How realistic would charging batteries with inductive power transmission be?

Question: I've read articles on inductive charging and related stuff on Wikipedia and now I wonder - what if I wanted to develop a battery (also a matching charger and the battery compartment) with completely insulated terminals that gives/accepts power via induction as in an inductive charging system? How practical would such battery be?
Comment: I think it is a good idea and practical. Especially in battery pack design.
Comment: You just have to keep the inductive element away from the cell electrodes in a pack.
Answer: Efficiency could be a bit of a problem.
The induction power transfer is done through a high frequency EM field.  This transfer is not 100% efficient as it radiates energy in other directions (careful design could increase transfer efficiency, but you'll never get a perfect transfer).  The generation of the HF EM field consumes energy.
Therefore, you may get at best 80% \$^*\$ of the energy transferred from the battery to the device.
Then there is the cost.  It's not a cheap system compared to what is essentially a bit of metal that is used currently.
Combine the two and what is maybe a 99.999% efficient piece of metal would be being replaced by a complex circuit costing many dollars and reducing the efficiency to maybe 75%.\$^*\$
Then of course, if the device is switched off, the battery will still be consuming power in generating a HF EM field that is not being used, so there would need to be a way for the device to turn off the battery - and turn it on again without any power (most easily done with good ol' wires...)
So nice as it would be, I can't see it really being practical.
\$^{*}\$These efficiencies are just made up off the top of my head and not to be quoted as accurate.
Answer: It will be problematic at best. Batteries are similar to capacitors in that you want to maximize electrode surface area inside the cell, while minimizing electrode volume, since the electrode doesn't itself store energy.
This large area of conductive material can develop eddy currents in the presence of an alternating magnetic field, dissipating a significant amount of inducted energy as heat. This heat will also serve to shorten the battery's life, and in the case of lithium batteries, reduce charge rate since the battery's temperature must be monitored and kept below a certain level, lest you start a fire.
Eddy currents are also a problem for high-current windings in planar transformers and foil windings in regular transformers. They are strongest near the transformer's gap.


SolusVM Migration

Question: I have an old server on which I am hosting about 30 OpenVZ VPS Servers. I have purchased a new server which is much more powerful and I plan to do a complete migration in the future. Currently I would like to know how to migrate VPS servers one by one, where the migrated VPS would keep all of the configuration, IP addresses and be completely independent from the server it was migrated from.
Answer: Actually you have to use the vzmigrate command to transfer VPS's one at a time
https://documentation.solusvm.com/display/DOCS/Migrating+OpenVZ+Containers
Or you can migrate whole /vz/private directory and then all configs from /etc/sysconfig/vz-scripts/ using something like this:
<code># cd /vz
# nice tar cpPf - private | ssh -e none -c blowfish IP_of_dest_server '(cd /vz; tar xpPf -)'
# scp /etc/sysconfig/vz-scripts/*.conf root@IP_of_dest_server:/etc/sysconfig/vz-scripts/
</code>

SolusVM Migration


About sharks and how they find fish

Question: Other than olfactory senses do sharks use some kind of sense that uses electromagnetic waves? Is this similar to an electric eel? I saw a book with the cover statement 'Sharks never get cancer'. IS this possible or just 'quackery' ? Could being constantly 'bathed' in some kind of electromagnetic field cause pre-cancer cells ( that are already unstable) to be 'disrupted'?
Comment: [Sharks do get cancer.](http://www.theguardian.com/science/brain-flapping/2012/sep/24/sharks-cancer). See also, ["Shark cartilage, cancer, and the growing threat of pseudoscience"](http://www.ncbi.nlm.nih.gov/pubmed/155747500). Contrast, [this nonsense](http://www.amazon.com/Sharks-Dont-Get-Cancer-Cartilage/dp/0895295202/ref=sr_1_1?ie=UTF8&qid=1412532193&sr=8-1&keywords=shark+cancer).
Comment: Oops, the link was wrong: [Shark cartilage, cancer, and the growing threat of pseudoscience](http://www.ncbi.nlm.nih.gov/pubmed/15574750)
Comment: I didn't say it was 'sense or nonsense'. Notice I asked if this was just quackery? But is cancer in sharks rare? What about electric eels, do they get cancer; is it rare? I read on wikipedia there is a biological paradox related to whales. They obviously have alot more cells than humans yet they don't get cancer as much as a random process would 'cause' if cancer causes are 'random'. Is this true? Why is cancer in the Heart rare?
Comment: Sorry, I didn't mean to imply that you were endorsing that view; just making an observation about the available literature on the topic.
Comment: Thank you for the response but what about my other questions?
Comment: I don't know the answers, sorry. I think that's probably best left for the answer space rather than comments anyway.
Answer: Sharks sense their prey with the normal senses, they see, hear and smell them.
They have a remarkable sensitive sense of smelling, which enables them to sense highly diluted traces of prey. They can also use their smelling to determine the direction where a certain smell comes from. This is achieved by the timing in which the senses arrive in different parts of the sharks nose. See references 1 and 2 for more details.
While sharks have eyes which are similar to that of vertebrates, they have an additional reflective tissue called "tapetum lucidum" behind their retina, which reflects the light back and therefore raises the sensitivity of the eye. It seems that a lot of shark species are either colorblind (because they only have rod cells but no cones) or they had only one kind of cone cells which allows them only to see one color. For sharks it is obviously more important to detect objects than to see colors. See references 3 and 4 for more details.
The sense of hearing of sharks is also highly sensitive and is able to detect sounds from far away. See also references 5 and 6 for more details.
The most interesting sense of sharks is their electrosensory organ. This is also called Ampullae of Lorenzini which is a number of sensory cells along the head and which are able to detect the weak electric fields that exist around living animals. This sense only works on a very short distance. See references 7 and 8 for more details.
Finally sharks have the so-called lateral lines (which are present in most fish), which is an organ which detects movements and vibrations in the water around the shark. See the Wikipedia page for more information.
And for the sake of completeness (already quite nicely answered by @Susan in the comments), sharks do get cancer. All cures which are made from shark and claim to be able to treat cancer are pseudoscientific nonsense. This also endangers many shark species as they get radically overfished. See references 9 and 10 for more details.

References:

Smell and Taste
The Function of Bilateral Odor Arrival Time Differences in Olfactory
Orientation of Sharks
Microspectrophotometric evidence for cone monochromacy in sharks.
Vision and a Carpet of Light
Hearing and Vibration Detection
Functional anatomy of the auditory system in sharks and rays
The Shark's Electric Sense
Electroreception
Mythbusting 101: Sharks will cure cancer
Shark cartilage, cancer and the growing threat of pseudoscience.
Comment: As far as I am aware, cells are not destabilized by weak electromagnetic fields. This is different for high energy, but then we are talking about denaturating proteins.
Comment: Excellent information. Is cancer in sharks rare? If an animal has some type of 'function' like the Ampullae of Lorenzini that 'uses' weak electric fields could this de-stabilize pre-cancerous cells that are already unstable to some extent.
Comment: Are they de-stabilized by microwaves or M.A.S.E.R.s?

About sharks and how they find fish


Difficulty with a Fourier Transform

Question: What would be the best way to take the Fourier transform of
$$
f(t)\cdot \cos\big(\pi(t-1)\big)
$$
I'm aware that when you take the Fourier Transform of $\cos(kt)$ you get two impulse at the location of $k$. And that the $(t-1)$ would create a complex exponential. But you can only apply the time-shift when both functions are time shifted (at least to my knowledge at least). Really the $\pi$ and the non-time shifted $f(t)$ are really throwing me off. Thanks!
Comment: It could be useful to rewrite $f(t)\cos(\pi(t-1))$ using Euler's formula; $\cos(x)=(e^{ix}+e^{-ix})/2$. What happens to the Fourier transform then?
Answer: It is easy to see that using the trigonometric identity in Equation $(1)$ below
$$
\cos(\theta_1 \pm \theta_2) = \cos(\theta_1)\cos(\theta_2) \mp \sin(\theta_1)\sin(\theta_2) \tag{1}
$$
We have
\begin{align}
f(t)\cos\big(\pi(t - 1)\big) &= f(t)\overbrace{\cos(\pi t - \pi)}^{\text{use Equation}\ (1)}\\
&\equiv -f(t)\cos(\pi t)\tag{2}
\end{align}
Which can be rewritten as
$$
-f(t)\cos(\pi t) = -f(t)\cos\left(2\pi \frac t2\right) = -f(t)\cos(2\pi f_c t)\quad\text{where}\quad f_c = \frac 12
$$
And we know the Fourier cosine modulation frequency-shift property in equation $(3)$:
$$
\mathcal F\big\{x(t)\cos(2\pi f_c t)\big\} = \frac 12\big[X\left(f - f_c\right) + X\left(f + f_c\right)\big]\tag{3}
$$
You can now easily use Equation $(2)$ and $(3)$ to find the solution.
Comment: i most def forgot about that trig identity. i will try that. thank you!
Comment: You're welcome. If this answers your question, remember to accept the answer.
Answer: We have signal $y(t) = f(t)cos(\pi t-\pi)$. You are modulating amplitude where bias is $\pi$. By using Euler's formula you can rewrite singal as:
$$
y(t) = f(t)\frac{1}{2}\left(e^{j(\pi t - \pi)} + e^{-j(\pi t - \pi)}\right)
$$
$$
y(t) = \frac{1}{2}f(t)e^{j(\pi t - \pi)} + \frac{1}{2}f(t)e^{-j(\pi t - \pi)}
$$
$$
y(t) = \frac{1}{2}f(t)e^{j\pi t}e^{-j\pi}  + \frac{1}{2}f(t)e^{-j\pi t}e^{j\pi}
$$
And then by Fourier transform we get :
$$
Y(j\omega) = \frac{1}{2}F(j(\omega -\pi))e^{-j\pi} + \frac{1}{2}F(j(\omega+\pi))e^{j\pi}
$$
$$
Y(j\omega) = -\frac{1}{2}F(j(\omega -\pi))  -\frac{1}{2}F(j(\omega+\pi))
$$
And we get this becuase $e^{-j\pi}=-1$ and $e^{j\pi}=-1$

Difficulty with a Fourier Transform


If white curtain scatters light, and thus doesn't form images, why do movie projectors use them?

