Function with infinitely many right inverses?

Question: I was thinking about a function with infinitely many right inverses but I could not come up with anything.
Does there exist a function with infinitely many right inverses?
Comment: "Don't forget the ${}+C$."
Answer: You need to find a function $f:S\to T$ which is:

surjective (so that a right inverse exists)
so that there are infinitely many right inverses, either

for which there is some $y\in T$ with $f^{-1}(y)$ an infinite set
or for which there are infinitely many $y\in T$ with $\#f^{-1}(y) \ge 2$

Any function with these two properties will have infinitely many right inverses. A simple example is the trivial function
$$f:\mathbb N\to \{0\}$$
for which the map $$i_n:\{0\}\to\mathbb N\\0\mapsto n$$is a right inverse for every $n\in\mathbb N$.
Comment: Indeed, with that method you can easily show that the set of right inverses can have any cardinality, by just replacing $\mathbb N$ with a set of the desired cardinality.
Comment: +1 I have to give kudos for having the simplest example possible!
Comment: To be precise, this $f$ does not have to be like that. Instead of the second bullet, you may simply have infinitely many points with non-singleton preimages (e.g. the projection onto ${\bf N}$ of $\{1,2\}\times {\bf N}$). In this case, there will be at least continuum many right inverses (assuming axiom of choice ;) ). (But you *must* have one of the two.)
Comment: @tomasz thanks for that. I have edited the answer to include this.
Answer: The function
$$f:\mathbb{Z}\to \{0,1\}:x\mapsto \left\{\begin{matrix} 0 \text{ if }x \text{ is even}\\ 1\text{ if }x\text{ is odd}\end{matrix}\right.$$has infinitely many right inverses, since it suffices to map $0$ to an even number and $1$ to an odd one.
Another example is $\sin$, for which any function of the form
$$t\in [-1,1]\mapsto \arcsin(t)+2k\pi $$with $k\in \mathbb{Z}$ is a right inverse. This also works for other trigonometric functions, of course.
A third example would be the floor function $f:\mathbb{R} \to \mathbb{Z} : x\mapsto \lfloor x\rfloor $; here it suffices to map any $m\in \mathbb{Z}$ to any $r\in [m,m+1[$.
Comment: @FreeMind: Asking for "two more examples" is an odd request that strongly suggests someone asked _you_ for three examples. Could you please clarify?
Comment: Could you please give two more examples?
Comment: @FreeMind Do you understand how Arnaud D. created the above two examples? If not, I would ask him for clarification.
Answer: For another example let $X$ be any infinite set, and let
$$f:X\times X\to X:\langle x,y\rangle\mapsto y\;.$$
For each $x\in X$ let
$$g_x:X\to X\times X:y\mapsto\langle x,y\rangle\;.$$
Then $g_x$ is a right inverse for $f$ for each $x\in X$. This is one of the most natural constructions. It can be generalized by letting $Y$ be any non-empty set, replacing each instance of $X\times X$ by $X\times Y$, and replacing the range of $f$ and the domain of the functions $g_x$ by $Y$.


Durlag's Tower in Baldur's Gate

Question: Im at the Durlag's Tower and I can barely kill one party of monsters before I have to sleep and charge spells for healing.
My party is lvl 2-3. Am I here too early?
Answer: Very much so.
Durlag's Tower is intended to be an optional, additional challenge for players.  The underground sections of the tower in particular are, in my judgement, second only to the final battle in terms of difficulty.
Durlag's Tower is intended to be tackled towards the end of the game.  The earliest you should be considering it is about the time you get access to the city of Baldur's Gate; if you want to be certain you're powerful enough, visit it just before the second plot-required trip to Baldur's Gate.
Answer: Definitely early. Return when you're at least level 6-7 and bring a good rogue with at least 90% in Find Traps. I was with Coran and it sucked as he is mulitclass and was really low in detect traps.
Answer: for a newbie, yes.
For a long term veteran, no.
level in BG1 (and to lesser degree, BG2) isn't really a big deal.
Most of your power comes from your gear, outside of mages, and even then they have options for low level play.
Once you know what you're doing and where to find good gear, you're pretty well free to go anywhere any time, that the game doesn't physically prevent you from doing so.
(BG2 is extremely rough under 8, due to enemies constantly spamming Death spell all over creation, but above 8, you can easily beat the game without gaining any further levels. Though Level drainers will be equivalent to death spells and need to be handled with utmost care).

Durlag's Tower in Baldur's Gate


How are compressor blades connected to the shaft in turbojet engines?

Question: The below figure is about rotor and stator blades of compressor . How these are connected to the compressor shaft in jet engines ?
Comment: Welcome to Aviation.SE! Could you edit your question to ask only one specific question per post? If you have multiple question you should ask them separately. It would be a good idea if you took our site [tour] and checked the [help] to see how the site works.
Comment: You're asking about rotor blades. Why not specify the compressor rotor? People may think you're enquiring after a helicopter rotor.
Comment: I would suggest reversing the terms to read "how are compressor blades connected to the rotor?"  I think that is more correct, and might clear up some some confusion.
Answer: There are three primary ways that blades are connected to the shaft

Circumferential dovetails  Here is a nice site demonstrating it.  Includes STL files so you can 3D print your own demonstration part.
https://cults3d.com/en/3d-model/tool/jet-engine-component-1-1-axial-compressor-circumferential-dovetail-slot-type
Axial dovetails Here is a video demonstrating blades with an axial dovetail being assembled.  This particular video is a turbine, not a compressor, but in theory the same method can be used.

Blisk "Blisk" is a contraction of "bladed disk". The blades and the disk are physically welded together (or in some cases machined as one piece out of a solid block of metal).  Here's a wikipedia article on blisks
https://en.wikipedia.org/wiki/Blisk

Each of these methods has advantages and disadvantages in terms of weight, cost, vibration, etc.  Which one is picked depends on the circumstances.  It is also common to see multiple different methods within one compressor. For example the LEAP-1A HPC has a 10 stage compressor.  The forward stages are blisks, and the aft stages are circumferntial dovetails.


Are highly nitrated cyclopentadiene compounds possible?

Question: Has anybody synthesized di- or higher nitrated cyclopentadienes possibly with methyl or other groups in the 1 position (analogs of TNT)?
Answer: Mono-nitrated cyclopentadienes and their benzo-analogues (indene, fluorene) have been prepared in the context of studies on nitro-aci-tautomerism.
As far as higher substitution is concerned, there seems to be at least a crystal structure of potassium dinitrotrichlorocyclopentadienide reported in Acta Cryst., B
In the abstract, the authors (Y. Otaka, F. Marumo, and Y. Saito) mention the preparation of this compound by Haga in 1969, (sorry, reference is behind paywall) via

nitration of hexachlorocyclopentadiene with alkali nitrite in an aqueous or ethanolic solution

NOTE: Hexachlorocyclopentadiene once was a favoured starting material in the synthesis of insecticides via Diels-Alder reaction. However, it is a potent teratogen and the "mother" of least five members of the dirty dozen (persistent organic pollutants) nowadays banned for good reason.
You might want to read the MSDS and then decide that you'd rather prefer to work with something else.
Comment: Thank you K.W. for the references.  No need by me for MSDS ;-) - not in the biz -- just a curiosity of mine in analogy to TNT!  I am sure that even if the more highly substituted CPD compounds could be made they would be horrendously explosive; maybe as stable as nitroglycerine itself!  Thanks again!  No reply needed.


Including compile instructions for GPL

Question: What, if anything, must be included with a project regarding how to compile it, to be fully GPL v3 compliant? For example if I'm using Netbeans and simply use it to compile and run the code, what kind of documentation would be required? The code is intended to work without any special compiler instructions (unless so desired).
Answer: The best way is to think this way: If I receive this code, which concise and accurate instructions would I need to be able to re-build the binaries from sources?
I should not assume that the recipient knows nothing about software and nothing about Java in this case. Instead I should provide the simple and good enough instructions that a basic software developer could understand and follow to rebuild from sources.
This becomes much simpler: I can simply state in a README that I used Netbeans Vx.x (and may be provide the Netbeans project files) or that I compiled the code with Maven (and provide a pom file) with Java 8 (and provide a link to fetch an OpenJDK 8).
If this was built on Linux, I may also provide a list of required packages to install.

Including compile instructions for GPL


Format Trello card title

Question: Can the Trello card title be formatted into three lines of text? I basically want to see more data on the cards when viewed on the board.
Answer: There are no plans to add such a feature. You could use the card description for more detail.
Comment: @BobbyGrace But, IMHO, the tooltip that now pops up when you hover the cursor over the pencil icon could show the description instead of showing the message "This card has a description". BTW, you guys have put together a smart tool, I should say; I am a new trello user, I have just been using it these days... :)
Comment: Thank you for quick response. Does the card description show on card cover when viewed on board?
Comment: No, since it's meant to be long and detailed. If we showed it, you wouldn't have any more space for cards.

Format Trello card title


"Related work" or "related works"

Question: Which expression should be used as a section heading of an academic paper: related work or related works? This is a question that has been bothering me for years, as googling shows that both have a large number of usages.
Answer: What is the context?
If the heading refers to things you produced in the same or relevant subject area, then work is uncountable, and the heading should be Related Work.
If the heading refers to your oeuvre or the output of a fellow artist, then work is countable in this case, and the heading should be Related Works.
Comment: +1 Works tend to refer to an individuals works, whereas work to a subject area.
Comment: I've never seen this section named "Related Works" in a paper, ever. But maybe this is depends on the field of the paper.
Comment: @bitmask Precisely; _works_ are "something produced by a writer, painter, musician, or other artist."
Answer: Related Work
However, there are at least three cases where a distinction may need to be made.

If it is a list of literary items (works), then it could be plural: Related Works.
If it is a paragraph on other related work done by the author, then singular: Related Work.
If it is a list of engineering projects, then plural: Related Works.

