How can I find out the screen resolution and dpi on my mac book pro?

Question: Can you please tell me how can I find out the screen resolution and dpi for the screen on my Macbook Pro? (I got it last year, 2009.)
Answer: Open the Apple menu at the very top-left of the screen and click on About This Mac. Click on the More Info button, which will open up a window with lots of categories of information. The Graphics/Displays category will tell you your screen resolution.
Comment: Note: On Yosemite (10.10.x) there's no need to press **More Info**, as the **Displays** tab is directly accessible from **About This Mac**
Answer: If you like terminal, then you can get via below command
system_profiler SPDisplaysDataType |grep Resolution

For example
>system_profiler SPDisplaysDataType |grep Resolution
          Resolution: 1920 x 1080 @ 60 Hz

Comment: good one, thanks for the cli option - here's the output on my ~2011 macbook air: `Resolution: 1440 x 900 (Widescreen eXtended Graphics Array Plus)`
Answer: This depends on the model of Macbook Pro (i.e. the screen size - 13.3", 15.4" or 17") you purchased, but the resolution and DPI (or PPI), for the 2009 unibody models, is provided by Wikipedia (here and here).
However, given the resolution and display size, you can easily calculate the PPI. In summary:
MacBook Pro 13.3":  1440x900 (127.68 PPI)
MacBook Pro 15.4":  1440x900 (110.27 PPI)
MacBook Pro 15.4":  1680x1050 (128 PPI)
MacBook Pro 17":    1920x1200 (133.19 PPI)

Comment: Thanks. Is resolution and display size are the only factor depends on how good? So a MacBook Pro 15" 1440x900 should look the same as 15" 1440x800 laptop? But why for some reason MacBook Pro always look better, picture seems finer/sharper?
Comment: So dum that they don't print that to the display settings. Now, we have to find out what model we have...
Answer: Or to view and change the resolution: Open the Apple menu at the very top-left of the screen and click on System Preferences..., then Displays. This will show a list of available resolutions with the current one highlighted.
Comment: This doesn't work well on Yosemite (OS X 10.10). The Displays preference panel doesn't show the resolutions - it just has a radio button "Best for display" or "Scaled". If you check "Scaled" it will show the resolution for an external display, but not for the retina laptop display. @jwaddell's answer *does* work though.
Comment: To calculate the DPI you do not need the (simulated) resolution but the number of (actual) pixels, I think. The latter is a fixed value (defined by the hardware); the former, though, depends on the mentioned MacBook's Display setting.
Answer: Open Terminal app and run this command: system_profiler SPDisplaysDataType. You will see output that looks like this:
$ system_profiler SPDisplaysDataType

Graphics/Displays:

    Intel Iris Graphics 6100:

      Chipset Model: Intel Iris Graphics 6100
      Type: GPU
      Bus: Built-In
      VRAM (Dynamic, Max): 1536 MB
      Vendor: Intel (0x8086)
      Device ID: 0x162b
      Revision ID: 0x0009
      Displays:
        Color LCD:
          Display Type: Retina LCD
          Resolution: 2560 x 1600 Retina
          Retina: Yes
          Pixel Depth: 32-Bit Color (ARGB8888)
          Main Display: Yes
          Mirror: Off
          Online: Yes
          Built-In: Yes

Comment: Any solution without the command line?
Answer: All these answers are good but the fastest way to find the mac resolution is to do SHIFT + COMMAND + 4 (screenshot shortcut). Move the cursor to the bottom right to get the coordinates.
Press SHIFT + COMMAND + 4 with the cursor in the bottom right corner
Source: Computer Science student at Chapel Hill
Comment: The text is black and tiny and I cannot read it when the cursor is in the corner.
Comment: To calculate the DPI you do not need the (simulated) resolution but the number of (actual) pixels, I think. The latter is a fixed value (defined by the hardware); the former, though, depends on the MacBook's Display's Font Size setting.


What evolutionary advantages are provided by ovoviviparity?

Question: I read that some sharks are ovoviviparous.  What advantages and disadvantages are provided by this type of reproduction as opposed to egg laying and live birth?
Answer: Reading this website (www.sharks-world.com/shark_reproduction) it seems that for most sharks the eggs develop inside the mother (ovoviviparity), and the young sharks ("pups") are born fully functional, but this is not true for all sharks (as you mention in your question).
This persons blog (morgana249/modern reptiles give birth to live young) discusses evolution of ovoviviparity in some reptiles, but not others. In some species this seems to have gone back and forth in their evolutionary history, which suggests that changing conditions favour one then the other at different times, possibly influenced by temperature, among other things.

The researchers stated, "These results suggest that parity mode is a labile trait that shifts frequently in response to ecological conditions."

This could be similar for sharks, although I could not find an article postulating this.
Alternatively, this could be because the mother does no "parenting"; the pups are immediately independent. Because sharks do not have many eggs at a time (according to the sharks-world website) each individual egg/pup has a higher "value" than each individual offspring in other fish species, which often lay many hundreds of eggs at once outside their body (oviparity). Therefore sharks that evolved this trait may have been selected because the offspring are more likely to survive if they are protected until fully functional within the parent.
No doubt there are other possible explanations, but as with all these questions along the lines of "What are the evolutionary reasons..." we cannot ever actually know, only suggest.


A Theorem by Von Neumann, which pertains a product of two Hilbert Spaces

Question: I'm writing my thesis on the EPR paradox (I want to continue my master degree in physics) but I'm having an unusual problem. One passage from the book I'm following at the moment justifies one important passage saying that "a theorem proven by Von Neumann tells us" but, since it is far from obvious, I'd like to check the proof for some insight on the matter. The problem is: Von Neumann worked in a lot of fields, so I'm having a hard time figuring out which theorem is this. Any research failed me. It would be most helpful if someone recognized the result and pointed me in the right direction for a proof.
So, without further ado here is the theorem as it is used in the book: let $H_1$ and $H_2$ be two Hilbert spaces (separable as it is common usage in QM, so we are treating with the space of square integrable functions) and let us have two complete basis of orthonormal states $\phi_i$ and $\psi_j$, one for each space. Let $\omega$ be an element of the direct product of these two spaces. The most general way to express $\omega$ would be $$
\omega=\Sigma_{i,j}c_{ij}\phi_i\psi_j,
$$
where $\Sigma_{i,j}|c_{ij}|^2=1$. Now the theorem by Von Neumann says that we can find two other basis for $H_1$ and $H_2$ which I will denote by $\alpha_i$ and $\beta_j$ such that
$$
\omega=\Sigma_i c_i\alpha_i\beta_i,
$$
where of course $\Sigma_i|c_i|^2=1$.
I apologize for my messy writing but I'm kinda technologically impaired, I hope you still managed to get the idea. Basically, it allows us to have a sum over one single index.
As I said earlier, I don't want to bother too much so I don't ask for a proof, just for a nudge in the right direction. Thank you!
Comment: Judging by the first expression for $\omega$, I conclude that you are speaking about tensor rather than direct product. (Also, that's what they usually do in physics, and I conclude physics judging by the name "state" :)
Comment: I do not know about the reference to Von Neumann, but $\sum c_i \alpha_i \beta_i$ is commonly referred to (in quantum information theory) as the Schmidt decomposition.  It is basically the same thing as the singular value decomposition (i.e. $c$ can be diagonalized by changing left and right bases).
Comment: Mr Degtyarev is completely correct, I did mean tensor product, I got my terminology mixed up. And I did check the bibliography, but as it turns out I was not as thorough as I previously thought. The theorem was the basis for the so-called "Furry's Assumption", and I quickly checked out what I thought the original work of Furry was. Sadly, as I'm new to the whole "hunting references" thing I mistook what was a simple letter from Furry for the original article, because they were in the same issue of Physical Reviews. I will post the solution to this as soon as I can for future reference.
Comment: Does the book have a bibliography or something that may give a clue where Von Neumann may have written down his theorem?  I ask because it is unclear to me how thoroughly you have checked the book.  (I sometimes forget the obvious.)  Gerhard "Obvious Never Writes To Me" Paseman, 2014.02.24
Comment: "I don't want to bother too much": what do you mean? I am afraid that [the actual English meaning of this sentence](http://forum.wordreference.com/showthread.php?t=1401867&langid=14) is the exact opposite of what you are trying to say. I guess that you should write "I don't want to bother *you*".
Answer: As noted by Dan Stahlke, this is precisely the singular value decompositon for compact (in this case Hilbert-Schmidt) operators, via the identification of an element $\omega$ of the Hilbert space tensor product  $H_1\otimes H_2$ with such an operator $T$.  The result can be deduced from the spectral theorem for the compact operator $T^\ast T$ just as in the finite dimensional case.
Edit after Nik Weaver's answer.  The correct statement of the result should talk about orthonormal sequences rather than bases.
Comment: I believe that at this point the question has a clear and definite answer, one I'm very satisfied with. Thank you all for bothering (now I believe I'm using this word in the right way) with such an elementary question, you have spared me countless headaches.
Comment: @Menghini: if you're satisfied with alpha's answer, you should click the "accept" button to indicate this.
Answer: Since no one noticed, I feel I should point out that OP's actual statement of the theorem is incorrect. It might not be possible to match up the two bases, for instance you could have the sum $\sum 2^{-n}e_n\otimes e_{n+1}$. It's impossible to reindex the two bases to get this in the form $\sum 2^{-n} e_n\otimes f_n$ because there's an element of the second basis that doesn't get paired with any element of the first basis.
(There's also the nitpick that he assumed $\omega$ is a unit vector, but that's less interesting.)
Comment: Indeed... and/but it's my impression that this sort of "edge case failure" of a "singular value decomposition" (and other stuff) is very often ignored in physics-y situations... :)  For years, my amateur reading of such stuff drove me batty over these details, until I "just let it go". :)
Comment: @paulgarrett you are a better man than I --- I was never able to get over this.


How do I publish the work of my elderly father, a "fringe" scientist?

