Publishing an incomplete idea

Question: I am working on an extension to my thesis work in robotics.  I believe that, in order to complete the result I'm moving towards, I'll need at least two, probably more, papers to provide a full solution.  The problem itself can be broken into several pieces that clearly build off of each other.  I'd like to publish each piece separately in order to keep the size of the paper reasonable.  Also, the first piece is actually of limited technical use but introduces the concepts, notations, and methods required for the further pieces.  Has anyone had any success trying to publish work that stands alone but is very obviously incomplete?
Comment: Will each paper clearly present a method, results, and discussion that tells a complete story?  If so, I think it is definitely reasonable to split your thesis into multiple papers.  It will also depend on the journal you are submitting to as some are more open to introducing concepts rather than analyzing hard data.
Comment: Maybe this varies by field, but I'm not sure why you are so concerned with keeping the size of the paper "reasonable".  If you need more space to present your work, and it can't be broken into pieces that stand alone, well, you write a longer paper.  What's the point of having 2-3 shorter papers if a reader has to read all of them anyway in order to get value?
Comment: Primarily, papers in robotics are often limited to under 12 pages, with huge page charges being imposed around the 8 page mark.  I feel that to explain the whole piece of work, probably around 20 pages would be necessary.
Answer:
Also, the first piece is actually of limited technical use but introduces the concepts, notations, and methods required for the further pieces.

The main question is whether this work is of independent interest or use to anybody but you.  All research is incomplete in some sense, and that doesn't bother people (everyone likes opportunities for further work).  So the issue is whether your paper is incomplete in the sense of not accomplishing anything interesting yet, or incomplete in the sense that there is still much more to do.
If there are people who want to read it now, on its own, then that's an argument for publishing it now.  If it has little value except as preparation for the next paper, and that paper is already written, then it might be OK, but getting it accepted on its own may be tough.  If it has little value except as preparation for a future paper that does not yet exist and might not pan out, then it will be really difficult to publish it.
Comment: Sounds like a scientific contribution. But be careful not to under-sell your case. In the paper, be as precise as you can in describing how the limited case will be helpful when dealing with more complicated cases.
Comment: That makes sense.  I would say that the first piece is of independent interest since it solves a problem in the field.  However, the problem that it solves is a limiting case that is rarely considered in practice.  That being said, this limiting case forms the basis for the more complicated cases that are considered, so perhaps it is relevant...

Publishing an incomplete idea


Why is there an extra plastic container in my toilet tank?

Question: I recently bought an older house, and the toilet tank is leaking.  In exploring the issue and googling around for toilet repair, I saw no mention of one of the parts that is in my toilet tank.  Within the tank, there is a smaller plastic container that surrounds the flush valve.  It seems to restrict the amount of water that ends up being used per flush, so perhaps it was added to reduce water consumption?  What is this thing, and how does its presence affect my approach toward replacing the different pieces of the toilet?
Comment: I'm voting to close this question because it hasn't needed another answer in *eleven years*.
Comment: That looks like a milk container cut in half.
Comment: @0A0D I assure you that it is not a milk container.  It definitely seems specifically built for the purpose (it has spacing for the bolts for example), and is made of much sturdier plastic than a milk container.
Answer: I believe that you are correct and that the container was added to reduce the amount of water used per flush. As for whether it will affect your fix - it might. If the tank is leaking then unless it is cracked then there are only two places that it could be leaking from - where the inlet connects to the tank or where the tank connects to the bowl. If it's leaking from the inlet valve then the container would have no effect other than giving you less space to work. If it's leaking form the spud washer (the rubber gasket between the tank and bowl) then you may need to remove it to get to the bolts that hold the tank to the bowl (though it appears that the container has indentations that go around the bolt heads so again it may just come down to the only effect being a more cramped space to work).
Comment: That barrier was part of the toilet as sold.  This was one of the early designs to meet the "low flow" requirements that were foisted upon us.  You were supposed to wink-wink, nudge-nudge, "forget" to install that damn -- so that your toilet would still work decently.
Comment: @jkohlhepp - Sigh. No. leave it in there. The toilet apparently flushes properly as is. That there is a leak only means that there is a leak. Using more water than necessary will not change things, other than you personally being wasteful and foolish by choosing to waste water. If we all save a gallon of water per day, then we will have saved a great deal of water. Since that single toilet will be flushed many times per day, this equates to many gallons saved by you alone.
Comment: Yes I believe that I can still get to the bolts...
Comment: @BrockAdams thx for the info Brock.  If I end up having to replace the flush valve I will certainly "forget" that piece.
Comment: @woodchips: If the toilet works well, sure.  But I've never known one of those older "LoFlo"s to be worth a {sneeze}.  (Many of the modern LoFlo's are {cough} too.)
Answer: I had a similar toilet that never flushed properly, resulting in multiple flushing and wasting water.  I removed the tank, removed the flush valve and plastic dam, re-installed the flush valve and my toilet finally works properly.
To ensure it wasn't wasting water I measured 1.6 Gal of water, poured into the bowl, marked it, adjusted the fill rate just a little until the water in the bowl hits the mark every time.
No, I didn't use a permanent marker in my bowl - I used colored tape that stuck until I removed it.


How do I understand the module structure on Yoneda Ext?

Question: Suppose $R$ is a (commutative) ring, and $M$ and $N$ are (finitely generated) $R$-modules. Then I know each $\mathrm{Ext}_R^i(M, N)$ has the structure of an $R$-module. On the other hand, via Yoneda's description of Ext, each $\varepsilon \in \mathrm{Ext}_R^i(M, N)$ corresponds to an equivalence class of exact sequences starting with $N$ and ending with $M$. My question is this: suppose $r \in R$ and $\varepsilon \in \mathrm{Ext}_R^i(M, N)$. How can I understand $r \varepsilon$ in terms of $\varepsilon$? To what extension does $r \varepsilon$ correspond?
Answer: we can just see the case $i=1$:
In general,if $M$ is $A-B$ bimodule(i.e.left $A$ module and right $B$ module and $(am)b=a(mb)$),N is $A-C$ bimodule,then $Ext^1(M,N)$ is a $B-C$ bimodule.the structure of left $B$ and right $C$ module as follows:

if $\varepsilon:0\rightarrow N\xrightarrow f X\xrightarrow g M\rightarrow 0$ is a short exact sequence in left $A$-modules.$\forall b\in B$,there is a left $A$-module homomorphism $\varphi_b:M\rightarrow M$ by senting $m$ to $mb$.take pullback with $\varphi_b$ and $g$,we get an element in $Ext^1(N,M)$ this is $b\cdot \varepsilon$.

similarly,if $\forall c\in C$,take pushout with natural right multiplication $\phi_c:N\rightarrow N$ and $f$,we get an element  in $Ext^1(N,M)$ this is $\varepsilon\cdot c$.
it is easy to Check this: structre of left $B$ module and right $C$ module has associativity. i.e. $(b\cdot \varepsilon)\cdot c=b\cdot (\varepsilon\cdot c)$.
As follows:
Then $\varphi_a=\alpha^-$ is using the unique map induced by kernel.
Now we consider the commutative case,we only need to check $r\cdot \varepsilon=\varepsilon\cdot r$,suppose $\varepsilon:0\rightarrow N\xrightarrow f X\xrightarrow g M\rightarrow 0$ is
a short exact sequence in $R-Mod$. Then consider the following diagram:

The $\beta^\prime$ make all the diagram commute. $\beta^\prime$ is also the induced map between kernel, so it is unique. It is also induced by $\phi_r:X\rightarrow X$, hence $\beta^\prime=\phi_r:N\rightarrow N$. By the diagram we have:$r\cdot \varepsilon=\varepsilon\cdot r$.
for $i>1$,the same.
Comment: Thanks for your comment, this is very helpful. It is still somewhat unclear to me what happens for higher Exts, though. Is there some way to extend what you have written? I'm happy to go read on my own, if there is some source that describes how to take this structure on Ext^1 and deduce the structure on Ext^i.
Comment: @EricCanton GTM4


What is the downloaded ISO file?

Question: I'm trying to create a bootable usb, but the boot and run linux software needs an ISO file according to the instructions on ubuntu help. I have no idea what that is or where to get it.
Answer: An ISO file is also sometimes called an image file. It is sort of an archive for CDs or USBs. This is indeed what you need to install Ubuntu.
Go to http://www.ubuntu.com/download/desktop and hit the Download button to get your ISO file.
You will have the choice between the 32 bits and the 64 bits versions of Ubuntu : choose the one that corresponds to your computer.

What is the downloaded ISO file?


How to provision nginx vhosts on Vagrant vm?

Question: I have a Ubuntu VM machine I'm running through Vagrant with nginx installed. It's pretty easy to ssh into the VM and setup a new nginx vhost whenever I need one. But what is the best practice for setting up nginx vhosts via Vagrant provisioning, or maybe using Puppet? Essentially I imagine some sort of config file(s) that sit in my host folder and when I provision, it parses these config files and creates a new vhost for me on the VM.
Answer: Have a look at https://www.vagrantup.com/docs/provisioning/ansible.html particularly https://www.vagrantup.com/docs/provisioning/ansible_local.html
With this you will be able to set anything you need on the vagrant VM.
Comment: Anible.com seems to be some sort of pay service. Where do I find Ansible playbooks?
Comment: Ansible sales Ansible-Tower (enterprise version with UI), ansible itself is free. Regarding playbooks you have to write them or you can download some at https://galaxy.ansible.com/
Answer: There is a vagrant plugin - hostupdater. It can automatically update /etc/hosts and add virtual hosts pointing to your guest machine
Vagrant file configuration example:
config.vm.network :private_network, ip: "192.168.3.10"
config.vm.hostname = "www.testing.de"
config.hostsupdater.aliases = ["alias.testing.de", "alias2.somedomain.com"]

Answer: You can use a configuration management tool. Just write a template for nginx, apply variables as needed, reload nginx, and Bob's your uncle. Ansible is extremely easy to use, you can use ansible-galaxy to pull geerlingguy.nginx, which is a role that easily configures the basics for you.