In general it is singular: Related Work.
See also, some random examples from Wikipedia:
Australopithecus afarensis
Answer: If would depend on the context of the writing in question. If you want to pluralize work to works it should be in the case of referring to the body of work as multiple discrete items (ie works of art).
In the case of writing --
works

John had done a great deal of writing for clients in the past on these same topics. His related works included a blog post on Engadget and a magazine article for Wired.

work

John had done a great deal of related work writing on these same topics in the past.

This gets back to @Gnawme's point about the work being either countable or uncountable. If you can substitute stuff or another amorphous noun, then use work.
Answer: It would depend on whether your use of the word "work" in context refers to a countable work or not. If you're talking about books, paintings, or other things that are referred to as "works", then use the plural. If you're talking about uncountable work, like "I've also worked in engineering and medicine", then it's probably uncountable and thus you should use the singular.
The distinction is not necessarily consistent. A list of books you have written would be called "works". But a list of software products you have written would probably be called "work". That is, it is common to say, "The author of 'Economics of Tibetan Agriculture', Mr Jones, has three previous works in this field ..." and then list the titles. But no one says, "The author of 'Tax Prep Pro version 4.2', Mr Smith, has three previous works in this field ...".
Answer: According to Google Ngram Viewer, the capitalized forms (as would be typical for section headings) are both used, but Related Work is considerably more common.

"Related work" or "related works"


1AWG with a smaller breaker?

Question: I am thinking about having an electric vehicle supply equipment (EVSE) installed.
In the interest of future proofing for an electric pickup truck coming on the market about a year from now, i would like to have 1 AWG wire installed for 100 amps @ 240 Volts (residential).
But my EVSE today is only supposed to draw 32 amps @ 240 Volts, so would it be safe to have wiring installed that is intended for up to 100 amps, and use a 40 amp breaker today incase the current 32 amp evse decides to malfunction, the smaller circuit breaker would trip at 40 amps, and switch out the breaker to 100 amps when the time comes ?
Thank You.
Comment: Since everyone is recommending aluminium without pointing out the risks: don't combine aluminium with copper haphazardly, make sure whatever is doing the cross-over is fine with both. You can't splice them together with ordinary splices, you'll need some marked Cu/Al to combat the increased oxidation or use a metal in between that's fine with both. That is, assuming the rest of your house uses copper. If everything is using aluminium already, there's no problem. Just, copper on aluminium leads to trouble.
Comment: You have not stated where you are. Although I have completely rewired several homes and installed new main panels over the years with home owner permits, where I live insurance (and government incentives) require that EV chargers specifically be installed by a licensed electrician. Also, in my jurisdiction home owners may only install copper, aluminum must be installed professionally which requires special handling to ensure a safe connection.  That you have had to ask this question also suggests that you may  want to have this done professionally. Enjoy your (lovely, quiet) EV!
Comment: I am in Minnesota
Comment: I understand your interest in future proofing, but it's very unlikely that batteries, or chargers will ever support 100A 240V. It's equally unlikely that you will want this. You are dealing with some very fundamental laws of physics and although we as humans are getting better at getting close to physical limits we are not likely to get to those levels of efficiency for household purposes ever.  You're far more likely to want a 3 phase power source, which are very expensive to get in homes.
Comment: I am thinking of having an electrician run a dedicated 240V line to the future EVSE that is designed to run on 100 amps @ 240V, i was previously thinking an all aluminum run from the panel to the EVSE, would it pose an issue to have copper and aluminum wire coming out of the same (only) panel ? (copper to all 120V outlets, light fixtures, appliances such as gas range and fridge currently)        Also, the EVSE instalation instructions say to use copper connections only on anything touching the evse.
Comment: @Sam I can tell you *real easy* how you use 100A on an EV.  We're already starting to encounter these cases here;  **the family has two EVs**. Either experience has satisfied their range anxiety, or their #2 is a plug-in, *with an fuel APU that gives it infinite range*.  Also, I fully expect plug-in F250s and Suburbans soon, and they will be power hogs. Also, 100A-class chargers are a thing, check out a Tesla Supercharge station.
Comment: @Sam     https://www.atlismotorvehicles.com/faq   look under "what will you do for home charging" - recomended 100Amp @ 240V for 1 fully electric pickup truck, coming to market in 6 months.
Answer: Sure, you can always upsize the wire.
However, a dramatic upsize introduces two complications.

the much-larger wire will not fit on the device.  It will need to be pigtailed to a suitably sized wire, such as a 6 AWG.

When dealing with #1 wire, it's not as simple as using a giant orange wire-nut the size of a salt shaker.  You have to use a connector such as a Polaris, which is an insulated lug terminal.   You could also use uninsulated lug terminals or split bolts, if you don't mind lashing it under unbelievable amounts of electrical tape.  You do need to insulate neutrals.

You are probably dealing with aluminum wire (I hope)

Generally all terminations sized for #1 wire are aluminum friendly; why wouldn't they, since aluminum is normal and expected at these sizes.  You just have to take care to use terminations rated for aluminum; a Polaris is fine, however I would not use a split bolt unless the smaller wire is also aluminum. Aluminum is fine to use at these sizes.
But yes, definitely lay the heavier wire.  The only case where I wouldn't is if the wire was in conduit, and the run is very short.  In that case, the pigtail adapters for the larger wire might be more expensive than just doing the whole run in the smaller wire.  It could be changed for the larger wire later.
Answer: You can run larger cable and use a smaller breaker but not the other way around. If your planning on 1 AWG for 100 Amps then you're talking about aluminum cable. You'll have to pigtail at both ends to a 8 AWG because the 1 AWG won't fit in the 40 Amp breaker or receptacle. That future 100 Amp load could be a strain on your panel so check into that along with your other planning.
Answer: Yes, having larger wire is always fine. Depending what size wire the terminals on the 40 amp breaker are listed for you might need a pigtail of wire that fits that breaker connected to your 1 AWG, but that's a common problem with a straightforward solution. You should consider using aluminum wire for a run this big, if you are presently looking at copper.

1AWG with a smaller breaker?


How long do moderators serve?

Question: Will we be holding periodic elections, and if so, is this to add more moderators or reelect the existing moderators?  In a broader sense, I'd be interested in hearing the level of commitment needed for this position.
Answer: If elected you moderate for as long as you want to, you won't have to stand for re-election (at least that's the way it is at the moment).
As a site grows more moderators may be added - either from the runners-up in the previous election or via a new election. Also if any moderators stand down an election may be held to find a replacement.
You're volunteering so how long you serve is up to you.
Comment: Additionally, because the current moderators were appointed [pro tem](http://blog.stackoverflow.com/2010/07/moderator-pro-tempore/) instead of elected, they will need to nominate themselves in the election if they wish to continue as a moderator.  All permanent moderators should be elected by the community.
Comment: @Rebecca: in that case, I'm really hoping it's standard practice for people with experience to wait 'til the last second to submit their own nomination.
Comment: @B Mitch - Don't forget there are three phases. Nomination, primary where there's public voting and election where there's a secret ballot. Depending on the number of candidates one or more step may be omitted.
Answer: See discussion at
Should Community Moderators be "elected for life", or have terms?
Consensus was:

Yeah, It should be 'for life'.
Comment: Thanks Jeff.  I knew it had to have been answered somewhere.
Answer: Speaking from experience, it's not a huge commitment.  This site is still fairly small and there are very few issues that come up that really require moderator attention.
With three moderators, I wouldn't expect this to take more than 5-10 minutes a day (tops) to pop in and review/resolve any outstanding issues.

How long do moderators serve?


Dapper.Contrib Generate Update Script With ROWLOCK

Question: I am using Dapper as ORM and generating insert,update script by Dapper.Contrib extensions. I want to generate Update script include Rowlock.
Is there any usage except changing generic code below in SqlMapperExtensions.
 public static bool Update<T>(this IDbConnection connection....
     var proxy = entityToUpdate as IProxy;
     ......
     ......
     var sb = new StringBuilder();
     sb.AppendFormat("update {0} set ",name);

     var allProperties = TypePropertiesCache(type);
     .......

Answer: Dapper.Contrib and the extensions there does not support ROWLOCK and there is no way to configure Dapper to use it, so right now you would have to modify the base code or add your own extension with support for ROWLOCK.


Correct way to use jack post

Question: These photos show the way the previous owners of my house used a jack post to brace sagging floor joists.  I'm not sure of their method, so I wanted to check what the correct method is.
Angle 1

Angle 2
Comment: @JimStewart - My hunch is that the joist would need to sag a fair bit to transfer tension into those metal straps, i.e. it might be structurally sound but it wouldn't leave the floorboards above anywhere near flat.
Comment: The root problem is the epsilon-minus who put the pipe in low through the joists, cutting the joists in their tension area.
Comment: There's a lot of wood and metal there doing absolutely nothing. You can simplify greatly.
Comment: It could be that the metal post could be removed, if it's in the way, but a structural engineer would have to sign off on the repair. The metal tension straps on the bottom and wooden compression reinforcement on the top may be enough to make this structurally sound.
Comment: Would the best technique for installing tension straps be jacking the floor slightly *up above flat* before installing the straps so that when the jack was removed there would be an increase in tension of the straps which would not allow the joists to sag below flat? Or would it be better to jack the joist perfectly flat and use an angled nailing technique to pre-tension the strap?
Answer: Typically, there is a beam put under the joists, then the post are put under each end of the beam. This detail is better suited for longer beams, covering more joists. Somebody has found new and unusual ways do do something there. I can see the logic of what they were trying to do, but makes for a lot of guessing still.
The problem really happened when the insulated pipe was drilled through the bottom edge of the joists.
Answer: Tl;DR The "correct method" is to remove that pipe and sister in replacement joists. The job that the previous owner did is a hack job / bodge job, and I wouldn't trust it.

