Can scripts run even when they are not set as executable?

Question: I can seem to run scripts (.sh) with and without them being set as executable. So where exactly this matters?
Answer: Let's say you have the file myscript containing the following:
#!/bin/bash
echo "Hello, World!"

If you make this file executable and run it with ./myscript, then the kernel will see that the first two bytes are #!, which means it's a script-file. The kernel will then use the rest of the line as the interpreter, and pass the file as its first argument. So, it runs:
/bin/bash myscript

and bash reads the file and executes the commands it contains.
Thus, for bash (or whatever interpreter your script requires) to "execute" the script, it only needs to be able to read the file.
So, for scripts, the execute bit just makes it a bit more convenient to execute it. As long as bash is executable, you can always run bash with the script file as argument, or run bash interactively and copy paste the script line by line into your terminal to have the commands executed.
Comment: What should I use instead of /bin/bash if I don't know the correct interpreter? Is there a command that runs the script according to the shebang line?
Comment: Thanks for explaining in detail. :) If I understood it right, any user access to bash just needs read access to the script to run it because bash will take the script as input and will only need to read it. I can stop this behaviour by taking the read permission of the script for that user. Right? So when does this executable permission is used & exactly matters?
Comment: Yes, if you use "bash myscript" then user only need read access for "myscript" (and of course executable for /bin/bash if bash is there within the path). However, if you make your script executable, things are a bit different. It's true that from the kernel's point of view, it will be "/bin/bash myscript" again if the first line is #!/bin/bash, but to reach that point, first you need to present the script as executable for the user or group. However, that's true if for some user the script is not executable but readable, (s)he can still "run" the script with "bash myscript" ....
Comment: @LGB So that's pretty much useless. Good thing is to cut the read permission away from a user for that script. Right?
Comment: @Ashfame: I would say useful rather than useless. The execute bit on regular files is not (and never was intended to be) used for limiting access. It seems like you're expecting that from it. If you have a binary executable, you must have execute permission on it to run it. However, if you have read access to it, you can always copy the file to your own home directory, in which case the copy will be owned by you, so you can add execute permission to it ... and run it. For directories though, it has a bit different purpose. See http://mywiki.wooledge.org/Permissions
Answer: Make sure you are not confusing "executing the shell script" with "run a shell script using sh".
This will not be affected by file permissions on file.sh:
sh file.sh

You are executing sh (which resolves to the program /bin/sh), which reads file.sh and executes it's code.
File permissions will have effect if you really execute the script itself :
./file.sh

Note that file permissions are not supported by non-Linux filesystems, like FAT. So even if you run chmod -x file.sh, the file will still have it's former permissions.
Execute permission is enforced by the filesystem. But programs can "execute" the code too by reading the file contents, which bypasses filesystem permissions on "execute".
Comment: I understand your point. But then is it for group or world or both?
Comment: @Ashfame If you set the executable permission, the script can be run directly by users who have that permission - whether they have it on a group, world or owner basis. But even people without execute permission can execute it by calling a different program (like `bash`) to do the execution - to block that you would have to take away their `read` permission as well.
Comment: `If you set the executable permission, the script can be run directly by users who have that permission - whether they have it on a group, world or owner basis` But how the permission is granted to different users by checking the executable permission? And I got your second point. You mean taking away their read permission of the script so that they can't even process it through bash. Right?
Comment: @Ashfame On the read permission point, yes. On how, you would call something like `sudo chmod g+x myfile.sh` in the terminal to add execute permissions for the file's group. See [File permissions tutorial](http://www.dartmouth.edu/~rc/help/faq/permissions.html). To manage permissions for several users simultaneously, you would use groups, see for example [Managing groups](http://www.yolinux.com/TUTORIALS/LinuxTutorialManagingGroups.html).
Comment: what i meant was when we add the execuatable permission in GUI, then its for whom? owner/group/world?
Comment: I have no nautilus at the moment, but you can try it yourself. Use `stat myfile.sh` after playing with nautlius. The most logical would be `chmod +x myfile.sh`. That is, execute permissions for owner, group and everyone with umask applied.
Answer: The exec syscall of the Linux kernel fails with EACCES if the file is not executable
While you can do sh myprog.sh (which just reads the files and interprets is), trying to run the program as ./myprog.sh cannot work, since when you do that:

your Bash shell on the terminal uses the exec system call on ./myprog.sh
the shebangs are interpreted directly by the exec system call of the Linux kernel as explained at: https://stackoverflow.com/questions/2429511/why-do-people-write-the-usr-bin-env-python-shebang-on-the-first-line-of-a-pyt/40938801#40938801
the Linux kernel refuses to execute files without executable permission

This can be verified with main.c:
#define _XOPEN_SOURCE 700
#include <errno.h>
#include <stdio.h>
#include <unistd.h>

int main(void) {
    char *argv[] = {"myprog", NULL};
    char *envp[] = {NULL};
    int ret;
    ret = execve("myprog.sh", argv, envp);
    perror("execve");
    printf("%d\n", errno);
    printf("%d\n", EACCES);
}

and myprog.sh:
#!/bin/sh
echo worked

If myprog.sh is not executable, main fails with:
execve: Permission denied
13
13

Tested in Ubuntu 17.10, gcc -std=c99.
POSIX 7 mentions that at:

The exec functions, except for fexecve(), shall fail if:
[EACCES]
Search permission is denied for a directory listed in the new process image file's path prefix, or the new process image file denies execution permission.

Further rationale can be found at: https://security.stackexchange.com/questions/66550/unix-execute-permission-can-be-easily-bypassed-is-it-superfluous-or-whats-the
Answer: Don't think of it in the way that. Can I execute this file? Think of it in the way that: Who can execute this file?
If the computer is yours and the file is yours I am sure you can execute it. You might want to look further into commands like chmod and chown, and file permissions.
I hope that helps.
Comment: Yes I know about them. That means, I (owner) can always execute it. Right? Then setting a file as executable is for the group or world or both?


how much atf oil is needed on a 2001 vw jetta when serviced?

Question: Some people say to put 5 qts. of ATF when doing the filter change on my jetta 2001, some say to use only 4 qts. what is the correct amount needed?
Comment: Welcome to Mechanics SE! Which transmission is in your car? the MkIV Jetta came with either a 4, 5, or  speed auto.
Comment: i believe its a 4 if im not mistaken
Answer: The 4 speed automatic transmission in that era of Jetta is an "01M"- total fluid capacity is 5.3 liters but for a simple fluid and filter change (as opposed to a complete flush) you only need 3 - 3.75l (as it won't drain completely)
Answer: To add to motosubatsu's correct answer, the most likely reason is that there's probably almost a liter "trapped" in bottom of the torque converter.
Most converters have a plug, which can be accessed [usually] by removing a sheet metal plate and rotating the converter to the correct position to remove the plug and drain.
You then put in about 4 liters, start the vehicle so that the pump refills the torque converter, and add another liter.  This is the correct way for a "proper job", but often it isn't done because it can be a real pain to accomplish this extra step.
I would never add the "capacity", as the 300 milliliters is likely "stuck" to various internal parts, depressions, trapped in the servos or valve body, etc.  The design capacity is a so-called "factory fill" which assumes a bone dry new or rebuilt transmission with no residual ATF.
In any case, the dipstick will tell you where to top up to when checked properly - which varies from vehicle to vehicle.
Some are checked hot, some cold, idling in neutral/park, or engine off.  The owner's manual or an online resource should yield the correct procedure.  It's very important this procedure is followed exactly, as idling while running yields a lower dipstick level than parked, off, and cold (the fluid is pumped and flung all over the place, very dynamic).  This can result in an underfill/overfill if you top up while not using the factory procedure.
Some dipsticks have multiple check points, and some even have the check procedure engraved into the dipstick blade.  And some have no dipstick whatsoever, and some even claim to have "lifetime" fluid.  Those you gotta love.  (Maybe they meant my lifetime...)  [sigh]
Comment: Good info :) IIRC the 01M was originally claimed to be "lifetime" fluid, then lots of them broke and VW quietly revised it to be 100k miles


My icloud password does not work when prompted on start up.

Question: This is a problem that is driving me nuts. I have tried everything I can find to get this to resolve. When I start my computer, I get a popup that wants my icloud password. I enter it and the password is not accepted. I then go to the browser icloud log in and I can log-in just fine. iTunes has issues as well. I plug-in my iPhone 6 (IOS 8) and the program does not see the phone. I went so far as to reinstall the ios in the phone.  Was better for a while but now just does not see the phone. Prior to the iphone everything worked without much trouble. But was not using iCloud sync service.  I also have a pop-upo on start-up requesting my Keychain password for call.app and sometime messenger.app.
Answer: You may need to run Keychain Repair to fix a few items in it that could be problematic. This issue is apparent due to the popups from the system requesting your Keychain password.
To check keychains for problems using Keychain First Aid:
Open Keychain Access, located in the Utilites folder in the Applications folder.
Choose Keychain Access > Keychain First Aid.
Enter your user name and password.
Select Verify and click Start. ...
If there are problems, select Repair, and then click Start.
Apple KB (Note article says 10.6 but it'll work on up to 10.10)
Run the Keychain First Aid and have it repair anything that could be causing an issue. Restart the computer and see if you get the same prompts. At that point, you may need to reset the Keychain (note: this will delete all saved passwords for applications, etc):
Open Keychain Access, which is in the Utilities folder within the Applications folder.
From the Keychain Access menu, choose Preferences.
Click General, then click Reset My Default Keychain.
Authenticate with your account login password.
Quit Keychain Access.
Restart your computer.
Source


What is a word or phrase meaning "ever so slightly" but with less emphasis on slightly?

Question: Imagine you have a serendipitous encounter with an old friend and they made your day "that much more" interesting. What is a good phrase meaning incrementally better but perhaps a little more sophisticated than that much more—something one would be more inclined to use as a compliment?
Comment: I think that "more much interesting* is a far better compliment than "a bit more interesting." Do you like your friends or not? However, "a bit more" may be what you are looking for.
Comment: The reason for nuance is that the encounter happened at an event and it would be arguably rude to suggest that the encounter was more interesting than the event, if that makes any sense. But, maybe I just lack a certain level of charm...
Comment: It would depend on the event, I suppose. A wedding? -- yes. A conference? -- no.
Comment: A wedding, indeed (;
Comment: You are excused. ;-)
Answer: Catching up with you was the icing on the cake.
From Cambridge:

the icing on the cake
something that makes a good situation even better:
I was just content to see my daughter in such a stable relationship but a grandchild, that really was the icing on the cake.
Answer: One phrase that comes to mind is "add color". If you add color to something you make it more interesting without diminishing the value of the original thing.


