Mathematics - 2023-07-01 (page 1 of 2)

Xander Henderson

00:01

@shintuku Look, you are the one that is getting angry about perceived aggression. That aggression simply doesn't exist. No one cares enough about you to downvote your questions just to be an "asshole". You are likely to be much happier if you stop assuming that people who simply disagree with you are specifically targeting you, or out to get you.

shintuku

see? you don't know what you're talking about, why do i have to be angry, and why should i think people are out to get me

Xander Henderson

I don't know why you choose to be angry and decide that others are "assholes". That's on you, not me.

Though perhaps "combative" would be a better description than "angry". I can't really assess your emotional state, though I can certainly describe the style of your interaction.

shintuku

ah there, something that sounds more like knowing what you're talking about

Ted Shifrin

@Xander Now you know one of the reasons I stopped interacting with said person.

Xander Henderson

@TedShifrin Indeed.

@mick Why? Who cares? What is the motivation behind this question? Why $2/3$ and not some other parameter? Why does it need to be meromorphic on $\mathbb{C}$? What are you planning on doing with this function? How much do you know about the general theory of Dirichlet series?

Sine of the Time

00:12

How do you pronounce Dirichlet? Using French or English?

Xander Henderson

@SineoftheTime "deer-REEKH-lay" (with the "KH" being like the "ch" in the Scottish word "loch"). I assume that this is the French pronunciation, as it is the one I received from my advisor, who is French.

Sine of the Time

Same, but instead of "-lay" I say "-let"

Xander Henderson

@SineoftheTime Boo! :P

D.C. the III

What is Stack Exchange endgame? why are they doing this?

Xander Henderson

But Dirichlet was German, if I recall correctly, so probably neither the French nor English pronunciation is entirely correct.

@D.C.theIII I would guess "money".

D.C. the III

00:17

Are they trying to find a way to be profitable?

just as I write you answer. lol

I guess that is always the answer when folks want to change things and make it difficult for their user base/ population/ etc

Xander Henderson

@D.C.theIII Yes. But the Q&A sites are not what they make their real money on.

D.C. the III

Where do they make money?

Xander Henderson

@D.C.theIII "Teams".

Sine of the Time

@XanderHenderson yes, instead of French I should have said German

D.C. the III

Ah....like Slack or Microsoft Teams

Xander Henderson

00:19

try.stackoverflow.co/explore-teams

D.C. the III

thnx for the link

Sine of the Time

I was wondering if in the U.S., after finishing an exam, you can reject your mark if you don't like it

Xander Henderson

@SineoftheTime No? In what context?

D.C. the III

fair....get to leverage the Answer databases that are for free but in a curated environment for the respective firm

Sine of the Time

@XanderHenderson Say you do Calc 1 exam and you don't like the mark, can you refuse the mark and repeat the exam?

Xander Henderson

00:21

@SineoftheTime Not generally, no.

But, like, I still don't understand the context.

Like, a midterm exam? A final exam? An AP or other placement exam?

What are the stakes of this hypothetical exam?

shintuku

some systems have 3 exams and you need 2 to pass or stuff like that

Sine of the Time

I don't know the procedure in the U.S., but in general I'm referring to the "final" mark

Xander Henderson

@SineoftheTime Most American institutions don't use high stakes examinations to assign marks to a course of study.

Typically, a semester long class will include at least two or three examinations (including a final exam), as well as other graded work (quizzes, homework, projects, presentations, etc).

Ted Shifrin

@XanderHenderson No, German. French would be sh.

Sine of the Time

It happened to me that I did an exam, but didn't like the mark so I repeated it

shintuku

00:25

@SineoftheTime there's not often a recuperatory exam no

Xander Henderson

@TedShifrin Like I said, I assumed that the pronunciation was French, as Michel is French, but maybe he uses the German pronunciation? He is actually usually pretty good about "correct" pronunciation.

shintuku

@SineoftheTime you can check MIT course syllabi to see the grading schemes, that's the standard stuff

Ted Shifrin

Europeans are better than Americans. I had assumed Dirichlet was French, but i think he was Alsatian with a German name.

