Why does the salt in the oceans not sink to the bottom?

Question: This is something that just occurred to me. If heavier elements sink, then how can the entire ocean be salty? Shouldn't the 'salt', because of its density, all sink to the bottom of the ocean? In theory, only the deepest parts of the ocean should be salty, while the top of the ocean is not. Yet, the only water in the world that isn't salty comes from rain and rivers. How can this be?
Comment: Sometimes it does, in brine pools at the bottom of the ocean. Watch this eel risk its life exploring one: https://www.youtube.com/watch?v=ZwuVpNYrKPY
Comment: This question clearly has Earth Science-specific answers and should stay open here. *Voting to remain open!*
Comment: You will have better luck with this on the physics stack. This question is entirely about what a solution is.
Comment: @TomášZato Interestingly, there are brine pool loving bacteria living there - not sure what they get their energy from, but they may not reject a fish from time to time.
Comment: I wander if the ocean brine pools have any cool fossils in them. I suppose lot of fish may not survive venturing in one and end up being conserved by the salt forever.
Comment: This question inspired me to post a related question on Chemistry.SE: [Why doesn't the solute settle out of a solution, such as brine, sugar water, or air?](https://chemistry.stackexchange.com/questions/118418/why-doesnt-the-solute-settle-out-of-a-solution-such-as-brine-sugar-water-or)
Answer: When dissolved in water, salt breaks up into sodium and chlorine ions, which combine with water molecules so they cannot easily sink. However, there is a tendency for streams of fresh water to float on salt water and rise to the top. This caused problems for British submarines in the Dardanelles Straits during WW1. Moving from almost fresh water to the denser salt water, they suddenly became more buoyant and rose involuntarily to the surface, making them visible to Turkish gunners on the shore. There are also parts of the ocean where there are pools of very salty water lying on the bottom in such a way as to clearly show the pool to any diver who happens to see it, as though it were a pool on land, so in some circumstances very salty water can sink.
Comment: Note that those [brine pools](https://en.wikipedia.org/wiki/Brine_pool) that you refer to are not caused by salt solidifying out of seawater, but of salt coming up from the seabed.
Comment: But isn't this independent of whether it is salt? More like differences in concentration (different density) and temperature (different density)?
Comment: @PeterMortensen Yes, it works for any solute. Indeed, it's not like salty water is 100% NaCl + water. But what Michael said still applies just as well - all solutes behave the same way. The main thing is how well the different solutions mix - if you let the ocean water settle, you'd get a pretty uniform distribution over time, since solute from the "saltier" part would migrate to the "sweeter" part (the difference in density isn't enough to overcome the energy favourability of the lower solute concentration) - though I'm sure that's not true for a kilometre deep column of water.
Comment: The submarine reference is fascinating but I cannot find any immediate source. Does anyone have a reference?
Comment: One of my main interests is military history, and I have read endless books on it and watched many TV documentaries, but I can't remember which ones I saw this anecdote in. However, I did see it, I have definitely not made it up. Your best chance of finding an original source would be to read books or internet articles on the Gallipoli campaign, especially the naval aspects. Submarines and sea mines. played an important role.
Comment: Dardanelles has layered structure with brackish upper part flowing generally to the south and more saline deeper part flowing to the north. During spring ( on the Gallipoli campaign session) thickness of the upper part is about 26-32 meters (of 55 m average total depth). The submarines of battle of the Gallipoli 7 meters height. The  visible part of the sea is approximately up to 10 m. So if denser layer lift submarine to above 26 m depth range then the top of submarine reach to 19 m depth so there is still 9 meters need to be visible and able to seen from the ground gunners.
Answer:
Why does the salt in the oceans not sink to the bottom?

Because there isn't any "salt", per se, in the ocean. Salt, as the compound sodium chloride (NaCl) does not exist as a solid in the ocean. It is dissolved into sodium and chloride ions (charged atoms) that exist within the ocean as a homogenous phase (that is, a "thing").
That said, water with sodium chloride dissolved in it is indeed denser than pure water, because after all, sodium and chlorine atoms are denser than atoms of hydrogen and oxygen. This leads to an interesting phenomenon: you can have layers of more-salty water and less-salty water that do indeed rise and sink. There are several YouTube videos that demonstrate this very well. For example this video shows dyed salty and fresh water, separated by a barrier:

and then when the barrier is released, the salty water sinks down:

Source.
Some other videos: one and two.
This phenomenon is extremely important for planet-scale ocean circulation, and has strong influence on our climate.
Comment: "because after all, sodium and chlorine atoms are denser than atoms of hydrogen and oxygen." My understanding is that volume(water+salt) < volume(water)+ volume(salt), so that would also make it more dense.
Comment: @Acccumulation's point is very important for a liquid. For a gas, it is the molecular weight that is more important than the individual hydrogen and oxygen atoms: as water they are a combined molecule H2O. In either case, "sodium and chlorine atoms are denser than atoms of hydrogen and oxygen" is not a good description of density.
Comment: @Gimelist Is the density of dissolved NaCl well-defined? To measure the density, you have to divide the mass by the volume, but how do you measure that volume of a solute? Since, as I said, volume is subadditive, how do you define how much of the volume of the solution is coming from the solute? Volume is a macroscopic property. Individual atoms don't have a volume, in a sense that corresponds to the ordinary meaning. "Volume" refers to the amount of space for which an object excludes other objects, but an atom does not necessarily exclude other atoms from occupying the same space.
Comment: @Acccumulation that's molar volume, disregarding massed.
Comment: @BryanKrause it is an excellent description for the layperson because no matter how you look at it, NaCl is whatever form is much denser than H2O in whatever (yet equivalent form). An accurate technical description is unnecessary in this case.
Comment: @Acccumulation in fact, the density of dissolved sodium chloride is well defined. It has a negative molar volume, so the density of of NaCl(aq) is greater than that of the same mass of H2O(l)+NaCl(s).
Comment: @Leukocyte you asked a question, and I gave my opinion. If you did not want an answer, why ask? Besides, I'm only one user and it's perfectly fine to disagree with me.
Answer: I'm a regular from the Physics Stack Exchange reporting for duty.
Why this is a serious question
This is a bigger question than you might be giving it credit for. The question is ultimately similar to asking why all the air molecules in the atmosphere do not fall to the floor. Your question comes from a very solid principle in physics which could be called the minimum energy principle.
The basic derivation is that if you define the power exerted by a force $\mathbf F_i$ on a particle with velocity $\mathbf v$ to be $$P_i=\mathbf F_i\cdot\mathbf v = |\mathbf F_i|~|\mathbf v|~\cos\theta,$$then Newton's law that the sum of forces on a particle $\sum_i \mathbf F_i = m~\dot{\mathbf v}$ is the mass times the change in velocity per unit time, directly implies that the sum of powers exerted on a particle $\sum_i P_i = \dot K$ is the change in kinetic energy per unit time. Drag forces exist and they oppose relative motion, so their $\cos \theta$ is negative and they will decrease kinetic energy, $\dot K < 0.$ Since energy is a conserved quantity (a "stuff," if you'd like: if you find more or less of it in a box, then it must have come from somewhere else where there is less or more of it), drag forces eventually rob energy from a system until it ends up at the minimum energy.
And it is a very useful principle, for example you can use it to very easily derive the principle of buoyancy and the effective force that must be created by the displaced water to produce that effect; you can't do Newton's laws easily when there are that many tiny little forces of little water molecules but you can absolutely compare total potential energy when an object is at the bottom of the ocean, the middle, and the top. It fails to describe certain things like static friction (why is my laptop on my desk and not on my floor?!) because it does not tell you how long such things take and requires an assumption of noise to eventually perturb you out of "local minimums" and such.
But surely the air has had enough time to fall to the ground if that were what it wanted to do. The air does not want to fall to the ground. And we can't steal our normal solutions for other things like "why don't clouds fall," "well what you think of as a cloud is actually more like a waterfall, there is constant movement of water droplets, the water gets a boost upward from heating the air around it as it condenses but it does tend to eventually fall but when it falls beneath a certain flat surface it evaporates again and becomes invisible and so the visible puff is constantly being fed by new water droplet formation and constantly sapped by falling water that becomes invisible…"—no. These are concrete particles that somehow avoid falling to the ground and we have to actually solve the problem.
Fluctuation-Dissipation theorem to the rescue
The minimum-energy principle describes something that we would call dissipation, energy leaving one system to end up in another system. These sorts of gates are always bidirectional: energy goes through in both ways. But mostly you don't notice it, and that's key to how the principle helps us describe things: energy always flows out, it never flows back in.
Until, well, it does. Energy of a bouncing ball spreads out among all of the different degrees of freedom of the floor, the air, but if it really goes all the way to 0 and sits perfectly and completely still, very soon the air will bump it and start it jostling and vibrating and moving again—just not moving very much. The same things that allow energy to dissipate must also be contributing constant energy fluctuations that prevent energy from going all the way to 0.
These fluctuations are collectively understood as temperature. Temperature is technically only defined for a system where all of its degrees of freedom in the ways it can move have come to the same average energy, and it is measured as that average energy. Temperature defines this average energy and the size of these fluctuations. So at room temperature for example we would say that every degree of freedom has 26 meV, 26 "milli-electron-Volts" of energy, or 0.026 of the energy that an electron would have if accelerated by a one volt battery.
So why does the air stay up? It is, basically, because the molecules of the floor are kicking the air molecules with enough energy to hit the upper reaches of the atmosphere. They do not actually go straight there; one air molecule bumps into other air molecules over a very short distance scale: but it transfers that energy and momentum to other particles which transfer that energy and momentum to other particles and in the end the air "prefers" to "hang out" near the ground but the fluctuations cause it to get bumped to an average height given by our temperature. So if you take the mass of nitrogen N2 of 28 amu, and the acceleration due to gravity of 9.8 N/kg, you can find out that this 26 meV temperature means that the atmosphere is ~9 km high on average, which does get you a good chunk into the troposphere where the air starts to thin out dramatically. Actually the theory says that if nothing else were to happen and the random kicks were to just launch a particle up into the atmosphere, it would have a random height sampled according to an exponential probability distribution, $P(h) \sim e^{-h/(9\text{ km})}$.
Similarly why don't the salt molecules fall to the ocean floor? Well, they do, and then they get kicked back up. The water at the ocean floor is saltier. The key difference is whether the salt in question dissolves in water (if it sticks to water better than it sticks to itself) or precipitates in water (it sticks to itself better): larger chunks of a piece of stuff that get bound together will tend to act as big massive chunks and then that thermal energy cannot kick it as high.
This is the general idea of the fluctuation-dissipation theorem, which states that fluctuation and dissipation (under some extremely broad assumptions called "detailed balance") always go hand-in-hand. Anything which can absorb light (dissipation) must radiate light into space (blackbody radiation, a sort of fluctuation). Every electrical resistor is also a noise source (Johnson noise). If energy can flow out of a system into some environment, then it will only flow out until they have the same average energy levels, and if you try to go lower, energy fluctuations from the environment flow back into the system.
Comment: Interesting. I'll have to read it several times until it will sink in (pun very much intended).
Comment: I don't see how this helps at all. The theory of hydrodynamics (HD) is an average over newtonian kicks and short mean free-paths. More importantly, HD is perfectly able to explain static stratification and density gradients via flux differences of up minus down. The FD-theorem which you quote is usually only of importance when the mean-free path of particles becomes comparable or greater than the system scale, otherwise HD is fine. Both for the ocean and atmospheric structure up to 100km height.
Comment: @AtmosphericPrisonEscape I think you are overthinking it? HD is the mean field approximation but FD is the fundamental cause; OP was asking for the fundamental cause.
Comment: I guess that's up to OP to decide that. I just don't think that a question to which the understandable answer would be, "salt is dissolved, and fluids of differing densities behave in the following way", can be expanded much by handwaving it away with FD.
Answer: Turbulence, because seawater is, almost, always on the move saltier water is mixed with fresher by wave action and, to a lesser extent in surface waters, by Brownian motion. In Fjordland the annual rainfall is so high (up to 8000mm) that there is a permanent freshwater layer several metres thick that you can drink from sitting over the salt water from the Tasman in the sheltered inlets. Even there this layer doesn't have a clear cut boundary but rather a mixing layer where the salt and fresh water exchange particles and homogenise over time. In bodies of water that don't experience regular circulation stagnation and anoxia set in over time but chemical solution of a number of dissolved salts still occurs.
Answer:
Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.
The actual oceans are stirred by currents, so this equilibrium concentration difference isn't present in them.

