@DanielSank You will be a mod on the QC SE. And I will vote for you.
@DanielSank The division between the professional and amateur level users will be probably much stronger as on the PSE... you will have to somehow deal with it. The SE never says it openly, but I think the increasing site stats are obviously very important for them.
While this case is actually posted by a troll, as notified by Akiva and many others
A distributive algebra where the multiplicative identity is idempotent is one of the most trivial mathematical structure in existence that is not the trivial structure
What? In which aspects am I trolling? (I am... shhh) I am simply asking for help.
This is why sometimes it is not easy for me to spot trolling, because my preference of weirdness means I have explored quite a few statements seriously that trolls just happened to like to use because most people will identify it as nonsense
@Vivek Sure it can be un-deleted in principle, but it was roomba-ed so there isn't in impetus to do so. Again, the mods don't generally intervene in the normal function of site processes.
@Vivek I think in this case it's probably better to just repost the question. The way you have it after your latest edit is just fine except for two things: (1) give it the homework-and-exercises tag, and (2) you can leave off the last sentence where you link to your work on the problem because it's not relevant to the question you're asking.
@JohnRennie .. can you please explain me why does time period required to travel in an orbit closer to earth more than that required in an orbit farther from earth...? Which is why fuel consumption by aeroplanes at higher level is less...
The time period is smaller for a lower orbit. That's for two reasons. Firstly the orbital velocity increases as you move to a lower orbit, and secondly the distance you have to travel is smaller.
@NehalSamee I'd need to see what the book says. If the orbit is circular then obviously the circumference of the orbit is $2 \pi r$, where $r$ is the distance from the centre of the Earth, so it decreases as $r$ decreases.
@Rick Ah, well in that case, presumably the proof would use whatever has been introduced in the book up to that point, or whatever prior knowledge the reader is assumed to have.
Ultimately all these things come down to experiment, though.
@Rick you can derive the Lorentz force law $F = q(E + v \times B)$ as the Euler-Lagrange equation for a relativistic particle coupled to an electromagnetic potential, using basically the same idea used to derive Newton's $F = ma$, if you are happy to use Lagrangians
@Abcd : I think so. See What is an Electron? by Frank Wilczek. He said "to understand the electron is to understand the world”. That’s good. But he also said "there are several inconsistent answers, each correct”. That’s not so good. But he also said "the proper quantum mechanical description of electrons involves wave functions, whose oscillation patterns are standing waves”.
I read in Neamen's "Semiconductor physics and devices" about the Kronig-Penning-Model and I saw the extended aswell as the reduced E-k diagrams. I've already seen many images like the one below. Does this imply, that the valence band always lies in a even Brillouin zone while the conduction is in a odd one?
(You are talking about the guy who wants to ban racial studies courses and thinks it's a question as to whether men and women can work in the workplace together, it's not a bug it's a feature)
I've just managed to turn two non-functioning Nexus 9 tablets into one perfectly functioning Nexus 9 tablet (and one paperweight) so I'm feeling a bit smug right now :-)
I honestly don't know what's up with conservatives trying to mark off certain pieces of artwork or entertainment as propaganda. Stories have been used to convey a key moral for a long long time: Aesop's fables, for example. Fuck, even the Bible is that. Greek mythology is full of messages about human values - that's propaganda.
Compared to those, propaganda that's inherent in fucking Disney movies are nothing. It's just standard simplification of power dynamics between the various characters involved. (which, incidentally, is why I don't watch Disney - I don't see the appeal at all)
Cosimo Bambi (born 1980, Florence, Italy) is an Italian relativist and cosmologist who is currently a professor of Physics at Fudan University in Shanghai, China.
Bambi's research interests include strong field tests of general relativity, modified gravity theories, gravitational waves, quantum gravity, accretion flow around black holes, baryogenesis, galaxy clusters, primordial black holes, whether black hole candidates obey the Kerr Metric, Inflation, antimatter, strange quark stars, neutron stars, naked singularities and other compact objects He has close to 100 publications in all the above...
I'd say them being so afraid of Mickey Mouse or a birth certificate etc has something to do with that, you probably wont find the answers in logicking it out directly
How much and what kind of correlations between A and B we need to find before we can be confident enough to claim a causal relationship between A and B?
Tanuj: Hi, I am otherwise analysing my second batch of data in my PhD. It's tedious and repetative, and the interesting thing only pops up when all the correlations are put together
Moreover, if the circuit is ideal, and the batteries both have internal resistance $r$, the equivalent resistance $r_e$ becomes $$\frac{1}{\frac{1}{r}+\frac{1}{r}}=\frac{r}{2}$$?
We have$$\int_{\mathbb{R}^3} e^{-(x^2+y^2+z^2)/a} e^{-i(x\xi + y\eta + z \zeta)} dxdydz $$ picking out the x-coordinate yields $$\int_{\mathbb{R}} e^{-x^2/a-ix\xi} dx = \int_{\mathbb{R}}e^{-\dfrac{1}{a}(x+ai\xi/2)^2-\xi^2a/4 }dx = \{x'=x+ai\xi/2)\} = e^{-\xi^2a/4}\int_{-\infty+ai\xi/2}^{\infty+ai\xi/2} e^{-x'^2/a}dx' = \\ = \{\text{By Cauchy's theorem}\}=e^{-\xi^2a/4 } \int_{-\infty}^{\infty}e^{-x^2/a}dx = e^{-\xi^2 a/4}\sqrt{\pi a}$$ and so the original integral should be $(\pi a)^{3/2}e^{-a(\xi^2+\eta^2+\zeta^2)/4}$
@JohnRennie...The book says :**If a satellite remains very near to the earth's surface , i.e. , if h is very small compared to R , i.e. those satellites that revolve around the earth in larger orbit , then their time period becomes large and velocity of rotation becomes small.**
Entropy is a property of a (dynamical) system. If the system is spontaneous, the entropy always increases. To my understanding, if you want to decrease the entropy you'll have to apply some exterior force or something - in any case entropy of the exterior of your system (if you think of your system as embedded in a larger system, namely, the universe) will increase
That's the second law of thermodynamics, that the entropy of the universe (in which your system sits in) always increases
@0celo7 I think these are evidence of the fact that even the rational section of the conservatives have their own propaganda to promote and propagate behind their veil of logical socio-political commentary. Which is fine, if they didn't accuse counter-propaganda of being harmful.