A jack post is used to reduce the span of a beam. The problem here isn't that your span is too short, it's that the capacity of your beam has been destroyed by drilling a large hole near the bottom of it. The solution isn't to use a jack post but to repair the beam.
The "best" way to do this would be to restore the beam to its original size by sistering in a replacement joist, but this of course can only be done if you remove the pipe that the hole was made for in the first place.
If you want to keep that pipe, you'll have to investigate other options. Potentially connecting a replacement beam underneath the joist would work, if clearance isn't an issue. You could even put a jack post underneath that additional beam if you want.
The above all applies to each joist that needs strengthening. They way the owner has tried to use a single jack post for two joists looks unsafe to me.
Answer: I would strip everything out of there, completely, after adding temporary wooden posts under the two joists. This includes the steel post, all wood blocking and extra joists, metal strapping, etc., right down to the bare original joists.
I'd then place a doubled joist crossways between the two joists in play, screwing it in place through the original joists. I'd then add double heavy-duty joist hangers, upside-down, on the end of the cross-joist, tying it to the original joists and transferring their loads.
I'd then mount the post to the bottom of the doubled cross-joist using 5/16" x 2 lag screws.
<code>         _____________________
      |x|                     |x|
      |x|\    cross-joist    /|x|  <--- screws/lags through original joists
      |x| |    (doubled)    | |x|
      |x| |                 | |x|
      |x|_|_________________|_|x|
                --------
hanger --↑         ||        ↑ -- hanger
                   ||
                 |    |
                 |    | < -- post
                 |    |
</code>
Comment: Plus, strapping like that only takes load when the joist flexes substantially. It does nothing for bounce or initial sag unless it's somehow pre-tensioned. The post and cross-joist will eliminate both concerns with gusto.
Comment: That's better than what's currently there, in terms of the cross-joist; but I still have concerns that the original joist is understrength. The metal strapping is better than nothing and you're proposing removing it but not replacing it with anything.
Comment: Why would that be in any way necessary if there's a post right there? It's not better than nothing because it serves no purpose, yet adds complexity and effort.
Comment: To clarify further, there's no concern with the pipe bore in this scenario--there's enough remaining of the joists to carry the load near the cross-joist. It's only a problem now because it's out in the middle of the original span.
Comment: If we leave the post in then agreed that the shear force is decreased compared with original design, and the reduce section due to the pipe bore is probably ok for that. The designed large sagging moment will be replaced with a smaller hogging moment (US English: negative moment), for which the reduced section is again probably ok. The strapping is not much use in a hogging situation as it will be in compression and at risk of buckling. So, thinking on it further, I agree that it doesn't serve much of a purpose.
Comment: Overall it'll *probably* be safe with your fix, but it just doesn't quite sit right to me. A hole that big and that close to the bottom of the joist is waaay off code (UK Building Regs being the only relevant code I have a vague idea about), and modifying the beam by turning it a two span beam with hogging moments would probably require some sort of engineering sign off in the UK. But +1 anyway as I think your solution should be safe.

Correct way to use jack post


How can I invoice a US company being a foreign non resident in USA?

Question: I'm a nonresident alien in US and I need to invoice a US company due to service.
The company can provide W8 or W9 forms to proceed with the payments, but I need to provide an invoice confirming that I'll be paying all income taxes.
Is this invoice "automatic" when I use this W8 form? If not, how can I provide this invoice?
Comment: I think you should ask that company to explain to you what it is that they want.
Answer: You should ask the company you are working with what they require in an invoice. One thing is certain, invoicing will not simply be "automatic" because you file a W8 or W9.
At a minimum, your invoice should include your name (or company name), contact information, a break down of the goods / services provided & prices + taxes, a total amount, the date, payment terms (e.g.: due on receipt, 2/15 net30, net 30) and please... for the sake of their bookkeeping and yours... each invoice should have a unique identifier (not the date), even if it is something as simple as "Invoice#1".


Is it possible to add an updated answer to a closed question?

Question: To this question:
Paragraph direction missing in Adobe illustrator CC 2018,
there is a better answer, which is the only way to solve the problem today. The problem is that the question is closed and cannot be answered, but it is shown in the first results of Google.
I spent long hours talking on Adobe's support center, time which could have been saved if the correct answer had appeared here:
https://helpx.adobe.com/il_he/creative-cloud/help/change-install-language.html
Comment: Its probably better that you reask a simiar question and then adress this in a new answer. Yes i have enough points to cast reopen but that does not halp i still need 5 others to concurr
Answer: Not really. But:

Anybody who already answered before closure can change their post.

You can vote for reopening. This would reset the question if others agree to open.
Comment: **1.** I have never commented there, and I have nothing to edit anyway.

**2.** I do not have enough points to request a reopening.


Probability of picking a random natural number

Question: I randomly pick a natural number n. Assuming that I would have picked each number with the same probability, what was the probability for me to pick n before I did it?
Comment: This is more a question for a psychologist than for a mathematician. Humans tend to pick certain numbers more often than other numbers. For example 7, 17, 35 and 37 are quite popular. No amount of mathematics would allow you to predict such a distribution without some facts from psychology. See here for some more details: http://scienceblogs.com/cognitivedaily/2007/02/is_17_the_most_random_number.php
Answer: There is no uniform distribution on the natural numbers. So the question itself is self-contradictory.
Some explanation:
You say that each number is chosen with the same probability. Say probability $c$.
Let's denote the probability to choose $n$ by $p(n)$. So you say $p(n)=c$ for any natural $n$.
For any distribution, the sum of probabilities always equals 1:
$$p(1)+p(2)+p(3)+ \dots = 1.$$
So $c+c+c+\dots = 1.$ But if $c > 0$, you get
$$c+c+c+\dots = \infty.$$
And if $c=0$ you get
$$c+c+c+\dots = 0.$$
There's no value of $c$ for which this sum equals $1$.
Comment: If this seems counterintuitive, think of a person choosing a "random natural number". Any normal person would choose a number with much less than a billion digits (I'm exaggerating on purpose), so he's actually choosing from a finite set of naturals, giving all larger ones 0 probability.
Comment: The point is that it's not possible to pick a natural number uniformly at random. Not that some are more likely than other, this depends on the distribution used. The point is that there is no uniform distribution.
Comment: So, are you saying that whenever I pick a natural number at random, some are more likely to get picked by me than others?
Comment: Yes. Here's an example: Choose n with probability $1/(2^{n})$. This is a valid distribution because $1/2 + 1/4 + 1/8 + ... = 1$.
Comment: @Thomas: Not "whenever I pick a natural number at random", but "in general, when I pick a natural number at random".
Comment: How about $c = 1/\infty$?
Comment: @Benjamin why is it impossible? I can definitely do it. E.g. I pick 123115435436134.
Comment: I don't mean you can't pick a specific number ;) I mean no uniform distribution on the integers/natural numbers exists. The distribution doesn't exists.

Try to think, what would p(n) be if I could only pick 1-6, like a dice. It would be 1/6.

Now add more numbers up to m to that die, we get p(n) = 1/m -> 0 as m-> oo. So the uniform distribution there would just be all zeros.
Answer: There's an aspect that doesn't seem to have been mentioned in the other answers yet.
The question presupposes that it is possible to pick each natural number with the same probability. Since this is not possible, it raises the question what may have led to the assumption that it should be possible. It's instructive to compare this with typical cases where there is a uniform distribution.
When we roll a die, there's a symmetry between the sides. There's no reason why any of them should be more or less likely than the others to come up, so it's clear that the probability for each of them should be the same (if the die is symmetric and we throw it hard enough).
If we spin a wheel, there's again a symmetry among the angles at which it might come to rest. There's again no reason why any of them should be more or less likely than the others, and it's clear that the probability should be uniform across the range of angles (if the wheel is symmetric and we turn it hard enough).
The idea that "I randomly pick a natural number n. Assuming that I would have picked each number with the same probability" seems to be modeled on such cases. So it's instructive to realize that there is no similar experiment that this corresponds to. As has been pointed out in some of the comments, asking a person for a "random" answer won't do, because there's no reason to except symmetry between small and large numbers. Another idea might be to mark the rational numbers on the wheel, choose some bijection mapping them to the natural numbers, and then choose the natural number that corresponds to the rational number at which the wheel comes to rest. But if you think about it, this doesn't make the sense that it does for real numbers.
So there's a direct correspondence between the impossibility of setting up a situation in which there is the required symmetry between all natural numbers and the impossibility of defining a uniform distribution on the natural numbers (or any countably infinite set).
Answer: If you want to choose a natural number from the set $\lbrace 1,2,3,\ldots \rbrace$ of all natural numbers, then user3533 is right. But if you pick a natural number from a finite set, say $A = \lbrace 1,2,\ldots,N \rbrace$, each number with the same probability, then this probability must be the reciprocal of the number of elements in that set. So, if $A = \lbrace 1,2,\ldots,N \rbrace$, then $p=1/N$. This follows immediately from
$\sum\nolimits_{i = 1}^N {p_i }  = 1$ with $p_1 = p_2 = \cdots = p_N = p$.
Answer: Some clarification should be added to the above answers.
By partitioning the reals into non-measurable sets, one can devise a way to relate a real selected uniformly at random from an interval such as [0, 1) to a natural number using a method by which all natural numbers have an "equal," however undefined, probability of being mapped to (here, equal simply means that no natural is given preference as to being mapped to over any other natural).  The problem is that, because non-measurable sets are used to do this, no meaningful cumulative distribution function can be established (as might be expected).  To see an example of such a selection process, see here:
Is this fraction undefined? Infinite Probability Question.
Answer: It would require a definition of a probability distribution with an infinitesimal probability mass at every natural number. Dirac delta functions of infinitesimal length.
In (Bayesian) statistics, functions that relax the axiom of "summation to one" are known as improper priors and have an infinite total mass. This loss of the axiom on tautology ($p(T)=1$ for any tautology $T$) comes with severe repercussions. You'll see Dutch book arguments that make this clear.
Note that there are many infinite sequences that people try to tackle with tools from probability theory. Most famous are the attempts to postulate  hypotheses about the distribution of subsequent primes. So, this means that questions like the one you have are very good to ask ourselves.
There is also the concept of natural density. The natural density of picking an even natural number is $1/2$.
Answer: Hi :) I've always had a nagging suspicion about drawing (uniform) random numbers from an infinite set. I'm not convinced it's possible: here's an intuition about why I'm sceptical: it would be nice if someone could explain where I go wrong. My counterargument is structured as follows: if it's possible to draw random natural numbers (i.e. from the whole infinite set) then there must be a probability of selecting an EVEN number: I argue that $Pr(even) = \frac{1}{2}$ AND $Pr(even) = 1$, causing a contradiction.
First we need to define:
URD: A "uniform random draw" for a set $S$, ($S = \mathbb{N} = \{1, 2, 3, ... \}$ in this case) is a random selection $x$ from $S$ such that every $y$ in $S$ has an equal chance of being picked. This is what we're doing in the video, and it's what we usually mean when we just say "random".
Consider the statement '$Pr(\texttt{n even}) = 0.5$', where $n$ is a random element from $\mathbb{N}$  -- this is what I assume most people would agree with. I disagree that this is true, I think it depends on arbitrary selection rules.
Firstly the intuition we normally have in mine: if you represent a natural number as a rounded scaler from 1 to infinity or a finite string of bits defining a binary number (like your computer does), then it's true that $Pr(\texttt{n even}) = 0.5$ : because it boils down to whether the last bit is 0 (even) or 1 (odd), and since both 0 and 1 bits are equally likely, it follows that Pr(even) = Pr(not even), which must sum to 1 so Pr(even) = 1/2. You can jiggle this for $Pr(\texttt{n is a multiple of m})$ to get $\frac{1}{m}$. It's easy to see that this way of drawing number satisfies URD.
There is another way to uniquely represent numbers, not just as a line or scale: we can represent n as a product of primes via the fundamental theorem of arithmetic.
Consider $n = 2^{a1} * 3^{a2}  * 5^{a3} * 7^{a4} * 11^{a5} * ..... $
If we start by drawing random URD numbers a1, a2, a3, ..., over $\{0, 1, 2, ....\}$ and then defining $n$ as above, we have drawn a random $n$. In fact, since every different sequence $\{a1, a2, a3 ... \}$ defines one, and EXACTLY one, natural number $n$, it also follows that this method of drawing $n$ should also satisfy URD.
But under this last method, $prob(\texttt{n is even}) = prob(\texttt{n not odd}) = 1 - prob(a1 = 0) = 1 - 0 = 1$
If you want to be more formal, you can note the following observation: suppose you have $N$ (non-empty) sets $S_1, S_2, ...., S_N$. We want to choose a random element $X$ from the cartesian product set $S = S_1 \times S_2 \times S_3 .... \times S_N$. Then drawing $X$ is equivalent to drawing $N$ elements $s_i$ from $S_i$, and then setting $X = (s_1, s_2, ..., s_N)$.
In effect, I've used this result in my argument above that $Pr(even) = 1$, because I've quoted the fundamental theorem of arithmetic and defined $S_i = \{\texttt{powers of the }$i$\texttt{th prime}\}$, e.g. $S_2 = \{1, 3, 9, 27, 81, ....\}$.
Since I've shown that Pr(even) = 1/2 and shown that Pr(even) = 1, it follows that it makes no sense to even assign a probability to drawing random numbers from the infinite set of natural numbers.
I assume I'm wrong somewhere, but I don't know where I've gone wrong?


