Viewing latex file and pdf file in split screen mode

Question: I want to have both latex source code on left half of screen and compiled pdf file on right side of screen.  How can I do ths
Comment: Welcome! Many editors allow this by default, check Texmaker, TexStudio, as examples, too many others do.
Comment: Depending on the tex system you may already have that ability For example basic versions of MiKTeX windows, ProTeX windows and TexLive windows all include such an editor MiKTeX and Tex Live use a simple TeXworks ProTeX includes MiKTeX but adds TeXstudio
Answer: Have a look at texstudio if you're beginning. I found it to be the best of texstudio, texmaker and kile for learning and quite user friendly. As you progress


Windows 11 Raspberry Pi Imager Access Denied

Question: After Preparing to write... (opening drive) i have access denied. Everything stops with removed partitions, but new aren't generated. Error i can see is Error writing to storage

Then i saw error
Comment: not a Raspberry Pi related problem
Comment: Use 'run as administrator'
Answer: If controlled folder access is turned on, you will not be able to even format the SD card as Fat32.
The solution is to allow apps exceptions thru controlled folder access.
Esp on win 11. so: Press Start, Type "Controlled folder access", and open that. you can now allow [specific] apps through Controlled Folder Access.
It is a security feature to prevent virus-like activity.
When doing those steps myself, the 2 most recent blocked commands shown in there were the pi-imager and the format32 commands!
once, they were both allowed though, then the 2 operations completed successfully.
Answer: In my case, I saw the error dialog from rpi-imager.exe of the cryptic message "error writing to storage" however I had no other indication of what the problem was.
I was using an SD card previously used with a Raspberry Pi 3 B. I'm not sure what was on it (possibly the old Windows IoT for Raspberry Pi 3) but I wanted to use the card with a recently purchased Raspberry Pi 4 B.
I was using a Dell mini-tower that has an SD card slot running Windows 10 Pro. When I first put the SD card into the slot, multiple windows displayed and I could look at files on the SD card. It appeared to be a Windows file system.
When I used rpi-imager.exe to install Raspberry Pi OS 64 bit, the dialog of "error writing to storage" displayed. The card was no longer readable by Windows so it appeared to have been reformatted or initialized in some manner but the rpi-imager.exe application couldn't install the OS onto the card.
At first I wondered if the write lock was set on the SD card but it wasn't.
Finally, in desperation I used an existing application, SD Card Formatter, to format the card which resulted in an SD card formatted for Windows.
Then I tried rpi-imager.exe again and received this much more helpful error dialog.

I then used the Windows Settings app from Start to access Windows Update & Security:
Windows Security ->
Virus & threat protection ->
Virus & threat protection settings ->
Manage Settings ->
Controlled folder access ->
Manage Controlled folder access ->
Allow an app through Controlled folder access

The last couple of applications that had tried to access a disk and been denied were listed with rpi-imager.exe being the most recent. I selected it to add to the Allowed List.
After allowing rpi-imager.exe to modify the SD card, the application was able to successfully write the image to the card. I then inserted the SD card into my new Raspberry Pi 4 and it booted and initialized successfully.
I had to redo the image after making a mistake with the Raspberry Pi OS configuration tool and had no problem reinstalling the OS on the SD card using rpi-imager.exe.
Answer: I had the same error. Just run the Raspberry Pi Imager "As Administrator".


Are there frequent itemsets mining algorithms based on linear algebra?

Question: Matrix equations of some sort or matrix decompositions often lie in foundation of many algorithms not only in data analysis but in many other fields. The wealth of already written libraries makes it tempting to formulate frequent itemsets mining problems in terms of said matrix equations and/or decompositions, yet after some search I haven't found any algorithms which would rely on linear algebra. Could some please show me if such algorithms exist or explain their absence?
Comment: What is an itemset? What is a mining problem for an itemset?
Answer: To elaborate on Vijay's answer
Firstly, it's not frequent itemset analysis, but you can use correlations to analyse the "shopping basket".  This is amenable to linear algebra analysis. So you could do PCA, where you would first sphere the data- to remove the frequency effect of each item ( eg milk, bread being most frequently bought). Then pca would identify items that have high positive or negative correlation. another linear algebra option would be non negative matrix factorisation ( to try to decompose the shopping basket as a sum of a 'minibasket' of few positive amounts of each item).
frequent item set analysis does not limit itself to linear relations ( correlations).Eg in  Wikipedia's example, you consider: $\text{onion}\cap \text{potatoes} \rightarrow \text{burger}$.  Now just as with linear regression, you could augment your dataset by creating cross terms and looking at the correlation between onion x potato and burger (represented as eg dummy variables ), however this quickly becomes impractical... which is why frequent item set mining is used. One might argue however that there are few nonlinear relations that can be effectively estimated and correlations dominate - I haven't worked on that data so i can't answer...


Shimano Nexus 3 stuck on lowest gear

Question: I have a bike with Shimano Nexus 3 gear, and it's stuck on lowest gear. However, if I move shift pin that changes gears it changes the gears. So Nexus itself seems to be working, but the pin is not returning to correct position when going to higher gear. Is there a spring broken that should return the pin to correct position, and if so, how should I fix it? New spring? New wheel? Lot's of WD-40?
Comment: So it sounds like you are saying the shifter may be broken.  When you manually move the pin it works, does the shifter move the pin as it should?
Comment: If I set the pin to 3rd gear, I can use the shifter to change to second but not up, and from second gear I can go to first, but not up. Shifter seems to be working but pin is not returning up
Comment: So it sounds like either your shifter or bell crank is the problem.  If you disconnect the shifter and the cable moves properly both directions while shifting, it's the bell crank, if not, then the shifter/cable/housing.
Comment: Comment for next generations: Description is unclear. Pin should return when going to LOWER gear in this hub. Its stuck, but shifts... strange.
Comment: ... If the internal spring would be broken, you probably won't be able to change gear from 3 to 2 once it was turned on (and, form 2 to 1 it wolud be even less possible). Problem with shifter is unclear - maybe its shifter suitable for Sachs Dreigang? WD-40 is good for test, but after all there is need to disassembly hub and grease it, because it is a solvent for grease.
Answer: Had same problem. Bell crank on the end of the axle is worn. Replace the shifter housing on the end of the axle. When worn, it won't push far enough on the shift rod. Cheap fix.

Shimano Nexus 3 stuck on lowest gear


Salary negotiation after an interview

Question: I got a job offer from one of the big 4 with a lower salary than I expected (25% less than what I earn currently). knowing that I can accept up to -10% compared to what I earn, because the position and the workplace are very interesting, what is the best way to negotiate? Do you think sharing my pay slip is the best approach to convince them?
Comment: If you've already told them your salary expectations, then you can repeat that to them, but either there's been a misunderstanding/miscommunication somewhere (possible but unlikely), or more likely the offer reflects the fact they don't perceive you being worth anywhere near the salary you expect, in which case, there's no harm in negotiating, but I wouldn't be optimistic about a favourable outcome.  Keep searching for jobs unless you're really backed into a tight corner.
Comment: Why not just tell them your salary expectations?
Comment: I did in my first interview with HR...
Comment: What country is this in?  Certainly the US say you would never, ever, ever show anything like a pay slip.
Comment: Is there a hiring manager involved? If there is, tell them what you're currently earning and that taking this position would be like taking a paycut. Don't depend on HR to have relayed that information to them. And don't offer to show your payslips. It's not like they have requested to see them, or have they?
Comment: Thank you all for your interaction and feedback... I have sent my counter offer today...fingers crossed
Answer:
I appreciate the offer but the absolute lowest I'm willing to go from the $100,000 I initially proposed is $90,000. Thanks!

Obviously don't send that unless you're prepared to continue the job search.
You could send the paycheck stub but I feel like that's providing information that they simply do not need. It's kinda like telling your employee what you intend to do when putting in a time off request instead of just putting in the time off request.
Like if you establish a pattern of providing excess information early on then what are you going to do when you want to take time off to interview at another company? In that scenario your options are:

all of a sudden, decline to tell them your plans (which, in and of itself, could look suspicious since it's a break from the norm)
lie to them and tell them that you're going to a doctors appointment when you're in fact going to an interview (and apparently a lot of people think even a white lie is a terrible thing)
Comment: Thanks Neubert for this detailed feedback
Answer: This will sound too obvious, but they may have simply taken whatever number you said, and took approximately 15% off that.
Regardless, you have 2 problems

They think you're willing to settle for less than the actual amount
Possibly, you may have given the impression that you don't care about money

Some possibilities:
Changing their impression of your best-alternative

Tell them you have received another offer, at exactly 100% of current salary (which is true in a way).
Give them some kind of reassurance that you're not just jerking them around - say that you find the work at their company more interesting and are excited about joining (also true).

Changing their impression of not being interested in money and/or not being willing to stand your ground

Rather than convince them your personality changed, and that you're not the nice guy/gal they fell in love with in the interview, an alternative trick is to introduce another invisible character who is telling you what to do. Yes, really. This unseen character will play the part of the bad cop. The equivalent of "let me go check with the manager" or "let me go home talk it over with my spouse" when buying a car.
So in this case, say you spoke with an experienced mentor (make up e.g. a former boss who who works at X, don't give a name, 2 sentences max). The mentor advised you to take whichever offer is the best salary, the conversation with them opened your eyes, and their advice is precisely what you will now be doing. Because you like this company better, you are hoping they can beat the 100% number by at least +XX ... Believe it or not, this kind of nonsense can work.

