Mathematics - 2021-12-27 (page 1 of 2)

Alex

12:00 AM

Well, laplace does not seem to be for the term $e^{-st}f(t)$ and here we have $e^{-st^{4}}f(t)$ for the last integral.

Ted Shifrin

Back to the kitchen for me.

BBIAB

leslie townes

xander i had not seen news of the cancellation on twitter. i had seen a lot of annoyance over no online option by people who were essentially boycotting what will now no longer take place. at least this move will appease their harshest critics.

...

it would surprise me if most fields that are still having their one or two 'big' meetings in person are still doing so in 10 years, covid or no covid.

Xander Henderson

@leslietownes Indeed.

David Choi

@TedShifrin thanks for your input; im gonna go away and think on it for a bit

Xander Henderson

12:19 AM

I am currently in charge of organizing the ArizMATYC meeting for October. I am planning for everything to be in person, but also making secret plans to do everything virtually (and will send out an announcement notifying folk of the virtual option about two weeks before the meeting).

But even in non-COVID years, we would be expecting a maximum of 80 people.

And travel is cheap, given that no one is going to be flying anywhere.

robjohn

@Alex I would be surprised if there were a closed form that did not involve a special function made for something like this integral.

leslie townes

this is the waste of big meetings. in my wife's field, many people regard the 'big meeting' as essential for some reason (likely historical only). but the major, broad-breadth talks and sessions at the events are not well attended. people go to see the 5 people they work with.

suggesting that you could cut travel costs of the 'event' by N/6 by just having five of each six people visit the sixth one.

Xander Henderson

@leslietownes Heh.

robjohn

@XanderHenderson I think that more and more things will go virtual. It just seems to make sense.

leslie townes

putting aside that everyone is emailing and zooming each other anyway.

Xander Henderson

12:27 AM

@robjohn I think that is absolutely true. And was already happening pre-pandemic.

I think that there are good reasons to hold small meetings in person (e.g. regional meetings, or very specialized meetings), but the JMMs need to go virtual.

Ted Shifrin

@leslietownes The January meeting used to be important for people looking for jobs. But when I was a postdoc and on the market, they assigned me an 8 AM slot at the SF meeting. No prospective hirers were at it, just some of my friends, and too many of them. Grrr.

I think I did have some on-site interviews, though.

leslie townes

it still had some of that when i was a grad student, but much less. things were moving onto mathjobs.org. i guess you could use the joint meetings to put your face to the name of an application, if someone you cared about but didn't already know was there.

these days you could also just find the phone numbers of the people you want to reach and text selfies to them.

and then "y no answer????"

then emojis like 😕👿💀💀💀💀💀👻

Ted Shifrin

@DavidChoi: What I told you about the maximum point was correct, but I believe I did not correctly compute the maximum value.

Yes, @leslie, I lived in the pre-historic and pre-email days.

leslie townes

before your position at UGA, you had to apprentice yourself to a mathematician in a village near athens for seven years.

fitting together broken maths in the math workshop behind the main storefront

by candlelight

David Choi

1:11 AM

@TedShifrin I just did some calculations myself, and I found the local maxima to be at $x = (1-\frac{1}{2^n})^{2^n}$, which gives has the value $(1-\frac{1}{2^n})^{2^n}(\frac{1}{1-\frac{1}{2^n}} -1)$. I belive this maximum value does indeed go to zero as $n \to \infty$ right?

@TedShifrin Looking back my original solution was just silly, as I just totally ignored the given domain. I guess that's why you don't do math in the middle of the night while sleep deprived 😅

Ted Shifrin

2:27 AM

@DavidChoi i think we agree. Well done. No problem.

robjohn

@XanderHenderson my wife and I have attended many more presentations from UCLA (where we both went undergrad) via Zoom. Those started in the spring of 2020, but are now becoming fewer and further in between. There are presentations from the Keck Observatory in Hawaii that we would never have been able to have attended before they became available on Zoom.

