@JohnRennie I got pretty good at searching paper textbooks anyways. If you were a bit familiar with the textbook already, you can find most things pretty easily with the index.
@JohnRennie I've found that "get the book and work through it start to finish" is a much rarer usecase (you'll do that at most once per book!) than "look up this one thing". PDFs are much better for the latter especially once the number of books expands beyond physical shelf size
@Semiclassical That's why I liked using the indices so much. If you didn't know the specific word you were looking for, you could look through index topics until something stood out as a good lead.
I found table of contents was good for finding higher level things that are covered by chapters or sections. Index was good for topics that are only mentioned in passing or just don't have their own section.
Knowing the ToC was definitely helpful for using the index too, since if you know approximate what pages are what topics, you have a better idea which page in the index will actually be on the topic you want.
Since sometimes the index has multiple pages listed if it comes up several times
@ACuriousMind Well, PDF started life as a file format for stuff that's intended to be printed. And not edited. But it's kinda mutated a bit since then...
@PM2Ring Don't get me wrong, the actual file format is, like many others, a historically grown abomination of compatibility nightmares, but with stuff like hyperref in TeX it's not hard to at least produce properly hyperlinked technical texts.
'Weeks later, Bergamo has earned the tragic distinction of being the hardest-hit province in the hardest-hit region, Lombardy, of Europeâs hardest-hit country. ' yikes
@Semiclassical Man that timing sucked for them. It was 2 days before the first death in Italy, and they were one of the first to get hit hard. You can't even blame them for not distancing, because people weren't fully aware yet.
I once looked into the PDF spec to figure out whether it would be feasible/interesting to implement a "print to PDF" option on my own for something. I decided to leave that for more desperate souls rather quickly :P
@JohanLiebert I have my doubts. Italy was one place it spread; but there were others. Based on how the US went, I kinda doubt we would have stopped that from happening, Italy or not.
so it's unfortunately rather plausible that such mass-transmission events were inevitable
"Valencia said last week that more than a third of their players and coaching staff had tested positive for the virus, implying in a statement that the clubâs participation in the Champions League first-leg tie against Atalanta is linked to the high number of positive tests."
@Semiclassical That's kinda how I see it. There's a tough balance to strike between "everything functioning the way people expect and are used to" and "prevent the spreading of a possible pandemic we know little about". I'm not sure how we could have known enough before it was too late, unless we had gotten lucky.
I don't have much need to create PDFs. Mostly, I just feed PostScript files to GhostScript. And those PostScript files are either hand-written, or created by a simple Python script.
âThe football match is one factor, but the hospital is the most credible explanation,â said Gori. âWe donât know exactly when, but on a certain day a patient turned up with pneumonia, but the symptoms werenât recognised. That patient was together with other patients who became infected, as well as doctors and nurses.â
He was literally blaming his ceiling height as a reason for not appearing on camera nearly all of last week as Trump did daily briefings and raised his approval to near/above 50%
But they'll be happy to provide you with a dozen Word templates and cheerfully ask you if you're sure your document shouldn't be a ::shudder:: Powerpoint
In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that
generalises the Kronecker delta. It converts any logical proposition into a number that is 1 if the proposition is satisfied, and 0 otherwise, and is generally written
by putting the proposition inside square brackets:
[
P
]
=
{
1
if
P...
It is very dense. And the use of Greek letters as well as Latin makes it even denser. Sort of.
But to be fair, RAM was very expensive back then, so coders did all sorts of stuff to keep the RAM footprint as small as possible.
OTOH, APL doesn't just blindly mix Greek & Latin. The Greek letters are for the built-in operators, the Latin for user variables & constants. I don't remember much about it, since I haven't touched it since the late 70s.
@YuvrajSingh... When I used to to live in West Bengal, in the rainy season it floods so much that the nearby play ground gets filled with water. In those days we used to go on fishing (and fun thing was that we used to catch fishes with polythene bags). Once the local people found a red fish which sort of looked like a pirahna. Those days were amazing!
I don't really mind people discussing how they're doing, but I do mind random news posts that do little more than push it back into my consciousness when I've just managed to escape it for a few minutes. If I'm the only one that feels that way, that's fine and I'll suck it up, but I'd appreciate a bit of restraint.
In quantum physics, Regge theory () is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer multiple of ħ but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1959.