As a final note, your reaction to any excuse about budgets or standard levels of pay should be very polite disbelief. Maybe a "yes yes of course, very understandable", painfully-fake-smile-and-nod, and then reiterate "but here's where I am, and here's what I'm looking for". If they're big-4, in whatever industry, then by definition they can afford the same salary that anyone else is paying.
Comment: Sorry to hear that. For the record "salary grid" is pure fluff wrapped in a delicately thin formality. If they didn't move at all on the number it's not a great sign for a long term future there, IMO.
Comment: Thanks Pete, I hope they will come back with big YES or at least proposing something close to my demand...fingers crossed
Comment: Sadly, they have not accepted my counter offer - they have a "salary grid" and do not want to make an exception - despite the fact that it is a major pay cut. I'm seriously considering accepting their offer because I don't see myself progressing professionally in my current role.
Comment: Thank you very Pete for this clear reply... I've sent my counter offer today and get this answer "we value your experience and motivation to join us and we are fully convinced that you would be great addition to the team. We will review your request internally and I will come back to you next week" Do you think it is a good sign.?
Comment: This answer helps me a lot to formulate my email
Comment: I'd say it's quite positive. At face value, they are saying the only thing in the way now, is possibly a little more haggling over the amount.... you don't have to say much in reply. See many other questions on this Stack about how to formulate that email.
Answer: Assuming you haven't discussed numbers before.

Read up on the negotiation and package strategies for your specific company, for example: https://fearlesssalarynegotiation.com/apple-salary-negotiation/
Make sure you fully understand the package (benefits, equity, bonus, 401k match, etc) and make an "apples to apples" comparison.
Send them an "opening" note. "I'm super excited about the role and the company but this offer is a very significant pay cut compared to my current compensation. How can we work through this?"
Take your next step based on the answer: Could be "Too bad, so sad", "What's your minimum number?", "let's review all the details of your package and not just focus on base", etc.

If you have discussed numbers before and the offer came in low despite of that, you can try the same approach but it's unlikely to work.
Comment: This was absolutely helpful for me...thanks Hilmar
Answer: I'd like to offer a slightly different perspective over the whole question. You seem to be in a dilemma over two incomparable things - money and "very interesting work".
There are so different that any attempt to trade one for the other is doomed, I dare say. A job can be basically interesting or dull. There's hardly such thing as a medium-interesting job, or a little bit above average interesting job, etc. Therefore, you cannot make a decision such as "if the salary is bigger by a degree, then I'd settle for a less interesting work by a degree" or vice versa.
Plus, your job and position, can change from interesting into dull at the snap of boss's fingers (and that does happen very often - no one would go advertizing the dull aspects of work. As soon as you are hired you may get assigned tasks quite different from what you have been led to believe and if you may be shown the door if you do not embrace that new reality.) Your own perceptions of what is interesting may change. You may quickly get into the new stuff and then reach a plateau. "Interesting" is quite subjective, while the amount of your salary would stay exactly as negotiated.
My advice would be to seek the salary which would keep you financially satisfied and only when that premise is being met, choose on the basis of purportedly very interesting work and position.
Also, do not forget that most employers show respect or disrespect to their employees on the basis of the salaries they pay them, not on employees' genuine interest and devotion to their jobs.

Salary negotiation after an interview


Why does the electric field vanish at infinity?

Question: When $r \rightarrow \infty$, $E \rightarrow 0$ for a point charge or set of charges or a finite charge distribution. While this seems obvious, I cannot find a reason why this is true when inspecting Maxwell's equations and the Lorentz force law. I thought however that all of electrodynamics was contained in Maxwell's equations and the Lorentz force law. Why then, does $E \rightarrow \infty$ when $r \rightarrow 0$.
Comment: 1. It's $E\to 0$. 2. If you didn't say $E\to 0$ as $r\to\infty$, you'd have $F = qE \neq 0$ at infinity. Does that make sense to you?
Comment: I fixed the question. What is inherently wrong with having $F =/= 0$ at $r \rightarrow \infty$. Couldn't $F$ just be really small, but nonzero.
Answer: You are correct that the vanishing of the field does not follow from Lorentz' force law and Maxwell's equations alone. An additional physical argument is needed:
If you didn't have $E\to 0$ as $r\to\infty$, you would have non-vanishing force $F = qE \neq 0$ at infinity. That is physically non-sensical because it would mean that a charge influences charges that are infinitely far away measurably. It is the physical boundary condition that we must impose on the physical solutions to Maxwell's equations in order to preserve locality, otherwise we would be living in a universe where every charge pulls or pushes on every other charge in a non-neglegible manner, no matter where these charges are.
It is rather evident that that doesn't describe our universe.
Comment: Coulomb's Law can be derived from Gauss's Law.  Is anything else (boundary conditions) needed?
Comment: So $E \rightarrow 0$ as $r \rightarrow \infty$ is a universal physical boundary condition (since expiremtnally we don't deal with infinite charge distrubutions unless we are approximating). Since this is a universal boundary condition, is this a law?
Comment: @garyp: You can equivalently base electromagnetism on Coulomb's law + SR (i.e. the transformation rules of electric and magnetic fields as well as the four-current), since you then can always go to the rest frame and use Coulomb's law, then transform back.
Comment: @Donald: Well, it's not *really* a law because you often solve for different boundary conditions, e.g. you have a capacitor known to be at a certain voltage, but it is something you have to say to derive things like Coulomb's law from Maxwell+Lorentz.
Comment: @garyp: Ah, I see what you mean. Have a look at [Wikipedia's comment on that](http://en.wikipedia.org/wiki/Gauss%27s_law#Deriving_Coulomb.27s_law_from_Gauss.27s_law), you need there the "boundary condition" that the field is spherically symmetric. You always need some kind of physically sensible requirement, be it the vanishing at infinity, or be it spherical symmetry, or be it something else.
Comment: Is the wave equation an example of a solution to Maxwell's equations using a different boundary condition?
Comment: @Donald: An equation is not a solution to another equation, but if you are asking if plane wave solutions are unphysical, then yes - these do not occur in nature, they are a convenient idealisation. The "infinite amount of energy" is another physical reason to assume vanishing at infinity, yes.
Comment: Couldn't another reason why this boundary condition holds is that since in potential form $E = -\nabla \phi - {\partial A}/{\partial t}$, and using the coloumb gauge since $\nabla \cdot A = 0$, $\nabla \cdot  {\partial A}{\partial t} = 0$ so ${\partial A}/{\partial t} = \nabla  × F$, hence $E = -\nabla \phi -\nabla × F$, the hemholtz decomposition which only works if $E \rightarrow 0$ as $r \rightarrow \infty$.
Comment: @Donald: Yes, Helmholtz decomposition also requires a rapidly decaying field, but then you are putting in the assumption that your field be Helmholtz decomposable. It really doesn't matter where you start, but *some* kind of assumption is always put in.
Comment: OK.  Then given: a stationary charge (not accelerating probably good enough), Gauss's Law, and curl $\vec{E}=0$,  Coulomb's Law follows, and that's what the OP actually asked about:  does Maxwell imply vanishing E at infinity.
Answer: Since you speak about point charge, let us check the Gauss law (to start with something well known)?
$\nabla \cdot E = \frac{\rho}{\epsilon_0}$
We know that divergence has something to do with flow across some closed surface (sphere surface is the best) around the $\rho$ - the same in integral form is:
$\oint\limits_{\delta\Omega} E \cdot dS = \frac{1}{\epsilon_0}\iiint_\Omega \rho dV$
$\Omega$ is volume around your charge (sphere for us), $\delta \Omega$ is the surface of the $\Omega$. I think I can use delta function for the point charge $\rho=\delta(x,y,z)$. This way we reduce the right side of the above to $\frac{1}{\epsilon_0}$, we can certainly have it a charge of one electron $e$, or some $q$, but always constant.
$\oint\limits_{\delta\Omega} E \cdot dS = const$
means, that whatever sphere $\Omega$ (diameter $R$) we use, the integral of $E$ over its surface is constant.
The last step : $\oint\limits_{\delta\Omega} 1 \cdot dS$ is the surface and goes like $R^2$ with $R \rightarrow \infty$. To keep the previous integral constant, you need $E \sim \frac{1}{R^2}$. The answer is  $E \sim \frac{1}{R^2} \rightarrow 0$ for $R\rightarrow \infty$
Was that correct? I wonder why \oiint doesnot work...
Comment: Your assuming that the electric field doesn't rotate as $r$ changes.
Comment: Should it with point charge?
Comment: OP is taking the position that from Maxwell's equations and Lorentz force law electrodynamics follows. Nowhere in those equations is the direction of $E$ specified.
Comment: @Donald though your question is answered, I don't see why this approach would be inadequate if the E-field is rotating?
Comment: I think this argument is fine, as long as *symmetry* is also invoked to argue what direction the E-field doesn't point.
Answer: using V.E=p/e0 in integral form that is gauss law you get your first answer E going to zero as r go to infinity.
Comment: I don't think this is right, because E could rotate such that E gets more and more perpendicular to the area vector as $r \rightarrow \infty$
Comment: what do u mean by E becoming more and more perpendicular to area vector as  r→∞
Comment: at infinite distance for a finite amount of charge with finite extension  in space we can consider E to be in radial direction at every point of gaussian surface. i.e. we have E*A = Qenclosed. as this area is infinte so that gives E=0
Comment: Why can we consider $E$ to be radial?
Comment: because at infinite distance the charge distribution can be suitably considered symmetric at the gaussian surface considered


What is the best armour in A Dark Room?

Question: What is the best armour in A Dark Room? I am saying this because I have got steel armour and is it the best? I have tried to get more steel swords and go far from my village, but, no luck.
Answer: Yes
Looking at the wiki for this game, the only effect of the various armours is to change your character's HP value as follows:
<code>nothing  10
leather  15
iron     25
steel    40
</code>
That would make steel armour strictly better than all other options.
I do not know whether this stacks with the gastronome perk.

What is the best armour in A Dark Room?