Ted Shifrin

I wonder if education and research will ever return to the old.

leslie townes

ted, if the next generation is stuck with only your viral tiktok dances about gaussian curvature, i think they will be well served.

Ted Shifrin

smacks leslie and pages munchkin

Semiclassical

o/

leslie townes

2:39 AM

robjohn you an astro person?

can someone tell me if it's 3 or 4 visible planets right now? or a week ago? i'm going crazy

we live near an airport, which doesn't help

Semiclassical

@leslietownes timeanddate.com/astronomy/night

leslie townes

hah this site is cool as hell, thanks

Semiclassical

huzzah for google

leslie townes

looks like i'm seeing venus, jupiter, saturn, and one or more airplanes

robjohn

3:02 AM

@leslietownes There are three: Venus is the bright one nearest the sunset. Jupiter is the next brightest almost on meridian at sunset. Saturn is approximately half way in between. Saturn is way dimmer and you need to wait until the twilight is much darker.

copper.hat

margaux was not bad last night, and no headache today...

leslie townes

3:15 AM

rob: thanks. we were seeing them on walks to see christmas lights after dark.

robjohn

@leslietownes I've been keeping an eye on them for a few months with the other people who walk their dogs in the park at the end of our street.

Ryan Unger

@robjohn princeton's policy seems to be purchasing nonrefundable tickets without insurance

hopefully I will indeed be reimbursed

leslie townes

someone in my wife's family has a pair of pretty good telescopes. he does weird events for some local society where members of the public can go to the beach and peek at stuff at 4am, or whenever. that's not for us, but we've looked through them during normal hours.

one time i was scolded by our accounts people for buying a nonrefundable ticket from LA to SF the day before a surprise trip. mid-week, in a season with normal weather where nothing would be canceled. "the client will only pay for refundable tickets." okay, but i did use the ticket and go to the meeting, and it was cheaper??? just tell them it was refundable?

add $50 to the invoice and let's you and me split $25?

Alex

3:32 AM

@robjohn I have been working on an alternative approach but have not been successful either. I don't know if it is possible to use derivative under the sign of the integral using the constant a as a parameter with something else. Thanks for the remark about special functions.

Here: math.stackexchange.com/q/4342659/941425 there is an interesting question that has not yet been answered.

robjohn

@RyanUnger I don't remember what I did when I was there, but I took whatever was least expensive, so I doubt I had insurance.

what tickets need to be refunded?

@Alex These look pretty ugly. Did you try them on a CAS?

my version of Mathematica does not seem to be able to do it

@leslietownes Actually, Mercury is there, too, but it is too dim to see easily, and much closer to the Sun than Venus at this time.

Too much haze here to see it well. One needs to be in clearer air than here.

hey, @Ted

Ted Shifrin

Rehi @robjohn …done cooking for tomorrow.

Alex

@robjohn no, in fact I now realise that because of your observation.

robjohn

@TedShifrin Now you can relax?

Alex

@TedShifrin vegetarian food?

Ted Shifrin

3:43 AM

@Alex hell no!

@robjohn Do I ever? PT early in the morning.

Alex

They say that vegetarian food gives you more years of life. I don't know if it's true, but meat is good. I guess it's a sacrifice one is willing to pay.

robjohn

@TedShifrin Ugh, sorry about that.

Ted Shifrin

No ugh required :)

Alex, after two heart surgeries and cancer … I’m not counting. I eat quite healthfully.

Alex

Among the healthy food that you can't eat? I have some problems with eating late, so I can't eat some acidic things for example.

@robjohn a question are you a physicist or a mathematician? I ask because of your status in the photos here at MSE. Very nice photos.

robjohn

@Alex the photos at MSE?

Alex

3:54 AM

@robjohn The link in their profiles here in MSE. I was reading a while ago one of your solutions and I took a look at your profile. So I found a link for the pictures "astrophotos" about the universe?

robjohn

I am an amateur astronomer and taught math at UCLA for a couple of years before being lured away by Apple.