"whichever is (the) less", vs "whichever is (the) lesser"

Question: I would like to have advice on the differences between "whichever is (the) less" and "whichever is (the) lesser".  Are they both grammatically correct?  If yes, under what circumstances should they be used, especially when being placed at the end of a sentence?  I found both in different legislations and government documents.  Thank you!
Answer: 1) Whichever is less
   Among very few things (two preferably)
2) Whichever is lesser
   Used for comparing among two or more number of things
3) Whichever is the least
   The thing which is less than all of the other things
Yes, they all may sound like they have the same meaning, and it's mostly up to you whatever sense you want to deliver to the reader.


Would it be possible to generate a memorized wallet address by using a batch of phone numbers?

Question: I was wondering if I was able to generate a bitcoin wallet by using a bunch of phone numbers i remember. I'm sure everyone can recall at least 5 or 10 phone numbers by memory. So in theory I can reference the wallet by just remembering the people thats associated with it. Say my wallet would consist of: john, sam, eva, jesse, and ben. but it would be referenced as phone numbers and in turn gets converted to a bitcoin wallet address.
Answer: You could use the phone numbers as a passphrase for a Brain Wallet.


What's the difference between apparent brightness and apparent magnitude? Are they the same?

Question: I know that the equation for the difference in apparent magnitudes can be represented as:
$\Delta m=-2.5\log\left(\dfrac{I_{1}}{I_{2}}\right)$
and the apparent brightness of a celestial object is shown as:
$\ B=\dfrac{L}{4\pi\ D^2}$
Some people in my class told me that$\ B$ and$\ I$ were the same thing but used in different cases. This explanation didn't help me though. While playing around with the equations, I found this nice relation:
$\ \dfrac{B_{1}}{B_{2}}=\left[\dfrac {\left(\dfrac{L}{4\pi\ D_{2}^2}\right)}{\left(\dfrac{L}{4\pi\ D_{1}^2}\right)} \right]$
$\ \space\ \space\ \space\ ={\dfrac{4\pi\ D_{1}L}{4\pi\ D_{2}^2L}}$
$\ \space\ \space\ \space\ ={\dfrac{D_{1}^2}{D_{2}^2}}$
So if$\ {B_{1}}={I_{1}}$ and$\ B_{2}=I_{2}$holds true, is this following equation also true?
$\ {\dfrac{D_{1}^2}{D_{2}^2}} \space\ = 10^\left(-{\dfrac{\Delta {m}}{2.5}}\right)$
$\ \space\ \space\ \space\ \space\ =\dfrac{1}{10^\left({\dfrac{\Delta {m}}{2.5}}\right)}$

However, if$\ B$ and$\ I$ are not the same, what is the difference between the two measurements? And can either one be used to accurately measure how bright a non-luminous celestial body (ie. a planet) appears from Earth?
Also... does $\ m$ have an SI unit? I've never used any units when I solve for it
Answer: Yes, $B$ and $I$ are the same things in this context. The $\Delta m$ you derived goes by the name "distance modulus" when one of the distances is set to $10\operatorname{pc}$. The thing to be careful of is that $I$ is also sometimes used for spectral radiance (or surface brightness) when working with radiative transfer. Spectral radiance doesn't obey the inverse square law, though, so there's no risk that we're confusing them here.
Comment: Absolute magnitude $=$ the magnitude at 10 parsecs.
Comment: Not at all. The formula works whether one distance is set to 10 parsecs or not, it just has a special name when one of them is set there (I don't recall which one, because I never use magnitudes, myself).
Comment: Ok thank you. So since one distance has to be set to 10pc, does this mean that I'm not able to use this to calculate the apparent brightness of a planet within our solar system?


Using grants while on unpaid leave

Question: When a professor goes on unpaid leave from her university, can she normally continue to use her grants to fund graduate students and postdocs?  Or, do all grants "freeze" until the professor returns?
Answer: I don't see any reason that a professor wouldn't be able to continue to use grants while on leave.  In fact, I'm on unpaid leave from my home institution right now, and have been able to use my grants (for travel support for myself), so that's one data point.
Comment: I'll add another "yes" data point. Unless the leave is disciplinary, I've never known an institute to freeze grants. And, often the leave is granted to give time specifically to work on projects supported by grants.
Comment: Thank you for the answers. Would this still be true even if the professor was on unpaid leave because she was planning to leave her university?
Comment: @anonymous555 Why not?  I think they still need to have an official appointment, but I think even 0% appointment (one with no pay) suffices.  It's possible that if the university really wanted to, maybe they could find some way to do this, but why on earth would they?  The PI would just transfer the grants and they wouldn't get the overhead.
Answer: The answer is "yes".  For instance, I was on unpaid leave this academic year, and used my grant to support a graduate student.
Answer: It depends on the breakdown of the grant. If there are students or staff who were hired to do the proposed work then I don't see any reason why they wouldn't continue being paid if they are continuing to work. The same goes for research related services and products. Sometimes sabbaticals are unpaid, but that doesn't mean that the work stops. Most grants are on a schedule, so PIs need to be making some form of progress on the project (whether or not they are getting paid from it).

Using grants while on unpaid leave


Is there a climber chest piece?

Question: Climbing is awesome, and climbing fast is better! I bought the Climber's Bandanna and Climber Boots, but can't find the third part of this set. Where can I find/buy it?
Answer: Yes. Climbing Gear, the chestpiece of the Climbing Set can be found in Chaas Qeta Shrine in the Necluda sea. Chaas Qeta Shrine is a Major Test of Strength, and the Climbing Gear is found in the chest at the end of the shrine.
Comment: @l0b0 If I recall correctly, those test of strength shrines also reset on a blood moon, so there's no need to save them for the weapons.
Comment: The whole set has an effect increasing your climb speed. Highly recommend.
Comment: Dang, and I was saving that because I thought I didn't need any more powerful weapons…

Is there a climber chest piece?


How to get bold version of blackboard bold fonts?

Question: Right now, I have \mathbb{C} and \boldsymbol{\mathbb{C}} both producing the same character.  What package/command do I need to get a bolder character?
Comment: Welcome to tex.sx.  See https://tex.stackexchange.com/questions/199333/turn-mathbb-characters-bold-in-math-mode (probable duplicate)
Answer: In the modern toolchain with unicode-math, \boldsymbol\mathbb works if you load a math font with a bold version (as of July 2019, XITS Math, Libertinus Math or Minion Math) or if you manually load a bold math font with, for example, \setmathfont[version=bold]{Minion Math Semibold}.
Otherwise, as Sebastiano beat me to saying, load mathalpha (formerly mathalfa) with a double-struck font that comes in bold (such as [bb=px]) and use its \mathbbb.
Answer: Here there is my proposal as an alternative. You could to use bb = boondox + mathalpha (as suggest by the user @Davislor - see comment and your nice answer), but it changes the nature of the symbol. You have always the bold.
Here there is a little code
\documentclass[a4paper,12pt]{article}
\usepackage[bb = boondox]{mathalpha}
\begin{document}
$\mathbb{R}, \mathbbb{R}, \mathbbb{Z}$
\end{document}

and a screenshot:
Comment: It might still be a good idea to use `mathalfa` in our examples for a while, because that's still supported for backward-compatibility and it might take a while for everyone to update.
Comment: Note that the package has been renamed `mathalpha`.
Comment: @Davislor I didn't know and thank you very much. Then in my book I change it, because I use this name.


How to remove the RSS feed icon form the content listing pages?

Question: I need to remove the syndication icon because I'm either not going to syndicate or I want to do it my own way.
Answer: If it's just the feed icon you need to kill, you could always just comment out or delete the line:
<?php print $feed_icons; ?>

from page.tpl.php?
Answer: If you have Omega theme comment out this line
<?php if ($feed_icons): ?>
<?php print $feed_icons; ?>
<?php endif; ?>

It is in region--content.tpl.php
Answer: better bet is to use David Norman's (deekayan) Jammer module.
Install it and then enable the following module's:

Feed Icon Jammer
Feed Jammer

the first, of course, removes the icon, and  the second prevents the front page from being published as an RSS feed.
Thank you
Answer: See Port to Drupal 7; a Drupal 7 version of RSS permissions is in the works and may already have some of the functionalities you require.
Answer: As marblegravy correctly suggest you should indeed remove the link from your theme. This is different for each theme, but for example in Bartik you can remove the following line in page.tpl.php:
<?php print $feed_icons; ?>

Just search for RSS or feed and you should find the link.
Additionally to prevent some smart crawler from accessing the feed, you can block access to it by implementing hook_menu_alter in a custom module. E.g. as follows:
/**
 * Implements hook_menu_alter().
 */
function MYCUSTOMMODULE_menu_alter(&$items) {
  $items['rss.xml']['access callback'] = FALSE;
}

For more fine grained control I recommend the module RSS permissions


Where to find comparative information about publishers?