Helium Lift Potential

Question:
A particular mass of helium is required to lift a particular weight.  If the weight stays the same and the mass of helium is decreased can the same lift force be achieved by increasing the acceleration of the helium gas?  Not to be an Einstein, but if I recall correctly, force = mass * acceleration.
Also, can helium gas be accelerated by heating it or by cutting it with a fan like propeller?
Lastly, when do we all get a flying saucer?
Answer: Normally when you speak of lifting by helium you are using the buoyancy of a balloon in the atmosphere.  If you decrease the mass of helium you decrease the volume of the balloon.  The lift capacity of a balloon is the difference between the weight of a balloon and the weight of the air it displaces.  If you can lighten the envelope you can maintain that difference with a smaller balloon and maintain the lift capacity.  The helium gas has no appreciable acceleration and there is no fan.
If you are doing something different to lift something with helium you will have to explain more clearly what it is.
Answer: Well, you could get more lift force out the helium by accelerating it.  If the helium, let's say in a balloon,  was initial moving upwards quickly and the object you're trying to lift was stationary, at some point the rope connecting them would go tight and at that point the rope will apply a downwards force on the helium slowing it and accelerating it downwards.  The helium would apply an equal upwards force on the rope giving you extra lifting force.
You could test this experimentally fairly easily.  Get a helium balloon, a string and a payload that is just a tiny bit too heavy for the balloon to lift.  With the payload on the ground, pull the balloon down to ground level so that the string is slack then release the balloon.  When the string goes tight the balloon should lift the payload off the ground but only very briefly.  Once the balloon is done accelerating that force goes away.
The scenario described above is easier to picture with something  denser and more streamlined moving upwards - say an arrow that's been shot up by a bow.  The thing about helium is that it's got such a low density.  This means that as soon as it's moving with any speed through air you are going to get substantial air resistance.  Your rapidly moving mass of helium will end up exerting an upwards force on the surrounding air - not the desired result.

Helium Lift Potential


Have nuclear explosions in space produced any debris that was subsequently tracked, or did all of them completely self-vaporize?

Question: This answer to Where in the solar system could a nuke be tested without anybody noticing? has got me wondering if nuclear explosions (nuclear tests) in space above Earth ever produced any chunks of space debris. Were there any objects from the exploding vehicles that were subsequently tracked or observed, or did all of them completely self-vaporize or at least only make particles too small to track?
Comment: There have never been any nuclear explosions in Earth orbit.
Comment: @prl okay I'll modify the wording, thanks for the *heads-up!*
Comment: @Fred, while it's true that not all the fissile material takes part in the reaction, it is all vaporized, along with the rest of the bomb parts.
Comment: @prl, sure, no nukes from a spacecraft that reached orbital velocity, but there were twenty above the Karman line.
Answer: The U.S. detonated five nuclear bombs above the atmosphere.  Not many minutes after one of these, nothing bigger than a molecule was left.  So no debris, only a few radiation belts of high-energy electrons, which persisted for up to a few years.  The other four explosions were likely similar.
As for the Thor launch vehicle, it was just a single stage (not trying to reach orbital velocity, so no second stage needed), so it was vaporized by the explosion.
The USSR also detonated some above the atmosphere.  These were extensively studied because of the widespread damage their EMPs caused to terrestrial electrical equipment, but I see no mention in these reports of material debris, either orbital or raining back down to earth.
Reports about the three low-yield 1.7 kT detonations of 1958's Operation Argus (the Wayback Machine's best link is 2011 Jun 11; 142 pages) are replete with references to radiation belts (Argus's purpose) and the radiation precautions for personnel.  But not a whiff in all of that about even the possibility of space debris.  Google's ngram shows that we'd hardly started talking about that until twenty years later, never mind figuring out how to track it or even detect it.  Because the launches were suborbital, any energy imparted to debris to achieve orbital trajectory must have come from the detonation.  It's a safe guess that any such energy transfer would instead have vaporized the debris: Hiroshima's 16 kT caused "complete destruction" for about a mile, which for this 10$\times$ smaller explosion equals a radius of the cube root of 5280 feet, or 17 feet, comfortably beyond the missile's radius.  Again, nothing bigger to track than a cloud of molecules.
Comment: It looks like there were about [20 tests total](https://en.wikipedia.org/wiki/High-altitude_nuclear_explosion#List_of_high-altitude_nuclear_explosions) with about eight very low yield events between 1 and 10 kilotons. I think the low-yielders might be the best place to look for surviving debris, rather than Starfish Prime.


How to change minecraft skin in alpha version

Question: Recently I tried to change my skin in minecraft alpha, but it wont change.
I've went into the .jar file of the related version, and changed the char.png file to a new one, but minecraft launcher keeps updating the .jar file, reverting my changes.
How do I stop it from doing that?
Changing the .jar file to "read-only" just crashes the game on launch.
Comment: Have you tried setting the file to read-only?
Comment: Yes, the game crashes on launch if its on read-only
Answer: The BetaCraft launcher allows you to change your skin for early versions, as well as fixing many other bugs present in early versions.
Comment: Looking for a different launcher sure can help, but is there a way to fix that issue without third party software?
Answer: So the solution that doesn't require you to use third-party launchers is pretty simple but can get messy if you are not careful.
In order to stop the launcher from rewriting the files, we have to create a modified version.
To do that, we first have to copy the original version we want to modify in the %appdata%.minecraft\versions directory, and rename the copy to something unique. For example: "TestVer". Its important to rename in the new version folder both the .json and the .jar file to the same name as the folder.
Now, there are changes that you have to do in the .json file. There are lots of different properties in .json file, we need to go to the "assets" property (do not confuse with "assetIndex" for example), find the "download" property inside the "assets", and delete it entirely. The next property to the "downloads" property should be "id" property, which is the version name. Change the "id" property with the version to the custom version name you made before.
There are lots of other properties with "id" and "downloads" properties, and the .json file is unorganized and messy, so be careful and don't delete anything under the "libraries" list(Lists in json are identified with [] symbols).
Be also aware that mismatching names could cause issues as well, example is added as image.
Now, in order to change the skin, you should open the .jar file as archive, and replace the char.png file with your modified char.png file. Notice that older versions had different skin templates, so you may have to change your char.png file to fit the template of the version, or it will be messy.
After those changes, open the minecraft launcher(or restart it if it was already opened), and you should be able to choose the new modified version, with the skin imported, and play it with no issues.
Credit for the solution, help and images to MasterCaver, who found the solution and guided me on how to make it work.
Source to the conversation with MasterCaver:https://www.reddit.com/r/GoldenAgeMinecraft/comments/e5pi0q/comment/kosfjzw/?utm_source=share&utm_medium=web2x&context=3


Are monks and lay people 100% allowed to sell sacred, consecrated or blessed images and objects?

Question: I learned that the monks of a monastery draw and consecrate or bless sacred images and then resell them.
Is all this permitted by the law of dharma?
Don't we fall into materialism by commodifying the things of the spirit?
I wonder the same thing about other objects, statues, malas, etc...
Answer: Good question.
The Vinaya Pitaka (Code of Ethics/Conduct for Buddhist bhikkhus/monks and bhikkhunis/nuns) clearly state that the ordained and novices cannot deal with money. They are not allowed to handle money, leave alone sell stuff in exchange of money.
If monks in a monastery are making goods and selling them, then is there a particular reason why they are doing so? Is the Abbott of the monastery allowing this for a purpose and for what duration of time?
In one of the Suttas, Buddha had mentioned that in the future, there will be monks in saffron and yellow who will not follow the teaching as mentioned by the Tathagata, who will have large followings and indulge in non-Dharma activities. Buddha also predicted that Buddhism would decline and disappear in 5000 years. We have crossed 2600 years since the inception of Buddhism, and we can already see a steep decline.
Comment: I understand, but what about the lay people who create these works, blessing them and then selling them? Is all this acceptable from an ethical/spiritual point of view according to Buddhism?
Comment: I just studied about the Tibetan **Ten Sciences**. One of the Major Sciences is the **Science of Fine Arts and Crafts**, which allows monks and laypeople to create, build, or manufacture things to facilitate people in their daily tasks or to provide people with service to make their (people's) lives easier. There is a long list of things that a Buddhist can create, build, or manufacture, both on the Dharma and about worldly things. Few among them are building idols, stupas, and monasteries, painting the faces of idols; building houses; farming; trading and commerce, and so forth.
Answer: I don't think problem is with people who are selling such commodities problem is with those purchasing it.

"Demand is the driver of economic activity; it is the spark that ignites the engine of the market, setting in motion the forces of production and exchange." - John Maynard Keynes

Merchants are simply doing there duty.
The people who demand such commodities are same people who are responsible for fall of all the Great Masters. I don't find even a single suttra in Pali Canon in which Buddha declared himself any kind of God or Supernatural Entity. There is no point in worshipping Buddha, this will be greatest disrespect to Teachings of Tathagata.
Selling Idols or using Dharma for personal gain is similar to destroying it,but it's the reality of society we live in, all the Knowledge from east is getting converted into commodities and sold in west. Yoga, Advait Vedanta or Zen are all getting converted into business.
This is excerpt from talk of Acharya Rajneesh (though I don't really agree with his way but I find his teachings worthy of respect).

The buddha is the most dangerous person in the world. That is why the world either kills the buddhas or worships them. These are synonymous: killing is a way of getting rid of them; worshipping is also a way of getting rid of them. When you worship a buddha, you are saying, "You are born a buddha, we are poor human beings. At the most we can put two flowers at your feet. Just leave us alone, we have so many other things to do." This is also a very cultured way of creating distance. That is why in every culture, either they have killed such people or they have said that they are incarnations of God. "It is easy for them. We are human beings, with all kinds of frailties, weaknesses; we cannot do it." Just to create a distance, so many stories have been created. And I have been wondering continually why no psychologist has the guts to go into those stories and expose what is hidden behind them. For example, Gautam Buddha was born when his mother was standing under a tree.Now, no woman has ever given birth to a child standing. Perhaps this was some accident, a kind of abortion. But the story is that Buddha was also born standing. As he came out of the womb, he stood on the earth, and the first thing he did was to take seven steps a newborn baby taking seven steps and then declaring, "I am the greatest buddha in the world."Now, the people who were creating these stories were trying to create a distance between themselves and these awakened people. They were not ready to accept them being as human as they are because then a great responsibility arises. If a human being can become a buddha, then what are you doing? Then it will be a great weight on the chest, it is better to put these buddhas as far away as possible. If you go to a Jaina temple you will see a strange thing; there are twenty-four Jaina tirthankaras, Jaina gods. All their ears are so big, the earlobes so long, that they are touching their shoulders. That is one of the signs that a man is a tirthankara. You cannot find anybody who has such long lobes unless he goes through plastic surgery or some kind of massage continuously milking a cow. like But why does this kind of thing happen? - just to make them different from you.