@Alex Ah, I forgot that I had put that link in my profile

Alex

Apple the technological future maybe with Amazon?

@robjohn :-) yes nice photos

leslie townes

@Alex more years of life... but what kind of life??

Alex

@leslietownes That is a good question. We know that there are vegetarians (I am not one of them), maybe they can tell us what their kind of life.

eating a healthy diet+ exercising+ being a healthy weight+ not smoking+and moderate or not drinking= live longer

leslie townes

4:12 AM

yeah. and if you look at various well-nourished religious communities, i think it's also noncontroversial that dropping meat and alcohol entirely are good, too.

robjohn

@Alex Thanks.

leslie townes

i grew up near a community of seventh-day adventists (no meat, no alcohol). it seemed like half of them were in their 80s and 90s.

lots of confounding factors there, though. i don't think they believed in partying hard, or doing donuts on the freeway when it feels like nobody's coming.

Ted Shifrin

@leslietownes Bah.

leslie townes

i'm drinking wine while i type this. i feel i should point that out.

robjohn

I had some prime rib for dinner tonight and then a slice of apple pie for desser... >thunk<

copper.hat

4:37 AM

i had the left over roast beef and i made croquettes out of the left over mash and fried them in puddles of HEALTHY olive oil.

Sultan Ahmed Sagor

hi

copper.hat

lo

Sultan Ahmed Sagor

I need answer of this question

1

Q: N invitations in Rashida's Birthdays

Rashida wanted to invite her friends to her birthday and she was born in April. In a leap year, she started sending invitations from February 16 and completed them by March 15. At least one invitation was sent each day but no more than 50 invitations in total. Therefore, there has been a specific...

leslie townes

this is intending to be some kind of application of the pigeonhole principle.

see mindyourdecisions.com/blog/2008/11/25/… and gary training for a triathlon for one example.

i wonder if rashida knows gary. i hope she invites him to her birthday.

PM 2Ring

There are some great apps & sites for astronomical data. But if you can code, it's pretty easy to access the data of the JPL Development Ephemeris. This ephemeris series was created to support NASA missions, and since the 1980s, the JPL DE has been the basis of The Astronomical Almanac published by the United States Naval Observatory and Her Majesty's Nautical Almanac Office.

You can access the current JPL DE through your browser via the Horizons website, but there are also a few APIs for automated use.

Semiclassical

4:43 AM

ooo, neat

PM 2Ring

Horizons covers the time span from 9999 BC to 9999 AD, which is rather cool, although the full range isn't necessarily available for every target, since the errors get too large. So you can get data for eg the Jupiter system barycentre spanning the full range, but data for Jupiter itself is restricted to a smaller range.

Sultan Ahmed Sagor

@leslietownes thanks for your hints

I am checking your link

PM 2Ring

Unfortunately, you can't set up a Horizons query and share a URL for it. However, the Horizons page does provide the query in its batch-file format, and it's easy to write code that uses that batch file. Here's a little Sage program I just wrote which accepts batch-file data, and prints the results.

sagecell.sagemath.org/…

leslie townes

PM can it tell me when the world will end? i don't think we're gonna need data to 9999 AD

Sultan Ahmed Sagor

Gary is training for a triathlon. Over a 30 day period, he pledges to train at least once per day, and 45 times in all. Then there will be a period of consecutive days where he trains exactly 14 times.

how can I find whether he trains exactly 14 times

PM 2Ring

4:54 AM

Here's a batch-file to test it with. It retrieves a month's worth of data for Venus, as seen at Los Angeles at 4:00 UTC = 20:00 LA time.