Xander Henderson

@SineoftheTime This is usually not possible. It is sometimes possible to withdraw from an examination before it is marked (e.g. if you think you have done poorly on the SATs (a college placement exam thing), then you can walk out and not have them marked).

Ted Shifrin

@SineoftheTime In the US you have to repeat the whole course.

Xander Henderson

00:27

But once something has been marked, that is typically the end of it.

Sine of the Time

@shintuku I guess the system of examination is different. In my uni, I follow the lesson for approx 3 months, then there is a session with all exams. There are three sessions (winter, summer and the one in September) and all teacher must schedule at least one "appeal" (don't know if it's the right name)

Xander Henderson

@SineoftheTime This is very much not how things are typically done in the US. Your course grade is almost never just the result of a final exam.

Sine of the Time

Here are all final written exam plus oral exam

at least in the math faculty

Xander Henderson

Indeed, lots of American institutions have explicit policies against all-or-nothing final exams.

one potato two potato

I hate oral exam

shintuku

00:30

@SineoftheTime yeah i heard of it, it's very different in that sense. US-style you have to try to make up for your grade in the next exam

Sine of the Time

@onepotatotwopotato Usually oral exams increase your mark :)

A couple of decades ago, the exams were only annual.

one potato two potato

My algebra professor always says that your IQ lowers by 30 when you're in front of the blackboard. But in an oral exam, I say lower by 50.

Xander Henderson

@onepotatotwopotato Many people do. Others really like them (personally, I would much rather be examined orally---there are more opportunities for me to demonstrate what I know, and to correct mistakes).

Ted Shifrin

00:51

I had oral qualifying exams for my PhD. My teaching experience as an undergraduate made me quite confident at the board.

But most students were terrified.

one potato two potato

There's not much chance to recover questions I couldn't answer in the oral exam.

Xander Henderson

@onepotatotwopotato Every oral exam I have ever taken (or given) includes some back-and-forth between the examinee and the examiner. If you mess up something major, the examiner will typically give you some kind of hint that you screwed the pooch.

one potato two potato

01:09

actually yeah, I have no good memory for oral exams so I may be biased.

Ted Shifrin

Why is memory different orally than on paper? Just panic, I assume.

one potato two potato

01:21

Panic of course. But I'm not very used to oral exams so it's hard for me to handle it when I'm panicking on oral exams. But I'm used to written exams so I can handle panic quite well and actually, I usually don't panic because I know how to prepare.

Xander Henderson

@onepotatotwopotato You might try working on that, some. In the Real World™, written examinations are rare, while oral examinations are quite common (in the form of, say, presenting an idea to a research group, or a proposal to a development team, or whatever).

Oral exams are much more like how the Real World™ functions (though still artificial).

one potato two potato

I'll keep that in mind.

Ted Shifrin

And everyone has to do a PhD oral exam and presentation, as far as I know.

Xander Henderson

@TedShifrin Not everyone. Only those people who are sick enough to want a PhD. :P

one potato two potato

01:38

One skill I learned is to keep talking about what I'm thinking when I don't know the answer immediately so that examiners can know what I'm thinking and give a hint if they want.

Xander Henderson

@onepotatotwopotato Yup. Don't claim to know something you don't, but clearly explain your thinking, and the bits and pieces which are relevant. If you're lucky, you will eventually either remember or work out out the details.

And, like, real math is collaborative. We explain to each other what we are thinking, and poke holes in the arguments of others.

Ted Shifrin

Good, potato. Sometimes you see how to do it with further hypotheses, so do that and then ….

@XanderHenderson Of course. Perhaps in error, I surmised potato might be headed there.

Daniel Donnelly

@XanderHenderson bits ? Do you mean binary digits?

Xander Henderson

@DanielDonnelly No. Just... no.

Daniel Donnelly

k :)

Ted Shifrin

01:50

You meant bytes and pieces.

Xander Henderson

No, I meant Reese's Pieces.

Ted Shifrin

That’s just peanuts.

Xander Henderson

In a hard candy shell!

And, if I recall correctly, enough sugar to kill an elephant.

Ted Shifrin

Oh chocs shucks.

Xander Henderson

Oh... shoot. It's Friday. I have homework to turn in.

Daniel Donnelly

01:52

Enough thc to make a horse cough

Xander Henderson

I should probably get that done.