Buddha's message was most clear and scientific of all contemporaries or old ones.
There's one more aspect to His Dharma that is Rebellion. Buddha was not alone, the whole movement was there in India against the orthodox school of thought. Orthodox religion of that time in India - Vedic Tradition was degenerated and such things like using Dharma for exploiting others was prevalent. The Shramana movement revolutionised the prospects of the social and religious dimensions of ancient India in such a way that even after many centuries these traditions continue to attract humanity across many countries.
Shramana traditions in ancient India were brought about by the ascetics who renounced worldly life to search for the truth about life and the universe. They included many groups, sects and varieties of opinions. The most famous among them were the Buddhists, the Jains, the materialist Lokayatas and groups like the Ajivikas.
In the Brahmanical order the Brahmins were privileged as intermediaries between deities and followers, and were considered the protectors of the sacred learning found in the Vedas. The Shramanas rejected the authority of the Brahmins and opposed the ritualistic orthodox ideas of the Brahmanas.
All the Shramanas sects denied the supremacy of philosophies of Vedic texts. Some of them like Budhha and Mahavira got enlightenment through meditation and after realising truth propagated the right way of life to their followers.
In conclusion the foundation of Buddhism was not enlightenment or such fancy stuff;  It was a Rebellion against the orthodox religion which had flaws just like
"monks of a monastery drawing and consecrating or blessing sacred images and then reselling them".
This is no way should be acceptable by any one who has lived teachings of The Blessed One.


Potassium chlorate from potassium chloride and hydrogen peroxide

Question: Why can't you make potassium chlorate using the chloride anion from the potassium chloride and having oxygen bond with it from hydrogen peroxide?
Answer: Do not attempt! Peroxide is not a strong enough oxidant to oxidize chloride ion to chlorate. Neither is oxygen. However, peroxide can oxidize chloride to poisonous chlorine gas.
Redox reactions are spontaneous if the two half reactions would produce a positive potential in a galvanic cell. Most redox half reactions have measured standard electrode potentials against a known standard so that they can be compared.
The reaction you want to do is:
$$ \ce{3H2O2 + Cl- -> 3H2O + ClO3-}$$
The two half-reactions are:

Oxidation:   $\ce{Cl- +3H2O -> ClO3- +6H+ +6e-}$
Reduction:   $\ce{H2O2 +2H+ +2e- -> 2H2O} \ \ \ \ E^ \circ =  +1.78 \text{ V}$

The reduction potential of hydrogen peroxide is on the table, but the reduction potential for the other reaction is not. However, the other reaction is the sum of two reactions on the table, so we can use Hess's Law.
$$\ce{ 2ClO3- + 12H+ + 10e- ->Cl2 + 6H2O} \ \ \ \ E^\circ = +1.49 \text{ V}$$
$$\ce{Cl2 +2e- -> 2Cl-} \ \ \ \ E^\circ = +1.36 \text{ V}$$
$$\ce{2ClO3- 12H+ + 12e- -> 2Cl- + 6H2O}  \ \ \ \ E^\circ = +2.85 \text{ V}$$
Since standard potentials do not scale by stoichiometric factor (it's in the Nernst equation instead), the value we just found also works for our oxidation reaction. However, since this reaction is reverse of the "reduction half-reaction", we need a negative sign:

Oxidation:   $\ce{Cl- +3H2O -> ClO3- +6H+ +6e-}\ \ \ \ E^ \circ =  -2.85 \text{ V}$
Reduction:   $\ce{H2O2 +2H+ +2e- -> 2H2O} \ \ \ \ E^ \circ =  +1.78 \text{ V}$
Overall: $\ce{3H2O2 + Cl- -> 3H2O + ClO3-}\ \ \ \ E^ \circ =  -1.07 \text{ V}$

This reaction is not spontaneous. Peroxide cannot oxidize chloride, at least not to the chlorate ion. Note that peroxide can and does oxidize chloride to poisonous chlorine gas in the presence of acid. This redox is spontaneous and will happen.  Do not attempt!

Reduction:   $\ce{H2O2 +2H+ +2e- -> 2H2O} \ \ \ \ E^ \circ =  +1.78
   \text{ V}$
Oxidation:   $\ce{2Cl- + 2e- -> Cl2} \ \ \ \ E^ \circ =
   -1.36 \text{ V}$
Overall: $\ce{ 2Cl- + H2O2 + 2H+ -> Cl2 + 2H2O} \ \ \ \ E^ \circ =  +0.42 \text{ V}$

Peroxide will oxidize chlorine gas to chlorate, but who wants to handle chlorine?
Answer: Potassium chlorate ($\ce{KClO3}$) has covalent bonds between the chloride and the oxygen, while potassium chloride ($\ce{KCl}$) lacks those covalent bonds to oxygen.
Hydrogen peroxide decomposes into water ($\ce{H2O}$) and oxygen gas ($\ce{O2}$) while oxidizing (LEO: Loss of Electrons is Oxidation) its environment. Peroxide is useful primarily for sucking electrons from a solution, which is very different from forming covalent bonds.
If you wished to dissolve solid potassium in water to make KOH peroxide would likely perform nicely as the peroxide would suck electrons from the solid K and thereby help it form ions ($\ce{K+}$) which would combine with $\ce{OH-}$ from the water to from KOH.
Comment: http://chemistry.stackexchange.com/questions/843/what-role-does-hooh-have-in-copper-ii-acetate-formation
Comment: http://chemistry.stackexchange.com/questions/87/how-may-copper-acetate-ligands-be-manipulated-to-change-colors
Comment: My mistake, I was unclear. Why doesn't the oxygen react with the chloride ion?


Increase size of partition on live production server (VMWare - Ubuntu 16.04 headless)

Question: I have come to a point with our production server that I am going to have to increase the size of the drive in the coming weeks.  The problem is such that, this server really can't go down for an extended period of time, though reboots and 5-10 minute fixes are acceptable during "regular maintenance periods".
I have increased the drive size from 128GB to 256GB on the VMWare side, but as expected the volume in Ubuntu remains.  My question is, is there a way to increase the volume size to get sda3 to "soak up" all the free space while the server is running?  I fear my problem is that I have a swap partition at the end of the drive currently, so this will have to be moved/removed.
I have viewed How to resize partitions? but it doesn't address the "hot add" concern (directly).
I have viewed   how to use the free space after increasing the size of the disk on VMWare Workstation but the only answer is ambiguous and does not address my concerns about "hot" adding free space to the partition.
Here is my setup:
parted -l
Model: VMware Virtual disk (scsi)
Disk /dev/sda: 275GB
Sector size (logical/physical): 512B/512B
Partition Table: msdos
Disk Flags:

Number  Start   End     Size    Type      File system     Flags
 1      1049kB  1000MB  999MB   primary   ext2            boot
 3      1000MB  122GB   121GB   primary   ext4
 2      122GB   134GB   12.0GB  extended
 5      122GB   134GB   12.0GB  logical   linux-swap(v1)

fdisk -l
Disk /dev/sda: 256 GiB, 274877906944 bytes, 536870912 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0xc95a459a

Device     Boot     Start       End   Sectors   Size Id Type
/dev/sda1  *         2048   1953791   1951744   953M 83 Linux
/dev/sda2       238706686 262141951  23435266  11.2G  5 Extended
/dev/sda3         1953792 238704639 236750848 112.9G 83 Linux
/dev/sda5       238706688 262141951  23435264  11.2G 82 Linux swap / Solaris

Partition table entries are not in disk order.

I fear my only recourse at this point is shutting down the server, booting from an ISO, and resizing that way ..  OR just spinning up another server and copying everything over onto the new, larger, server.  Can this be done reasonably in a production environment?
Answer: Yes, after deleting the swap and extended, you can resize the partition easily with any partitioning tool.  Some partitioning tools, like gparted, will also automatically (if the resize2fs program is present) resize the filesystem on the expanded partition. Other partitioning tools, you will have to do it yourself manually.  With the space now available, you can follow your procedure to increase the size of the virtual vmware.
  Backup everything first of course, just in case, and check how much swap you normally use, since if you are using swap, you will need to deal with that problem.


Examples of random deployment in wireless sensors networks

Question: I have been doing some research and have found a lot of papers on the subject of random deployment in wireless sensor networks, but I haven't found a single example of its usage. Has it been used before? What could be a very concrete context in which it could be used?
Thanks in advance.
Answer: One scenario that I've heard discussed is the idea that an airplane flies over a remote area and drops wireless sensors.  They fall somewhat randomly, and then need to establish a network amongst themselves.


PRIOR ART REQUEST: US20150066784 "Automated Clickwrap and Browsewrap System"

Question: I would like some help finding prior art for US20150066784.
The patent describes a system focused on the browsewrap vs. clickwrap distinction when it comes to legal agreements, but the entire system seems like a industry best practice.
I view that the clickwrap implementation (a checkbox with the "I Agree" text) to make sure the user agrees to an agreement has already been best practice for a while now, popularized more and more since the Zappos lawsuit.
Even a system of tracking users to keep track who agreed to certain agreements has been best practice, though not popularized as much.
I currently found 2 examples of prior art, but it would be great to see if more prior art exists.
Examples of prior art (especially for for 1st and 6th claims):
1. A method for monitoring end-user viewing of agreements over a computer network
6. A method for monitoring end-user affirmative consent to agreements over a computer network
Hasn't this be already done by the Agreeable Records plugin for WordPress, first launched in Jan 2014 ?
Need to track when a user logs in and agrees to your terms? Agreeable Records tracks
the user's email and IP address with every login agreement, allowing you to keep
detailed records of a user's agreement to your terms & conditions. Requires Agreeable
plugin.