MAKE_EPHEM=YES
COMMAND=299
EPHEM_TYPE=OBSERVER
CENTER='coord@399'
COORD_TYPE=GEODETIC
SITE_COORD='-118.24100,+34.05420,0'
START_TIME='2021-12-20 4:00'
STOP_TIME='2022-01-19 4:00'
STEP_SIZE='1 DAYS'
QUANTITIES='1,4,9,10,20,24,47'
REF_SYSTEM='ICRF'
CAL_FORMAT='BOTH'
TIME_DIGITS='MINUTES'
ANG_FORMAT='HMS'
APPARENT='AIRLESS'
RANGE_UNITS='AU'
SUPPRESS_RANGE_RATE='NO'
SKIP_DAYLT='NO'
SOLAR_ELONG='0,180'
EXTRA_PREC='NO'
RTS_ONLY='NO'
CSV_FORMAT='NO'
OBJ_DATA='YES'

leslie townes

PM's hacking my computer!

make him stop! 😲😲😲

PenAndPaperMathematics

Jesus, it's ephemeris is getting lower and lower - it's headed straight for Earth!

-"Don't Look Up"

Alex

What's happened here???

hahahaha

PenAndPaperMathematics

I'm a detective of mathematics - see my hat?

Sultan Ahmed Sagor

ok.

Alex

5:01 AM

@PenAndPaperMathematics Oh, Nice :3

PM 2Ring

The JPL DE is produced by integrating the equations of motion of the major solar system bodies, including perturbations from 343 asteroids. The equations include corrections for General Relativity, and are least-squares fitted to ground- & space-based observations. Data is tabulated in the form of Chebyshev polynomials, for accurate interpolation.

This answer space.stackexchange.com/a/56140/38535 has a Horizons program that shows the Moon & Sun angular sizes & positions relative to the STEREO-B space telescope. This one astronomy.stackexchange.com/a/28036/16685 makes an interactive 3D plot of the solar system barycentre.

This one astronomy.stackexchange.com/a/47345/16685 can create distance plots for any bodies that Horizons knows about.

leslie townes

5:19 AM

copper, you've got an at-bat here.

copper.hat

5:39 AM

had to look up the meaning of at-bat, was there a convex question?

leslie townes

distance plots for bodies horizons knows about.

i dunno, it seemed like there were possibilities there.

there's a subdivision near here called something like Horizons or Pathways or something. i always joke with my wife that it sounds like a halfway house.

sentenced to 5, got out in 2 but i've got to do 3 at Horizons.

that's a very specific observation. i think somebody more qualified than i am could find an innuendo in PM's remarks about distance plots.

that was the at-bat.

copper.hat

reminds me of my puzzlement on my gre

love_sodam

Schur–Zassenhaus theorem

The Schur–Zassenhaus theorem is a theorem in group theory which states that if G {\displaystyle G} is a finite group, and N {\displaystyle N} is a normal subgroup whose order is coprime to the order of the quotient group G / N {\displaystyle G/N} , then G {\displaystyle G} is a semidirect product (or split extension) of N {\displaystyle N} and...

leslie townes

oh cool, that relates to something we were doing the other day.

PM 2Ring

@leslietownes On Astronomy.SE, we occasionally get questions from people who want to know if the Earth will get destroyed when the Sun becomes a red giant, in 4 billion years or so. But IMHO, that's kind of irrelevant, since the Earth will be pretty-well uninhabitable in around a billion years, and things will be fairly unpleasant in half a billion. See en.wikipedia.org/wiki/Timeline_of_the_far_future

leslie townes

5:44 AM

i think earth will be uninhabitable far sooner than that.

admittedly, not for reasons astrological or astronomical.

copper.hat

people will evolve into cockroaches. we have seen examples at the highest level of government already

i mean, nowadays i put ice cubes in my wine, surely that is strong evidence for adaptation?

leslie townes

i had a german friend who did that once without asking in my apartment.

i looked it up later and apparently it was normal where she came from.