Question: Is there any reference for comparing publishers (or at least major ones)? Writers choose a publisher based on fame or by chance, but is there any system for rank of publishers? Or providing statistical data such as the number of published volumes, magazines, factors of business success, etc.
Comment: What a GREAT question. One of the most useful I have seen on this site. @Standback, I understand what you're saying, but I think most new authors would be willing to see almost any comparative data available.
Comment: I'm not quite clear on what kind of measurements you'd like to rank publishers by. A lot of data is pretty much unavailable - e.g. accurate size of book runs, payment rates to authors, etc. I can see why you'd be interested in what metrics might be available, though!
Comment: @Standback In fact, I address a problem that the public fame of publisher is very chancy, just depending what books we are aware of. In addition, I was unable to find the very basic information, even the number of books published.
Answer: Well I don't really think there is a clear answer in this case. You might be able to pull the information together by looking through Locus or other field related magazines. Even so with a bit of looking around I can find some older rankings of publishers. Such as the 2011 Ranking of the Global [Book] Publishing Industry and the 2011 Publisher Survey Results. That might provide some of the information you are looknig for.
That being said, most writers will choose a publisher based on what they publish. You wouldn't send a piece of military sci-fi to Harlequin, they would never be interested in it. On the other hand Tor on Baen books might be a much better fit. You want to find a publisher that is already in that field. This is true for both books and for short fiction.
Keep in mind that a most of the book publishers want submissions to come in through agents, on the other hand a good agent will know who the best publisher for a story is. As for finding an agent, it will work much the same, find one that works in the field your trying to write for.


django model linking with another model to create a form

Question: I am trying to develop a scoring sheet app for my club.
I have models for Player, Scoresheet, Season ,etc.
What I would like to achieve is basically when a game takes place, the scoresheet model will have a form where the person can capture the total score of the team and also the goals of each player.
My issue is how do I link the players stats to the scoresheet in a form, for example
the player model has goals scored, freekicks taken, red cards, yellow cards.
I want the scoresheet model form to be able to fill out that stats for each player.
I am aware that something is missing or I am doing something wrong. I am not sure what it is.
my Models are as follows
<code>class Player(models.Model):
    user = models.OneToOneField(User,on_delete=models.SET_NULL,null=True,related_name="playeruser")
    Player_name = models.CharField(max_length=40)
    Player_surname = models.CharField(max_length=40)
    Player_ID = models.CharField(max_length=40)
    Player_Email = models.CharField(max_length=40)
    Player_Contact = models.CharField(max_length=40)
    category = models.ForeignKey(Category,on_delete=models.CASCADE,related_name="pcategory")
    Player_preferred = models.CharField(choices=Roles,default="default",max_length=16)

    def __str__(self):
        return self.Player_name + " " + self.Player_surname

class Score_sheet(models.Model):
    season = models.ForeignKey(Season,on_delete=models.CASCADE,related_name="season")
    category = models.ForeignKey(Category,on_delete=models.CASCADE,related_name="sscategory")
    players = models.ManyToManyField(Player,related_name="players")
    captain = models.ForeignKey(Player,on_delete=models.CASCADE,related_name="captain")
    Date = models.DateField()
    Venue= models.CharField(max_length=40,null=True,blank=True)
    description = models.TextField(null=True,blank=True)
    goals= models.IntegerField(null=True,blank=True)
    freekicks = models.IntegerField(null=True,blank=True)
    redcards = models.IntegerField(null=True,blank=True)
    yellowcards = models.IntegerField(null=True,blank=True)

    def __str__(self):
        return str(self.season) + " " + self.Venue
</code>
Answer: Use django forms, you van create the forms you want.
docs
scoresheet.add(player)
Comment: I am using django forms, the issue is that I need to add players stats to the scoresheet, or I'm just doing everything incorrectly.
Comment: See updated answer ,use .add and the players are linked


Tag children needs synonyms

Question: I think we need to create a few synonyms for the children:

kids
infrant(s)
toddlers
Answer: Synonym mapping for 'infant' already existed, I added the others. Tags don't need to be created before one is legitimately used (unused tags get cleaned up anyway) but I feel synonyms are essential to help new users tag posts correctly. (For instance, someone posting about children could think the word 'kids' and not have a suggestion pop-up because it hasn't been set as a synonym.
Answer: I don't think we need to create synonyms until they have been actually used by someone. Pre-emptively increasing the number of tags doesn't sound like good idea to me -- we have a ridiculous amount of tags already, and there's no need to increase it unnecessary.
Comment: Personally I don't mind either way. I thought we aleady had a synonym or two for this one though.

Tag children needs synonyms


MAMP pro PHP Error handling grief

Question: So mamp pro is all set up using PHP 5.3.6 / cache is XCache, error handling set to Display Startup errors - write to All errors and warnings - to set to Display and Log both checked.
restart the server, intentionally wrote some code that should bring up an error..
<?php
   echo stupid;
?>

Yes this is all thats in the code.
I get nothing! No errors, only in the log.
I don't want to have my console open the entire time watching for errors, I want them printed on the screen.
The only way I can get this to work is by doing an INCLUDE on this code at the top of EVERY SINGLE PHP file.
error_reporting(E_ALL);
init-- yad yada ('display_errors', 'on');

From what I'm reading elsewhere, it seems like this is a big problem..
So how can I set up my mamp pro PHP.INI file to work properly and print directly to my browser?
Answer: I changed it in MAMP/bin/php/php5.3.6/conf/php.ini
You can change display_errors and display_startup_errors

MAMP pro PHP Error handling grief


how to work with Subversion

Question: I have downloaded Collabnet Subversion for Windows and Tortoise Svn.
I have created a repository with Tortoise Svn. But When try to open Repo Browser and give path as svn:/// ..it doesnt point to my repository.
I have followed the steps indicated on this website.
Any other useful tutorials to view at ??
Thanks in advance.
Answer: Agent SVN is a plug-in that implements the MS-SCCI so it will work with Visual Studio 2005.
Answer: My advice is that you install VisualSVN Server. You don't really need to configure stuff with the command line and a text editor.

how to work with Subversion


Broblem for wallet blockchain privet key

Question: When I want to convert btc from my wallet blockchain, they ask me to enter my private-key. When I enter it, I am asked to enter the password for the private-key. I do not know the password for private-key.
Is there a solution?
Answer: Without more information, I see a few posibilities:

You may have a BIP38 encrypted private key.

see: https://github.com/bitcoin/bips/blob/master/bip-0038.mediawiki
I suspect that maybe you are trying to claim a paper wallet?  If so, you need to know the password, or brute force it (unlikely).

If you are referring to a blockchain.com (formerly blockchain.info) wallet, those are proprietary to them and use their own format for the keys.  Again, you need to know the password, or brute force it.

If you don't have the password to your key any longer, then there are some wallet recovery services on the internet, which are risky and take a large percentage of the balance.  You can google "bitcoin wallet recovery", and always check reviews before engaging with one of these services to check their reputation.  Even so, they may be unable to recover the password.
Barring that desperation, do not provide your private key to anyone!
Answer: yes, depending on how much knowledge and effort you want to spend. But it is cumbersome, and requires a deep learning curve. Normally the private key should have 51 chars starting with "5", or 52 chars starting with "K" or "L". In rare cases you might have a hex value private key, that is a 32 characters long string. (Never post your private key here!!!).
Also you need to verify, if you have a "xpriv key" - that is a slightly different way of presenting a priv key, and has additional usage. This plays a role, when reloading into another wallet.
I am not familiar with blockchain.info, and if the private key is somehow encrypted with this password - maybe some research required. If it is encrypted, then this is not of much help, and I can't do anything for you.
So if you have one of those priv keys beginning with "5" or "K" or "L", then you have options:
You might get a wallet (like Electrum), and load the priv key there. It would then show you the corresponding address, and you can verify, if it is correct. It would then also show the funds.
Also you can assemble a transaction manually, sign it manually, and get it relayed to the bitcoin network. But this requires a good amount of sophisticated knowledge of the bitcoin network (at the command line layer).


In Zec. 3:2, what is the meaning of "a brand plucked from the fire"?

Question: In Zec. 3:2, what is the meaning of "a brand plucked from the fire" (אוּד מֻצָּל מֵאֵשׁ)?
Hebrew text:

וַיֹּאמֶר יהוה אֶל הַשָּׂטָן יִגְעַר יהוה בְּךָ הַשָּׂטָן וְיִגְעַר יהוה בְּךָ הַבֹּחֵר בִּירוּשָׁלִָם הֲלוֹא זֶה אוּד מֻצָּל מֵאֵשׁ
Comment: This is talking about Joshua the priest. The next passage shows that Joshua is being restore to the priesthood and Passage 7 talks about how Joshua will be keep charge of the priestly role if he walks in the G-d's ways.
Comment: I have no doubt that the wooden poker was called that because it was shaped like a serpent and that its head glowed red like an "apple".
Answer: A similar phrase occurs in Amos 4:11 where Yahveh says that Israel was "like a brand plucked from the burning" (כְּאוּד מֻצָּל מִשְּׂרֵפָה). "Burning" (שְׂרֵפָה) is evidently related to "fire" (אֵשׁ), since the former is produced by the latter (cp. Isa. 64:11).
Gesenius (p. 20) wrote that the noun אוּד referred to "a wooden poker, so called from the fire being stirred with it." Supposedly אוּד is related to an unused verb אוּד which means "to bend, to inflect; hence, to turn, turn over" (ibid).

Thus, the idea is that the noun אוּד is something one uses to turn things over that are baking/ burning in a fire. The noun אוּד occurs three times in the Tanakh:

Isa. 7:4
Amos 4:11
Zec. 3:2

The LXX translates each occurrence by a declension of the noun δαλός, meaning "a firebrand."
Jastrow (p. 22) notes that אוּד also occurs in tractate Beitzah 33a (English | Hebrew) (cp. Shabb. 143a; English | Hebrew). In this particular context, the אוּד can be taken out of a "wood shed" (בית העצים), which implies that the אוּד itself is wooden. In addition, the אוּד may be broken (נשבר) and set on fire (used as fuel) (להסיק). The context seems to confirm that אוּד is a wooden instrument.
In the context of Zec. 3:2, the fire represents Yahveh's wrath and judgment. Compare:

