The h Bar

0celo7

00:02

@Semiclassical I mean take like $\sin(x^{100})/x$. That's asymptotic to $0$ as $x\to\infty$ but the derivative certainly won't be (I hope)

Semiclassical

$Ai(x)\sim\dfrac{e^{-\frac23 z^{3/2}}}{2\sqrt{\pi}z^{1/4}}$ @0celo7

0celo7

@Semiclassical I was saying maybe $q$ oscillates violently as $s\to\infty$ so the derivative might be strange

Semiclassical

Sure, there are problematic examples like that. But here I think the exponential supression rules that out here

0celo7

in noncompact PDE we have a stronger type of asymptotic called $o_1$ that means the derivative is also asymptotic

@Semiclassical well all you need is an oscillation that is wilder than the suppression, but I don't know what q looks like so that might not matter here

like $e^{-x}\sin(x^x)$

Semiclassical

00:25

For reference, the underlying DE is $q’’(s)=sq(s)+2q(s)^3$

0celo7

@Semiclassical do you have a pretty picture of a solution?

ideally superimposed with Ai(s)

Shing

00:41

Would anyone be kind enough to recommend some must-read-paper for someone study introductory quantum field theory?

Semiclassical

I have some but not on phone. But there’s a set of slides with nice pictures I’ll link

math.nist.gov/~DLozier/SF21/SF21slides/Olver.pdf

See slides 6-9

0celo7

this fluid mechanics book is so 2002

it talks about cigarettes and compact disks

@Slereah Amazon really understands my interests, but the ad is completely wrong... i.gyazo.com/ef085f0febc340e5111abb444e69f199.png

@Semiclassical I don't get it, what was [16]?

Semiclassical

no clue either

all I'm really interested in for this purpose is the pics on slides 8,9

0celo7

@Semiclassical um, does Ai --> 0?

Semiclassical

as x goes to infinity, yes

Airy's DE has two solutions, one vanishing at infinity and the other diverging at infinity. Ai is the former.

0celo7

00:52

so why not just say that q(s) ~ 0?

(I think ~ is transitive?)

er, actually I don't think ~ 0 is defined, nvm

@Semiclassical what am I looking at on slide 8?

there's two new things

Semiclassical

yeah, he doesn't explain that well there. but I think it's equivalent to assuming $q(s)\sim c Ai(s)$ with $c\approx 1$

one is a little above 1, one a little below, one equal

0celo7

so the solution is highly unstable?

Semiclassical

I think so. but there's some subtlety that I'm not sure about

the tricky thing is that what he's using to define his solutions is not the airy asymptotics per se. rather, there's a description in terms of the so-called stokes constant which tell you how the asymptotics change as you move in the complex $s$ plane.

numerically, though, it's definitely quite sensitive to what value of $c$ I use

0celo7

@Semiclassical ah the joys of the shooting method :)

Semiclassical

yeah

for $c>1$ you get poles on the real line I think, and for $c<1$ it's got that oscillatory behavior

$c=1$ is special in that it diverges as $x\to\infty$ but not for any finite z

0celo7

01:03

"I mow the lawn with a scythe and commute to work by bike. "

the insane guy who wrote this book lol

Semiclassical

that's commitment I guess

0celo7

@Semiclassical does it make sense to have $s$ be complex and look at the whole solution?

Semiclassical

though commuting to work by bike isn't so strange

@0celo7 yeah

0celo7

so you expect complex poles then for $c<1$?

Semiclassical

hmm. good question

0celo7

01:04

@Semiclassical this guy is legendary here for cutting grass with a scythe

Semiclassical

hmm, relevant abstract: arxiv.org/abs/1410.3338

"We show that the well-known Hastings-McLeod solution to the second Painlev\'{e} equation is pole-free in the region $\text{arg }x\in[−\pi/3,\pi/3]\cup[2\pi/3,4\pi/3]$..."

that's the solution that's being studied here, to be clear

0celo7

Figure 1

Semiclassical

nice

ffs why is my computer so slow right now ugh

0celo7

delete system 32

Semiclassical

riiight

ahah

carma.newcastle.edu.au/jon/Preprints/Books/MbyE/Second-Ed/…

slides 4,5,6 and esp. 8

so $|c|<1$ leads to oscillatory stuff, $|c|=1$ is monotonic, and $|c|>1$ has poles on the real line

DanielSank

01:37

$\renewcommand{\infty}{See, Craig, you can mess with mathjax}$

Semiclassical

lol

rob

I migrated the post below at the asker's request, but the receiving site rejected the migration. I think it'd be fine to re-open, but I don't like reversing myself without feedback. Have a look and vote. Thanks.