PM 2Ring

I grew up during the Cold War, when there was always the lingering possibility of a thermonuclear war. The odds of that happening are much lower these days. But of course we now have climate change, and the possibility of far worse pandemics on the horizon.

copper.hat

omg. someone brought a magnum (as in pistol) into my house once

leslie townes

as long as we have enough ice cubes for the wine, we are OK.

copper.hat

5:49 AM

i mean without my permission and they were not service folks

i was mad

leslie townes

haha, that's funny.

that's probably happened to us without us knowing.

copper.hat

nothing against guns per se, but there are certain rules, even at my level

even some friends of suspect talents would not do that

unless i was a mark, of course

leslie townes

one time we were at a friend's house and sought coasters for our drinks, so we did not ruin our hosts' dining table. it was suggested by our hosts that we look in a drawer of an end table. and the only thing there was a .45.

copper.hat

that's funny

leslie townes

i said something like "there's only a gun in here, are there coasters somewhere else?" very smoothly, although i could tell my wife was upset.

copper.hat

5:51 AM

hopefully no kids in the houuse

leslie townes

thankfully no.

copper.hat

have yet to teach my daughter to shoot

my son can manage a .22 at least

more stick shift driving today

leslie townes

have him go up marin. stick 101.

PM 2Ring

@copper.hat And comic book characters becoming politicians.

leslie townes

PM: please don't disrespect donald duck in that way.

copper.hat

5:53 AM

@PM2Ring that was the protot cockroach

@leslietownes marin is next, figured he needs a little lead in first, we hit the freeways and point richmond today

leslie townes

have him do every spoke of the circle before marin, and then ZOOP up marin.

a joke you can do before you get to the top is: "we're almost there, we just need to gain a little altitude." keep repeating this remark until he laughs or you have a car accident.

copper.hat

:-) the wrx is a bit challenging normally, serious turbo lag, marin will be interesting

i realised that in left hand drive automatic cars, one tends to drive with a dominant right, so gear changes require that be unlearned first

i am trying to inspire him by sending wrc rally videos

i suspect this is the opposite of what many parents do with their 18 yo son

looking for my khia video

leslie townes

i'm trying to think of some other driving challenges in that area.

Alex

youtube.com/watch?v=O3XGynvy_V4 it's the correct

:-(

leslie townes

if the gilman/80 on-ramps are still a complete no-mans land with no signals, maybe that?

copper.hat

5:59 AM

he's good with the general challenge, its just the stick shift adaptation. he needs to wean himself off his right hand first (sounds bad).

i want a quiet place that needs lots of steering & gear changes at the same time :-)

leslie townes

i learned on the state highways between napa and sonoma, which have some of that

plus drunks on the weekend for a fun obstacle course

copper.hat

i suppose i could bring a bottle in the car with me

Alex

Riemann's hypothesis the holy grail of mathematics?

leslie townes

or a few cans

PM 2Ring

A couple of decades ago, there was a guy here in Sydney who drove around in a left-hand drive car, with a St Bernard in the passenger seat. The car had a small racing-car style steering-wheel, which wasn't visible over the dash, and a large fake steering-wheel for the dog. :)

leslie townes

6:07 AM

did the dog buy into the bit, or was he an unwilling participant?

PM 2Ring

The dog loved it.

leslie townes

i could see my cat enjoying something like that, but i don't drive the right kind of car

PM 2Ring

It's a bit less believable with a cat, though. Unless it's a really big cat.

leslie townes

yeah, it wouldn't work. olivia isn't even 9 lb.

PM 2Ring

Cats would be terrible drivers. They'd never use their turning indicators.

Ryan Unger

6:19 AM

@robjohn jmm

same as @XanderHenderson presumably

copper.hat

my brother worked as an orthopaedic surgeon in sydney for a while, at the time apparently the fun thing to do was to take the roof of a car, turn it upside down and take rides in it while towed by another vehicle. all fun until a sudden stop occurs and my brother gets another on his roster.