Deu. 29:24
Eze. 22:21
Jer. 4:4
Jer. 15:14
Jer. 21:12
Lam. 2:4
Zep. 1:18

At the time the prophet Zechariah prophesied, Israel (or, more specifically, the Kingdom of Judah, to whom Zechariah prophesied; cp. Zec. 1:12) was in captivity/ exile in Babylon. Exile/ captivity was considered a punishment/ curse imposed upon the people for disobedience (cp. Deu. 29:28). It was used in order to prompt Israel towards repentance (cp. Amos 4:11: "but you have not returned to Me").
While Yahveh's anger was kindled against His people (Isa. 5:25), the adversary (whether the angelic Satan himself, or a human adversary) stood to accuse Israel. However, Yahveh rebukes Satan, for Yahveh had chosen Jerusalem (Israel).
Jerusalem (i.e., Yahveh's people) is a wooden firebrand, a people punished but never entirely consumed by their punishment. Rather, they are rescued and spared by Yahveh Himself. The purpose of the punishment is to provoke His people to repentance.
Answer: a brand .... like a cattle branding for men are called cattle. , a burning of a sign into the forehead.        Hebrew letters: Tav - resh - samech - vav
Tav (the mark, sign or BRAND), resh (the head of a man-conscience),
samech (thorn or sin ), vav (hooked or attached or added)
Tav --The brand
Resh -- on head of a man
Samech --Sin -- the Thorn
Vav -- Connected - branded
The Brand on the head of a man, the THORN - the sin that connects.
Literally, branded with the THORN the MARK of the hot branding iron, the slave brand of the Whore.
.
what the MARK of the beast is.
6 witnesses: the mind determines what the hands do.
-1 Timothy 4:2 Such teachings come from the hypocrisy of liars whose own CONSCIENCES have been BURNED, as if with a RED-HOT BRANDING IRON.
-Isaiah 3:24 Then, there will be instead of perfume, a stench; instead of a belt, a rope; instead of well-set hair, a shaved scalp; instead of a rich robe, a sackcloth skirt; and a SLAVE-BRAND instead of beauty.
-Romans 1:28 And even as they did not like to retain God in their knowledge, God gave them over to a REPROBATE MIND, to do those things which are not convenient;…
-Titus 1:15 Unto the pure all things are pure: but unto them that are defiled and unbelieving is nothing pure; but even their MIND and CONSCIENCE is DEFILED.
-Micah 7:4 The best of them is a BRIAR, the most upright worse than a THORN hedge. The time of your watchmen — of your punishment — has come; now they will be CONFUSED.
-Deuteronomy 32:30 After all, how can one chase a thousand and two put ten thousand to rout, unless their Rock SELLS THEM to their enemies, unless Adonai hands them over?
Answer: The "brand plucked from the fire "from Zechariah ch. Three vs two could mean "is this, not a man plucked from the fire "where the fire is a state of mind for that man plucked from the fire."
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).
Answer: The brand plucked out of the fire could mean mean that what was once intended for man's use of showing ownership is now property of God's and is only to be used of God for his purposes
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).
Answer: @Yeddu is correct to point out that the line refers to Joshua, the high priest who worked together with Zerubbabel in the first stages of the restoration of the Temple. However the "brand from the fire" does not refer to Joshua himself. Rather, it is an instrument by which he himself will be qualified for his office:

Now Joshua was clothed with filthy garments, and was standing before
the Angel. Then He answered and spoke to those who stood before Him,
saying, "Take away the filthy garments from him." And to him He said,
"See, I have removed your iniquity from you, and I will clothe you
with rich robes." And I said, "Let them put a clean turban on his
head." So they put a clean turban on his head, and they put the
clothes on him. And the Angel of the Lord stood by. (3:3-5)

In context, the "brand from the fire" is the means by which Joshua's filthy clothes (whether literal or symbolic) would be burned after they were removed from him, to be replaced the rich garments of his priestly office.
The scene is reminiscent of the call of Isaiah:

I said: "Woe is me, for I am undone! Because I am a man of unclean
lips, And I dwell in the midst of a people of unclean lips; For my
eyes have seen the King, the Lord of hosts."
Then one of the seraphim flew to me, having in his hand a live coal
which he had taken with the tongs from the altar. And he touched my
mouth with it, and said:
"Behold, this has touched your lips; Your iniquity is taken away, And
your sin purged." (Is. 6:5-9)

The prophet Zechariah had high hopes for Joshua and his partner Zerubbabel, the appointed governor who was a lineal descendant of King David. He presented them as Two Olive Trees (4:11), "anointed ones" who stand before the Lord. Joshua had been somehow polluted and was unqualified for his mission.
The "brand from the fire" is the means by which Joshua will be cleansed in preparation for his task, much as Isaiah, a man of "unclean lips" was cleansed by a live coal in preparation for his.
Answer: Gen 3:18
"Both thorns and thistles it shall grow for you;
And you will eat the plants of the field;
יְהֹוָה עוּר
Lev 21:9
And the daughter of any priest, if she profane herself by playing the whore, she profaneth her father: she shall be burnt with fire.


What is the continuity of Government chain of succession for the People's Republic of China?

Question: Many countries have protocols in place which determine who the successor to the leadership of that country will be in the event that one or more of the leaders or their successors die.
What is the PRC's chain of succession?  How is the chain of succession determined?
At what point of simultaneous removal of political office holders or those appointed by them does the chain of succession become unclear even to the Chinese? Who is likely to be in charge at that point?
EDIT
To make this more clear, I'm talking about a potential assassination and/or terrorist action that more-or-less simultaneously removes the Paramount Leader and a variable number of his successors.  I'm interested in knowing who could take immediate, emergency, leadership of the nation and have the power to act to resolve the state of emergency.  Don't tell me that there wouldn't be a state of emergency if the Paramount Leader and a lot of his successors were killed.
Restoring the day-to-day government is beyond the scope of this question.
Answer: This is what I found in Russian sources:

First successor is his deputy (vice-chairman of the PRC).
Second successor is the Chairman of the All-China Assembly of People's Representatives (legislature).

The constitution does not specify further successors but I assume the further successor should be the deputy of the Chairman of the Assembly (at least it is the logic one would employ in the USSR).


forms authentication fails for POST request, .Net MVC

Question: In my .Net MVC application, I have default controller, which anyone should have access (as it contains the welcome page, register, login, password reset methods etc). All the other controllers have been inherited from a controller with authorize attribute.
I can browse to default/index, and default/register pages(i.e. any request of GET type). But any POST request to a default controller action acts like they need authorization. For example, when the user enters email/password and click login, it makes a POST request to default/login.
I tried with setting location paths in webconfig but still no luck. I have noticed that every POST request returns the form authorization cookie with empty in its value, while GET requests do not send back auth cookie.
Any idea what I have missed?
Thanks a lot in advance :)
Anuruddha
Answer: You can try with this
<code>[HttpPost]
[AllowAnonymous]
public ActionResult Index()
{
    //...
}
</code>


Splitting a circle into 3 equal parts using 2 lines

Question: The picture probably explains my question best.
I need to find a way to divide a circle into 3 parts of equal area with only 2 lines that intersect each other on the outline of the circle.
Also I need to check, if whatever diameter is between those lines, also splits circles with a different diameter into equal parts.
And lastly, and probably the most difficult question: How do I have to calculate the angle between x lines that all intersect in one point, so that the circle is split into x+1 parts with area = 1/(x+1) of the circle?
I tried my best, but couldn't even find a single answer or the right strategy to tackle the question...
1
Comment: 2. Yes. If you find the red lines so that they divide the blue circle into 3 parts of equal areas, then the green circle is also dividd into 3 equal parts.
Answer:
To find the angle $x$ between the red lines you need to solve the equation $$\sin(x)+x=\frac\pi3.\tag1$$
This can be done only numerically.

Yes it divides also the green circle in three equal parts.

Observe the essential difference between the cases with even and odd $n$. Whereas in former case the diameter drawn from the common intersection point is one of the "red" lines, in the latter case it is the bisector of the central angle. Let $x_k$ be the angle of a red line with the diameter. Then the following are the equations to find $x_k$:
$$
x_k+\frac12\sin2x_k=\frac\pi{n}k, \quad\text{with}\quad
k=-\frac n2+1\dots \frac n2-1.\tag2
$$
Observe that the numbers $k$ are integer for even $n$ and half-integer for odd $n$. For $n=3$ the equation $(2)$  reduces to $(1)$ with $x=2x_\frac12$.
Comment: Hi. How did you get the first equation?
Comment: I computed the area of the middle part ($x $ is the angle between the lines) and equated the result to one third of the circle area.
Comment: Got it, thanks.
Comment: @aarbee If you find the answer useful you can upvote it.
Comment: Sure, done :-).
Answer: Given the angle $\theta$, split by the diameter containing $B$, consider the following diagram:

$\overline{BO}$ is the line through the center and $\overline{BA}$ is the chord cutting off the lune whose area we wish to compute.
The area of the circular wedge subtended by $\angle BOA$ is
$$
\frac{\pi-\theta}2r^2\tag1
$$
The area of $\triangle BOA$ is
$$
\frac12\cdot\overbrace{r\sin\left(\frac\theta2\right)}^\text{altitude}\cdot\overbrace{2r\cos\left(\frac\theta2\right)}^\text{base}=\frac{\sin(\theta)}2r^2\tag2
$$
Therefore, the area of the lune is $(1)$ minus $(2)$:
$$
\frac{\pi-\theta-\sin(\theta)}2r^2\tag3
$$
To get the area divided into thirds, we want
$$
\frac{\pi-\theta-\sin(\theta)}2r^2=\frac\pi3r^2\tag4
$$
which means we want to solve
$$
\theta+\sin(\theta)=\frac\pi3\tag5
$$
whose solution can be achieved numerically (e.g. use $M=\frac\pi3$ and $\varepsilon=-1$ in this answer)
$$
\theta=0.5362669789888906\tag6
$$
Giving us