Question: I am trying to figure out the best way to publish my elderly father's life work. He says he would be considered a "fringe" scientist or an independent researcher. Should we self-publish? The subject matter would be of great interest to those interested in earth-moon systems, and the Egyptian Pyramids. How should we proceed?
Comment: Does "fringe" mean "crank", "legitimate but not studied", or "could have been done by a professional but done by an unconnected amateur"?
Comment: So is this a re-write of Fingerprints of the Gods?
Comment: I'm certain this is a duplicate.
Comment: Thank you all for your comments.
Comment: https://academia.stackexchange.com/questions/114009/is-it-possible-to-publish-a-deceased-relatives-unpublished-work-with-them-as-th
Comment: https://academia.stackexchange.com/questions/137447/a-famous-scholar-sent-me-an-unpublished-draft-of-hers-then-she-died-i-think-he?r=SearchResults&s=1|35.4051
Answer: There are precedents for this.
J.S. Bach assumed that his music would be forgotten after he died. It would have been it if weren't for the efforts of Mendelsohn, Schuman and others. Nowadays Bach is considered by many to be the greatest composer whoever lived. His work is to be heard ubiquitously.

For about 50 years after Bach's death, his music was neglected. This
was only natural; in the days of Haydn and Mozart, no one could be
expected to take much interest in a composer who had been considered
old-fashioned even in his lifetime.
https://www.britannica.com/biography/Johann-Sebastian-Bach/Reputation-and-influence

With regard to publication by children of a parent's work, there is the case of Pierre Fermat.
Fermat was a great mathematician by any measure. However his widespread recognition by the general public was the result of his so-called Last Theorem. This came to light purely as a result of his son reproducing a note from Pierre's handwritten note in a margin.

Written in 1637, it wasn't actually his last theorem, but nobody knew
about it until his son found it five years after Fermat died. Years
later, after all of Fermat's other theorems had surrendered to
mathematical proof, this remarkable theorem resisted all assaults.
https://www.famousscientists.org/pierre-de-fermat/

Self-publishing is always an option even if it ends up being simply a treasured family keepsake.
Without knowing the details (Did he visit and excavate the pyramids? Did he decipher hieroglyphics that no-one else could?) it is difficult for us to answer.
I think you need to consult an expert in the field. Alternatively you need to get a publishing agent in the field of interest. They will negotiate the traps and tricks of the publishing industry for you (at a fee of course).
Comment: I appreciate your answer. The information you've shared here is extremely useful!
Answer: The way I'd suggest proceeding depends on the answers to a couple of questions:
Question 1: can your father present robust enough evidence for his ideas to get them through peer review?
If the answer to question 1 is "yes", then you can submit a paper (or several papers, depending how many separate original insights your father has to publish) to a peer-reviewed journal in a relevant subject area, through the usual channels as detailed on that journal's website.  (Presumably you'll want to choose a journal that doesn't charge its authors publication fees, so make sure you read the small print on the journal website.)  You don't need to be affiliated to a research institution, nor to found a company: I've definitely seen papers in peer-reviewed journals with the author's home address given where the institutional affiliation would usually be.
If the answer to question 1 is "no", then you need to ask yourself:
Question 2: can your father tell a compelling enough story to make a book of his ideas a marketable proposition for a regular, for-profit publishing house?  (I'm guessing that the advent of print-on-demand services means that this is not as high a hurdle as it used to be, but its height is still non-zero.)
If the answer to question 1 is "no" but the answer to question 2 is "yes", then you can pitch such a book to a publishing house.  How to go about this is somewhat outside my bailiwick, but there's some sensible-sounding advice here.
If the answers to questions 1 and 2 are both "no", then I'm afraid you are in the territory of self-publishing or what's pejoratively called "vanity publishing".  That's even further outside my bailiwick than the previous option, but as I understand it, in this case, you don't need detailed procedural advice, just the ability to hand over some money, and to read contracts thoroughly so you know what you're getting for that money.  (Again, I'm guessing that the advent of print-on-demand services means that the amount of money you'll have to hand over is less than it used to be.)
If you're unable to determine with any confidence the answer to question 1, then your situation is slightly trickier.  However, people on orthodox academic career tracks quite often find themselves in this position too.  The traditional way to deal with it is to submit an abstract to, then present a paper at, a conference with peer-reviewed proceedings.  That way, one gets input from the relevant scholarly community, via discussion at the conference, to help work out the answer to question 1 and/or to help improve the paper to make sure the answer to question 1 is "yes".  However, this would involve you in paying out registration fees for the conference and travel costs to get to the conference, which you probably don't want to do.  Fortunately, the internet era has made available a way of achieving the same benefits without those costs: submitting a paper to a special type of peer-reviewed journal that has the process sometimes known as "Interactive Public Peer Review" (that name for the process is a trademark of one particular journal publisher, Copernicus Publications, but I'm pretty sure there are other journal publishers that have an analogous process, albeit under a different name, for some or all of their journals).  (As for other types of journals, check the small print on the journal website if you want to make sure you're choosing a journal that doesn't charge author fees.)
Answer: "Independent Researcher" is a perfectly honorable profession. If you have something worth publishing, I suggest you write it up properly and submit it to a suitable journal. You don't need to be university faculty or an industrial researcher to be published.
Self publishing is sure to leave you with almost no audience unless one of you is already very well known.
But when you say "fringe", you may have a hard time if the ideas are impossible for people with open minds to accept. But fringe can also mean just "not well known". That is fine. Publish and you can become known. But know the standards of any journal you submit to.
You will need to decide if joint authorship is appropriate, also.
Comment: I think that another way to go would be to find authors in the field that already have existing "crazy" ideas (I know there's one or two that have appeared on the Joe Rogan Podcast, particularly with pyramids) and try to collaborate with them. Those would be your allies OP.
Comment: We appreciate your input and will take your words to heart!
Answer: A few years back I was in a position when I had to submit a paper but could not use any affiliation. You could say I was between jobs or maybe in a job where I could not use my affiliation for independent research.
I spent a few 100 dollars and registered a company. I registered with IEEE to get an email address. This is perfectly legal.
In your case, the motto of your company is to do research in the ancient ways of Egyptians or whatever. You both are its stakeholders. Now you are not independent researchers. You work in a company.
Legally and for all practical purposes, you are no less than researchers affiliated to universities or research labs.
Comment: This is going to make them look more like cranks, not less.
Comment: Thank you for your contribution! You have helped us more than you know!
Comment: @Arno I don't even want to use that term. And it is not the people they should be worried about but the reviewers. People in the free world are 'free' to conclude whatever they want.
Answer: You might get the widest readership by posting on something like arXiv (for math, at least). At least if your father's work can be put into reasonable pieces that at least vaguely resemble referee-able journal papers, they would likely accept.
The main possible obstacle is that arXiv would want "an endorsement" from a more established scholar... but/and for anything presented in a reasonably dignified, serious way, this ought to be feasible.
Self-publication won't reach anyone. Journal publication hardly reaches anyone any more, either, except for the fanciest journals, which are very status-and-orthodoxy-sensitive. The "arXiv" (for math) -like on-line archives are by far the highest-profile way to publish, and are not behind paywalls.
Comment: Curious: is the down-vote just for fun, or is there some genuine disagreement with the idea of arXiv-publishing as opposed to self-publishing? Or... what?
Comment: I'm not responsible for the downvote, but given that her father has no academic affiliation the endorsement required to post in the arXiv might not be an option. Most academics would only endorse somebody they trust and have collaborated with.
Comment: @B.Núñez, I generally agree that it's not always so easy to get an endorsement for arXiv, for example, but I think it's worth some effort, given the alternatives.


Question about changing mass under conservation of momentum

Question: In class today, my professor was teaching conservation of momentum. One example she used was an open cart rolling on a frictionless track while in the rain. As the cart collects water, the mass increases; and due to conservation of momentum the velocity must decrease, in order to keep momentum constant. However, the way I understand it, since velocity is decreasing, that means it must have negative acceleration, implying net force is no longer 0, implying momentum is not constant. What am I misunderstanding here?
Answer: The net force on the cart is not $0$.  The cart is interacting with the rain in the cart, giving up some of it's momentum to the rain so that it travels the same velocity as the cart.
The net force of the cart and rain system is $0$.  Any force the rain puts on the cart is directly opposed by the force of the cart on the rain inside it.
As rain enters the system, it's momentum needs to increase so that it can move with the same horizontal velocity as the cart.  This comes from the momentum of the cart, therefore the cart + rain system still conserves momentum and has no net force acting on it (except for the vertical forces of rain falling; but those don't affect horizontal movement here).
Answer: This is really the same situation as an inelastic collision between two objects, the cart and the water.  Before the "collision", the cart has mass $M$ and horizontal velocity $v$, and the falling rain has mass $m$ and horizontal velocity $0$. The horizontal momentum of the system is therefore $P = Mv$.
After the "collision", the cart and the rain have the same velocity $v'$. There were no external horizontal forces acting on the cart and the rain, so the momentum is still $P$, and the velocity $v'$ is given by $P = (M+m)v'$.
Momentum is taken away from the cart and added to the falling rain by the internal forces acting between the water and the cart.
Think about a different situation where the cart collides with a number of small rocks spaced along the track, and each rock sticks to the cart in a totally inelastic collision. In that case, its should be clear that momentum is transferred from the cart to each rock by the equal and opposite impact forces on the cart and the rocks.
In the original problem, it is hard to visualize exactly what is the force between the cart and the water, but the good thing about conservation of momentum is you don't need to work out all the local details of how the rain water sloshes around inside the cart to find the global behaviour of the system - i.e. the change in speed of the cart.