Recency weightage on stock forecast error

Question: Say I want to forecast retail stock for 1 month, on daily basis. The error will be calculated using SMAPE, but I would weight the error using recency, i.e., the nearer the weight from now the higher weight. Is there a good weightage scheme I could I adopt?
Answer: What is "good" will depend on what you want to do with your forecast. This has been called the "Cost of Forecast Error".
Another important aspect is whether it needs to be explainable to your (possibly non-technical) audience. (Or whether you want to impress them with your math-fu.)
Something like an exponentially decaying weighting scheme may make sense: weight next week's forecasts with $1$, the week's after with $0.9$, then $0.9^2=0.81$ and so forth.
Comment: Thanks, I hope to have daily weight differences (rather than weekly), and exponentially decaying weighting cannot sum to 1 for all weight (and it can be decaying too fast if I used it for daily)..do you have some other suggestions?
Comment: I am thinking of say 3 days horizon, day 1 with 3/(3+2+1),day 2 with 2/(3+2+1),day 13 with 1/(3+2+1)...how would you think of this?
Comment: That is a possibility. I wouldn't say that weights *need* to sum to one. Especially if you use sMAPE, which is hard enough to interpret. (For instance, if your actual is zero, the sAPE contribution is 200%, *regardless of the forecast*.)


Chebyshev's Theorem regarding real polynomials: Why do only the Chebyshev polynomials achieve equality in this inequality?

Question: In the book Proofs from The Book by Aigner and Ziegler there is a proof of 'Chebyshev's Theorem' which states that if $p(x)$ is a real polynomial of degree n with leading coefficient $1$ then
$$ \max_{-1 \leq x \leq 1} |p(x)| \geq \frac{1}{2^{n-1}}$$
In the proof $g( \theta ) = p( \cos \theta )$ is written as a cosine polynomial $ \sum_{k=0}^n \lambda_k \cos(k \theta)$ and it is then proved that this can't be less than $|\lambda_n|$ (which happens to be $\frac{1}{2^{n-1}}$) everywhere.
Afterwards it is claimed that 'The reader can easily complete the analysis' to show that the Chebyshev polynomials are the only ones for which equality occurs in the above inequality. I haven't been able to figure this out. Can someone explain why this is true? (preferably building on the proof as it was done in the book or by some other simple argument.)
edit: here by Chebyshev polynomial I actually mean the monic polynomial that you get after dividing the $n$-th Chebyshev polynomial by $2^{n-1}$.
Answer: Let $p(x)$ be a monic polynomial of degree $n$. Let $T_n(x)$ be the Chebyshev polynomial of degree $n$. Assume that $|p(x)|\leq 1/2^{n-1}$ for all $x\in[-1,1]$.
Set $q(x)=T_n(x)-p(x)$. Then since $T_n$ and $p$ are both monic polynomials of degree $n$, $q$ is a polynomial of degree at most $n-1$.
Now let $x_k=\cos(k\pi/n)$ for $k=0, 1, \ldots, n$. At these points $T_n(x_k)=(-1)^k/2^{n-1}$ by $T_n$'s definition. Now $$q(x_k)=T_n(x_k)-p(x_k)=(-1)^k/2^{n-1}-p(x_k)$$
But $|p(x_k)|\leq 1/2^{n-1}$ for each $k=0, 1,\ldots, n$. So that $q(x_k)\leq 0$ when $k$ is odd and $q(x_k)\geq 0$ when $k$ is even.
The Intermediate Value theorem implies that for each $k=0, 1,\ldots, n-1$ the polynomial $q(x)$ has at least one zero between $x_k$ and $x_{k+1}$. Thus $q(x)$ has at least $n$ zeros in the interval $[-1,1]$. But the degree of $q$ is less than $n$. Thus $q$ is equivalently $0$. Thus $T_n=p$.
Comment: This is quite similar to how the inequality was proved in the book, but I see a problem here.
 You proved that $q$ has at least one zero in each of the intervals $ \[ x_1 , x_0 \] , \[x_2, x_1 \] , \dots , \[ x_{n} , x_{n-1} \]$. But some of those zeros mights coincide, giving us a total of less than $n$ zeros. (e.g. if $x_1$ is a zero then it lies in both of the first two intervals.)
Comment: That's a pointed observation. I'm trying to account for it.
Answer: An alternative proof works by interpolation (it can also be formulated using divided differences) and the case of equality can be handled more easily.
Let $M=\max\limits_{[-1,1]}p$.
It is well-known that for every polynomial $f(x)$ with degree at most $n$,
and any $n+1$ distinct base points $a_0,a_1,\ldots,a_n$, the divided difference
$$
f[a_0,a_1,\dots,a_n] = \sum_{k=0}^n \frac{f(a_k)}{\displaystyle\prod_{j\ne k}(a_k-a_j)}
$$
is equal to the coefficient of $x^n$ in $f$. (Just read the coefficient of $x^n$ in Lagrange's interpolation formula.)
Define the base points $a_0,a_1,\dots,a_n$ by $a_k=\cos\frac{\pi k}{n}$.
As $p$ is monic, we have
$p[a_0,a_1,\dots,a_n]=1$ and similarly, since the leading coefficient in $T_n$ is $2^{n-1}$, we have
$T_n[a_0,a_1,\dots,a_n]=2^{n-1}$. By the definition of the base points, $T_n(a_k)=(-1)^k$. The product
$\displaystyle\prod_{j\ne k}(a_k-a_j)$ is positive if $k$ is even and negative if $k$ is odd. Hence,
$$
1 = p[a_0,a_1,\dots,a_n]
= \sum_{k=0}^n \frac{p(a_k)}{\displaystyle\prod_{j\ne k}(a_k-a_j)}
\le \sum_{k=0}^n \frac{\big|p(a_k)\big|}{\bigg|\displaystyle\prod_{j\ne k}(a_k-a_j)\bigg|}
\le \sum_{k=0}^n \frac{M}{\displaystyle\bigg|\prod_{j\ne k}(a_k-a_j)\bigg|}
\\
= M \sum_{k=0}^n \frac{(-1)^k}{\displaystyle\prod_{j\ne k}(a_k-a_j)}
= M \sum_{k=0}^n \frac{T_n(a_k)}{\displaystyle\prod_{j\ne k}(a_k-a_j)}
= M \cdot T_n[a_0,a_1,\dots,a_n]=M\cdot 2^{n-1}.
$$
This proves $M\ge2^{-(n-1)}$. To establish equality you require $p(a_k)=(-1)^kM$ for every $k$; that determines the polynomial $p$ uniquely.
Answer: Starting from the function
$$ p(\cos \theta) = g(\theta) = \sum_{k=0}^n \lambda_k \cos (k\theta), $$
like in the orginal approach, a discrete variant of Parseval's formula works, too.
Again, let $M=\max |g(\theta)|=\max\limits_{[-1,1]} |p(x)|$.
For every integer $m$, it is easy to verify that
$$
S_m := \frac1{2n} \sum_{j=0}^{2n-1} \cos\frac{jm\pi}{n} =
\begin{cases} 1 & 2n \,\, \text{divides}\,\, m \\ 0 & \text{otherwise.} \end{cases}
$$
Then
\begin{align*}
M^2 &\ge
\frac1{2n} \sum_{j=0}^{2n-1} \left| g\bigg(\frac{j\pi}{n}\bigg)\right|^2 \\
&=
\frac1{2n} \sum_{j=0}^{2n-1}
\left(\sum_{k=0}^n \lambda_k \cos \frac{jk\pi}{n} \right)
\left(\sum_{\ell=0}^n \overline{\lambda_\ell} \cos \frac{j\ell\pi}{n} \right) \\
&=
\sum_{k=0}^n \sum_{\ell=0}^n \lambda_k \overline{\lambda_\ell} \cdot
\frac1{2n} \sum_{j=0}^{2n-1} \cos \frac{jk\pi}{n}
\cos \frac{j\ell\pi}{n} \\
&=
\sum_{k=0}^n \sum_{\ell=0}^n \lambda_k \overline{\lambda_\ell} \cdot
\frac1{2n} \sum_{j=0}^{2n-1} \frac{\cos \frac{j(k+\ell)\pi}{n}
+\cos \frac{j(k-\ell)\pi}{n}}{2} \\
&=
\sum_{k=0}^n \sum_{\ell=0}^n \lambda_k \overline{\lambda_\ell}
\frac{S_{k+\ell}+S_{k-\ell}}2.
\end{align*}
Since $0\le k,\ell\le n$, $2n$ divides $k+\ell$ if and only if $k=\ell=0$ or
$k=\ell=n$, and $2n$ divides $k-\ell$ if and only if $k=\ell$. So,
$$
M^2 \ge \sum_{k=0}^n \sum_{\ell=0}^n \lambda_k \overline{\lambda_\ell}
\frac{S_{k+\ell}+S_{k-\ell}}2 =
 |\lambda_n|^2 + |\lambda_0|^2 +\sum_{k=1}^{n-1}\frac{|\lambda_k|^2}2.
$$
Comment: The first equation "$S_m = 1$ if ..." doesn't seem quite correct to me. Is it possible that it should be $2 \pi$ instead of $\pi$?
Comment: Yes, you are right. I will fix it.
Comment: Hope it is better now.. :-) We have to take the values of $g$ where the leading term $\cos (n\theta)$ is $\pm1$.
Comment: Alright. Thank you very much for both of your answers! Both proofs are very interesting for me.


If my phone is powered off will i still receive my bitcoin

Question: I sent someone Bitcoin but they said they didn't receive it because their phone is powered off but I got a complete transaction confirmation
Answer: The recipient doesn't need to have a wallet online to receive Bitcoins.
This is because the transfer of the money is recorded in the blockchain - which every full node (wallets etc) worldwide has a copy of.
Bitcoin wallets don't actually contain money. So they don't literally receive money. The only really important data in a wallet is the secret number known as a private key.
Answer: You should first check on the transaction (tx) id generated when you sent the funds and then check it on any btc explorer (https://btc.com/) to confirm that it was sent and how many confirmations.
You should use that as a proof that your funds were sent properly.