Ted Shifrin

Homework for whom ?

Daniel Donnelly

Your dad

son

:D

user4539917

Your job

Xander Henderson

@TedShifrin I enrolled in a creative writing class over the summer.

Daniel Donnelly

01:53

Neato

Ted Shifrin

Oh, cool.

user4539917

Nice.

Daniel Donnelly

CC?

Ted Shifrin

Late to start a short story!

Xander Henderson

I am supposed to submit a 1000 word bit of "flash fiction" before midnight. It is mostly done, but needs some editing.

Ted Shifrin

01:54

Ah.

Xander Henderson

@DanielDonnelly Yes, at the CC where I work.

Daniel Donnelly

Nice, cubic centimeters

metric system

Well, I would flash the bowl then flash the paper with words

Xander Henderson

@TedShifrin That's next week---we are supposed to turn in a max 7000 word fairy tale rewrite. I'm going for a Hansel and Gretel kind of thing, but with modern tech.

Daniel Donnelly

a flash in the bowl a day keeps the doctors at bay

user4539917

7,000 words :O

Daniel Donnelly

01:56

@XanderHenderson maybe use technology to generate a paper? I thought you programmed too - is that right?

Xander Henderson

@DanielDonnelly I code badly. :P

Daniel Donnelly

oh

Nice

Everyone does

hence it's a hard problem

Xander Henderson

But I was more referring to the fact that Hansel and Gretel have a cleverphone.

user4539917

What's the longest assignment?

Daniel Donnelly

Hanibal and Gretchen

The longest assignment is infinity

Great questoin, but it's a little broad

you're going to need to narrow the scope down a bit

Xander Henderson

01:58

@user4539917 The $< 7000$ word thing for next week is the longest, I think. If I read the schedule correctly, we switch to poetry next week.

user4539917

∞ + 1

Xander Henderson

Er... the week after next.

Anywho, I really do need to get this thing done. Laters.

Daniel Donnelly

Be creative

You are creative

b/c you do math

user4539917

cya pal

have fun

Daniel Donnelly

Viel Spass

Smoken Sie eine bitte Cheba

*ein I mean

That's some German that I invented so probably doesn't read sensically

user4539917

02:18

You should write a poem on the poetry of logical ideas :P

> Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

Xander Henderson

03:16

@user4539917 About 20 years ago, I proved that the square root of 2 is irrational, in sonnet form.

I mean, not a very good sonnet. The syllable pattern was not quite right. But I got the rhyme scheme correct. And the meter was... okay.

user223626865

04:42

Classic proofs set in poetic form, sounds like a convincing reason for human flourishing.

ODE TO HIPPASUS (a song about √2)

►

Thomas Finley

07:14

0

Q: Starting from generating function of Legendre polynomials prove that: $\int_{-1}^{1}xP_n(x)P_{n-1}(x)dx=\frac{2n}{4n^2-1},n=1,2,3,\cdots$

Write the generating function for Legendre's Polynomials. Starting from generating function prove that: $$(2n+1)P_{n}(x)=P'_{n+1}(x)-P'_{n-1}(x),$$ and hence prove $\int_{-1}^{1}xP_n(x)P_{n-1}(x)dx=\frac{2n}{4n^2-1},n=1,2,3,\cdots$ (Here, $P_n(x)$ denotes Legendre Polynomial of degree $n$) I tr...

ordinary-differential-equations

Need help with this edited post.

Daniel Donnelly

07:43

Got a riddle for you

1 - 4 = ?

-3

+ 6 = 3

-8 = -5

+9 = 4

etc.

Do that and then you'll see the pattern. Isn't it amazing the alternating sums of composites form patterned sequence!