What is the name of this chord

Question: I'm sure this has been asked before but I cannot find in anywhere. Say you are in the key of C major. What is the name of a dominant chord on the 6th scale degree, i.e. A C# E G. This device is ubiquitous in pop music, and off the top of my head 'Fallen Down' from the Undertale soundtrack is the first simple tune that comes to mind which features it. I have been mentally referring to this as a Neapolitan chord but this  is a different harmonic device.
Comment: Unclear: the name of the chord is of course **A7**, or **VI7**. What more are you looking for? Some clarification in the question title and in the body of the question might be helpful, but any more detailed explanations would require more information about the context in which the chord is found.
Comment: Again, context matters. It is likely a _secondary dominant_, e.g. in the common **I - VI - ii - V** "Rhythm changes" variation.
Comment: The "name" of the chord is independent of the context within the progression.  As has been stated it is A7 (regardless of the key).  Being in C identifies the root as being on the 6th degree of the key and Tim's answer describes that dynamic.  But the chord is identified by its formula (1, 3, 5) = Maj, (1, b3, 5) = min, (1, 3, 5, b7) = dom 7, etc, etc.
Comment: @DavidBowling I was just wondering if this chord had a name, really. A name might mean I could find pointed information on its history and usage. I hit a break in my search with the term 'VI7' and It seems as though it's so elementary and ubiquitous that it doesn't have one
Comment: @DavidBowling Yes that sounds about right, or rather, consistent with how I hear it. The example I mentioned in the OP goes I - IV - IV - iv. Another example is the progression I - VI7 - ii - IV. The contexts that I am thinking of are essentially when it is juxtaposed with the root chord so you get the really nice voice leading of the one to the flat two or vice versa.
Comment: @ggcg -- a quibble: sometimes a context is required to even name a chord. Symmetric chords (i.e. dim7 and aug) need context to identify the root, and other chords are ambiguous in isolation (e.g. m6  and m7b5).
Answer: Often it'll be a secondary dominant or V/V, V/ii, V/iii, V/vi. In other words, it's non-diatonic (containing C#), and often leads, in this case, to Dm. It's the V of Dm, - A7. It can be named VI7, but that doesn't give much of a clue as to what it's actually doing in relation to other chords around it. But if it doesn't lead to Dm (ii), then it's more of a standalone, and can be labelled VI7.
So to sum up, in key C major, it's called, in RN, V7/ii. Or simply, A dominant 7.

What is the name of this chord


Photon absorption requirements

Question: If I blast a material with photons at a frequency strictly greater than the difference between any two energy levels of all electrons existing in that material, will any of these electrons jump to a higher energy state?  Some say the energy match must be exact.  Some say the balance moves on as a lower energy photon, which might be eternal if lower than any bottom level  Intuitively, the material should heat up. How is this heat manifested?  Thank you
Comment: Is this frequency greater than the ionization energy?
Comment: Is the material an atom/molecule, with discrete electronic energy states, or a solid with a continuous band?
Comment: Gilbert, I am an electrical engineer asking a basic question here, not one pertaining to a new state of matter.  I am trying to understand how photons interact with traditional solids. I understand that the electron energies in solids are modeled as discrete.  You mention a continuous band.  Are you thinking of the traditional conduction band where perhaps electrons might be accelerated by an electric field an take on a continuum of energies?
Comment: Sorry, i guess this would habe to be greater than the ionization energy.  Seems like it should do something.  I pose it in order to understand those who say that the photon energy hf must exactly match an energy shell difference in order for it to be absorbed.
Comment: The ionization energy pertains to gases.  I was thinking of solids here but there must be something similar for solids, probably larger
Comment: ...and intermolecular forces might confuse the issue.
Comment: Closely related to the "work function" for solids
Answer: There is Compton scattering

the X-rays are scattered through an angle $θ$ and emerge at a different wavelength related to $θ$  . Although classical electromagnetism predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.

These Feynman diagrams can be used for modeling the interaction of photons with particles and/or fields.
The models are complicated, example :

Direct determinations of electron momentum densities in solids by measuring Compton scattered photons
  in coincidence with recoil electrons will allow more precise testing of electronic structure calculations.

In the case of solid matter, the electrons in the diagram may be  virtual, representing the interaction of the photon with the field and the loss of energy of the photon. How the energy is dissipated will depend on the solid, its lattice rotation and vibration levels as the excess energy turns into kinetic energy and heat.
Answer: Given a particular material, one would find that the material has a particular absorption spectrum. This represents a function with the probability density for a photon to be absorbed by that material as a function of the frequency (wavelength) of the photon. So, if your photon has a frequency that does not match the energy differences between the energy bands of the electrons in that material, then the probability for absorption would be low. Therefore, the material would be transparrent for the photon at that frequency.
However, one would find that the absorption peaks in the spectrum have a finite width. So, even if the frequency does not match the energy difference exactly, there is still a nonzero probability that the material can absorb the photon. What happens with the difference in energy? Well, that can go into (or be borrowed from) other forms of energy, such as thermal vibrations in the material.

Photon absorption requirements


What is the speed of a standard airliner during the different phases of the flight?

Question: I would like to know how does the speed of an airliner vary as a function of time.
Answer: Ballpark:

At the gate, 0 knots
Taxi, 5-30 knots (usually 10-20)
Takeoff, 150 knots (rough ballpark)
Climbout below 10,000', 250 knots
Climbout above 10,000', 270-320 knots
Climbout above 28,000', Mach .78 (ballpark)
Cruise, Mach .78 (groundspeed ~450 knots +/- wind)
Descent above 28,000', Mach .78
Descent 28k to 10k, 280 knots (up to 330 knots, if ATC requests)
Descent below 10k, 250 knots
Traffic pattern,200 knots
Final approach, 140 knots
Taxi in, 10-30 knots
At the gate, 0 knots

Edit: these are fairly typical 737 numbers; other aircraft will have differences. Regional jets will typically be slower; 747 and 777 will often be faster (especially for takeoff and cruise).
Comment: At the two 747-100/200 carriers I worked for, cruise was 0.86. Management at both companies advocated for 0.84, but both elected for cost reasons not to maintain the autothrottle systems that made that easy. Trying to maintain 0.84 manually was a seesaw operation that flight engineers might try for awhile. The easy thing to do, and which almost everyone did, was to select a power setting that put the airplane at 0.86, where it would stabilize (due we felt to a drag rise there) and not require continual adjustment.
Comment: @jjack Mach 0.78 is within the usual range of cruise speeds for at least some common aircraft types, but something over Mach 0.8 could occur too. See the charts under Cost Index-Cruise Speed Relationship in http://ansperformance.eu/references/library/airbus-cost-index.pdf for example.
Comment: @Terry: That worked well when fuel was 50 cents per gallon.
Comment: Cruise: 0.78 only? I've got figures above 0.8 in my mind, but I'm not totally sure.


speed of gas molecules when they escape to space

Question: I wonder if the escape velocity of gas molecules is the same as the one of rockets, which is 7.8km/s. And do oxygen escape at all or not? Are they too heavy?
Comment: 7.8 km/s is for orbit, and escape velocity is sqrt(2) times larger. If it's moving at orbital speed, it could remain suspended up there if neutral, if we ignore the Newton's cannonball issue (which is possible since it can start out in the exosphere to begin with). However, it's unlikely to stay neutral for long, and it will be acted upon by the magnetic field.
Answer: Yes, the general process of losing gas molecules is possible. It's called atmospheric escape.
The escape speed mechanism you mentioned is just one way in which it happens. Since lighter molecules move faster, they tend to be nearer the escape velocity. The Earth has lost (and continues to lose) hydrogen over the course of its history due to this. Oxygen is heavier and isn't as susceptible to this process, though I won't claim it doesn't happen to some degree.
Answer: The speed of a molecule is given by:
$$V_{rms}=\sqrt{\frac{3k_BT}{m}}{\tag1}$$

with v in m/s, T in kelvins, and m is the molecule mass (kg). The most probable speed is 81.6% of the rms speed, and the mean speeds 92.1% (isotropic distribution of speeds).

The mass of an oxygen molecule is $5.313\times 10^{-26}$ kg. This gives $v_{rms}$ a value of about 460 m/s at 0°C.
There will not be a lot of molecules able to reach the speed necessary to escape the gravity of Earth.
Added:
The temperature at 100 km above the ground is about 200 K, about the temperature of dry ice. The $v_{rms}$ of an oxygen molecule at this temperature would be about 390 m/s.
The escape velocity remains the same, independent from where you start.
Comment: Could you also add info about the temp in the upper atmosphere as well as escape speed?
Answer: Escape velocity on the surface of earth is 11.2 km/s which is 11200 m/s. RMS velocity is given by
<code>      Vrms = √(3RT/M)
</code>
where M = molecular mass of oxygen = 32 g/mol = 0.032 kg/mol (converting to SI unit). If oxygen must escape earth then Vrms = Vesc
That gives T = 160000 Kelvin temperature.
Comment: Please do elaborate
Answer: Yes, the escape speed will be the same as for a rocket launched from the same altitude, which, depending on how high up you want to consider an escape from, may or may not be approximately as much as on the surface, which is actually 11.2 km/s, not 7.8 which is orbital speed.
The reason for this is escape speed is independent of mass, due to the fact that gravity's action upon an object can be conceived of in purely kinematic terms - that is, in terms of the geometric parameters of the object's motion - position, velocity, acceleration alone, with no reference to the dynamical parameter, mass, which describes the responsivity, actually the resistivity, of a physical object to an applied force (responsivity would be $\frac{1}{m}$, so massless objects are infinitely responsive to applied forces, while heavy ones show little response.). In particular, that gravity accelerates all objects the same way, independent of their mass, so that mass need not show up in considering the kinematic evolution of an object in a gravitational field (but does show up as a parameter in the description of the establishment of that field by an object). This is a deep fact about gravity which serves as the basis of Einstein's general theory of relativity and permits it to be described in purely geometric terms as due to a modification of the geometry of spacetime.
As a result, a molecule, a rocket, Elon Musk's car, and the manhole blasted from the Nevada Test Site in 1957 (which, sadly, almost surely vaporized due to ram pressure against the atmosphere, i.e. it burned up on exit as opposed to the more familiar, but symmetrical, burn up on entry due to similarly high velocities) as a result of an underground nuclear test - all would have the exact same escape speed.
More specifically, the escape speed of any object, no matter the mass, from a spherically-symmetric gravitator, which the Earth approximates, of mass $M$ is
$$v_\mathrm{esc} = \sqrt{\frac{2GM}{r}}$$
where $r$ is the radial distance from the center (Technically this would not be 100% correct for within atmosphere because it treats the whole mass including atmosphere as below the escaping object, but that atmosphere mass is negligible compared to the Earth's mass.). For Earth, $r = 6371\ \mathrm{km}$ and $M = 5972\ \mathrm{Yg}$ (that is, $5.972 \times 10^{24}\ \mathrm{kg}$), and with those parameters you get a $v_\mathrm{esc}$ of 11.2 km/s. At the conventionally-stated top of the atmosphere, usually taken as 100 km, so effectively $r = 6471\ \mathrm{km}$ the $v_\mathrm{esc}$ is about 11.1 km/s. At 408 km, about the altitude of the ISS, $v_\mathrm{esc}$ is 10.8 km/s. Thus gas molecules at each location will need to have at least this much speed to escape. In practice, they may need more because of collision with other molecules can dissipate their energy. The relevant parameter is the mean free path of the molecules which is the average distance it can travel before colliding with another molecule, and the number of collisions on the way out along with the masses of those molecules (assuming elastic collisions, which isn't quite right since molecules can break or get their electrons bumped into higher orbitals, processes which absorb energy making it inelastic). So it's a rather complicated calculation to get the actual speed required for a truly successful molecular escape with high probability (a molecule could "get lucky" with a large free corridor in front of it but that's not as likely) and also the needed starting altitude. But the minimum speed (i.e. assuming a perfect free corridor all the way out) is the usual escape speed from the molecule's starting height.
Now when a molecule has actually escaped, which is how it seems your original question is worded, that is, it is very far from the Earth, its speed will have slowed by whatever amount is needed to supply the remaining energy required to fight the last of the gravity well to exit (and anything lost due to collisions). If the molecule had additional energy above and beyond this, which is almost certain, it will have residual speed. And this residual speed could be rather variable as to its exact quantity.
As for who can escape, that depends on the mass. At any given temperature, and so a given average kinetic energy, things with more mass will move more slowly, so oxygen will have a harder time escaping than nitrogen, which in turn will have a MUCH harder time escaping than hydrogen - which is why there is very little free hydrogen in Earth's atmosphere, but giant planets like Jupiter and Saturn are practically made of the stuff, due to having huge gravity wells (which are also supplied by the hydrogen itself). This is also important in considering possible conditions on extrasolar planets. In particular, it appears from all the data we've gathered so far with missions like Kepler to be a fairly robust conclusion that if a planet has about more than 5 or 6 Earth masses or so, its observed density drops dramatically, meaning that it has accrued what is almost surely a large hydrogen envelope (though proving that definitively is hard without spectroscopic measurements). There are exceptions, of course, but it's a sigmoid-shaped (stretched out S-shaped) graph with the center of the "knee" of the sigmoid (the S) is at this mass level. This is because there is finally enough gravity to achieve the necessary hold at that point, more or less (in particular the escape speed is $\sqrt{5}$ times more, not counting change in the radius, and thus the kinetic energy per unit mass to escape is 5 times more, so a molecule 5 times less massive than, say, nitrogen, will be just as hard to escape as nitrogen is, and that's about 6 amu (or 6 "Daltons", Da) for a diatomic molecule, $\mathrm{H}_2$ is 2 amu, so we're rather close.).