Remeshing deletes the insides of the mouth

Question: In order to create a mouth that opens and closes i created an inside of a mouth like most characters.
the problem is every time i remesh the model it gets removed and the mouth becomes stitched again.
i don't know how to solve this issue i need to remesh all the time in order to polish the face but with this issue i can't remesh after creating the insides of the mouth
help please.
Answer: There is no way to keep a closed mouth from resealing when remeshing, but you might be able to find an easier way to unseal it, perhaps with Boolean. But anyway, why are you remeshing the head over and over?


Which way does current flow if induced by a magnetic filed if two current are produced in opposite direction simultaneously?

Question: I am studying how electric charge can be made to flow due to a change in the magnetic flux through a conductor, I understand if the magnetic flux changes there is an induced EMF in such a way to oppose the motion that caused it (Lenz's Law) however this confuses me as if this now induces a current then surely the force that is now created by this current (EMF) now creates another current that opposes the original current. So my question basically is which induced emf is dominant in this system?
Comment: Typo: It's "Lenz's" law
Answer: I have a limited understanding of this myself but I think in a lot of cases the induced back EMF of the resulting current is assumed to be negligible compared to the original induced EMF.
If you really want to take into account the induced current opposing the original current then I believe you would have to account for the self-inductance of the conductor. The self-inductance tells you how the conductor opposes a change in the current flowing through it, which in this case is caused by a change in magnetic flux through the conductor, by the conductor itself creating a back EMF to oppose the change.
Here is an example to show how this could work:
Let the change in the magnetic flux caused by the initial magnetic field $B_1$ through a current loop's area in a small amount of time be $\frac{d\phi_1}{dt} = \epsilon_1$.
Let the loop have self-inductance $L$ and resistance $R$. The change in magnetic flux will cause a current that creates a magnetic field $B_2$ opposing the original magnetic field $B_1$. The current will have size $I_1 = \frac{\epsilon_1}{R} = \frac{1}{R} \frac{d\phi_1}{dt}$.
Now, this generated current $I_1$ produces its own magnetic field $B_2$ which generates its own change in magnetic flux through the current loop. This additional change in magnetic flux generates an opposing emf $\epsilon_2$ to the originally produced emf $\epsilon_1$ which in general is far smaller than $\epsilon_1$.
This opposing emf $\epsilon_2 = L \frac{dI_1}{dt} = \frac{L}{R} \frac{d^2\phi_1}{dt^2}$ so the opposing current is $I_2 = \frac{\epsilon_2}{R} = \frac{L}{R^2} \frac{d^2\phi_1}{dt^2}$
Thus, $I_{net} = I_1-I_2 = \frac{1}{R} \frac{d\phi_1}{dt} - \frac{L}{R^2} \frac{d^2\phi_1}{dt^2}$ (in the direction of the original current $I_1$).
However, I believe that if $\frac{d^2\phi_1}{dt^2}$ is sufficiently large the value of this could be negative and produce current in the opposite direction of the originally produced current $I_1$.
I'm not sure if the math or assumptions of this derivation are correct but I think the general idea behind it is sound. If there are any issues please let me know in the comments below.
Answer: simply put, the first EMF is the dominant one as it is the result of the greater change in flux (or the greater force applied on the charges).
As for the math, the previous answer seems to have the hang of it and avoid repeating their work. Cheers


Why is my water pump humming and starting slowly?

Question: I was going to include more information and a video clip but I'm away from home and my water now does not work so I'm posting sooner rather than later. I have a bilevel house with a water pump in a crawlspace. I don't have the model number or other information on hand right now, but it's a few decades old. Recently, the pump is taking extra time to run, similar to a car engine trying to turn over. I hear a low hum as usual before it kicks on, but the hum is now lasting for 5-10 seconds. When I flush the toilet, I can't run water afterwards for a minute because if I do, the toilet stops flushing and no water can come out. In the shower, the water stops running or only dribbles, every 10 minutes or so, which is less time it takes to empty the water tank. I have well water and a septic, if that helps at all, and this problem is fairly recent, it's only been occurring for a week or so. Is my pump bad or could it be something else?
Comment: I would check 2 things will the pump motor spin easily? If it is stiff the bearings may need greased or replaced. If the pump motor spins freely I would check for a bad capacitor or a centrifical start winding the contact may be bad or gunk on the springs may keep it from switching to high speed until it gets hot. These items are somewhat common to old motors. I would also agree that your pressure tank could need an air charge because it should have enough volume to allow the toilet to fill without the pump turning on.
Answer: Sounds like the "pump is bad", which may be caused by any number of conditions that need to be examined prior to burning out the next one.
For example, we bought a place in which the 230VAC had been fed to the pumphouse using 12AWG Romex strung 150 ft through the bushes. This probably resulted in excessive voltage drop before the power got down the hole to the pump, causing premature failure in a 1.5 hp pump more than 200 ft down.
There could be other problems with algae, sediment, clogged pipe, low water, inadequate pressure tank for your home, etc.  A deep well pump over 15 years old, or so, may be due for replacement anyway.
Answer: It sounds that you have more than one problem.  Your pump sounds to me to be suspect. Also, I think you need to have the pressure tank checked closely.


How to gain definition on my biceps?

Question: I am a 17 year old guy, 190 lb, 5'11", work out six days a week after school targeting various muscle groups each day (legs, arms, chest, etc.). I have been working primarily on gaining strength, not mass, and have been achieving that. I feel that my arms in general are lacking. I have no definition to my biceps at all. Any ideas on how to achieve this effectively?
Comment: Can you give details on what you currently do each day? Also, what's your nutrition look like?
Comment: Rope-Climbing. Best Bicep exercise ever. And eat something after training.
Comment: What exercises do you perform to target your arms?
Comment: @JohnKugelman Usually on arms day i do barbell curls (10 at 90, 10 at 50, another 10 or til fail @ 90) bicep curls, lat pulldown, pull-ups, and bench about 100-120
Answer: Definition comes from lowering your Body fat.  Chalking up my hands and doing heavy Deadlifting has given me more strength in my forearms than any isolated movement.
Answer: I would recommend you perform exercises that isolate the biceps. For example, one arm dumbbell curls. There are many other exercises you can perform, but, the point is to try and isolate the muscle.  Try to do 10 to 12 reps.
Answer: Well basically to build muscle you need to be lifting HEAVY, if you can do more than 10 reps, go up weight. to really tear the muscle and make it grow, train biceps twixce a week. do isolation exefcises such as bicep curls, do 5 sets of 10 reps, then continue with other exercises.
the main reason people who lift don't gain muscle is because they don't eat enough protein... not enough protein.. impossible for new musxcle to grow? as you are 190lbs you need to be eating 190 g of protein MINIMUM... tuna Is 17g, a cup of milk is 8.5g.... as you can see it is hard to meet the requiements, try a protein shake to assist this. and make sure you have it directly after you train. go up weighr every 3 weeks and always change routines
Answer: If you want definition in your biceps, you need to train them like a body builder would: lots of isolation work, moderate to high rep range, and lots of volume.
Personally I can't stand training that way and although I don't have studies in front of me to prove it, anecdotal I know it causes a lot of injuries. Isolation work is a terrific way to develop tendinitis and overuse injuries and imbalances.
As you said you are strength training, so I would pick from strength training exercises. Specifically:

Palms-toward-you weighted pullups. If you can do 5x5 with a 45lb hanging off of you, you will have developed biceps.
Deadlifts and cleans. These train the bicep primarily via isometrics but as a staple for strength training they are hard to beat.

Your biceps, measured by force or size, are tiny compared to the "big movers", and as such should lag behind them. Further, you want to develop them as part of your overall body. Check this study on what was found out about baseball players who have biceps that are more than 76% the strength of their triceps:

These findings suggest that the ratio of biceps concentric to triceps
  concentric functional strength strongly predicts elbow-injury status
  in baseball players. Assessment of this ratio may prove useful in a
  practical setting for training purposes and both injury diagnosis and
  rehabilitation.

Stick with whole body compound work. To be honest at 17 you shouldn't have big biceps. What you should be doing is laying the foundation of fitness that will have you with shocking athleticism in the next 5-10 years.

How to gain definition on my biceps?


How to create pesistence storage for ubuntu live boot?

Question: I'm trying to boot Ubuntu 20.04 directly from  ISO file (that is stored in my HDD) using Grub-customizer but i want to preserve my changes in  persistence storage. Is there any way create persistence storage?
Comment: Welcome to Ask Ubuntu: You can create a file or partition labeled "writable", (in previous versions it was labeled casper-rw). This file can be maximum 4GB and you can also have a 4GB persistent home-rw file. Files should be on the root partition. Alternatively you can create a ext4 persistent partition labeled "writable", (and "home-rw" partition if you wish). You need to add a space and the word "persistent" after "--" in /boot/grub/grub.cfg.
Comment: @user.dz should note that casper-rw is not working when adding persistence booting 20.04 ISO files. It has been changed to "writable" https://askubuntu.com/questions/1236445/casper-rw-persistence-files-not-working-with-20-04
Comment: No: The .iso file is read-only.
Comment: And for more details, check Ubuntu Wiki at https://wiki.ubuntu.com/LiveUsbPendrivePersistent . @C.S.Cameron :)
Comment: @hack tech I should also note that there are problems booting 20.04 ISO files using GRUB 2.04, you can either use GRUB 2.02 or a workaround is to run `rmmod tpm` before `loopback loop some.iso` in grub.cfg
Answer: Booting ISO Files on HDD
Basic GRUB loopback menuentry for Booting ISOs is:
menuentry "isoname ISO" {
    set root=(hdX,Y)
    set isofile="/[path]/[name].iso"
    loopback loop $isofile
    linux (loop)/casper/vmlinuz boot=casper iso-scan/filename=$isofile --
    initrd (loop)/casper/initrd
}

Where hdX is the disk and Y is the partition number of the ISO location.
[path] is the path to the ISO file, [name] is the name of the ISO file
Multiple ISO files are allowed, with one or more menuentrys per ISO file. (each ISO can have multiple persistent files).
If we want a persistent OS add the word "Persistent" to the GRUB menuentry.
If using a persistent partition make it ext4 and label it casper-rw for 19.10 and previous ISO files.
For 20.04 ISO files label the persistent partition "writable".
Only one persistent partition is allowed per drive,
If using persistent files, each ISO can have it's own persistence file(s).
Each ISO can have a "writable" ("casper-rw') file up to 4GB and an optional "home-rw" file up to 4GB.
Persistent files must be located on a FAT32 partition.
If more than one persistence file is used, a persistence-path must be given. Just the unique name of the persistent files folder is required. One set of files per folder.
Ubuntu versions 18.04 and previous use GRUB 2.02 for booting versions 19.10 and later use GRUB 2.04 for booting in UEFI mode. GRUB 2.04 has problems booting ISO files.
Workaround for booting ISO files in GRUB  2.04 UEFI mode is to add "rmmod tpm" to the menuentry, if booting in UEFI mode. This may give an error message in BIOS mode, ignore it.
If the host system is pre-19.04 GRUB 2.02 should be in use and workaround is not needed.
Ubuntu 20.04 comes with a File System Check every boot, it can be disabled by adding "fsck.mode=skip" to the menuentry.
Scrolling during boot can be disabled by adding "quiet splash".

