved) caused by the virus, e.g sneezing enhances flu transmission, while others are unintentional immune responses. But it is not always clear or easy to define which some are. For example the lung scaring and inflammation caused by Covid causes death in some people but also increases coughing and hence airborne transmission in others. As long as the virus caused mortality rate is not high enough to stop is spreading then it continues to survive which is all it cares about biologically speaking.

>>12523536
>(((why did my asthma er visit bill my insurance $6000+?)))
>(((What the fuck is going on?)))

Why are elliptic curves considered to be curves of two variables? It's just [math]\pm (x^{3}+ax+b)^{\frac {1}{2}}[/math] which is one variable.

Are there any supergroups of the integers under addition?

Let [math](X,\mathcal{A}), (Y,\mathcal{B})[/math] be measurable spaces and [math](X \times Y, \mathcal{A \otimes B})[/math] their product. Is it the case that for any [math]E \in \mathcal{A \otimes B}[/math], its indicator function is the pointwise limit of measurable rectangles? i.e., must there be [math]A_n \in \mathcal{A}, B_n \in \mathcal{B}[/math] such that [math]\chi_E = \lim_{n\to\infty} \chi_{A \times B}[/math]?

>>12522796
>>12524207
The integers are a subgroup of the rational numbers, hence the rational numbers are a supergroup of the integers.

Does mysterymeat3 post here?

How much does electricity weigh? Say I have a gigawatt of electricity, how much weight would that be?

>>12525752
Your intensity is the amount of charge flowing through the circuit every second
An electron has a charge of [math]−1,602 ×10^{−19} \text{C}[/math] and a mass of [math]
9,109 ×10^{−31} \text{kg}[/math]
You do the math

I just ate one seed from https://en.wikipedia.org/wiki/Jatropha_podagrica and didn't look the plant up until after, when my tongue started tingling.
How long do I have fellas?

>>12525792
So if I have a battery it'll have stored more weight if it's charged. That's cool!

Is DNA polyester?

Retard here, how do i find x?

>>12528387
Use the fact that 150 is equal to 90 + the two highlighted angles.

>>12524901
God bless that faggot. I really like the stuff he translates.

>>12528438
Thanks for the clue, but how do i find those angles though? I got 60° left, line A and B are parallel to each other

>>12525752
> Say I have a gigawatt of electricity, how much weight would that be?
Nothing. Although you can convert energy to mass via E=mc^2. Weighing electrons isn't meaningful because electricity storage doesn't add or remove electrons, it just moves them. E.g. a capacitor which stores one coulomb of charge has the same number of electrons as one which is discharged, it's just that one coulomb of electrons has been moved from the positive plate to the negative plate.

>>12528446
Amen.

What happens when positron collides with muon?

>>12528470
You don't know how to calculate the angles in a right-angled triangle??

>>12528678
They'll just scatter off each other. An anti-matter particle only annihilates it's exact counterpart.

Do there exist any good resources on the information theory of black holes not written for physicists? My thermodynamics sucks ass, and I'm mostly interested in the information theoretical results.

>>12528851
There is no information theory of black holes. There is quantum information theory and the black hole information paradox but they are two very different things.

>>12528874
That would explain why my search came up dry. I read it does exist, but whoever wrote that must've gotten mathematical information theory and whatever else there is confused. Thanks for your reply.

For about a year now for fun I've been identifying birds and mushrooms in a journal but I'm wondering if my log system is good or if it's missing something, I know taxonomies a thing so I wondered if there's sort of standards

birds
common name, season, weather, time of day

mushroom
common name, area, placement (tree, ground mud etc), any notable features

is there a better way to be doing this?

If I wanted to project a vector onto a subspace, having a non orthogonal basis, do I have to orthogonalize the basis? or orthonormalize it? or can I just project the vector onto those linearly independent, but not orthogonal vectors?

Hey /sqt/! I need to know how to get 300k starting any job I want. What degree is best for this?

>>12529216
Firstly, there's no "the" projection onto a subspace. It has to be in a direction of some vector(s).
Secondly, I suppose you're talking about orthogonal projection. No, it's not necessary to have an orthonormal basis, but the computation will be a bit harder. In an orthonormal basis, the coordinates of the projection are just dot products with the corresponding basis vectors, this is not true in a non-orthonormal basis.