Basically they saying that it takes energy to separate a homogeneous solution into parts which are more or less concentrated (and hence more or less dense). Taking into account the gravitational energy, it follows that the least energy state of a column of water is saltier at the bottom.
Comment: The answer is no! Salinity almost does not change with depth. Here is an example from the Challenger Deep: https://link.springer.com/article/10.1007/s10872-005-0053-z
Comment: Then the answer to the formulated question is that it does not sink because is dissolved and the currents (and temperature gradients, by the way) prevent equilibrium from happening. I just don't want people to get a misconception. Salt in the ocean is pretty evenly distributed (except near rivers). The differences in salinity with depth are minimal compared with the gradients in temperature.
Comment: So to paraphrase, salt *does* sink to the bottom, but only somewhat, so that the bottom of Challenger Deep is nearly three times as salty as the surface?
Comment: @TannerSwett: This sounds correct. "Exponential growth" isn't really very impressive between $0$ and $1$.
Comment: @arkaia As the University of Illinois page states, the actual oceans do not reach the equilibrium state because of currents. Gravitational differentiation (over thousands of km) is significant inside the Earth, resulting in the heavier elements sinking to the core.
Answer: But it does, but according to each salt's solubility and density. Soluble salts tend to mix into the water and keep suspended. Insoluble salts separate from the solution and creates deposits in the oceanic floor.
One famous example was the "de-ironing" of the seas, when iron salts were deposited in the bottom due to the oxigenation of the oceanic water, by the time of the emergence of aerobic, photosynthetic organisms.
Great Oxidation Event: https://en.wikipedia.org/wiki/Great_Oxidation_Event
"The oxygen then combined with dissolved iron in Earth's oceans to form insoluble iron oxides, which precipitated out, forming a thin layer on the ocean floor".
https://en.wikipedia.org/wiki/Banded_iron_formation
Comment: Geochemists use "salts" most commonly to talk about soluble compounds. I have never heard anyone refer to insoluble compounds (and iron oxide) as a "salt". So while this answer is technically correct, it may be a bit misleading.
Comment: Salt, in the parlance of this response, is a result of a reaction between an acid and a base (in the broadest sense, i.e. Lewis acid, etc).
So Iron is an electron "giver", i.e., a base, and Oxigen an electron "taker", i.e., an acid.
The reaction "Fe+2 + O2 -> Fe+3 + O-2" (unbalanced, the signs are electric charge of the ion) means that Fe2O3 is a salt, in this sense.
Comment: no, in the parlance of geochemistry and ocean geochemistry in particular, "salts" are always soluble compounds like halides, nitrates and some sulfates. Your definition of a Lewis acid includes too many inorganic compounds to make it useful in the field of geochemistry.
Comment: Sure, geochemistry has a specific nomenclature.
Chemistry in general has many definitions of salt, and the most basic is the result of a reaction between an acid and an alkaline compound.
The answer _does_ explain how some of the salt gets deposited in the ocean's bottom, though.
Answer: And then there is the saturation issue. Salt can be dissolved in water to a certain degree only. Once that degree is exceeded the salt begins to fall out and sink to the ground. If I remember well the limit for water is something like 35g per litre (depending on the temperature)
Comment: This seems to suggest that (contrary to the question) salt *does* sink to the bottom. Can you back this up, i.e. shows that this effct actually takes place in the oceans?
Comment: not directly related to this answer but when seawater freezes(in the arctics)the salt will be consentrated and sink down to the bottom of the ocean,this does lower the salt consentration in the ice.
Answer: Salt does sink to the bottom in the oceans.
Why? Your question referring to salt. Salt is a solid chemical compound. Take a lump of rock salt of sodium chloride, throw it into the water: it will sink to the bottom. The reason is that the density of sodium chloride with more than 2 g/cm3 is higher than the density of seawater less than 1.1 g/cm3.
Of course, the salt lump will be dissolved sometime and no longer exist. But then it's no salt anymore. Then there are only fast and somehow moving loose cations and anions in the water.
Answer: Salt does not sink to the bottom in the seas and oceans, because it dissolves in water!
If you want to get salt from the seas and oceans, try to vaporize them :-)...
Answer: The definition of a solute that is capable of dissolving in a solvent is that the force of attraction between the atoms in a solute are not strong enough to keep the molecule together when surrounded by the many negative and positive partial charges that make up the solvent. I don't know exactly how many ion-dipole bonds Cl- and Na+ form with H(partial charge δ+) and O(partial charge δ-), respectively, but there are enough ion dipole bonds between these atoms that the bond between Na and Cl isn't strong enough to keep it in solid form so it dissolves into its ions and forms ion dipole bonds with the water. At the bottom of the ocean these ion-dipole bonds are still in effect (I'm unsure how the pressure do to the weight of the water above it effects these ion dipole bonds however) but the density of the ocean water, as illustrated in this diagram I found on google, does appear to increase in density with depth but after 1000 m it seems that the salt water can't be compressed anymore to increase its density.
Answer: Actually it does. But the thermo-haline cycle of cold water and upwelling mixes that water around. In stagnant stand, the salt will accumulate on the bottom. But ocean currents and the rise and fall of varying temperature water flushes that salt and moves it around.


How do I prevent water from stinking?

Question: I have recently purchased new swamp cooler at home. It was working fine for a 3 days then the water in it started to stink , But I used to remove water completely every day and fill it with new supply of water but still the problem persist and I cannot open the cooler to wash it. Can anything be done to prevent that odour?
Comment: Check the owner's manual and if it has no objection, then put some lemon juice in the water to inhibit mold.  You could use vinegar but that would not smell very good either.
Comment: If your cooler is contaminated enough for the water to start stinking so soon, do you trust the water quality? Better return the cooler to the seller and cool your water in a different way in my view. Bottles in the fridge work well.
Comment: @Willeke No it is not actually water cooler. It is used to decrease temperature of room , like Air Conditioner. Or I think it is called as **swamp cooler** .
Comment: Maybe "Desert cooler" is a synonym
Answer: Usually, you need to change the water in 4-5 days but if it stinks that bad as you said then there are many reasons for it:

Might be the water you are using is not good.
The Pad used in water are not clean, this might be the major reason it stinks. You can change your pad or better if available honeycomb pad is good for the cooler you can go for that too.