Question: I tried to look up for answer about why don't white objects form images like mirrors do. Answers suggested the reflection wouldn't be specular. But how could you be convinced, as projectors use them well to reflect light and produce clear images?
Answer: If a screen reflected as a mirror, a viewer would see the image of the projector with a light beam coming out. Good materials for a screen for conventional projection of images have to scatter light back as point sources on their surface. White surfaces do that, they scatter light as point sources incoherently thus the eye perceives "white" .
The wavefront of the beam of the projector has a space distribution which carries the image , i.e. different frequencies and intensities for the different colors of the image projected. These hit in space different point sources which reflect back the specific color as if it is coming from that point source, and thus the image is formed for the observer.
Comment: a person is not a light source to start with,the mirror reflection is secondary and is not strong enough as a light source. In addition the point sources of a screen, in contrast to a mirror,disperse incoherently the light falling on them . the important thing from the light of the projector is that it is coherent, the phases between the frequencies are fixed  and the beam trajectory is linear. This is not the case from the light reflected from a person on a white screen.
Comment: Thanks, but i am still concerned about what the difference between the light coming from the projector and light coming from a person standing in front of the curtain would be. Wouldn't the light coming out of the person (or his clothes) too be the combinations of different frequencies and intensities for different colors. Why doesn't the screen show same effects in this case?
Comment: "a person is not a light source" tats new


how do i use conditional probability to find the answer

Question: Your e-mail provider has a very good spam filter that only 1.5% of all
e-mails passed the filter are spam. A lot of spam e-mails are trying to phish for your personal
information so they ask you to go to an unknown web site where you are asked to enter this
information. About 98% of the spam email will ask you to click on a link without providing you
with the explicit url. In addition, 3% of the legitimate e-mails will ask you to click on a link
without the explicit url being shown. For a random e-mail in your inbox (so this email has
passed the filter), if you are provided a link without the explicit url, what is the probability that
the e-mail is spam? BONUS: Why is your answer counterintuitive?
Comment: Need a self-study tag?
Comment: I think a tree with 2 levels of branching is the way to start: Begin with spam/no_spam, with .015/.985 probabilities respectively. Then each of those branches has explicit_url/no_explicit_url.
Answer: $P(spam|no URL) = \frac{P(no URL|spam)P(spam)}{P(no URL)}$
Therefore
$P(spam|no URL) = \frac{(0.98)(0.015)}{(0.015*0.98)+(0.985*0.03)}$
It's not counterintuitive if you understand Bayes and realise the prior probability is what really drives the posterior if it's small, but for an undergraduate answer: it's counterintuitive because it seems like it would be more "likely" that since 98% of spam comes without links and only 3% of legitimate comes without links and this doesn't have a link so it's gotta be spam, but the probability of it not being spam is higher.
Answer: This is evidently self-study, so I'll explain a general method rather than giving you the answer.
The law of total probability is a simple way to approach problems of this type. Suppose you want the probability that some event A happens, but you have to consider two possible scenarios B and C. The law of total probability says:
$$P(A)=P(A|B)P(B)+P(A|C)P(C)$$
In other words, "Total Prob of A" = "Prob of A with B" + "Prob of A with C". The conditional probability of B given A is just the proportion of the total probability made up by the first term: "Prob of A with B" / "Total Prob of A".
Now try setting A to be "link is provided without URL", B to be "e-mail is spam" and C to be "e-mail isn't spam".
You will find that the e-email probably isn't spam even when a URL-less link is provided, i.e., even when it looks like spam. The reason has to do with the quality of your spam filter, but I'll let you figure out the reason in more detail.
Answer: The approach using the branches on the path is a reformulation or restatement of Tilefish Poele's answer.
There are two paths to No Explicit URL:
A: Spam --> No Explicit URL (with probability 0.015 * 0.98)
B: Non_Spam --> No Explicit URL (with probability 0.985 * 0.03)
In the universe of No Explicit URL, the probability you want is A / (A + B), as in TP's answer.


Which APP should I use if I want to draw a workflow with mathematical expressions on Mac?

Question: I want to find a graphic application that can draw basic workflows with mathematical expressions. For example, I want to draw something like the following figure from "Implementation and Optimization of Differentiable Neural Computers" by Carol Hsin.
Comment: `https://www.overleaf.com/learn/latex/LaTeX_Graphics_using_TikZ:_A_Tutorial_for_Beginners_(Part_3)—Creating_Flowcharts` code since the link would break at the dash. https://tex.stackexchange.com/questions/168314/how-to-use-latex-commands-to-draw-a-flowchart
Comment: See [this Meta answer](https://apple.meta.stackexchange.com/a/2181/88313) for important guidelines that should be followed when asking for a hardware/software recommendation. It will help everyone by preventing unnecessary answers for items that don't fit your request and could help prevent down votes and closure.
Comment: Hi, I've changed the title. Does this help clarify my request? I find LaTeX is too complex and it is hard to find a friendly document to start with. Could you please offer a simpler tool? or a more friendly document and application for LaTeX that can help me draw the above picture? Thanks @ankii
Answer: Keynote on the mac can do both. It has standard shapes and the ability to draw lines connected to those shapes.  It's a simple way to draw a flowchart. If also supports mathematical expression thru latex. There is an option to insert an equation and you can define anything you like by using latex.
Here is a link to help you with Latex. On this link, you can see what the latex command is for most any symbols you can imagine. I use this page to help me find the correct latex command to put in Keynote.
I have included a very simple and crude flowchart I made in about 5 minutes using Keynote.  The math equations are bogus as I was just trying to show the capabilities of Latex.
Answer: Omnigraffle can make flow charts very easily. It's very good at linking lines to boxes, so that you can reposition the boxes and retain the linking.
Comment: Hi, I used Omnigraffle for sometimes, it does not support mathematical expressions. And expression copy-pasted into could be very blurry somehow. I want something that supports both flow charts and mathematical expressions
Answer:
Photoshop and InDesign could do some of that. I am not sure of fonts being mathematical, so see if you can find 3rd-party fonts for the same. Adobe Illustrator is used for vector graphics extensively.

The industry-standard vector graphics software  is used by millions of designers and artists to create everything from gorgeous web and mobile graphics to logos, icons, ..

https://www.adobe.com/products/illustrator.html
Autodesk SketchBook can also help draw basic shapes rectangles, lines.
Same for https://draw.io
I'd still add LaTeX as an option. You shouldn't be scared of it.
https://www.overleaf.com/learn/latex/LaTeX_Graphics_using_TikZ:_A_Tutorial_for_Beginners_(Part_3)—Creating_Flowcharts gives an introduction. Use templates given on that site to start drawing. Use https://tex.stackexchange.com/ for reference or asking doubts.
https://tex.stackexchange.com/questions/168314/how-to-use-latex-commands-to-draw-a-flowchart gives you a working solution too.
Comment: Photoshop is a terrible idea: it's a bitmap editor for photos, not a drawing package for vector objects. Illustrator would be the Adobe tool best suited.
Comment: See if you can make that em dash in the URL work, and replace code with link.
Comment: I somehow completely missed illustrator!
Comment: Also, Ps exports png right ? and vectors can be drawn using Pen tool I guess. How come it can't draw vector objects ? Or do you mean that it is tough to draw using it ?
Comment: Well, OK: it can draw paths and text, but it's primarily a bitmap editor and you have to raster and flatten those elements to save in some of the formats: Illustrator is a tool much more suited to the task of grouped boxes, text and lines semantically linked.
I often see people suggesting PS to edit text in a PDF and it drives me potty!!!


Cannot summon Durnehviir even after unlocking all 3 shouts, even in an open area

Question: I've been scratching my head over this for the past few hours. I have spent 3 dragon souls and unlocked the 3 words required for the  Summon Durnehviir shout. I followed the advice of other answers in this site, and did the shout in an open ground near Whiterun, pointing to the ground. But nothing happens. One thing I noticed was that when I use the shout, it usually just says "Dhur", and if I shout several times, once in a while the shout changes to "Dhur-nah", but that's it. Nothing else happens. I saw on this page: http://elderscrolls.wikia.com/wiki/Summon_Durnehviir "Unlocking the first word, for example, results in the Dragonborn shouting "Dur", but nothing else happens". This seems to be exactly what's happening to me, but I've already unlocked all 3 words. Please help!
Answer: Ah, ok, I figured it out. I had to press and hold the 'Z' key until the dragonborn shouts all 3 words. Just hitting 'Z' caused only the first word to be spoken.
Comment: That applies to all shouts. You need to hold the key to use the higher levels, i.e. all the words. Using a higher level shout also incurs a higher cooldown and some shouts only work by using them at level 3.
Comment: You can easily see other shouts that you need to go this with when the cooldowns for word 1 and 2 are like 10 seconds and word 3 is 300
Answer: I've been trying to post on many forums for this answer because my experience with durnehviir was completely different from what I've seen on forums and on youtube. Took me a few days of trying here and there. Pointing at the ground and holding the shout button didn't help, and a flatter open space didn't either. I tried in several places..
So*** of course purchase the 3 levels***
Randomly walking towards Arkngthamz, you have to take some big detour around the mountains around Fort Sunguard. I have a picture of the exact location but this site says the file is too big. On the skyrim map, it's almost directly south of morthal all the way to almost to the border of the map.
Anywho, there's a dragon burial ground in the area, with a spirit-light-thing shooting directly from it to the sky. At the time there was a dragon flying about it, but then some dawnguards showed up, battle with them, dragon disappeared and then shortly returned aftewards (in the air). I tried shooting at it, but it was completely uninterested. It finally touched down and i started shooting at it, when I realized I was shooting at  Durnehviir (name on 'enemy health bar'). I put two and two together and viola.
I shouted to the ground inside of that spirit light thing dragon burial ground, and the rest is the same as the other forums. You have to shout 'summon durnehviir' 3 times waiting 2 in game hours in between each shout. And that's it. Totally came about on accident.
Ps: The dragon burial ground was still lit up after SOUL TEAR was unlocked completely, so idk if all that was a coincidence. And sorry for the long response. Also it seems you have to summon durnehviir 3 more times after that if you want him to fight for you


What do the purple lines represent in the Industrial Tech Map?

Question:
They only started appearing after the first students arrived in the Community College, so I assume it has to do with the tech level. What does it mean exactly?
Answer:
Does education spread across cities to increase tech level, and how far?
Tech points are generated at a community college or university as sims enter the doors of the education building. If you turn on the tech dataview, you'll see tech points reaching out from the school to your industry as purple lines, as well as each industry building's accumulated tech points. The purple lines deliver tech points to industry buildings. When enough points are accumulated in a building, that building moves up a tech level.

