The h Bar

12:01 AM

@ACuriousMind I guess my real question is given a map $f:\Omega\to M$, $\Omega\subset\Bbb R^m$ open, $M$ a manifold, how to extend it to $\bar f:(-\epsilon,\epsilon)\times\Omega\to M$ such that $\partial \bar f/\partial t^0=v\in T_pM$ at $p\in M$. $v$ is any vector.

And I think I want $\bar f(0,t^1,\dotsc, t^m)=f(t^1,\dotsc, t^m)$.

Hmm.

@ACuriousMind Ever heard of this?

I can't multiply functions into $M$, so this is quite nontrivial.

ACuriousMind

what has that to do with partial and total derivatives? oO

0celo7

@ACuriousMind Oh, nothing.

user218912

hi!!!

ACuriousMind

@3075 hey

0celo7

@3075 Hello.

ACuriousMind

12:07 AM

Started uni yet?

user218912

well I moved in to residence, but I begin my first classes next monday. xD

0celo7

Why xD?

user218912

idk I've been using it a lot lately.

ACuriousMind

@0celo7 I'm guessing it's nervous laughter :P

user218912

I'm taking analysis, algebra, physics and icelandic history.

user218912

12:09 AM

and compsci

ACuriousMind

Nice, Icelandic history! :D

0celo7

@ACuriousMind Do you remember how to construct a curve so that its velocity is some given vector?

ACuriousMind

@0celo7 Hm?

0celo7

You just work in a chart and give a Taylor expansion that converges in the chart with first order terms given by the vector?

ACuriousMind

Why should I remember that, I don't think I've ever done that :P

0celo7

12:10 AM

Because it would come in really handy right now :D

ACuriousMind

Can't you...just pick a Riemannian metric and pick the geodesic with that vector as initial velocity? :D

0celo7

@ACuriousMind ...

You're too smart for your own good. I'm looking at a new way of defining geodesics here.

Trying to define mixed partial derivatives of maps $f:\Bbb R^m\to M$.

ACuriousMind

@3075 I forget, are you studying physics or compsci or something different now?

0celo7

Should make geometric analysis much clearer, those kinds of derivatives are everywhere.

ACuriousMind

@0celo7 The first sentence I'm used to hearing; the second sounds a bit crackpotty ;)

0celo7

12:13 AM

@ACuriousMind No, it's in a well-respected geometric analysis book. It's fine.

user218912

@ACuriousMind physics. :D

0celo7

time to get out all the geometry books

user218912

condensed matter probably. but I keep changing so don't take me seriously.

ACuriousMind

@3075 I don't take anyone seriously who claims to want to go into a particular field in their first semester ;)

user218912

but it always ends up being physics though, 100%.

user218912

12:15 AM

@ACuriousMind true

0celo7

spoiler alert you become an icelandic tour guide

user218912

lol XD

0celo7

Spivak has a whole section on the various definitions of the tangent bundle

I hope he has the construction

@ACuriousMind Just to make sure:

I have $v\in T_pM$. I want $c:(-\epsilon,\epsilon)\to M$ such that $c(0)=p,c'(0)=v$.

Pick a chart centered at $p$. Then define the coordinates of $c(t)$ as $v^it$. Doesn't that work?

Where $v^i$ are the components wrt. the partials of the chart at the origin.

I'm 99% certain that works.

ACuriousMind

Looks reasonable

0celo7

@ACuriousMind Your construction with geodesics is the same, just that the chart is a normal coordinate neighborhood.

user218912

12:20 AM

@0celo7 I'm bootcamping windows 10 on my macbook.

0celo7

DJ Khaled - Nas Album Done ft. Nas

►

user218912

I thought you said you only listened to trap.

0celo7

No?

And that's pretty trappy actually.

ACuriousMind

Aug 30 at 22:31, by 0celo7

I'm on a strict diet of mathematics and trap

0celo7

But I can link trap if you want.