Final menuentry may look like:
menuentry "Ubuntu 20.04 ISO" {
    set root=(hd0,3)
    set isofile="/isos/ubuntu-20.04-desktop-amd64.iso"
    rmmod tpm
    loopback loop $isofile
    linux (loop)/casper/vmlinuz boot=casper iso-scan/filename=$isofile fsck.mode=skip persistent persistent-path=/persist-1/ quiet splash --
    initrd (loop)/casper/initrd
}


Create M3U playlists for iBasso DX50 on Linux

Question: I'm using an iBasso DX50 as my music player and I use Linux as my primary OS. I need to create M3U playlists to be imported into my iBasso DX50. I would try and edit some of the files myself but I don't know what the root to SD-Card path looks like from inside my iBasso. Any ideas?
Comment: Removed software rec portion of question which is off-topic here.
Answer: Example for create M3U playlist:
All files type *.mp3, *.wav and *.wma
<code>$ find . \( -name \*.mp3 -o -name \*.wav -o -name \*.wma \) \ > playlist.m3u
</code>
All files type *.WAV, *.Mp3, etc (not case sensitive)
<code>$ find . -iregex '.*\.\(mp3\|wav\|wma\)' > playlist.m3u
</code>
Without recursive search in directory
<code>printf %s\\n *.mp3 > playlist.m3u
</code>
And, finally:

How to use the import/export playlist function? After the playlist is built in the DX50, press the thumbnail icon in front of the
  playlist to unfold the options. Press "export playlist", then one can
  find a M3U playlist under the M3U folder under the internal flash.
To import a M3U playlist, load the M3U playlist into the internal flash or a Micro SD card. Then find the M3U playlist under Directory.
  Press the M3U playlist to start importing the playlist.

From DX50 user guide: http://www.ibasso.com/uploadfiles/20141203/201412031740555098.pdf


How can I remove Google Chrome as default browser and switch back to Safari?

Question: Somehow my computer got a virus on it. It seems Google installed something called Chrome.app on my computer. Instead of Safari opening links, Chrome now does it. How can I remove this virus and restore order?
Comment: Google Chrome is a very legitimate web browser made by Google. It is, in fact, the most-used browser in the world, and many, many smart people use it. It's not a virus (in fact you probably should be using it) and it's definitely not "hijacking your searches". You can certainly change your default browser back to Safari as RedEagle mentioned, and even delete Chrome if you don't want to have it. Rest assured, your computer was not "infected" by Google. If you don't believe us, you can download a trustworthy antivirus app like Avast or BitDefender and run a scan.
Comment: Might want to research about Google Chrome a bit more. Take a look at [the Wikipedia article](https://en.wikipedia.org/wiki/Google_Chrome).
Answer: Open Safari, then click "Safari" in the bar up top, then in the dropdown menu, click "Preferences". There, you should find where you can change your default browser back to Safari.
To get rid of Chrome afterwards, open your Applications folder in Finder and move the Chrome app into the trash.
Comment: Please don't use comments for follow-up questions, post a new question instead (and add a link to the question above if context is required).
Comment: @chromaticsyllabus What do you mean?
Comment: How do I stop it from hijacking my searches though?
Comment: Don't forget to empty your trash afterwards so Chrome doesn't hang around in your trash can.


Stakeholder vs. Investor

Question: What is the difference between stakeholder and investor? According to the Oxford advanced dictionary, both of them invest money on something, but is there any difference?
Answer: I usually find the subtle difference between the terms stakeholder and investor in the context of software development or project management.
In general, stakeholders are people (or entities, organizations) that can gain something or lose something by involving in a project. The important point that makes stakeholders different from investors is the benefits for stakeholders doesn't have to always be financial gain. It might be a better system. It might be their creditability. Though money usually gets involved.
On the contrary, the term investor is rather specific in this context. Investors invested in the project with their money (usually called funding or capital), and they specifically expect to gain financial returns.
In short, when both terms are used in the same context to emphasize the difference, an investor can be considered a stakeholder, but not all stakeholders can be considered an investor.
Comment: Of course, ***invest*** doesn't necessarily refer to money – one can *invest* time and/or energy into a project – but a person who does that generally wouldn't be called an ***investor***.
Comment: I am studying CS, and I was having trouble with understanding the role of stakeholders in Software Development. It helped. Thanks!
Answer:
stakeholder :A person or organisation with a legitimate interest in a given situation, action or enterprise.

Whereas an investor contributes money to a project in anticipation of making a profit, a stakeholder need only have a legitimate interest in it.
For example, as a homeowner I have an interest in whether an airport in built next to my land since the noise from the airport will be a negative externality and could reduce the value of my home.  So while I have not invested in the airport construction project I am a stakeholder in the decision to approve it.
In the typical business usage of stakeholder, stakeholders are given a say or a vote in a decision while those who may be affected but are not given a vote are merely affected parties.
It's also interesting to note that the original meaning of the word was a neutral, mutually trusted party who held the stakes for a wager (in essence an escrow account manager) but that the meaning has changed in recent years.  Again from Wiktionary:

The last definition essentially contradicts the historic definitions and hence the word has become a contronym. The last definition refers to one who has an interest in an issue, whereas the initial definitions refer to one who does not have an interest in the property held. The last definition has gained significant use since the 1990s, especially when discussing corporate governance.
Comment: "So while I have not invested in the airport construction project I am a stakeholder in the decision to approve it." This example makes very clear the difference. Thanks a lot.

Stakeholder vs. Investor


If PF is withdrawn by an NRI staying in USA does it become taxable as per US laws?

Question: I have been service in an Indian company for 10 years and now getting transferred to US. I want to keep the PF and not withdraw as I don't need money and it will earn good 8.5% interest for next 3 years. I heard that if I withdraw this money later when I start filling taxes in US all the interest earned on PF (even the interest in previous years and not just these 3 years) will need to be declared as income and would come under tax. Is this true?
My assumption was that only interest earned after I convert to NRI status is the one which becomes taxable. Please clarify.
Comment: I guess you'd be better off talking to a professional, but in general, it is best to explain the terms you're asking about or at least refer to the legal system you're asking about. I added the tags for you, since it is clear that you're asking about some Indian retirement system.
Answer: According to indian laws :

Any interest income accrued on EPF post retirement/resignation is
  taxable in your hands

So if India is taxing it, there should be a dtaa with US, which can help you out.
Reference:


What are the potential rift bosses?

Question: Last night, while doing some Nephalem rifts, I encountered both "The Butcher" and "Zoltun Kuule" as rift bosses, only they were renamed slightly (The butcher had a different name, and a subtitle of "Meat Chopper"). Both retained several of their boss abilities from their original Acts, but this was the first time I'd encountered former bosses in a rift. Others seemed to be randomly generated champions. Does anyone know, or have enough experience to say, where the rift bosses are picked from?
Comment: I think he means what pool of characters. So far, EVERY rift guardian I have fought was a boss. I have gotten Rakanoth several times.
Comment: what do you mean by "where the rift bosses are picked from"?
Answer: Here is a non complete list of rift bosses :

Agnidox (N/A)
Bone Warlock (N/A)
The Binder (N/A)
Blighter (Herald of Pestilence)
Bloodmaw (N/A)
The Choker (N/A)
Cold Snap (Izual)
Crusader King (Skeleton King)
Ember (Nekarat the Keywarden)
Erethon (Death Maiden)
Eskandiel (Malthael)
Flesh Carver (The Butcher)
Gluttony (Ghom)
Infernal Maiden (N/A)
Lord of Bells (Cow King [Easter Egg])
Mistress of Pain (Cydaea)
Perdition (Rakanoth)
Perendi (Mallet Lord)
Raiziel (N/A)
Reformed Warden (Warden)
Rime (Xahrith the Keywarden)
Rokrak (Fallen Champion)
Stone Singer (Sand Golem)
Sand Shaper (Zoltun Kulle)
Satrix (Writhing Deceiver)
Spider Queen (Queen Araneae)
Tethrys (Succubus)
Voracity (N/A)

I'll complete and cross check it later with data from achievements.
Comment: Raiziel is one also
Comment: There's one called Choker that I hate because of her insane poison damage... she's the only one I ever remember though.