Also note that a college can only raise buildings to tech 2 whereas universities can get them to tech 3. On the map (if you have both institutions) you will be able to see two different lines being generated (slightly different shades of purple w/ the univ line being above the college line)
Comment: The space station great work also does this.
Comment: Correct -- the space station is the only way for one city in the region to (indirectly) raise the tech level in another (ie: you will want to have a university in your electronics city to up your electronics production, this means you can research the Space Center great work & and you can save a ton producing your own computers).


Ethers and Web3-React: Cannot estimate gas when trying to connect with contracts deployed on testnet and using Alchemy as node provider

Question: I'm trying to connect with contracts deployed on the Rinkeby testnet using a node provider. When I was testing using hardhat as a local node, the contracts are called with no problem, but when I change to Rinkeby, I get an error cannot estimate gas; transaction may fail or may require manual gas limit (error={"code":-32000,"message":"execution reverted"}, method="call" for all the contract functions I'm trying to call. I've seen forums saying that it's usually due to the node being unable to estimate the gas limit and that I should manually set it.
By the way, Web3-React and Ethers.js don't contradict each other despite the naming. Web3-React is simply a React state machine that dynamically keeps track of my current wallet address, chain id, and browser provider Web3Provider, which I also use to create Contract instances using its signer. I use Ethers to create the Contract instances, format and parse data, and use its getDefaultProvider method to connect me to Alchemy. I made sure my rinkeby account had ether, and to change my local contract address variables to those of the ones deployed.
I'm also honestly a bit confused on what to do next, shouldn't the app suffice with just the Web3Provider instance from Web3-React? I've read on a lot of tutorials but nothing that explains something like this specifically.
Some example code below to show how the project is structured:
I've been keeping track of variables from Web3-React globally via React Context like this:
const value = useMemo<ContextWallet>(
    () => ({
      ...
      isActive: web3React.active,
      account: web3React.account ?? undefined,
      chainId: web3React.chainId,
      library: web3React.library,
      ...
      connect,
      disconnect,
      ...
    }),

For clarification, web3React.library essentially returns new Web3Provider(window.ethereum) where Web3Provider is imported from @ethersproject/providers. web3React.account returns from the ethereum request eth_accounts, web3React.chainId is from the request eth_chainId or net_version, and web3React.isActive lets us know whether the connection is working or not.
To create a contract instance via a signer I use the following functions:
export function getContract(address: string, ABI: any, library: Web3Provider, account?: string): Contract {
  if (!isAddress(address) || address === AddressZero) {
    throw Error(`Invalid 'address' parameter '${address}'.`)
  }

  const contract = new Contract(address, ABI, getProviderOrSigner(library, account) as any)
  return contract
}

export function getProviderOrSigner(library: Web3Provider, account?: string): Web3Provider | JsonRpcSigner {
  return account ? getSigner(library, account) : library
}

function getSigner(library: Web3Provider, account: string): JsonRpcSigner {
  return library.getSigner(account).connectUnchecked()
}

As for the provider to Alchemy, I did it like this but I don't really know what to do next:
getDefaultProvider(getNetworkName(Number(CHAIN_ID)), { alchemy: ALCHEMY_API_KEY })

The next snippet is an example of how I call a contract function:
const depositEth = async (amount: number, gas: any) => {
    setLoading(true)
    if (!farmContract || !vaultContract) return
    try {
      const tx = await farmContract.depositEth({
        value: parseEther(amount),
        gasPrice: gas,
      })
      await tx.wait()
      await farmContract.once('EthDeposited', (sender, amount, tx) => {

        // At this point, the transaction should have been mined already
        console.log('EthDeposited event detected: ', tx)
        wallet.reload()
      })
    } catch (err) {
      console.log('error depositEth ', err)
      wallet.reload()
    }
  }

Can someone offer some suggestions or advice on how to solve this step?
Thanks!
Answer: you should put gasLimit either manually or dynamically in last argument of SC method call.
 const tx = await farmContract.depositEth({
    gasLimit: <estimate number>,
  })

for getting the gas limit dynamically, use this before calling the actual method:
const estimateGas = await farmContract.estimateGas['depositEth']()
const tx = await farmContract.depositEth({
    gasLimit: estimateGas,
  })

Also, you can add new a bit margin to gasLimit using this:
export function calculateGasMargin(value: BigNumber, margin = 1000):BigNumber {
  return value.mul(BigNumber.from(10000).add(BigNumber.from(margin))).div(BigNumber.from(10000))
}

wrap gasLimit with calculateGasMargin:
{
    gasLimit: calculateGasMargin(estimateGas),
}


Tumble dryer induction motor wiring

Question: I have removed a motor from our old Hotpoint tvf770p tumble dryer. The motor was working fine (the rear drum bearing had worked through the bearing and rear casing). I am considering using it on my son's blower for his forge (he's a blacksmith). The motor has three wires, the black and red wires go through the capacitor while there is also a separate white wire. Does anyone know: a) what is the white wire, b) how do I wire it up? The tumbler had a reverse drum cycle so I suspect it may be something to do with changing the motor's direction of rotation.
Comment: Nope.....single phase, 240volts.
Comment: I'd **guess** it is a 3 phase motor, so you need all wires to power it, not just the red and black one.
Comment: Usually there have 3 terminal twin caps in one (start/run): find the service manual
Comment: Just because the dryer ran from 240v/1ph does not mean the motor is definitely single-phase. In some usage cases, BLK-RED-WHT is synonymous with U,V,W. Tony's right, the service manual is likely the only source of correct information. Can likely find something on an appliance parts website.
Comment: Any info on that red sticker/name plate??
Comment: Can you post photos of the nameplate please?
Answer: This is a PSC (permanent split phase capacitor motor) that has two windings that together produce the rotating field. One is fed through the run capacitor, so that the current through it is out of phase with the other winding. They are normally wired as below. The connection between the capacitor and the  neutral side can be either internal to the motor, in which case 4 wires come out, or external, so that there are 3 wires, and the cap is commoned elsewhere.

To reverse these motors, you need to reverse either one of these windings, which would require a two pole changeover switch, so specifically reversible motors are connected a little differently.

(picture from here) On these motors the two windings aren't differentiated 'main' and 'auxiliary' as is normal - the auxiliary is usually a higher resistance which allows the main winding, which takes more current to use more of the available space. The windings are identical, and the cap is connected between them. Imagine that the white wire on yours is connected to the 'L' terminal on the first diagram, and the red and black at the two right hand corners. That way, whichever one the switch connects to becomes the main, and the other the auxiliary, which reverses the sequence of the field.
For single direction, you just need to connect up the white, and whichever of the red or black produces the right rotation, and leave the other side of the cap connected to the motor winding and nothing else.

Tumble dryer induction motor wiring


How can I prove that my article has not been submitted to another journal?

Question: I just submitted a paper to some journal. Since they didn't specify a template, I used the IEEE template. Unfortunately, they immediately rejected my paper because they think I already submitted the same paper to one of the "IEEE Transactions" journals. I know for sure that's not the case. But how I can prove to them that my paper is not submitted to another journal. Is there a database for a list of submitted papers?
Comment: That's pretty rough. No, there is no such database, but you typically need to fill a form / check a box while submitting that you are not submitting published work, and that it is not under consideration elsewhere.
Comment: Your question's a bit vague. Did you use the IEEE template to submit to another journal, which rejected because they thought you've submitted to IEEE transactions? What exactly did the rejection email say - did they say they're rejecting because your paper's under consideration at IEEE transactions?
Comment: Yes they specify that main cause of the desk rejection is the IEEE header.
Answer: If I understand you correctly, they thought it was a double submission because the template you used included the header "IEEE Transactions on ..."?
Email the editor and explain that there has been a misunderstanding. If you make it clear that you only used the template because there was no template specified and you liked that one, a reasonable editor will probably at least remove you from their blacklist, unless they have other reasons to find your submission shady. They may or may not agree to consider your submission after all.
As a side note, "IEEE Transactions" is not even a journal. There are many "IEEE Transactions on <Topic>". If the template really only said "IEEE Transactions" you could note this in your explanation.
Comment: Thank you, I did contact the chief Editor explaining my situation. I hope this clarify the situation. Thank you.
Answer: Of course no such database exists - it would be an incredible breach of review secrecy if people could look up what papers I currently have under review.
That said, the much more important question is why you even have this problem. A journal would never assume that a paper is already under review elsewhere without a strong reason. Maybe one of the reviewers reported the paper as double submission (I have done this in the past when I received two very strongly related parallel submissions).
Even if you really are innocent and they just jumped to this conclusion based on the template, there  is nothing to do than to move on. A journal can choose to reject your paper for any reason or no reason at all. You can of course contact the EiC and clarify, but if they don't believe you, you don't really have a recourse other than never submitting there again.
Answer: There is no such thing as "submitted paper database".
There is also no method to prove that you did not submit the paper anywhere else - the journal relies on your (signed) statement "I did not submit the paper to any other journal.". If the journal still rejects the paper on this ground without providing any evidence for this claim, this is a red flag. The only thing you can do is to approach the editor and certify again that the paper has not been submitted anywhere else.
I can imagine that the journal may have some guidelines on formatting (but no template) and that your paper would not have been rejected if it would have been formatted according to the guidelines. (It may look weird to use a template specific for one journal but submitting to another, though. On the other hand, many people use AMS templates for preprints…).
Comment: Yes, they specified the reason of the desk reject by "look up left" pointing to the heading. I will be ok to submit to another journal but what bothers me is the fact that  I will listed on their blocked list for  a small detail like that.