ACuriousMind

12:21 AM

Could reasonably be interpreted as "I currently only listen to trap"

0celo7

Fetty Wap "My Way" feat. Monty [Official Video]

►

ACuriousMind

Although I have no idea what "trap" is and don't particularly want to know

user218912

okay, I listened to some trap recently and it was good.

0celo7

Young Jeezy - Thug Motivation 101 - Standing Ovation

►

user218912

this is gangsta rap though.

0celo7

12:23 AM

2 Chainz - A Milli Billi Trilli (Official Video) ft. Wiz Khalifa

►

@ACuriousMind there

Anyway

I need $\bar f$

ACuriousMind

@0celo7 GEMA.

0celo7

Damn book says it's possible

I'm not so sure

@ACuriousMind oh come on

@ACuriousMind Work in a chart, then define it as a sum, bump function the added part to make it decay within the chart and have everything be globally defined?

i.e. $\bar f$ is a homotopy of $f$ around $p$

DanielSank

@3075 'sup?

user218912

hey

0celo7

no that doesn't work

the curve might lead out of the chart, bad things happen then

DanielSank

12:31 AM

@ACuriousMind see comments here.

I have a feeling you'll 1) agree with me, and 2) explain what I'm trying to say better than I can.

ACuriousMind

@DanielSank I left a bunch of comments there already but they're all gone

DanielSank

@ACuriousMind XD

ACuriousMind

Probably because most of them pertained to an earlier iteration of the question

DanielSank

@ACuriousMind ah

I am baffled by how often folks talk about "what kinds of people" should use this site.

The only thing we should talk about is what questions we support.

It's kind of troubling: peterh and heather are both harping on the "who" thing and I really think this is a bad idea.

I think it's a common mistake made when one doesn't understand the essence of what a good question is and how online information resource communities function.

That's why articles like this exist.

ACuriousMind

I agree with you. The model of SE is precisely designed to focus on the users and personal interaction less than your average internet forum.

3

DanielSank

12:43 AM

I love you, @ACuriousMind.

ACuriousMind

@DanielSank Thanks <3

0celo7

Oh but when I say that I'm a creep

user218912

12:59 AM

lol

dmckee

@0celo7 Oddly there are people who just exude creepiness in real life. I always feel like someone needs to take them aside and have a heart-to-heart with them. but I don't know them well enough, and may not be the best model of non-creepy behavior, anyway.

DanielSank

@dmckee You come off as pretty not creepy to me.

ACuriousMind

Maybe he stands too close and breathes into your ear in real life? :P

0celo7

@dmckee I like to think I'm not one of those people.

@ACuriousMind I'm reasonably sure I can make my construction work locally, but finding a global extension seems highly nontrivial. I have reasons for wanting the extension to be global.

Geometry sucks

NeuroFuzzy

1:15 AM

@ChrisWhite It seems like smoothing out particles is practically the only option. Thanks though! It sounds more and more like the practical answer for this problem will be in numerical simulation, so that's a good enough starting point.

0celo7

@dmckee How are they supposed to fix their behavior

dmckee

@0celo7 In most of the cases that I'm familiar with they need to take a step back from a focus on control or sex. Have some relationships in which neither features. Learn how to identify conversation that is just social noises and doesn't represent a call for anything to be fixed, and how to participate in such conversation.

0celo7

@dmckee The people I'm aware of that "exude creepyness" are those who don't have relationships.

dmckee

@0celo7 Yeah, in part because they either are or come across as being intensely focused on those things. So people avoid them. So they don't get any practice being a social animal. So they continue to be creepy.

So step one is understanding that they have to interact with people without those things foremost in their minds.

NeuroFuzzy

1:43 AM

It strikes me as strange that the classical theory of light and matter has so much trouble describing both at the same time.

0celo7

Ok, how about this.