E-bike brake lever sensor wires loose

Question: In my E-bike, sensor wires has come out from the left side brake lever. Please see attached photo from link below. How do I re-connect wires to sensor. How do I get access to sensor terminals? Do I have to buy a new brake lever with sensor cable attached?
Comment: For some models it's possible to replace the sensor and wiring without replacing the brake lever.  I've done this with Tektro but finding spares was hard.
Answer: Based on the photo, there's a small knurled plastic ring around the cable.  Try unthreading that and the switch should come out.
Then you'll need to strip the wires and solder to the switch, and provide mechanical support using heatshrink etc.
When you refit the switch, make sure the wires are not being pulled.  I'd suggest adding more zip-ties to hold the wires to the brake cable for support.
Do take progress photos and add them as an answer of your own.  If you feel this is beyond you, anyone handy and competent with electrics/wiring should be okay to do this.

The purpose of this sensor is to cut off the motor if you start braking.  If you're comfortable with letting off the throttle, or coasting to brake, then the motor should shut off any assistance.
The sensor switch is probably a "normally closed" and will open when you press the brake lever.  So to get the bike working temporarily you could bare and twist the two wires together.
Your last resort is to buy a new left-hand brake lever with a sensor.   Also, check the right-hand lever and make sure the wire is not under strain now.
Comment: Thank you Criggie for prompt reply. I removed the black colour small knurled plastic ring but switch won't come out.
Comment: my best option is to twist the two wires together and ride. When I brake, stop pedalling which will stop the motor. Later I will buy a left brake lever and join the existing wires to new brake lever wires as I do not have access to other end to remove the existing wires completely and connect the new wires.
Comment: @WimalPerera the downside of the is if you shift gears while timing a gap in traffic, the pedalling to change gears will cause the motor to kick in.  When I borrowed an ebike with a broken cable to one brake, I had to get into the habit of  always using both brakes
Comment: The fault I saw was that the manufacturer had cable-tied the wire to the brake cable to relieve strain, really close to the switch.  That worked until the barrel adjuster on the brake lever was used for its intended purpose a couple of times.  And the switch could be NO or NC.  It's a logic input to the motor controller rather than necessarily part of a fail-safe circuit. I still reckon the switch should come out somehow.
Comment: @chris Noted your comments. I am in contact with e-bike local supplier to direct me to their recommended service shop to have a look. Bike shops near me won't look at it as make of my bike was not sold by them.
Comment: @WimalPerera I've found that with the e-bike I used to look after.  The LBS would deal with normal bike stuff (including rebuilding the motorised wheel) but electrical bits were up to me.  That's no problem as I do simple electronics and wiring quite a lot, but sourcing parts was hard.
Comment: I have enough electronics junk and other scrap materials that rather than twisting the wires together I'd make a temporary on/off switch mounted on the bars (using a fitting from an old front light or phone bracket).  That's not an option for everyone of course
Comment: @chris, Good Idea. I will try to mount a switch.
Answer: I faced same problem and fixed it.
As per this picture, I reconnected two wires with solder.

E-bike brake lever sensor wires loose


Why does our eyes got wet when we feel emotional or whenever we are hurt?

Question: I was thinking like whenever when we feel emotional or whenever we got hurt we got tears from our eyes but why is that happen ? Why our eyes got wet ?
Comment: the other answer does not discuss specific nuclei or larger structures within the brain
Comment: The other question is only about emotions.
Answer: The lacrimal gland, the major source for tear production, is situated just above the eye. It sends it's secretions to the eye via the lacrimal duct. Tears secreted collect in the conjunctiva of the upper lid. There is also a nasolacrimal duct which drains the tears from the eye into the nasal cavity. Hence the sniffles when we cry.
How is it controlled? The lacrimal nucleus in the brain is the major source for innervating the lacrimal gland, is a subnucleus of the superior salivary nucleus in the tegmentum of the pons (part of the brain stem). The lacrimal nucleus is connected to the lacrimal gland by the facial nerve (more specifically the greater petrosal nerve). This is parasympathetic (meaning it is part of the autonomic nervous sytem) and the neurotransmitter transmitting the signal from nerve to gland is acetylcholine (the receptor is muscarinic subtype of the cholinergic... though strangely wikipedia says nicotinic subtype is involved as well, but maybe this is simply poorly worded and is just refering to the ganglia stopover between pre/post ganglionic parasympathetic neurons), this information helps explain how some drugs affect lacrimation (tearing up).
Taken from source (1) [I do not know how reliable this website is]: How is the lacrimal nucleus told to start lacrimation? The lacrimal nucleus receives projections from the autonomic nervous system as well as from various brain structures, including the frontal lobe, globus pallidus, thalamus, and hypothalamus. The projections from the frontal lobe are thought to be important in human psychic lacrimation (crying because of emotions).
What I know: Another brain area called the limbic system is involved in production of basic emotional drives, such as anger, fear, etc. The limbic system [in the case of sympathetic nervous system it would be the hypothalamus specifically, but this is irrelevant here since parasympathetic nerves cause lacrimation] also has a degree of control over the autonomic system. As I under stand it, the frontal lobe usually inhibits the limbic system.
Again from source (1): While humans across the world produce psychic tears in response to both positive and negative emotions, and while similar emotions have been identified in other animal species, no reports exist of other animals showing psychic lacrimation.
according to wiki (3): Compared to tearing for physical reasons,  tears for emotional reasons have s different chemical composition. They are composed of more protein-based hormones, such as prolactin, adrenocorticotropic, and leucine enkephalin (a natural pain killer), which is suggested to be the mechanism behind the experience of crying from emotion making an individual feel better.
sources:
(1) http://carta.anthropogeny.org/moca/topics/lacrimation-tearing
(2) http://en.wikipedia.org/wiki/Lacrimal_gland#Innervation
(3) http://en.wikipedia.org/wiki/Tears
Comment: you are explaining in great detail the process of How, but not the Why.
Comment: good catch... not only do I have no idea on "the why", but some of the info in my answer way be inacurrate for "the how"... I'm hoping someone posts a better answer and then the credit is given to them...
Comment: don't Dogs and Cows shed tears? I thought they do
Comment: maybe, but i only know about humans
Comment: Without having anything but intuition, I would tend to think that it is a communicative signal, i.e. laughter the other way round. It helps individuals in social groups to infer the state of mind of other group members.


Issue Pushing Code to Heroku Public Key Error

Question: I am having a problem pushing the code from this tutorial: http://newsinternational.github.com/iot-assistant/ to heroku. I am at step five. When I issue the    git push heroku master    command, I get the error    Permission denied (publickey). Fatal: The remote end hung up unexpectedly.    I already tried: Permission denied (publickey) when deploying heroku code. fatal: The remote end hung up unexpectedly and https://devcenter.heroku.com/articles/keys
Answer: Check your .ssh config for heroku. Go to the .ssh folder and open the config file
cd ~/.ssh
subl config

The 'subl' is for Sublime Text, but you can use whatever editor you wish. Look for the line "IdentityFile" and make sure it has the non public key listed:
IdentityFile "/Users/ircmullaney/.ssh/id_rsa"

not
IdentityFile "/Users/ircmullaney/.ssh/id_rsa.pub"

That did it for me.


Identity column re-seed: when it is necessary?