Tiling with different rectangle

Question: If a rectangle R can be covered by non-overlapping rectangular tiles, each of which has at least one side with integer length, is it true that R must also have a side with integer length?
Answer: Here is a tricky proof (I don't remember where I found it a few years ago ...) :
Consider an orthonormal system and a rectangle K whose sides are parallel to the axes and let :
$$A(K)=\iint_Ke^{2i\pi(x+y)}\,dx\,dy$$
The condition that at least one side of K has integer length is equivalent to $A(K)=0$.
Now, if we suppose that $R$ is tiled by such rectangles, we get $A(R)=0$ as a sum of integrals that are all zero.
Answer: Here's a cute proof for which I'll only give hints. Suppose you have such a tiling of the big rectangle:
Colour all integer edges of tiles red (if any of our tiles have all four integer edges, choose two opposite edges and leave the other two uncoloured for simplicity). We now need to show that there exists a red path which begins from one edge of the large rectangle and ends at the opposite edge. Why does the existence of such a path prove the result?
Why would it be even better if we start at one corner and end up at another corner?
For every vertex that meets a red edge, what are the possibilities for how many red edges are touching that vertex? (consider the case that the vertex is a corner of the large rectangle or it is not - if it is not, what are the possibilities?).
Given this, if we start at a corner of the large rectangle and start moving along red edges, and we never take any edge more than once then, first, why can we always keep moving along this path in such a way and, second, why will we always end up at a corner?
Answer: Here's another proof using a standard checkerboard method. Overlay a checkerboard pattern onto the large rectangle such that each black and white square has side-length $1/2$ and in such a way that a black square is aligned with the top-left corner of the large rectangle. Let us suppose that the large rectangle does not have an integer-lengthed side, so that the checkerboard necessarily has more black area than white area (why does this happen if and only if we assume the large rectangle does not have an integer-lengthed side?)
Now, every tile of our rectangle has an edge of integer length, so what proportion of each tile is coloured black and what proportion is coloured white?
If we add up the black and white areas of our large rectangle by the areas covered by tiles, what does this tell us? Why does this mean our large rectangle must have an integer-lengthed side?

Tiling with different rectangle


Blender 2.82 Eevee smoke problem (density)

Question: I use Blender 2.82 for 2 days now. I have real problem to get nice results with smoke. I cannot generate dense smoke. I tried everything. Nothing helps. I had no such a problem with previous version (2.81).
The smoke is very weak, thin (not dense). Changing density in Principle Volume Shader DOES NOTHING. I tweak it from 1 up to even 1000000. The smoke is still weak and very transparent. I checked once more similar situation in earlier version and density (in volume matarial) changes a lot. Even with small values. I cannot make the visual change in 2.82
blend file
Answer: I had a same problem until I tried to solve yours one.
I have found that the most helpful is decreasing Volumetrics End Distance or increasing Volumetrics Samples amount.

For some reason I couldn't make the smoke render with OpenVDB cache. So I changed it to modular Uni Cache and made a full bake.


To attain moksha, must you be born as a Hindu?

Question: Imagine that a person is living in the USA or anywhere in the world like Africa is peaceful, loving, and worships God but does not know anything about moksha. Will he get moksha or he will again be born in Aryavarta to follow the teachings of Vedanta, and then be allowed to be free. Can Christians, Muslims, and people from other religions get moksha?
Answer: Anyone who is peaceful and loving and worships faithfully can attain Moksha. The guru Ramakrishna said it most clearly:

Wherever I look, I see men quarrelling in the name of religion - Hindus, Mohammedans, Brahmos, Vaishnavas, and the rest. But they never reflect that He who is called Krishna is also called Siva, and bears the name of the Primal Energy, Jesus, and Allah as well - the same Rama with a thousand names. A lake has several Ghats. At one, the Hindus take water in pitchers and call it ' Jal ' ; at another the Mussalmans take water in leather bags and call it ' pani '. At a third the Christians call it ' water '. Can we imagine that it is not ' Jal ' , but only ' pani ' or ' water '? How ridiculous! The substance is One under different names, and everyone is seeking the same substance; only climate, temperament, and name create differences. Let each man follow his own path. If he sincerely and ardently wishes to know God, peace be unto him! He will surely realize Him."

This, of course, is simply one guru's statement, but we can also look at the Bhagavad Gita to confirm this. Krishna says:

In whatever way people surrender unto Me, I reciprocate accordingly. Everyone follows My path, knowingly or unknowingly, O son of Pritha. [4.11]

In other words, it does not matter how you worship or who you believe you are worshipping, all worship is considered a path to god, enlightenment, and moksha.
Answer: No. Ultimately moksha needs divine grace and is independent of what religion or dharma a person is following.

This Atman cannot be attained by the study of the Vedas, or by
intelligence, or by much hearing of sacred books. It is attained by
him alone whom It chooses. To such a one Atman reveals Its own form.

Katha Upanishad I.ii.23


I don't know where to go next! What should I do?

Question: I was playing Pokémon Sun/Moon, but then I got confused at the directions I was given and I stopped playing for a while and now I can't remember where I'm supposed to go next. How can I know what my next objective is?
Answer: On the bottom screen of your 3DS, Rotom will give you a reminder of your next step every time your current objective changes or you load the game, and you can prompt Rotom to remind you where you're supposed to go by tapping the yellow face that displays your position on the map.
By tapping the map on the bottom screen anywhere but on the current position marker, you can open and view a full map of Alola, which displays a purple flag marker over your next destination.
Comment: Is this flag still there after you've defeated the top 4? I haven't seen it since.
Comment: @Jutschge Since there is no plot objective after finishing the main story, there is no purple flag in the postgame.
Comment: Well there is the UB Storyline which could be considered an additional "mini-story".
Comment: @Jutschge And that's not the main story, so it has no marker on the map.
Comment: @Jutschge For the Ultra Beast story, as long as you find Looker, he can remind you where you need to go next at any time.


Why does C need arrays if it has pointers?

Question: If we can use pointers and malloc to create and use arrays, why does the array type exist in C? Isn't it unnecessary if we can use pointers instead?
Comment: What do you mean by "array type"? `int x[6];` ?
Comment: This is a perfectly valid question asked out of thoughtful curiosity. Up voted +1.
Comment: I didn't know there was an "array" type in C.
Comment: I upvote this question more because there is some interesting discussion to be foundin the answers.
Answer: Arrays are faster than dynamic memory allocation.
Arrays are "allocated" at "compile time" whereas malloc allocates at run time. Allocating takes time.
Also, C does not mandate that malloc() and friends are available in free-standing implementations.

Edit
Example of array
#define DECK_SIZE 52
int main(void) {
    int deck[DECK_SIZE];
    play(deck, DECK_SIZE);
    return 0;
}

Example of malloc()
int main(void) {
    size_t len = 52;
    int *deck = malloc(len * sizeof *deck);
    if (deck) {
        play(deck, len);
    }
    free(deck);
    return 0;
}

In the array version, the space for the deck array was reserved by the compiler when the program was created (but, of course, the memory is only reserved/occupied when the program is being run), in the malloc() version, space for the deck array has to be requested at every run of the program.
Arrays can never change size, malloc'd memory can grow when needed.
If you only need a fixed number of elements, use an array (within the limits of your implementation).
If you need memory that can grow or shrink during the running of the program, use malloc() and friends.
Comment: @AraK, I think by allocation at run-time he means that the software has to request the memory from the OS (with the call to `malloc`), as opposed to just adjusting the stack-pointer (and thus "allocated" at "compile time").
Comment: The allocation of both happens at run-time. The difference is that C allows you to provide the size at run-time for one but not the other.
Comment: Can u give me more details what happen in compile time and run time when an array is located? Even an example would be helpful. thanks.
Answer: It's not a bad question. In fact, early C had no array types.
Global and static arrays are allocated at compile time (very fast). Other arrays are allocated on the stack at runtime (fast). Allocating memory with malloc (to be used for an array or otherwise) is much slower. A similar thing is seen in deallocation: dynamically allocated memory is slower to deallocate.
Speed is not the only issue. Array types are automatically deallocated when they go out of scope, so they cannot be "leaked" by mistake. You don't need to worry about accidentally freeing something twice, and so on. They also make it easier for static analysis tools to detect bugs.
You may argue that there is the function _alloca() which lets you allocate memory from the stack. Yes, there is no technical reason why arrays are needed over _alloca(). However, I think arrays are more convenient to use. Also, it is easier for the compiler to optimise the use of an array than a pointer with an _alloca() return value in it, since it's obvious what a stack-allocated array's offset from the stack pointer is, whereas if _alloca() is treated like a black-box function call, the compiler can't tell this value in advance.
EDIT, since tsubasa has asked for more details on how this allocation occurs:
On x86 architectures, the ebp register normally refers to the current function's stack frame, and is used to reference stack-allocated variables. For instance, you may have an int located at [ebp - 8] and a char array stretching from [ebp - 24] to [ebp - 9]. And perhaps more variables and arrays on the stack. (The compiler decides how to use the stack frame at compile time. C99 compilers allow variable-size arrays to be stack allocated, this is just a matter of doing a tiny bit of work at runtime.)
In x86 code, pointer offsets (such as [ebp - 16]) can be represented in a single instruction. Pretty efficient.
Now, an important point is that all stack-allocated variables and arrays in the current context are retrieved via offsets from a single register. If you call malloc there is (as I have said) some processing overhead in actually finding some memory for you. But also, malloc gives you a new memory address. Let's say it is stored in the ebx register. You can't use an offset from ebp anymore, because you can't tell what that offset will be at compile time. So you are basically "wasting" an extra register that you would not need if you used a normal array instead. If you malloc more arrays, you have more "unpredictable" pointer values that magnify this problem.
Comment: @Ed Swangren: while a common coding practice is to set pointer variables to NULL after freeing them: A) not everyone does this, and B) in data structures which can have multiple pointers pointing to the same thing, this can't prevent the problem
Comment: multi dimensional arrays seem to be hard to impossible to do with something like `_alloca` though, without some overhead that C apparently wasn't be ready to take. Also `sizeof` wouldn't be quite as easy to implement to still yield a compile time result (the compiler would basically have to back-track the pointer to see what initializer was used for that pointer, and then decide whether to yield sizeof of the pointer, or the "array")
Comment: "worry about accidentally freeing something twice" - deleting a null pointer is a no-op as defined by the standard, i.e., it is safe.  Now, the fact that you are calling delete on a null pointer probably indicates another problem, but the call itself is safe.
Comment: @litb: multidimensional arrays are not hard to do, some extra burden of work goes onto the programmer (i.e. keeping track of the array dimensions themselves) but there is no performance penalty. See my comment to your answer.
Answer: Arrays have their uses, and should be used when you can, as static allocation will help make programs more stable, and are a necessity at times due to the need to ensure memory leaks don't happen.
They exist because some requirements require them.
In a language such as BASIC, you have certain commands that are allowed, and this is known, due to the language construct.  So, what is the benefit of using malloc to create the arrays, and then fill them in from strings?
If I have to define the names of the operations anyway, why not put them into an array?
C was written as a general purpose language, which means that it should be useful in any situation, so they had to ensure that it had the constructs to be useful for writing operating systems as well as embedded systems.
An array is a shorthand way to specify pointing to the beginning of a malloc for example.
But, imagine trying to do matrix math by using pointer manipulations rather than vec[x] * vec[y].  It would be very prone to difficult to find errors.
Answer: See this question discussing space hardening and C. Sometimes dynamic memory allocation is just a bad idea, I have worked with C libraries that are completely devoid of malloc() and friends.
You don't want a satellite dereferencing a NULL pointer any more than you want air traffic control software forgetting to zero out heap blocks.
Its also important (as others have pointed out) to understand what is part of C and what extends it into various uniform standards (i.e. POSIX).
Answer: Arrays are a nice syntax improvement compared to dealing with pointers. You can make all sorts of mistakes unknowingly when dealing with pointers. What if you move too many spaces across the memory because you're using the wrong byte size?
Comment: In C, arrays and pointers both use the same method of working out how many bytes to move by.
Comment: @Artelius, Not at all. Arrays use their type to know what offset to use upon indexing and their own address to know the base address to start, while pointers use the address stored in them to know the base address, and they don't know about offsets (you have to tell them manually). +1 :)
Comment: @litb: What are you talking about? Arrays and pointers *both* use their type signature to know what offset from the base address to use (though you're right that the source of this base address is different).
Comment: Well, yes, but when you have a multi-dim array `int[2][2]`, then advancing by `sizeof(int)` is wrong when you do `a[1]`, you have to advance by `sizeof(int) * 2` :)
Comment: IMO, the phrase "using the wrong byte size" implies that omouse believes that pointer arithmetic is always done in bytes (a misconception among many C beginners - I thought this was the case myself at one point). Multi-dim arrays are an issue but I don't think they were the issue omouse had in mind. If he had something else in mind he is welcome to make it clear.
Answer: Explanation by Dennis Ritchie about C history:

