How to convince someone with calculus or plots that the curve $x y - 1 = 0$ is connected over complexes?

Question: Some curves defined by polynomial equations are disconnected over reals but not over complexes, e.g., $x y - 1 = 0$. How can we convince someone with background only on equations over reals that the curve drawn by above equation  is connected over complexes? Is a plot or something possible, for example? It will be a 4d plot if x and y are expanded to real and imaginary parts.
Any other plot, or algebraic way to show connectedness?
Comment: @AlexL Even if your post wasn't exactly what the OP was looking for, I think it was a very good way of seeing the solution. Please consider un-deleting your answer.
Answer: A solution over $\mathbb{C}$ is a pair $(z, 1/z)$ with $z \neq 0$. Consider another solution $(w, 1/w)$. There is a path from $z$ to $w$ in $\mathbb{C}$ which does not cross $0$ (this is the difference with $\mathbb{R}$), and this yields a path from $1/z$ to $1/w$ by inverting every point on the path. From this we get a path from $(z, 1/z)$ to $(w, 1/w)$ which lives inside the solution set.
You can draw the corresponding plots explicitly. It is especially easy on the unit circle, where inversion is just complex conjugation. For example, to go from $-1$ to $1$ in $\mathbb{C}$ you can take the upper semicircle of the unit circle. The "inverted" path (inverting every complex number on the path) is exactly the lower semicircle. This shows how to go from $(-1,-1)$ to $(1,1)$ (which wasn't possible over the reals) via the complex domain.
Comment: Good answer, but it is still a bit hand-waiving in the end than what I was looking for. How would one plot this curve? It is still poits (x,1/x) in complex dimension, so we have to plot it in 4D, right? Not sure I completely understand the last paragraph.
Comment: I identify a path in $\mathbb{C}^2$ with a pair of paths in $\mathbb{C}$ (in the same way one can identify a path in $\mathbb{R}^2$ with two paths in $\mathbb{R}$); one can view it as projection to the axes (complex axes here). The last paragraph has an explicit example of such a pair of paths. These two paths (which you can draw in the same copy of $\mathbb{C}$) are two different views/shadows of a path in $\mathbb{C}^2$ (views along two different complex axes), which together determine the path in $\mathbb{C}^2$ uniquely.
Answer: You can connect any two complex points $u, v$ with a spiral
$$u^{1-t}v^t$$ where $t$ runs from $0$ to $1$.
More precisely, in parametric polar coordinates,
$$\begin{cases}\theta=\theta_u(1-t)+\theta_vt,\\\rho=\rho_u^{1-t}\rho_v^t.\end{cases}$$
(You can very well eliminate $t$.)
Then the curve $(-\theta,\rho^{-1})$ corresponds to the inverse points and is a similar continuous spiral.
Comment: what is the direct relation with the example system I have in the question?


What does the tag "drush" mean?

Question: I noticed the drush tag for the first time yesterday but can't figure out what it means and there's no description on the tag wiki.  The only word I know that's close to that is "drash" but I assume this is a different (related?) word?
Comment: See http://chat.stackexchange.com/rooms/468/conversation/drush.
Comment: Just to add to the mix, me now have the tag [tag:parshanut-theory].
Comment: See also http://meta.judaism.stackexchange.com/q/1870.
Answer: Re-stating and extending what I said in the chat msh210 linked to in a comment here:

We have parshanut-torah-comment, whose wiki says "interpretation of the Torah by close reading, not derivation", but whose current de facto meaning, I think, is more like a general "interpretation of Tanach."
We have midrash, which should, I think, refer to questions involving the body of literature known as "The Midrash" and referred to in the second sense here.

I suggest three possibilities:

Merge and synonimize drush with parshanut-torah-comment, and have them both refer to all Tanach interpretation.
Have parshanut-torah-comment refer to all instances of Tanach interpretation (as I believe it does now), and reserve drush for questions about the methodology of Tanach interpretation (as it partially does now, although currently not exclusively and probably not exhaustively). This may lead to re-tagging of a bunch of questions currently under the former tag.
Have parshanut-torah-comment refer specifically to peshat/"close reading" questions as its wiki currently states, and have drush refer to questions that involve more extended derivation (and perhaps a third tag for methodology). I suspect that this would require a great deal of re-tagging of questions currently under the former tag.