Numerical Details
The iteration from this answer, applied to $\theta+\sin(\theta)=\frac\pi3$, is
$$
\theta_{n+1}=\frac{\pi/3-\sin(\theta_n)+\theta_n\cos(\theta_n)}{1+\cos(\theta_n)}\tag7
$$
Here is the result of this iteration starting at $0$;
$$
\begin{array}{l|l}
n&\theta_n\\\hline
0&0\\
1&0.5\color{#AAA}{23598775598298873077107230547}\\
2&0.5362\color{#AAA}{45321326153808318904236597}\\
3&0.5362669789\color{#AAA}{24456230942633093381}\\
4&0.53626697898889055276\color{#AAA}{1878717471}\\
5&0.53626697898889055276244906787\\
6&0.53626697898889055276244906787
\end{array}
$$
Comment: Hi. How you got $\pi-\theta$ in the first line?
Comment: If you mean the area $\frac{\pi-\theta}2r^2$ in $(1)$, that is because $\angle BOA=\pi-\theta$, and the area of a sector with angle $\alpha$ of a circle with radius $r$ is $\frac\alpha2r^2$.
Comment: Got it, thanks!
Answer: Connect the ends of the chord (red line) with the center. You get isosceles triangle. Let $x$ be the angle opposite to the base (i.e. chord) in that triangle. You want: $$\frac{r^2x}{2}-\frac{r^2 \sin x}{2}=\frac{r^2\pi}{3}$$ or $$x-\sin x=\frac{2\pi}{3}$$ I do not think it can be solved analytically but it can be solved numerically with the answer $x \approx 2.60533$ radian. The same logic can be applied to more than 3 pieces. The angle you are looking for is $\pi-x$
Comment: Hi. I think you subtracted the area of triangle from the area of sector, and obtained area of segment. But I think this segment's area is not one third the area of circle. Or maybe I have not understood things properly. Can you please elaborate?
Answer: Too long for comments
If you want to solve $$\theta+\sin(\theta)=\frac\pi3$$ what you can do is to expand the lhs as a Taylor series and use series reversion. Using ths simple
$$y=\theta+\sin(\theta)=2 \theta -\frac{\theta ^3}{6}+\frac{\theta ^5}{120}-\frac{\theta^7}{5040}+O\left(\theta ^9\right)$$ this would give
$$\theta=\frac{y}{2}+\frac{y^3}{96}+\frac{y^5}{1920}+\frac{43
   y^7}{1290240}+O\left(y^9\right)$$ Making $y=\frac \pi 3$ and computing
$$\theta=0.53626300$$
You could also use the $1,400$ years old approximation
$$\sin(\theta) \simeq \frac{16 (\pi -\theta)\theta}{5 \pi ^2-4 (\pi -\theta) \theta}\qquad (0\leq \theta\leq\pi)$$ and solve the cubic
$$-\frac{5 \pi ^3}{3}+\pi\left(16  +\frac{19 \pi }{3}\right) \theta-16\left(1+\frac{\pi }{3}\right) \theta^2+4 \theta^3=0$$ which shows only one real root (not very nice formal expression) which is $0.53631167$.
Since, by inspection, you know that the solution is close to $\frac \pi 6$, you could perform one single iteration of Newton-like method and have explicit approximations which will be better and better increasing the order $n$ of the method. For example, Newton method would give
$$\theta_{(2)}=\frac \pi 6+\frac{1}{3} \left(2-\sqrt{3}\right) (\pi -3)$$ Halley method would give
$$\theta_{(3)}=\frac \pi 6+\frac{2 \left(2+\sqrt{3}\right) (\pi -3)}{45+24 \sqrt{3}-\pi }$$
As a function of $n$, the results would be
$$\left(
\begin{array}{ccc}
 n & \text{estimate} & \text{method} \\
 2 & 0.536245321326154 & \text{Newton} \\
 3 & 0.536266784935255 & \text{Halley} \\
 4 & 0.536266978676557 & \text{Householder} \\
 5 & 0.536266978987702 & \text{no name} \\
 6 & 0.536266978988890 & \text{no name} \\
 7 & 0.536266978988891 & \text{no name}
\end{array}
\right)$$


How do I write a spec for an existing language?

Question: I have a working interpreter for my language Trilangle, and I have a decent but informal grasp of the language's semantics. Though I've alluded to undefined behavior and a difference between what the interpreter does vs what's part of the language, I don't have a formal spec written. How could I go about writing up a formal spec for the language?
Comment: I feel like this isn't a perfect duplicate of the other question: that one is asking about the format, while I was trying to ask about the process. "Do you need to?" isn't an answer to the other one, for example. I'll admit that the questions are similar, though.
Answer: Broadly, there are two ways to specify a programming language:

Denotational semantics which directly gives meaning to terms in the language and says what terms have the same meanings as what other terms;
Operational semantics which define the behaviour of programs in terms of an execution model, i.e. how each term in the language should be executed on some abstract machine or formalised virtual machine.

Since you have an interpreter already, the implementation of the interpreter already describes a virtual machine that can execute programs in your language. The interpreter has some data structures representing the program's state (typically the evaluation context, plus values passed between functions in the interpreter), and for each type of AST node, it has instructions for how the program's state changes when that node is executed.
So, operational semantics are probably the way to go. You can go more or less formal, but a full specification for your language can consist of essentially translating the core of the interpreter into human language: describe what the program state consists of, and how each kind of statement or expression affects that program state.
If there is any part of that core which you don't want to be specified, simply don't include it in the spec. However, do write enough to specify the parts of the behaviour you do want to specify. For example, if your language has expressions like a() + b() and your interpreter consistently evaluates a() before b():

If this consistent order is supposed to be part of the language specification, write something like: "a binary operator expression evaluates its operands from left-to-right, then the value of the expression is computed by applying the operator to those values."
If this order is supposed to just be an implementation detail, write something like: "a binary operator expression evaluates its operands in an unspecified order, then the value of the expression is computed by applying the operator to those values."
Or if even the fact that the operands are evaluated is an implementation detail (i.e. you don't care about side-effects, or there are none): "the value of a binary operator expression is the result of applying the operator to the values of the operands. An implementation may optionally omit evaluating the operands, if it determines that their values are not needed for the computation."

It's fine to be overly specific, particularly in your first draft ─ it may be easier to start by just describing exactly how your interpreter works, and then modifying the spec later as you decide which parts of it are implementation details. You may notice from above that it often takes more words to specify less about how the program is executed, so you aren't necessarily wasting effort by specifying too precisely.
It's also worth adding that this kind of specification doesn't literally mean that an implementation of your language must be a direct translation of the "virtual machine" described in your spec, only that when it executes programs they must have the same behaviour as if they were executed by such a machine. You don't need to keep saying the words "as if" all the way through your specification, as this should be understood by readers; but it probably won't hurt to add one paragraph somewhere making this explicit.

Why have a spec?
Silvio Mayolo's answer argues that you may not need one. I would say it's a good idea to have a spec, even if your language has only one implementation and it's maintained by you alone.
A spec is a source of truth for what the correct behaviour of a program is. It makes clear to users of the language which behaviours of your interpreter they can rely on in future versions, and which they shouldn't.
It can also be used to judge whether a suspected bug in your interpreter is really a bug. If I have a program in your language which seems to be misbehaving, you probably don't want me to just always file a bug report on your issue tracker, because many such "bugs" are really caused by people like me thinking that the language should do something different to what you think it should do. But if you have a spec, then I can compare your interpreter's behaviour with the spec and make an objective judgement about whether the observed behaviour contradicts the spec.
If there is a difference between the observed and specified behaviour, then either the interpreter or the spec needs to be fixed. But the spec describes what you thought the interpreter would do, so chances are, the spec is more accurate to your intent than the implementation is.
Answer: Frame Challenge: Do you need one?
Lots of languages get by just fine without a formal spec. Raku is formally defined to be "the semantics that pass the Raku test suite". There's no specification document; it's just code that checks conformance. Ruby is defined even less formally, as "whatever the official MRI interpreter does at this moment". Especially if what you're writing is a hobby language, a good case could be made for defining the spec as "what my interpreter does", or "things that pass my tests" if the tests are thorough enough.
As a side note: "undefined behavior" is usually a term for things the interpreter does not or cannot catch and therefore is permitted to assume will not occur. Since you seem to be detecting those errors in your interpreter, I might be more inclined to call them "panics" rather than "undefined behavior".
Comment: I will point out that these warnings are all gated behind the `-w` flag. Some of these are substantially slower than not checking — most notably, checking for overflow on multiplication requires division, since C++ doesn't have fullwidth/reporting-overflow operations the way e.g. Swift does.
Comment: Counterpoint: Even if you don't write a full spec, attempting to define the semantics of a language formally often reveals things you didn't consider when implementing the language. Sometimes that's a bug in the implementation, and sometimes it's a general case of a feature that you didn't consider because it didn't occur to you.
Answer: tl;dr: Don't sweat it, but still do it.
As someone currently writing two(!) language specs for languages that nobody will likely use, I agree with @kaya3: write the spec as a check for yourself.
I also want to add that there will be times when the implementation does something that the spec says nothing about. This is still useful because it shows you the blind spots in your language's design.
As for how to get started: don't sweat it too much. Just document random things in a random order. Copy+paste will help you reorder things later.
This works especially well on things like specifications because one section that follows another does not have to be related to the previous section. The writing does not have to transition smoothly.
In addition, the wordsmithing does not have to be great or even good. The spec can just be a bunch of notes you write to yourself that you clean up later if necessary.
I think you'll be thankful to just have those notes, no matter their quality.
Answer: The Formal Grammar
As the question didn't limit itself to just semantics, I'll like to answer from a syntax point of view.
The formal grammar is not related to the semantics of the language but is nevertheless an important aspect of a language specification. The formal grammar is the set of rules that explain how to get each possible, valid input code string for the specified language. A popular method of writing a formal grammar is the Backus–Naur form
, which can be thought of as a meta grammar for writing a formal grammar.
For an example of a real life formal grammar, the Python full grammar specification may prove useful, though it is pretty long.
Additionally, it may be helpful to have a syntax reference that explains just the syntax of the language.
Comment: While this might be a good point in general, an esolang with single-character instructions is not exactly conducive to BNF-style grammars.
Comment: True, I was thinking pretty generally when I answered. That said, I would really like to see a formal grammar for an esolang. That would be pretty neat.