Question: During one of the last lessons at university (I'm a student), lecturer asked us to develop a database (MySQL Server if it matters) and tiny client app that would consume the database as data source.
One of requirements was that the identity column (which is the PK in every table) must be sequential, because it is a good practice (as per lecturer words). That is, when table row is deleted, it's PK must be reused in subsequent inserts. I have average knowledge in RDBMS, PKs and identity columns. From what I understand, that identity column is just a way to let DB to auto-generate PKs when inserting rows and nothing more. And identity column value shall not be related to row attributes in any way (as long as it is not natural key).
This requirement (strictly sequential identity column) was suspicious to me. I tried to ask the lecturer what is wrong if identity is not sequential (with gaps caused by deletions), but got very abstract answer like "it is convenient for users and useful for DB administrators who maintain the database". No specific examples. The argument "convenient for users" sounds silly, because it doesn't have any meaning in business domain.
Therefore I'm curious if these reasons are real? I can think only of one case when identity column reseed is required -- when identity space is exhausted. But this is more design issue when identity column type was chosen incorrectly, say simple int instead of bigint or uniqueidentifier when table contains billion rows. Suppose, an identity column is a clustered index: can gaps in identity column affect index performance? Maybe there are other real-world reasons for automatic identity column re-seed after each delete I'm not aware of?
Thanks in advance!
Answer:
That is, when table row is deleted, it's PK must be reused in subsequent inserts.

What universe is your lecturer from??
That is grossly inefficient.  If you try to do that, you will cut your performance prospects down by a factor of 10.
If you need gapless numbers for auditing reasons, build them explicitly, not directly from database tools.  And never delete rows, but flag them as "deleted".  This will add to the messiness of queries, since they will have to ignore such rows.
In MySQL, InnoDB requires the existence of a unique PRIMARY KEY for each table.  But that is the extent of the requirement.  The key can even be a string.
Gaps are a convenience to the users and DBAs, not an inconvenience.
I can think of one case where gapless would be convenient -- chunking into groups of 100 rows at a time.  But there is a simple workaround using LIMIT 100,1.
Gaps have zero impact on performance.  That includes non-numeric indexes.  And non-unique indexes.  And composite indexes.
Sure, you can run out of ids.  I think I have seen it happen twice in nearly 2 decades of using MySQL.  I may as well worry about being struck by an asteroid.  It's low on my things-that-keep-me-awake-at-night list.
Gaps occur from (at least):  INSERT IGNORE, IODKU, REPLACE, DELETE, ROLLBACK (explicit, or due to crash), Multi-master replication (including Galera and Group Replication).  Do you really want to come up with workarounds for those?!
Feel free to have us sanity-check anything else that lecturer says that is suspicious.
Answer: Reusing an identity value, should in general be discouraged.  Either the value is used entirely internally, in which case it's actual value is immaterial, or it is also used externally in which case reusing the value is very likely going to lead to a misidentification.
Take the obvious case of an invoice or purchase order number, these might easily come from an identity column and be exposed externally, but you would never want to reuse them for precisely that reason. Both refer to specific transactions which you would not want to get confused.
Resolving such issues can be a big hassle when companies merge or are acquired.  Creating such problems on purpose? Not wise.
Answer: The reuse of PK id values has problems and generally should be avoided.
First, the implementation of auto_increment columns doesn't provide the guarantee of being gapless. Indeed gaps will occur if you rollback an insert on an auto increment column.
Secondly the gap ID may refer to existing data that hasn't been deleted (due to missing FK constrains). If they translate to member numbers communicated outside the system then that poses potential business identity risks.
Thirdly, bigint unsigned won't run out of IDs for a significant time even given an extremely large insert rate.
The biggest pain with gaps is coming across auditors who insist its an audit flaw. For DBAs they know gaps exist and why.
Answer: I won't echo everyone else's comments that that reusing a PK is a bad idea but I have come across times where an identity column needed to be re-seeded.
Corruption of the PK index itself.
Granted this was using MS-SQL and many, many years ago but it still is relevant. Many years ago for the company that I work for, someone thought it would be a good idea to re-use PC's as servers in our 150+ remote locations after they were too old to be used by the clients and then stick them in a closet with no ventilation. When no Because we all know that a pile of junk 10 year old computer in a tiny room with temps of 120+ running mission critical databases could only result in good things. Like 40% failure rates and me rethinking my career choice. We would replicate the data back to the corp headquarters but more often than not, these failures would result in bad things happening to the databases. One of those things were the database having corrupted indexes which would seize up the database and the replication process. Twice in this great environment, the only solution to fix replication was to reseed the indexes and then reestablish replication. We did replace the servers later before ditching them completely.


Post-hoc power analysis of complex sample survey data

Question: I am working with a complex sample survey data using Stata to determine the predictors of a given dependent variable. As part of my analysis result I want to report the post-hoc power for each predictor. However, post-hoc power analysis in Stata (and other softwares I know) is done assuming the data is generated through a simple random sampling. I thought dividing the complex survey sample size by the design effect used in estimating the sample size to get the effective sample size and then doing the power analysis on the effective sample size. However, I am not sure if that is a proper course of action. What would you suggest in this regard?
Comment: The answer to [this post](http://stats.stackexchange.com/questions/22406/power-analysis-for-ordinal-logistic-regression/22410#22410) on CV addresses power analysis for ordinal logistic regression using simulation method in R. May it be possible to do simulation for post-hoc power analysis for complex sample linear regression that involves multiple imputation (preferably in Stata)?
Comment: [Another post](http://stats.stackexchange.com/questions/37969/power-analysis-with-weighted-survey-data) on CV addresses power analysis with weighted survey data. The answers suggest using simulation to estimate power. However, how to do simulation for complex sample surveys (involving stratification, clustering and weighting) is not shown in the answers. In fact, my data is also complicated by multiple imputation.
Answer: I did exactly this in a recent secondary data analysis of complex survey data. I was performing a two-level mixed regression model and ascertained the power of the study to detect significant differences given different effect size estimates (0.2, 0.5, 0.8).
I used three different ICC values (based on previous research) to estimate three estimate design effects. Used these to determine three candidate effective sample sizes. And then determined the power of the study (for each predictor) to detect small, medium, and large effect size differences.


Where can I find coordinates for Special Use Airspace (e.g. restricted areas) in the USA?

Question: I am looking for exact specifications for a few prohibited and restricted areas near me so I can plot these areas in other mapping software.
I can use sectional charts to estimate, but I am curious if there is some kind of listing that contains coordinates that define these SUAs.
Answer: As Pondlife says, this answer tells you where to look: All special-use airspace is defined in JO 7400.10. Version C is current as of February 16 2021.


Lightweight alternatives to Matlab in linux

Question: I want to learn some basic things using Matlab. I'd prefer a lightweight one in Linux. Is there any alternative?
Answer: There are several alternatives:

Octave is very similar to Matlab. For everyday use
(without various toolboxes) Octave can be used as a
transparent replacement.
SAGE is also great, but perhaps closer to Maple/Mathematica
in functionality than Matlab.
Scilab has many features from Matlab/Mathematica.

If you like to program and has a use for the large number
of extension libraries available in Python, I would definitely
choose Python/Scipy/etc. If you need a simple monolithic package
with linear algebra capabilities and syntax identical to
Matlab then use Octave.
You can find many other alternatives here.
Answer: You can start Matlab with the <code>-nodesktop</code> switch to run without the very heavy Java GUI. You can still draw plots and other things from this mode and it is in practice fully functional, with some obvious differences (no point-and-click UI).


Flag as not an "Answer" when "Question" does not contain a question

Question: If a "question" post does not actually contain a question, is it appropriate to flag an "answer" to that post as "not an answer"?
Answer: Re: Flag or not an "Answer" when "Question" does not contain a question
Summary: I think the part about the question is the primary issue in that situation.
Unclear (vague, insufficiently defined etc.) questions can lead to problems, when people try (usually with good intentions) to answer them.
Therefore for a situation where:

a "question" post does not actually contain a question

I suggest on the question:

add a polite & constructive comment to the OP recommending improvements;

and/or

vote to close it as "Needs details or clarity" and (optional, but recommended if not done in the point above) explain in a polite & constructive comment what specifically is wrong/needed.
Adding that explanation makes it easier for the OP to understand how specifically they are being asked to improve the question. Also it helps other site members to see when the missing material has been added, and then they can vote to reopen it (and those helping in the reopen review queue can see whether the requested information has been added to the question).

Regarding the answering of unclear questions. Generally, unclear questions shouldn't be answered, as explained here (especially the first bullet point):

Answer well-asked questions
Not all questions can or should be answered here. Save yourself some frustration and avoid trying to answer questions which...

...are unclear or lacking specific details that can uniquely identify the problem.
...solicit opinions rather than facts.
...have already been asked and answered many times before.
...require too much guidance for you to answer in full, or request answers to multiple questions.
...are not about electronics design as defined in the help center.

Don't forget that you can edit the question you're answering to improve the clarity and focus – this can reduce the chances of the question being closed or deleted.

The use of the "Not An Answer" (NAA) flag should be limited to really clear cases where a post is not an answer, and that would apply irrespective of the quality of the question e.g. when an "answer" is really someone new asking a related question, or just a rant about the topic etc.
More details and examples of when to use the NAA flag here:

How do I properly use the "Not an Answer" flag?
When should you decide whether to flag a posted answer as Not an answer?

As you see in those linked Meta article, a genuine attempt to answer a poor question shouldn't be flagged as NAA. That user might be misguided and perhaps is unable to resist attempting to answer a question which they really shouldn't do (see above), but that doesn't make it NAA. (However it might be a valid NAA for other reasons, unrelated to the question.)
Answer: In the general case you describe, you should not flag it as "not an answer".
According to How do I properly use the "Not an Answer" flag?:
Do not use this flag when:

The user posts a partial answer to the issues presented in the question

The answer makes an attempt to answer the question, even if it is wrong or inaccurate or you disagree with it

More likely in the case you describe, if you see a problem with the question, you would flag the question, or vote to close it if you have that privilege.
Answer: No!
IMHO
Preamble:
I see a significant number of questions which may not contain any "?"s but whose point in question is entirely clear to me. This may be because the OP does not have English as a second language or they do not have a good command of English. A question does  not necessarily need a "?", which is a construct which is desirable but not essential in every case. Having one or more usually helps.
IF the intended question is clear I wonder why people do not  spend the usually minimal time required making it into a formal question.
If the question is not a clear one the problem may be as above or because the reader does for some reason not grasp what is actually being asked.
In that case a comment asking about what is being asked also takes little effort.
Answer:
One or more examples would be extremely useful.
In the case of answers, if someone has answered an apparently unclear or apparently non existent question then they, at least, consider that it is a question  and can be answered AND they have done so.
A comment to the answerer may be of value to them and you.
Comment: "*IF the intended question is clear I wonder why people do not spend the usually minimal time required making it into a formal question.*" I'd have thought it pretty obvious. Because, for all OPs with language difficulties, there's many more who post a badly-written question they just can't be bothered to write properly. Editing for them rewards and encourages that laziness. Worse, it does not teach them to document well, an essential engineering skill. Instead,advise that in comments, eventually downvote/close. Give them a route to improve it themselves and, from there, to learn and progress.
Comment: @TonyM  I agree with your comment :-). I had in mind those who are clearly or probably in trouble with the basic system or language. The perceived lazy I tendd to (attempt to ) guide.