Embryonic C
NB existed so briefly that no full description of it was written. It supplied the types int and char, arrays of them, and pointers to them, declared in a style typified by
int i, j;
char c, d;
int iarray[10];
int ipointer[];
char carray[10];
char cpointer[];

The semantics of arrays remained exactly as in B and BCPL: the declarations of iarray and carray create cells dynamically initialized with a value pointing to the first of a sequence of 10 integers and characters respectively. The declarations for ipointer and cpointer omit the size, to assert that no storage should be allocated automatically. Within procedures, the language's interpretation of the pointers was identical to that of the array variables: a pointer declaration created a cell differing from an array declaration only in that the programmer was expected to assign a referent, instead of letting the compiler allocate the space and initialize the cell.
Values stored in the cells bound to array and pointer names were the machine addresses, measured in bytes, of the corresponding storage area. Therefore, indirection through a pointer implied no run-time overhead to scale the pointer from word to byte offset. On the other hand, the machine code for array subscripting and pointer arithmetic now depended on the type of the array or the pointer: to compute iarray[i] or ipointer+i implied scaling the addend i by the size of the object referred to.
These semantics represented an easy transition from B, and I experimented with them for some months. Problems became evident when I tried to extend the type notation, especially to add structured (record) types. Structures, it seemed, should map in an intuitive way onto memory in the machine, but in a structure containing an array, there was no good place to stash the pointer containing the base of the array, nor any convenient way to arrange that it be initialized. For example, the directory entries of early Unix systems might be described in C as
struct {
    int   inumber;
    char  name[14];
};

I wanted the structure not merely to characterize an abstract object but also to describe a collection of bits that might be read from a directory. Where could the compiler hide the pointer to name that the semantics demanded? Even if structures were thought of more abstractly, and the space for pointers could be hidden somehow, how could I handle the technical problem of properly initializing these pointers when allocating a complicated object, perhaps one that specified structures containing arrays containing structures to arbitrary depth?
The solution constituted the crucial jump in the evolutionary chain between typeless BCPL and typed C. It eliminated the materialization of the pointer in storage, and instead caused the creation of the pointer when the array name is mentioned in an expression. The rule, which survives in today's C, is that values of array type are converted, when they appear in expressions, into pointers to the first of the objects making up the array.

To summarize in my own words - if name above were just a pointer, any of that struct would contain an additional pointer, destroying the perfect mapping of it to an external object (like an directory entry).


Failed to connect to mongodb in ubuntu?

Question: I followed this tutorial: http://howtonode.org/express-mongodb
Its strange, the first time I followed the tutorial everything worked.
But now, one day after I wanted to play with the code again I coudn't start
the server. This is what I get:

alex@alex-System-Product-Name:~/blog2$ node app.js Express server
  listening on port 3000 in development mode
node.js:134
          throw e; // process.nextTick error, or 'error' event on first tick
          ^ Error: failed to connect to [localhost:27017]
      at [object Object]. (/home/alex/blog2/node_modules/mongodb/lib/mongodb/connection/server.js:189:47)
      at [object Object].emit (events.js:67:17)
      at [object Object]. (/home/alex/blog2/node_modules/mongodb/lib/mongodb/connection/connection_pool.js:110:14)
      at [object Object].emit (events.js:67:17)
      at Socket. (/home/alex/blog2/node_modules/mongodb/lib/mongodb/connection/connection.js:301:10)
      at Socket.emit (events.js:64:17)
      at Array. (net.js:836:27)
      at EventEmitter._tickCallback (node.js:126:26) alex@alex-System-Product-Name:~/blog2$

Any suggestions to fix this problem?
EDIT:
I just did:
alex@alex-System-Product-Name:~/blog2$ sudo service mongodb start
mongodb start/running, process 9847
alex@alex-System-Product-Name:~/blog2$ sudo service mongodb status
mongodb stop/waiting
alex@alex-System-Product-Name:~/blog2$

Not sure if it is running.
and this is what I get if I type $ mongo in the command line:
alex@alex-System-Product-Name:~/blog2$ mongo
MongoDB shell version: 1.8.2
Tue Nov 15 08:09:50 *** warning: spider monkey build without utf8 support.  consider rebuilding with utf8 support
connecting to: test
Tue Nov 15 08:09:50 Error: couldn't connect to server 127.0.0.1 shell/mongo.js:79
exception: connect failed

Comment: Are you sure mongodb is running? It seems like node can't connect to it.
Answer: This fixed the problem:
http://www.synchrosinteractive.com/blog/1-software/47-mongodb-repair-on-ubuntu
Apparently mongodb creates a lock file when the database crashes or something.
Deleting that file and repairing mongodb fixes the problem:

Manually remove the lockfile: sudo rm /var/lib/mongodb/mongod.lock
Run the repair script: sudo -u mongodb mongod -f /etc/mongodb.conf
  --repair
Answer: The error seems to indicate that MongoDB is not running.
When running MongoDB unattended, you provide the mongod process with a --logpath parameter which points to a file. Check that file to see the reason mongod is failing.

Failed to connect to mongodb in ubuntu?


Decomposition of Lie group into factors when one is not simply connected?

Question: As far as I am aware, for a group to be the direct product of groups it is sufficient that $G\cong H\times K$ as a set and $H$ and $K$ are normal in $G$. For Lie groups, normal groups corresspond to ideals of the Lie algebra. For $G$ compact, given an ideal $\mathfrak{h} \subset \mathfrak{g}$, we can always find a complementary ideal $\mathfrak{k}$ such that $\mathfrak{g}\cong\mathfrak{k}\oplus\mathfrak{h}$ by using an appropriate inner product, however, in order for the the group to be a direct product proofs require that $G$ be simply connected. As it seems we can get the product structure on $G$ from using the fact that $exp$ is surjective, I am not sure where the requirement for $G$ to be simply connected comes in... Additionally, if $G$ is not simply connected, is there a condition one can add to ensure the group is still a direct product?
Answer: First, your original supposition is wrong:  If we let $G = \mathbb{Z}_4$ and $H = K = \mathbb{Z}_2$, then $G\cong H\times K$ as sets (since both are $4$ element sets), but $G$ is not a non-trivial direct product.
In the Lie group setting, it makes more sense to ask that $G\cong H\times K$ as smooth manifolds.  There are still counterexamples:
Let $G' = S^1\times SU(2n)$ and $G = G'/\pm(1,I)$. We let $H$ be the image of the $S^1$ factor in $G'$ in $G$, and $K$ be the image of the $SU(2n)$ factor.
Because $H$ and $K$ are images of normal subgroups under a surjective map, they are normal subgroups of $G$.  Further, we claim that $G$ is diffeomorphic to $H\times K$.
To make this diffeomorphism, we first let $\phi:S^1\rightarrow SU(2n)$ be given by $\phi(z) = \operatorname{diag}(z,z,z...,z, \overline{z}, \overline{z},...,\overline{z})$, where there are $n$ copies of $z$ and $\overline{z}$.  Then $\phi$ is a homomorphism, embedding $S^1$ into $SU(2n)$.
Now, let $f:G'\rightarrow H\times K$ be given by $f([z,A]) = (z^2, \phi(z)A)$.
This is well defined:  $f([-z,-A]) = (z^2, \phi(z)A) = f([z,A])$.
This is injective:  if $(z^2, zA) = (w^2, wB)$, then $z^2 = w^2$ which forces $z = \pm w$.  If $z = w$, clearly $A=B$.  If $z = -w$, clearly $A = -B$, so $(w,B) = -(z,A)$, so $[w,B] = [z,A]$.
This is surjective:  Given $(w,B)\in H\times K$, let $z$ be any square root of $w$.  Then $f([z, \phi(z^{-1})B]) = (w,B)$.
This is smooth:  If one precomposes with the map $G'\rightarrow G\rightarrow H\times K$, one gets the map $(z,A)\mapsto (z^2, zA)$, which is obviously smooth.  Since $G'\rightarrow G$ is a submersion, $f$ must be smooth as well.
The inverse is smooth:  At a point $(w,B)\in H\times K$, we pick a square root of $w$ and call it $z$.  Then, locally, the inverse of $f$ at $(w,B)$ looks like $([\sqrt{w}, \sqrt{w}^{-1} B])$.  Since the square root function, viewed as a map $\mathbb{C}\setminus\{0\}\rightarrow \mathbb{C}$ is locally smooth (if we keep picking the same branch), this is smooth.
As far as your intuition regarding $\exp$, the issue is that we could have $\exp(h) = \exp(k)\neq e$ for some $h\in \mathfrak{h}\subseteq \mathfrak{g}$ and $k\in\mathfrak{k}\subseteq \mathfrak{g}$.  For the $G$ example above, the vector $h = \pi \in \mathfrak{h}\oplus\mathfrak{k}$ and $k = \pi I$ exponentiate to $(-1, I)$ and $(1,-I)$ in $H\times K$.  But in $G$, these get identified to the same (non-identity) point.
Finally, to answer your last question:

Suppose $G$ is any compact Lie group for which $Z(G) = \{e\}$, i.e., $G$ is centerless.  If $\mathfrak{g} = \mathfrak{h}\oplus\mathfrak{k}$ with both $\mathfrak{h}$ and $\mathfrak{k}$ ideals, then $G$ is a direct product.