Changing pad would be costly so better you can search for cooler odor purifier liquids, they are present in various odors khas, rose etc. They are easily available at any nearby cooler shop.
Hope this would be helpful for you.
Answer: Swamp coolers I've used in the past didn't hold onto water long enough for it to develop algae and bacteria growth that would smell.  The evaporation that cools the air requires making up water -- in a dry climate, at the rate of several gallons per day.  This is often an automatic process, governed by a float valve inside the cooler and supplied by a line connected to a faucet or water pipe side tap, but turning off the water supply should result in the cooler running dry in a few hours, at most.
If your swamp cooler isn't requiring this amount of water added, it's likely that it's also doing little or nothing to cool your air due to high ambient humidity.  If this is the case, a swamp cooler is the wrong kind of air cooling system for your climate, and you'll have to invest in a refrigerant based system.
If a swamp cooler is all you have, you might shop for products intended to kill algae and bacteria in small fountains -- they should work as well in a swamp cooler.  Whether they're "safe" for a high evaporation system is another question, but they're unlikely to be worse than breathing bacteria growing in the water and then being shot into the air (this is the usual source of Legionnaires' Disease, among other unpleasantness).
Comment: No it is actually working well , sometimes I need to wake up at 3 /4 am to turn it off , because room becomes so cold. I have only problem with odour.
Answer: Removing the water daily will not significantly decrease the bacteria unless you thoroughly clean it also. I had a friend who had a similar issue with a "water wall" in a retail environment. Per my suggestion she experimented with small amounts of bleach added to the water until she found a balance between killing the flora and fauna, and killing her customers.
Answer: It is possible that some creature might have died inside the cooler, possibly because of the blades. It could be a lizard. Then when its body decays, a horrible smell results. Such a situation is often mistaken to be due to water odour. But freshly filled water should not smell in a day. You'll have to get the cooler opened to inspect it.
Comment: No , it is certainly not that.
Comment: Are you sure? Because a bad smell means something is rotting/decaying because of bacteria. And water should not smell in a day, that too when it is circulating, i.e. in motion.
Answer: Add fluoride. It is present in toothpaste and mouthwash. Perhaps you can buy it pure.
It takes a long time to degrade chemically, and creates a very unfriendly environment for bacteria and microorganisms.
Comment: Fluoride is also present in tap water.
Comment: @Chenmunka Yes, at very low levels. Increased levels are OK if it's not drinking water, and in any case it's better that chlorine.
Answer: add some bleach to it, that should kill the bacteria. they are right though, water shouldn't smell that bad. spray everything with bleach and add it to the water
Comment: That answer has already been given.

How do I prevent water from stinking?


Residence Card, proving dependency and health insurance

Question: My husband and I have been in the UK for more than a year studying a masters. My husband just got a job and has Italian passport (I am a non-EU), therefore i was thinking of applying for a residence card as EU spouse of a qualified person. I see that one of the things they ask is to prove dependency. How can I prove this? I was thinking of showing my husband's wage slip, is this enough or should I also show that he transfers cash to me? He hasn't done this yet since till last month we were financed by a scholarship...
Additionally, about the "Comprehensive Sickness Insurance", my husband gets this by his employer but after the first 3 months of employment, therefore should he get a Health Insurance in the meantime or is it ok with what is stated in the contract? Thanks!
Answer: It is not necessary for a non-EEA spouse to prove that dependency on the EEA spouse.  See for example the guidance document Free Movement Rights: direct family members of European Economic Area (EEA) nationals (PDF), page 10:

A child aged 21 or over and any relatives in the ascending family line must prove they are dependent on the EEA national sponsor or their spouse or civil partner.

(emphasis added)
Note that there are two categories of relatives who must prove dependency; spouses are not among them.
Comprehensive sickness insurance is required only of students and those of independent means.  See for example the guidance document EEA(FM): guidance notes (PDF), page 9:

Comprehensive sickness insurance (students and self-sufficient persons) 
Evidence of your sponsor's comprehensive sickness insurance for any period in which they were a student or self-sufficient person, such as their European Health Insurance Card (EHIC) (formerly form E111), S1 (formerly E106/E109/E121), S2 (formerly E112), S3, policy document from a private medical insurer – see notes for sections 15 and 16.

(emphasis added)
Since your husband is a worker, he is neither a student nor a self-sufficient person, so there is no need to worry about comprehensive sickness insurance.


How can you install elementary OS without installing the bootloader?

Question: I want to install eOS but i already have an Arch install with grub2. Can i skip eOS's grub installation and use my existing one?
Comment: I think you can but I haven't tried
Answer: To install elementary OS without installing the GRUB boot loader:

Boot up an installation media an select "Try elementary OS". This will load a live session instead of loading the installer directly.
Open Terminal and enter the following command. This will launch the installer with the option to not install the boot loader:
ubiquity -b

Continue installation as normal. The GRUB boot loader will not be installed.
Answer: I would suggest you to install grub to the partition where you install your eos. You can select grub partition while partitioning your hdd.

Then update your grub from Arch Linux using sudo update-grub. (Then hide your eos grub if needed)
Answer: I went ahead and installed it anyways. When prompted to select the location for the bootloader I went with the same drive I'm installing to, which had Arch and grub2 in it. The installation went well, and the previous grub2 was replaced, leaving me with all my old boot options with the addition of eOS.
Comment: but it would be great if someone confirms that you can install it without installing grub
Comment: I would have suggested skipping selecting the location for the bootloader. Choose the default swap area, your root and location of home partition. When all is finished, restart your computer. If grub doesn't recognise your new OS, boot into arch and reconfigure grub from there. It should be able to recognise the new partition and create a boot entry for it


Tax filing for Summer Internship

Question: I have a couple questions regarding the tax filing procedure. I am still a dependent on my parents, and my parents normally do the taxes each year. However, last summer 2014 I worked a summer intern at a hospital. My total income for the internship was $11100. After taxes, I made around $7700 . Basically my question is whether I need to file taxes separately, or can my parents still take care of it. For instance, can my parents still claim me as a dependent? Also, am I eligible for a tax refund? Over the summer, my total federal withholding was around $1600.
Answer: Yes, you need to file a tax return.
For a single individual under the age of 65 who is a dependent, the filing threshold is $6200 or more of earned income, and your income is above that.
Since your parents claim you as a dependent - you cannot claim an exemption for yourself, but as Joe said,  you'll still have the standard deduction.
Answer: It's going to depend on more details like your age, whether or not you are a student, do you still live at home, etc.
The IRS has a calculator to help determine your status as a dependent.
You will need to file a tax return regardless because your earned income was over the standard deduction amount.
Comment: I am not married and 21 yrs old and a college student in NYC living with my parents.
Comment: If they paid for more than half your support, they can claim you as dependent. Use the calculator to make sure, though. When you file your tax return, I predict a refund.
Comment: Or you could just ask if they are claiming you as a dependent (assuming they are doing it correctly)
Answer: As a dependent, you lose your 'exemption' but not your standard deduction. For a single person, that's $6200, leaving $4900 to be taxed at your rate, 10%. I predict a federal tax bill of $490, and you've already paid $1600, so I smell 'refund'.

Tax filing for Summer Internship


Technique to win this same colored bishop endgame

Question: The following endgame is a same-colored bishop endgame which I had on a game in Lichess. I tried for approximately 30 moves to try and win this game, but in the end, I got nothing more than a draw. I just felt that I was better due to white having 4 isolated pawns and 3 on light squares. Stockfish 11 evaluates the position as -4.3 at depth 40. The position in black to move. Please explain to me the technique to win this endgame.
Answer: The key here is zugzwang - White has an ideal defensive position at the moment, his king stops yours penetrating, his bishop covers the weak pawns on g4 and c4, and the pawn on a5 you can't easily get at is it is on a black square. BUT when white has to move he will either have to move his king (letting your king in), or move his bishop (leaving a pawn undefended) or move his a pawn (giving you an extra passed pawn)
So how can you take advantage of this? Well... if your bishop was on e6 and it was white's move he would be in zugzwang, and would either immediately drop a pawn (through a bishop or pawn move) or very soon afterwards (through a king move). Now note you can't just move your bishop straight to e6 as this would leave a position where you, not white, has the move. What you have to do is lose a move with the bishop - sometimes called triangulating with the bishop in reference to the similar idea with the King:
<code>[Event ""]
[Site ""]
[Date "????.??.??"]
[Round ""]
[White ""]
[Black ""]
[Result "*"]
[FEN "8/1p6/5p2/P1p1k1p1/b1P1P1P1/4K3/4B3/8 b - - 0 1"]

1...Be8
    ( 1...Bd7?! 2.Bd1 Be6 3.Be2 {And white is OK for the moment
    } )
    ( 1...Kd6?? {Trying to get to the a pawn} 2.e5+ Kxe5 3.Bf3 Kd6 4.Bxb7 )
2.Bf1 Bd7
    {so losing a move}
3.Be2 Be6
    {Now white has the move and has to give you something}
4.Bf3
    ( 4.Kf3 Kd4 )
    ( 4.Kd3 Kf4 )
    ( 4.Kf2 {Stockfish's Choice} 4...Kd4
        ( 4...Kxe4?? {Be Careful!} 5.Bf3+ )
    5.Bf3 Kxc4 6.e5 fxe5 7.Bxb7 Kb5 8.a6 Kb6 )
4...Bxc4
    {and wins}
*
</code>
There's a free course at chessable (https://www.chessable.com/) called "Basic Endgames" which covers this, amongst many other things
Comment: I noticed the triangulation. I rejected it due to the following line 1...Be8 2.Bf1, Bd7 3. Bd3, Be6 4. Be2. Now it's black's move so essentially white triangulates as black does to stop zugzwang, but for some reason, I completely missed that white can't play 3.Bd3 because his g4 pawn is under attack.
Comment: I have to admit I find zugzwang very hard to spot over the board ... But the endgame course I mention has definitely helped even if it is only a few examples in there.


Question about a Question's Answer

Question: So if I find a question from several years ago that obviously doesn't have any current activity how can I ask a question about an answer given to that question? I know that if I open a new question and reference that question it will get downvoted and most likely closed. If I comment on the old question will it be seen by the people who answered the question or not?
Comment: Do you have an example of what you would ask?  If you are just asking how does this work I can see you getting a negative response.  If you ask a detailed question on what parts of the answer you don't understand and why then that should be okay.
Comment: wait... you have a solution to get 2 activities and you need a third one? Unless I'm REALLY out of whack with android (to be fair I don't really do mobile dev), you should be able to adapt the answer of 2 to 3... Anyway if you have a precise case, link the question? People will be able to give you more detailed information ^^
Comment: yea.. basically the question was reguarding an android application and the OP had 2 activities with one main activity, but I have 3 activities and was just wondering if how to apply it to my app vs. their app... but my main point in this question is should I start a new question referencing that question or should I comment on the old question?
Comment: @thatdude1087 you should really edit that kind of information into your actual question.
Comment: I would say unless you try to adapt it and fail and show what you tried and what your problem is it would just get marked as a dupe.
Answer:
how can I ask a question about an answer given to that question? ....If I comment on the old question will it be seen by the people who answered the question or not?

Comment on the post (once you have 50 reputation).  The owner of the post is always notified when someone comments on it or edits it.  You can "ping" up to one additional user in the comment string with <code>@username</code>.  Then both the post owner and the other commenter will get a notification.