Example of a Noetherian ring that is not a homomorphic image of $\mathbb{Z}[t_1,\dots,t_n]$ or $F[t_1,\dots,t_k]$

Question: I need to prove or disprove the claim in the title, and I do believe there is indeed a Noetherian ring that is not a homomorphic image of $\mathbb{Z}[t_1,\dots,t_n]$ or $F[t_1,\dots,t_k]$, where $F$ is a field. I'm thinking about local rings, such as $\mathbb{Z}_{(2)}$ or a direct sum of Noetherian rings, such as $\mathbb{Z} \oplus \mathbb{Z}$ will do the trick, but I'm not exactly sure how to show they are not homomorphic images of the above two types of rings.
Answer: A ring of formal power series $\,K[[X]]$ or $\;\mathbf Z[[X]]$ is such an example.
$\mathbf Z\times\mathbf Z$ is the homomorphic image of $\mathbf Z[X,Y]$ by the mapping $X\mapsto (1,0)$, $Y\mapsto (0,1)$.
Comment: Thank you for your answer! If possible, could you also comment on $\mathbb{Z}_{(2)}$ as well? I have been trying to show that it is not a homomorphic image but to no avail (or maybe it is a homomorphic image..?)
Comment: I really don't know. The localisation  at an element $\mathbf Z_n$ is of course the quotient  $\mathbf Z[X]/(nX-1)$, and the localisation at a prime is a direct limit of such quotients, but being a direct limit doen't prove it's not such a quotient. If I find something, I'll post it.
Answer: Let $R = \mathbf{Z}_{(p)}$ where $p$ is a prime. Let $\frac{a_1}{b_1}, \dots, \frac{a_n}{b_n} \in R$ be a set of finitely many elements. Consider every rational number $\frac{a}{b}$ that can be expressed as a polynomial in $\frac{a_1}{b_1}, \dots, \frac{a_n}{b_n}$. The denominator of such a rational number, in reduced form, must be some monomial in $b_1,\dots,b_n$, or a divisor thereof. Since there are infinitely many primes, $\frac{a_1}{b_1}, \dots, \frac{a_n}{b_n}$ cannot generate $R$ as a $\mathbf{Z}$-algebra. Thus $R$ is not a homomorphic image of $\mathbf{Z}[x_1,\dots,x_n]$ for any $n$.
Also in $R$, the element $p$ is not invertible, thus $R$ cannot be a homomorphic image of $k[x_1,\dots,x_n]$ unless $p$ is also not invertible in $k$. This implies that $\operatorname{char} k$ must be $p$. But in this case $p = 0$ in $R$, a contradiction.
Comment: I suppose that a homomorphic image of $k[x_1,\dots,x_n]$ contains $k$, and $\mathbf{Z}_{(p)}$ doesn't contain any field.
Answer: Here is a much more general result:
Note that finitely generated $\mathbb Z$- or $F$-algebras are Jacobson rings. In particular any noetherian local ring, which has a non-maximal prime ideal is a an example of a noetherian ring, that is not a quotient of a polynomial ring over a field or the integers.


Git repository for a project that has files in unrelated directories

Question: I need to publish several related Arduino projects on GitHub.  For this purpose, I'm figuring out how to run Git.
In my project, I have split the code into libraries and the higher level application.  Libraries are shared across several projects.  Arduino environment (like many others) dictates the directory for the libraries that the libraries should reside at <arduino>\libraries\<my_library> .  So, the files necessary to build the projects are split between several unrelated directories.  From what I've read, Git repo is, by definition, one directory.
I'd like the libraries and the projects to commit together to the same repo on GitHub.  Of course, I could copy the library files manually, but that can introduce human error.
Prior art

There were some answers in this thread.  But, I don't yet understand Git well enough to get what VonC is suggesting there.
In this one, the O.P. didn't solve the problem, judging from his comments.

Any suggestion, insight or reference is really appreciated!
Answer: Have a look at using Git Submodules for the libraries that are going to be shared across different projects.


unable to mount blank-dvdr disk

Question: I have inserted a blank disk into my dvd-rw but in ubuntu its showing an error that unable to mount the place is already mounted?
Answer: gnome-fallback-mount-helper I do not have this in my list of startup applications.
I'd like to know how I can get rid of this notification as well. It serves no purpose to tell me that it failed to mount it twice, because it is already mounted once. I'm not sure what that even means??? The popup is intrusive, and disrupts my activity, especially if I have to swap many blanks. At the very most, this notification should be in the corner like a notify-send message.
Answer: VENKI,
I disable gnome-fallback-mount-helper in startup applications and the error message don't appear anymore and now I can burn CD/DVD with Brasero normaly.

unable to mount blank-dvdr disk


Can an expanded version of an article be considered an unpublished work?

Question: I submitted an entry to a contest that requires the work not be published. I met that criterion. I have substantially rewritten the article - it's now six pages instead of two. Basically expanded a short work to a full chapter for a book. The contest announcements are in October. My question is, are the two works considered different or are the same since they're on the same basic topic?
Comment: Your question is _will publishing the enlarged version breach your agreement with the contest organisers_. That is a matter of law (not writing) and will depend upon what you signed and the jurisdiction within which the contest is based.
Comment: Welcome to Writers! Please don't take our criticisms as hostility; we welcome questions like these, and only look to improve them. I hope you find this site useful.
Comment: @Fortiter - Agreed. This depends on the terms of the contest as much as anything else. Without knowing more about that, this question is difficult to answer.
Answer: It depends on the contest. If it is clearly mentioned as a part of their rules and regulations that the article should not be an extended / revised version of a published one, I would give it a skip. If it doesn't, as a matter of ethics, I would inform / confirm from the authority if it is acceptable.
I would suggest confirming with the committee now itself, as in case of a no, you still have some time left to work on a new article.
Answer: Basically it is the content that matters. No matter how long or short the article is .
The article should not be less than the minimum number of words required. If they are more, its fine.
Further, regarding the length as per my opinion ; the policy is not breached.
Still you can check this with rules and regulations of the contest.


Against what scenarios should I backup my database?

Question: I'm building a website with very sensitive data stored in my database. Losing any of it is not an option, and that's why I'm thinking to do an incremental backup every hour or so. I work on it alone, so I use only one database super-user (am I wrong?). However, I'm not sure even how my database could be damaged. Let's assume that from SQL Injection i'm 100% safe, and that DELETE/UPDATE queries are never performed (that is, by me). So, what else should I worry from?
I need to know because I couldn't find explanation, and because only then I'd know if I should backup off-site or on the same server, because if the only option is that my server itself is hacked somehow, what point would it be in saving another backup on it?
Comment: Answer varies based on architecture, deployment, etc. Perform a proper threat modelling. Don't backup on same server just in case disaster strikes or HDD decides to crash and you don't have RAID. Think of Hot Replication and read about RPO and RTO which are metrics to be considered when thinking of BCP / availability.
Answer: Short answer: hardware failure, programming error, operator error, malevolent actor (all sorts of attacks and "hacking").
Slightly longer answer:
The moment you care about your data (anytime other than a testing environment), you should backup your database regularly and keep the backups in a safe location (not the same machine, maybe not even the same datacenter if you want resiliency in the face of network outages). Also be careful to not overwrite your backups with new ones, you don't want to propagate bad data into your backups.
Once you've done all that, you need monitoring that your backups happened properly, verification of your backups, and recovery testing (where you try to restore your backups to make sure your process works).
Hacking is kind of the least of your concerns, the most common problems are programmer/operator error and hardware failure.
Comment: Thanks for the answer. However my biggest fear is hackers hacking into my server file system or to my database ( I can't think of how though, but I'm sure there are ways unfortunately).
And also, should I use third party backup services such as Rackspace, or maybe set up another database instance on amazon aws and programmatically back up to it?
Comment: @sermonionx I thought this was supposed to be "very sensitive data".  Remember that there's no such thing as "the cloud" - it's just somebody else's computer.  How much do you trust somebody else to keep your data safe?
Comment: Why yes, it's very sensitive data. However, losing it is not an option, since it wouldn't be less worse than having it stolen. As for the moment, I can't afford my own data center so I have to store it on amazon or azure or such.
I must have backups on another machines so yes, I'm afraid of backup exposure, but what can I do?
Comment: Depending on how sensitive this is, you can either rely on the cloud's security features to prevent access to your backup, or encrypt them. The same applies to the database host, use all the security features available for authentication/authorization and even encryption-at-rest if you can. But again, if losing your data is not an option, you're more likely to lose it due to the other factors mentioned so keep them in mind as well.
Comment: Thanks. You see, what I have in mind is encrypting certain data before it enters any database, and the key will be hard-coded on my app server script. Is it likely that my script files will be hacked as well? And is it a safe approach, considering that if I lose the script file (or simply the key) somehow, my data would be unrestorable.
Comment: If someone were actually targeting your data, they could try to get onto your web server and possibly find your hard-coded encryption key in the files there (as you mentioned in your first comment above). I don't know how difficult this is or how frequent it occurs though.


gdal_warp some geotiffs change SRS

Question: Hello I#m quite new to GDAL. I have some Geotiffs that I want reproject.
I tried that with one file and it works great, but because the TIFF has to be slightly rotated for the conversion I have some black areas after that. This is Ok but I have not 1 I have arraound 100 Tiff files and when I built a simple loop with a gdal_warp command for every file I have 100 files with black areas. Is there another command or option where it takes the missing parts from next file ?
Comment: Welcome to GIS.SE. Can you please **edit** your question and provide more information about your specific problem. Are you perhaps trying to **mosaic** adjacent images? What do you mean by "missing parts" and how are they related to the "next file"? Please also consider posting your loop so we can see if the error might be in your code.
Comment: There are many ways to handle the nodata areas. For example read again http://www.gdal.org/gdalwarp.html and try -dstalpha. If you now open the warped images with QGIS the the black areas have turned into transparent. Some other programs can't deal with alpha channel but they want to know the nodata value -> try with -dstnodata.
Answer: Using GDAL at the command line, you can build a virtual raster file to be used by gdalwarp or any other tool:
<code>for %%N in (D:\Karten\gdal\gdal2tiles\NL25\*.tif) DO gdal_translate -of vrt -expand rgba %%N D:\Karten\gdal\gdal2tiles\NL25\%%~nN.vrt
gdalbuildvrt -allow_projection_difference index25.vrt NL25\*.vrt
</code>
The first line is only necessary if your data comes with paletted colours.
Comment: Thanks Andre, so steps are 1. Bulding a virtuell raster (vrt file) from all TIF files and 2. Add a parameter to my gdal_warp loop to let it know the vrt. Or ist there a commandline option like *.tiff for gdal_warp , too ?
Comment: You just use the vrt file (index25.vrt in my case)  as input for gdalwarp. No loop needed there.

gdal_warp some geotiffs change SRS


Devices folder in Finder?