0

Q: The alternating partial sums of composites $1 - 4 + 6 - 8 +9 - \dots$ are the sequence $-3,3,-5,4,-6,6,-8,7,-9,9, \dots$

While there is no known "pattern" in alternating sums of the ordered primes, I thought what about the ordered composites? $$ 1 - 4 = -3 \\ -3 + 6 = 3 \\ 3 -8 = -5 \\ -5 + 9 = 4 \\ 4 -10 = -6 \\ -6 + 12 = 6 \\ 6 - 14 = -8 \\ -8 + 15 = 7 \\ 7 - 16 = -9 \\ -9 + 18 + 9 \\ 9 - 20 = -11 \\ -11 + 22 = 1...

elementary-number-theory summation unique-factorization-domains pattern-recognition alternating-expression

Eureka!

s.harp

cambridge.org/core/journals/judgment-and-decision-making/…

> Joey went to the store and bought a pack of chips. A bottle of water costs $3.00, a pack of chips costs $1.00 and a pack of gum costs $2.00. How much did he spend in total? […] Performing the sum to reach $6 is incorrect, but in a specific way. It is not random noise. […] 74% of participants responded correctly with $1, and 24% with the mindless math answer of $6 (N = 196).
> In contrast, consider the same problem with harder numbers: Joey went to the store and bought a pack of chips. A bottle of water costs $1.05, a pack of chips costs $0.75 and a pack of gum costs $1.70. How much did he…

user 726941

08:11

^When and why people perform mindless math

> When faced with difficult tasks, people are often eager to start doing something. But this eagerness may preclude them from correctly representing the problems that they are so eager to start solving. When we ask people to “take their time”, we have to be more specific about when they should take their time. The execution of operations gives the illusion of progress, but if the problem is represented incorrectly, it remains just that, an illusion.

Daniel Donnelly

Mindful maths

user 726941

is accurate maths

the problem is people have been conditioned to the importance of working quickly

Alex D

Hello, all. I'm just trying to understand one of the exercises in Arnold's *Ordinary Differential Equations*. Neither the exercise nor the provided answer seems to be making sense. If anyone can help, that will be much appreciated.

Exercise 4 in chapter 1, section 4 on Quasi-homogeneous Equations:

Choose the weights of the variables so that the differential equation of the phase curves of Newton's equation $\ddot{x} = Cx^k$ is quasi-homogeneous.

Provided answer:

The equation of the phase curves is $dy/dx = Cx^k/y$. Consequently $2\beta = (k + 1)\alpha$.

Daniel Donnelly

1 - 4 + 6 - 8 + 9 - 10 + 12 - 14 + ...

Alex D

In this context, quasi-homogeneous means a DE of the form $dy/dx = F(x,y)$, where $F(e^{\alpha s} x, e^{\beta s} y) = e^{rs} F(x,y)$.

In other words, if you multiply both of the inputs to $F$ by some special constants, it's the same as multiplying the output by some other special constant. If this works, the factor $r$ is called the "degree" of the quasi-homogeneous function.

One thing I am struggling to understand: the problem statement doesn't mention $y$ at all. It appears that the use of $\ddot{x}$ in the problem statement implies there is some other independent variable, which for almost all the examples in the book would be called $t$.

But then the provided answer talks about $dy/dx$.

The mention of "phase curves" in the problem and answer also seems to imply, from the way that term is used through the rest of the book, that there should be at least 2 dependent variables $x$ and $y$ which are functions of an independent variable $t$. The "phase curves" should be all the values of $(x,y)$ which you get if you start from some point in phase space and then follow the evolution of the system with increasing $t$.

But again, the problem statement doesn't say anything about what $y$ is in this case.

Not sure if this is worthy of posting as a question on MO. I may just be misunderstanding the terminology used in the problem statement.

PM 2Ring

12:24

@s.harp Related: the missing dollar riddle

PM 2Ring

12:34

@XanderHenderson In the Western world, written exams are a relatively new innovation, first becoming popular in the 1700s, but they were used in China at least 1000 years earlier. en.wikipedia.org/wiki/Exam#History They were mostly adopted to save time, which was necessary as more men sought higher education. Of course, they can also help to reduce subjectivity & bias.

PM 2Ring

12:47

@XanderHenderson Nice. I was reminded a few days ago of the Indian mathematician-astronomer Aryabhata (476–550 CE). He gave many important results in trigonometry, but rarely gave proofs. Fortunately, several later writers did give proofs in their commentaries on his work.