0

Q: Minimizing entropy generation in storing heat

I am working on a cogenerative PV (Photovoltaic) array. The idea is to generate electricity from the solar cells while cooling them to both increase solar conversion efficiency and extract waste heat from the array. On a good day, the cells could easily get up to 40°C, and capture some finite (le...

DanielSank

$\infty$

Interesting. The borked macro doesn't affect uses above the definition.

Oh darn, I can't delete that message now.

0celo7

$

$\infty$

@rob pls ban Daniel for breaking the chat

bolbteppa

@Slereah with the recent re-establishment of the Sorbonne, if a person gets a bsc/msc/phd from some affiliated lab, can they now say they got it from the Sorbonne? :p

0celo7

02:39

@BalarkaSen dear god Hempel is all in the PL category

0celo7

02:58

press.princeton.edu/titles/1156.html

this actually seems neat

Balarka Sen

03:13

@0celo7 PL is life

0celo7

@BalarkaSen if you think that, we are mathematically incompatible

Balarka Sen

I agree

if you read Mazur-Hirsch I am going to read it too btw

0celo7

@BalarkaSen remind me in 10 years...

Balarka Sen

gg

0celo7

maybe I'll read it when I finish Federer

(in 10 years)

Balarka Sen

03:17

i cant fix a proof

annoyed

0celo7

@BalarkaSen story of the past two weeks for me

but replace "a proof" with "GR"

Balarka Sen

physics is unfixable

u have no hope

sorry

0celo7

what proof did u break

I want to learn K theory

Balarka Sen

i have curves in R^3 which are epsilon-close to being tangential to the distribution dz = xdy. i want a curve which is tangential to it

endpoint fixed

@0celo7 since when did you get interested in homotopy theoretic stuff

smoothing theory, K-theory,...

there are heavily homotopical

0celo7

@BalarkaSen smoothing because I refuse to use PL without knowing it's equivalent to Diff

K theory because it's used in conformal geometry

@BalarkaSen what does that distribution look like

Balarka Sen

03:25

it looks twisty

0celo7

I have no idea what $dz=xdy$ even means

Balarka Sen

dz - xdy is a 1-form on R^3

look at zero set

it vanishes on a 2-plane distribution

0celo7

oh you mean the kernel

Balarka Sen

yeah

0celo7

who writes that as dz = x dy?

if you say russians I will leave

Balarka Sen

03:27

lol

i was going to say Arnold

0celo7

that's it

don't talk to me or my son ever again

Balarka Sen

you have a son

0celo7

he's a cat

Balarka Sen

oh i see that dude

the einstein

0celo7

this talk on tuesday is going to be a disaster

but! I can blame it on physics being incompatible with mathematics

Balarka Sen

03:32

lets hope there wont be a skeptic de grande do destroy your talk

0celo7

@BalarkaSen I still don't know what I want to talk about

I might just go freestyle

Secret

04:47

High command, it is true that Balarka Sen is now slightly more weird since The Incident, causing the weirdness level to only drop significantly only if the Lockdown Trio were present all at the same time. But that does not mean we don't need to be cautious. Until The Plan is completed, he and the two other members of the Trio has to be continuously monitored

The status of h bar still remains unstable and if we are not careful, the weirdness will be drained completely, making it inhospital to THEM

DanielSank

05:59

@vzn this

Hey, anyone here care about quantum many-body physics?

John Rennie

06:32

@Slereah I was offered a job by the atomic weapons research establishment. I even went for the interview but the place was horrible. The staff seemed to be all failed academics. Presumably they were the only people desperate enough to accept a job there.

Anonymous

06:56

@JohnRennie That sounds strange, considering that it operates under the British government. Are there better private organizations which does that kind of research?

John Rennie

@Blue I think the vast majority of scientists disapprove of nuclear weapons and wouldn't want to work on them. I only applied for a job there out of curiosity to see what it was like. I would only have accepted the job if I had no other job offers.