Look at the coordinates of $f$ around $p$

we get a bunch of coordinate functions on some ball $U$

Then we write $f^i+\varphi(t^0)\Phi(t)t^0v^i$

where $\varphi(t_0)$ is a bump function and $\Phi(t)$ is a product of various bump functions such that $\Phi(0)=1$

we need $\Phi$ to force this here to be well-behaved near the boundary of $U$

we then define $\bar f$ to have the coordinates of that above on $U$ and to be $f$ elsewhere

Actually, I can compose with a diffeomorphism from the ball to all of $\Bbb R^n$, and then I should stay within the chart everywhere.

I dislike this proof.

DanielSank

2:55 AM

PSA: SQL is complicated.

dmckee

@DanielSank Once I'm beyond the mokey-see-monkey-do level I always go to software carpentry for my SQL needs.

And if you have gone beyond that level then, yeah, its complicated you poor, poor man.

0celo7

What is SQL?

dmckee

@0celo7 Deep, dark database magic. And a way to call forth the great old ones—like Little Bobby Tables—and end the world.

Her daughter is named Help I'm trapped in a driver's license factory.

0celo7

what?

dmckee

DROP TABLES is the SQL equivalent of rm -rf /. It's the end of all things for the database to which it is issued by a sufficiently privileged user.

0celo7

3:01 AM

what is rm -rf / :(

dmckee

I'm going to have to report this to the geek ethics committee. We may have to take away your decoder ring and lapel pin for the interim.

3

0celo7

What?

I'm not a geek

dmckee

@0celo7 You discuss topology and general abstract nonsense in a physics chat. You were admitted in abstentia last spring. And now you'll have to appear before the ethics committee.

But on the upside if you never got the decode ring and lapel pin, that's one less thing for the committee to do.

0celo7

@dmckee Topology is hardly abstract nonsense

dmckee

No, but category theory is "general abstract nonsense", and you throw *orphisms around way to casually

0celo7

3:07 AM

I don't know any category theory! Category theory terminology was chosen so that all the orphisms can be unified

Right now I'm looking at differential equations, hardly abstract

@dmckee I will accept being a "mild nerd."

But not a geek.

dmckee

Someone posted xkcd 747 just the other day, and it is bang on:

The definitions I grew up with were that a geek is someone unusually into something (so you could have computer geeks, baseball geeks, theater geeks, etc) and nerds are (often awkward) science, math, or computer geeks. But definitions vary.

0celo7

I don't have a strong opinion on the matter.

I'm just telling you I'm not a geek.

DanielSank

3:25 AM

@dmckee oh my goodness "general abstract nonsense" made me blow a large quantity of air out through my nose.

Also that Geeks/Nerds diagram is perfect.

0celo7

:(

John Rennie

4:16 AM

@peterh I was commenting on an answer not on the question. However the answer is now deleted so I can see how it would look like I was commenting on the question. I haven't voted either way on the question.

@ArtOfCode Eh? Not me. Some other John perhaps?

0celo7

@JohnRennie Duffield.

John Rennie

Figures

0celo7

@JohnRennie CW got a day's ban out of it.

John Rennie

Well ArtOfCode is generally pretty objective about these things so whatever Chris said he probably shoudn't have said it.

0celo7

Can you see the deleted messages?

John Rennie

4:23 AM

No. In fact I can only see six posts by Chris and none of them look like a prelude to an argument.

0celo7

Hmm, I wonder what a "minimizing" sequence of a functional is.

Ah, ok.

$(\gamma_n)\subset \Omega_{p,q}$ is a minimizing sequence if $\lim_{n\to\infty}L(\gamma_n)=\inf_{\Omega_{p,q}}L(\gamma)$.

Seems reasonable one can always find such a sequence.

@JohnRennie I have an interesting physics "theorem"

John Rennie

@0celo7 go on then

0celo7

@JohnRennie In any potential force field, there exists at least one periodic motion of a rigid body.

John Rennie

I assume you mean a central potential ...

0celo7

I don't think so, why?

John Rennie

4:33 AM

Or at least one with a minimum

0celo7

I think it has to not have a maximum.