>>12529291
Yes, I'm talking about orthogonal projection. Is it necessary to have at least an orthogonal (better if orthonormal) basis? Because I usually calculate it through orthogonal decomposition theorem, but I've found that projecting onto a non-orthogonal basis gives the wrong answer

Is there a some online envirement where I can do long division and long long multiplication? In notepad/word/mathtype editor it's kinda clumsy. In google I can find only calculators for these things. Real paper is fine, but if I could, I want do it on computer.

How long do coffee withdrawal headaches last?

>>12502293
This is a LEGIT stupid question I'm just terrible at this stuff

deck of 52 cards random order yadda yadda

I draw a card then shuffle it back into the deck and I'm going to repeat this 10 times except if I draw a Heart, Club, or Spade I get an additional "free" draw. In addition, once I've drawn just 1 Heart I then stop, remove all the Hearts from the deck and the go back to drawing, and if I draw 3 Clubs total I stop and remove all the Clubs from the deck and then go back to drawing, and finally if I draw 5 Spades where I then stop and remove all the Spades from the deck and go back to drawing.
I'd only stop once I reach my 10 time draw counter.

At the end I understand instinctively I would have drawn something between 10 cards(all Diamonds and thus no redraws) and 19 cards (maximum amount of redraws). What I really want to know is what the average number of each suit of card I'd have drawn before having to stop. By using math.

>>12529983
like 6 days

Could I feasibly cover all of Baby Rudin in three months if I've only ever done proofs in Velleman?

This course seems to cover up to chapter 9 in around that time:

https://kurser.math.su.se/mod/page/view.php?id=693

>>12530107
Shit that sucks.
Thanks.

Can anyone recommend a textbook for any of the three topics?
>Differential Equations
>Linear Algebra
>Probability and Statistics

>>12530557
>Diff E
Well there's Evans, or Strauss (PDE)
And there's Tenenbaum (ODE)
For a lighter treatment of both try "Riley, Hobson, and Bence"
>Linear Algebra
See Axler or Hoffman
>Probability & Statistics
IDK really, Feller vols 1&2 maybe for probability alone

Google Cambridge Math Tripos Schedules and see the reading lists for each paper in the pdf. Or have a look at the /sci/ wikia

>>12530102
That is a legit stupid question mainly because of how horrendously complicated it would be to calculate. The number of objects can change at any point based upon the pick order. There is no elegant permutation expression for that scenario.

>>12530102
For something that complex, you'd write a program to generate the graph.

Each possible state is (n,h,c,s), where n is the number of draws remaining, h,c,s are the number of hearts, clubs and spades drawn respectively. Possible successor states are
n>0 => (n-1,h,c,s)
n>0 ∧ h<1 => (n,h+1,c,s)
n>0 ∧ c<3 => (n,h,c+1,s)
n>0 ∧ s<5 => (n,h,c,s+1)
The probability of any given successor state is the probability of the prior state divided by the number of possible successor states (1-4).

So you enumerate the tree in breadth-first order starting with (10,0,0,0), p=1, summing the probabilities for identical states (there are multiple paths to a given state; e.g. drawing a diamond then a club and a club then a diamond both yield (9,0,1,0), p=1/16, so they sum to p=1/8; if you don't merge these you'll end up with exponential growth).

Then, at each level of the tree sum the probabilities of the states with n=0 to get the probability of finishing on that step. From that, you can calculate the expected value. I get E=18.81 (0.897 probability of finishing on the 19th step, i.e. of getting 1 heart, 3 clubs, 5 spades).

FWIW, the number of possible states at each step is:
1, 4, 9, 16, 24, 32, 39, 44, 47, 48, 48, 47, 44, 39, 32, 24, 16, 9, 4, 1
So you could actually draw the graph by hand. It would be laborious, but feasible.

What's the best high school physics textbook?
I know the best one is "University Physics", but is calculus based, and although I can get it, The Exam I'll do isn't CalBas.
Or it doesn't have nothing to do?

>>12530883
That was wonderful!!