Anonymous

@JohnRennie "vast majority of scientists disapprove of nuclear weapons and wouldn't want to work on them"....that's nice to hear :P

John Rennie

I was offered the job back in the early 1980s but even then it was clear that the UK was winding down its work on nuclear weapons. I think the work they do now is just maintenance rather than designing anything new, and I doubt it's very exciting.

Balarka Sen

What we need is to stir up another war

John Rennie

Isn't that what Trump is attempting to do in Korea?

Balarka Sen

07:03

Unclear

Anonymous

I see. As for me, I'm totally fine with doing weapons research as long as there is no mass manufacturing endeavour. But then again it is even better for world peace if such research is minimized.

Balarka Sen

But once we have a war, the nuclear research and engineering would be hip again

Anonymous

War isn't as cool as it sounds.

Balarka Sen

@Blue no manufacturing, no money pal

John Rennie

I'm not sure how much scope there is for research in nuclear weapons. I'd have guessed the area was pretty thoroughly understood by now.

Balarka Sen

07:05

hm

i guess

the boiz in the cold war finished doing the good stuff

lılostafa

ncase.me/trust

4

Another cool game from ncase about why people do/don't trust each other, based on game theory

ooolb

how can someone dislike the moon this much

Slereah

07:32

@JohnRennie too bad

Might be fun designing nukes

"This is my new bomb, it kills everyone everywhere"

Secret

08:20

I would rather having people start making bombs and kill all of us humans. Because humans are so boring and a waste of universe resources

Slereah

Well you know what I say, lead by example

Secret

actually, I am not sure if fusion bombs makes a cleaner kill than fission bombs

John Rennie

@Secret fusion bombs use fission to start the hydrogen fusion, so they are just as dirty as fission bombs

Secret

right

hmm guess an antimatter bomb is needed to prevent radioactive fallout, but antimatter is super hard to produce so whatever...

Slereah

@JohnRennie I've heard of some fissionless designs

Though I don't think they were ever tried

Did you ever wonder if your toothpaste was used for evil, @JohnRennie

John Rennie

08:32

@Slereah personal care products have limited applicability as weapons of mass destruction

Though didn't the US attempt to assassinate Castro by putting poison in shampoo or something similar?

@Secret antimatter:matter fusion is a hopelessly messy process that spits multiple hadrons out in all directions. While it doesn't produce the radioactive fission products that U235 creates it will induce secondary radioactivity in the matter around it.

Slereah

I think the US came up with like 50 plans to assassinate Castro

Antimatter is also not something that's very energy efficient to produce

@0celo7 en.wikipedia.org/wiki/John_Duffield

All this time he was producing GDP

Anonymous

08:55

Visual Studio's random number generator seems to be buggy! Every time I run the program afresh (after re-building it), it gives the same output. Only if I put the code in a loop, it gives new results each time. (I just used rand())

Slereah

Maybe you need to generate a seed first

then just put like seed = md5(timestamp)

Anonymous

I don't know what that is. Checking...

Anonymous

@JohnRennie Do you have idea about this thing? ^

Anonymous

3 mins ago, by Blue

Visual Studio's random number generator seems to be buggy! Every time I run the program afresh (after re-building it), it gives the same output. Only if I put the code in a loop, it gives new results each time. (I just used rand())

Slereah

Also what do you mean by "visual studio"

What language are you running on visual studio

Anonymous

09:01

Visual Studio doesn't have gcc I think. It uses some in-built C libraries (I think)

Anonymous

I haven't tried it using the gcc compiler...got to check

Slereah

"The rand function returns a pseudorandom integer in the range 0 to RAND_MAX. Use the srand function to seed the pseudorandom-number generator before calling rand."

Did you use srand

srand( (unsigned)time( NULL ) );

is advised

Anonymous

I was just reading about srand()

Anonymous

Trying

Anonymous

"rand() function is used in C to generate random numbers. If we generate a sequence of random number with rand() function, it will create the same sequence again and again every time program runs. Say if we are generating 5 random numbers in C with the help of rand() in a loop, then every time we compile and run the program our output must be the same sequence of numbers."

Anonymous

09:04

Aaaaaahhh!