The plugin is specifically built for this, but many other form plugins for WordPress allow developers to add the "I Agree" checkbox on their web forms:

the Contact Form 7 plugin and its ability to add checkbox for agreements acceptance, first mentioned in 2012.

PrivacyCheq and its Cliqwrap system is being described similarly:
CliqWrap stores user acceptance of your TOS / EULA, allowing new games to bypass
requesting duplicate approvals. When your legal agreements change, one button resets
approvals so all users will see the new terms at next login.

The WP E-Signature plugin for WordPress seems similar to this (a public mention of launch was in May 2014, but the domain name was registered in 2010), including tracking users who agreed to specific agreements, but users agree to the agreement via their e-signature:

(source: approveme.me)
Comment: one need to also check out if agreements are user specific.
Comment: @Pushpak Could something like [WP Digital e-Signature](https://www.approveme.me/wp-digital-signature-plugin-docs/article/wp-digital-e-signature-active-campaign-email-automation/) be considered prior art in regards to this? It's more focused on e-signature, but the web forms are still implemented using clickwrap implementation and they agree to a specific agreement (NDA, etc.)
Comment: In order to get the best help from the community, it would help to have a date so that we know when "prior" is.
Comment: @McKay Good point, thanks. Updated with what I could find.
Comment: Out of curiosity, what's the goal behind finding prior art for this patent?
Comment: Can we all agree not to call applications patents? This is an application, not a patent. It may never become a patent and if it does, its claims are likely to change. I'm all for finding prior art for over broad applications, but using the term patent confuses people.
Comment: The application got a non final rejection, the claims will probably be narrowed in the response.
Answer: I found this, it's called End User License Agreement Detection and Monitoring, this is what the abstract says:

"An approach is provided for detecting and monitoring end user license
  agreement (EULA) compliance is provided. A request to access a
  executable software code is received from an end user. A EULA version
  corresponding to the requested executable software code is identified.
  A determination is made as to whether the end user has accepted the
  identified EULA. If the end user has not accepted the identified EULA,
  then an out of date EULA notification is sent to the end user, the
  EULA is sent to the end user requesting an acceptance to the EULA. A
  EULA response is received from the end user. If the end user accepts
  the EULA, then the end user is allowed access to the executable
  software code."

hope this helps! :)
Answer: Browsewrap Agreements: Register.com, Inc. v. Verio, Inc.; Tracy, James J.
Not an expert in electronic but Seems to be listing most of the contents with inference and observations. Probably teaching the same.
Are Browse-Wrap Agreements All They Are Wrapped Up To Be?


Referenceing dll's in an user directory fails in Visual Studio

Question: I have a c# solution with some projects. For the solution I have created a folder for extenal libs. I have copied some Telerik-dll's from the instalation to the libs folder.
Now my problem:
When I add the dll's to the projectes (I choose the copied dll's from the libs folder) Visual Studio takes always the dll's of the installation source and not the dll's of my libs folder.
How can I fix this? I'm afraid that my colleagues could not compile the solution because the dll's are referenced to a missing directory (would happen if they don't have installed the correct Telerik version).
Thanks
Edit:
For example:
I reference with the file chooser
"C:\vendors\Libs\Telerik.Windows.Controls.Input.dll"
Visual Studio references
"C:\Program Files (x86)\Telerik\RadControls for Silverlight Q2 2011\Binaries\Silverlight\Telerik.Windows.Controls.Input.dll"
Answer: Properties of the references - set Embed Interop Type to false and set Copy Local to true
Comment: I am not sure if that is the answer of my question. I have added an example.


Is it correct to use 'Forgot password' or 'Forgotten password'

Question: Many websites use the phrase 'Forgot password?' when prompting users to renew their login passwords. Is this correct usage or should it be 'Forgotten password?'.
Comment: Whenever I see 'Forgot password?' on a website I always answer in my head: "No, I have not forgot my password, I have forgotten my password"
Comment: It doesn't need to be fixed and, in fact, is better than *forgotten password*, which reads as an adj + noun phrase instead of a question.
Comment: But can't that be fixed? `Forgot your password?` and `Have you forgotten your password?`
Answer: Awesome question.

Forgot password?

This is short for "You forgot your password?" which is simple past which specifies something that happened at a specific time in the past, namely, right when you came to the site, it was then that you "realized you forgot your password".

Forgotten password?

This is short for "Have you forgotten your password?" which is present perfect which means starting at some point in the past and continuing up to and including the present.
So technically the second is correct if you are describing the psychological act of forgetting. But it sounds odd since the question is really asking, "Did you just try to remember your password and you forgot it at that moment?"
So my vote is for "Forgot your password?
Comment: "Our" sounds patronizing to me. Unless it's a typo; my vote would go to "Forgot your password?".
Comment: @Thomas – The whole "Forgot your password?" thing is patronizing; might as well go whole hog and have something like "Oh dear, have we forgotten our password?" pop up after a failed authentication attempt.
Comment: @JamesWaldby-jwpat7 I disagree that "Forgot your password?" is patronising. But perhaps that's a BrE-AmE difference. The tone in which it is said would make a difference though. Either way it's certainly more informal.
Answer: The past participle of to forget is forgotten or forgot, in the same way the past participle of to get is gotten or got.
In my experience, forgotten as in forgotten password is seen as an adjective; Forgot password? is understood as Have you forgot your password?
Comment: Yep. *Forgotten password* + link reads as "click here to see a forgotten password". The other way is much better.
Answer: Both are acceptable depending on the context.
"Forgot password" could simply be an informal (shortened) way of saying "I forgot my password." We commonly miss out pronouns to be succinct. In this case, the words form a statement.
Similarly, "Forgot password" could be a shortened form of the question "Have you forgotten your password?".
"Forgotten password" uses the gerundive (Attributive Verb), and thus is also perfectly fine, in that the page is directing the user to their forgotten password. Here, the words form a noun phrase.
Comment: Arigatou for the explanation Noldorin :)
Comment: @shramee No problem. :)
Answer: It is not wrong to use "Forgot Password" but there must be a question mark at the end. So the correct form is one of the following.

Forgot password?

Forgot your password?

Google, for example, does it correctly.
Answer: Yep! By itself, without other context, ("forgotten password"), I'd be reading "forgotten" as a participle (a verb form used as an adjective, describing the noun "password").  reference: more participle info.
In a different context ("Have you forgotten your password?"), the same word becomes part of the verb phrase ("have forgotten"), which tells what the "you" did.  No longer does it describe "password"; now "Have...forgotten" is the verb (what you did), and "password" is the direct object of that verb (the thing you forgot). reference: more direct object info.


Minecraft on Cairo Dock Opens Another Instance

Question: So i "installed" Minecraft using this video http://www.youtube.com/watch?v=NZIbcWpdSA4 and put it on my cairo dock. However whenever I open it, it opens another instance of the icon. Is there any way to fix this?
Comment: This is 100% speculation, but my knee-jerk reaction for doesn't work on Ubuntu/Cairo/Unity is software shouldn't use Java.
Comment: so you are saying there is no way to get a .java on cairo to not open a new instance?
Comment: It's probably related to how the cairo and unity docks detect that an app is running (like they find "java" as opposed to "someJavaApp.jar")
Answer: Old question but the issue is still there. The solution is simple. Follow these steps.

Open the application that creates an additional icon in the dock, minecraft in this case.
Make sure if is not hidden behind any other windows since you're going to have to click on it.
Right click on the minecraft icon in cairo dock, and select "edit"
Expand "Extra Parameters"
Click "Grab" button to turn your cursor into crosshairs
Click on minecraft window. This should put minecraft application class beside the "grab" button and eliminate that duplicate icon right away.
Click Apply -> Close

Hope it helps someone.


Formal models of rigid discs of any radii

Question: sorry if this is a too vague. For $K$ some non-archimedean discretely valued field the rigid disc of radius 1 $\mathrm{Sp} \, K\langle T \rangle$ has a formal model $\mathrm{Spf} \, K^{\circ} \{T\}$. I just read a bit about Berkovich spaces and his theory allows discs of any radius $r$: $K\langle r^{-1} T \rangle$. Is there some theory of "formal models" in this context?
Comment: @PiotrAchinger: If you want your theory to allow extensions of scalars, you'd better not identify $\{|T|\le r\}$ with $\{|T|< r\}$. Otherwise, after base changing to a field $L$ with $r\in|L^*|$ (which exists) and changing the variable, you will identify $\{|T'|\le 1\}$ with $\{|T'|< 1\}$.
Comment: Potentially related: M. Temkin "On local properties of non-Archimedean analytic spaces. II." Israel J. Math. 140 (2004), 1–27. From the MR by Grosse-Klönne: "The key discovery is an efficient notion of reduction for general k-analytic spaces. For example, the reduction algebra $\tilde A$ of an algebra $A$ as above is defined here as the $\mathbf{R}_+^\times$-graded algebra associated to the spectral seminorm filtration on $A$. " Link: https://mathscinet.ams.org/mathscinet-getitem?mr=2054837
Comment: Also, I don't know if for $r\notin |\overline{K}^\times|$ it is safe to identify the closed disc $\{|T|\leq r\}$ with the open disc $\{|T|<r\}$ (I guess not, since the former should be qc). But of course $\{|T|<r\}$, being quasi-paracompact, admits a (somewhat complicated) formal model.
Comment: Thanks Piotr! I wasn't aware of Temkin's 2. paper of this name. I will check it out.
Answer: Not really an answer as I am not familiar with Berkovich stuff.
But, ... in classical rigid geometry, one also has a disc of any rational radius $r$. If $r=\frac{a}{b}$ and $\pi$ is a uniformizer of $\mathcal{O}_K=K^{\circ}$, then $\textrm{Spf}(K^{\circ}\{T, U\}/(T^b-\pi^{a}U))$ is a formal model (Raynaud style) of the subdisc $K\langle r^{-1}T\rangle$. However, it may not be as nice as you may want. For example, its special fiber is not reduced. It becomes so after a sufficiently large extension of $K$.
Since the formal models are basically the same in both theories, the discs in Berkovich with radii in $|K|$ should have these kinds of models.
Comment: The "sufficiently large extension" in this case is simply $K(\sqrt[b]{\pi})$.
Comment: Thank you. I know about this formal model, but as you said it's much less nice than I would like it to be. E.g. $\mathrm{Spf} K^{\circ} \{T,U\}/(T^b-\pi^aU) \rightarrow \mathrm{Spf} K^{\circ} \{T\}$  is not an open immersion etc...
Answer: The formal models used in Berkovich geometry are the same that are used in rigid geometry. In particular, their generic fibers are built from spectra of quotients of Tate algebras of the form $K\langle T_1,\dotsc,T_n\rangle$, called strictly $K$-affinoid in Berkovich's terminology.
To answer your question, one checks that, for $r\in\mathbf{R}_{>0}$, the algebra $K\langle r^{-1}T\rangle$ is strictly $K$-affinoid if, and only if, $r\in \lvert K^*\rvert^\mathbf{Q}$. (For the if direction, use the trick in A.B.'s answer. For the only if direction, use that the supremum of a function on a strictly $K$-affinoid space belongs to $\lvert K^*\rvert^\mathbf{Q}$.) So, you will not get any formal model for $K\langle r^{-1}T\rangle$ if $r\notin \lvert K^*\rvert^\mathbf{Q}$.
On the other hand, as pointed out by Piotr Achinger in his comments, Michael Temkin worked out a theory of reduction for all $K$-affinoids, strict or not. It has properties very similar to the usual reduction of affinoids, with objects only slightly more complicated, actually graded versions of the usual objects. For $r\notin \lvert K^*\rvert^\mathbf{Q}$, the reduction of $K\langle r^{-1}T\rangle$ is $\tilde{K}[r^{-1}\tilde{T}]$, where the notation means that $\tilde{T}$ has degree (with respect to the graduation) $r$. It follows that $\tilde{K}[r^{-1}\tilde{T}]$ has few homogeneous elements, only the monomials. As a result, its graded spectrum, which is Temkin's reduction of $K\langle r^{-1}T\rangle$, has only two points: the generic point $(0)$ and the closed point $(\tilde T)$.