Back in those days, people didn't have the modern attitude towards rigorous proof. And in the Indian tradition, it was standard to present knowledge in a poetic form. I guess it makes sense when paper is precious and you want students to memorise your teachings. It's much easier to memorise stuff when it's written as rhyming couplets. I assume the students would recite that stuff in a sing-song voice. :)

冥王 Hades

Beef Goulash

I like puzzles

sunny

From knowing $\mathbb{N}$ and $\mathbb{Q}$ are both countable infinite, and the fact that the power set of any set yields a cardinality strictly greater than the set, can we conclude that there is a bijection between $\mathcal{P}(\mathbb{N})$ and $\mathcal{P}(\mathbb{Q})$?

I do not think so, since we don't know how much the power set "raises" the cardinality of a set, right?

The reason for the question is a passage in my lecture notes stating that $\mathcal{P}(\mathbb{N})$ and $\mathcal{P}(\mathbb{Q})$ do have the same cardinality because $\mathbb{Q}$ is countable infinite. I do not see the reasoning behind that argument.

PM 2Ring

13:03

But since $\mathbb{N}$ and $\mathbb{Q}$ are both countable infinite we have a bijection between them, so they have the same cardinality, and hence so must their power sets.

Prithu Biswas

2

Q: If |A|=|B|, then $|P(A)|=|P(B)|$

If $|A|=|B|$, then $|P(A)|=|P(B)|$ This is what I have done so far: Assume $|A|=|B| \Rightarrow \exists$ a bijection $f:A \to B$ Define $F: P(A) \to P(B)$ where $ F(S)=\{f(a)| a\in S\}\subseteq B $ Claim: $F$ is injective Suppse $ F(S)=F(S') \Rightarrow s=s'$. Let $$ a \in S \Rightarrow f(...

discrete-mathematics proof-verification proof-writing

sunny

@PM2Ring hmm, this is exactly my confusion I guess, but I will look into what @PrithuBiswas linked

Prithu Biswas

Let G be any group and Let N be any subgroup of G. If the product of any two right cosets of N in G is also a right coset of N in G, prove that N is normal.

Can anyone give a hint?

shintuku

13:20

@PrithuBiswas quotient is group iff N normal

Alessandro Codenotti

@sunny Any map $f\colon A\to B$ induces a map $P(A)\to P(B)$ by $f(X)=\{f(x)\mid x\in X\}$ for any $X\subseteq A$. Check that if $f$ is a bijection then so is the induced map on powersets

sunny

@AlessandroCodenotti ok, will do, thanks!

Jakobian

13:39

my productivity increases ten-fold when I'm not at my computer

2

computer is good for researching stuff though

geocalc33

Does there exist a pair of smooth manifolds $(M,N),$ $M \ne N$ related by an isometry $g,$ s.t. every smooth regular foliation of $M$ satisfies some differential equation on $N,$ and every smooth regular foliation of $N$ satisfies some differential equation on $M?$

from what I understand, smooth regular foliations of $M$ and $N$ resp. satisfy particular types of differential equations whose forms depend on the equipped metrics. Restrict a foliation on $N$ to the metric of $M$ and ask whether it satisfies some D.E. w.r.t. metric of $M.$ And vice versa.

Jakobian

14:01

@PrithuBiswas I assume that by product of $Na$ and $Nb$ you mean $(Na)(Nb)$ where $AB = \{ab :a\in A, b\in B\}$?

Then taking $b = e$, you have $NaN = Nc$ for some $c\in G$

so you need to somehow prove we can replace this with $aN = Nc$ and $c = a$

we have $c = n_1an_2$ for some $n_1, n_2\in N$ so $Nc = Nan_2$, thus $NaN = Nan_2$ for some $n_2\in N$

@PrithuBiswas try carrying over from here

PM 2Ring

@sunny You might like oeis.org/A002487 "a(n)/a(n+1) runs through all the reduced nonnegative rationals exactly once"

Jakobian

this will imply $aN\subseteq Na$ for all $a$, and by taking inverses...

Thomas Finley

14:46

In this case, I dont understand, the portion "differentiation will show ...."

I mean differentiate which one?

And differentiate wrt what?

This is a chapter on Exact differential equation

Thomas Finley

15:12

@SouravGhosh Do you have any ideas bout this?