Anonymous

That's the culprit

Anonymous

Lol

John Rennie

You need to use srand to set a random seed

Slereah

Using the timestamp directly isn't necessarily advised if you're doing secure stuff btw :p

Anonymous

Awesome. This works great. Learnt something new today :P

Anonymous

09:11

@Slereah Yeah, I'll keep that in mind, hehe XD

Slereah

Otherwise knowing at what time a number was generated allows you to narrow down what number that could be

Anonymous

I think there some third-party truly random number generator libraries for C, online (I doubt how much truly random they are...but anyway :P)

Slereah

You can generate some fairly random numbers if you're using hardware stuff

like if you're measuring voltage on the CPU and only keeping the least significant digits

Anonymous

Yup, that's one of the useful ways to generate random numbers :)

Anonymous

And then you have the superposed states of qubits :P QC guys would like that method

Slereah

09:17

x86 processors have TSTR—Thermal Sensor Thermometer Read Register

You can just measure the temperature

Let's see to how many digits

Anonymous

I heard there's some serious research in this area (in cryptology departments...which I don't know much about...but it sounds interesting)

Anonymous

@Slereah Yeah, temperature, light intensity, all those stuff. I once made one using a Arduino XD

Anonymous

My light sensor was pretty pathetic though

Slereah

Apparently it's just degrees directly

Anonymous

(cheap arduino stuff)

Slereah

09:18

Not very good for randomness

on 8 bits signed

just in case your CPU freezes

Physics Meta

0

Q: Modified question on hold won't reopen

I posted this question (previously called "Lagrangian of two pendulums tied together") five days ago, whereafter it was soon closed as off-topic. The reason for this was understandable: it looked as if I was asking for the solution of some exercise. As I realized my mistake, I radically rewrote ...

support closed-questions specific-question reopen

Balarka Sen

09:38

@Slereah I really like the aesthetics of this image

Grim Reaper grinning at you from the distant from a picture frame littered with SHUTTERSTOCK watermarks

Slereah

A grim foreshadowing of the future!

Anonymous

@JohnRennie There's a certain program: paste.ofcode.org/uCVGfy7YGwELcyhy2jW5sE which works fine on VS. But when I execute if from cmd using gcc, it gives 100s of errors saying that there are null characters in the code. I'm not sure how to deal with this

DBinJP

10:01

is this an on-topic chat or a casual chat?

Anonymous

@DBinJP casual....mostly off-topic chat :P But you're free to ask physics questions...

DBinJP

I was going to ask how to reset motivation and confidence when you've become mentally exhausted.

Anonymous

Well, you can ask that.

DBinJP

... 'kay.

how to reset motivation and confidence when you've become mentally exhausted?

Slereah

Amphetamines.

DBinJP

10:07

what, like, advil?

Balarka Sen

please

Slereah

It's the Paul Erdös approved way

Balarka Sen

methamphetamine > amphetamine

Slereah

Also take a vacation if you can I guess

Balarka Sen

temporarily go on a different intellectual adventure/exercise than the one that mentally exhausted you

thats how i regain motivation

in other words do a productive procrastination

DBinJP

10:14

yeah, problem is i seem to have ruined my life doing that

jumping around different fields, not mastering a single one

Balarka Sen

the fix is to not jump around vastly unrelated fields i think

DBinJP

i have this problem of losing interest in whatever i'm supposed to be doing

Balarka Sen

stay on related disciplines so your random walk is limited to a specific thing at least superificially

DBinJP

i have tried to do that ...

Balarka Sen

what do you work on?

DBinJP

10:17

medical physics

been learning ubuntu linux, data science, statistics ...

tried R but it's too austistic even for me

returned to MATLAB

Balarka Sen

mm i see. thats something i hardly have any expertise on so i cant suggest anything specific. maybe the others here can though

DBinJP

i think my main problem is my research advisors are neither researching nor advising

Anonymous

@DBinJP What's the problem with R ? I mean the things you mentioned aren't very unrelated...statistics...data science...etc

Anonymous

Those things are useful even in experimental physics

DBinJP

i think i didn't have time to learn a new language (i.e. new commands), and R was too picky about data frames and how data is structure

d

matlab is pretty simple -- is it an array? make it one, and you can proceed

R is like, you have to name the rows and columns and which type of array and use different commands for each of those things ... ...

too many layers blocking me from actually using the data

Slereah

10:22

Just use C if you don't like that :p

You can just use arrays with anything!