I know that if I open a new question and reference that question it will get downvoted and most likely closed

Why do you think this is the case?  Yes, poorly researched questions will be downvoted, and some may be closed as duplicates.  But if you take your time to write a good question, there is no reason why your question can't stay and even get upvotes.  If you have a specific question about the answer, and you clearly indicate the parts that you do understand and the ones you don't, that would be a decent question.
Answer: This really depends on the question you would ask and the type of answer needed to suit you.
If you are going to ask something really simple that isn't clear to you in the answer and the response would be something like "you can add this variable here" then I would start with a comment and see if you get a response.
If your question will need a more detailed answer and it will be potentially helpful to others, then go ahead and ask a new question and link to the older one. Just make sure to be clear what you don't understand about the given solution.

Question about a Question's Answer


Regarding tumors and their developement

Question: If certain cells or tissue in a specific part of the body are for some reason overworked; like the cases of severe acid reflux damaging the throat repeatedly and the cells in the throat having to do growth and repair a lot more than they would with a healthy person -- or problems in the stomach attacking the stomach lining a lot, causing 'extra' growth and repair; could these situations of 'extra' growth and repair cause various cells used in these processes to mutate with all the cellular division and replication required? And maybe some of these extra-growth-and-repair induced mutations might cause the apoptosis mechanisms to malfunction?
Comment: If a cancerous cell has a horrendous amount of mutations and yet it still functions ( if abnormally) it must be able to keep existing without 'alerting' the immune system or interfering 'too much' with other subsystems. How is this possible? Wouldn't all the mutations if 'expressed' cause all sorts of 'activity' the cell or other neighboring systems might not be able to cope with?
Answer: There is indeed a positive correlation between gastric reflux disease and esophageal cancer, and also between stomach ulcerations and stomach cancer. There are more than one possible mechanisms for these correlations to arise, but what you are proposing is definitely a prime suspect.
http://www.webmd.com/heartburn-gerd/news/20130523/chronic-heartburn-may-raise-odds-for-throat-cancer-study
http://www.ncbi.nlm.nih.gov/pubmed/10658066

Regarding tumors and their developement


Is there any possibility to obtain German Citizenship before 6 years without marriage?

Question: I read many times that the minimum requirement for period lived in Germany is 8 years and can be dropped to 6 years (I am talking about non-married to German citizen).
My question is, can this be by any mean less than 6 years even by 2 or 3 months? And when can I start the process of application?
Comment: It is indeed possible. I like your user name. The answer to your second questions is as soon as you qualify.
Comment: So, does that mean I can obtain a citizenship certificate after for instance 5 and a half years?
Comment: Sorry, misread your question. I can't find any way to obtain German citizenship under 6 years unless you were born stateless in Germany and lived there the entire time. I had to check the German language legal sites to be sure.
Comment: 6 years is the minimum, though one can indeed start the process and get into contact with the Bürgeramt a few months before that already. If you need to renounce your previous nationality (i.e. you're non EU), that will be the part that takes a lot of time.
Answer: Exceptions to the normal eight year residency requirement include:

People who have completed an integration course may have the residency requirement reduced to 7 years
If an applicant is especially well integrated and has a higher command of German than the basic requirement for German citizenship (i.e. C1 or C2) they may have residency requirement reduced to 6 years. (Comment: a well paid job or high qualifications in chore subjects are also "helpful" establishing desirability)
The spouse of a German citizen may be naturalised after 3 years of continual residency in Germany if they have been married at least 2 years.
Refugees and stateless persons may be able to apply after 6 years of continual residency.

The majority have an eight year residency requirement minimum, so the lower limit is already a huge reduction and concession. No way would an application be accepted before the minimum. You will have to fulfil all the requirements including citizenship test and language exam to B1 (minimum) in the same way, so even if one of the above categories is applicable, the information is widely available in German and there will be a requirement to be proficient enough to read and understand everything at the time an application is submitted. To be sure a six year residency requirement is going to be accepted, you should ask beforehand to avoid disappointment.
Q: "And when can I start the process of application?"
A: As soon as all the residency and other requirements are fulfilled. You will need two to three months collecting and translating all the necessary paperwork before you submit the application and it is my experience you need 4-6 weeks to make a preliminary appointment to see a case worker, so applicants can certainly start the ball rolling before their time/date requirement is up. A police check is also done before papers are finally submitted by your case worker.
I have been through the whole process myself this year and was helped and advised well at the Bürgerbüro in my local Rathaus. Each town and state is different, but in Berlin applicants should make a personal appointment at the Staatsangehörigkeitsbehörde where they will be advised about an application relevant to them and their country of origin. A good starting point for research is Wikipedia German nationality law A lot more information is available via local Einbürgerung services and via their web pages, which are sometimes in English. Be careful of companies or web sites which claim they will expedite applications. Applicants will also have to have a certain amount of interaction with authorities in their country of origin, depending on where and whether they will be required to renounce citizenship. My application was submitted and dual citizenship (I'm from an EU country) granted within three months in Schleswig-Holstein, but waiting times vary a lot from state to state.
Answer: I'm assuming you were not stateless and born in Germany. In which case, No.

Exceptions to the normal residence requirements for naturalization include:

persons who have completed an integration course may have the residence requirement reduced to 7 years
If a person shows that he/she is especially well integrated and has a higher level of command of the German language than the basic requirement for the German citizenship (i.e., higher than CEFR level B1) may have the residence requirement reduced to 6 years
refugees and stateless persons may be able to apply after 6 years of continual residency
former German citizens

Six years seems to be the minimum possible time frame depending on circumstances.
Comment: That is very useful but my question was if I can be qualified in a time shorter than the 6 years.
Comment: Ah I see. I think I read your question wrong. Then the answer would seem to be 'No'. I'll have to update my answer, but I want to do a bit of research first, just to be sure.


What is the difference between 学科 and 专业?

Question: I guess below college there are only 学科, and in college or even higher (if any) both 学科 and 专业 are merged as the same. That's why this year's first-rate university and 学科 evaluation does not include 专业.
Answer: When we talk about the courses we choose in college, they are pretty much the same thing, but actually they are just different from the purposes of their courses.
学科 is for academic purpose, studying a certain science or academic field.
专业 is based on social professions and the social division of labor, learning skills and knowledge of a certain industry or business.
Answer: In this context, 学科 means 'subject/ course' For example, 'mathematics'(数学科) and 'art' (艺术科) are both subject/ course you can pick in university. One can be 'major in mathematics' and 'minor in Art'
专业 is short for '学科专业'(subject major)' as in 'major in physics' (物理专业/主修物理)

From Google Translate
学科专业- major
Comment: I understand a college student has to learn a number of 学科 in his or her 专业.
Answer: There also seems to be a diffence in usage betweeen Taiwan and mainland China: In the latter, 专业 generally refers to your major or field of study, while in the former 主修 (more literally "major") is used instead.
To answer your question (as a non-native), you could say something like 虽然我的专业是数学,但我还是觉得别的学科都是有价值的。("Even though my major is maths I still think that other academic disciplines have a certain worth.")
Answer: 學科 has two general meaning:

Subjets that are distinguish due to the content of the knowledge.
A collectively calling of all the paper knowledge, to apart from 術科 (subject or course in military/physical/design training, any training that is not associated with studying books)

專業 we normally take it's meaning as "Profession"
When talking about "專業" in college courses, we normally refer to the category of "專業科目" (professional courses), which normally happens to be the courses related to students major, or even more difficult.


About gaining weight

Question: I'm 19 years old, 5"7 tall and weight 45kg.
What should I do to gain at least 10kg within 1 month without supplements? And is my height normal?
Comment: Adding 22.5 pounds in a month... I think you'd be hospitalized
Answer: 10kg weight gain in 1 month is likely to be mostly fat, and I don't think it's a realistic goal. Why do you want to gain 10kg in one month?
If you want to gain weight really quickly, just increase your calorie intake. Eat a lot of food. Drink a lot of milk.
If you want to gain weight in a way that will be good for you, you'll need to include a well-rounded strength training program such as Starting Strength or Stronglifts so that you turn those extra calories into muscle, rather than fat. Even on these programs, 10kg in one month is not realistic.
Your height is normal.
Answer: You won't be able to gain weight that fast, however you will be able to gain weight if you increase your calorie intake massively.
If you don't care how you look you can read up about how Matt Damon and other actors put on weight by eating junk food all day.
But hopefully you want to be healthy and be in shape, so you need to do massive compound exercises such as leg press, shoulder press and bench press with free weights.
Then you need to eat every 2 hours mostly protein and carbs.  Minimum 6 meals a day.  I am talking 3 steaks, 4 chicken breasts, fruit, wholegrain pasta, cheese, 6 glasses of milk, 6 eggs - you literally have to be constantly feeding yourself.
Then you need to organise your supplements - protein shakes 3 times a day etc.

About gaining weight


Is there any book for modern optimization in Python?