Are you interested in the idea?

No, it should have a maximum.

John Rennie

In a potential with a maximum but no minimum the body will just shoot off to infinity and there will be no periodic motion.

0celo7

Oh, it's fixed, forgot to mention that.

Pinned but free to rotate.

John Rennie

You've lost me now. Are we talking about rotational motion of a rigid body? So no translation?

0celo7

Yes.

John Rennie

4:40 AM

That doesn't sound very interesting ...

0celo7

@JohnRennie The proof is super hard!

John Rennie

Your potential can only a function of angle, so it must have an equal number of maxima and minima, and there is only one degree of freedom.

0celo7

Equal number of maxima and minima?

John Rennie

Yes. The potential can only be a function of the rotation angle, and $V(\theta)=V(\theta + 2\pi n)$.

0celo7

@JohnRennie I'm not so sure about what you're talking about, and I'm also very tired

But I have another theorem

Given integers $n,m$ there is a periodic motion of the double pendulum under which one segment makes $m$ rotations and the other makes $n$ rotations.

John Rennie

4:48 AM

@0celo7 Ah, 3d rotation, not rotation about a single axis. I'm tired too.

Maybe now isn't the best time to be discussing theorems ...

0celo7

@JohnRennie Perhaps.

::reads same paragraph on Banach spaces for the fifth time::

Where am I?

I have an issue with geometric analysis

They're solving topological problems using PDEs, so they write everything in coordinates

Certainly you can't cover the whole space with a chart

user116211

5:55 AM

What sort of nonsense is this?

user116211

0

A: Infrared remote flashes blue light in camera

Those green eyes and that contagious smile and those lips… and the way they verbalize And New York city, what a beauty to our eyes Then you held my hand for the first time You looked at me and smiled Everything was perfect Everything was great I was on a fairytale It’s a dream when I’m awake But...

Secret

obviously a poem of some sort that is not an answer. Mayeb that guy is a bot of some sort

John Rennie

@MAFIA36790 just downvote and vote to delete if you have the rep.

Actually it made me smile, which is not bad going for 7 a.m. on a gloomy Tuesday morning.

user116211

@JohnRennie I do have the rep ;P flagged

Secret

This is the source: taylorswift.wikia.com/wiki/I'm_Alright_(lyrics)

user116211

6:02 AM

@JohnRennie Maybe copied from some novel.

Secret

For some reason someone is copying the lyrics of taylor swift as an answer

user116211

@Secret :D

John Rennie

Actually I have a grudging respect for Taylor Swift. I think she's an intelligent lady and very good at what she does. There are far worse adverts for the human race, some of them members of this site :-)

Secret

By the way, first downvote ever

user116211

@Secret Mark this date ;)

John Rennie

6:05 AM

@Secret I used to be very reluctant to downvote because, well, it seemed petty and mean. But downvoting is an essential part of the site functioning.

user116211

I don't get what part of a rational mind does allow some to post such thing as a serious answer ;/

Secret

By the way, about that question, I can actually see the flash from the remote directly as a very dim red glow so red that makes ordinary red looks reddish orange

user116211

@AnkitSharma: o/

Secret

The major reason I don't downvote is because I lacked the knowledge to access the answer on how relevant it is, it is made worse by my free associations, which can often make any answers that at least have something remotedly linked to the question to make some sense in my mind

The reason I can confidently downvote that one is that no conceivable wordlviews will allow that as an answer

For anything else, often "I am not very sure" will appear as an excuse to hinder me downvoting

DanielSank

@JohnRennie Hey, that's not nice!

John Rennie

6:18 AM

@DanielSank The truth hurts :-)

DanielSank

@JohnRennie Be nice, dude.

It's in the rules.

It would be a shame for a would-be contributor to show up, see our chat calling people here bad adverts for the human race, and leave ;)

I'm guilty of bad manners too.