Water heater wont work

Question: My gas water heater wont heat until I turn it up to nearly all the way to the maximum temperature, indicated with letter "C" in the image. If I turn it down lower than "C" the gas flames stop and the water never heats up. I also noticed some rust on the top of the heater. What are my solutions to make the heater work at "A" level of temperature or is there any best practices out there to maintain this gas heater which has serial number "..1998" probably the year it was manufactured.
Answer: The rust on your water heater and the cracking of the top surface is indicative of another problem.
Your thermostat might be broken, the heating element (where the gas is actually ignited to heat the pan) might be broken.
Just looking at the unit and the rust and given you have this other issue I will suggest you replace the unit, because if you are not a professional in the industry that can be very dangerous for you. Working with Gas is highly dangerous even for professionals.
That said the cost of a service person to come look at the issue and the cost of any part to repair the unit you might be looking at $200-$400. For that kind of money you can buy a unit have it installed.
You did not say where in the World you are located so if you are in the United States...
Many states have rebate and credit programs, some local municipalities have rebate and credit programs and lastly even your gas company might even rebate and credit programs, the gas company might even install the unit for free (after all they would not want you to use an electric Water heater for the next 20 years would they ?)
You might be able to end up with a brand new , highly efficient unit for the price of the servicing to fix your unit.
Comment: Some municipalities also provide discounts when replacing an old inefficient unit with a newer more efficient unit.
Comment: This heater should be replaced before it fails catastrophically. Looks like the flexible supply lines should also be replaced. Entirely too much corrosion on the right hand supply line (hot?). You should also replace the cut-off valve if it is an old style "gate" valve. If it is a "ball" valve then probably it is OK.
Comment: Current prices for a 50 gallon gas water heater at the big box home improvement store near me is around $700.  They are a lot more expensive than I remember and installation isn't cheap either.  Not saying this heater shouldn't be replaced, but it's going to cost a lot more than $400.
Comment: @JPhi1618 I have seen them for $500 and up searching online only of course as I have been shopping for one myself.  With all of the rebates and credits that might be available you can get back $300 to $400 on a unit that might cost $800 to $1200 and gas companies sometimes make sweeten the deal. In the long run even if the op buys a unit outright with no rebates or credits $700 out of pocket is a good deal considering this unit will probably fail terribly   with in 6 mos to a year (why spend $400 on a repair and then $700 in 6 mos to replace it). I think op may end up $4to500 with new unit.
Comment: @Ken, yea I haven't researched rebates, so that makes sense.   I just know I was surprised by how expensive they have gotten.  The last time I needed to buy one they were _much_ cheaper.  Agree that OP should replace. That thing is ancient and crusty.

Water heater wont work


Historical energy market data for European power Futures and Options?

Question: I have been trying hard to find some historical futures and options electricity data for EEX offerings. I need the data for a model I am writing, however I have not found any free resources so far. It is quite straightforward to web scrape their current tables with data for each type of future/option contract, however I would be glad if someone have found a free source for their historical data on futures/options?
Answer: You can also try asking the exchange. If you are a researcher or academic etc they might give you a copy for free. If you are part of a commercial org, the main data providers almost certainly have this data, so try to find someone who has access to a terminal etc.
Answer: I have been trading power options for a long time, and outside buying data from EEX, the other source are brokers (ICAP, Prebon, Spectron and some others) offering data rather expensively.


Can I become head of all factions in Morrowind?

Question: On Elder Scrolls Oblivion and Skyrim you can join all factions and become the leader. I'm also playing Morrowind and I'd like to know if I can do the same, because I've read that some guild missions conflict with other guild missions.
Comment: Again, a more descriptive title would be very beneficial.
Comment: Just so you know, you can't use "guild" and "faction" interchangeably. Skyrim factions are Stormcloaks and Imperials, while Skyrim guilds are thieves, Dark Brotherhood, etc. For the life of me, I can't seem to remember any Oblivion factions (that you can side on)...
Answer: Yes certain factions conflict with each other. I tried to keep the following list relatively spoiler-free so I apologize for vagueness.
Great Houses
The Great Houses of Morrowind are mutually exclusive and as such, you can only join one of the three choices (Hlaalu, Telvanni, or Redoran) without the use of a bug.
Everything Else
The Fighters Guild quest "The Code Book" is in direct conflict with the Thieves Guild and will make it so you can not join the Thieves Guild. There is a way to get around this as explained on the wiki page linked below.
Any Fighters Guild quest offered by Sjoring Hard-Heart make the Thieves Guild hate you at a minimum or kicked out of it at a maximum.
A Tribunal Temple quest, "Slay Raxle Berne", will block off being able to join the Berne vampire clan.
The last one I can find deals with the Mages Guild. One of the final quests they give you will make it so you can no longer be a part of House Telvanni.

There is an entire wiki page dedicated to quest timing that talks about conflicting quests. You can find it here.
Comment: You're somewhat overstating few things. Code Book *is* better done before being in Thieves - you can simply convince the girl. Later it's pretty hard to do without causing trouble (unnoticed stealing it  is needed). Also one doesn't even need to get this crazy task from Archmage, and it's the most problematic way to replace him.


Is duplicate title tags an issue when they're redirected?

Question: According to Google Webmaster Tools, I have a number of duplicate title tags. This happens because my products all have two URLs: /products/product and /product/product-category/product.
/products/product is redirecting to /products/product-category/product, so should I worry about all the duplicate title tags? Does it matter what content is on a page that is redirected?
Answer: Google Webmasters provides the details of the Duplicated titles present for your site.We need to download those information.Then We need to use rel="canonical" in the suitable https://googlewebmastercentral.blogspot.in/2013/04/5-common-mistakes-with-relcanonical.html way to solve this issue.
Else the Google treats it duplicate content https://moz.com/learn/seo/duplicate-content is explained clearly here with pictures.
In E-Commerce site when similar products are repeated this issue occurs.At that time rel="canonical" is used in the main page. So that Google robots treats it as main page and other similar pages are following it.http://www.goinflow.com/duplicate-content-ecommerce-seo/ . This solves the Duplicate Title tag issue & Duplicate content issue also.For dynamic content this would be https://stackoverflow.com/questions/16325842/how-to-prevent-duplicate-title-tags-on-dynamic-content helpful.
And also minimize Redirection as far as possible because it slows down site speed.(https://varvy.com/pagespeed/minimize-redirects.html). Because Page Speed is one of important ranking factor.(https://moz.com/blog/how-website-speed-actually-impacts-search-ranking) . So we need to think of Page Speed as well.
Answer: Its won't be any issue, but I believe instead of using 301 redirection you need to use canonical tag to avoid such duplicity issues. 301 redirection work best at domain level