What are the potential rift bosses?


inside brick chimney

Question: I have a house, weatherboard, which has a chimney that, i think, used to service two adjacent rooms.The fireplaces have been closed in and the interior wall removed leaving a triangular shaped wall around the chimney. An old wood heater has been fitted into the triangular shape on one side.I'm told this is very unsafe.Has anyone heard of this before and any suggestions re making it safe for a wood burner?
Thanks in anticipation
Karyn.
Answer: Unfortunately, some questions are not for the innerwebs.  This is one of them.
Find your local LICENSED chimney sweeper. He needs to check your chimney, make sure that not only is the chimney ready for fire, but that all additional openings that may be hidden are properly sealed off.

inside brick chimney


Electronics used for cooking

Question: I have a project where I want to be able to cook food (very similar to a crock pot).  What would anybody here recommend to use to convert AC to useable DC and what should I use to heat the food?  Should I use cartridge heaters?  How many watts would be OK?  Also, I would need to turn on/off the heating element so what should I watch out for?
Comment: If you are asking this question, I question if you have the knowledge necessary to safely to complete this project.
Answer: nearly all simple cookers use AC power to directly run a heating element. The elements are usually just wire coils, or sometimes flat resistance wire types. since the quantity of food being heated varies it is nearly always necessary to incorporate a thermostatic controller in order to vary the power.  On toasters this is accomplished with a simple variable timer to allow you to adjust how long the bread is exposed to the heat.  On crock pots and the like there is a variable thermostat which keeps the contents being cooked at a steady temperature. If you do use a heating element with exposed wire remember to keep it well insulated.  The coils are live power and can be lethal if you come in contact with them.  Also remember to use a thermostat which can handle the load presented to it by the heating element. If you can't easily find a thermostat for the current needed, then use a relay to handle the power.  The amount of power needed will be influenced by several factors. The quantity of food to be cooked, the size of the oven, the final desired temperature, how fast it needs to cook, and other factors.  If you look at similar sized units you can find out a good approximation of what you need by taking notes of their power needs.
Comment: Do you have any recommendations for good solid state relays to handle A/C and capable of many many cycles?  Also, what good heating element should I use?  Thoughts?
Answer: Consider buying a crock pot of suitable size (should only be US$15-$30, less than if you try to construct one from your own parts) and modify it as necessary to automatically turn on/off the AC power to meet your cooking needs.
Answer: Another good choice is an old 2 gallon type coffee pot.  it's temperature setting works off of a thermo-switch at about 180 degrees F.  They can be had for pennies at your local thrift store.  I have used them from such sources my entire life and they seem to last decades in hard use. If you do build your own, consider using a solid-state type relay from your local electronics supplier.  if you get one which is slightly overkill it should last forever and it can be switched on and off using low voltage sources.

Electronics used for cooking


Prove any unit $u$ in $\mathbb{Z}[\zeta_{p}]$ is a product of a root of unity and real unit.

Question: Given $\zeta_{p}$ is a $p^{th}$ root of unity for some odd prime $p$ I was able to show for any unit $u$ that $\frac{u}{\overline{u}}=\pm \zeta_{p}^{k} $. Thus we have $u=\pm \zeta_{p}^{k} \overline{u}$.  The problem is that I can't seem to prove $\overline{u}$ is a real unit (which I suppose would mean $u$ is a unit in $\mathbb{R} \cap \mathbb{Z}[\zeta_{p}]$).  I tried by contradiction using the fact $\omega^{k}+\overline{\omega^{k}}$ is a real number and thought when substituted with $\frac{u}{\overline{u}}$ and $\frac{\overline{u}}{u}$ respectfully I'd see their sum equal a complex number.  If anything it showed $u$ should be a complex number.  Any insight or hints would be greatly appreciated!
Comment: If $\overline{u}$ is real then so is $u$. What you need to show is that if you {\em change} $u$ by a suitable root of unity then the new unit is real.
Comment: See [here](https://math.stackexchange.com/a/992559/11619). Unfortunately I'm not 100% that Bruno's otherwise great argument is watertight towards the end. See S.Gau's comment.
Answer: In your formula for $u/\bar u$, you must show that only the sign + can occur. At least two kinds of proofs can be found in textbooks, but they both use a zest of arithmetic in a hidden way:
1) Directly for $\mathbf Q(\zeta_p)$, on using divisibility by $(1-\zeta_p)$ in the ring $\mathbf Z[\zeta_p]$. See Washington, prop. 1.5, or Marcus, ex. 12 of chapter 2.
2) Via the algebraic theory of CM-fields which provides, with obvious notations, the formula $Q_K:= [E:WE^+]= 1$ or $2$ for any CM-field $K$ (Wash., thm. 4.12). But for $K=\mathbf Q(\zeta_n)$, the choice between the values 1 and 2 needs arithmetic arguments: the same proof as in 1) gives $Q=1$when $n$ is a prime power; when $n$ is not a prime power, an additional argument modulo some power of $2$ gives $Q=2$.


What happens if I mark a question as 'no action needed' and it is found to be a duplicate later?

Question: As the question says, what if it turns out to be a duplicate later? Will it impact negatively in any way towards my account or so?
Comment: @ivarni no I haven't failed any audit. Was just confirming if I  must check for duplicates
Answer: Finding duplicates often requires some experience in the technology concerned. Reviewers are not expected to have that, so no you don't need to find whether the question is a duplicate.
If the question is clear, well written, on-topic then it's OK. If not then "no action needed" is the wrong choice.
The object of a review is to ensure that a question is one we're able to answer. If the mechanism that we later provide that answer is duplication then the question asker got their answer so everyone's happy.
Comment: *Reviewers are not expected to have that* I have heard the opposite from some people (maybe Cody?) in chat a few months ago. Whoever it was said that when an action to take isn't obvious, reviewers should skip posts they don't have enough expertise in to judge quite confidently. (Not that I think so too, that's just what someone said)
Comment: If I said that, I wasn't really speaking with duplicate-finding in mind. More of, if you don't know a technology well enough to know whether the question contains a minimal, reproducible example, then that's a good time to Skip. If a Python programmer indicated that a Python question is problematic, thus putting it into a review queue, a non-Python programmer should not overrule their assessment lightly, as there may well be some problem that they missed due to lack of experience with the language. @CertainPerformance
Comment: NO the questions are perfect, have all necessary details and formatting. I just wanted to know if I am supposed to check for duplicate during reviewing
Comment: You did that's why accepted it. Maybe the question at the end confused you. Sorry for that...
Comment: Nothing I've said contradicts the rule that if you're not confident then skip is the right answer. Duplicates are not always obvious, terminology may be different, examples vary etc.


Chinese to Chữ Nôm converter online

Question: Why it is very hard to find the Chữ Nôm for the very common Hanzi 有 ?
Maybe this Hanzi was not so used in the past ?
This looks very strange, and any light on it is welcome !
Comment: **đánh** is the [Quốc ngữ](https://en.wikipedia.org/wiki/Vietnamese_alphabet) of 「打」 (not Chữ Nôm). On that page, **Nguyên tiêu** is the Quốc ngữ transliteration of the poem 「元宵」 (which is written in Classical Chinese), and the section under **Dịch nghĩa** (譯義, which means *translation*) is the Vietnamese translation of 「元宵」. There is no Chữ Nôm on that page.
Comment: Your question doesn't make sense - it's like asking to convert the English letter A into the Swedish alphabet. 「有」 already exists in Vietnamese Hán-Nôm, what exactly are you looking for by "converting it to Chữ Nôm"?
Comment: You should try a Vietnamese site for luck.
Comment: When i was looking for Chữ Nôm of 有  and  打 (the name of my company : 打有 ) i succeeded to find Chữ Nôm of 打 :  đánh.  But strangely i was unable to find the Chữ Nôm for 有. The very interesting website https://chunom.org doesn't give any Chữ Nôm for this very common hanzi. More : on the other very interesting website http://www.nomfoundation.org/nom-project/tale-of-kieu/Glossary-of-characters-in-a-version-of-Kieu gives a very small frequency for  有 (hữu) in the well known "tale-of-kieu" and i still wonder why frequency is so different from the use in Chinese (有 is ninth in frequency).
Comment: @dROOOze  I am sorry, maybe something went wrong : i think we do not speak about the same thing. The content of this page :  www.thivien.net/Hồ-Chí-Minh/Nguyên-tiêu/poem-9nGoTWzYHnMiK0mDAEFGOA  may have misled me : Chữ Nôm is the first part (hanzis) or the second part which is not Vietnamese  ? I take the first part for usual hanzis, since they seem to not be written in an other way !  i'm puzzled :-)
Answer: 有 hữu isn't used in Vietnamese, which is why you don't see it on Chữ Nôm websites. It is only used in Literary Chinese texts (漢文; Hán văn; 文言文). "打有" can be transliterated into Vietnamese as "Đả Hữu". Đánh is the Nôm reading (喃) of 打, while đả is the Sino-Vietnamese reading (漢). It would still be written as 打有.

Chinese to Chữ Nôm converter online


Adding and subtracting values that don't exist

Question:
Above is a part of calculation involving the binomial coefficient. I understand the steps. What we have done is that we added and subtracted the same terms (those drawn in a red box) so that nothing changed by this step. But these terms don't exist in the definition of a binomial coefficient.. So is it logical to add or subtract a value that doesn't exist?!  I hope that I were clear in presenting what was unclear to me.
Comment: These coefficients are defined as zeroes.
Comment: Well, you can't just throw them away.  You must either define or demonstrate that they are equal to 0.  If you want to take it literally: There are 0 ways to choose a negative number from a positive number, and there are 0 ways to choose more numbers than are offered.  That sounds like a joke but .... dang if it isn't true.  Or, for convenience we can simply define them as 0 as Yves suggest.  Or we can define them recursively as celtschk suggests at the end of his answer.
Answer: I guess you are used to the definition of the binomial coefficients as
$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$
However if you cancel out the $(n-k)!$, you get
$$\binom{n}{k} = \frac{n(n-1)(n-2)\cdots(n-k+1)}{k!}$$
And if you write it in this way, you see that there is no problem with having arbitrary values for $n$. For example, you have
$$\binom{\pi}{3} = \frac{\pi(\pi-1)(\pi-2)}{6}$$
Or in your case,
$$\binom{n-1}{n} = \frac{(n-1)(n-2)\cdots ((n-1)-n+1)}{n!}$$
Now notice that the last factor in the numerator is  actually zero; therefore the whole binomial coefficient vanishes.
Another way to get to the same result is to notice that there is a recursion formula,
$$\binom{n}{k+1} = \frac{n-k}{k+1}\binom{n}{k}$$
which is easily checked by inserting the original definition. By assuming this recursion formula to hold further, we then get immediately
$$\binom{n-1}{n} = \binom{n-1}{(n-1)+1} = \frac{(n-1)-(n-1)}{(n-1)+1}\binom{n-1}{n-1} = 0$$
OK, that takes care of the first term, but what about the second? Even with this definition, you'd still get $(-1)!$ in the denominator. There are again at least two ways to tackle this.
The first one is to observe that $\binom{n}{k} = \binom{n}{n-k}$ and just assume that this also holds also outside the original range. Then you get
$$\binom{n-1}{-1} = \binom{n-1}{(n-1)-(-1)} = 0$$
A second way is to solve the recursion formula from above for $\binom{n}{k}$:
$$\binom{n}{k} = \frac{k+1}{n-k}\binom{n}{k+1}$$
Then we get immediately
$$\binom{n-1}{-1} = \frac{-1+1}{n-1-(-1)}\binom{n-1}{-1+1} = 0$$
In any case, you get that those extra terms added are well defined and have the value $0$.