(So, for example, $SO(4)/\pm I$ must be a direct product, and indeed, it is $SO(3)\times SO(3)$.)
Proof:  Let $\pi: G'\rightarrow G $ denote the universal cover of $G$.  Using the group theoretic fact that $\pi(Z(G'))\subseteq Z(G) = \{e\}$, it follows that $Z(G')\subseteq \ker \pi$.  The reverse inclusion $\ker \pi \subseteq Z(G')$ is always true for the universal cover (see this answer by Jack Lee and the references he gives).  Thus, $Z(G') = \ker \pi$.  Of course, writing $G' = H\times K$ (where $H$ and $K$ are the unique simply connected groups with Lie algebras $\mathfrak{h}$ and $\mathfrak{k}$), it follows that $Z(G') = Z(H)\times Z(K)$.
Then $G = G'/\ker \pi = (H\times K)/(Z(H)\times Z(K)) = (H/Z(H)) \times (K/Z(K))$ is a direct product, as claimed. $\square$
Edit  Your claim in the comment is correct:

Theorem  Assume $G$ is a connected compact Lie group with Lie algebra $\mathfrak{g}$, which decomposes as a sum of two ideals $\mathfrak{h}\oplus \mathfrak{k}$.  Assume further that $H:=\exp(\mathfrak{h})$ and $K:=\exp(\mathfrak{k})$ intersect only at $e\in G$.  Then $G$ is Lie isomorphic to $H\times K$.

Proof:  Consider $f:H\times K\rightarrow G$ given by $f(h,k) = hk$.  This is clearly smooth because the multiplication in $G$ is smooth.  This map induces an isomorphism on the Lie algebra level, so it follows from general Lie theory that $f$ is a covering.
However,  $f$ is injective:  if $f(h,k) = e$, then $hk = e$, so $h = k^{-1} \in H\cap K =\{e\}$.  An injective covering map is a diffeomorphism, so we are done.
Comment: Thank you for such a thorough and informative answer!
Comment: Dear Jason, sorry to bother you again after you put such trouble into your answer, but just so I know I have fully understood: the problem here is that even though the lie algebra split $\mathfrak{g}\cong\mathfrak{k}\oplus\mathfrak{h}$, we don't necessarily have $exp(\mathfrak{k})\cap exp(\mathfrak{h})=\{e\}$. So if $G$ is not simply connected, checking this would be enough i.e. the statement "if the lie algebra of $G$ is the sum ideals $\mathfrak{h}, \mathfrak{k}$ and $exp(\mathfrak{k})\cap exp(\mathfrak{h})={e}$, then $G$ is the direct product of Lie groups" is true?
Comment: I am not certain, but I think that's right.  That's certainly the condition you need on the group level to guarantee that that $G$ is isomorphic to $H\times K$.  (That is, for an abstract group $G$, if you have normal subgroups $H,K\subseteq G$ with $H\cap K = \{e\}$, then $G\cong H\times K$).  I am not 100% confident about the topological aspects, but I would bet everything works.  I'll think about it for a bit and then edit the answer if I can get all the details straight.


How to burn one's bridges in Latin?

Question: If you leave a situation or a job in a way that makes you unwelcome to return ever again, you can be said to burn your bridges in English.
Is there an idiom in classical Latin for irrevocably destroying one's earlier relations?
Can you provide a classical use example?
The English phrase could be translated as pontes suos exurere, but I have never seen anything like it in use.
Comment: The same exact phrase as in English is attested in Italian, so I wouldn't totally exclude your tentative translation.
Answer: Hmm. I don't know of any corresponding idioms in Latin, but in general Latin is a pretty concrete language, shunning metaphor when it can, so my suspicion is that the way to say this is going to turn out to be rather prosaic.
Translated from metaphor, "burn your bridges" means something like "break connections of goodwill." In looking for less fanciful expressions that mean the same thing I find for example in Virgil's Georgic IV

rege incolumi mens omnibus una est;
  amisso rupere fidem, constructaque mella
  diripuere ipsae et cratis solvere favorum.

And in Cicero's De Amicitia 85

Nam implicati ultro et citro vel usu diuturno vel etiam officiis repente in medio cursu amicitias exorta aliqua offensione disrumpimus.

If I had to bet, I'd say it's going to be something boring like that, alas.
Comment: Thanks! I will wait to see if others have ideas to offer before accepting an answer, but this is excellent. Is your *Georgics* an intentional English plural of a Latin word or a typo?
Comment: The latter! It no longer exists!

How to burn one's bridges in Latin?


Can I tie into a 12 gauge 20 amp line with 14/2 NM-B to run a light?

Question: My refrigerator line is 20 amp with 12 gauge wire. Can I tap into that with 14/2 wire, and run a light switch and 1 LED light?
Comment: The only place I have ever seen tap rules used on branch circuits in a home is on the range circuit in conduit.
Comment: Is the refrigerator the only thing in the circuit now?
Comment: Yes, the refrigerator has it's own line. I'm running one led can light for my pantry and that's all it's for. It will all be done in the junction box that exists now.
Comment: I understand about the light shorting out could cause a wire fire because it won't have the power to flip the breaker, if I run a 12 gage wire to a 15 amp breaker plug won't it trip that first?
Comment: After the 15 amp plug breaker extend 14/2 wire from there?
Comment: @Nate - You can splice a #14 conductor to a #12 wire but only if you change the breaker out to a 15A breaker, but why would your do it. Note: I know of no NEC reference which allows tap rules to be applied to any branch wiring, especially residential. If anyone can point it out I would appreciate it.
Answer: You must use 12/2 to extend a 20amp circuit.   -Or- the breaker can be downgraded to 15amp if the circuit contains 14.   (If downgrading the circuit, you should also tag the wire in the panel "circuit contains 14 gauge wire" to eliminate confusion in the future.)
What you're missing:. Under normal circumstances that segment of the circuit would normally carry little watts/amps as you point out.  However in the event of a fixture fault, or even defective bulb in that fixture causing a direct short, the wire would overheat and catch fire, because it's 15 amp wire carrying a dead short.
Comment: In an industrial context, there's a section of code called the Tap Rules which cover "too-small" wire branched off a trunk. However there are a bunch of other protections in that code - not least, mandatory steel conduit/raceway - to avert disaster.
Answer: NO.
The whole circuit needs to support the 20 amps (12 gauge).
My answer is based on common sense.  I am no electrician, just a handy guy.
Comment: Your common sense has correctly captured the concept that breakers protect wires and devices.  Indeed, given a partial short, the 14AWG wire would overheat faster than the breaker expects, so the (delayed)  thermal-trip protections in the breaker would trip too late.
Comment: So from the plug run a 12/2 wire to a 15 amp tripper outlet then can i run 14/2 wire to the switch then to the light?
Comment: @nate there's no such thing as a 15A tripper outlet.  Some people think GFCIs are also overcurrent devices but they're not, they wouldn't know or care if you passed 30A through. **In fact 15A GFCIs are *rated* for 20A passthrough**.  You cannot buy a GFCI+receptacle that is only 15A.
Answer: You could put an inline fuse that's < 16A in the junction box to protect the 14 AWG wire from overload. 14AWG is not meant to carry more than around 15 Amps unless it's in the open air to allow cooling.
edit: It's only for safety. In case someone still wants to do it improperly and use 14 AWG wire on a 20A circuit. Of course it's not the proper way to do it, but it could be the only way to save a ton of money without compromising safety if the 14 AWG wire is already installed.
Comment: The problem here is the "inline" part of "inline fuse".  You can get a type S fuseholder in a plate that mounts to a 4" square box, but even then...I'm not sure if that'd be Code compliant (feeder/branch hybridization problems + issues with a branch circuit OCPD outside a switchboard or panelboard)
Comment: Fuses are an outdated means of protecting mains circuits.


Can we rewrite $Tr(ab^2)$ as $Tr(f(a)b)$?

Question: Can we rewrite $Tr(ab^2)$ as $Tr(f(a)b)$ where $Tr:F_{2^{kn}}\rightarrow F_{2^{k}} $ is trace map, $k \neq 1$, $f$ is a function just depends to $a$.
Comment: Assume  there are more terms inside.. Then also assume we get $tr(g(a)b)$ for some $g$. Now we can more easily talk about distrubition.. This answer can be a good trick for such ideas. // For base field, we can use such a trick for all 2-powers..
Comment: In this case, i dont think it will help, i just need to find $f$. I am trying to solve my problem in different sense but i really want to find this answer, because it will be really helpful.
Answer: No.
The reason is that the function $B_1:(a,b)\mapsto tr(f(a)b)$ from $\Bbb{F}_{2^{kn}}\times\Bbb{F}_{2^{kn}}$ to $\Bbb{F}_{2^k}$ is $\Bbb{F}_{2^k}$-linear in the variable $b$. Irrespective of what the function $f$ might be.
On the other hand the function $B_2:(a,b)\mapsto tr(ab^2)$, while additive, is not $\Bbb{F}_{2^k}$-linear in the variable $b$.
===
More concretely, for fixed $a,b$ such that $tr(ab^2)\neq0$ we run into the following problem.
If $e\in\Bbb{F}_{2^{k}}$ is not an element of the prime field we get
$$
B_1(a,eb)= eB_1(a,b)
$$
while
$$
B_2(a,eb)=e^2B_2(a,b).
$$
So if $B_1(a,b)=c=B_2(a,b)$ for some choice of $f$, then $B_1(a,eb)=ec\neq e^2c=B_2(a,eb).$
Comment: Thanks for answering. It is really right.


Which Dark Events take priority over others?