Sourav Ghosh

$M(x, y) dx+N(x, y) dy=0$

user 726941

^used a lot in thermodynamics

Sourav Ghosh

Partial derivatives ☺

$M(x, y) dx+N(x, y) dy=0$

$\mu(x)M(x, y) dx+\mu(x)N(x, y) dy=0$

$M_1(x, y) dx+N_1(x, y) dy=0$

$M_1(x,y)=\mu(x)M(x, y) $

$N_1(x,y)=\mu(x)N(x, y)$

Check $M_1(x, y) dx+N_1(x, y) dy=0$ is exact.

Thomas Finley

15:50

@SouravGhosh Well, the condition that a differential equation is exact, is that $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}.$ But in here, $\frac{\partial M_1}{\partial y}= \frac{\partial M\mu(x)}{\partial y}=\mu(x)\frac{\partial M}{\partial y}.$

Similarly, $\frac{\partial N_1}{\partial x}=\frac{\partial N\mu(x)}{\partial x}=N\frac{\partial \mu(x)}{\partial x}+\mu(x)\frac{\partial N}{\partial x}$. But how to show that indeed, $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ ?

That was tbh, precisely my problem.

Ted Shifrin

16:48

You’re asking the wrong question. The answer to the right question is immediate.

shintuku

17:10

do quotients of free objects generate the entire category? i.e., any X is quotient of a free X, substitute "group, abelian group, module" for X

Thorgott

17:23

in those cases, yes

in general, it depends on the setting

shintuku

noted, thank you

Thorgott

one satisfying thing to consider might be if you have a forgetful functor $U\colon\mathcal{C}\rightarrow\mathcal{D}$, then a "free object functor" is a left adjoint $F\colon\mathcal{D}\rightarrow\mathcal{C}$. if this exists and $U$ is faithful (which forgetful functors usually are), then it follows that the counit $FU\Rightarrow\mathrm{id}$ of the adjunction is an epi (exercise), so every object is a "quotient" of a free object.

usually, though, one doesn't care much about free objects and cares about the more general projective objects, specifically in very nice categories that are called abelian categories (of which abelian groups and modules are examples), the property that every object be a quotient of a projective object is then called "having enough projectives" and very important in homological algebra

shintuku

is "free object functor" also sometimes referred to only as "free functor"?

Thorgott

ye

shintuku

nice thanks a lot i'll read more into this

Ted Shifrin

17:50

Howdy, @Thor.

robjohn

Howdy, @Ted

Ted Shifrin

Howdy, @robjohn. How was the park?

Thorgott

hi @Ted

Jakobian

fortune.com/well/2023/06/29/…

I wonder if it turns out to be carcinogenic

PM 2Ring

18:18

@TedShifrin "I'm told that even in Germany the ß is now passé." Not really, but since the orthography reform of 1996 there are some situations where it's no longer used. OTOH, in 2017, it finally got an official upper-case form: ẞ See en.wikipedia.org/wiki/%C3%9F#Development_of_a_capital_form

I don't speak German, but one of the mods in the Physics chat wouldn't dream of writing Gauß with "ss". :)

PNDas

Hi! There is question: if $T\in\mathcal{D}'(0,1)$ and $\frac{dT}{dx}\in L^2(0,1)$ then show that $T\in L^2(0,1)$. How to do this? I know that $T'=0$ implies $T=T_c$.

The problem is can I write if $f\in L^2(0,1)$ then can I write $T_f=T_g'$ for some $g\in L^2(0,1)$?

May be I can do like this: $\frac{dT}{dx}=T_f$. Let $f_n\in C_c^{\infty}$ such that $f_n\to f$. I can consider $T_{f_n}\to T_f$. Now I can find $g_n\in C_c^{\infty}$ such that $T_{g_n}'=T_{f_n}$.

Okay got it. I didn't need to do all that. The interval is bounded.

Thorgott

18:50

my surname contains a ß

robjohn

@TedShifrin It was nice, in the shade. It is supposed to be warm today.

@Thorgott $\{\text{S}\}$

Ted Shifrin

@robjohn It's definitely warming up here, although nowhere near TX/LA proportions.

robjohn

I was looking at LV stats and glad we are not visiting there this weekend

High there today is 108° and on Monday 113°

Ted Shifrin

19:07

Not the climate for I.

robjohn

No triple digits, yet, here.