Security measures for Thunderbird and Pidgin

Question: I want to install Thunderbird and Pidgin. Is it safe to give passwords in these applications. Please tell me what security measures should be taken while using these kinds of applications.
Answer: Thunderbird can encrypt your password if you set a master password.
Please read for more details: https://support.mozillamessaging.com/en-US/kb/master-password


How to differentiate between a singular noun's possession and its plural one in spoken English

Question: In spoken English if for example:
someone says "cars tires" then how to know if the speaker is talking about car's tires or cars' tires. Because the pronunciation is same for both.
Answer: There is no way to tell. You have to determine it from context (were we previously talking about one car or several cars?). If you are speaking and want to make it clear you could say something like "the tires of all the cars" or "the blue car's tires" (in the case where there's only one blue car we might be talking about) .
Comment: Perhaps a better example would be "the tires of the blue car"
Comment: @jonathanjo that sentence doesn't have any ownership apostaphies in it, the "tires" can only mean plural. And we usually say tyres are ON cars unless they are stacked in a pile in the corner. "what them? they are the tyres from the vauxhall"
Comment: @WendyG, not using the apostrophe is part of why it avoids the ambiguity that was asked about.

How to differentiate between a singular noun’s possession and its plural one in spoken English


Display custom field values from posts on frontpage

Question: How can I pull a custom field with meta_key "proprty_feature" (and has a value) for all posts and display them on my frontpage? Would like to display the post name as a link above the value..
Answer: Within your main post loop you would add something like,
get_post_meta($post->ID, 'property_feature', true);

A basic example of what your main loop might look like ( it depends on your theme) to include a title and your custom field.
//start the loop
<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>

//add post link and title
<a href="<?php the_permalink() ?>" rel="bookmark" title="Link to <?php the_title_attribute(); ?>"><?php the_title(); ?>

//add your custom meta value
<?php echo get_post_meta($post->ID, 'property_feature', true) ?>

//close loop
<?php endwhile; else: ?>

Comment: I apologize..I'm not sure if I'm following you..this will display a list of posts along with a corresponding custom field? So I can just put this in index.php?
Comment: Yes but I provided the example only to show you where it fits in. The loop example is extremely basic and very likely your theme has more styling and options. The important bit of code you need is the get_post_meta which as it sounds gets your post meta box based in name or key and returns the value.


How can I have attributes that get extracted for i18n in ZPT macros?

Question: I'm using Pyramid with ZPT templates to make a web app. I'm attempting to make a form template macro library to make life easier for things like setting current values of form fields, etc. I'm also using the lingua message extractors to automatically pick up strings for localization. I can't figure out how to make the extractors work with attributes on macro tags though. For example, say I have a macro that looks like this:
<tal:block metal:define-macro="text">
    <input type="text" name="${field}" value="${request.params.get(field) or default_value}"/>
</tal:block>

And I use it in a page template like this:
<tal:block tal:define="field 'fred'; default_value _('initial value')" metal:use-macro="form.macros['text']"/>

The text "initial value" won't get picked up by the message extractor. Is there a way to make this happen? I'd like to keep the strings inside the template if possible, I know I could work around this by having all the strings for default values generated in the view callable. Maybe there is there a better way of passing values to macros for use in attributes?
Answer: You need to use [lingua] to version 2 (or later) to extract messages from templates for this to work.


How to set the clock in a Honda City 2018

Question: I've done it once before (last daylight saving change) but even with the owner's manual I can't work out how to set the clock. I've tried with both the car on and just in accessory position but following the instructions only reset the trip meters. What am I missing?
Answer:
Start with the key out of the ignition
Insert the key into the ignition
Turn the key two clicks to "On" (not "Start")
Using the Up/Down controls on the steering wheel, select "Settings" on the dashboard display

If all has gone well, you'll see "Adjust alert"
If something went wrong, you'll see two speed alert settings. Start again by removing the key from the ignition

Use Up/Down until you see "Adjust Clock"
Press the Select button (between Up and Down)
Adjust the hours with Up/Down/Select
Adjust the minutes with Up/Down/Select


What gift does Clarke give his boss, Mr. Shirley in Nation Lampoons Christmas Vacation?

Question: In the movie, Clarke gives a gift to his boss and all of the boxes are the exact same shape. Is it everyone hinted/explained what the gift was? And why they were all the same?
Answer: According to IMDB trivia, the gift was a desk organizer. To explain why, see this question and answer However, a desk organizer is still speculation as it isn't revealed in the movie. It may be somewhere in the script, though.

All the presents that were on the credenza when Clark went in to give
  his to Mr. Shirley are identically shaped, and likely the same gift.
  It is a desk organizer. When this movie came out, pen sets came in an
  L-shaped arrangement. The writing instruments were on the flat part,
  and the raised section held Post-It notes. Paper clips and other
  holders were also a possibility.

Source


What's the meaning of 구 in the word 구남친?

Question: I can't find where the syllabus 구 comes from. What does 구 mean?
Comment: It means "ex-."
Answer: As @user2326230 said, '구' in the '구남친' means old or ex-.
This 구 is written as 舊 in Chinese. https://hanja.dict.naver.com/#/entry/ccko/cf039f0ab84541778e6a31794fb76889
新 has the opposite meaning 'new'. Thus 구 and 신 are often used together as a single word '신구(新舊)' meaning old and new as in a phrase 新舊交代 (Exchange between the old and the new).
Comment: That answer has already been given.
Comment: @Chenmunka I partially disagree. I wanted add some extra information.
Answer: As user13229973 mentioned, '구' means 'old' or 'past'. '구' or '전' 남친 can be translated to 'ex-boyfriend'.
But, I'm not sure if this is what the originator wants.
There would be more accurate answer if a sample sentence be provided.

What’s the meaning of 구 in the word 구남친?


Nomenclature priority of prefixes consisting of identical letters but containing different locants

Question:
I have no idea how to name this compound. Can someone please help give the IUPAC name for this? Also mention the IUPAC nomenclature rules followed while naming.
Answer: The compound that is given in the question consists of a cyclohexane ring with two substituent groups: 1-chloroethyl and 2-chloroethyl.
The correct numbering of locants is stipulated by Rule 14.4 in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book):

P-14.4 NUMBERING
  When several structural features appear in cyclic and acyclic compounds, low locants
  are assigned to them in the following decreasing order of seniority:
  (…)

However, the given case is not explicitly mentioned in this rule.
The correct numbering is actually indirectly given by Rule 14.4 (g):

(g) lowest locants for the substituent cited first as a prefix in the name;

Since the correct order of citation as a prefix in the name is given by Rule P-14.5.4:

P-14.5.4 When two or more prefixes consist of identical Roman letters, priority for order of citation is given to the group that contains the lowest locant(s) at the first point of difference.

Thus, '1-chloroethyl' is cited before '2-chloroethyl' in the name, and thus a low locant is assigned first to the 1-chloroethyl group.
Therefore, the complete name for the compound that is given in the question is 1-(1-chloroethyl)-4-(2-chloroethyl)cyclohexane.
Comment: Shouldn't one of the aliphatic chains be the main chain because they have the chloro functional group?


How do I get SMS messages to be sorted in chronological order?

Question: I just got an HTC Desire HD, and it's sorting my SMS texts by what the sender has sent up at the top of the conversation page, and what I reply down below. It's almost like two conversations in chronological order, but it's not mixing them together. When it says I have a new text, it's actually the one I sent them and I have to scroll up to read the reply. How do I get the the SMS conversations to read in an answer-response chronological format?
Comment: This sounds weird. On HTC the default message app does exactly what you want. You sure you are not using a replacement?
Answer: I don't know how your stock messaging app works, but HandcentSMS does this exact thing, and very well at that!


What does a router do with a packet if it can't find the destination IP address in its routing table?