Does grass absorb juglone from black walnut trees?

Question: If grass grows near a black walnut tree, will they absorb the infamous juglone? If so, would it it be a lot or would plants near them be okay to eat/feed still?
Comment: I'm not entirely sure if this is on-topic here. It might be better suited to [Biology](http://biology.stackexchange.com). =/
Comment: I cut my neighbor's grass and its a pain to ride the mower under the low-hanging limbs of the black walnut trees to cut the **thick, tall** grass which grows robustly under them. If juglone has any negative effects on grass, I am not witness to them. The pines and oaks (to lesser extent) are a different story.
Answer: Don't know why I'm being told my answer was deleted, but I'll try adding another one since I was in the process of editing it when it was deleted.
I cut my neighbor's grass and its a pain to ride the mower under the low-hanging limbs of the black walnut trees to cut the thick, tall grass which grows robustly under them.  If juglone has any negative effects on grass, I am not witness to them.  The pines and oaks (to lesser extent) are a different story.
Regarding the comment:

I'm asking if plants absorb and retain the juglone. Basically, does it poison stuff that does grow in it?

Ohio State University Extension Fact Sheet

Many trees, vines, shrubs, groundcovers, annuals and perennials will grow in close proximity to a walnut tree. Certain cultivars of "resistant" species are reported to do poorly.

This seems to indicate that even if a plant is resistant, its still affected and must be taking it up to some degree. Although I have a fair understanding how plants exchange H+ ions for other cations in the soil solution, I don't have an understanding how plants take up complex compounds.... but I know they do.  The articles I have read on the matter, mostly repeat what I just said... they don't know either.
Interestingly enough, kentucky bluegrass appears to grow better under black walnut trees:

The beneficial effect of black walnut on pastures in encouraging the growth of Kentucky bluegrass (Poa pratensis L.) and other grasses appears to be valid as long as there is sufficient sunlight and water.

In any case, it seems likely that plants readily absorb juglone.. whether its toxic to them or beneficical.
Other quotes of interest may include:

Juglone is poorly soluble in water and does not move very far in the soil.
Walnut leaves can be composted because the toxin breaks down when exposed to air, water and bacteria. The toxic effect can be degraded in two to four weeks. In soil, breakdown may take up to two months.
Black walnut leaves may be composted separately, and the finished compost tested for toxicity by planting tomato seedlings in it. Sawdust mulch, fresh sawdust or chips from street tree prunings from black walnut are not suggested for plants sensitive to juglone, such as blueberry or other plants that are sensitive to juglone. However, composting of bark for a minimum of six months provides a safe mulch even for plants sensitive to juglone.

It would be interesting to see a study where bluegrass grown under walnut trees and then used as mulch for tomato plants would inhibit the growth of the tomato plants. Unfortunately, I can find no such study.  My guess is yes, there would be some effects.
In light of this, I'm going to save the grass I cut from under my neighbor's trees and use it to fertilize my bluegrass lawn.  Hopefully the juglone in the grass will help my grass grow and hinder the growth of the weeds.  Perfect! :)
Comment: hmm...so what if you grew a tomato plant or something with juglone around. If you got tomatoes to grow, could you eat them without issue?
Comment: @Ullallulloo Its possible to experience some allergy type symptoms (according to OSU), however I doubt the tomatoes would grow since they are the test for the toxin in the walnut compost. Juglone does affect animal cells according to this http://ict.sagepub.com/content/11/1/68.abstract which claims it inhibits tumor growth. A better question would be concering corn since juglone seems to help corn to grow much like bluegrass. Would the corn be safe to eat? OSU says walnut trees are suggested for pastures and must be safe for horses. I've found nothing about corn safety.


PCIe bus error severity=corrected id=00e5

Question: It's 2018 year and I found a lot of questions related to it but there's no answers to solve it.
Every time I turn on my laptop I got this error message before the login screen.
journalctl log
I bought this lapton 2 months ago. This is the model: Asus X541UA
I have tried with several Linux distros, the only one does not show that error was Ubuntu 17.10 Gnome, but I hate Gnome. I need a Ubuntu derived distro for work and I love Kde, so I use either Kubuntu or Kde Neon.
I just installed Kubuntu yesterday, sometimes it does not show the error, but most of the time it does.
uname -a output:
Linux RtPcK 4.13.0-25-generic #29-Ubuntu SMP Mon Jan 8 21:14:41 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux
Some refs I have:
PCIe Bus error severity=Corrected
https://bugs.launchpad.net/ubuntu/+source/linux/+bug/1521173
Answer: Try this steps:

cp /etc/default/grub ~/Desktop
Edit grub. Add pci=noaer at the end of GRUB_CMDLINE_LINUX_DEFAULT. Line will be like this:
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash pci=noaer"
sudo cp ~/Desktop/grub /etc/default/
sudo update-grub
Reboot now

:) Enjoy.


Technological progression over 1000 years

Question: Would it make sense to go from the technological equivalent of the 18th/19th century to a cyber-esque/modern society in the span of 1000 years? Are there any reasons that can be applied for this comparatively slow progress? or does this just not make sense?
Comment: 18/19th century is too late -- the Industrial Revolution was already in full swing. The first half of the 17th century is the latest time when relatively small changes could slow down scientific and technological progress -- e.g., have Leibniz and Newton die of some childhood disease. (And no, nothing you can do will slow it down as much as requested; at best you can get one or two hundred years more of pre-modern world; but eventually, somebody *will* discover calculus.) If you want to delay modern society by 1000 years you must start very much earlier -- for example, in the 5th century BCE.
Comment: Many factors could justify this kind of slow progress, among them war / famine / epidemics could impede research budgets.
Comment: Slow down, no. But take that long, easily. Just lob in a nice plague, a very successful Warlord, a new religion that bans all but the elite from reading, a plague of meteors poisoning the crops, etc, etc, etc. A sufficient setback can easily nullify hundreds of years of progress. We've had all of those (except the meteors, that's due next month), which is why the Roman Empire could not go to Mars in the year 750AD.
Comment: @AlexP I am not sure that even the 17th century would be early enough. Many advancements in science and technology were proposed/conceptualised by several different people approximately at the same time, but history recorded only 1-2 persons as authors. There is no guarantee that killing baby Newton will result in no Newton physics. It will be just known under some other person's name. Perhaps, only a complete cultural change and massive depopulation could bring the desired effect.
Comment: If you have time I would recommend reading Thomas S. Kuhn's ['*The Structure of Scientific Revolutions*'](https://www.wikiwand.com/en/The_Structure_of_Scientific_Revolutions).  Whether you agree or disagree with his views on science and technology, the book provides a lot of examples that could be useful for your project. It might also help with finding specific methods for slowing technological progress in your world.
Answer: In fact, the problem is what we saw people talk. Your question is good. You must have read a lot of books to find out what is going on in Earth's History.

We are humans and we live on a planet. This planet offers us many advantages and also makes it difficult. We, humans tried to live. But when trying to do that we were divided into tribes. Why were we divided? Because of our perception and the interpretations that result from this perception. Mankind's perception and mankind's interpretations. These 2 ideas define our history. Because of these two words, tribes A, B, and C have fought each other to find out who has the right perception and interpretation. Some of them tried violence. Some of them tried diplomacy. And mankind has come this far.

In the 21st century, we are analyzing the Earth well but not enough. Our technology and perception has changed some but our main perception still is the same. For instance, being religious or not religious. From the first human to now it still is the same. That is my comment but I comment what I read. If I'm wrong you can tell me. Another example, in the USA there are two main powers. republicans and democrats. Then let's take a quick look at history, such as Greek history. You can see the same main powers. Now we don't just call them democrats though, we call them pagans vs religious.

You will ask another question? Why am I saying that technology affects perception for humans. It is simple. For example, if you think like Elon Musk, and believe there is only money and technology are powers, so you work to earn them to increase your powers. In ancient perception, technology was also main power but the prestigious power is human power. That was the perception I suppose :) .
The concepts of information and technology are somewhat different. They should not be confused with each other. Information is always needed. Technology, on the other hand, has shifted to being a scientist in today's perception. "Scientism" other word. So everyone works in this area today. Because the prestigious main power is science and innovating tech. In older times, the number of these studies were low. For example, when a scientist found technology in ancient times, people valued that person. But the prestigious power of ancient times was manpower. Strength-muscle strength was in the foreground.

ed. shamelessly appropriate Trioxidane comment from the What are the most important factors that determine the balance of power between kings and nobles and merchants?

To quote Varys of a Game if Thrones: a king, a priest and a farmer stand around a sellsword in the middle. Each tells the sellsword to kill the others. Who will he obey? The king with money? The priest with eternal salvation? The farmer with food? Who is the power? After a debate of the conundrum he says that" power resides where people believe it resides".