Question: There's numerous kinds of Dark Events in game that can be set upon you.   I've seen some seemingly normal and not so impactful events, like Rural Checkpoints or making the cost of recruits a little bit more expensive for the duration of the month, but I'm curious if there's a list of which Dark Events are the most important to counter ASAP as opposed to other Dark Events?
Comment: I don't think there's going to be a strict ordering where specific ones are more important all the time. It's going to depend on your circumstances at the time. The one that makes recruits more expensive is irrelevant if you have enough recruits, but could be devastating if you've just had several casualties. Might be more useful to ask for a list of all the event types, and what might make each one critical.
Comment: I'm pretty sure there's some game killers, ones that come to mind are raising Intel costs by 100%, 2 weeks progress to Advent facility, or adding progress to avatar project
Comment: This feels very opinion-based to me. I don't really agree with the rankings you've provided in your answer, because it heavily depends on your playstyle. For example, even on Commander/Legend, I love extra pods (more experience) and pay almost no attention to the Avatar progress because it's so easy to knock back down.
Answer: After playing through this game on a Commander/Ironman run and struggling many times to prioritize Dark Events in which some basically ended my runs, I came up with a few events that I found to be more important than others.
Ordered from most lethal to least:

Chryssalids on every mission

There's nothing worse when a trooper is caught offguard by an unactivated Chryssalid pod that activates as soon as you end your turn.   Having Chryssalids on every mission can be very dangerous as keeping a healthy top tier squad is a priority for most runs as the enemies only get tougher as time goes on.

Avatar breakthroughs

When you have many missions to go through, adding progress to the Avatar bar can be a killer; especially if you don't have resistance comms in areas with ADVENT Blacksites

Vigilance

100% increase in intel costs for the entire month; Intel takes a while to build up and is used in almost many other things like research, Black Market, Resistance Comms, so keeping your Intel well stocked can be the difference between the loss of an entire run and winning the game.

Show Of Force

Adding more enemies means more chances your squad can get hurt

Rural Checkpoints

Reduces supplies of next Supply Drop by 50%

Rapid Response

Show Of Force, but only on Guerilla Ops missions; same logic, more pods = more chances to maim or kill your squad members

Anything Else
Comment: Isn't Vigilance the one that increases detection range? The intel cost one is Alien Cypher, and IIRC, it doesn't affect the black market. I think one of the devs mentioned that it doesn't affect facility leads, either; does any other research cost intel? I didn't pay much attention to research costs.
Comment: Need a description of the event for the ones identified by title. If one of those is reinforcements on every mission, then that seems wrong to include. I always ignore that one. Reinforcements are free xp. They drop in after you already know where, and trigger all your overwatch shots.
Comment: @DCShannon I'm not sure what difficulty you're playing on, but having too many pods can be a killer in some maps, like time based VIP extraction, retaliation missions, or terminal hacking. There are some enemy dark events that are immensely helpful, such as Faceless in every mission, as Faceless are your only source of Mimic Beacons.
Comment: Currently playing Commander Ironman
Comment: It's one thing to get flanked by a pod, but having extra pods adds more risk for your team especially when the game wants you to play aggresively.
Comment: *"advent equipped with poison rounds"* seemed like one you'd like to avoid. More enemies on one side is more problems, but also more opportunity to level up.


How much space does each world take up?

Question: I have minecraft PE running on an ipad3 with 64 GB memory.  When I sync with itunes I notice that the apps are now taking up about 20GB of memory.  I have recently added some other apps but think that adding extra worlds in minecraft might be responsible.
Roughly how much space should a world take up from the stored memory on my ipad?
Answer: The space is takes up in alpha 0.8.0 is 20MB per world on Android, possibly the same for iOS. Since alpha 0.9.0, endless worlds are supported so i couldn't tell you that. If you want to see the total storage of the minecraft pe app, go to Settings, Usage, wait for it to load and then search for Minecraft. Also, if you want to know what app uses the most storage, it is sorted by usage so the app that uses the most storage is on the top.
Answer: Minecraft: Pocket Edition worlds can take up any amount of space on your device. This is becuase of the "Infinite" world type released in alpha version 0.9.0. The size of the world will increase as you explore.
You can check how much storage Minecraft is using by going to your device settings:
Settings > General > Usage
This menu displays the amount of space each app on your device uses, including Minecraft.
Answer: They can take up any amount of data due to the new infinite worlds. You can, however, turn this off when you create a world
Answer: Minecraft isn't infinite, after passing 30 million blocks the game will crash.
It'll use 20GB on your hard disk and its all uncompressed data.

How much space does each world take up?


Biological differences between people from space-bound colonies and planet-bound colonies

Question: So I wrote a question a little earlier about the differences in mindset between people born from planetside colonies vs. those born in space [it's linked to save me from explaining the whole system - please tell me if this is wrong, I'm new] [here is the link: Differences in mindset between people born in space and people born planetside].
 Anyways, so I was also wondering if there would be any physical differences. There is a lot of travel between planetbound and spacebound colonies, but a lot of people also stay in one place for their entire life, and some groups stay for generations.
 As I said in my other question, there is artificial gravity in space, but it's less than the regular true gravity on planets/moons [the levels of which would vary]. People in space get access to fresh plant-food [that's what I'm calling it] since flora is grown via hydroponics and LEDs. People born planetside are exposed to sunlight [through the windows of their habitat of course], and have a small amount more space.
 For reference, these people have been living in these ways for a coupla' hundred years, so not a huge amount of time in evolution's terms [though I guess there is evidence of certain species evolving a lot faster than considered normal].
 A few differences I can think of could be height [less gravity = more allowance to grow taller], muscle mass [less gravity = less strength required to move], slight differences in colouration [more sun exposure = more melanin],  differences with eyes [smaller environment + long time spent there = eyes working better up close], and maybe something with circulation as a result of the way the "gravity" is distributed in a centrifugal spinny thing. I am more asking about changes to biology as a result of living in that environment, even if they are un-seeable or minor, not really changes in genuine health or appearance.
 Are there any differences I may have missed?
Comment: I know I posted a question already today, but I thought it was unclear and badly worded, so I'm going to come back to it a little later when I've figured out what I want to say.
Comment: It looks like you're looking for help brainstorming ideas for your world rather than asking a specific answerable question. Questions like this with many valid answers are too broad for this site. Can you [edit] your post so that you're asking a single more specific question?
Comment: This is the [SE Meta post](https://meta.stackexchange.com/a/89241/835863) on limits for questions. I am not sure if the WB.SE has its own rules regarding the number and frequency of questions the user may ask (I did not find any). || I do not think that this question is too broad or unspecific. However, it would be better to reword your question in such a way that it does not ask for ideas (this community does not like it). It would also help if you could include your research. [cont.]
Comment: [...] Please note that the WB.SE is not meant to be a place where world creators start their research. It is presumed that questioners did research on their own but met some difficulties or problems with understanding and/or application of their research and then came to the WB.SE to ask for help with these particular difficulties/problems. In other words, it is expected that you already know something about potential physical differences and are seeking to verify your conclusions or checking if you have missed something.
Comment: @Otkin I should probably reword it anyways since I don't want people to get confused. I've tried to do research on the rest of the internet but it isn't helping since it's a weirdly specific question, so I thought I might ask you people. I will edit it when I can :)
Comment: I added a little more info, but it's probably not enough ...
Comment: this one - it heavily depends on the environment, and honestly, when things are done in a right way, there is no difference. Also, it depends on technologies available there and a few hundred years for space future is quite a good amount of time to have some nice futuristic stuff including good medicine and the ability to guide control development of the body of a human. So it is better to focus not on a difference, but on - what good stuff they all can have - the difference between them and today and potential here is boundless - whatever possible it is possible.
Comment: @MolbOrg Yeah, I guess you're kinda right in a way. I'm just curious if those environments would have a physical toll on someone.
Comment: it may if you make it. But if we look at what people will probably try to make - they'll probably try to eliminate such things for health reasons - and can they - yes. Also, today if you look around - you will see people of all kinds of physical appearances - brains are more important - so this way your other q was better.
Comment: @MolbOrg Yeah, I guess. Do keep in mind a lot of these people wouldn't have access to the kinds of technology that eliminate those health risks. I agree my other question was better though lol.
Comment: I am also asking for biological adaptations to the people's environment, whether that's noticeable or not. I should probs clear that up.
Comment: "Do keep in mind a lot of these people wouldn't have access to the kinds of technology that eliminate those health risks." - I do not see a reason for that, it is in their best interests as individuals so as groups of people, groups starting from city to country and such levels if you like to call it that way. If you handwave a reason, you need to add it to the question and put some context about that. If you just think there should be one, then the q I mention, big old comp in space, it allows to develop nanotech, all kinds of it, and after a few hundred years in space, they have it, everyone
Answer: For starters, think of the long-term impact of lower gravity settings on the human body. Humans lose bone density, and muscle strength since less is needed in lower gravity. Over generations, perhaps people in space bound colonies would be smaller.
Also, diet is important to consider. It seems plants are more sustainable than meat for space-bound colonies. Consider the long-term impact of plant-based diet, such as B12 deficiency.
Comment: @sprout You can also do aquaculture. Tilapias, IIRC, can be raised in a very limited space.
Comment: Huh, okay. Being smaller might also help moving around in more cramped spaces.
Comment: Meat can be produced artificially. We can do it now. There is no reason to believe that human civilisation capable of building huge space habitats is unable to produce artificial meat.
Comment: They do grow artificial meat, however not everyone eats it :)
Comment: @Otkin Oooh, I'll have a look into that :D
Answer: If you're using the original specifications for O'Neill Cylinders as a stepping off point then your Space Born are going to have a series of slight differences stemming from the fact that they live in an atmosphere with a sea-level oxygen pressure but total pressure closer to that at 5500 metres above sea level. This will effect the structure of their skin, lungs, eyes, ears, mucus membranes, and heart, but not in massive or immediately obvious ways. Any experience with the thicker air of sea level on Earth would likely be extremely uncomfortable, possibly lethal. At the minimum they'd be rapidly fatigued, unless and until they had time to adapt, as their chest muscles worked overtime to move twice the weight of air for the same amount of O2.
Their sense of balance may be very different if they live under spin induced pseudogravity depending on the diameter of their habitats due to their degree of Coriolis compensation being different to those on planets.
There is a lot of debate as to the exact effects of lower gravity on long term musculoskeletal development but I would expect that anyone born and raised in micro-gravity is going to have lowered bone and tissue densities. This will probably make them relatively weak and breakable, but if their home habitat is kept at Earth gravity then this shouldn't be a cause of difference.
Skin pigmentation could go either way depending on the typical UV load. It should be noted that at present one of the most promising class of foods for space grown food rations are fungi. Most fungi are naturally high in bio-assimilable Vitamin D so Space Born may tend towards higher skin pigmentation than one would otherwise expect, more Melanin in the skin means less Vitamin D production when exposed to UV radiation.
Eyesight could go in a number of directions, I can make arguments for either greater or lower light sensitivity, colour perception, distance optimisation, etc... depending on the exact details of life in space.
Comment: @sprout O'Neill engineered based on an atmosphere that was half the total pressure of Earth at sea level but with the same partial pressure of oxygen so people could still breath normally. For physically mature earthlings heading into orbit that wouldn't make much of a difference but people born under that regime are going to develop differently.
Comment: I didn't think of oxygen pressure, I'll certainly be looking into that :) Thanks for the answer!
Answer: Okay, I tried to hint at that in the comments but it seems I need a little bit more Space.
No difference
There are at least 4 reasons, why I think that way:

health reasons, aka how biology works
environmental reason, why and how we would like to move in space
technological reasons, what we are capable of doing in space
Today's reality - on this planet, there are people of all shapes sizes, and a variety of colors - so different from who - all of them? Why?