Question: Is there anyway that I can view the /dev folder with its contained pseudo-files inside of Finder? I can access it just fine in the terminal with cd /dev, but in Finder it doesn't show up even with AppleShowAllFiles active.
Comment: What is the reasoning?  /dev doesn't contain actual files, it is just referencing devices connected to the machine.
Answer: No, just had a fiddle and it appears there is no way to do that.
Neither of these work:
In terminal:
open .

will open the current directory in Finder.
Unhiding it with:
sudo chflags nohidden dirname

Does not work either. (Error --> chflags: dev/: Operation not supported)

Devices folder in Finder?


which better unclickable or clickable images

Question: are there difference between unclickable or clickable images?
for example page load time and another things because I see people use them
So I was wondering which one is better
Answer: unclickable images give you a better page load time, if you want a page to load fast make them unclickable since page load times really influence for example customers when buying stuff online.
please see :
https://smallbiztrends.com/2019/02/page-load-speed-impacts-buying-decisions.html


Are there any issues I should know about with unit test of Windows 7 Phone code?

Question: I am assuming that as the code is standard C#, I can just use nUnit, TestDriven.net etc.
Have I missed something?
What "traps" have other people hit trying to do this?
Answer: Have you looked at the Silverlight Unit Testing Framework which is now part of the Silverlight Toolkit?
It's not been ported as part of the WP7 toolkit but some people have reported some success in using it anyway.
Answer: If you are talking about testing C# code in a Silverlight-based project, then there are some steps that need to be taken in order to use frameworks such as nUnit. The C# code in a Silverlight project will compile against the Silverlight framework binaries, so the binaries for nUnit won't work as-is since they are compiled against the standard .NET framework.
If you want to use nUnit, you can setup a regular C# class library and reference your Silverlight C# files into this project. You want to add them as a link, which is detailed here. From personal experience, this can get a little crazy because your file is linked in two places and the ability to link over the files are limited (if your Silverlight C# code references any Silverlight-specific binaries, you cannot perform this linking trick).
The other option is to use the Silverlight Unit Test Framework, the binaries for which can be found here. This works much like the Silverlight unit tester in the Silverlight Toolkit, except that it runs on the phone as a phone app.
Answer: I would suggest WP7-CI. I have had success with it, and it's the only thing I could find so far that works with Asynchronous unit tests, if you'll ever need them.
See also my question:
Is there a wp7 mango unit test runner alternative to NUnit that supports the [Asynchronous] meta tag?


Viewing multiple 3D file formats in one program

Question: I want a multi-3d-format-file browser.
I'm looking for a program that has the following features:

Similar to ACDSee or Irfan View which allows browsing files with 3D geometry or files produced by Blender
Very easy to use (this it is very important)
It would be nice if such program was portable, but it is not necessary.
No trial version.

What I found so far

3D-No Plugins, IIUIC it is for online browsing or for being a interactive tool on website (like flash or java programs)
Octaga, Web 3D viewer of VRML, which is not what I need
MeshLab, portable open source program for editing and viewing 3d files
3D Exploration, shareware
some other 3d viewers
GeeXLab can also be used to view models
Comment: well, I think he wants a multi-3d-format-file browser...
Comment: @kokbira Yes I do want this program. :)
Answer: Hard to answer precisely without having more details about about the 3d formats you intend to use (Blender can export in a variety of formats). Because of the total absence of standards for 3d file formats, this is a big deal, as no software will handle all the hundreds of possible formats.
Also could you be more specific about what you want to do: drag-and-drop files to the main window, rotating objects independently, etc.
That said, if you limit yourself to a specific file format, whatever it is, you can use a pipeline to convert to a "quite standard" file format (to me .ply, .stl. or .wrl), and then import the converted files to a software used as a viewer. Easy-to-use is quite relative when it comes to 3d, so the better is to try, my pick was meshlab, but it has a lot more functions than just browsing and it can be confusing.
Converting to VRML and viewing in an internet browser may be a possibility as well.
Well, that was a vague answer indeed. But I think there is no ultimate tool for what you want. I personnally use at least 10 different software for my 3d data (coming from different sources).
Answer: F3D can open many 3D file formats, including glTF, stl, obj, vtk.
F3D is a free, opensource VTK based software.
<code>f3d file.gltf
</code>


Why do gold deposits form only in certain areas of the earth?

Question:
In the map above you can find that most elements are spread evenly throughout Earth's crust and that they are available all around the Earth. However, gold can only be found in certain areas of the planet such as Australia and Canada. Is there a specific reason to why gold can only be mined at these locations or is it just a coincidence?
Comment: The map is only showing larger deposits that are still available to be mined. For example, lead&zinc, copper, and iron were mined extensively in the UK (Cu & Fe were large deposits) but all are considered economically exhausted. Gold is still being mined in Wales albeit in small quantities, and it is/was recently being extracted in Scotland as a byproduct. I guess my point is that a lot of these minerals are more evenly distributed once you include worked-out deposits and smaller deposits.
Comment: http://earthscience.stackexchange.com/questions/391/in-what-geological-situations-can-i-find-gold/532#532 may be tangentially relevant.
Comment: I notice that map doesn't show any gold deposits in California or Alaska/Yukon :-)  It also doesn't show any in Nevada, even though there is fairly significant gold mining being done: https://en.wikipedia.org/wiki/List_of_active_gold_mines_in_Nevada
Comment: From your map, it seems to me that gold is actually pretty much evenly distributed on earth. At first glance, it is found (according to your map) in several west-african countries, in Congo, South Africa, Indonesia, Russia, China, South Korea, Kazakhstan, Egypt, Brazil, Peru, Canada and Australia.
Comment: I am by no mean a specialist in that domain, but [Goldfarb et al. 2001](http://www.sciencedirect.com/science/article/pii/S0169136801000166) seems to be a nice review on gold deposits and the maps they are presenting are likely to be more accurate than this one.
Comment: How do you get evenly distributed from that map? There is some pretty strong clustering almost as if surface conditions combine with underlying geology and tectonics affect the location of minerals.
Answer: I'll take the form of the question given by another person here and attempt to provide a different answer.
So what you are asking is: "How did gold become so concentrated in certain parts of the world?"
So yes, gold is all around but the concentration is too low to make extraction of it worthwhile. You need some process to take small amounts of gold from a large volume and turn it into large amounts of gold in a small volume where it is convenient to build a mining facility and get it from the Earth.
One of the most common process to concentrate gold is through the action of hydrothermal fluids. This is basically heated water flowing through the Earth's crust. Heated water with certain properties such as acidity (pH) or dissolved anions (think chlorine-rich seawater is more corrosive than your tap water) can dissolve solid gold and put it into solution. Just like regular water can dissolve table-salt or sugar and put it into solution.
So you have this hydrothermal fluid flowing through huge masses of rock (mountain-like, but underground) for a very long time, and when it goes up to the surface, it is channelled into thin conduits of fluid flow. During their ascent the conditions change (be it temperature or pH, etc.) and the water are not capable of carrying gold with them anymore. This results in the deposition of gold in that specific region.
I made an example, that I hope will help you understand this in a clearer way:

So in here you have rain water, entering the Earth in a large area and getting hotter as they descend down. It becomes possible for them to dissolve the gold from the large volume of rock.  But also, because the water (now steam or a supercritical fluid) are hot they start to ascend upwards, usually through a narrow zone. When they cool down again, gold forms as a solid. For example, gold associated with quartz veins commonly forms through this process.
Now, what happens if these gold-bearing quartz veins are exposed on the surface? They may erode by rain and snow and get concentrated in river beds. So you can either mine the original quartz vein or the nearby river bed.
Comment: Awesome free hand drawing!
Answer: Gold has primary origin in hydrothermal veins and contact metamorphic deposits and pegmatites.
Also occurs in placer deposits of secondary origin.
It is more easily found in veins that is related to igneous rocks rich in silica.
The main sources of gold are in hydrothermal quartz veins with pyrite and other sulfides. Gold is mechanically mixed with sulfides and not by chemical substitution.
In most of the gold grain is so finely disseminated that its presence can only be detected with microscopic techniques. Plenty of 0.004 ppm in the Earth's crust.
Answer: I do agree with Gimelist how gold is accumulated through hydrothermal fluids, adding that the main driver is for this process is volcanism.
There is, however, something interesting to be noted. We can find very 'old' gold of the Archean, more than 2 billion years ago, and mainly during 2 periods of the Archean, mainly hydrothermal gold in very old greenstone belts of the type described by Gimelist. Think of Canada, South Africa and Australia.
However, there is also very 'young' gold, Tertiary/Quaternary, in the Andes, Rockies, and Philipines, Papua New Guinea and Indonesia. Those are along the 'ring of fire', and it seems you need, at least nowadays, subduction of an oceanic, and maybe old, crust, to form strong volcanism that creates the hydrothermal processes described by Gimelist.
There is some gold during a few other periods, one around the formation of Pangea. That is the gold we find for instance in Spain. But worldwide it is much less than the other 2 periods, the ones from the Archean and the Tertiary/Quaternary one.
It is at least very interesting that we find mainly gold from mainly 2 periods, old and young, and that there is substantially less found in rocks from other era's.
Answer: I must agree some countries seem to have more gold than others. Using Australia as an example; There is more east coast gold finds, yet the west coast has produced more gold. The east coast states are more populated, so it would make sense more gold deposits where found.
I read theories that gold was formed from stars going nova after the big bang. Prior to Earth's final formation these now ancient meteors/asteroids deposited gold all over the world. Gold would be found closet to the Earth's core. As gold is a heavy element and Earth's early stages, naturally more gold would be found closer to the core. Confused as Uranium is also heavy but only found in the Earth's crust. Once again I looked to Australia for answers.
Australia recorded only 180 impacts, compared to other countries recording over 900. Both Western and Northern Australia record three times more impacts than the East coast. The west coast produced veins of gold while the east coast produced huge nuggets and flecks. The east coast of Australia suffered volcanic eruptions. While the western and northern have few if any inactive volcano's. The vast plans would explain the veins, spread of impact over distances. All confirming the theory but not why uranium is found in the crust in these areas. Perhaps uranium was formed over time from impact of these asteroids or took longer to cook than gold during the big bang. Its odd though that uranium is proficient in the same areas.
I'm just a backyard scrub but for my two bob answer to your question, I'd say gold is more evident on larger continents that are more accessible. Remember Australia is wide as the USA with fewer mountain ranges and a tenth of the population.
In the 1900 a man near death and surely out of his mind returned to town claiming to of found a reef of gold a mile long.  Harold Bell Lasseter had rode west to find his fortune, on finding it he lost his way home and the location of his fortune. For 30yrs Lasseter insisted on continuing the trek looking for his goldern mile, until eventually he died of malnutrition and exhaustion. Kalgoorlie in Western Australia was dicovered soon after. Kalgoorlie mines produce 850,000 ounces (28 tonnes) of gold per year.
Lasseter reef has never been found.
Comment: Whether elements sink to the core or go to the crust has almost nothing to do with their weight. It's related to their chemical affinities with the major stuff making up the earth. Uranium goes with silicates, so that's why it's in the mantle and the crust whereas gold is partitioned to metal, that's why it's most likely in the metallic iron core. The reason why we still have gold in the crust considering that there shouldn't be any is still a subject of debate, and yes, meteoritic input of gold (and other elements) early in Earth's history is a possible cause for this.
Comment: That said, the distribution of gold has little to do with its initial formation in stellar processes and its abundance in the crust (whether it's meteoritic in origin or not). Remember, the question about the distribution, why it's in some places more than others. Not about the quantity, or why we have a certain global amount.
Answer: Gold is found all over the world. Where it happens to be most economic to mine depends on a range of random factors, including political factors.
One big factor in gold mining is the cost of labor. Places where labor rates are low are more likely to have people mining gold. There are places in Africa where people dig up gold with their bare hands.
There is probably plenty of gold left in California, but do you really want to restart hydraulic mining, washing entire mountains into mud to get that gold? Hydraulic mining was banned in California over a 100 years ago, but hey as long as you are willing to destroy every mountain in the Sacramento valley, we could start it up again and turn California into a gold mining district.