John Rennie

@SpaceOtter what causes complications is when some component of the universe has a weird equation of state i.e. it's energy density is not inversely proportional to volume. When components like this are present it's possible to have a flat universe that is accelerating.

The usual statement that a flat universe is the one that just fails to slow its expansion to a halt applies to a universe containing only regular matter.

In the days of old when we thought that regular matter was all that existed you'd often see people assuming a link between geometry and expansion. These days you often still see the assumption, but we now know it isn't justified.

John Duffield

7:17 AM

@NeuroFuzzy : make sure you read about renormalization.

@JohnRennie : IMHO energy is conserved, full stop.

@SpaceOtter : don't forget that two out of three answers were always going to be wrong. And if two of the answers are wrong, maybe the third one is wrong too.

Secret

7:38 AM

Thinking about the degrees of freedom in a plot of a set of linear data

So you have a set of n dimensional data, taking the slope will be a function of 2n arguments (where each pair lies in each dimension)

If you now have some sets of n dimensional data with each set indexed by some parameter k, then taking the slope of each set will give you n slopes. These can then be plotted against k to make a 2 dimensional data set

It's as if you are projecting a $n^k$ dimensional object onto the k-n plane

Geometry is really just an interrelation between different elements within a set...

Sorry mistake, the generalisation of slope in n dimension is the gradient, which is a function of n variables

[Dimensions] These two sets of data (can be readily generalised to n dimensions) have identical direction and magnitude for a vector that represents their trends. However they are clearly different in the way the data points are distributed. Therefore there is an extra degree of freedom needed in order to plot them as points

Might need to look up how gradients work in discrete data sets...

It also does not help that direction is actually a complicated thing that requires more than one paramter in general to specify

One can then easily see that discrete,, finite systems have properties that will be considered weird in the perspective of continuous, infinite systems.

For example, there is a unique solution 0 to the equation $(\frac{d}{dx}-1)f(x)=0$ but in general the unique solution to $(\frac{d}{dx}-\mathbf{I})\mathbf{y}(x)=\mathbf{0}$ is nonzero due to the kernel being nontrivial

Actually I made a mistake here, might need to tidy it up later...

peterh

8:28 AM

Wow, good to see that I am still here.

Secret

I think I need to ask acuriousmind later on reminding me how to find the kernel $L$ of a linear operator in the space of functions, because clearly we cannot use gaussian elimination here since any possible matrix representation of the operator is continuously infinite

$$Ly=0$$

David Z

@peterh and why wouldn't you be here?

Secret

As for the kernel of a nonlinear operators, one subtype is root finding in functions (because can we treat our f as a nonlinear operator acting on x which live in the vector space $\mathbb{C}$)

Another subtype forms the whole discipline of homogenous solutions to partial differential equations

Googling so far seemed to find no general algorithim to solve for y given known L

most examples reduce to solving homogenous linear differential equations

ACuriousMind

10:33 AM

@DanielSank General abstract nonsense is actually a semi-technical term (if you didn't know already, but the laughter implies you didn't)

2physics

@ACuriousMind hi, what does it mean?"At the core that is all there is to it. " do you know?

Secret

@acuriousmind In functional analysis while there is a well known theorem that said the kernel of a linear operator $L$ is a closed subspace of the vector space where the elements in it were acted on by $L$, is there exist any general algorithm to find the kernel given a known $L$, analogous to how in matrices, we can find its kernel by computing using gaussian elimination?

ACuriousMind

@2physics What? The sentence you quoted means something like "This is the full explanation/the full extent. There is nothing deeper here".

2physics

ok..so maybe it was sth like this : "at the core"(adverb) + "that is all"(referring to the last sentence) + "there is to it" (is sth like: there is about it) ..

John Rennie

@ACuriousMind: I agree about the noise cancelling question not being a duplicate - I should probably not do the review queue first thing in the morning :-)

Secret

10:48 AM

@acuriousmind More simply, is there exist any algorithm to find the kernal of the linear operator L if the vector space L is from is something that is continous and/or infinite like in the space of functions?