Getting root access on meizu x8 (Andriod 8.1.0)

Question: I tried various methods that I can found on the web to get root access, but none of them worked. I do not trust the vendor-provided method of getting root access. Does anyone know a way to get root access on meizu x8?
Comment: What all did you try? your question is not clear. Do you know how to manually root? if no have you tried one-tap root apps?
Comment: try to root manually then
Comment: This seems to be the firmware for your device. [meizu X8 Flyme](http://www.flymeos.com/firmwarelist?modelId=125&type=1)
Comment: Can you get the boot.img from the firmware? If yes I will answer an official answer on how to root.
Answer: Disclaimer: I take no responsibility on the steps below. Root at your own risk.
As per Aayush's comment, I would advice you to read up more on rooting. Make sure you understand the ins and outs and the consequences of rooting, nd the possibility of bricking your device, before you attempt to root.

Install Magisk Manager on your device.
Copy the boot.img to your device.
Run Magisk Manager.

On the right near Magisk click on Install.
Untick Recovery Mode.
Click on NEXT.
Tick the "Select and Patch a File"
Now select the boot.img file you copied to your device. This will patch the file and save it to you Download folder.
Copy the patched file to your PC.

Enable USB debugging and OEM Unlocking in your developer settings.
Unlock the bootloader (usually this can be done in fastboot by running fastboot flashing unlock. If this doesn't work google "unlock bootloader" with your device name). This will factory reset your device, you will loose all data.
Flash the patched boot image file in fastboot fastboot flash boot <path-to-the-patched=image-file>.
Reboot your device fastboot reboot.
After setting up your device again, install again Magisk Manager on your device. And follow the directions. It will install the Magisk (Note: it will install Magisk not Magisk Manager which you just installed yourself) to your device and you should have root).

GOOD LUCK
Comment: Sruly, your effort is great!(+1) but i'd recommend Joy Jin not to root his device since he doesn't has proper knowledge and there's a high possibility of him bricking his phone.


What happens if I plug a USB-C device into a computer with only a USB-A port?

Question: If I use a USB-C -> USB-A adapter, can I expect the device to work as normal, just with type-A speeds? Or is there more to the USB-C standard that could cause the device to not work properly?
Answer: An adapter should handle any differences or adjustments between the connector types, provided it is an adapter appropriate for the job.
In other words, if the adapter says it'll work for you needs (power/charging vs connecting the device to a computer) I'd trust it's claim and report issues as warranty problems.
Answer: Depends a lot on the cable, just like there are some cables that are USB 2.0 but have just 2 internal wires instead of 4 so it works just for power, but not for data (so called "charging cables", usually chinese knockoffs)
From https://en.wikipedia.org/wiki/USB_Type-C:

The capabilities of USB Type-C cables depends on (1) USB modes supported, (2) Amount of power supported for charging and (3) Alternate modes supported by the cable. There are cables which support only USB 2.0 with up to 480 Mbps data rate. The cables which support USB 3.0/USB 3.1 Gen 1 can handle up to 5 Gbps data rate at full duplex and are marked as super-speed cable. The cables which support USB 3.1 Gen 2 handle up to 10 Gbps data rate at full duplex and are marked as super-speed+. The charging capacity of USB Type-C cables may go up to 5A (100W), but 3A (i.e. up to 60W) cables are commonly available. Support for alternate modes requires extra connections for optional pins as well - like additional super-speed lanes, and 'side-band use' pins. The support for alternate modes usually adds an extra bandwidth requirement to the cable - in addition to the bandwidth already needed for USB data transfer. There are USB-IF certification programs available for cables.

USB Type-C is a 24-pin plug so there's a lot more potential for making cheap knockoffs just for charging, or slower bandwidth. For USB-A I'd say you should be good to go, but doesn't hurt to buy quality cables. USB Type-C specification defines two differential pairs for USB 2.0 data bus, so it should be compatible (if the wires actually do exist in the cable, that is). That said, I rather doubt they would make a charging-only adapter, so yeah.
Answer:
If I use a USB-C -> USB-A adapter, can I expect the device to work as
  normal,

Yes, but... there are "legacy cables", and "legacy adapter cables". They all are cables.

just with type-A speeds?

-no, since there is no "just Type-A speed", the Type-A USB3.1 connector is perfectly capable of SuperSpeed+ (Gen2) 10Gbps speeds, at least those who are certified as such.
So yes, if you use an appropriate "Legacy Adapter Cable", your device is expected to work as normal. The Type-C standard specifies several variants of Type-C (plug) to Type-A (plug) cables, one group for USB 2.0 only speeds, and the other group for  USB 3.1 speeds. The USB 3.1 cable assembly must have all good-quality wires to support the Gen2 10Gbps speed. Therefore your device will not suffer at all.
The legacy Type-C-to-Type-A cables have reduced number of data wires, only USB 2.0 D+ and D- wires. The cable can be identified by white plasic (not blue) inside the Type-A plug. This cable will work for your device too, but at the USB 2.0 rate.
The Type-C plug of a legacy cable must have its CC pin pulled up to VBUS with 56k resistor. This value indicates to your device that this is a standard  USB port, so the device will not to try charging itself with excessive current that the standard port cannot handle. Cables with 22k and 10k pullups are illegal and might cause damage to USB host computer, there were few scandals regarding "dangerous Type-C cables"
The "plug-plug" cables should be distinguished from "Type-C plug -> legacy receptacle, aka adapter assemblies". The standard defines only two types of legacy adapters, micro-B USB2.0 receptacle to Type-C plug, and full-featured USB 3.1 Type-A receptacle to Type-C plug. In this case the C-plug must have 5.1k pull-down on CC pin, indicating that the Type-C port should reverse its role to HOST mode. Therefore, if your device is capable of Dual-Role-Data mode (formerly OTG), it should provide VBUS, and you should be able to connect a mouse or keyboard or a self-powered hub.
In total, the Type-C connector specifications v1.2 defines 15 (fifteen!) types of cables (there used to be 17). Welcome to the future, of USB cable confusions.


How to prove the following relation for rank of matrices?

Question: If $\mathbb{A}$ and $\mathbb{B}$ have same rows then how to show that the following relation holds $$\operatorname{rank}([\mathbb{A~B}])=\operatorname{rank}(\mathbb{A})+\dim(\text{Proj}_{\mathcal{A^C}}\mathcal{B})$$ where $\text{Proj}_{\mathcal{A^C}}\mathcal{B}$ is the projection of span of $\mathbb{B}$, denoted by $\mathcal{B}$, on the orthogonal complement of the span of $\mathbb{A}$, denoted by $\mathcal{A^c}$. $\dim$ denotes the number of dimension.
Comment: Deos $[\mathbb A \mathbb B]$ mean the matrix which contains column of $\mathbb A$ and then columns of $\mathbb B$? (Or is it product of the two matrices,) When you say "span of a matrix" do you mean the spaces generated by columns? (Or the space generated by rows?)
Comment: Did you mean to say that the two matrices have "the same *number* of rows" rather than just "the same rows"? (If you say that they have the same rows, it seems that $\mathbb A=\mathbb B$, or maybe they are not exactly the same but the order of rows might be changed.)
Answer: If I understood your question correctly you have the space $\mathcal A=[\vec a_1,\dots,\vec a_k]$ generated by the columns of $\mathbb A$ and $\mathcal B=[\vec b_1,\dots,\vec b_l]$ generated by the columns of $\mathbb B$. And you are asking about the dimension of
$$\mathcal A+\mathcal B=[\vec a_1,\dots,\vec a_k,b_1,\dots,\vec b_l].$$
You can write each vector $\vec b_i$ as
$$\vec b_i=\underset{\in\mathcal A}{\underbrace{\vec b'_i}}+\underset{\in\operatorname{Proj}_{\mathcal A^c}\mathcal B}{\underbrace{\vec b''_i}}.$$
From this you get
$$\mathcal A+\mathcal B=[\vec a_1,\dots,\vec a_k,b''_1,\dots,\vec b''_l]=\mathcal A \oplus \operatorname{Proj}_{\mathcal A^c}\mathcal B$$
and this implies the claim about dimensions.


How to construct a perfect BST from an unbalanced BST with n elements (assuming that n=(2^i)-1, i is natural)

Question: How do I construct a perfect BST from an unbalanced BST with $n$ elements (assuming that $n=2^i-1$, $i$ is natural). ** At the worst case of $O(n)$**.
Answer: A simple way is as follows: do a symmetric visit of the BST (in time $O(n)$) and write down the elements in increasing order to an array $A$. Then reconstruct the BST from $A$.
If you're fine with a recursive algorithm, and the positions of $A$ are indexed form $0$ to $n-1$, then the root $r$ of the new BST will be exactly the element $A[\frac{n-1}{2}]$. The elements in $A[0], \dots, A[\frac{n-1}{2}-1]$ will be those of the subtree $L$ rooted in the left child of $r$, and the elements in $A[\frac{n-1}{2}+1], \dots, A[n-1]$ will be in the subtree $R$ rooted in the right child of $r$.
Notice that $|L| = 1 + \frac{n-1}{2}-1 = \frac{2^i - 2}{2} = 2^{i-1}-1$ and
$|R| = 1 + (n - 1) - (\frac{n-1}{2} + 1 ) =  (n - 1) - \frac{n-1}{2} = \frac{n-1}{2} = 2^{i-1}-1$, so you can apply this algorithm recursively.
The time required is $T(n) = T(2^i - 1) = 2 T(2^{i-1} - 1) + \Theta(1)$, with $T(1)=\Theta(1)$, which has solution $T(n)=\Theta(n)$.