How to check if my usb drives are vulnerable by BAD USB

Question: Mark pointed out that only one chip type is vulnerable to BAD USB, id like to check if mine are, am using only Kingston flash drives here so can you tell me if they are, or if there exists a list somewhere i could check this? thank you.
Comment: *Mark pointed out that only one chip type is vulnerable* Only one? Can you [edit] and add a reference link?
Comment: Adam Caudill and Brandon Wilson demonstrated *Bad USB* at Derbycon and put their [exploit kit up on GitHub](https://github.com/adamcaudill/Psychson). Maybe you can use that code or someone develop a tester based on it?
Answer: You need to determine what flash controller your device has. Different devices may have different controllers even if they have the same manufacturer - it seems to only depend on what the factory had at the time.
One way is to disassemble the device and read the label on the controller chip
Another (non-invasive) way is to use software such as ChipGenius. This can be found via Google on a number of Russian sites. Make sure to check your copy for malware. "usbdev.ru" is one source of usb software/firmware programming files.
After you know the controller in use, you can search around to see if it is vulnerable or use / modify the manufacturer's firmware flashing tool to flash your own firmware onto it. If you succeed then the device is probably vulnerable. If afraid of "badusb" I would avoid micro-controller based memory controllers and stick to those which use single use chips.
Similar research was performed into flash memory in SD cards a while before "badusb" emerged and this CCC talk is quite interesting. It explains the reasoning behind using micro-controllers because of flash quality / economics. Much of the information applies to USB flash drives as well.
Comment: Thanks for your reply, so if i check it using chip genius i would see in the controller section if the manufactor is phison and then i could guess that the USB device is vulnerable most likely, right?
Comment: Yes - ish. It should tell you the exact model of Phision chip. You can then look for a firmware file and flasher for it. You may find a PoC for your chip or may not. If you can flash firmware or brick the device then I imagine it is likely vulnerable. Though I can't guarantee either way unless ASIC / ROM hardware (= not vulnerable) or there is a PoC for that chip (= vulnerable).
Answer: A quick Google search indicates that you can't really find that out without dismantling the device. Manufacturers can change controllers for an existing product.
The best defence is to not use a USB device that you have not purchased yourself.


Phase 10 skip card

Question: I am player one and use my skip card on player three.  When their turn of being skipped passes, can I use another skip card to the same player to block them from completing their Phase on my next play?
Answer: From the rules (found here):

A player may only be skipped once per round. If player one skips player two, then player two can not be skipped until player one plays again.

So if you are player one, then sure - you can skip them again.

Phase 10 skip card


Brewer's Best Conditioning Tabs

Question: Does anyone know how long it takes for these to carbonate a 12 oz bottle?
Answer: It depends on the health and quantity of the yest remaining in the beer and the temperature where the bottles condition, as well as the strength and pH of the beer. There's no one answer, but if your beer is "normal", i.e. not excessively strong, not sour, and only recently pulled from the fermenter, 2 weeks would be a normal time if the bottles are at about 20c. After this time, just test them every now and again until you're happy.

Brewer's Best Conditioning Tabs


Wave and particle properties of protons and electrons

Question: Do both electrons and protons have wave and particle properties and if they do, do they show them at the same time?
Comment: Remember, they are not real waves but rather probability amplitudes that is probability waves. They are both simultaneously associated with probability waves. Think of the atom where the electrons are described with standing waves.
Comment: @user36790 Technically you are espousing the Copenhagen interpretation and there are many other [interpretations of quantum mechnics](https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics). While the Copenhagen interpretation is the most popular method of interpreting the Schrödinger equation, there are many other explanations that do not interpret $\Psi$ as a probability amplitude and $\Psi^*\Psi$ as probability density.
Comment: @Jonathon: You are absolutely correct. By far, however, the best theory is Quantum Field Theory. Nevertheless, I thought it would be better to talk about the conventional one:)
Comment: I would say that both wave and particle properties aren't "shown at the same time." Our perception of particle or wave property is the result of the experiment, and isn't a limitation of the  particle.
Answer: Actually, everything has wave-particle properties and is given by the deBroglie equation: $${\mathrm p}\lambda = h$$ where $\mathrm{p}$ is momentum (mv), $\lambda$ is wavelength and $h$ is known as the Plank constant ($6.626\cdot 10^{-34}\;\mathrm{J\cdot s}$).
As you can see as the mass of an object increases, the wavelength decreases. So in macroscopic objects that we an see, such as ball, its mass (therefore momentum) is so big compared to $h$ that the wavelength is really, really small, so we can't observe it. For light waves, it is the opposite. Due to their relatively large wavelength, they have a really small mass. However we can do experiments that show the particle nature of light. Such as the photoelectric effect which can only be explained by thinking of light as a particle rather than a wave.
Electrons which have a mass of $9.011\cdot 10^{-31}\;\mathrm{kg}$ are in between the two examples that I have given you. It turns out that their mass is perfect for their wave and particle nature to be observed. Protons are roughly 1840 times heavier than electrons, however we are also able to observe their dual nature.
The answer your second question is that they do exhibit these wave and particle properties at the same time. An electron can't simply decide to be a particle for a certain instant than decide to become a wave in the next moment. All objects exhibit their wave-particle properties at the same time.
Comment: @ssavec - It goes beyond that; "buckyballs" (C60) and much larger molecules have been shown to interfere with the right apparatus. See [this old Nature News story](http://www.nature.com/news/2011/110405/full/news.2011.210.html). I've just sort of come to accept that the only reason "I am" where I think I am is that almost all of me can almost always be found where I expect to find me to well within experimental tolerances. (I barely notice the fuzziness around the edges, and, honestly, that's probably just my eyes showing their age.)
Comment: The wave nature of neutron is used in diffraction experiments, see https://en.wikipedia.org/wiki/Neutron_diffraction


What will happen to my digital games after I die?

Question: After recently reading this, I wonder if the games I downloaded and currently own on Steam can be passed on to my son.
Will Steam allow transfer of ownership of my account? If it is written in my last will and testament, will they accept it?
Comment: PROTIP: give him your password.
Comment: @kotekzot: This will, however, not be a proper transfer of license. Unfortunately, the answer to the question depends too much on your local laws (and those change too) to be of much use. In doubt: contact a lawyer, don't ask random strangers on the internet.
Comment: @MartinSojka or you could just leave your password to your son.
Comment: @Ramhound I very much doubt they are going to bother.
Comment: @kotekzot: If the lawyer is any good, he'll keep you informed on the status quo changes when you come over every few years to update your will. You *do* plan to update it to your current situation and the changing laws every few years, right?
Comment: You realise that the story about Bruce Willis isn't true don't you?
Comment: @ChrisF: Bruce Willis story may not be true, but the problem itself is.
Comment: @MartinSojka and that matters because? Worse than depending on current laws, this question depends on time. Consult a futurologist?
Comment: @kotekzot - This works until Steam decides to lock your account because they were notified you passed away.  Before you think Valve couldn't do that, when the information is posted in say your newspaper, the city is also normally given.  They can use social media also to conclude you are dead.
Answer: Well, it's a bit more clear cut for games than music.
Games are software, software is always required to have valid license to be used. Using software in a breach of license is piracy. Steam EULA makes it very clear that you don't own the games:

Valve hereby grants, and you accept, a limited, terminable,
  non-exclusive license and right to use the Software for your personal
  use in accordance with this Agreement, including the Subscription
  Terms. The Software is licensed, not sold. Your license confers no
  title or ownership in the Software.

Also according to EULA games nor account cannot be transferred to another person:

You are entitled to use the Software for your own personal use, but
  you are not entitled to: (i) sell, grant a security interest in or
  transfer reproductions of the Software to other parties in any way,
  nor to rent, lease or license the Software to others without the prior
  written consent of Valve, except to the extent expressly permitted
  elsewhere in this Agreement (including any Subscription Terms or Rules
  of Use);

There comes interesting part. If you're living outside of European Union, the choice of law is WA, USA. So you're out of luck. However if you live in European Union, there is interesting part about choice of law:

For EU Subscribers:
You agree that this Agreement shall be deemed to have been made and
  executed in the Grand Duchy of Luxembourg and that it is subject to
  the laws of Luxembourg, excluding the law of conflicts and the
  Convention on Contracts for the International Sale of Goods (CISG).
  However, where the laws of Luxembourg provide a lower degree of
  consumer protection than the laws of your country of residence, the
  consumer protection laws of your country shall prevail. In any dispute
  arising under this Agreement, the prevailing party will be entitled to
  attorneys' fees and expenses.

Why is it interesting?  There have been some countries, where it has been ruled that preventing re-sale or transfer of software licenses is violation of free market, thus the "non-transferable" clauses are invalid. And there have been rulings confirming it on EU level.
Comment: @Hackworth: I don't live in the Lawyerlandia, I don't need to be a lawyer to read EULA. In fact you too should have read that EULA before clicking to accept it.
Comment: Are you speaking as a lawyer? Inheriting stuff is typically different from regular transfer of goods and rights.
Comment: What does you or me reading the EULA or not have to do with the question at hand? Interpreting the EULA is the question here, and while speaking as an outsider myself, in Lawerlandia hardly anything is ever as simple as a first glance would suggest. By that I mean, death and a Will might well be a case different from those covered by the EULA, since if you die, all your stuff and rights are inherited by some entity, be it your son, other relatives, or ultimately the state. Consumer protection laws may not apply, since a dead person may no longer be a consumer in the legal sense.
Comment: In Lawyerlandia, if anything is ever up for any kind of interpretation whatsoever, then a case could go either way. Considering Valve has always tried to come off as "the nice company," it's a safe assumption that they wouldn't fight against it. They might, but the fact that they acknowledge the difference in laws suggests differently.
Comment: @Hackworth: it's not about consumer rights, but about legal rights to software licenses. And EU says they are transferable, thus making part of EULA which contradicts that invalid in EU.