PM 2Ring

We like to call Australia "The Clever Country", but there's no shortage of idiots.

copper.hat

to be fair, i think such things are uniformly distributed.

plus a health dose of irish genes

he worked in iraq at the end of the iran-iraq war and had to treat a lot of folks who were injured by bullets loosed by merrimakers.

one poor kid was paralysed

and on that happy note...

leslie townes

lifting the AK skyward and toward albany.

copper.hat

back to my white wine sans glace

i'm telling you, watching narcos mx is changing my whole life perspective

a new motivation has come over me

leslie townes

6:29 AM

i knew someone who had to do UN 'peacekeeping' in the balkans. they called that stuff 'slivo-shooting' because it was accompanied by slivovitz (not transcribed correctly).

shooting at the sky is something innate.

copper.hat

i can understand the deep drive to do something destructively stupid

leslie townes

we just throw potatoes at each other in this house.

copper.hat

whoa, potatoes are sacred don't you know

peeling spuds was one of the select non violent punishments in boarding school

when going to sleep, i now count sheep modulo various coprime factors.

leslie townes

in accordance with the sheep remainder theorem. good luck.

copper.hat

baaaaa

have not made a contribution (other than khia) lately, off in search of something convex

Lalit Tolani

6:41 AM

Suppose we have a function which satisfies following relation

$$f(x)=\int_0^xf(t)dt$$

I found $f(x)=e^{x+c}$

copper.hat

that can't possibly be true. set $x=0$ to get $f(0) = 0$.

Lalit Tolani

Yes that's the problem, you caught it at the exact point

copper.hat

the only solution is $f=0$.

Lalit Tolani

But How

The equation I get is $f'(x)=f(x)$

copper.hat

and...

leslie townes

6:46 AM

your analysis, correctly performed, might show that f(x) = C e^x for some scalar (not necessarily positive, and not necessarily nonzero).

now enforce the initial condition.

Semiclassical

an integral equation contains more info than the differential equation

in particular, the integral equation contains (enforces?) the initial condition

Lalit Tolani

@leslietownes Hmm but how can $e^c=0$ be true in real numbers for some c.

Semiclassical

it can't. that's the point

copper.hat

it can't , why would you say that it is?

Koro

creation of a counterexample to: if f is defined on [0, $\infty)$ and is such that the sequence $(f(an))$ converges to $0$ for every $a\gt 0$ then $\lim_{x\to \infty}f(x)=0$.

Semiclassical

6:47 AM

what you've found is a family of solutions, parametrized by $c$

it's just that this family of solutions doesn't include $f=0$

Koro

Let $f$ be such that $f(n\sqrt 2)=0$ for all $n\in \mathbb N$ and that $f(x)=2$ if $x\ne \sqrt 2 n$ for any $n$. I think this works.

Semiclassical

if you write the family instead as Ce^x, then f=0 is in the family. slightly different

Koro

nope it doesn't if a is rational :(

Lalit Tolani

@Semiclassical So basically I have found a family of solutions which doesn't include the actual solution

Semiclassical

if you write it as $e^{c+x}$, yes

leslie townes

6:51 AM

just pay very close attention to how you 'find solutions.'

if you make hypotheses in order to arrive at where you go, write them out and see what happens if those hypotheses aren't satisfied.

Semiclassical

now i wonder what the simplest way to prove $f(x)=\int_0^x f(t)\,dt\implies f=0$

Lalit Tolani

@Semiclassical But then I can show that this isn't only true when we have positive coefficients that is $f'(x)=f(x)$ has solutions of type $Ae^x$ as @leslietownes said above

copper.hat

depends on what you mean by simple, bellman gronwall lemma leaps to mind

Semiclassical

yeah, "simple" is always slippery

copper.hat

implicit in such things is what universe $f$ lies in.

implicit is that $f$ is integrable

Semiclassical

7:00 AM

what i had in mind was something like $f(x) = \int_0^x \int_0^t f(t')\,dt'dt$

copper.hat

yep, hence my previous comment and absolute continuity

Semiclassical

and appeal to the Cauchy repeated integral formula

copper.hat

a little fixed point something or other.

appealing to picard is probably the easiest.