Question: I was reading Modern Optimization with R (Use R!) and wondering if a book like this exists in Python too? To be precise something that covers stochastic gradient descent and other advanced optimization techniques. Many thanks!
Comment: I can recommend `PRML` by Bishop, but it's not an optimization-only book.
Comment: @Dawny33 I am actually looking for a book which is dedicated to optimization and has codes available in Python. Bishop's book has optimization for individual techniques and is not learning method agnostic. ALso it does not have Python code!
Comment: @Dawny33 although some genius created code of own in Python, however it misses many chapters like SVM and others. https://github.com/masinoa/machine_learning
Comment: This book is math heavy, i am looking for something which is code heavy.
Answer: There is a tutorial Modern Optimization in Python and a corresponding video Modern Optimization in Python | SciPy 2017 Tutoria. Although they are not books, I think they may be helpful to you.
Answer: You should look for this book
Pyomo — Optimization
Modeling in Python
Answer: You should be able to translate code written in one language -- even pseudo-code -- to another, so I see no reason to avoid books for R. If you want one specifically for python, there's Machine Learning in Action by Peter Harrington.
One of scikit-learn's core committers is a releasing a book in October: Introduction to Machine Learning with Python: A Guide for Data Scientists.
Comment: I just now read some sample pages of the book and it appears that the first book you referred is very hands on. It has implementation of gradient descent in the chapters itself. I will look forward for the second book. Thank you very much!!
Answer: Try the ND Pyomo Cookbook: https://github.com/jckantor/ND-Pyomo-Cookbook. That is a collection of notebooks showing how to use Pyomo to solve modeling and optimization problems.
Answer: I found this question useful for me.
Nevertheless, I agree with Erme namely you should be able to translate code written in one language to another.
Recently I've found this book and strongly recommend Algorithms for Optimization.
Algorithms are shown in Julia Code, but the syntax of this language is very simple and in many cases similar to Python.
Here can be found a short review of the mentioned book:

https://machinelearningmastery.com/books-on-optimization-for-machine-learning/


Which exercises are ok in days between push ups

Question: i love push ups and im doing (5-6) push ups at this moment and increasing the amount every session, but as i heard about rest days i want to know what exercises are ok to do during rest days? Actually im not intrested in gym yet and i want some relatively easy to perform home exercises thankyou :)
Answer: If you want to let your "pushup muscles" rest, that's good.
I would suggest throwing in pullups and squats, either on the same day as you do pushups, or on the days in between.
This way, you're not only training chest/triceps, but also working upper back, biceps, and legs.
There are a million different bodyweight exercises you can do with minimal equipment. I would suggest trying to find a good number, so you can have some variation in your training.
Comment: @PooyaEstakhri - Arms isn't a single muscle. When doing pushups, you use triceps to extend the arms. When doing pullups, you use biceps to curl your arms. The overlap between these two exercises is minimal. In general, pushing and pulling use different parts of your body, as a rule-of-thumb.
Comment: @PooyaEstakhri - Yes, absolutely! When you start in the upper position and lower yourself slowly, we call that a "negative rep". It's the best alternative when you can't do a regular pullup, because it works all the same muscles. Even when you can do a few pullups, it's a good idea to keep doing negatives as a supplement just to get more work done.
Comment: But arms are involved in both push-ups and pull-ups so is it okay to try pull-ups in the rest days ?
Comment: Thx Alec, At this moment I'm not able to complete a single pull-up so I'm just hanging or jumping and keeping myself up for some seconds is that okay to train this way ? (Specially in rest days)
Answer: In addition to Alecs good answer and the comments I wanted to add, that there a a lot of different dodyweight trainings availible today.
Starting with different polpular Books like
Mark Lauren - You are your own gym
https://www.marklauren.com/
or perhaps in your case better:
Paul wade - Convict conditioning
http://www.dragondoor.com/b41/
which are delivering a huge amount of knwoledge and how to increase your strength and "health" without a gym/equipment.
(Also there are autors like Ross Enamait, Pavel Tsatsouline, Kelly Starrett... just to not only give you two names and countless forums and homepages online, google hundred push ups program).
Especially Paul Wade has a program to increase your ability to do push ups, pull ups, squats and leg raises from the very basic in Step one to extreme hard (one arm variants) in the last Step. Just have a look into one of those to better plan your training/extend your knowledge.
Now back to your first question. The needed rest in between workouts depents strongly on the amount of excercise you have and you perform as well as genetics. There are athlethes who can train several times a day without the need of a specific rest and others who have to plan their training very carefully to not overtrain/get enough rest. To be honest, just try whats goof for you. If you can perform push ups every day, do so (while at best mix in some other exercises to train the whole body). If you feel sluggish or you feel pain while trining stop and increase your rest. Try to listen to your body. He knost most of the time what's good for him.


Why are geodesic airframes no longer produced?

Question: Why are geodesic airframes no longer produced?  Do they cost more than conventional structures?  Are they not as strong as conventional structures?  I assume it is insufficient cost benefit ratio, but how does that work out?
 Wellingtons under construction. Photo: Royal Air Force
Comment: Probably because the skin will take a lot of the load. especially in a pressurized craft
Comment: A search for "isogrid & aircraft" shows interesting (including current) applications. Isogrid structures are considered for composite airframes too, but at the moment they are not cost-efficient compared to state-of-the art manufacturing concepts.
Answer: Geodesic (sometimes also spelled geodetic) designs were used in aviation as early as 1909, in the Schütte-Lanz SL1 airship. It had a wooden structure with fabric covering, and Professor Johann Schütte, the scientific head of this design, used the most efficient method conceivable. However, planning the shape of all structural members was an enormous amount of work, and stretching an existing ship by inserting a new section was almost impossible. For those reasons, the late Schütte-Lanz airships used aluminum frames with conventional design, just like Zeppelin did from the beginning. Diagonal wire bracing was used to take up shear loads.

Geodesic frames are good in transferring both bending and shear loads. This is helpful when the aerodynamic covering is not stiff enough to contribute any shear stiffness, as in the case of fabric covering. However, when the skin is made from the same material as the frame, it can carry shear loads and a geodesic frame would not improve matters. Now it is better to carry longitudinal loads in longerons and shear in the skin.
But geodesic constructions are not dead. CAD makes the design effort manageable, and in some cases they give a weight advantage. Look at the casing of the EJ200 engine: It uses a geodesic reinforcement to make the casing light and strong and to prevent harmful vibrations. In the end, a jet engine casing is a big pressure vessel and needs to be strong, stiff and light.

photo by Julian Herzog, CC-BY
Answer: The switch from internal frames to structural skin airframes -- called monocoque construction -- is fairly well covered in Wikipedia:

Early aircraft were constructed using internal frames, typically of
  wood or steel tubing, which were then covered (or skinned) with
  fabric3 such as irish linen or cotton. The skin added nothing to
  the structural strength of the airframe and was essentially dead
  weight beyond providing a smooth sealed surface. By thinking of the
  airframe as a whole, and not just the sum of its parts, it made sense
  to adopt a monocoque structure and it did not take long for various
  companies to adopt practices from the boat industry such as laminating
  thin strips of wood

That being said, we are still producing tube and fabric airplanes, particularly taildraggers based on classic designs, such as this American Champion Citabria and this Super Cub:
Comment: dat little Cubbie's got such a cute face!
Answer: It started when the usual way of building was a steel-tube frame, with wooden formers attached to carry the skin.
Early geodetic planes were still fabric covered, but the entire airframe structure was now in the skin, leaving the interior open for payload like people or ordnance. It was much lighter and stronger, though patented and many builders simply don't want to license-build as much of their plane from somebody elses' ideas.
Once metal skins were being used, it wasn't the only monocoque option, though it was still superior to the usual orthogonal structures. Still more expensive though.
"Geodesic" should refer to the field of mathematics itself. Geodetic applications of it work for space-frame structures or mapping a globe, etc.
Answer: Geodesic airframes are useful for purpose-built crop dusters, built from 4130 stainless steel tubes. The chemicals on board could easily react with aluminium, which is still used for skin panels but not as a structural member: the skin plates are only for covering, not for taking any of the prime loads. The construction method is one of the reasons why they look unlike any other plane, with the angular cockpit shape and all.
Other than that, monocoque construction has completely taken over from geodesic frame construction - when the skin plates are the main load bearers the airframe is lighter.
Comment: Is that the only reason they look different? I would think the requirement for good visibility in low-level flying is pretty important.
Comment: I was under the impression that the odd shape of dusters had more to do with the need to keep the CG forward by inserting the chemical tank between the engine and the cockpit.
Comment: You say "Crop dusters have..." as a fairly blanket statement covering _all_ crop dusters. Would that be better stated as "Some crop dusters have..."?
Comment: @jamesqf - you mention visibility. To me (IANAP) the visibility out of that looks _terrible_ with that very long hood and the pilot sitting directly over the wing, though I'm willing to be convinced that I'm very wrong.
Answer: As other answers already note, the major attraction of geodetic framing was to provide a lighter and stronger structure than internal framing, with the not inconsiderable bonus of leaving much more internal space for fuel and payload.  The geodetic frame could directly carry a fabric skin in a streamlined shape, instead of requiring the addition of (heavy) falsework merely to carry the skin.
Some modern aircraft are still built in a frame-and-fabric manner, such as the Aviat Husky, though most use a more generic "space frame" construction rather than geodetic framing.  These are almost universally General Aviation aircraft designed principally for VFR flight.
A general disadvantage of fabric-skinned aircraft is that they do not easily support cabin pressurisation; it would be necessary to install a second, internal pressure hull to retain a sufficient air seal.  While this would not be especially difficult to achieve, it does reduce the main advantage of the geodetic frame, in the context of aircraft designed to regularly fly above about FL120 (where most people start to experience debilitating hypoxia) without carrying oxygen for every occupant for the entire cruise phase of the flight.
Instead, metal-skinned and composite aircraft are typically designed so that the skin forms the pressure cabin as well as the aerodynamic surface, and also carries some of the structural loads so that less internal framing is required.
Answer: One area where geodesic airframes have seen a recent resurgence, is 3-d-printed model airplanes.
I've seen an example where the fuselage and wings and tail surfaces were all of open geodesic construction, similar to the well-known Vickers "Wellington".  The model was covered by a heat-shrunk plastic film such as Monokote.
Here's a website featuring many examples of such models-- https://www.3dprintedrcplanes.com/
This link describes the process of designing and 3-d-printing double-walled structures for model airplanes, with an internal geodesic structure between the inner and outer walls-- https://www.rc3dprint.com/post/3d-printing-geodesic-internal-structure
Answer: They ARE still produced. See for example the EU research project from 2013 here: http://www.transport-research.info/project/advanced-lattice-structures-composite-airframes
Comment: Welcome to Aviation.SE! Please consider adding more details to your answer, to make it more qualitative.
Comment: There is an interesting PDF if one searches a bit on the linked page. However, it seems the subject is research, not yet production.
Comment: Link no longer works.


How to install PHP `mbstring` extension in Ubuntu?