Purpose of compatibility equations in linear elasticity

Question: I have a vague understanding of the compatibility equations for linear elasticity. They appear to be necessary in obtaining a unique displacement field. However, why is it that, in my papers I've come across, the compatibility equations aren't solved for in the linear elastic numerical formulation? Are they not a governing set of equations for linear elasticity?
Answer: A reasonably complete discussion of compatibility can be found at https://en.wikipedia.org/wiki/Compatibility_(mechanics)
There are six strain-displacement relations and only three displacements in continuum mechanics.  The compatibility conditions will be needed if you wish to compute displacements given strains.  However, most numerical formulations of mechanics are displacement-driven and the need for those equations typically does not arise because one uses: displacement -> strain -> stress -> force.
For force-driven formulations, one has to make sure that the displacements are compatible.  That is because the direction of computations goes as: force -> stress -> strain -> displacement.
Comment: What about in the case of boundary conditions. If given a boundary condition in terms of traction/stress, and we are after a displacement field solution, wouldn't this necessitate the need of the compatibility equations?
Comment: Even in those cases we typically numerically formulate the problem as f = K u rather than u = K* f.  The function spaces for the unknown fields are chosen so that they satisfy the needed integrability conditions (including jumps).  It is extremely rare to see strains being integrated directly, but the assumption that they are integrable is implicit in all formulations.
Comment: For more on the subtleties involved, see: Angoshtari, A., & Yavari, A. (2015). On the compatibility equations of nonlinear and linear elasticity in the presence of boundary conditions. Zeitschrift für angewandte Mathematik und Physik, 66(6), 3627-3644.


What can I use as a waterproof shield for my Rycote?

Question: Hi everyone, im looking at doing some recording of smashing up fruit/vegetables and i want to make sure i dont mess up my gear by getting any juice/water etc all over my Softie. Is there a decent way i can put something over it that will give a little protection that wont get in the way of my recordings?
Answer: I'd recommend a pop screen/shield as used for vocal recording, or a wire clothes hanger with pantyhose/nylon hosiery stretched over it. Not waterproof, but the tension and small gaps will probably catch most of the watery goop. Using anything less porous would probably color the sound. If you need something larger, stretch similar material over a DIY frame of PVC piping, held in place by appropriate grip equipment.
You're using a softie, but a rigid zepp or blimp will largely do the same thing as described above, and you can wash or rinse them off. A good reason to own a (relatively cheap) Røde blimp as a "stunt zeppelin!"
Comment: Thanks! Iv got an old pretty large pop shield i could use. Never thought about one of those! Should stop most the direct juice/debris from getting on my gear :)
Answer: I use a old window screen with a towel laid over it on top of a 12 foot pole. keeps the rain from hitting. The towel will get too wet but then I swap it out for a dry one. Stay away from the Rycote duck, I have it and it is worthless
Comment: Good to know since I was thinking about buying that Rycote duck. I will try your towel trick the next few days when it's raining again.
Answer: If you don't want to mess up your softie/pop screen something like this might work :
(source: edelstahl-in-bestform.de)
Don't know how it's called in english, but it's one of those things you put on top of your pan.
But as NoiseJockey alreadys said: you can wash everything off.
Comment: That is called a splatter guard here in the US, and is a great repurposing of existing tech!
Answer: This is a full on rain cover: Remote Audio REM-RMAN Rainman Boom Mic Rain Cover
Could work for your needs, but might be a little over kill. I always travel with it for shoots, but I haven't actually needed to use it, so I'm not sure how well it works.
Comment: I also recommend the RA Rainman for light rain, but won't really protect from front-facing splatters that well. One could put it on backwards, but it will definitely color the sound.
Answer: A plastic bag works. It modifies the sound slightly, my guess you will not notice it. Does not work with rain as the drops makes a sound. But recording sound effects, the "splash" might actually add to the sound.


How can i bake multiple kinds of cheesecake at the same time in a spring-form pan?

Question: I'm new to baking , so i was wondering how can i bake different kinds of cheesecakes in a spring-form pan at the same time?
Example:
i want to make NY cheesecakes with three different flavors in the same pan , say one is chocolate cheesecake , one is strawberry flavored and one is peanut flavored , how should i divide the pan into three different sections so the flavors don't mix?
(I want to bake them together in the same spring-form pan)
Comment: I suppose you saw the answer that suggests a strip of folded aluminum foil? Think "straight" instead of "circle" (the asker there explicitly wanted rings).
Comment: Related, at least partially duplicate: https://cooking.stackexchange.com/questions/84824/pie-with-2-different-fillings
Comment: @Stephie well that was interesting , but i don't want to do it like that , picture that a circle is 360 degrees , i want to divide it to three 120 degree sections and fill each with a different flavor , but i want to keep them separate , and bake them at the same time in the same pan , as i don't have enough ingredients to make 3 separate ones , and if i want to make 3 separate ones with the amount of ingredient  i have , it would become too thin.
Comment: @Stephie yeah didn't see that , why don't you add the answer then instead of commenting it? although i should try it first i guess it would work fine
Answer: Before you start separating your pie, you need to be sure that your fillings all need the same baking time and temperature. If they are from the same basic recipe and just have some extra flavors, you should be ok, if they are smaller amounts of different recipes, check the instructions carefully or ideally, make them as full pies once and note the actual parameters - random recipes from the Internet can be quite different, not all bloggers use an oven thermometer etc.
But assuming that this is taken care of, you simply need something that has the right length (radius of your pie tin), is food safe, heat proof, and water resistant. For similar problems I have used:

Aluminum strips (fold a few times to get some stability)
Cardboard strips wrapped tightly in aluminum foil or baking parchment.
A pie divider (a special gadget that goes into a regular pan, separating it, similar to this pie pan, comes also in square).
Glass cut to match the shape of the tin - although that was a loaf tin.

Once you have the tool of your choice, the real challenge is to keep them upright during filling and getting the tin into the oven. A kitchen helper is highly recommended.


Compare skewness of many distributions with few observations

Question: I have a dataset with page view data for about 500,000 users, divided into two groups. Each user can visit up to 5 pages, each as many or as few times as they want. So for each user, I have the distribution of number of visits to each page. I would like to compare the 'average skew' in distribution between the two groups. Roughly, users in one group are more likely to have distributions that look like this {3,0,0,0,0} and users in the other group are more likely to have distributions like this {1,1,0,1,0}. How can I compare the degree of skewness between the two groups? I thought of using the average Gini coefficient or entropy for each group, but each user has so few observations. How can I do this?
Comment: What does "skewness" mean when we're looking at counts in nominal (i.e. unordered) categories? Do you mean something more like "concentration" into few categories rather than spread over many? I guess you could think of that as skewness in the values of the counts.
Comment: Not easily . . .

The skewness coefficient is a pretty flaky statistic. I suggest avoiding it. Are you sure you wouldn't do just as well comparing their ranges, or number of different pages visited? And is it the same 5 pages for each? If not, what is the meaning of "(1,1,0,1,0)" versus "(1,1,1,0,0)"?
Comment: It is not the same 5 pages for each; there is no difference between (1,1,0,1,0) and (1,1,1,9,0). It's just the distribution of how many views they did for each of the 5 pages they were offered. Neither number of pages nor range is exactly what I want, since neither fully captures the difference between someone who looks at many pages once each and someone who looks at one page several times. Maybe I can report both?
Comment: Yes, that's what I mean.
Answer: Seems like all you need is a reasonable score that quantifies how much disparity there is between site visits. Since you need to compute 500000 such scores, something simple seems best.

Maybe your first thought is the best one - the Gini index.
Here's another simple one: After ordering the counts $y_1<y_2<\ldots<y_5$, compute $$\frac{y_5-y_3+1}{y_3-y_1+1}$$
So for (3,0,0,0,0) the score is $\frac{3+1}{0+1}=4$, and for (1,1,1,0,0) it is $\frac{0+1}{1+1}=0.5$. The idea is that $y_5-y_3$ is the difference between the max and the median, and $y_3-y_1$ is the difference between the min and the median, so you're comparing the two halves of the distribution. $1$ is added to each so you never end up dividing by $0$. Like then Gini index, this is a function of the order statistics.
Another simple measure of disparity is the SD of the logs. For nonzero data, $SD(\log ay)=SD(\log y)$ for any $a > 0$, so it is scale-invariant. It measures relative variation in the data. However, you'd have to add some constant before logging to avoid taking the log of $0$. In your examples, the SDs of $\log(y_i+1)$ are $0.62$ and $0.38$ respectively.

Note that options 2 and 3 are not scale-invariant, due to adding $1$ (or something) before dividing or logging, whereas the Gini index can be computed without any adjustment for the zeros, and is scale-invariant. So the choice might be based on that. Is (10,0,0,0,0) really the same as (3,0,0,0,0), in terms of your behavioral model? And is (4,4,4,0,0) the same as (1,1,1,0,0)?
Comment: Thank you so much for these excellent suggestions! With regard to the Gini index, is it reasonable to use with so few observations (5)? Will it be at all meaningful?
Comment: Well, I think so. You're not analyzing each one, you're just using it as a way to score the respondents.


How can the Wiener process be nowhere differentiable but still continuous?