== Details ==
The simplest example of Regge poles is provided by the quantum mechanical treatment of the Coulomb potential
V
(
r
)
=
â
e
2
/...
the bohm stuff doesn't start until chapter 3, so you might appreciate that much at least
(my own sympathies are towards the "Bohmian velocity field" setup more than the historical setup. analogies to Hamilton-Jacobi theory don't do as much for me as "hey, the probability distribution generates integral curves")
(because what you're able to prepare is the initial wavepacket, not the particle's position within said wavepacket.)
(knowing the initial wavepacket and the potential is enough to determine what paths are possible. but it doesn't determine which path is actually taken. that is still a matter of statistics.)
(It doesn't matter if we can't prepare it's position it'll still follow a path which is solved by some equation which becomes the new F = ma even if we're prevented from seeing the path, it's still there, ahhh :p)
Quantum scattering is so hard, right here we have to know asymptotic approximations to confluent hypergeometric solutions to a radial wave function after isolating off it's $r \to 0$ and $r \to \infty$ behavior just to even get started
(if you could prepare the initial wavepacket -and- know where the particle is within that wave packet, then you would be able to predict the particle's trajectory. but that's not an option even in Bohm: in order to know where the particle is, you have to measure its position. and once you do that, you no longer have the initial wavepacket. if you prepare the wavepacket again, then you again no longer know where the particle is.)
(an additional subtlety (one which I'm not confident is helpful to the Bohm position) is that one can't really "measure" the position of a particle to infinite precision. at best, one localizes the particle to a very volume of space. but in that case one has really just traded one initial wavepacket for another, highly localized packet)
in 3D, i think it comes down to saying that $d\Omega = r^2 \sin\theta ~d\phi\,d\theta$ is invariant under rotations
e.g., if you were to rotate your coordinate system and pick $r,\theta,\phi$ according to that system, you'd still have $d\Omega=r^2 \sin\theta \,d\phi\,d\theta$
Besides the proof. Is it true that $d(R_0R) = R_0d(R)$? If so, how can we reconcile it with the invariance of element of integration under constant rotations?
(as in: for an infinitesimal rotation, we have $R=e^{\epsilon A} = 1+\epsilon A+O(\epsilon^2)$. Hence $\det R = 1+\epsilon (\text{tr} A)+O(\epsilon^2)$, and therefore $\det R=1$ for all $\epsilon$ requires $\text{tr} A=0$. So the generator $A$ must have zero trace.)
First of all, you need to know that any external force can change the mechanical energy of a system.
The proof of :
$$\Delta E_m=W=-Q$$
Maybe you can use the first law of thermodynamics, it can be helpful !!
It's given by the following relation :
$$\Delta U=W+Q$$
Note that : $\Delta U= U_{fi...
Maybe I am missing something, but I am confused by the use of $\Delta U=0$ here
@AaronStevens : what is missing is the (physically reasonable) assumption that the body is initially and finally in equilibrium with the surroundings. ie, the initial T,P = final T,P, hence, initial U = final U. For such a system, we may indeed conclude that the net work done by friction is equal to the total heat dissipated, But I agree, the comments don't make sense
Yeah that answer is confusing. It doesn't explain terms or really explain why it's doing what it is with them. It seems like the type of answer that only makes sense if you already know exactly what they are talking about.
@JMac : well, its "high school physics". We all at least know how physical arguments are packaged to us when we are in high school. Totally incoherently ;) (personal experience)
@insomniac I actually had an okay experience with HS physics. Practically all the math and science teachers at my school were actually pretty passionate about the subjects, thankfully. I actually felt like I came out with a pretty good grasp on the basics.
My grade 11 advanced math teacher didn't understand rounding though, so I guess it all evened out.
Lol. I had a few good ones too, now that I think about it. for some reason, more good math teachers than physics teachers. I think chemistry was the worst for me personally. All the chemistry teachers I had in HS seemed to encourage mindless cramming. No wonder I ran as far away from chemistry as soon as I had the chance.
Its all very subjective though. A friend who is now a chemist credits a chemistry teacher we both had, so..
I had one really bad math teacher, one really good one, and two pretty good ones. Practically all the science teachers I had were into their subjects. My biggest gripe with a science teacher was that my grade 11 chemistry teacher was more hardcore than I would have wanted. We only realized when we graduated and checked our transcripts that it actually counted as an IB course.
anyone else play piano and notice that they aren't making much progress after practicing throughout a day, but when they come back the next day they're suddenly much better at the part?