Question: What is the  PHP mbstring extension, and what is the best way to install it on Ubuntu 14.04?
Answer: EDIT: Dylan Pierce has confirmed that you can already install some PHP 7.2 extensions in the same way you would for PHP 5. For mbstring in particular, you can execute:
sudo apt-get install php7.2-mbstring

To complement sparkmood's answer, this now works for PHP 7.2 if you already imported ondrej's PPA for it.
sudo apt-get install libapache2-mod-php7.2

Don't forget, either PHP 7 is available through ubuntu's official repositories or you will need an external PPA.
Comment: I've figured it out:

`sudo apt-get install php7.0-mbstring`

Also works for other php extensions you might need like:
`sudo apt-get install php7.0-zip`
`sudo apt-get install php7.0-dom`

I really like how brainless it is to install/activate these modules. I just wish I didn't have to go on an internet wide goose chase for them.
Comment: You can just use package `php-mbstring` without the version number
Comment: Why is nobody fighting this version-in-name stuff? -_-
Comment: I believe that as soon as version 7 covers all of the old 5 libraries, you won't have to write 7 to get the latest and greatest. Not doing so would probably break build scripts or cause unexpected behavior.
Comment: After installed in Ubuntu 16.04 with LAMP is needed to restart Apache2 service `sudo service apache2 restart`
Comment: After installing this package, where is the mbstring extension? I can't find it in `/etc/php/7.0/mods-available` like the others. I've tried uncommenting the extension in `php.ini` but it doesn't know the the path to the extension.
Comment: I can't find it as well. I needed it to install software that performed a check on PHP extensions and `mbstring` was one of the required ones. It recognised it as installed, so even though I'm not sure where it is, I guess it's in there, somewhere! Sorry I couldn't be of more help.
Comment: I initially tried to install it like you did but some of the extensions where not available, and I tried not too long ago. This is cool though, because it seems more and more work is being done in the PHP 7.0 versions!
Comment: Do you need to enable the extension in the php.ini file? Some tutorial I was following wants me to do that in the /etc/php/8.1/apache2/php.ini file, but two other tutorials don't mention doing this.
Answer: sudo apt-get install php-mbstring

I have installed mbstring in php7.0-fpm (7.0.15-0ubuntu0.16.04.4)
Comment: This is correct for Debian Stretch. No need to add the version number.
Internally a sub-package with version number is loaded.
Comment: E: Unable to locate package php-mbstring (on buster)
Comment: I have added version because i have tested on above version. thanks for you comment
Comment: This is vastly superior to specifying the version on the cli as it seems to adapt to the installed version.
Comment: My experience using the sury package repo on debian 9 (stretch), I had to specify the 7.2 version, because php-mbstring is only supported until php 7.2. By not using the php prefix version, it kept saying it doesn't exist since by php7.4 (the latest release of php as of today). Make sure to install only php7.2 and not above or it might not work as expected.
Comment: @geoidesic First update sudo apt-get update and then try
Answer: mbstring is built in libapache2-mod-php5 package, so you can use this command for installing :
sudo apt-get install libapache2-mod-php5

As described in package details :
 dba dom ereg exif fileinfo filter ftp gettext hash iconv json libxml
 mbstring mhash openssl pcre Phar posix Reflection session shmop SimpleXML
 soap sockets SPL standard sysvmsg sysvsem sysvshm tokenizer wddx xml
 xmlreader xmlwriter zip zlib.

Comment: When I run your line, it break my LAMP - l have to re-install :(
Comment: I have already installed apache2 on my server now if I install "libapache2-mod-php5" on my server will it any problem.
Comment: This is poor advice. While some systems have Apache2 installed, many others may not. Executing this command risks breaking otherwise working systems. (Yes, I know I'm years late, but maybe it'll help someone not try this fix.)
Answer: If you're using php 5.6
Install php 5.6 mbstring package:
sudo apt-get install php5.6-mbstring

Then add the following line to the bottom of your php.ini file:
extension=php5.6-mbstring.so

Restart apache:
sudo service apache2 restart

To find your php.ini file, create a file and insert the following line:
<?php phpinfo(); ?>

Then open with a browser to see where your php.ini file is located.
Answer: In my case it was already installed, but I just needed to do phpenmod mbstring, followed by apachectl graceful.
Answer: For Ubuntu 14.04 extension mbstring should be built in.
For Ubuntu 16.04:
sudo apt-get install php7.0-mbstring

See also Introduction to Multibyte String
Answer: It requires adding another source for apt for install in 18.04..
Download Page for php7.2-mbstring_7.2.7-0ubuntu0.18.04.2_amd64.deb on AMD64 machines
If you are running Ubuntu, it is strongly suggested to use a package manager like aptitude or synaptic to download and install packages, instead of doing so manually via this website.
You should be able to use any of the listed mirrors by adding a line to your /etc/apt/sources.list like this:
deb http://security.ubuntu.com/ubuntu bionic-security main universe
Comment: +1 I had to use this solution as well for my Google Cloud Ubuntu 18.04 LTS install before I could use apt-get for the 7.2 mbstring extension, then I was able to use the accepted answer.
Answer: Since the mcrypt itself (the package that php-mcrypt uses to do its crypt stuff) is no longer supported after PHP7.2, As of today, to install it specifically for php7.2, you'll need to make sure when installing to prefix all php7.2 extensions with php7.2-.
While initially the commands suggested by others to just install it work, when using it with an  framework version that requires mcrypt (such as Laravel4.2), it will require you to install mcrypt using pecl. Follow the fix here


Complex numbers in optics

Question: I have recently studied optics. But I feel having missed something important: how can amplitudes of light waves be complex numbers?
Answer: With any simple harmonic oscillator there are two quantities we are interested in, the phase and the amplitude. Complex numbers are an easy way to represent both of these in a single value, especially as a complex number can be written in the form $Ae^{i\theta}$ where $A$ is the amplitude and $\theta$ is the phase. This doesn't mean light has some "imaginary" component. The complex number is just a mathematical model for the light.
There are lots of ways in which complex numbers make it easier to construct mathematical models. If you have access to a copy of Roger Penrose's book "The Road to Reality" have a look at chapter 4 where he discusses this aspect of complex numbers.
Comment: So, if I reiterate all those calculations with real amplitudes, I am to get exactly the same results? I still feel a bit skeptical: as QM has been built upon optics, I could ask the same question, though in that case complex amplitudes make part of an axiom... I couldt not formulate a precise question, but I am still not satisfied ...
Comment: **So, if I reiterate all those calculations with real amplitudes**
Yes, but only if you keep track of the phases as well. Remember that waves with opposite phases will cancel so you can't just add up amplitudes and ignore the phase. You can do this without using complex numbers, but it's a lot more work.
Answer: John Rennie's Answer, that complex numbers simplify calculations with sinusoidally varying quantities by letting you do linear operations with complex exponentials and then reverting back to sinusoids at the end of your calculation, is altogether correct and a summary of what is called the phasor method for dealing with any quantity that varies sinusoidally with time (usually - occasionally a co-ordinate replaces time).
But there is also a very special relationship between complex numbers and Maxwell's equations (and thus with optics) that holds regardless of whether the variation is time-harmonic or not and is unique to Maxwell's equations. This is the notion of diagonalising or decoupling Maxwell's equations. Let's look at the Faraday and Ampère laws:
$$\partial_t \vec{B} = -\nabla\times \vec{E} \tag{1}$$
$$\partial_t \vec{E} = c^2\,\nabla\times \vec{B} \tag{2}$$
two coupled first order equations. You can solve them by brute force elimination, thus ending up with second order equations. Alternatively, to simplify things, we can uncouple them by diagonalising them. We seek a field $\alpha\vec{E} + \beta\vec{B}$ which does this: it so happens that if we put $\vec{F}_{\pm} = \vec{E} \pm i\,c\,\vec{B}$ then we get two decoupled, first order equations by adding $\pm i\,c$ times (1) to (2)
$$\partial_t \vec{F}_\pm = \mp\,i\,c\,\nabla\times \vec{F}_\pm \tag{3}$$
which simplifies the solution of Maxwell's equations (often the $i$ is written on the LHS to emphasise that Maxwell's equations are the first quantised Schrödinger equation for the photon). Try this: there are no other superposition weights that work: $\pm i\,c$ are the unique ones that do diagonalise Maxwell's equations.
So we could choose either $\vec{F}_\pm$, assume $\vec{E},\, \vec{B}$ are real-valued (which of course they are in the laboratory), solve Maxwell's equations with the complex $\vec{F}_+$ (or $\vec{F}_-$: it doesn't matter which) then split our complex number solution into real and imaginary parts to get the real valued $\vec{E}$ and $c\,\vec{B}$ at the end. This trick, and the vectors $\vec{F}_\pm$, are named the Riemann-Silberstein method and vectors, respectively (after Bernhard Riemann and Ludwik Silberstein).
However, it turns out that if instead we keep only the positive frequency parts of both $\vec{F}_\pm$ (i.e. we replace $\cos(\omega\,t+\delta)$ by $\exp(-i\,\omega\,t-\delta)$) exactly as in the phasor method, then it can be shown that a wholly left circular polarised field has zero positive frequency component in $\vec{F}_+$ - only $\vec{F}_-$ is nonzero. Likewise, a wholly right circular polarised has only a zero $\vec{F}_-$ part and the $\vec{F}_+$ is nonzero.
So, not only are Maxwell's equations diagonalised by the eigenvalues $\pm i\,c$, their diagonalisation by this unique, complex number splits the fields precisely into their circularly polarised components.
Answer: Isaac, let me say you are not the only one who feels this way. I had recently been tutoring an undergrad course (on nonlinear optics) and was almost shocked to find most of the students getting muddled in the usage of complex no.s. In fact, in the process, they had a hard time in also understanding/appreciating the beautiful physics.
In my opinion, it's disappointing that the lecturers/professors do not emphasize enough that the complex representation of electric field amplitude contains an additional term
c.c. (or sometimes H.c.)
c.c. stands for complex conjugate; H.c. means Hermetian conjugate and you can see that the addition of this term would make the overall quantity (on LHS) as real.
So, an electric field of the form $ E(z,t) = E_0 e^{i(kz - \omega t + \phi_0 )} + c.c.$ = $ 2\cdot E_0 \cos(kz - \omega t + \phi_0)$ indeed describes a real/physical wave.
Of course, while doing the maths it may become cumbersome to carry around the c.c. term through a series of equations, and so it is dropped (but implicitly, it is still there).
Perhaps the simplest reason for justifying the usage of this representation is that multiplication of two or more light waves - which can be encountered in several phenomena such as interference - can be simply understood by the addition or subtraction of the terms in the exponent.
As in, two waves $e^{i\omega_1 t}$ and $e^{i\omega_2 t}$ will produce terms $\propto$
$e^{i(\omega_1+\omega_2) t}$, $e^{i(\omega_1-\omega_2) t}$ etc.
Compare this with having to use trigonometric identities and you'll understand the beauty of using complex no.s in optics.