Running functions simultaneously from an akka actor

Question: From an actor (akka.actor.Actor) how can I execute a method twice simultaneously? Try to do it with Futures, but if the future does not respond, the actor does not take more requests ...
Comment: How about to actually include some piece of code in your question that represents your current issue?
Comment: "if the future does not respond, the actor does not take more requests" - that doesn't seem right, i.e. that's not the case if you use Futures in the intended way. Could you post the code in question?
Comment: Sorry.. I assumed it was very simple. :(
Answer: Generally, actors should not block. Dealing with actors, you should think in dataflow manner. Draw a dataflow diagram like this:
          --> methodCall1 --> |----------|
 actor1 /                     |  actor2  |
        \ --> methodCall2 --> |__________|

Actor2 can be inplemented as an Akka actor, which counts incoming messages and reacts when both messages has arrived. In this case, methodCall1 and methodCall must know actor2 and send messages to it.
Or actor2 can be a CompletableFuture which is derived from the future of one of method calls using method thenCombine.


With the crossbow expert feat can I still gain advantage from flanking?

Question: I'm playing a fighter who has taken the crossbow expert feat which allows me to not have disadvantage within five feat of an opponent. Do I still need to be using a melee attack to gain advantage from flanking?
Answer: It depends - the text of the rules are inconsistent.
Rules-as-written, whether or not the flanking optional rules benefits your crossbow fighter depends on one crucial question... hexes or squares?

Flanking on Squares. When a creature and at least one of its allies are adjacent to an enemy and on opposite sides or corners of the enemy's space, they flank that enemy, and each of them has advantage on melee attack rolls against that enemy.
...
Flanking on Hexes. When a creature and at least one of its allies are adjacent to an enemy and on opposite sides of the enemy's space, they flank that enemy, and each of them has advantage on attack rolls against that enemy.

Even if you're using hexes, I would suggest that the rules as intended were that you must be using a melee attack to gain the benefit of flanking, and this is an oversight in the hex-based flanking description. I would have looked back to previous editions' rules about flanking to help gauge the intention; however, 3.5e and 4e actually disagree on this subject. Where 3.5e mandates a melee attack, 4e offers the benefit to any attack against a flanked enemy. So, that's no help...
However, were I your GM, I'd personally not need much persuading to allow a Crossbow Expert feat-user to gain the benefit of flanking if making a ranged attack against an adjacent enemy - and given the inconsistency within the rule itself, plus the fact it is an optional rule to begin with, it's really the GM's call as to whether flanking is melee-only or not.
Answer: Yes, Flanking only requires an Attack Roll.
The Variant flanking rules from the DMG on page 251 state (emphasis mine):

...gives combatants a simple way to gain advantage on attack rolls against a common enemy.

Thus, the attack can be any Attack Roll (ranged, melee, or spell.)
A difference of language
As Carcer notes in their answer, the language for Flanking on Squares is different than that of Hexes AND that of the intro on flanking. Whether or not the error is in the Squares text or in the other two places is unknown without an errata, but given that it is the same in two places and different in one, I think we can assume the difference is the outlier and that flanking only requires an Attack Roll.
Comment: That quotation looks like a vague overview of what flanking is for, while the passage **Flanking on Squares** is precise rules text. I wouldn't be so quick to assume the intro text trumps the detailed specific rule text.
Comment: @starchild It's the combination of the introduction to Flanking, and then the specific applications for Squares and Hexes. There are two examples of General Attacks (Basic Flanking description and Hex specifics) vs one example for Melee only(Square specifics.) If you had to say one was wrong, would you say that one that was different or the two that were the same?


Unparsed aapt error(s)!

Question: I'm working with Android in Eclipse and was trying to combine code from a template project I found into the skeleton project that Android creates when you start a new project.  This is not an initial setup; have gotten several projects running and although I'm new to Android coding I have been working for several weeks without this problem  so the environment is set up fine I think.
The error I'm seeing is -
Unparsed aapt error(s)! Check the console for output

At one point I cleared the console messages and now even after closing the project and Eclipse, then reopening I get no console messages and none of my source or resource files are flagged.
What is aapt and where should I look for the source of this error?  Thanks in advance for your help.
Comment: Try here: http://www.anddev.org/sdk-adt-emulator-problems-f16/unparsed-aapt-errors-check-the-console-for-output-t12615.html
Comment: Found that by simply deleting the error on the 'Problem' window (right click | delete) will remove error.  Then re-run the app and the Console will once again display the issues that need to be tracked down.
Answer: I sorted this out. So for anyone else still on the learning curve with me, the solultion is as noted in my comment. In addition -
aapt = Android Asset Packaging Tool
From the Developers Guide -
"The Android Asset Packaging Tool (aapt) takes your application resource files, such as the AndroidManifest.xml file and the XML files for your Activities, and compiles them."
The solution for me was simply to delete the error on the 'Problem' window (right click | delete). Then, force a rebuild by rerunning the app. Any remaining problems will now show up and be logged so you can track them down.
Hope this is helpful to others.
Answer: This happened for me when I accidentally attempted to "run" an Android XML layout file.  It created a file with the layout name and _out.xml appended.  I needed to delete that file before I could perform any further builds.
Answer: This is what I did using Eclipse ADT, and that error disappeared:
Window > Preferences > Android > DDMS > Base local debugger port: 8600
I changed the value from 8600 to something else, example: 9999
Finally, I went to Project > Clean... > Clean all projects > OK
The error disappeared.
Answer: May occur when the project is created (New Android) and Fields: minimum required SDK, Target SDK, compile with and Theme are not filled in correctly.

Unparsed aapt error(s)!


Can I convert a radiator to radiant floor heating in a room?

Question: I am purchasing a new home, and designing some renovations to several rooms.  The house has a gas boiler and radiators throughout the house.  For the kitchen and upstairs bathroom, I will be putting in tile flooring.  To save space, I am wondering if installing PEX tubing for radiant floor heating using the supply and return from the radiator is a possibility.  Can this be simply installed in place of a radiator, or does the entire radiant floor heating system (thermostats, control modules, etc.) need to be installed as well?
Answer: You may be able to use the existing radiator piping to some extent, but a number of other changes will be required:

Lower water temperature. Because the radiant heating runs under your entire floor, it is typically run at a temperature similar to a hot summer day (around 85 degrees Fahrenheit). Cast iron radiators are usually run at around 150 degrees F, which would be painfully hot to stand on. So if you are keeping any radiators, your system will need to support running at multiple temperatures. According to this piping schematic from hydronicpros.com the device that can both control your boiler and mix water for a lower-temperature section is called a "variable speed pump mixing control".
System balance. Changing the way a room is heated may take it out of balance with the rest of your home, leading it to get too hot or too cold. You'll want to get a professional to assess whether this will require additional thermostats / control modules, or whether there's a simpler way to balance things.
Under-floor access. For hot water radiant heat, you'll need to install PEX on the underside of the subfloor. I don't think you can do that without access from underneath. Probably not a problem for your kitchen but may add some work for the upstairs bath. Correction 2 Feb 2012: Actually, there are hydronic systems that can be installed above an original subfloor (inside a newly poured cement layer, under tile). These may cost more and would likely change the level of your floor, but are worth considering.

One alternative you may want to consider is electric radiant heating. Electric radiant is available in mats that are layered with thinset between the subfloor and tile. The mats can be custom made to the shape of your room, e.g. to flow around a kitchen island. The system will come with a temperature sensor and control that is typically mounted in a wall box next to the light switches for the room. In this case, you'd simply remove the radiators, and use electric heat for those rooms instead.
Answer: I have done this to some of my renovations and I was able to do two types of installation. One was to save space in a bathroom with a radiator and the other was to save space in the kitchen just like you stated. I ran the pex (has to be heating PEX with oxygen barior) straight from the supply and back to the return of the existing radiator pipes. I first mounted reflective insulation to each joist bay leaving 1-2" gap between it and the new subflooring. I then zig zagged the PEX through each joist by mounting it with clips close to the top of each joist so that it would be as close as possible to the new subflooring (new plywood). I then did my cement board and layed my tile. It worked well enough to heat the small bathroom with no problems.
Comment: Hello, and welcome to Home Improvement. Thanks for the answer; keep 'em coming. And, you should probably [take our tour](//diy.stackexchange.com/tour) so you'll know how best to contribute here.
Answer: One partial answer is to deliberately decouple the pex from the floor.  E.g. if you have a crawl space, mount the pex a couple inches below the subfloor.  Fill in the joist space below with paperbacked 4" insulation bats. (Less if you want the crawl space warmed.)  The Pex now warms the air, which in turn warms the subfloor.  This gives more even heating, but the floor does respond as fast to thermostat changes


User keeps asking for Android Trojans RATs on at least 3 sites - Should be kicked off

Question: This user  Gregor keeps asking for somewhere to download Trojans.  He has been at it for 20 days or more.  He has asked here 3 times and has also asked on Software Recommendations, Information Security and Super User.  I think that he should be shut down before he finds a Trojan to wreak havoc on us all.
Comment: In short, I disagree about "kicking" a user based on this. I agree the questions are not suitable, but I don't think that I am seeing the same reason. Please note that on the meta sites downvotes indicate disagreement in discussions (or proposals) and are not about your question being bad.
Answer: Thanks for bringing this to our attention. Generally (from a community member perspective) I don't find these questions suitable for this Q&A site.
However, given links were already shared and sites offering what the user searches abound (minus the search/filter options), I don't exactly see what's wrong with asking for malware?
It's a stated (as was communicated to us mods) policy by SE to not have worry about the legality or have them enforce laws (besides, which jurisdiction should be considered?). The issue is similar to questions about cracking, I think. And so is the conclusion: downvote unsuitable or low quality questions independently of the legality aspect.


Plato, a student of Socrates and a teacher of Aristole

Question: Did Plato believe in a lot of questioning, just like Socrates?
Comment: Hi Ethan, welcome to the site.  A question like this needs more details in order to draw good answers.  Can you provide a little background that would lead to more than just a "yes" or "no" answer?
Answer: Much of our knowledge of Socrates derives from Plato's dialogues, so it is hard to say how much questioning or of exactly what kind Socrates did. The legend is that Socrates was stimulated in his career of questioning by the oracle of Apollo at Delphi. When asked whether anyone was wiser than Socrates, the oracle answered that there was none wiser. This puzzled Socrates, who didn't think he had any wisdom or knowledge at all. He went about among the supposedly wise in Athens and, by questioning them, discovered that they had no wisdom or knowledge at all. He then set about questioning anyone he could about philosophical matters such as the definition of holiness, courage, virtue.
We have a good many dialogues which Plato wrote after Socrates' death. These are full of questions, with the main questioner generally given the name of 'Socrates'.
One difference is that Socrates questioned whoever would discuss philosophy with him. He was very much a mixer with ordinary people. Plato discussed, and used question and answer, among select friends and the students at his 'Academy', which has been called the first university. Unlike Socrates he separated his philosophical inquiries from engagement with the general citizenry.
Another difference is that while Socrates wrote nothing (nothing that has survived, anyway), so that his questioning was all 'live' - a matter of talking with people, much of Plato's questioning was done in writing, hence the dialogues which he composed; these were literary productions.
Hope this helps. Chris Sunami is right : you need to ask more detailed questions if you're to get the best out of the site. So, more detail next time, please.