My inclination is toward something along the lines of (2).
Separate, but related, is the question of whether these tags should refer to all of Tanach or just the Chumash.
Comment: For strict, close reading, "pshat" would be my first try, in combination with a tag for that parsha, sefer, etc.  For methodology, my first guess would be to start typing "interpretation" or "method" and see where it gets me.  In my recent questions I typed "talmud" because (1) I actually was talking about talmud there but (2) even if I weren't I tend to think of this as "talmudic reasoning" even if it's later.  Does any of that help?  I'm not saying these should be the tags or synonyms -- just that that's where my thinking, confronted with a blank line for tags, leads me.
Comment: Is any of this the same as exegesis?
Comment: When posting a question about either actual interpretation or methods of same, I don't think I would have found my way to any of those tags on my own.  (Ok, demonstraby I didn't. :-) )
Comment: @MonicaCellio Let's make some synonyms! What tag names would you first think of for such topics?
Answer: I think the drush and midrash tags are too ambiguous without good tag wikis, and both have been used for too many things to make them useful, as have the parshanut-torah-comment and tanach tags. (We also have an agada-stories-legends tag and a pentateuch-chumash tag.) I suggest we have:

A tag for questions about d'rasha as a method. Included would be things like 10910 and 10873.  Proposed tag: drush-method (to distinguish from other possible uses).
A tag for questions about d'rashos (halachic or aggadic, including those in midrashim). Included would be things like 8788 and 2290.
A tag for questions about stories found in aggadic midrashim. Included would be things like 10917.  Proposed tag: midrash or agada-stories-legends (both exist, not sure how they differ).
A tag for questions about how to read/understand p'sukim. Included would be things like 8291 and 10069.  Proposed tag: parshanut-torah-comment (exists).
No general tag for questions about topics covered in Tanach, like 10945 and 10915. These can have sefer-specific tags like malachi-bookof or parasha-specific tags like parashat-ki-tisa, but there are way too many of them for a general (or even pentateuch-chumash) tag to be useful.  Proposal: delete the tanach and pentateuch-chumash tags.
Comment: Is the second item a viable category?  It seems pretty general -- if not in intent, then in the way it will end up being used.  Other than that, I agree with this approach.
Comment: @MonicaCellio, good point: it may be too broad or ill-defined. Feel free, of course, to tighten it up.
Comment: I edited this to add some proposed tags for these categories.  This is the approach I favor, but it's a community decision and I hope others will weigh in.

What does the tag "drush" mean?


Should I include resume references in this situation?

Question: I'm applying for a job opening and I don't normally list references unless it specifically says to include them with the resume. However, this job posting says "must have references" and I don't know if they mean to include them with the resume or just to have them available when asked for. Does anyone have advice on this? I don't want to look like an idiot by including them and wasting space if that's not what the hiring manager meant.
Answer: They need to be available when requested.  That's all this means.
The phrase is basically code for "must have experience and be dependable".
Comment: Thank you. That was my gut feeling but this is a really important job for me and I wanted to be sure.
Answer: Say "references are available on request" in your response. That's a nice, standard, positive answer. The early stages of the HR process are too busy to consider someone's references. That's a step after candidates have been selected.
Comment: Honestly, I would avoid saying it. It's already assumed. It conveys nothing of value. It is therefore just empty noise and wasted space on a CV.
Answer: Ask your references for a Letter of Reference. That's a good way to capture someone's clear statement about your skills and accomplishments. A letter of reference will have the name, title and contact information of the reference on the stationery of the company. It's not just for a full employment -- If you complete a big project for someone and move on to a new project or manager, get a letter of reference for that project.
A letter of reference is evergreen. You are spared the trouble of keeping in touch with old contacts. Sometimes those old managers retire, drop off the grid or die. They aren't available to take a phone call, but the letter is always ready.
When a potential employers asks for references, send them copies of your letters.
Frequently when I've asked for those letters, my reference will have me write the letter and just sign it. That allows me to tailor the language and point out accomplishments that the manager or co-worker might not know about.