Semiclassical

yeah

PM 2Ring

Well, first show that $f(0)=0$. Then since $f(x)=Ae^x$, $A=0$. Plus some details. ;)

Semiclassical

7:02 AM

even simpler here since Picard-Lindelof has you switch to the integral equation anyways

copper.hat

yesm its a fixed point thing using absolute continuity of the measure $\int_A |f|$.

Semiclassical

neat

copper.hat

basically Picard-Lindelof in disguise

differential/integral inequalities are interesting

and neglected

Lalit Tolani

Wait, I thing I got it, please check whether I am correct or not

The correct solution for equation will be

$|f(x)|=e^ce^x$

copper.hat

no. stop. read/listen.

the differential equation is $f'=f$ and the solutions are of the form $f(x) = ce^x$ for some constant $c$.

Lalit Tolani

7:06 AM

@copper.hat Yes

copper.hat

since $f(0) = 0$ then we must have $c=0$ so the solution is $f(x) = 0 e^x = 0$.

Lalit Tolani

Yes

copper.hat

so we're done, right? i can go back to my wine and convex problem hunt?

Lalit Tolani

@copper.hat I will take 30 sec more of your life

copper.hat

you can have $29.\dot{9}$.

Lalit Tolani

7:10 AM

the diffrential equation we get is $f'(x)=f(x)$ which gives $|f(x)|=Ae^x$ where A is positive and hence general solution can be written as $f(x)=ce^x$

copper.hat

where are you getting the absolute value from?

Lalit Tolani

$\int \frac{dy}{y}=\ln|y|+c$

leslie townes

if f' = f identically iff (f/e^x)' = 0 identically iff f/e^x is constant. that's how i'd do it.

the formalism with definite integrals works but you need to keep track of the absolute values and c's and do all kinds of goofy case analysis to justify the formalism.

copper.hat

the general solution of $f'=f$ is $f(x) = c e^x$.

leslie townes

simpler in this one instance to just go for the jugular.

Lalit Tolani

7:13 AM

Yes it's clear now, now you can resume your wine and convex problem hunt, Thankyou all , it's really annoying when Maths tricks you

copper.hat

indefinite integrals can be confusing.

Anjani Gupta

7:30 AM

Hi! Anyone active?

Can someone give me an example of a function $f:\mathbb{R}\to\mathbb{R}$, which has well defined derivative at a point say $x_{o}$ but not differentiable on any neighborhood of that point?

leslie townes

something like f(x) = x^2 if x is rational and 0 otherwise oughta do it. |(f(x) - f(0))/(x - 0)| <= |x|.

Anjani Gupta

In the complex case, $f(z)=|z|^2$ has well defined derivative at z=0, but not differentiable in any open neighborhood around 0.

copper.hat

was that a request for assistance or a quiz?

Anjani Gupta

Oh great Lesllie! It seems to work.. The reason I was looking for such a function was clarify the definition of differentiability.

Assistance.. no quiz. Not enrolled in any formal school :P

leslie townes

copper: are you giving us a quiz?

copper.hat

7:47 AM

i am. Q1 (5 pt.) how many bags of cement does it take to ruin a driveway?

love_sodam

If $G$ is a nilpotent group then for $H<G$ with $[G:H] = n$, $g^n\in H$ for all $g\in G$.

copper.hat

8:03 AM

i found a question and added the convex tag so i could get my nightly pedantic fill.

i see quantum crypto fusion is still absorbing lots of funding.

this is real perpetual motion

i think 99% of my rep comes from users that will be removed. some conspiracy theory here...