What is today's equivalent of a world system?

Question: Buddhism mentions "world systems." What's the equivalent terminology for a world system in the parlance of contemporary astrophysics?
Comment: The problem is that astrophysics investigates only the observable psycho-physical universe so it has no term for the richly layered and structured 'world-system' of Buddhism, which would include the world of physics but not be limited to just the gross surface layer.  . . . .
Answer: I don't think it refers to parallel universes as an alternate dimension of the sensous realm because the world systems shake when the Bodhisatta gains final attainment which would be strange if an eventuality caused effect over multiple worlds which are supposedly closed systems with laws of conservation, essentially closed systems of information. To me an eventuality causing a tremble over a multitude of such systems is philosophically like magical thinking as far as i can tell.
Also when the Buddha delivers a discourse such as the Brahmajala Sutta the ten thousandfold world system shakes.
Furthermore given that afaik i've never seen a declaration of a thousandfold multitude of formless realms i think it is the thousandfold world system that undergoes expansion and contraction and the vastness of the universe of form explains the variety of sub worlds which could be planetary systems or galaxies.
Another point is that there is only one Buddha in a world system simultaneously (mn115).  Which is significant because if Buddhas can supposedly teleport and if one followed an intepretation of one Buddha per solar system (as some people do) then a Buddha could meet another and this would be contradictory.
I think there are the 31 planes and it is a single expanding & contracting field of form that is inhabited by a multitude of galaxies with suns and habitable planets. I also think there is only one Maha Brahma per expanding system and one Buddha at a time.
Another point worth mentioning is that during a world system contraction, beings are said to be for the most part inhabiting formless realms.
Answer: World system in the context of the likes of Saṅkhār'upapatti Sutta, I believe, are humanoid planets.
From what you can infer from Kosala Sutta 1 this looks like a galaxy:

Bhikshus, as far as the sun and the moon revolve, illuminating the
  quarters with their light, there extends the thousandfold
  world-system. In that thousandfold world-system there are
  a thousand moons,
  a thousand suns,
  a thousand Sinerus,
  the kings of mountains,
  a thousand Jambu,dīpas [Jambul Continents],
  a thousand Western Goyāna continents [Apara,go,yāna],
  a thousand Northern Kuru continents [Uttara,kuru],
  a thousand Eastern Videha continents [Pubba,videha],
  four thousand oceans,
  four thousand maharajahs [emperors],
  a thousand heavens of the Cātum,mahārājika [the
  4 great guardian kings],
  a thousand heavens of Yāma [the Yāma devas],
  a thousand heavens of Tusita [contented devas],
  a thousand heavens of Nimmāṇa,ratī [the devas who delight in creating],
  a thousand heavens of Para,nimmita,vasavatti [the
  devas who lord over the creation of others],
  and a thousand Brahma worlds.
  And in that thousand-fold world-system, MahāBrahmā is
  regarded as the foremost.
  Yet even in MahāBrahmā
  there still is uncertainty, there is change.
  Seeing this, the instructed noble disciple is revulsed
  with that.
  Being revulsed with that, he becomes
  dispassionate toward what is the foremost, not to
  speak of the inferior.

Also see:

Parallel universes by Piya Tan
Buddhist Cosmology by Ajahn Sona
THE BUDDHIST COSMOS: A Comprehensive Survey of the Early Buddhist Worldview; according to Theravāda and Sarvsātivāda sources By Punnadhammo Mahāthero
Answer: Based on Piya Tan's Parallel universes, I'm not sure whether there is a modern equivalent term -- because if a type of object is real (e.g. "tiger", "dog", "grass") then I'd expect to find a word for it in several languages -- but if it's mythological then not (because different cultures don't have the same myths).
I doubt it has anything to do with contemporary astrophysics.
I'd avoid calling it a "system" (which a contemporary audience might confuse with e.g. "a solar system").
I imagine it's something like a "horizon" -- but in the second sense of that word:

1 The line at which the earth's surface and the sky appear to meet.
'the sun rose above the horizon'
2 (often horizons) The limit of a person's knowledge, experience,
  or interest.
'she wanted to leave home and broaden her horizons'

I might also term it as a "field of view" -- like someone might say for example that, "microscopic and macroscopic are different fields of view".
Comment: Aka Umwelt in the technical (semiotic) sense. Or perhaps a superset of all homomorphic umwelts.
Answer: Interesting question.
Remember modern day language, the scientific method, Newtonian physics, and higher mathematics only came into existence relatively recently in history around the 17th-18th Century whereas the Pali canons were orally transmitted more than 2,000 years before that.
So understanding exactly what's meant in more modern day terms is tricky but the suttas give us some hints:

"Ānanda, a galaxy extends a thousand times as far as the moon and sun
  revolve and the shining ones light up the quarters.
In that galaxy there are a thousand moons, a thousand suns, a thousand
  Sinerus king of mountains, a thousand Indias, a thousand Western
  Continents, a thousand Northern Continents, a thousand Eastern
  Continents, four thousand oceans, four thousand Great Kings, a
  thousand realms of the Gods of the Four Great Kings, a thousand realms
  of the Gods of the Thirty-Three, of the Gods of Yama, of the Joyful
  Gods, of the Gods who Love to Create, of the Gods who Control the
  Creations of Others, and a thousand Brahmā realms.
This is called a thousandfold lesser world system, a 'galaxy'.
A world system that extends for a thousand galaxies is called a
  millionfold middling world system, a 'galactic cluster'.
A world system that extends for a thousand galactic clusters is called
  a billionfold great world system, a 'galactic supercluster'.
If he wished, Ānanda, a Realized One could make his voice heard
  throughout a galactic supercluster, or as far as he wants." (AN 3.80)

The words "sahassadhā loko" or thousandfold-world is translated as "galaxy" here.
Looks like to me "world-system" or lokadhātu more refers to something like a solar system rather than the entire universe since thousandfold up to billionfold world-systems are mentioned.
It's mentioned that there are thousands of moons and suns in the thousandfold world system more similar to a galaxy.
But remember this was written long long before the concept of a galaxy was ever mainstream so it's still unknown exactly what's meant.
In my opinion certain terms should remain untranslated as it's still unknown exactly what's meant in modern terms.
When debating Menander Nagasena says:

"This world system, O king, is a one-Buddha-supporting world; that is,
  it can bear the virtue of only a single Tathāgata. If a second
  Tathāgata were to arise the world could not bear him, it would shake
  and tremble, it would bend, this way and that, it would disperse,
  scatter into pieces, dissolve, be utterly destroyed." (Mil 6.1.1)

Indicating that the Earth would explode if two sammasambuddhas appeared at once which indicates that the "world-system" word is more related to the Earth and this solar system rather than the entire universe.
Also indicates that on other world-systems different Buddhas can appear more similar to Mahayana Buddhist concepts.

What is today’s equivalent of a world system?


Grub does not open automatically

Question: I have been using elementary OS for some time now(months). I have it dual-booted with Windows 10. What I did to open elementary OS was to press "esc" while booting, then choose boot options, then ubunty and after that grub would open. Thats how I have been using elementary OS. If I don't this windows 10 will be booted automatically. Someone please help me I want grub to open at automatically when I start my system(laptop) and I can choose windows or Elementary OS then.
I have a HP laptop with specifications:
i-3 6006U
8GB DDR4 ram
1TB Rom
Answer: This needs to be changed in Windows, as that OS loves to take control of the boot partition. Fortunately, it's not too hard to fix.
In Windows:

Open "Command Prompt" as administrator
Run the following command:
<code>bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi
</code>

Restart the machine to test

Grub does not open automatically


Mysql alter table question

Question: I have a huge table in my mysql 5.6.19 database -around 5.7 gb of data- and there is a need to alter a description column which is currently set to text, to be able to contain around 500000 chars. Now my question is what is the right way to preform such a proccess. What will be the effect of the disk space when doing it? Can indexes be possibly harmed after this operation? Any help would be highly appriciated here. Thank you very much
Answer: You need to ALTER a column from TEXT to MEDIUMTEXT?
Such an ALTER will copy the table over, making the change as it goes.  At the end, rebuild the indexes and will RENAME the table back into place.  The table will be blocked from (at least) writes for the duration, which could be hours.
For a less invasive approach, see pt-online-schema-change.  It will add a Trigger to the table so that writes are tracked while it copies the table over.  It ends with a brief finishing lock to flip the table into place.
Either approach will take about 5.7GB of spare disk space.  Caveat:  If you have innodb_file_per_table = OFF, the spare disk space will not be freed when finished.  I recommend ON when creating 'big' InnoDB tables.
Answer: There are tools that allow MySQL DBAs to perform online schema changes. Both of them come from heavy hitters in the world of MySQL.
The first tool is Percona's pt-online-schema-change.
Documentation is comprehensive and Percona need no introduction in the MySQL world.
The other tool is Shlomi Noach's (called online-schema-change again!) and is available here.
Percona's toolset is written in Perl and Noach's is written in Python - so it might be down to a preference for one or the other.
In any case, both sets of tools are worth checking out for any MySQL DBA.
Comment: Thank you very much about those tool. Do i need to take anything under consideration as im running a slave replication in production? Will this tool work fine with it? The percona one
Comment: Search for "replication" on this [page](http://www.fromdual.com/online-ddl_vs_pt-online-schema-change). Interestingly, one of the participants in the discussion at the end is Shlomi Noach who wrote one of the tools, but he comments on replication using pt-online-schema-change - the other (i.e. Percona's) tool. Also, see the Percona documentation page above (again, search for replication).

Mysql alter table question