Question: Taking a class in financial derivatives (book we use is Tomas Björk's Arbitrage theory in continuous time) but can't understand the exact meaning of how the Wiener process is defined. In the book one can read: "the Wiener process will be a continuous function of time which is non-differentiable at every point. This a typical trajectory is a continuous curve consisting entirely of corners and it is of course quite impossible to draw a figure of such an object." Just by looking at a trajectory of a Wiener process I'll say it is nowhere differentiable and thus non-smooth and non-continuous but here he says it is still continuous?
Comment: Continuity is a weaker property than differentiability.
Answer: Think of the Wiener process as a curve into which you could zoom in ever deeper and deeper and it will still be completely wiggly (= a fractal). That means that even if you tried to put a tangent line onto it, it would find no stable support (= no differentiability) - yet the whole curve is completely closed, i.e. could be drawn without raising your pen (= continuity):

(Source: http://en.wikipedia.org/wiki/Wiener_process)
Comment: this gif is really making me dizzy ^^
Comment: @Probilitator The gif actually looks like some old-school flight simulator in the mountain area :)
Comment: @Ilya now that you say it - it can no longer be unseen :D
Comment: I would be careful with such explanation, though. For example, a straight line is extremely self-similar on various scales, however it is perfectly smooth. Also, one can say that smoothness is exactly local similarity to straight lines, isn't it?
Comment: @Ilya: It is always good to be careful, right ;-) Yet I think you described the trivial case of self-similarity. It is a little bit like which function is its own derivative? Well, the exp-function, right? But there is also a trivial case: f(x)=0... Yet this isn't very helpful when you try to solve a differential equation...
Answer: There are many examples of "non-random" curves that are continuous everywhere, and yet differentiable nowhere. For example, the one defined by the formula
$$
  f(x) = \sum_{k=0}^\infty 2^{-k}\cos(2^kx).
$$
You may think of it as a limit of partial sums $f_n(x) =\sum_{k=0}^n 2^{-k}\cos(2^kx)$. Each $f_n$ is differentiable, and consists of a combination of sinusoids with different frequency and magnitude. As $n\to\infty$ there are more and more frequencies present, which makes tangent lines (very much related to differentiability) behave poorer and poorer. In the limit, there is no single point which admit a tangent line.
Comment: +1 well earned for making the answer to this question three-dimensional ;)
Comment: @Probilitator: thanks. 3d - is some quant joke I fail to understand?
Comment: nope - it refers to the three prespectives our answers provide ;)
Answer: The most basisc understanding of continuity  of curve is:

You can draw it with a pen/pencil without lifting your hand. Thus the
  curve has no jumps that will force you to raise/shift your palm in
  order to continue drawing.

The function $f(x)=|x|$ is continuous but not differentiable at the origin. If you look at the relevant Wikipedia entries on continuity and differentiability the difference will become clear.
Also note that the continuity of the Brownian-Motion is the main reason why hedging in continuous time works so well theoretically. If one introduces jumps thus making the paths no longer continuous the theory becomes much more elaborate and complicated.
Comment: Thanks, should have googled it better but thought there was something special about it. With jumps, you mean like if introducing dividends or just sudden larger jumps in share price?
Comment: Dividends can work like jumps if you don't pay them out continously. E.g. if dividends are only paid once a year they will have the effect of a jump - the stock price will go from one value to another with no values in between. You can also always introduce stochastic jumps - just google "Jump diffusion models for option pricing" - !! also spread the word about this site ;) !!
Comment: Thanks, will do. Believe the ones in my class will have use of this site as will I!
Comment: +1: I think the example of the absolute function is a good one!
Answer: I know this answer is years later but in case anyone looks this up, I'm hoping I can help.
I can go through all of the mathematical proofs, but instead I'll try to give some intuition.
By way of background, functions that are non-differentiable at any point but continuous at every point was first discovered by Karl Weierstrass.  If you have trouble getting your arms around it, you have good company!  Even other famous mathematicians decried them - Poincare called them 'monsters', Hermite called them a 'lamentable scourge'.  Intuition said that if the function were continuous it would only be non-differentiable at only small parts of the domain.
But the basic ideas are:
A function is continuous at a point if being 'close' to the point means that the function value is close; f(x) is continuous at X if x being close to X implies that f(x) is close to f(X).
A function is differentiable at a point not only if it is 'close', but points close have to be approaching at a uniform speed; velocity is the derivative of position.  Being differentiable implies being continuous.
So f(x) = absolute value of x is continuous at x = 0; f(0) is also 0; being close to x=0 means f(x) is also close to 0.  But this function is not differentiable at x=0, since approaching 0 from the right comes in with a 'speed' of 1 but from the left is -1.
So what is going on with Brownian motion?  The result is kind of intuitive - at each point it 'jumps' with a value from a standard normal. It will still be continuous, because the small interval is sufficient to keep it 'close' to the last point - the 'jump' multiplied by the infinitesimal interval is small enough for the function to stay 'close'.  However, it isn't differentiable, because the size of the last 'jump' (on the left of the graph) won't be the same as the jump on the right side, so it isn't approaching at the same speed; on any interval, there will be lots of different 'speeds'.
Now to be a little more rigorous, Brownian motion is non differentiable at every point ALMOST SURELY and continuous ALMOST SURELY; without getting too technical, this means it happens with probability one (but may fail on a set of measure 0).
Comment: I was reading the earlier answers , where it says that a continuous function (such as brownian  motion) can be drawn without taking your pencil off the paper.  Not to be pedantic, but is this true for brownian motion?  Isn't the arc length infinite ? So it would take you an infinite time.


Challenger Bus panel

Question: I have a challenger panel with a burned bus and bad breakers. I'm looking to replace them. I called my local shops and they said they don't carry this anymore. Is there a replacement option without going to remove the entire box? I am mainly looking to replace the interior components Bus and breakers. I don't mind other brands as long as they fit. The panel is 100 amp and I have attached images of the label and the bus. Thank you.
Comment: Can you give us close-up photos of the busbar damage?
Comment: What vintage is the panel and breakers? Have you gotten estimates for complete replacement?
Comment: Also, who do you have for an electric utility, and I take it this is mounted on the outside of your house, correct?
Comment: Specifically we need to see the bus damage under the lower 100A breaker (the upper 100A will not remove easily). The goal is to see how bad the bus damage is. You can't just strut into a shop and buy a new busbar; you'd have to be very lucky on eBay or find a specialist used-panel trader.  The buses being nearly unobtanium, I'm hoping to save the bus. Challenger panels' buses are perfectly fine (other than damage done to them by failing breakers, obviously). The breakers are all bad, but there's a super easy fix for that.
Comment: A new panel's busbars won't fit because nobody makes panels that narrow anymore.  Code now requires wire bending space (see that neutral) which is why all small panels died.  I have a list of panels I can't replace because of this, including some 12 space FPEs barely 10"x12".
Comment: This is all the images I have. The bus is damaged. The breakers are really bad. They are also made by challenger. If bus replacement is not an option, is there a panel I can find to replace with this existing ?
Comment: You want me to remove the old breaker and take a picture to see if we can rebuild the existing bus?
Comment: @Wyatt if you can remove that lower 100A breaker (with the upper 100A breaker off) and get us a closeup of the damaged section of the bus, that would be great.   Hard to tell what exactly is going on with the busbar damage with your photos so far...
Answer: Haven't heard back from you, so here goes.
About the panel/breakers
This thing you have is a meter-main with 12 breaker spaces.  The main is "backfed" meaning the main breaker is just one of the breakers.
The Challenger breakers are known to be defective. And because of that, many electricians treat Challenger panels as if they're defective.  They're not. There's nothing wrong with Challenger panels.  The breaker problem can be very easily solved: Eaton "BR" breakers are cross-listed for it.  Take a look at any BR breaker, it says

Type BR
  Type C

Type C is for your panel.   Ba da bing! That's easy.
By the way, if the home inspection report had said something about that and you said "meh, whatever", replacing those Challengers with BRs would have prevented this.  So next time you see something like that on an inspection report...
About that bus
Your plan, as you have presented it, is to "just replace the bus" using a components supply chain that does not exist in real life.  This brand has been out of production for 30 years.  Compatible buses go in the trash every week, but nobody thinks to upcycle them onto eBay or Craigslist becuase they are obsolete and connecting with a buyer is extremely unlikely.  There are companies that specialize in old Challenger panels, and you can try, but this is an odd duck even among Challenger.
So replacing this bus is not gonna happen.
As far as finding a modern bus that will fit, the problem is panels of this style are also obsolete: the very compact buses and gutters are now illegal due to "new" rules regarding wire bending radius (see that neutral wire for why).
So fuggedaboutit.  You only have 2 options: Save this bus or replace the entire meter-main assembly.  Chassis and all.   I'll talk about saving this bus.
Saving the bus
The bus position containing the melted breaker (9-12) is permanently useless.  So now we have two questions:

Is the bus underneath the fried breaker intact enough to use the bus area below it?  (Because the feeder wires will reach there).
Is the bus underneath the main breaker intact enough to continue in service?

Either way, we are going to change all the Challenger breakers here for Eaton BR/C.  The Eaton BR2100 ought to do the trick, at $40 each.  Betcha didn't think you could get out of this for $100, did you? :)
If all busing is in good shape
In this case, we leave the main breaker at its position, and fit the feeder breaker in positions 13-16.  The cable will reach.  Easy peasy!
If the bus below space 9-12 is fried, but the main is OK
In this case, we leave the main breaker where it is.   We move the feeder breaker to positions 5-8.  Any remaining breakers go to positions 1-4; no breakers exist below the main.   This will involve extending the feeder wires; pull new wires if they're short, otherwise extend them with insulated Polaris lug splices.
If the bus under the main is roached
In this case, you will need to remove the bus bars which come off the meter socket, and replace them with #3Cu XHHW wire.  This will need to be physically protected where they come through the hole.
The main breaker is then moved to spaces 13-16 (below the melted breaker), and it will need to be bolted down the same way it's bolted down now.   The feeder breaker is moved to spaces 17-20.  That leaves spaces 21-22 for anything that is now above the main breaker. Remember this panel permits "BR/C" duplex or quadplex breakers, which you can put in spaces 21-24.
Answer: I have replaced a couple of these. The back plane is narrower than today's panels (code required space). The one good thing I have found in all but 1 case was that there were boards on the inside the of the studs to make the panel fit 16 on center. This means I was able to rip the spacer boards out and a new panel fit in between the studs. Just a note to help and save $ on this upgrade I have found raco (Hubble) brand "insiders" the best clamp / bushing to save time and $ with remodels.  (I have no connection or interest in Hubble/raco other than I love this product) on top of going with a modern panel I would get one with more spaces, this can make the retrofit easier by itself and I almost always suggest a service upgrade (get a 150 or 200 amp panel) it's only a few $ more. I have never been asked to downsize a panel but have been asked to upsize the same home 3 times. If they went with my original suggestion they would have saved thousands and several days less without power.