Complex numbers in optics


Equilibrium constant and reaction Quotient

Question: does reaction quotient After equilibrium has been achieved make any sense?
At equilibrium point rates of forward and backward reaction are same and the system is in dynamic equilibrium.The graph of concentration vs time shows a straight line parallel to x axis after equilibrium point.
Reaction quotient refers to ratio of concentration at any stage.This means that after equilibrium point reaction Quotient value will same as equilibrium constant as no more products are formed.So how can it have a value more than that of K ?!
I have been thinking about this for hours but I get more confused with time.
Comment: These two answers provide some insight into the relationship between $K$ and $Q$, but the main thrust is that at equilibrium $Q=K$. http://chemistry.stackexchange.com/questions/4410/k-eq-vs-k-c/4419#4419 and http://chemistry.stackexchange.com/questions/4977/le-chateliers-principle-how-can-the-equilibrium-shift-while-kc-remains-consta/4982#4982
Answer: $K$ is just the specific value of $Q$ for which $\Delta_\mathrm r G = 0$.
In that case:
$$\begin{align}
\Delta_\mathrm r G &= \Delta_\mathrm r G^\circ + RT \ln Q \\
0 &= \Delta_\mathrm r G^\circ + RT \ln K \\
\Delta_\mathrm r G^\circ &= -RT \ln K
\end{align}$$
For any system not at the equilibrium it is possible that $Q < K$ or $Q > K$. What is the "forward direction" is just a convention, it depends on how you decide to write the equilibrium. There is nothing special in one direction or the other. The system will "move" toward the direction that leads to equilibrium in both cases. In the first case the reaction will consume reactants to generate products, while in the second case the opposite will happen.
You can express this idea also in terms of the ratio $\frac Q K$. If it is > 1 then the reaction will consume reactants. This is also often referred to as the "Le Chatelier principle".


As a Buddhist with a Muslim family, community, and background... how do you integrate/cope?

Question: Coming from an Islamic background and having a community/Sangha that is loyal to the religion of Islam, how do you harmoniously integrate yourself and your Buddhist study and practice with the community you were born in including within a mosque?
Answer: I'm 26 and I considered myself becoming Buddhist when I was 14. I come from a very loyal Islamic family and I totally think that Islam is a beneficial religion... containing within it the simplest and easiest spiritual practices of all Abrahamic religions because it has a meditation+yoga-like prayer system, calling all practitioners to Practice with single-mindedness towards a singular God every day five times a day (namaj).
I made a lot of mistakes over the years in expressing these ideas with simultaneous conviction and non-defensiveness that is my power now.
Islam is a very strict religion on the the level of the 1st two trainings:

morality: unconditionally forbids all intoxication and has many other moral codes
concentration: routine concentration practice of prayer, using mantra method combined with yoga

Thus, even though I am Buddhist I don't run away from Islam. I fully embrace it and espouse the half-muslims to actually practice it because it has many health benefits.
I go to mosque when I can and when I am required to with my family and community and I integrate Buddhist science of spiritual practice to practice with single-minded mindfulness and not the ignorant desire-filled prayer most people probably do.
Buddhism is a religion that is fully integrated within my Islamic community and if I speak about Buddhism I speak about it without ever mentioning the word Buddhism or Buddha. I merely reference the practices such as yoga and meditation and pranayama which are nondenominational and conducive to the actual reason for namaj (improve concentration and oneness with Allah--a concentration object).
Thus, when I speak about Islamic practices, I find myself always integrating the nondenominational, spiritual principles of Buddhism within the structure of Islam.
Islam is a great religion and can be fully subsumed into the spiritual science of Buddhism. Practice the Buddhist virtue of modesty and let no one know of your attainments and your vigorous concentration practice.
Mentally discard silly Islamic/religious that you know by Buddhadharma are only created to help people stay doubt-free and cultivating practice concept and enjoy spiritual practice with your community!
Use the phrases and phrases you learned from within Islam. Display complete devotion to Islam and spiritual science in general. Islam isn't that complicated at all... it is easy to blend in and be spiritual, continue to use the Buddhadharma but always appear Muslim by practicing Right Speech within your community.
Answer: There is an e-book about the similarities between the two:
Common Ground Between Islam and Buddhism
by Reza Shah-Kazemi
with an essay by Shaykh Hamza Yusuf
introduced by
H. H. the Fourteenth Dalai Lama
H. R. H. Prince Ghazi bin Muhammad
Professor Mohammad Hashim Kamali
Answer: Islam comes from a Buddhists back ground. The Buddha taught that, Eliminating the ignorance which is driven by Pancakkhandha is the road to enlightenment for all sentient beings.(Pancakkanda, the five Aggregates)
Buddhism is still alive and well in Sufism.
Comment: *"...Islam comes from a Buddhists back ground..."* - Is that your own opinion? If not, could you then add a reference to that statement? Thank you.
Comment: The (more important) part which answers the OP's question is the last sentence.
Answer: Well certainly Allah is mentioned by The Buddha as Maha Brahma.

"He is Allah , the Creator, the Inventor, the Fashioner; to Him belong the best names. Whatever is in the heavens and earth is exalting Him. And He is the Exalted in Might, the Wise." (Quran 59:24)

Similarly the Great (Maha) Brahma is described:

"But there is Brahma, the Great Brahma, the Conqueror, the
  Unconquered, the All-Seeing, All-Powerful, the Sovereign Lord, the
  Maker, Creator, Chief, Appointer and Ruler, Father of All That Have
  Been and Shall Be." (DN 11)

Usually whenever people speak of a Creator that existing in the beginning of the universe they are referring to the same Maha Brahma that The Buddha spoke of.
This means Judaism, Christianity, and Islam likely came from the Brahma worlds or beings influenced by the Brahma worlds.
The angel Gabriel is likely an attendant of Brahma.
Maha Brahma in Buddhism is mostly good but sometimes influenced by the Evil One (Satan, Mara), is extremely powerful and knowledgeable but not all-knowing and all-powerful, but He usually praises The Buddha.
Certain virtues and morals that lead towards the extremely long-lasting Brahma worlds are also in-line with what helps one achieve arahantship, but The Buddha goes further and beyond the Brahma worlds towards arahantship here and now.
The Brahma worlds last for an extremely long time but eventually disappear towards the end of the universe-system, so arahantship here and now or going to the Pure Abodes is preferred.
Of course an arahant in the world is extremely rare, even during The Buddha's time there were few arahants.
Going to the Pure Abodes after death is also extremely rare.
Going to the Brahma worlds after death is also extremely rare.
It's much more common for people to go to hell, the animal womb, the realm of ghosts, or a lower heavenly world after death than the Brahma worlds.
Sariputta explains in MN 97 how to get to the Brahma worlds, by encompassing your awareness with good will, compassion, appreciation, and equanimity.
Similar teachings and virtues to what Muhammad says:

"Do you love your Creator? Love your fellow-beings first"
"They will enter the Garden of Bliss who have a true, pure, and
merciful heart"
"Adhere to truth, for truth leads to good deeds and good deeds leads
him who does them to Paradise"
"Ye will not enter Paradise until ye have faith, and ye will not have
faith until ye love one another"

This means the majority of people will most likely not go to the Brahma worlds after death (including most Muslims).
The majority of rules and virtues in Islam seem mostly inline with achieving arahantship minus the violence and sex allowed so it shouldn't be that difficult to integrate.
The Buddha forbids violence for monks under all circumstances whereas Islam allows violence in some circumstances.
The Buddha forbids sex for monks whereas Islam allows it under certain circumstances.
But the majority of rules in Islam are inline with achieving arahantship likely because they lead towards the Brahma worlds, and most of the things that lead towards the Brahma worlds are also inline with what helps one achieve arahantship.
But remember that arahantship directly comes from extinguishing mental fermentations (asavas) not from merely doing good deeds alone (which makes achieving arahantship easier but doesn't directly cause arahantship).
Answer: If Buddhism is regarded as 'psychology' rather than as 'religion', there will be no competition/conflict between the two.
Of course, if this attitude is adopted, generally the 'belief' aspects of cultural Buddhism (such as Buddha statues, reincarnation, etc) must ideally be dropped.
If the ancient Greeks did not introduce alien Buddha statues into Buddhism & if the ambitious Buddhist rulers & clergy did not taint their scriptures with Brahmanistic ideas (for the purpose of religious conversion), Buddhism may have lasted longer in central Asia due to not being falsely regarded as a form of idolatry.
Comment: How would you know you are not following a false imaginary modern form of Buddhism?
Buddhism is a great religion and it doesn't deserved labeled 'tainted'.
Comment: This comment displays not-knowing ("avicca") of the fundamentals of Buddhism where liberating truth is verified by each insightful practitioner: "'sanditthiko akaliko ehipassiko opanayiko paccattam veditabbo vinnuhi". MN 117 explains there are two kinds of Right View: "noble" ("lokuttara") & "tainted ("asava")". Cultural Buddhism is tainted since any kind of notion of reincarnated "self-view" is obviously tainted.
Comment: @Yinxu I deleted a series of comments which degenerated into criticizing each other (using words like "You" and "I"). Generally, if one wants to critique, question, or improve an answer, one can do that using just one (first) comment, rather than several. After your first such comment I recommend you let the answer's author have the last word, and don't post further comments unless it's 'a discussion' and *not* 'an argument' (and the subject of the discussion should continue to be answer, not the author). If you still don't like the answer you can downvote and/or post a better answer yourself.
Comment: Well, there's no way I could answer this specific question since I am not a Muslim myself.