Koro

8:38 AM

I think this works: $f(n\sqrt 2)=1$ for every $n$ and $f(x)=0$ else.

as a counterexample to: if f is defined on [0, $\infty)$ and is such that the sequence $(f(an))$ converges to $0$ for every $a\gt 0$ then $\lim_{x\to \infty}f(x)=0$.

nope, it fails when $a=\sqrt 2$ :(

Koro

10:18 AM

Is $2^r$ irrational for every rational r in (0,1)?

PM 2Ring

2:41 PM

@Koro Of course. Let $2^{p/q} = u/v$, with $\gcd(p,q)=\gcd(u,v)=1$. Then $2^pv^q=u^q$. Now $v$ divides the LHS, so it must divide the RHS, but that's impossible, since $v$ & $u$ are coprime.

AMDG

2:58 PM

Merry Christmas!

Lalit Tolani

4:15 PM

How do we solve the functional equation $f(x+y)=f(x)+4y(x+y), f(1)=3$ where x,y are real numbers

Substituting x=1 gives $f(1+y)=4y(y+1)+3$

which further gives $f(y)=4y^2-4y+3$, however this doesn't satisfy the original rule

Where's the problem?

leslie townes

i'll trust your algebra. do you have any general reason to expect that the functional equation has a solution with f(1) = 3? it might not.

Lalit Tolani

So basically my solution is inconsistent

leslie townes

assuming your calculations are correct, the original problem is inconsistent and does not have solutions

and your calculation is the proof of that

the way you derived an expression for what f would have to be looks completely fine to me

Lalit Tolani

4:33 PM

Yes that makes sense, thankyou @leslietownes, by the way you are from which part of world

leslie townes

california, los angeles area.

Lalit Tolani

Cool

Ted Shifrin

After we secede in the next decade, that might be the right answer!

Koro

@PM2Ring I realized that. Thanks.

copper.hat

6:24 PM

i thought california split into 4 states years ago

leslie townes

haha i love reading about those proposals

even the people who are serious about them are clearly like "ok, there's this, and there's this, and, uh... hm... who gets fresno? ah, who cares"

copper.hat

its a bit like brexit and that idiot farage. ohh, i got my way and screwed the country up so sayonara...

i think our last administration had a few similarly minded contributors.

leslie townes

?? brexit was an astonishing success??

anonymous

in major league baseball, a fastball travels the distance (60 ft 6 in) from the the picture to the catcher in 0.41 s. On average, the batter connects with the ball 0.28 s after the start of the swing. Using these figures , estimate how long the ball is in range to be hit by the batter. In other words, by how much time can the batter be off in the start of the swing and still hit the ball?

Please help?

copper.hat

6:40 PM

well, one big plus for brexit is that if my daughter tires of her current career path, there is always the lucrative lorry driver option.

anonymous

~~picture~~ pitcher

Oops 🤭

copper.hat

i am a baseball ignoramus, but i imagine one needs to make some estimates to solve this problem, is this a science olympiad fermi question :-)

leslie townes

that's pretty fast pitching

copper.hat

what has a water jug to do with it all?

anonymous

It's actually a "Portfolio Project" question in a highschool algebra textbook.

rb3652

6:55 PM

Hi all

anonymous

Hi

leslie townes

that explains why the numbers don't make very much sense :)

anonymous

:)

copper.hat

i don't really understand the model of what is happening that they are looking for

leslie townes

it's a disaster of a problem. skip it if you have the option

copper.hat

6:57 PM

ask for clarification

leslie townes

the catcher is going to get hit by the bat if he's got his glove at the tip of home plate

anonymous

They want us to "Draw a diagram and explain your reasoning."

leslie townes

training yourself to contort your mind to ill-formed problems is not a good activity.

unless you are being forced to do it.

the ball's going fast. it's hittable only when it's within some small distance of being caught. the problem doesn't give you much of an idea of that distance. you might need to know a bit of baseball to estimate that.

also, backing out when you can begin the swing from an 'average' swing is hopeless.

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$Mathematics$ Mathematics