DBinJP

and the documentation -- MATLAB is like, "here's the command, here's an example, very clear"; R made documentation about documentation just for the sake of having it, like latex

so i spent too much time reading documentation without actually learning how to do what i was wanting to do

Anonymous

There are tons of good lecture series on R on YouTube. I'm learning it currently. Doesn't look too out-of-the-world. But then I'm going at a very slow pace.

DBinJP

yeah, 'very slow' -- i ran out of time for that

i needed to clean up messy data and start using it

not start from scratch

but i do like hadley's tidydata ideas

Anonymous

@DBinJP Well, you're running out of time...for "what"?

DBinJP

to do my research and publish a paper and graduate

what i'm trying to do now, except i'm burnt out

Anonymous

10:26

Seems like you're not enjoying your research ?

DBinJP

i'm not

strikes me as a waste of time

Anonymous

Hmm. I see now

lılostafa

@Slereah Isn't crack better?

Slereah

Cocaine is for businessmen

Anonymous

Maybe someone more experienced can give you suggestions for that. I'm not the right person

Anonymous

10:28

Good luck though

DBinJP

thanks

CooperCape

ola

DBinJP

hola?

CooperCape

I don't do languages.

DBinJP

ola = ?

CooperCape

10:31

probably

lılostafa

@Slereah but still much better

Wolf of Wall Street - Clip - Crack Smoking Scene

►

DBinJP

why's leo always doin' drugs man

Slereah

I wonder how Erdos on amphetamines acted like

DBinJP

every movie leo's always upset about something

Slereah

Imagine him just rambling on number theory

DBinJP

10:33

> Erdős never married and had no children.

you don't say ...

dang, this dude's like the St. Francis of math

lılostafa

@Slereah The good thing about Amphetamine (compared to crack or cocaine) is its lengthier high time

It's better suited for scientific work

Constantine Black

Any thoughts on this meta question will be great and helpful: it seems that the professor of the class does not think he could answer a similar question; physics.meta.stackexchange.com/questions/10367/…

DBinJP

@ConstantineBlack i've always seen this website say it's not for homework help

'this' = stackexchange

but i think i've also seen homework solutions posted here

won't it just be downvoted or closed if off-topic?

Slereah

Erdos is quite famous

Among the math crowd

DBinJP

i can see why

Slereah

10:40

He's the Kevin Bacon of math

DBinJP

kinda forgot kevin bacon ...

Constantine Black

I'm asking on meta because I don't think it's a homework question- if it is valid to be posted then the question is about the possible hypothesis or whatever that would make the second part of the problem correctly solvable.

That' s because the given relation cannot give right results for the second part for both t=0 and t=infinity. Or it seems so to me.

lılostafa

I think a 15-20mg dose of amphetamine should be prescribed to all math or physics students. especially before their exams:

Slereah

>ego inflation

>increased libido

Might be a joke about Feynman here

lılostafa

:)

analysis enhancement, focus enhancement, memory enhancement, motivation enhancement, thought acceleration, thought organization.....these are gold to those trying to solve difficult problems

Balarka Sen

10:46

who cares about solving difficult problems

its all bullshit

lılostafa

@BalarkaSen Those who have exams or are doing research

Slereah

you wouldn't say that if you were on drugs

Balarka Sen

aka bullshit

@Slereah good drugs are the hallucinogenics

DBinJP

What's the point of these exercises, anyway?

nvm

Slereah

@BalarkaSen good hallucinogenics are good

Bad hallucinogenics are bad

DBinJP

10:49

what i mean is that i think there's not enough time spent teaching how to use computers

Balarka Sen

science is just a device humans developed to keep themselves from being bored

Slereah

Did you ever read the side effects of nutmeg

DBinJP

and too much time spent solving problems by hand

so i'm glad to hear the problem must be solved with matlab rather than by hand

Balarka Sen

its all just a big bullshit

DBinJP

@BalarkaSen i'd say that's only partiall ytrue

Slereah

10:50

"Nutmeg intoxication can vary greatly from person to person, but is often associated with side effects such as excitedness, anxiety, confusion, headaches, nausea, dizziness, dry mouth, redness in eyes, and amnesia.[21][24] Nutmeg poisoning is also reported to induce hallucinogenic effects, such as visual distortions and paranoia.[24]"

DBinJP

TV is more literally such a device these days ...