That said: Bhikku Thanissaro have stated strongly that there is no indication that rebirth is simply a metaphor in the scripture, but is a fundamental aspect of the path: http://www.accesstoinsight.org/lib/authors/thanissaro/truth_of_rebirth.html
Comment: @Dhammadhatu "If the ancient Greeks did not introduce alien Buddha statues into Buddhism".... Are you just writing whatever or you have a proof for this?
Comment: @Epic See for example "Pre-iconic phase" and "Iconic phase" in [Buddhist art](https://en.wikipedia.org/wiki/Buddhist_art), and related topics such as [Aniconism in Buddhism](https://en.wikipedia.org/wiki/Aniconism_in_Buddhism) and [Greco-Buddhist art](https://en.wikipedia.org/wiki/Greco-Buddhist_art).


Game theory and differential equations

Question: Does anybody know, any (advanced/classic) textbook that combines game theory with differential equations in mathematical economics. Specifically, I an interested in asymmetric information problems.
Comment: Why do you think ODEs are relevant to games with asymmetric information?
Comment: Weibull's [*Evolutionary Game Theory*](https://books.google.ca/books/about/Evolutionary_Game_Theory.html?id=m98ed0_Na1sC&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false) has a chapter (Ch. 6) on ODE and its applications in evolutionary games.
Comment: @Michael Greinecker, neither I know that, nor I think that they are relevant...I am still searching and I am asking if there is some textbook that mat contain also asymmetric information. If there is not then I am not going to paint it black
Comment: @Rodrigo de Azevedo, it is a field that i am eager to leran!
Comment: If evolutionary game theory is an option then use https://mitpress.mit.edu/books/population-games-and-evolutionary-dynamics#preview-drawer.
Answer: At the intersection of differential equations and game theory one can find differential games. Arguably, the most famous applications of differential games are in warfare, e.g., the homicidal chauffeur problem. However, not all differential games are of the pursuit-evasion kind.
Whoever wants to learn differential games may wish to learn optimal control theory first. To the neophyte, I would recommend Evans's book (chapter 6 is on games):

Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory [PDF], Department of Mathematics, University of California, Berkeley.

The next step could be the following books on applications to economics:

Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, Gerhard Sorger, Differential Games in Economics and Management Science, Cambridge University Press, November 2000.

Luca Lambertini, Differential Games in Industrial Economics, Cambridge University Press, April 2018.

and, more on the stochastic side:

David W. K. Yeung, Leon A. Petrosjan, Cooperative Stochastic Differential Games, Springer, May 2006.

Unlike Evans's book, I have never read these ones. My listing of these books is not an endorsement.
Answer: This is probably an old question. However there is a book on PDE's and game theory.
Game Theory and Partial Differential Equations, Pablo Blanc and Julio Daniel Rossi.
If you found other books on this matter, I would like to know as well.

Game theory and differential equations


Moving king into check

Question: Can a player move their king into check if the opponents piece that is able to take king, is putting opponents king in check?
Comment: I think you will have to make an actual diagram with moves for this question to be clear.
Comment: player 1 moves his queen to put player 2 in check. Player 2 moves his rook just in front of his king to block player 1 queen. Player 2's rook is protected by his king (ie rook is next to king) Player 1 then moves his king into path of player 2's rook putting player 1's king in check. Can player 1 put his king into check or is this an illegal move?
Comment: In other words, Can a rook that is between it's king and opponents queen be identified as a piece that cannot be moved and allow opponents king to be moved into rooks path? Or is this a case where a king cannot move into check?
Comment: I don't think the player can move his king into a check position in the first place. Is this an illegal move?
Comment: player 1 moves his queen to put player 2 in check.
Comment: That move would be illegal. As my answer states, it is illegal for Player 1 to make a move such that his king is in check, even if the checking piece cannot move. See the linked question in my answer for a more thorough discussion.
Answer: It is never, ever legal to move into check. Period. No ifs, no buts. No exceptions whatsoever.
That's the best way to think about it, since it gives the least scope for confusion. If you want to think of it in terms of capturing the king ending the game, look at it this way: if you move into check, your opponent can capture your king, which immediately ends the game. It's irrelevant if your opponent's capture caused him to move into check too: you can't retaliate by capturing his king because the game already ended.
Comment: It may also be useful to recognize the difference between the rules involving check, versus a rule that says that a player whose king is captured loses: a player who has any move available that does not put the king in *immediate* danger must play such a move, but if all of a player's moves would place the king in immediate danger when it isn't already, the game ends without the player being obliged to put the king in danger.
Answer: No. Check is check, even if the checking piece cannot legally move. There is extensive discussion of this in the answers to the question illegal (?) move can put a king in check?.
Comment: But can the player who moved his king into check make an illegal move?
Comment: I don't understand your question. Can you update the original question with an explicit example?
Answer: I'd rather be more cautious and answer this question taking into account the time control used in the game because, as you will see, there are some concessions that regulations grant when the players have less time to think.
If each player's thinking time is at least 60 minutes:
The move in question is indeed illegal, as others have commented. End of story. Even though nobody notices the irregularity for a while, as the rules indicate (emphasis mine):
7.5.1 An illegal move is completed once the player has pressed his clock. If during a game it is found that an illegal move has been completed, the position immediately before the irregularity shall be reinstated. If the position immediately before the irregularity cannot be determined, the game shall continue from the last identifiable position prior to the irregularity. Articles 4.3 and 4.7 apply to the move replacing the illegal move. The game shall then continue from this reinstated position.
End of story?
There might be a rare exception in case the game has ended (by checkmate or resignation) without the mutual check (or any other irregularity) being noticed, and the players have signed their scoresheets. I am not sure what happens if the illegal move is noticed after that because:
5.1.1 The game is won by the player who has checkmated his opponent's king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7.
5.1.2 The game is won by the player whose opponent declares he resigns. This immediately ends the game.
Rapid chess
When all the moves must be completed in a fixed time of more than 10 minutes but less than 60 minutes for each player; or the time allotted plus 60 times any increment is of more than 10 minutes but less than 60 minutes for each player.
In my opinion, the problem is more clearly described in other questions  (both marked as a duplicate of this one):
Is it legal for a move to put both sides in check?
Simultaneous check
Surprisingly, the rules specifically mention the situation of a mutual check:
A.4.4 If the arbiter observes both kings are in check, or a pawn on the rank furthest from its starting position, he shall wait until the next move is completed. Then, if an illegal position is still on the board, he shall declare the game drawn.
Otherwise, it is understood that the game can continue. For reference: A position is illegal when it cannot have been reached by any series of legal moves. (article 3.10.3)
Now, if this actually happens in a real game, the use of the word illegal to describe the move after the game has ended is arguable, because the move was illegal at its time, but now it is part of a legal game supported by the rules!
For other irregularities, the procedure is similar:
A.4.2 If the arbiter observes an action taken under Article 7.5.1, 7.5.2, 7.5.3 or 7.5.4, he shall act according to Article 7.5.5, provided the opponent has not made his next move. If the arbiter does not intervene, the opponent is entitled to claim, provided the opponent has not made his next move. If the opponent does not claim and the arbiter does not intervene, the illegal move shall stand and the game shall continue. Once the opponent has made his next move, an illegal move cannot be corrected unless this is agreed by the players without intervention of the arbiter.
To be completely precise, these Rapid rules do not apply if certain conditions are met. According to A.3.1, the Competition Rules shall apply to Rapid chess (i.e. the illegal move cannot stand) if:
A.3.1.1 one arbiter supervises at most three games and
A.3.1.2 each game is recorded by the arbiter or his assistant and, if possible, by electronic means.
Otherwise, the Rapid chess rules do apply and the illegal move has a chance to stand.
Finally, I have to mention that these Rapid chess rules also apply to Blitz, when all the moves must be completed in a fixed time of 10 minutes or less for each player (or the allotted time plus 60 times any increment is 10 minutes or less).
Comment: I think this answer misses the point: in all cases it **is** illegal to put one's king in check, and that's clearly what the OP was asking about. What happens *after* an illegal move is played indeed depends on the time control, but that's a bit off-topic here and might cause even more confusion for the OP.
Comment: I thought it should be relevant because the rules specifically mention the OP's question. And the OP should know that if their opponent makes an illegal move in blitz **and** the OP does not notice the irregularity, it may stand.

Moving king into check


Is there any software (with a graphical user interface) for creating Style Layer Descriptors?

Question: Is there any software that can easily create a Styled Layer Descriptor (SLD) without using a  script?
Comment: I second that mention of QGIS and the "save as SLD" plugin - it will even allow you to publish it directly to GeoServer without having to "save" to a file first.
Answer: You can try these:

Altas Styler
Udig
Kosmo or OpenJump
And Qgis either natively or with the help of the SLD plugin
Answer: If you are an ArcGIS Desktop user. Have a look at GeoCat Bridge:  http://geocat.net.
If you're looking for webbased solutions, try GXP Styler: http://gxp.opengeo.org.
QGIS now has native support for SLD.
Answer: Here are two more options:

You can install the GeoExt Styler extension and use it directly to set the styles.
If you have ArcGIS desktop, and want to convert from your Map Documents/ layer files to sld files without any headaches, you can use Arc2Earth. They even have a free (free as in Beer) community edition, which you can use to export the sld files of layers one at a time. As someone who is far too invested in ArcGIS desktop, I can't  overstate how easy it has made my life.
Answer: You can use Tilemill. it allows you to export SLD (compatible with mapnik)
Answer: Use geoserver CSS module
http://docs.geoserver.org/latest/en/user/extensions/css/index.html
It creates SLD by it's own, there is no need to learn SLD.