ACuriousMind

@2physics Yes, although "That's all there is to it" is sort of a fixed expression meaning there's nothing more that can be usefully said about whatever "that" refers to.

John Rennie

Though annoyingly now I've retracted the close vote I can't VTC as not physics ...

ACuriousMind

@JohnRennie I know it's easy to let similar question titles mislead one into duplicate voting, it's not a big deal, but since three people had already upvoted your comment I had to leave a publicly visible comment stating it's not a duplicate.

2physics

so, like what you said : basically that is the full explanation about it(the issue). thanks!

John Rennie

I'm extra cautious about closing when the dupehammer applies, but I must admit if there's no dupehammer and I think a question is rubbish I don't always check carefully to see exactly what sort of rubbish.

ACuriousMind

10:54 AM

@JohnRennie Yes, the retraction system could use some work, there are several posts about it in meta.SE, but it seems SE is too busy congratulating themselves that one can retract votes at all to do something about that :P

John Rennie

There are things in life I worry about more :-)

ACuriousMind

It's not exactly top priority on my list either

2physics

sorry another question

what does it mean : for example when we write the numbers like this 17266(63). does it mean "17266+63 and -63" or does it mean "17266 or 17263"

Secret

Suppose we have an equation that describes what it means to solve for the kernel:
$$Ax=0$$
If A is a nxn matrix, then the x can be easily solved for by performing gaussian elimination on A
However if A is a general linear operator, how to solve for x?

ACuriousMind

@2physics Ugh, I hate that bracket notation, but I think it means your first option.

Don't take my word for it, though

David Z

11:03 AM

Whenever I've seen it, that's what it means. I've never seen the second meaning.

2physics

you just saw it :D

John Rennie

$17266(n)$ means $17266\pm n$

2physics

thanks agaiiiin. and for the record, fellas I hate the function analysis.. well to be honest, I used to hate its teacher :D:D I didn't learn "advanced engineering math " and didn't attend his classes and went to the math department to ask teachers about his course syllabus and find some references on that course(which the function analysis was just a portion of it) .. at the end of the day I realized I need more than a year to be able to study all of those references and books on my own ..

and that was the day I really understood and touched the feeling of a man who is sure that he will be failed, weeks before taking an exam :D:D

Loong

@2physics bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

see Subsection 7.2.2

John Rennie

Wow, a 134 page PDF explaining how to denote uncertainty. I suppose it's important to be thorough about these things.

Loong

11:17 AM

@JohnRennie Yes. BIPM are the guys who "make" SI units.

The corresponding ISO standard is this one: iso.org/iso/catalogue_detail.htm?csnumber=50461

John Rennie

I wonder if anyone but the authors has ever read it from cover to cover :-)

Loong

Another relevant reference pdf in this context: bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf

and the corresponding ISO standard: iso.org/iso/catalogue_detail?csnumber=45324

Secret

18

Q: I'm getting notified of chat messages from ignored users

If I add a troll to the chat's ignore list, can we make it so that they don't show up in the SE Network inbox when they ping me? If I have it set up like this: I shouldn't be seeing this:

Conserving pings @ seemed to be not working well

2physics

Secret

People became too paid attention to low priority posts, got bogged down by them, and thus in a the kid who cried wolf fashion, ignore all the high priority posts in the process

2physics

11:31 AM

@Loong I don't understand the first one

why .35 mg ??!

Secret

There are 2 users who put me on ignore and data suggests there's a third

Loong

@2physics 0.00035 g = 0.35 mg

2physics

I know

there is no sign of 35 in the first one

it is 100.021 47 g and where did .35 come from??

Loong

@2physics Note the quotation marks in the examples: Instead of "m = (100,021 47 ± 0,000 35) g" you can explicitly write "m = 100,021 47 g with (a combined standard uncertainty) u = 0,35 mg."

2physics

and about the second one; 100.021 47(35) it says the number in the () shows the numerical value referred to the corresponding last digits . which means we can substitute 47 with 35 according the numerical results. am i right?