Question: If a router receives an ARP request in which the destination hardware address is a broadcast address, and if the destination IP address is an address that the router cannot find in its routing table. What will the router do in that situation? Is it going to cache pair IP/hardware source address and send ICMP message "Destination network unreachable" back to the source?
Comment: ARP requests are broadcasts, and routers do not forward broadcasts. Unless the request is for the host (including a router), an ARP request will be dropped by the host, and the host doers nothing else..
Comment: On a LAN, hosts communicate directly. Routers route packets between different networks. A host will use ARP to get the MAC address of a router if it needs to send traffic to a different network, but ARP is only for traffic on the same network.
Comment: @RonMaupin So the router in this situation does nothing ?
Comment: Router do nothing .. it will just drops the packet if destination ip is not found in routing table..
Comment: Did any answer help you? if so, you should accept the answer so that the question does not keep popping up forever, looking for an answer. Alternatively, you could post and accept your own answer.
Answer: ARP is a layer-2 thing -- it's how layer-2 address (MAC) is associated with a layer-3 address (IPv4). The router (any node) will only respond to ARP requests for addresses it owns -- the addresses assigned to it's interface(s) or aliases. It will silently ignore all others.
If your router is setup to handle the ancient bad idea of proxy-arp, then yes, it will respond to any request for which it is capable of reaching. So if there's a route to the requested address -- include a default route, it will answer with it's MAC, otherwise the request is ignored. If you have two proxy-arp'ing routers, one with a route, one without, both will see the request, but only the one with a route will answer.
If nothing answers the ARP request, the requesting node itself will generate a "host unreachable" error.
Answer:
What does a router do with a packet if it can't find the destination IP address in its routing table?

If a router has no route to the destination IP, it drops the packet and returns an ICMP Destination unreachable message to the source IP.

If a router receives an ARP request in which the destination hardware address is a broadcast address, and if the destination IP address is an address that the router cannot find in its routing table.

The router only anwers ARP requests for one of its own IP addresses. All other requests are ignored. Whether is knows a route to the ARPed IP address or not doesn't matter. (As @Ricky has already explained very well, including the obsolete proxy-ARP bit.)


Do chemical engineers play a significant role in space exploration?

Question: I am going to be beginning a degree in chemical engineering next year and also have a significant interest in space travel. I was wondering how much of a role chemical engineers play in space exploration. I understand there is a strong need for fuels and heat resistant materials and so forth, but how significant is this? Is there any significant  need for chemical engineers in the space industry? And if so, in what section are they most likely to be working?
Comment: Figuring out how to make rocket structures out of carbon fiber. Or perfecting paraffin-based hybrid rocket stages. Working out how to process ores in space, or manufacture fuels. Designing better radiation shielding. I bet there isn't any aspect of space exploration a sharp chemical engineer couldn't come up with a valuable angle on.
Comment: Read [John D. Clark's *Ignition!*](http://library.sciencemadness.org/library/books/ignition.pdf) An excellent history of rocket propellant research, a good read, and the author often has a wicked sense of humor.
Comment: @JerardPuckett That looks very interesting but is apparently very heavy on chemistry. Would someone with only an (advanced) understanding of high school level chemistry enjoy it as much?
Comment: If you're looking for perspective on the field, yes.
Comment: http://www.lpi.usra.edu/publications/books/lunar_bases/LSBchapter07.pdf
Answer: I would say chemical engineers play less of a role in space exploration than aero/astro, mechanical, software, and electrical engineers. I'll try to back this up with evidence before I share my anecdote.
According to the Bureau of Labor Statistics, most chemical engineers work in manufacturing (of chemicals). Designing new chemical products (like fuels or composite materials) is more of a scientist's role rather than an engineer's and typically requires a master's degree or PhD.
A typical chemical engineer in a non-research role (so probably with a bachelor's degree) works as a process engineer. A process engineer is usually tasked with profitably mass producing a product. That entails using thermodynamics, fluid mechanics, heat/mass transfer, and chemical kinetics to design, optimize, and operate a chemical plant or refinery. Aerospace engineers, however, largely go into the space industry since they've specialized in things like aerodynamic fluid flow; structural design; guidance, navigation, and control; instrumentation and communication; robotics; and propulsion and combustion.
I certainly wouldn't say it will be impossible for you to get a job in the space industry with a background in chemical engineering. You can do anything if you work hard and focus on developing the right skills. I do think majoring in something that is already more common in the space industry will increase your chances of getting a job right out of school.
I've gone down a career path similar to the one you're considering. I majored in chemical engineering for my BS, but I really want my career to have something to do with advancing space exploration. This has proven difficult so far. Since I haven't yet successfully switched to the space industry, I'm trying to develop skills relevant to space companies (CFD, propulsion knowledge) and working toward an MS in aero/astro engineering. I'm sure I'll make the transition eventually, but I think if space exploration is really what you want to do, you might save some time and effort focusing on the right things earlier than I did.
Answer: Yes a chemical engineer is a huge asset in space exploration. Anyone who says otherwise doesn't actually know what a chemical engineer learns.
Chemical engineers are essentially mechanical engineers with a deep understanding of chemistry (reactions, gases, liquids, solids, energy & mass transfer).
For some reason people see the description "chemical engineer" and they assume a chemical engineer only understands chemistry, when in reality a chemical engineer learns not only learns mechanical engineering, control systems engineering and chemical physics (energy, matter and space) but also how to combine all fields together.
Some examples of where chemical engineers are required:

Life support systems (oxygen, water CO2 scrubbers, etc).
Waste treatment systems.
Control systems (process control engineer & APC engineers)
Understanding the environment due to the composition of elements and chemicals present.
How to use resources from different environments and convert them into usable processes, energy or materials.
Energy generation from available materials present.
Deep understanding of all the light and radiation in space (radiation chemistry/photochemistry/etc).
Material selection in space (huge specialisation as a chemical engineer).
etc..

These are all areas that chemical engineers are experts in.  Its unlikely a mechanical engineer or aerospace engineer would have much training in these areas.
How do I know this?  I am a chemical engineer, I deal with most of the things I mentioned above and regularly have mechanical and electrical engineers come to be for help and guidance in these areas.
Comment: On the other hand, what you can do is less important than what the hiring manager thinks you can do. Or how well the hiring manager understands your training relative to the usual people he would hire. A chemical engineer who was hired as a chemical engineer and then demonstrated all these competencies to his colleagues is in a different situation than a new grad with a degree in chemical engineering applying to a position that does not call for a chemical engineer.


How will Big O be with quantum computers?

Question: I don't even know if this is the right place to ask this this...but how will Big O be with quantum computers? More specifically, will the worst case always be constant? If yes, how will this change our understanding of current algorithms? For example, will this mean that the difference between an algorithm running at Big O(2^n) and another running at Big O(n^2) in traditional computers be insignificant in a quantum computer? Would time complexity even be an issue with quantum computers? This might have a very obvious answer but I don't know the answer (and I'm really am curious).
Answer: Big-O has nothing to do with quantum computers. This should be obvious by the fact that Big-O notation was introduced in 1894, long before we had any knowledge of quantum theory … or computers for that matter.
Big-O is simply a convenient notation for classifying growth rates of functions. Big-O doesn't care how you interpret those functions.
So, the definition of Big-O will not change for quantum computers for the simple reason that its definition has nothing to do with computers.


$100-$200 monitor with displayport daisy chaining

Question: I don't need a super fancy monitor, but I would like it to support displayport daisy chaining. All the monitors I can find with this feature are >$300
Answer: I have a Dell U2417H that supports DP daisy chaining.  You can find used monitors on eBay for ~$120.  Besides supporting DP daisy changing it is a very good monitor.  The picture quality is great and it even has a built in USB 3.0 hub for easy access to your USB ports.
Comment: haha, that is almost exactly the monitor I'm borrowing that led me to ask this question (I have the U2419H) and I agree it's pretty great. Thanks for the Ebay suggestion, I'll check it out!
Comment: Sure enough! There were used but otherwise complete and working U2417Hs on ebay for $94 (under 1/3rd of the new price!). I got two of them for 70% of what a single new one would cost. Absolute steal. Thanks again for the suggestion!
Comment: No problem! Glad you found what you needed :)


Protect previous migrated field values on system of record migration

Question: I have a successful migration of content type A, B and C. In the migration of C, I have entity reference fields that get populated with the correct values coming from migration A and B.
My reference fields is a multi value node entity reference field. To prevent the values being over ridden from my previous migrations, I use the system of record method.
https://www.drupal.org/node/1117454
https://www.drupal.org/node/2550939
The example is very specific to a commerce migration.
<code>// If "updating" a product, protect these fields.
        // We know its updating if the product exists in the database with the sku.
        // Migrate updates by deleting an entire entity and replacing with
        // the new one. We circumvent the removal of the values of these
        // fields by pulling them and overriding the defaults provided
        // in the mapping.
        // You could do the same with a nid id found with a title, or something similar.
        // $row->migrate_map_sourceid1 is usually the entity id you're looking for,
        // our example here uses a commerce_product and loads it with the provided sku
        if ($product = commerce_product_load_by_sku($row->sku)) {
            // Use the metatdata wrapper to pull values
            $product_wrapper = entity_metadata_wrapper('commerce_product', $product);

            // field_stock
            // Some products have a NULL stock, lets keep the zero default if NULL
            if ($product_wrapper->field_stock->value() !== NULL) {
                $row->stock = $product_wrapper->field_stock->value();
            } else { $row->stock = 0; }

            // field_max
            $row->max = $product_wrapper->field_max->value();
        }
</code>
I am not sure how I would use my prepare row, current content types, their ids etc to remove the current values, update the new values, and then add the previous ones again? Or am I misunderstanding how this is suppose to work? Thanks in advance!
Answer: My solution was to use the prepare($node, stdClass $row). This basically takes the current values and joins them to the new ones.
https://www.drupal.org/node/1222668#comment-4795190


When do the player data files update in Minecraft SMP servers?