Health, biology
This one is tricky to explain, and sure it is rather my perception aka opinion.
Let's take this one as an example before I bring some more complex generalizations
It is quite a known thing that vision suffers in microgravity, due to a change of liquid redistribution in the human body. The pressure difference, which we talk about - it is in a hundred pascals, this much heart is capable of to create, or even less. It leads to excess pressure in eye-ball, which leads to distortions and potentially permanent damage(this one is my guess based on other things)
The problem is just one example, which is chosen for it being known, the fact it is hard to do anything about it with our current means(unsolved yet for decades), but the reason for it also appears to be simple and it could be fixed if we had better means to address such problems.
So it's funny to make up fancy stuff like muscles this or that differences - to amuse readers and viewers, preferably producing elf-like creatures cuz it sells better, but it not funny to have anemia because of your Osteoblasts and Co do not develop proper ways, leading to dysfunctions of blood-producing parts. (problem with bones is real, but potential anemia due to that I do not recall it firmly, maybe it just my imagination)
Now more general statements:
a human body is capable to endure a lot, but it needs to understand that it, the body, did develop from a Single Cell, a process called ontogenesis in general, which includes embryogenesis as well(at least by me). This is an amazing process - it is something wonderful - but all kinds of minor deviations do produce all kinds of mistakes in it. It is robust to many factors, which we have here on earth, but it is also selectively weak against the factors which we may have here on earth.
Meaning the development process is quite a sensitive thing, and it is possible to be sensitive especially for factors that we do not have on earth, and this sensitivity and results of it will be, most likely for reasons of the evolution process, to be negative. Reasons for that can be imagined as - there are too many things to break, but there is only one good result to have, as if it would be another way around evolution would skyrocket and would be easy as pie, but no it takes millions of years, millions of generations. Reasons can be expressed in more formal terms, but not the point.
In general - one has to protect that development process to have healthy humans, and if one can't do that, there is no place in space for them - it is the current motto of any space agency, and there is no point in changing that in the future for them or groups of people - we are looking for better future, a regular one - we already have it. And we move in space for that better future now, or else there is no point.
This brings us to the next reason:
Environmental reason

why and how we would like to move in space

There already are reasons to recreate a proper environment for humans in space, as health reasons, but it goes along with other reasons as well.
We would like to have a nice place to live, because if it is not nice - we already can have that in any place on Earth.
To have "a nice place to live" - it includes a lot of stuff, how it looks, how it feels, its size, how many people there are, and such.
For psychological reasons, for biological reasons, for healthy society(as society) reasons, it makes sense to have an environment that resembles or feels like a good place on earth.
One can imagine some tin can, submarine situation - but if billions of people are not capable to change it for the better - they deserve that - I mean it is within their capacities to make a good environment, and it is that ways from the very beginning - because it can and should be the attraction for all those people who decided to move from earth to space, in initial migration wave.
With O'Neil principle aka concept aka cylinders - just as an idea, but a better implementation, not like it was envisioned back then(cuz critical mistakes were made) - but the scale and stuff - hundred thousand, millions of people per space hab, with enough space for people, and recreation of nature there.
Yes, not everything can be recreated, but I as city dwellers do not care - if there are some forests to move once in a few years - I call it good enough. Real nature lovers, active sky cave divers, and such - please stay on earth, keep an eye on it.
Apparent gravity and pressure and light(spectrum) and such - can be recreated and there are reasons to invest efforts in doing so.
All that possible to make with technologies which are available today, but also it brings us to technologies potentially available in the future:
Technological reasons

what we are capable of doing in space and because of space

Today one of the emerging technologies is generative design - it comes as a pack with neural networks and simulations of physical processes and digital design practices.
In essence, it is the automation of finding solutions and implementations for our practical needs.

quite a good depiction of such a system was that expert system from the Iron Man movie(first one and it emerged a few times later as well) when Tony asks it to make something that he envisions, and it does. For those who paid notice to it.

It is a powerful tool, it can be, maybe less in the way as it was envisioned in the movie, but it can be as effective as that one.
And there is another cluster of problems - protein folding simulations used in medicine and not only there - to make better stuff, find useful stuff, and such.
All that together connected with nanotechnology, elements of which we have today, in technological fields so as in biological, medical applications (have or envision to have)
All mentioned processes are, at the moment, CPU-hungry processes and due to this and other factors may not be so cheap. And that(or a different one) Big Computer In Space once implemented can make a significant push to the technologies development.
As one of the well-recognized technologies are gray goo like nanotech, it is desired by many(I guess) even if some not so well informed authors maybe had a bad influence on the perception of it by the public, in the past - but I guess not many will deny advantages of such technology.

what a right implementation and right use of it can be is a different topic and it has some stuff that needs to be understood correctly to imagine a correct picture and many do it wrong. But fixing that is out of the scope of this answer.

So having put K1 energy in technology development, it would not be surprising to have plenty of good technologies to use, including, nanotech which is quite a universal tool - as for environment creation so for health keeping, maybe finally we will live for few hundred years after that. (I mean there are incentives besides space-related ones)

I know some people classify nanotech as magic stuff, good to have, never will happen - okay, let's address that without nanotech

It is certain that thanks to technologies we have today if we have an opportunity to use them on a greater scale, the aforementioned K1 energy budget will accelerate our development, and improve our technologies in a big way. (Not a singularity)
With such an energy budget - there is also no apparent reason to imagine that some significant portion of people in space will have lack access to those technologies (most of them) and have any difficulties in this aspect.
They do not have a lack of energy, because of sun and microgravity(for curious, this) - and it has big consequences on production, the efficiency of production becomes less relevant, to a certain acceptable degree, than it is now on earth, at least you for sure won't bother about 5-10% difference and consider convenience and practicality in the first place and efficiency difference in the second place.

I mean, as of today, the depiction of space capacities in sci-fi is lacking accuracy in a big way, it is understandable it is easier that way to make plots and such, and reuse special effects and writers from different areas of entertainment production.
ISS problems scale badly for the sizes of millions of people in space. I mean a station for a million people is a totally different beast than ISS.

The explanation is not full and probably lacking, but as-is - I did my part, but if you investigate space, instead of handwaving problems, then it may be a better work, try to not fall victim to usual tropes as many of them make no sense, and if you will, never mention me, lol.
People of the Earth, as of today
This is the shortest one - there are all kinds of people on this planet - short, long, big, small, etc.
Why? Because selection factor for a long time is about our intellectual capacities, not our physical body. (because we live in societies)
If you can distinguish USA citizens, then sure, you will notice a difference in the appearance of space folks - as they will be descendants of those who moved in space and it will be not everyone, maybe, depends on your story, how did they move in space.
Etc. I guess you can think along the lines on your own. Difference from who, if we already have all kinds and shapes.
Didn't mention it in the biology section and will do it now. There is another group of people, who imagine making biological modifications for everything, to adapt that way - meaning introducing changes deliberately.
A big topic on its own, but rather exception, because of the convenience of technological solutions in that regard, there is no need for special adaptations as long as we have technological means to solve problems and create proper conditions for ourselves. The advantage and convenience of technological solutions are in that one can change them at will easily - space suit is one of such technological means - which can be worn and un-worn(?). A car, tank, airplane - also are such solutions, meaning technological means are universal, while biological adaptations are not.
Conclusion
This way, I have reasons to think - there is no reason for any difference to exist. And are reasons to solve problems even if there are some factors. And people are well capable to do so.
Comment: That was an interesting read, and I think I get where you're coming from. Thankyou for your contribution :)
Comment: @sprout yes, my motto is space for a better life for humans in space and on earth, or it is not worth it. And all things I look at telling me it is possible to make it that way - a better life and for people in space and for those who stay on earth. It's probably better for those who are in space, but yeah, who I'm to judge, lol, earthlings will get a good share of the fun/profits it's just that their planet isn't big enough to fit it all.
Comment: Yeah, you have a point. I wouldn't necessarily say changes in environments [and biology to adapt to those environments] would be negative, though. They're just differences :)
Comment: @sprout minor in 50 generations mostly as result of recombination of existing genetic pool(so not really new) and if you let people die, like in medieval Europe, letting sufficient child mortality to happen - for selection to work, or do eugenics and be strict who marries whom, or artificial wombs and precalculate stuff based on gene sequencing - 5-10 generations - difference won't exceed stuff one can get by training, best case scenario. 50 generations - the number comes from a selection experiment conducted on foxes in Russia, for purposes of their domestication.


How much support for other SF offerings?

Question: Having noticed questions tagged as "salesforce.com", I'm wondering how the other offerings fit in on this site. I think integration questions are welcome, but what about questions solely about the other sites, such as data.com? Are questions explicitly and only about other Salesforce technologies appropriate for this site?
Comment: that may offer to remove the salesforce.com tag - like having a UBUNTU tag on the ubuntu SE site.
Answer: I think as the site grows there should be no reason why Salesforce's other offerings can't be covered also, but given that the most configurable product is Salesforce/Force.com I suspect most of the questions will fit nicely regardless.
All that aside, questions regarding Heroku should probably only be here if they involve an integration with the platform, otherwise they're akin to questions on C++ or Java and should be on Stackoverflow.com instead. Chances are, questions that don't fit will get flagged and moved to sites better suited.
Answer: If it's an integration to that site in any way, I think it's appropriate.  If it's solely 3rd-party related, I think it's off-topic.
This is from the About SF -

This is a free, community driven Q&A for Salesforce
  administrators, implementation experts, developers and anybody
  in-between.

I wasn't here from the days on area51, so I don't know all the changes that got to this point though.