Loong

11:38 AM

@2physics you can replace "47" with "47 ± 35"

The form "l = 23.478 2(32) m" is also used in ISO 80000 Quantities and units.

Here "(32)" represents a standard uncertainty equal to 0.0032 m.

2physics

11:56 AM

are 100.021 47(35) and 100,021 47(0,000 35) the same?

yup then

yea they are the same. thankyou

Secret

::Cryptic statement: There is a reason I have said nothing about it today. Let's see how good your memories are::

cerberus23

12:15 PM

Anyone has any idea how "uni" (one) is our universe ?

oh my bad wrong place

user116211

Too broad or primarily opinion based?

user116211

-1

Q: What for do you use the Debye-Scherrer and how does it work?

What is the difference between Bragg and Scherrer? What is difference at the breadboard and what was the goal of the two physicist (Debye and Scherrer)? Did they also worked with X-Rays? Have to make an presentation on it and don't know what to tell about their experiment.

x-rays

user116211

12:32 PM

For me, it's unclear ;P

Secret

12:53 PM

Too broad, the OP is trying to ask for the significant results of the experiments done by those 4 guys and what is the difference in how the experiments were carried out

Space Otter

1:10 PM

@JohnDuffield Thank you for explaining that. Makes total sense now

John Duffield

@SpaceOtter : explaining what?

Space Otter

@JohnDuffield Geometry and expansion

last night

Secret

@ACuriousMind How to show that the shift operator $T(p(t))=p(t+1)$ is invertible, thus showing that the kernel of $T$ is trivial?

0celo7

@Secret write down the inverse?

If you find the inverse of a map explicitly, you know it's bijective.

Secret

ok, so I am guessing the inverse will be $S(p(t))=p(t-1)$

0celo7

1:15 PM

Yes

Secret

Ok, here's a more general question, how does one deduce some linear map in $\mathcal{C}(\mathbb{R})$ is invertible especially when the inverse is not easily guessed with some anzat?

Recently I have been thinking about solving for eigenvalues and kernels of linear operators in $\mathcal{C}(\mathbb{R})$ but I found myself kinda stuck and wondeirng if functional anlaysis have nice theorem or general algorithms that can help solve eigenvalues for some linear maps (because recently from Math chat I was told it is possible in some cases and you need to know more details about the linear map)

For example, if $T$ is a linear differential operator, then finding its kernel is like solving the differential equation $Ty=0$. Howeer I am not sure if there exists more elegant methods in solving for $T$

David Z

ach, I totally forgot we have a chat session today. I thought it was next week.

Anyway, anyone who has something to put on the agenda, ping me before it starts

or wait, is it AMA day?

It is, never mind then.

7

Q: September 6 Physics AMA Secret: question pool

I am Secret and will be the next guest for AMA on September 6 at The h Bar.16:00 UTC (2:00 Syd time and 12:00 EDT. For other timezones, check here). Post questions you like to ask below AMA took place in informal format. Post questions below to get ideas on what topics others are most intereste...

discussion

0celo7

1:33 PM

@Secret $\mathcal C(\Bbb R)$?

Secret

Space of all smooth functions, is that how you notated it?

0celo7

No, $C^\infty(\Bbb R)$.

John Duffield

@SpaceOtter : my pleasure.

0celo7

Are the functions $\Bbb R\to\Bbb R$?

Secret

yes

0celo7

1:34 PM

Then $C^\infty(\Bbb R)$

Secret

ok

0celo7

Linear maps in $C^\infty(\Bbb R)$ are boring.

They are all of the form $x\mapsto ax$.

Secret

wait, so the shift operator is no longer a linear map in $C^{\infty}(\mathbb{R})$ (because it is in $P(\mathbb{R})$?)

0celo7

The shift operator is definitely not a linear map in $C^\infty(\Bbb R)$.

It's a linear map ON $C^\infty(\Bbb R)$.