In OP's situation taking a 1,000 years to go from low-tech to high-tech there is no problem in that - humans are those who define how fast it goes. If they decide AI-overlords is not exactly a future they like, they may take their time to sort things out, before progressing further. There are other examples from the Roman empire to the Apollo program where it is not technologies that decide what's next, but it is a result of decisions made by humans as a collective (in general, a prominent example is Japan) or as their leaders (Steve Jobs, Musk, state government, there is no end to the list).
So take your time, whatever it takes, if there aren't urgent matters to solve like running out of oil, but fusion tech does not mean AI-overlords.
Comment: I'm not native myself, soo, not in a position provide feedback on it. But what I think can improve situation is to have some conclusion. You made your point by examples, so now it is the time to sum it up by some short enough cinclusion/ending, making a statement which adresses OP question directly, in a condenced form, which will help readers to verify if they understood your examples in a way you intended them to be understood.
Comment: Made an edit, so feel free to remove it or adjust it the way you like
Comment: "humans are those who define how fast it goes" - history is rich with examples of societies that decided that it should go slowly. All of those societies collapsed, yielding to those ones which decided otherwise.
Comment: Maan language is rough, but the answer contains a point. To summ it up - processes in society have more influence on what we do, including technological development, than technologies themselfs. Thus any time frame can be legit.
Comment: if it is less clear i can correct
Comment: Not sure if it helpfull, but try https://www.grammarly.com plugin, it spellchecker+ in its free version it detects some word order and some sentence readability issues, at least as a tool which indicates some problems.
Comment: Thanks i read what you wrote.
Comment: Mic Edge has a corrector but not for gramar. Only word. I will use this extention.
Comment: I reworked your answer grammatically-wise to the best of my English (foreign but still fluent), which should help make things clearer. However, there are still spots I couldn't refine, because the ideas I had could change the exact meaning you wanted to convey. As a tip, punctuation (commas "," and dots ".") as well as subject defining words ("we", "they", "a/the", but also possessive like "my/mine", "our/ours"...) are important, so focus on making simple sentences with these, then improve them by adding flavor : connecting sentences with "then" or "because", adjectives...
Comment: I've attempted to edit some of the language of this answer. It's conceptually a good answer but it needs polish on the english used. I agree that humanity decided how fast our technology progressed and there are many examples of how our beliefs have influenced how fast science/technology have been introduced or even theorized. And our history shows many examples that such things can be lost only to have to be rediscovered.
Comment: I try to write better. I use google translate.
Comment: For the post. I tried to describe the relationship between human perception and technology. Because what we are doing is about our perception.
Answer: "Are there any reasons that can be applied for this comparatively slow progress?"
Could be, facing some extra limiting factors:

resources (ex. no easily available oil)

low population, limiting number of innovators

lower IQ (in premodern society it was going slowly up on genetic level, while after industrial revolution in modern one the higher survival rate means slight selection in favour of lower which until end of last century used to be masked by better nutrition and education; so let's say you enter industrial revolution with already lower IQ, make some improvements, face intellectual decline and achieve stagnation)

Alternative:
A calamity making history cyclical and causing civilization to crumble. Let's say nuclear war, a few centuries of rebuilding, another nuclear war, another rebuilding.
EDIT: 1000 years of slow industrial revolution? The global warming is going to be awesome and at some moment can become one of hurdles.
Answer: A body in motion will remain in motion unless acted upon by an outside force
I love Newton's first law — it can be applied to so much in our lives. The speed of technological and scientific advance is very much one of them.
Let's start with the basics. Speaking of the species and not of any individual, humanity is naturally inquisitive. When faced with a problem, we'll work out a solution. When faced with hordes of oncoming potential BBQ, we invent a pike. When faced with the possibility of being alone on a Saturday night, we'll invent music. And when music proves insufficient, we'll invent gloves to make picking roses easier and an entire process for extracting the essence of the Cacao bean.  I think it's not an understatement to say that humans love to tinker.
Especially when we're motivated.
And there's your loophole. The outside force to slow everything down. How do you demotivate humanity, especially when our reaction to most outside forces led to the aphorism, "Necessity is the mother of invention."
So, knowing that the, shall we say, wrong kind of motivation will speed up the discovery of science and technology — what's the right kind of motivation that will slow it down?
I'm going to suggest you'll need, well... a series of unfortunate events. (Honestly, I wasn't looking to use that phrase... it just became, well, a necessity....)
1. Regular Depopulation
Your first best motivator for slow advancement will be regular depopulation. Plagues, wars, famines, droughts, more plagues, regular falls of a mycorrhizoid spore,1 evolution of a particularly nasty badger... Humanity will eventually figure out how to overcome all these things, but if you keep the population low enough and spread out enough, it'll take forever.
This helps you for a couple of reasons that would normally increase the fertility of innovation.

Low communication
Low leisure time
Early age of employment
Shorter life spans
Difficult acquisition of wealth

2. Lower Birth Rates
If a constant string of wars and disasters depopulating your world isn't your fare of choice, let's try something simpler: lower birth rates. One thing that appears very true: the more people you have to work on a problem, the faster you'll solve it with more creative results. So, if we use this chart as our reference, you want to take 1,000 years to get from 1750 to 2021. That was 0.75 billion to 7.8 billion people for an average of 20 million new people "net" (meaning after all the reasons they're getting killed are taken into account) each year. You need to effectively divide that by four or more.
3. A Fertile Landscape
Curiously, history suggests you need winter to spur innovation. Areas with low population growth but highly fertile landscapes where people could happily live in grass huts and be simple hunter/gatherers did not innovate nearly as quickly as areas with limited growing seasons, limited resources, and/or strong climate changes between seasons.
4. Finally, let's make humanity more competitive and/or aggressive
Let's use music as an example. During the Renaissance music advanced tremendously due to patronage. Wealthy leaders and families would sponsor musicians (and artists of all kinds) to increase their personal status with the new. Yes, there were vendettas and wars, etc... but what if people were naturally more competitive? What if our social mores didn't favor compassion and life quite so much?
What if the Medici's were satisfied with a little new, and then went out of their way to make sure no one else found anything new?
This much more centralized, selfish, concerted effort to control innovation could justify a much longer delay. It's not enough to destroy a person's work — it's reasonable to destroy the person. In this way you actually minimize the number of clever problem solvers in your world. Given enough time, evolution would begin to favor the socially adept rather than the technologically adept.
After a thousand years you'd have your modern cellphone-using, Netflix-watching cyber-surfers — but the consequence of the longer period might be a species of humanity that's much more naturally politic than we all are today.
That's almost scary to think about....

1 It shouldn't surprise you that SciFi/Fantasy writers have come up with reasons to retard scientific progress. This one comes from Anne McCaffrey's Dragonriders of Pern series of books. The spores, called "thread," were a lifeform on a planet with an orbit that brought it close enough to the planet Pern to move some between planets. It was a neat plot device that, combined with the socio-economic conditions surrounding the politics of dragon riding, acted to retard scientific progress — in fact it caused it to regress.
Comment: Taking time tending to basic necessities is indeed impeding. It's often talked in survival guides that making a house will take a lot longer if you spend half your time eating, and the same thing happens when working on science. [Dr. Stone](https://en.wikipedia.org/wiki/Dr._Stone) anime/manga tackles this issue headfront in the first episodes, as an example.
Answer: The end of science
Every 20 years or some person in some scientific field declares that they have reached the end of science, and no more progress can possibly be made in their field. Then we discover more stuff and keep going.
However, theoretically there should be an end to science and scientific development. If you were to make every possible scientific advancement possible, by putting atoms into every possible configuration to make something with it, you would still have a finite number of ways to arrange the atoms and scientific advancement would end eventually. It might take a very long time but it will happen.
The amount of scientific progress we have made follows a logistic curve. The more science you have the easer it is to discover new things, but the more things there are to discover the easier it is to discover them. We see that scientific discovery has speed up over time, but for now it just looks like an exponential curve. However, we may see that it is indeed a logistic curve if we start to see the rate of scientific advancement decrease.
Since we don't know where this boundary is we can't say when the end of science will be. But based on the fact that research is still increasing in speed it is likely we are not near it. But if the end of science is near then we might soon experience a slow down in discovery. This might be enough to stop or at least reduce funding for more research. The reason everything is cyber/modern might be because that is the end of science and this is best way to have things once all technology is discovered.
Story based reasons
The religious group your story is centered on bans science and makes science progress very slowly or backwards for a bit. Zombies eat people's brains and books. Jesus comes back like he said he would and people spend more time on the spirit than science. Stuff like that.
Comment: Any scientist who declared an end to science would be treated like a moron by other scientists.
Comment: I mean, here is a ted talk about that with physics, https://www.youtube.com/watch?v=gWPFJgLAzu4
Comment: Ted talks are not great sources for science, they are better than main stream media but that's not a high bar.. Also end of physics is very VERY different than the end of science.
Answer: Mass depopulation, societal collapses and the dystopic ban of scientific research could all realistically slow down discoveries to a significant extent.
If you are willing to have some fantasy elements too your ("cyber-esque") story, you might as well achieve it in a smoother way: introduce a new promising field of science that would have somehow diverted the attention of global research for a few centuries (pre-Victorian social order without telegraph, radio communications, industries).
It is an idea largely inspired from "The Road Not Taken" by Harry Turtledove. A short story in which most alien civilisations discovered a very practical antigravity technology early on. Paradoxically, the highly convenient antigravity technology stifles further technological development as all the creative energies of societies that find it go into perfecting it (to perform simplistic FTL interstellar travel and wars of conquest on a galactic scale). In contrast, humanity advanced further technologically by exploring other fields of science.
Of course, this is an idea could be used alongside the other limiting-factors that I initially wrote about: after a terrible plague that almost sent humanity to a new Dark Age, scientists discovered a way a new field of science (...)