In 50 years you'll have the conservative right turning into the radical social-justice left that they abhor.
I mean people don't want entertainment to be disjoint from the current social affairs in their country, especially not in this age of irony where we filter and perceive everything that happens around us through ironical gallows humor
Black Panther is the most political of the MCU movies, and it is also well praised by both the critics and general alike. I have watched it and I also like it
@Blue Well, the immediate thing is a postdoc, but I wish to be able to work a bit on some of the personal projects I want to do, such as doing some pure maths, making a minecraft mod and summarising all the ideas I have in my entire life
In the past, I always failed myself during the holidays because I end up procrastinating and wasted the time
Anonymous
@Secret Oh. So you're staying in academia. Maybe you could find out something interdisciplinary between pure math and computational chemistry (but I guess that would be very very rare)
Anonymous
Although data science nowadays does involve a lot of rigorous math
But the projects I want to do, because of their often study like nature, does require a lot of focus, but my problem is I get distracted easily
Well, there's actually a lot of involvement between maths and computational chemistry (the various numerical solvers will require you to understand things like sparse matrices, various things about eigenvalues as well recursive functions)
It will get even more interesting in a few years, because of the massive power promised by quantum computers
when we have more qubits and also the error algorithms are more mature, then computational chemistry and computational physics will explode with discoveries very rapidly
Anonymous
Exactly my thoughts :). I'm expecting (although my expectation might change with time) to pursue higher studies in the interdisciplinary fields relating to QC,QE,DS,ML, etc. Allows for a lot of flexibility
Anonymous
@Secret Also, I think in the future such people as you will be in high demand in the pharmaceutical area
How is \begin{align} S &= \frac{1}{2} \int d \tau [ m \dot{x}^{\mu} \dot{x}_{\mu} - i m \psi^{\mu} \partial_t \psi_{\mu} ] \\ &= \frac{1}{2} \int d \tau [ m \dot{x}^{\mu} \dot{x}_{\mu} + i m \dot{\psi}^{\mu} \psi_{\mu} ] \end{align} describing an electron in first quantized language, the first part is the einbein relativistic action of a particle, how is the extra part not describing an extra particle, apparently both functions describe the same particle...?
Apparently if you work out the ang mom current the $\psi$'s build up the spin angular momentum, and the $x$'s build up the orbital angular momentum, but I mean it's absolutely crazy adding an extra spinor function and it all describing one electron of mass $m$
Hmm, well it's supposed to be a Majorana spinor and they exist for $D = 1$, the action is supersymmetric, which is what it was introduced for, but then the guy says it also describes an electron which is pretty jarring
I think we can add Portuguese (if that's what it is) to the list of languages to be translated :\
If you were on a desert island, you'd probably come up with this model before the normal Dirac Lagrangian to describe a relativistic electron, this is pretty insane thinking about it
If $G(x,t) = \dfrac{1}{\sqrt{4\pi at}}e^{-x^2/4at}$ is the Green's function that solves $u_t - au_{xx} =0, \quad x\in \mathbb{R}, t>0$ with $u(x,0) = \delta(x)$ then is $G(x,y,t) = \dfrac{1}{4\pi at}e^{-(x^2+y^2)/4at}$ the Green's function that solves $u_t - a(u_{xx}+u_{yy}) = 0, \quad (x,y)\in \mathbb{R}^2$ with $u(x,y,0) = \delta(x,y)$?
If you know what susy is, and you take the NG action and apply the general idea of susy to the fields you can determine the supersymmetric NG action as a means to close the susy algebra, I thought susy came from string theory out of unavoidable necessity as if by magic, hmm
"The last two representations O(Ξ) and O′(Ξ) describe states which look like massless “objects”, particle-like in the sense that they have four-momentum, but with bizarre helicities: each representation contains an infinite tower of helicities, one with integer helicities, the other with half-odd integer helicities. These have no analogues in Nature"
"The close relation of the two sectors is soon after formalized by Jean-Loup Gervais and Bunji Sakita[17] who write them in terms of a world-sheet σ-model, with different boundary conditions, symmetric for the fermions, antisymmetric for the bosons. They call the transformations generated by the anticommuting Virasoro opertors, supergauge transformations, the first time the name “super” appears in this context."
That first paragraph in sec 4. on dual models is kind of shocking, up to "this early example of fermion-boson kinship led, through an unlikely tortuous path, to modern Supersymmetry", i.e. experiments hint at some link
"the Regge shadow of the bosonic t-channel’s ρ-meson averaged the fermionic resonances in the s-channel! This was totally unexpected since these two contributions, described by different Feynman diagrams, should have been independent."
'It is crucially important to distinguish between local supersymmetry -- supergravity --and global supersymmetry -- a solution to supergravity which has at least one Killing spinor. What the LHC looked for is the latter. What string theory predicts is the former.'