Very different.

Secret

o sorry for the mistake, I was trying to ask about eigenvalue and kernel solving for linear maps ON $\mathcal{C}^{\infty}(\mathbb{R})$

because we don't generally have the nice tools we can use in matrices

0celo7

1:38 PM

Oh, that's functional analysis.

Secret

Yes, for one specific problem in the past, I have been trying to solve this question from me misreading the question (thus accidentally booting the question into functional analysis territory)

2

Q: Solving for the spectrum and eigenvectors of the "shift operator(?)" $T$ in $P_3(\mathbb{R})$?

This question is inspired from accidentally misreading this question in my tutorial exercise in my linear algebra course because I forgot the 3 in $P_3(\mathbb{R})$ (The actual question can be easily solved by considering the matrix of $T$ and then the eigenvector is found to be the constant p...

linear-algebra functional-analysis spectral-theory

0celo7

But that operator does have some eigenvalues

I see a bunch of eigenfunctions with eigenvalue 1

Periodic functions, constant functions (second one is a subset of the first)

Secret

So the general solution are periodic functions of period 1, and the way I use to to solve it is the most elegant way possible (i.e. that functional anlyst when seeing this question, will solve it by computing the recurrence relation)?

0celo7

no idea, I'm not a functional analyst

Secret

by the way how do you calculate the eigenvalue is 1?

0celo7

1:43 PM

Bbl

Secret

ok nvm then

Too bad ACM have put me on ignore, guess I have to try my best to search further

Space Otter

@secret How do you cite questions so they show up like that in chat?

Secret

You just post the link and the chat will do the rest. Make sure not to put any linebreaks

same things applied for youtube videos

0celo7

ACM put you on ignore?

@Secret the eigenvalue being 1 is clear...think about it.

Space Otter

-1

Q: Why doesn't the normal force make things move?

Why won't two blocks kept in contact on a horizontal frictionless surface move, due to the normal force? No exterior force is applied to them from any direction (except for gravity).

newtonian-mechanics forces

oh thats cool thx

Secret

1:50 PM

@0celo7 Highly likely, otherwise he would not failed to noticed two @ ed questions. ACM used to respond to any pings directed at him in 2 mins, especially if it is academic related topics

Space Otter

Only two things are infinite...

Secret

This is why I use my @ s very springly, because they are use to distinguish things that I want to ask other on from the incoherent random rambles

Therefore, if there are more than 5 @ messages having no response in sucession, (plus monitoring the frequency of the user's responses), I will know when someone ignore me

0celo7

@Secret 2 minutes?

Secret

that's rough number, but ACM respond quick to academic questions

0celo7

He must find your questions more interesting than mine.

Secret

1:54 PM

From what I have seen throughout my time on chat, ACM occassionally ignore your questions, but later on when you guys talked again, he will answer. In geenral, ACM took on averag 2 mins to respond to any acadmeic questions thrown to him, especialy those with a @, regardless of users

And whenever ACM ignore your questiosn, you will often said something along the lines of "don't give me a slient treatment"

I also knew my logic above on how to detect ignore make sense because that's how I knew Danu ignored me and unignored me

Space Otter

Who's ACM?

Secret

Acuriousmind

user116211

@SpaceOtter WHHHat?

Space Otter

right

Secret

It is also important to emphasise that ACM increased in paying attention to my posts before the "deadly statment" is because of me asking him to analyse where my communication weirdness came from. However that extra attention he used caused him to focused too much on my low priority posts

and that seemed to cause a mental toll on him

Aug 31 at 14:31, by ACuriousMind

@0celo7 Well, I was tired of seeing all those weird and unconnected posts in the chat. And Secret also asked why it's so hard to understand him and how to do better. So I thought I would actually engage with his communication style and try to point out where it's flawed.

This is the deadly statment

Whenever a deadly statement is mentioned, it is followed by ignore

After this and a short message by him afterwards, there are no longer any responses to the @ s directed at him

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