How to find the associated conservation law from a given symmetry

Question: It is a very well-known fact that any conservation law associated with some given PDE has an associated invariance (by Noether's Theorem). However, it is completely mysterious for me how to compute/derive these conservation laws just by knowing the invariances of the equation. For example, the one-dimensional nonlinear wave equation $$
u_{tt}-u_{xx}+f(u)=0, \qquad (t,x)\in\mathbb{R}\times\mathbb{R},
$$
is invariant under space translations. On the other hand, it is "well-known" that associated to this space translation invariance is the momentum conservation of the equation, that is, $$
P(u,v)(t):=\int_{\mathbb{R}} u_x(t,x)v(t,x)dx=\int_{\mathbb{R}}u_{0,x}(x)v_0(x)dx=P(u,v)(0).
$$
Nevertheless, I have no idea how to derive this conservation law (generally speaking) just by knowing that the equation is invariant under space translations. What about time-translations for example, what is its associated conservation law? Please, don't misunderstand me, I do know how to explicitly derive the momentum conservation directly from the equation, what I would like to know is how to derive it from the space-translations invariance. Any hint suggested reading or answer is very welcome!
Comment: The equation you wrote is variational. So you can use the general formalism there to make the computation starting from an appropriate Lagrangian. (Here the action is $$-u_t^2 + u_x^2 + F(u)$$ where $F$ is an antiderivative of the scalar function $f$.) Following https://en.wikipedia.org/wiki/Noether%27s_theorem#Field_theory_version you can get a conserved current $j$. Integrating $j^0$ along $\{t = const\}$ gives you the time-independent conserved quantity.
Comment: Conceptually, Noether's theorem is saying that a 1-parameter family of diffeomorphisms of the space F of fields induces a Hamiltonian flow on T^*F, and the Hamiltonian (Noether charge) is then conserved under that flow. I wrote a blog post about this a couple of years ago: http://jde27.uk/blog/noether.html - in particular the conservation of field momentum associated with space translation is worked out. Admittedly, I find it easier to think about going from the conserved quantity to the symmetry (from Hamiltonian to its flow) but that's just because differentiating is easier than integrating.
Comment: I don't know if it'll help to answer your specific question, but I hope you won't mind my taking the excuse to share Baez's exposition [Noether's theorem in a nutshell](http://math.ucr.edu/home/baez/noether.html), which I've always found second to none on this subject.
Comment: @BenMcKay Every conserved current is equivalent to one s.t. its conservation condition takes the form $\mathrm{d} j[\phi] = \xi \cdot E[\phi]$ (no derivatives of the equations $E[\phi]=0$). Applying the [Helmhotz operator](https://ncatlab.org/nlab/show/Helmholtz+operator) to both sizes gives $H(\xi \cdot E[\phi])=0$, implying differential conditions on $\xi$. On appropriate equivalence classes, $j \leftrightarrow \xi$ is a bijection. When $E[\phi]=0$ is variational, the condition on $\xi$ is the same as being a symmetry of the Lagrangian.
Comment: Time-translation invariance implies the conservation of energy.
Comment: This theorem is known to hold for variational problems in very broad generality, but I don't think there is a theorem of this type for nonvariational problems in any generality.
Comment: I should have written "...applying the [Euler-Lagrange operator](https://ncatlab.org/nlab/show/Euler-Lagrange+complex) to both sides...". The Euler-Lagrange operator starts off a sequence, in the same way that the exterior derivative starts off the de Rham sequence, where the Helmholtz operator is next in the sequence.
Answer: To be blunt, the answer to your question is Noether's theorem (often precised as Noether's first theorem). So, essentially you already knew the answer to your own question.
However, the other answers are missing a degree of pragmatism. The calculation of the conserved current, once you know the Lagrangian and the symmetry is straightforward and mechanical. Namely, suppose you have a Lagrangian density $L[\phi] = L(x,\phi(x),\partial \phi(x), \partial^2\phi(x), \ldots)$, which depends your dynamical field $\phi(x)$. The variational principle will be $S(\phi) = \int L[\phi] \, \mathrm{d}x$, where $\mathrm{d}x$ is the coordinate volume form.1 An infinitesimal local field transformation $\phi^a \mapsto \phi^a + \delta_{\xi}\phi^a$ is allowed to be coordinate and field dependent, $\delta_\xi \phi^a = \xi^a[\phi] = \xi^a(x,\phi(x), \partial \phi(x), \partial^2 \phi(x), \ldots)$, and commutes with coordinate derivatives, namely $\delta_\xi \partial^n \phi^a = \partial^n (\delta_\xi \phi^a) = \partial^n \xi^a[\phi]$ for any $n\ge 0$. The example of time translation $\xi^a[\phi] = \frac{\partial}{\partial t} \phi^a$ is illustrative.
Such a local field transformation is a symmetry of the Lagrangian when its variation vanishes modulo a total divergence, $\delta_\xi L[\phi] = \partial_i J_0^i[\phi]$. The next step is a bit unintuitive, but it makes the calculation of the conserved current mechanical. Consider now the variation $\delta_{\varepsilon \xi}$, where $\varepsilon = \varepsilon(x)$ is an arbitrary function of the coordinates $x^i$. Using integration by parts, we can put the variation of the Lagrangian into the form
$$ \tag{$*$}
  \delta_{\varepsilon \xi} L[\phi]
  = \varepsilon\partial_i J^i_0[\phi] + (\partial_i\varepsilon) J^i_1[\phi] + \partial_i(-)^i .
$$
The leading term has to agree with $\delta_\xi L[\phi]$ when we set $\varepsilon \equiv 1$. The desired conserved current corresponding to $\xi$ is
$$ J_\xi^i[\phi] = J_0^i[\phi] - J_1^i[\phi] . $$
You can get the current in one step if you use integration by parts to directly put the variation of the Lagrangian into the form $\delta_{\varepsilon \xi} L[\phi] = -J_\xi^i[\phi] (\partial_i \varepsilon) + \partial_i(-)^i$, which is a formula that can be found in some physics textbooks on QFT.
The proof of Noether's theorem in this form is also straightforward (and a reshuffling of the standard proof). It only relies on the usual lemma that any density $N[\varepsilon, \ldots]$ that linearly depends on an arbitrary function $\varepsilon = \varepsilon(x)$ (and possibly any other fields) has a unique representative modulo total divergence terms, namely $N[\varepsilon, \ldots] = \varepsilon N_0 + \partial_i(-)^i$, with $N_0$ unique. The Euler-Lagrange equations $E_a[\phi]=0$ are defined by the identity $\delta_\xi = \xi^a E_a[\phi] + \partial_i(-)^i$ for arbitrary $\xi$. So, when $\xi$ is a symmetry, using $(*)$ and one more integration by parts, we find the identity
$$
  \delta_{\varepsilon \xi} L[\phi]
  = \varepsilon \xi^a E_a[\phi] + \partial_i(-)^i
  = \varepsilon \partial_i J^i_\xi[\phi] + \partial_i(-)^i ,
$$
which implies that $\partial_i J^i_\xi[\phi] = \xi^a E_a[\phi]$, which vanishes when $E_a[\phi] = 0$. In other words, $J^i_\xi[\phi]$ is a conserved current.

1 If you change the independent coordinates $x^i$, the Lagrangian will change by the appropriate Jacobian. Working with differential forms allows you to keep everything more manifestly invariant.
Answer: You can find an overview of methods to obtain conservation laws from a wave equation in On the structure of conservation laws of (3+1)-dimensional wave equation. Noether's method requires that the PDE follows from a variational principle for a Lagrangian (as pointed out by Willie Wong). A direct algorithmic method to obtain conservation laws from a PDE without variational structure is described in the cited paper.
Answer: It's been a while since I've thought about this stuff so take this with a grain of salt. Also, I'm only familiar with this in the context of a finite dimensional phase space, whereas the phase space is infinite-dimensional in the example you give and I'm not sure what extra subtleties that introduces. But the finite-dimensional case might still provide some useful intuition.
Those two caveats aside, I hope the following is of some use:
We can define a canonical symplectic form on phase space in terms of the Lagrangian. The symplectic form gives us a bijective correspondence between tangent vector fields and 1-forms (it works the same as with Riemannian manifolds, the key is just that we have a perfect pairing on tangent spaces). We also have a Poisson bracket operation {A, B} between scalar fields A and B. {A, B} is the Lie derivative of B along the tangent vector field corresponding to the exterior derivative of A (obtained using the correspondence between 1-forms and tangent vector fields provided by the symplectic form).
A continuous symmetry is a flow that preserves the Hamiltonian H and the symplectic form. To a continuous symmetry, we can associate a unique tangent vector field that generates it, which corresponds to a 1-form (which happens to be closed). We can then integrate that 1-form to get a scalar field, which I will call S. We have that {S, H} = 0, this basically says that the vector field corresponding to S generates a symmetry. But the Poisson bracket is anticommutative, so {H, S} = 0, implying that S is a conserved quantity (since the vector field corresponding to H generates the time-evolution flow). Therefore, continuous symmetries correspond to conserved quantities.


My e-bike wiring is damaged and I don't know where to begin

Question: I was given a bike with an electric rear hub. I'm mechanically inclined but I've never had the opportunity to tinker with one of these. I'm fairly experienced with AC and DC electronics as well.
If anyone could help with where to start, I'd appreciate any advice or direction at all.
Thank-you...
Comment: Gidday and welcome to SE.  Good work for reading the tour page.  Problem with this question is its very broad and that might be enough for it to be closed.  Feel free to use Edit to describe the problems you're facing, and what troubleshooting+results you've achieved already.
Comment: I've never worked on one of these, but there should be good manufacturer's documentation online somewhere, since bike shop mechanics need to service them.  What sort of damage is present?
Comment: This isn't the right forum unfortunately as you really need someone to walk you through this. I'd suggest https://endless-sphere.com/forums/
Comment: @DanielRHicks - not if its some random chinese thing from ebay (though those are often electric front hubs). This going to be something that is difficult to diagnose over the internet and probably doesn't fit the stackexchange format.
Answer: First thing to do is check all the parts are present.  Without knowing your specific bike, you will probably have

A bike - thing with two wheels, etc.
Built into the bike will be a motor, probably in the middle of one wheel, but some designs have the motor between the pedals.  Rarely, some use a rubbing roller to push the wheel, but these are uncommon.
Battery - it should be fairly obvious.
Charger - lack of a charger is a strong indicator that the bike might be stolen.
Optional head unit / control panel - If the bike has one, it will likely be on the handlebars, and have some buttons and possibly a display or at least some LEDs for charge remaining.

Either in the battery pack or in the head unit will be a DC to AC converter.  Many ebikes have a 24 or 36 volt DC battery, but the motor itself is probably an AC unit for efficiency.
If you're looking at resistances, expect megaohms across the motor, and that it has 3 or 4 wires going to it.   You can't just connect the battery to the motor and have it go.
Make sure the battery is charged fully, then connect it, and turn on the bike.  You may need a key or card to do this, and lack of this is another indicator of a stolen bike.
When it starts, read the display, look at the LEDs, listen for beeps, and any bad messages should be referenced with the manufacturer's info.  This will be unique to the system, not necessarily the bike brand.
Modern ebikes tend to be "pedelec" meaning they give the rider an assist when pedalling motion is detected.  Older bikes tend to be throttle based, where you have a rheostat or a simple button for "add power"   Buttons are easy to troubleshoot, sensors are much less straightforward.
Other than that, its all getting very specific to your bike's electric system.  More details could help.