@TedShifrin Nor I

Sorry; on my phone.

However, it is slated to get to 97° here, today.

Ted Shifrin

Only 77º here today, 80º tomorrow (but "feels like" 87º).

robjohn

The humidity and lack of a breeze can be a killer.

Ted Shifrin

The humidity in GA was ugggggh.

robjohn

Tomorrow is 97° tomorrow, as well.

The humidity in New Jersey was horrid.

I left as early in June as I could and returned as late in September.

D.C. the III

19:17

@TedShifrin speak in international units please.

metric

Ted Shifrin

You mean Kelvin?

D.C. the III

Freedom

If I knew my memes better I would already have known you were using Freedom units........losing touch with the youth I am

Ted Shifrin

There's never been anyone like @Hippa for memes!

robjohn

@D.C.theIII I will be getting Freedom Fries for my son this afternoon.

Ted Shifrin

Oh, yes, happy Canadian day.

D.C. the III

19:24

Thank you I suppose. Being more aware of history does put a damper on these things nowadays......but I do appreciate the intentions

@robjohn I looked it up and not surprised on its origins at all......🤣

Ted Shifrin

I'm going to ignore our Dependence Day on Tuesday.

robjohn

@TedShifrin No longer Dominion Day

D.C. the III

of course the term Freedom Fries got weaponized....lol

robjohn

@TedShifrin I have to BBQ for about 20 old people on Tuesday

Ted Shifrin

Ah, yes, I remember your telling me about your tradition.

D.C. the III

19:27

So not much red meat going to be on the grill then? mostly corn and veggie shis kebabs?

Ted Shifrin

Of course, red meats!

D.C. the III

I'm just inquiring due to the old people comment....of course a bbq without red meat is blasphemy......I wonder if my opinion will change when I reach your guys' age....

robjohn

@D.C.theIII No, they bring burgers and hot dogs, and the ones who want to be mean bring fish.

D.C. the III

lol

robjohn

I require foil for the fish. No messing up the grill.

Ted Shifrin

19:31

There are wonderful fish grilling contraptions. I had one that I used with the grill in GA. It holds a whole fish (of moderate size) poifecktly.

D.C. the III

As should be.....only tuna steaks or whatever fish steak can go without foil

I have one of those contraptions

Ted Shifrin

Tuna should barely be cooked. It isn't wonderful for grilling.

D.C. the III

aslo learned the hard way to make sure to grease it first

robjohn

is it like a fold-over cage?

D.C. the III

Yea. I usually sear my tuna steaks. 2-3mins max aside making sure the middle remains pink

yes..fold cage

in a pan

Ted Shifrin

19:33

That's way overcooked, DC.

Tuna should literally be raw in most of the middle. Just a whisper of cooking ... like a whisper of vermouth in my martini.

D.C. the III

I may be over doing it numbers wise, but there is about 1/4 of an inch cooked on each side if we are talking about an inch thick tuna

robjohn

@TedShifrin Is just taking it out of the fridge and letting it sit in the heat here enough?

Ted Shifrin

Almost :)

D.C. the III

your recommendation about a year ago on how to put my garlic into anything being cooked with oil has done wonders to my cooking.

Ted Shifrin

I like to do it au poivre with a trace of olive or sesame oil (depending on the accompanying food).

I told you, DC. I'm a better cooking instructor than math instructor.

D.C. the III

19:37

I just looked up au poivre, that is actually how I cook the tuna.

in terms of centre being pink.

Ted Shifrin

au poivre means with chunks of peppercorns on the flesh :)

I still say pink (like red meat) is way too much for tuna. It goes white, anyhow.

D.C. the III

I usually brush it with a light glaze of olive oil then salt and pepper on one side so it isn't excessively salty and enjoy. Maybe not full sized peppercorns, but cracked peppers corns from the grinder...

PNDas

How to find singular support of $T_H$? Where $H$-Heaviside function.

Ted Shifrin

What is $T_H$?

PNDas

Actually, it'd be better if I put it like this: What is the largest open set on which $H$ is equal to some smooth function.

@TedShifrin distribution generated by $H$.

It seems the set is $\mathbb R\setminus\{0\}$. But how to prove it?