Slereah

IIRC one effect described was "vision of demonic animals"

which sounds mildly worrying

Balarka Sen

@Slereah Sounds like my thing

DBinJP

nutmeg::humans as catnip::cats?

Slereah

No, it's not the fun kind of high

Balarka Sen

10:51

@DBinJP yeah but you cant pretend you're doing IMPORTANT STUFF when watching TV

Slereah

I can

Constantine Black

It is supposed to be a computational physics class... but it's pretty basic and that's why I don't know if I must make some hypothesis to solve the second part or not; the professor thinks he cannot answer that.

Balarka Sen

can you get funding for your TV watching time?

DBinJP

@BalarkaSen good point, but it seems the people who watch tv don't care about that when they're doing it

lılostafa

@BalarkaSen I mean, it's like turbo mode. You shouldn't normally use it too much but sometimes it really helps

Balarka Sen

10:52

get funding from the authorities and then ill believe you

DBinJP

@ConstantineBlack well, yeah, you have to connect the dots to see what the math should be when the box partitions start with different amounts

Balarka Sen

@Slereah bad trips are the best kind of trips

Slereah

@BalarkaSen feel free to try

Although don't buy all the nutmeg at once, nobody's gonna believe you're baking 2000 pies

Constantine Black

Well, yeah... but I begin from where? From the given relation? From more fundamental assumptions? This is not a statistical physics class, the given relation is just given and does not stated from where it came as a result.

DBinJP

oh.

@ConstantineBlack The question is not clearly asked, I think, but I think you may just assume it to be starting from the time there were that many particles from the first part of the question.

e.g. t = 3 minutes instead of t = 0

but i would state this reasoning

*the reasoning for this assumption

or t = 3 seconds rather (shrug)

(i think it wouldn't stay a vacuum for minutes ...)

goodnight

Constantine Black

11:01

I have no idea what these nanoparticles are and why the partition is such. It's just an exercise to be solved in matlab so I'd like to ask on the main site if there is a proper way, from the given relation, to understand how to model the second part of the problem or if even matlab can somehow find a solution- solving a system perhaps for both partition.
@DBinJP Yes I also thought that; but it's just an assumption I make and it bit of frustrates that the professor cannot state if I must assume anything or not.

Prathyush Poduval

11:11

Hey @Blue you there?

Anonymous

Yeah, but will have to leave soon

Prathyush Poduval

@Blue You have a chegg account right? Do you mind checking out an answer for me?

Anonymous

Sorry, I disabled it a month back...

Anonymous

Not paying anymore

Mithrandir24601

@Slereah nutmeg is so good though

Prathyush Poduval

11:15

@Blue Oh okay

thanks

Slereah

@Mithrandir24601 will actually bake 2000 pies

Physics Meta

1

Q: About the validity of a question regarding the modeling of a system for a matlab problem

I'm posting this on meta to ask if it is OK to post a specific question. In more detail: I've been given a problem that needs to be solved on matlab. The problem states that a box of nano particles is given and that at $t=0 $ all the particles are confined in one part of the box and that part is...

discussion scope questions software-questions

John Rennie

11:34

@Blue I bet you've written it using unicode! :-)

@Blue Unicode text represents every character by two bytes, and for ascii characters the upper byte is always zero so for would be \x0 f \x0 o \x0 r. If you asked gcc to compile source code written in unicode it will have a fit about all those \x0 characters.

Slereah

Shael Riley - Bit Pop

►

Constantine Black

11:49

I will just change the relationship given so that it satisfies the appropriate physical conditions.

Anonymous

@JohnRennie Uh oh. Any way to interconvert?

Anonymous

gcc isn't unicode compatible...weird!

Slereah

@JohnRennie Depends on the encoding!

There's dozens of unicode encodings

John Rennie

@Blue Linux doesn't like unicode. It prefers the UTF encoding.

Slereah

UTF-8 is just 8 bits but can widen if you have the appropriate codepoint as the first nibble

Up to 64 bits

Anonymous

11:57

I see. Hmm. Do I have to type the whole thing again, then? :P (to run it using gcc)

John Rennie

@Blue easy :-)

Open the source file and choose File/Save as

To the right of the Save button is a little arrow. Click that and choose "Save with encoding" and set the encoding to Western European codepage 1252.

That will convert it back to ASCII.

Transcript for