Challenger Bus panel


How to unstake ALL my EOS from EOS Voter Greymass

Question: I have 8 EOS still staked on Voter Greymass. 6 EOS Staked to CPU and 2 to Bandwidth. I want to unstake all my EOS and transfer them to my Ledger key.
Unfortunately every time I try to do this I get the error message pasted below, even if I try to unstake just 1 or 2 EOS at a time.
Please, could anyone help me?
Thanks a lot
Answer: The problem is that you don't have enough resourcecs staked to complete the action of unstaking your resources.
There are some services (such as bloks.io) that offer 5 free transactions per day, you can use them to unstake and transfer your funds


Module installation via web browser

Question: I've a question regarding the installation of modules via the web browser. At the moment, I can easily upload both themes and modules to my Drupal site via sftp, but when I attempt to do the same using the module 'Update Manager' (i.e., through the web server itself, to avoid the hassle of adding the theme/module manually) I get an error that reads "Your server does not support installing modules and themes from this interface..." How does one enable the fix? I've read through some documentation regarding module installation but the comments seem contradictory, with some users suggesting a chown prompt and others saying such a solution is a breach of site security and thus to be avoided. Is there any consensus on what to do in this situation? Any help would be appreciated.
Answer: You need to install the php5-ftp package and reload your webserver to load this extension.
Answer: For installing module has many way:

Install by browser: in module page in drupal installing ftp by ftp url. This link is module page in drupal
Install by drush with drush en module_name
Install with ftp. With ftp software upload module files in sites/all/modules and go to module page in drupal and install this.

Module installation via web browser


comment-kill for entire region

Question: Is there a similar command to comment-kill that kills all comments in a given region and saves them to the kill ring?
Comment: Presumably you don't just want to kill the region or copy it to the kill-ring. Instead, you want to kill only the comments in the region.
Do you want them *concatenated* in the kill-ring, as one ring entry? Or do you want each comment to be a separate kill-ring entry. The question could be clearer.
Comment: You can narrow to region, put point at the beginning of the region, and call `comment-kill` with a large numeric prefix-arg. Pitingly that does not concatenate all kills. You can reach that with the following advice (caution: hacky!): `(defun comment-kill-ad (fun &rest args) (kill-new "") (let ((last-command 'kill-region)) (apply fun args))) (advice-add 'comment-kill :around 'comment-kill-ad)`
Answer:    (defun ar-kill-comment-atpt ()
      "Deletes comment at point if any. "
      (interactive "*")
      (ar-th-kill 'comment))

Requires stuff from https://github.com/andreas-roehler/thingatpt-utils-core providing the ar-th-kill basics.
Deletes all comments at point. Narrow to region before in order to restrict.

comment-kill for entire region


Is There An Initiative To Sequence The Genomes Of Critically Endangered Species?

Question: I realize that there are many isolated efforts to sequence the genome of a particular endangered species such as the orangutan or the snow leopard. However is there a concerted effort to sequence the genomes of every species on the brink of extinction? Also, is there an effort to sequence the genetic diversity of the surviving populations, since it would be very difficult to re-create alleles that would be needed if the species were to ever be resurrected.
Comment: Not an answer but I remember watching a documentary about a huge, international, "seed bank" containing cells from various species. So, not their genomes as such but the species themselves. I'll see if I can find a reference.
Comment: It seems like genomes are more valuable than spaceships.
Comment: It doesn't seem like there's a crowd-funded solution. That might be something to look into if you're interested.
Answer: The seedbank terdon mentions is the Norwegian Svalbard Global Seed Vault located at Spitsbergen island:
http://en.wikipedia.org/wiki/Svalbard_Global_Seed_Vault
However, the closest thing to a concerted initiative for sequencing animals I know of is the Genome 10K project:
http://genome10k.soe.ucsc.edu/
Their list of first 101 vertebrata proposed for sequencing contains 29 species with status RED from the red list. Most of them are only proposed, but the sequencing of the following are already in progress:

crested ibis (Nipponia nippon)
Amur tiger (Panthera tigris altaica)
cheetah (Acynonyx jubatus)
lion (Panthera leo)
domestic yak (Bos grunniens)
bactrian camel (Camelus bactrianus)

and that of the Chinese softshell turtle (Trionyx sinensis) has funding secured. Already complete are the giant panda, the chiru, and the polar bear.
And some surprising fact: where the funding is secured it is/was funded by the Beijing Genome Institute. A shame if this would remain the only one.
Comment: http://www.arthropodgenomes.org/wiki/i5K


What is the grammatical function of "が" in this context of counting people?

Question: In an anime I've been watching, the protagonist goes to a village where one of his friends came from, where all the people in the village have the same hair color as his friend. (with "〇" being the name of his friend) He says "〇が一人、〇が二人、〇が三人...". English subs say "One〇, two〇s, three〇s...". He says this out of surprise of the amount of people that look like his friend due to their hair. I'm a bit confused as to the use of the particle "が" in this context. Is "が" taking the place of "の" or  being used as some other sort of possessive particle? Is it a certain way of counting people? Or something else entirely?
Comment: Are you familiar with what が is used for?
Comment: Somewhat. I know the general gist of it's uses, but I'm just not sure what the use of it is in this context(e.g. is it being used to mark the subject, and why would it be used instead of something like "の").
Answer: This が is a plain subject marker, and it's not interchangeable with の. This 〇が1人 is a contracted version of 〇が1人いる. いる has been omitted because it's redundant when counting things.
In English, you count sheep like "One sheep, two sheep" (but not "There is one sheep, there are two sheep", which is too cumbersome). In Japanese, we say "羊が1匹、羊が2匹".
Grammatically, this 1人/1匹 is an adverb. Japanese people count things using adverbs by default. See: How to list numbers of things


1999 Honda Civic xD hatch back overheating

Question: My Honda has been overheating when it is in idle. The temp gauge will jump to max really fast. After driving it for 5-10 mins a white sweet smelling smoke will come from the coolant reservoir. I checked my coolant after driving around and it was boiling in the reservoir. I flushed my coolant and changed my temp sensor. What could be causing this overheating problem?
Comment: does it overheat while moving?
Comment: How much mileage does the Civic have?
Comment: It does over heat while moving but at a significantly reduced rate. It will be at normal temp the. When I stop at a red light it will start overheating and smoking. Also there is no leak into the ground so if there is a link it would be I to the engine.  I just hope that it is not the head gasket.
Answer: If this is all while you are parked and idling the car, the first place to look is the cooling fans directly behind the radiator. While moving, the motion of the car forces air through the radiator cooling the fluid flowing through it. When stopped, the ECU should be starting one (or two depending on the car) electric fan on the back of the radiator. This pulls cool air across it accomplishing enough cooling to prevent the boil-over you're seeing. If the fans are no longer working, or the sensor that turns them on is bad, then no fans, and the car boils over.
Also, check the level of the coolant when the engine is warm, but before it has boiled the coolant. The overflow tank should be marked as to the proper levels.
Do you know what the ratio of coolant to water is in your car right now? It should be 50/50. If there is too much water, it will boil at a lower temperature.
An easy way to test this is to start the car, and just let it idle. If you can feel the top radiator hose getting hot, and no fan, then you have narrowed down the problem. If the fans don't come on, try looking for voltage on the connector that runs the fans. If there is a voltage present when the car is warming up, then the fan is bad. If you can feed 12V directly to the fan and they run, then the fans are fine and either the sensor, the ECU, or perhaps a wiring issue is preventing the fans from being told to come on. One additional thing to check is that the ground is good between the fan and the battery. Try checking the resistance between the negative connector on the fan and the battery negative. It should read less than 1 or 2 ohms. If it's more than that, you have a bad ground. I learn this one the hard way. Replaced a perfectly good circulator fan only to find out the new one did the same thing. The problem was a bad ground at a cold solder joint where someone had tried to splice extra length into the harness.
Answer: Here is a Popular Mechanics article that discusses the sweet smell coming from the Civic.
http://www.popularmechanics.com/cars/how-to/a536/2423551/
[The sweet smell information is below.] All credit goes to Popular Mechanics.
(1) SMELLS LIKE:
MAPLE SYRUP
WHEN: After the engine has warmed or possibly even after it's shut off for a few minutes.
THE CULPRIT: Coolant containing sweet-smelling (but toxic) ethylene glycol is leaking from somewhere. It could be coming from a radiator or heater hose, a failed intake manifold gasket or cylinder head. It might be coming from a leaky radiator cap or the radiator itself, especially if you smell it outside the car. A strong odor inside the passenger compartment probably means a bad heater core.


Google API tutorials

Question: I want to create a program like when we give the country name it should display the provinces inside that country and the same thing has to happen until getting the house address. (e.g. if I give one country's district name it has to give the villages name under that district).For that, I need to know which google API can help me to do so and I also want to know is there any tutorials available for this requirement.
Answer: Don't know about google but OpenStreetMap has boundary relations which contains the inner divisions as members. e.g. https://www.openstreetmap.org/relation/4583216
Comment: OpenStreetMap has matured a lot and could be a really great resource for what you want to do.

Google API tutorials


Is The One Ring playable with just two people?

Question: Is The One Ring RPG playable with just two people, one as the player and one as the loremaster?
Answer: It should be; there is very little non-traditional about it. The most non-traditional element is the courage system.
The hope system, to some extent, is geared for 3-4 players. Since it has both individual and group dynamic elements, it may not be as good in a 1-on-1 game, but it should still work. The one element that is problematic is that one can always draw from the pool with group permission if one is the sole member of the group.
Also note: a larger group, in addition to having more hope in the Fellowship pool, has more diverse skills available, and thus is likely to need less hope spent in play.
The Travel System is brutal with less than 4 players, but that can be solved by NPC companions, or by playing a Dunedain.
Comment: @OpaCitiZen Actually, no. The refresh of the pool is Number of Party Members + number of hobbits in the party. Aragorn on his own has only 1 courage to refresh for all rolls on the adventure. The party of 13 has 17 courage per session they can refresh amongst the whole... and so, if any one character is forced to use some, there is a deeper well to pull from to replenish it. Moreover, with a larger party, there is less likelihood of needing to spend some.
Comment: That could explain why Aragorn-like characters could gather so much resolve - alone they had to worry about their own survival only, pushing on to fight and struggle for a higher purpose. :)