Question: I'd like to know exactly when the <playername>.dat files are saved on the server. (I'd like to run a script that tracks the players' locations and inventories, and this is crucial to whether this script will work or not.)
Answer: I decompiled the Minecraft server version 1.2.5 using the Minecraft Coder Pack and quickly stumbled through the code:
The players inventory and location gets saved into the <playername>.dat when:

The server stops
The player disconnects

So one possible way to go if you wanted to keep track of your players locations and inventories would be to use an event-based plugin wrapper such as Bukkit and write a plugin which does whatever you want with the players information as soon as he disconnects (or at any other time).
If you cannot or do not want to use Bukkit, you could possibly try to monitor file updates with a third-party software.
Comment: The script runs every few minutes and it logs the data from the .dat files... The whole idea is to see what the player is doing while they are online, so I'd need something that makes the server update the files regularly... Thanks for the input.
Comment: You're welcome. The server by itself will not update the files more reqularly, your only way here would be using some sort of modification to the server, either using a wrapper such as Bukkit, or to change the source-code yourself.


how can i get the reply of text message on some perticular number with info using nexmo api

Question: I am using the nexmo api for send text message.Now my requirement is like when i will send the message to somebody then it will reply on some perticular number like XXXX.So i can run some api for checking anybody have make response with some information like userid,message time and other custome parameter.I have refer this link
  [1]: https://docs.nexmo.com/ but i have not get any shortcode on which i can get reply of message.So anybody have idea how can i fulfill my requirement?Or does nexmo provide the shortcode?
Thanks in advance.
[nexmo document][1]
Answer: You can purchase a virtual number from Nexmo, and use that to collect replies. Just use that number as the from when sending outbound messages.
Here are the Nexmo docs on inbound messages.
[Disclaimer: I work for Nexmo.]


May I post a question about commissioning and finding someone to build a custom keyboard here?

Question: May I ask this at Hardware beta?

How do I commission and find someone to build a custom keyboard?

See Need light touch keyboard for neuro problems
Also, may I not set a bounty on this site?
Comment: I'm kinda mixed on this, I do know there's folks who will build 'custom' keyboards, and there's folks who literally build bespoke input devices - slaw device comes to mind. I also feel like you need to talk to folks who know keyboards to get a better idea of the problem space and budget. You might be able to 'simply' buy a keyboard with replacable key switches and slowly swap out switches to your liking, which is a broader problem scope
Comment: https://chat.stackexchange.com/transcript/message/62681112#62681112 bit of a conversation on the topic. I'm a bit of a keyboard nerd, though not 'obsessive' so I might be able to give basic information on the problem domain :D
Answer: It's my understanding based on the Help Center that:

we can help for recommendations of single, specific components

... and from the on-topic page that:

your question should be:

a request for a product recommendation
a request for information that will lead to a product decision

... which I would interpret to be just short of "How do I commission and find someone to...", so I think the answer here would be: no.
Re: your question on bounties, You cannot create bounties on per-site metas, if you're asking about bountying a question here on the Meta site. If you're unable to start a bounty on the main site, it might be worth opening a separate support question for that, as my interpretation of the Help Center is that you'd need a minimum of 75 reputation for the bounty privilege -- which you have at the moment. There are some other criteria listed in the What is a bounty? Help Center article, such as:

To avoid overly promotional bounties, if you are offering a bounty on a question that you have already posted an answer to, your minimum spend is 100 reputation (not 50).

... which would theoretically take you below the 75 reputation threshold after you set the bounty, but that shouldn't prevent you from creating that bounty. If you're having this problem (placing a bounty on the Main site), please open a separate Meta question so that we can dig into the details.


Important (interesting) unsolved problems

Question: I think it would be interesting to have a list of important unsolved problems in mathematics.
What are the important (interesting) problems in your field of work? It would be especially nice, to have a list of "non-mainstream-problems" in the miscellaneous areas of mathematics.
Comment: There are already at least two good resources for this: Wikipedia and the open problem garden.  I think we're straying into encyclopedia territory here.
Comment: Let's not delete this, but it's possible we should close it. Please have a look at the discussion at http://tea.mathoverflow.net/discussion/8/are-open-questions-acceptable-how-should-they-be-treated/#Item_0 about open questions. I don't think this question is good, as asked -- it would be better to be more specific, and ask about important unsolved problems in particular fields. There are just way too many problems that fit the current criterion.

If anyone else agrees, let's close this one and try again with something more specific.
Comment: Does the Stack Overflow software give you some finite set of reasons for closure to choose among?  'Cause this isn't "not a real question"...
Comment: @Alex: yes. The options are "off topic", "exact duplicate", "subjective or argumentative", "spam", "blatently offensive", "no longer relevant", and "too localized". Which would you have picked?
Comment: Thanks for pointing that out. Do you think, i should delete this question?
Comment: @Scott: I agree. This is too broad to be useful.
Answer: The big open problem around where I work (D-modules) is the Jacobian Conjecture.  This states that if you have an algebraic map f from C^n to C^n whose jacobian determinant is a non-zero constant, then f has an inverse.
The reason its related to D-modules is because is equivalent to Dixmier's conjecture, which states that every non-zero endomorphism of a Weyl algebra (the ring of polynomial differential operators in n variables) is an automorphism.
Its important to know about, not so that we can try to prove it, but so that we know what simple sounding things are hard.  Several times, I have played with a simple sounding proposition for an hour or two, before realizing that it is equivalent to Dixmier's conjecture.  Hence, I regard the conjecture as a "Here There Be Monsters" warning.
Answer: There's an excellent internet resource for exactly this question called the "Open Problem Garden" moderated by Matt DeVos and Robert Samal.  Currently it's got a bit of a graph theory/combinatorics bent, but it's well set up for people to post and read open questions in all subjects.
Comment: "a bit of a graph theory/combinatorics bent" is a bit of an understatement :-) There's 135 Graph Theory problems listed, more than Number Theory, Analysis, Algebra, Topology AND Combinatorics combined... Very interesting attempt though! I'll try to do my part to make it better.
Comment:  I just checked out the "Open Problem Garden" and I think the above comment is an understatement. I think that maybe this question is a valid one for MathOverFlow.
Answer: In some fields, like analytic number theory, new methods (and improvements in the known ones) are most important. For any particular open problem, and a powerful new method that solves it, there are usually several other open problems that also can be attacked by the new method. In such a situation it is hard to say that some particular one of those problems is peculiarly important. (Of course, analytic number theory does have a peculiarly important problem)


Hypothetically giant telescope

Question: As the James Webb telescope is getting ready for launch after years, I wonder in a purely hypothetical scenario, a telescope which is as huge as the diameter of Earth will make what kind of interesting observations possible. I am not asking about plain resolution improvements or the background math etc, but some examples which are actually the result of the known laws of physics to conceive what can be limits of what can be seen by telescopes, or if there is any limit at all if one aims to see farthest and faintest objects in the Universe.
Comment: Have you made any research (internet search) effort?
Comment: Diffraction limit of a telescope is the phrase you're looking for.
Comment: @YashasSamaga finally I found something
Comment: @KyleKanos good point. Helped me find relevant links.
Answer: The answer lies in the resolvable angle formula:
Angular resolution = 1.22 × Wavelength / D
D is the diameter of the apparatus. It also follows that by cleverly using an array of telescopes rather than one large telescope with the size of Earth, D can be effectively increased. In this regard, launching many telescopes in a solar orbit will be more practical.
Citing from a previous essay, seeing an alien creature with a comparable size to humans at 20 light years (the nearest candidate planet) will need an array with the diameter of 100 million kilometers with a cumulative mirror surface area of almost 1000x Earth surface. This way the alien will only map to a single pixel. Therefore, a direct observation of alien life outside the milky will be even more impractical using the available technology.

Hypothetically giant telescope


Where does the energy go if a ball hits the ground WITHOUT bouncing?

Question: so if a very un-bouncy object hits the floor and crashes into it rather than bouncing, where does most of the energy go? Does it simply turn into heat from friction? Or does it go into the Earth's movement by an imperceptible amount?
Comment: Possible duplicate of [if a body is stopped by means other than friction, where does energy go?](http://physics.stackexchange.com/q/205573/)
Comment: Mostly into deformation of the object, I'd say.
Answer: The energy has several options to get dissipated into:

Major part of it is turned into heat as a result of friction.
Some part gets transmitted into sound energy, causing the sound we hear when the object falls.
A very feeble amount gets transformed into light energy.
Another miniscule portion is utilised in deforming the object and thereby increasing the internal energy of the body.
Comment: I'm not sure I agree with the static friction part - the majority is dissipated as mechanical deformation (including _internal_ friction), some of which you get out as sound. I'm mainly questioning the 'static' part of your answer.
Comment: @JonCuster But if you look at it, it goes like this.... the ball falls, does not rebound, there is friction force between the ground-surface and the ball-surface and this friction cannot be overcome, so there is no movement of the ball. This friction is static friction, obviously. :-)
Comment: Well, but all the energy is lost to heat and deformation, not to static (non-moving) friction.
Comment: @JonCuster Okay, I have edited it. is it fine ?
Comment: I would say is not friction if there is no component tangential to the surfaces. If the ball does not bounce back it means it deformed beyond repair, like a clay ball would.
Answer: The majority of the energy is dissipated as mechanical deformation (as Jon Custer has stated).
Visualizing the situation can help a lot. All matter is somewhat elastic - there's no such thing as infinite elasticity. When an object collides with something, the force of the collision takes time to spread out across the object. Imagine a slow-motion view of crash-testing a car. It crumbles as it decelerates, and is unlikely to "bounce back," although this does happen with enough energy. A bean bag is also unlikely to bounce, as it is designed to deform and absorb the collision.
Hard objects are very likely to bounce because they don't deform as much (or as permanently). So instead, the waves that propagate through the object will be "corrected" and the matter will fall back into place. This causes the object to bounce, and produce an audible sound. The lack of deformation is what causes the bounce. This is why billiard balls bounce so well - if ceramic deforms, it breaks.
Heat is the final source of dissipation. Back to the car wreck  in slow motion, the bending metal will create measurable heat. Also the bean bag will produce heat with friction between the internal components. Do this sometime: get a piece of metal and bend it back and forth over and over. It will get hot. Same thing with a piece of plastic. The deformation directly causes heat to be produced.