[Above] Hydraulic mining. We could make California a gold mining region again, but do we want to?


Is understanding value for different features next step for object recognition?

Question: Once the artificially intelligent machines are able to identify objects, we might want to teach them how to value different things differently based on their utility, demand, life, etc. How can we accomplish this and how did we start to value things?
Answer: From your question I can assume you are a beginner in the field of AI. Welcome to this exciting field.
To answer your question, we have not yet been able to create a truly artificially intelligent program. They are all apparently intelligent but are just a set of simple/complex rules. An artificially intelligent agent must have at-least 2 aspects in the inside of its head/program. The ability to logically derive conclusions, and a capability for learning (these combined with ability to to take inputs and respond).
Now, logical reasoning part is the field of AI. Lots of simple codes performing complex task already exists.
Your question is based on the learning part, which is handled by Machine Learning programs. They learn iteratively. Object recognition is only one part of ML. They can also predict. Anyways, object recognition is done on the basis of maximizing reward/minimizing penalty (Cost function). Now, this minimizing of penalty is done by giving different weights or valuing different attributes of the objects differently. So this has already been accomplished. Depending upon the task at hand, we supply the attributes which are related to the final task ,otherwise the attribute is of no use. Like economics has no influence on weather.
We also have this thought process by selecting things depending on the goal we need to accomplish, sometimes we select things consciously sometimes we are hardwired by genes to do so (Touching fire). So you see, ML methods are modeled on how we do things and we do things based on weight-age to different factors. If we don't give proper weight-age we either learn by the penalty/punishment imposed upon us or our genes get wiped out from existence and thus the same behavior of not giving proper weight-age is not passed on.
So in short, a ML learning algorithm recognizes objects or does some final task (especially in games like chess) based on the utility or influence of the given features of current state on the final result.
Answer: You have asked two questions. How humans began to put a valuation to things and how to accomplish the task of valuation within an artificial intelligence construct. Human valuation is accomplished through trial and error experience, subjective choice and relative comparison, among other things. Valuation in an AI construct would be data-driven, objective and perhaps absolute. The choice of a valuation method would be determined by the choice of or desire of outcome.
Comment: I had this review task given to me for your answer as a new user. I would like to point out that in this community it is desirable to give a detailed answer along with explaining why or how you came to the conclusion. Also if you are speculating or have part knowledge of the answer you can write it in comments.


What mathematical processes does a GPS receiver use to determine position?

Question: I'm writing a report on the mathematics of GPS, but I'm wondering what methods the GPS actually uses. What I've done is set up the four sphere equations and solve them using the Newton-Raphson method for four variables (using the Jacobian matrix of partial derivatives). But is this what a GPS receiver actually does, with the an initial guess and iterations? Because I saw that on several websites, but I've also read about other methods such as a least squares solution. Or is this something that depends on the receiver?
Answer: There are two versions that I was taught on a GPS course (admittedly a lot of years ago):

take partial differential equations of the distance equations (with an unknown time error)
a closed form solution by Steve Bancroft (which I knew as the "King Radio" method, but since King got absorbed by Bendix, then by some other avionics manufacturer, that obviously got lost somewhere).

If you are doing the PDE method, which was by far the most common, I recall being cautioned against making the initial point estimate at (0,0,0) in ECEF. Apparently there are numerical stability issues, so perhaps assume somewhere on the surface of the earth. It will likely only take 1-2 iterations given that other errors will dominate, so the position doesn't matter much.
Answer: The German Wikipedia explains also a closed form solution for the four sphere equations:
https://de.wikipedia.org/wiki/GPS-Technik#L.C3.B6sungsverfahren_f.C3.BCr_4_Gleichungen_mit_4_Unbekannten
However, I don't know whether it is actually used by current GPS Receivers.


Link to my Facebook profile and to my website on share buttons

Question: I have a website with links to news. Each story has a Facebook share button and a tweet button. When an user retweets the new, the tweet has a reference to my twitter profile. Is there a way to do the same for the share button on facebook? This is: when an user shares through Facebook a link of any of the news shown in my website, the message displayed on his wall, will be accompanied by a link to my facebook profile and to my website.
Answer: Instead of sharing the link to the news directly, why not share the link of the page on your website which contains the link to the news? The purpose of the "Share" button on your website is to get you more social traffic, not the news sites!


Gas Sensor output voltage to concentration

Question: I am using figaro tgs gas sensor (2600, 2602 and 2620) to sense breath from human. What I obtained is the output voltage. However, I would like to convert the voltage to concentration in ppm? Since these gas sensors can sense more than one gas. Is there any way?? Thanks.
Answer:
I would like to convert the voltage to concentration in ppm?
Is there any way??

the datasheet for those devices would have the answers for you. Generally, you read the datasheet BEFORE deciding on using them or not. not that otherway around.
Answer: This is one of the datasheet. I have calibrated it using the clean air factor in datasheet and got the Rs/R0 ratio. However, from there, I not sure how to find the concentration for each gas.
Comment: The conditioning is 7 days. Turn it on with all wires connected and wait 7 days. Then you have to calibrate it with a known concentration of the gas that you want to measure. You might also use the data from the datasheet, for example from the "sensitivity characteristics" graph. A single sensor detects multiple gasses, and there is no way to tell which gas it is. If you combine more than one sensor, you might distinguish a few different gasses, but that is not in the datasheet. I think you have to use a known concentration of a gas and collect the data from all sensors.
Comment: Thanks for the reply. I refer to https://jenslabs.com/category/electronics/ketosis-detector/ and http://sandboxelectronics.com/?p=165  For the first link, I not really sure where the value got to convert from resistance ratio to ppm...The second link use the gradient in the datasheet for each line and generate the ppm value from ratio got. Can it be use?
Comment: The TGS2600, TGS2602 and TGS2620 are not designed to breath on. The TGS822 (in the first link) is. In the datasheet is a graph of ppm versus Rs/Ro. The most common (and also cheapest and poor quality) are the "mq" gas sensors. You can find examples for ppm when you search for: arduino mq gas sensor ppm
Comment: But 2600, 2602 and 2620 also show the Rs/Ro versus ppm graph. I can obtain the Rs/Ro ratio, will it means if I use the same method shown in the link I can get the concentration as well?
Comment: I think that is specific for the TGS822. Every sensor might have the same shape of the curve, but for the TGS822, the calculation is split into two parts. A calculation for the resistance below 3600Ω and a calculation above that. I don't know if the 3600Ω can be used for other sensors. The overall accuracy is not very good, perhaps a simple calculation will do.
Answer: If you want to measure concentrations of individual gases you would have to separate them and detect them separately using a chromatography column. In the case of gases this is known as gas chromatography (GC) and for liquids it's LC, with the most popular one being HPLC (high performance liquid chromatography, or sometimes called high pressure liquid chromatography). This is actually a really fun thing to do as a project and I stumbled on this question because I want to make my own GC using the sensor you mentioned.
The principle is fairly simple. Most modern GCs have a carrier gas, usually an inert gas like nitrogen or helium, at a steady flow rate and it passes through a column. You inject your sample into this carrier gas flow and then your sample also passes through that column.
Most columns are packed with a material like silica gel or long alkanes (usually around 18 carbon atoms). Silica has more affinity for polar compounds (like alcohols) while alkanes have more affinity for non-polar compounds like butane, hexane, etc.
If you have a mixture of compounds, like in human breath or lighter fuel, they pass through that column at different rates depending on affinity for your stationary phase (the column) and also size of the molecules (heavier molecules like hexane pass through it more slowly than the lighter propane just due to size).
At the end of the column you get the gases coming out separately, depending on the quality of your separation with the ones being less retained by the column coming out first.
A small problem with this is that the separation takes time and can take up a lot of time depending on conditions. Most GCs operate at about 200 degrees Celcius to increase the speed but also to make sure that everything actually is in the gas phase.
For a hobby project I just want to do it at ambient temperature first using lighter gas (which I know is a gas at room temperature) and for a column I will use bentonite clay, which they used back in the old days before silica and it's cheap. Kitty litter is made from bentonite clay as well so it's easily available. As a carrier gas just normal air using for example an aquarium pump or other small membrane pump.