Ted Shifrin

19:45

For any $\epsilon>0$, you can give a smoothing that agrees with $H$ outside $(-\epsilon,\epsilon)$.

There is no largest open set, but that is the sup, I guess.

I have forgotten technical definitions.

@robjohn surely knows this in his sleep.

PNDas

Singular support of a distribution T is the complement of the largest open set on which $T=T_f$ where $f$ is smooth.

Ted Shifrin

Who says there is a largest open set?

PNDas

You can take unions of the open sets

robjohn

I'd guess that the singular support would be $\{0\}$

Ted Shifrin

Yes, but there needn't be an $f$ on that union.

Me too.

This is a max vs sup issue.

PNDas

19:51

I read a property that sing. support(T) is subset of support(T). And another property says that support($T_f$)= support(f).

Ted Shifrin

support of a function is the closure of the set of points where it's nonzero.

PNDas

Yes

So it's not useful here.

Ted Shifrin

Well, you just said the support of $T_f$ is the support of $f$.

Something's fishy.

PNDas

?

Ted Shifrin

$x_0$ is in the singular support iff for every $x\ne x_0$, there is a smooth function $f$ so that $T=T_f$ in a neighborhood of $x$. Or something like that.

I'm not looking in books.

That was wrong. That assumes the singular support is just $x_0$. $\Sigma$ is the sing. supp. iff for every $x\notin\Sigma$ blah blah blah?

PNDas

19:59

Okay I consulted another book. Their definition is different. sing. support(T)={$x\in \Omega$ such that there is no open set $x\in U\subset \Omega$ such that $T|_U$ is smooth.}

Ted Shifrin

That looks like what I said.

Maybe.

But with both definitions, robjohn and I get $\{0\}$, which is what it should be :P

PNDas

Hmm Thank you.

But support of distribution can be defined as the complement of the largest open set on which T=0

right?

Ted Shifrin

That still makes no sense to me.

robjohn

I use the complement of union of the open sets on which the distribution can be represented by a smooth function.

for the singular support.

PNDas

This definition of support is correct. If we have distributions on U and V such that they match on U \cap V then we have a distribution on U\cup V. Now, so if T is zero on U and V then there is a distribution on U \cup V. Now to prove that this distribution is also zero, you use partitions of unity.

If $\varphi\in\mathcal{D}(U\cup V)$ then $T(\varphi)=T_1(\varphi\psi_1)+T_2(\varphi\psi_2)=0$

robjohn

20:15

@TedShifrin It is also the Feast of Father Junipero Serra today.

PNDas

For the first time I saw the word "beatified". The article said: Serra was beatified by Pope John Paul II. I thought the pope beat him.

Ted Shifrin

20:41

@robjohn A name all over SF, too.

robjohn

@PNDas He seems to have done that to himself.

leslie townes

where's copper when you need him

Jakobian

in the copper mine

robjohn

someone's ears were burning.

copper seems too hard to knead.

copper.hat

i dropped from favour with my grandmother when i did not attend JP II's mass a few miles away from her place (where i was staying at the time) because i was too lazy to get up.

Ted Shifrin

20:49

And you dare complain that your children were lazy ...

Has Munchkin chased any ducks today?

copper.hat

@TedShifrin chore wise they are lazy.

Ted Shifrin

You see? You complain.

leslie townes

no ducks yet. maybe later!

copper.hat

curmudgeon is the word that appears most frequently

Ted Shifrin

I was once called one of those, too, copper. But only once :D

copper.hat

20:54

i think i am an optimist when it comes to expectations of people. then folks like mjt, boebert, jordan, biggs get elected and i wonder :-)

Ted Shifrin

I'm long past optimism. Somebody posted somewhere on FB wondering how MTG could have been elected to Congress. My answer was simple: Because the people in NW GA are just like her.

SAMIR ORUJOV

Hi there. I need help with a question:math.stackexchange.com/questions/4728893/…

Ted Shifrin

copper, maybe you can help. It looks sorta down your alley.

copper.hat

i glanced but got lost in notation. perhaps the wine i had last night is having effect

SAMIR ORUJOV

I am new to math and to mathstackexchange.

@copper

Ted Shifrin

20:58

That's very long-lasting effects, copper.

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$Mathematics$ Mathematics