Wasnt Prop Muhammed more powerful than Prop Suleman

Question: Asalamualikum, Ive had this question for sometime now, but Im too afraid to ask someone in person.
Prop Muhammed is deemed as the best prophet of all time, and that there were times when rock spoke about him, trees moved for him.Where as it is said that Prop Suleman had great control over all the realms , the Jins, the Animals, The Wind, the Sea etc. Didnt prophet Muhammed have the same power over all the realms, if yes then why did you not use them in the wars he fought.
 Thanks in Advance.
Comment: None is powerful but Allah all you talk about are gifts and favors of Allah. And we are not in the position to discuss Allah's will. As a Muslim you shouldn't say "it is said that..." as either you believe it as it as quoted in the qur'an or you don't believe what is in the qur'an.
Answer: How Prophets are ranked?
In Islam the prophets are not ranked by power. They are ranked by servitude (عبودیه). Same in the real world. Who's your best family member? The richest? The strongest? Or simply put the one who's nicer to everyone — regardless of money and physical power?
Prophet Muhammad is a better prophet because he's a far better servant. Could he have asked Allah for divine aid? Absolutely. But the higher a prophet is, the less demands he makes to Allah. He just acts normal. Then if Allah wants to aid him with angles or help him with animals, Allah will let him know. Otherwise the prophet will try to be normal as possible.
Most of the times the prophets performing miracles were a result of: The angel Gabriel came to the prophet and said: put your staff to the water, and so Prophet Moses did, or throw your staff and we'll do the rest.
It's not like Prophet Moses was specific and said oh Allah open the river. Or if people asked the prophet to do a miracle, then he wouldn't just say, alright let me split the moon. It was more like, let me pray to Allah. He'll help me. How? Idk. He's my lord. It's Allah's job to figure it out. My duty is to pray to him.

Tradition of Allah - Trying his servants
Allah has many traditions. One of them is to have his servants tried (with hardship).
One of the most important things we all get tried with is pride (کبر). Pride and arrogance are the enemy of service and humility. Satan lost his position because of showing pride. Cain became Cain because of his pride1.

Nahj al-Balaqa. Sermon 192
  - Taking lessons from the past peoples
Certainly, if Allah were to allow anyone to indulge in pride He would
  have allowed it to his selected prophets and vicegerents. But Allah,
  the Sublime, disliked vanity for them and liked humbleness for them.
  Therefore, they laid their cheeks on the ground, smeared their faces
  with dust, bent themselves down for the believers and remained humble
  people. Allah tried them with hunger, afflicted them with difficulty,
  tested them with fear, and upset them with troubles. Therefore, do not
  regard wealth and progeny the criterion for Allah's pleasure and
  displeasure, as you are not aware of the chances of mischief and
  trials during richness and power as Allah, the Glorified, the Sublime,
  has said:
What! Think they that what We aid them with of wealth and children, We
  are hastening unto them the good things? Nay! They (only) perceive
  not. (Qur'an, 23:55-56)
Certainly, Allah the Glorified, tries His creatures who are vain about
  themselves through His beloved persons who are humble in their eyes.

So Allah has to try his apostles as well. The greatest prophet will go through harder tests. Many people think if a person is poor then it means Allah is not happy with him or if he's rich, then Allah is happy with him. But Imam Ali is saying that's wrong. It's all a mechanism to test those who have over those who don't have. Certainly if Allah wanted he could have given all his prophets all the gold and all the power in the world but he doesn't do such because:

same sermon
If the prophets possessed authority that could not be assaulted, or
  honor that could not be damaged or domain towards which the necks of
  people would turn and the saddles of mounts could be set, it would
  have been very easy for people to seek lessons and quite difficult to
  feel vanity.
They would have then accepted belief out of fear felt by them or
  inclination attracting them, and the intention of them all would have
  been the same, although their actions would have been different
[Basically things would get a little mixed if the prophet was all
  powerful. As in you don't know if this person who's here in the mosque
  and praying is here because of his fear of the prophet or because he
  seeks power by being close to the prophet , or his here because his
  sincere faith in Allah?]
Therefore, Allah, the Glorified decided that people should follow His
  prophets, acknowledge His books, remain humble before His face, obey
  His command and accept His obedience with sincerity in which there
  should not be an iota of anything else; and as the trial and
  tribulation would be stiffer the reward and recompense too should be
  larger

Examples of prophet's humility
Prophet Mohammad sat (on the floor) while he ate. He ate like slaves [I think it refers to sitting without leaning against the wall or some stiff pillow]. He fixed his shoes himself. Rode the donkey without a saddle while giving a ride to another on his back.
Prophet Moses ate so little that his body went super thin.

Example of prophet's tests:
Prophet Noah was tried with his son. He lost him in the great flood
Prophet Ibrahim was tried with sacrificing his son.
Prophet Yusuf was tried with being shunned from his brothers, getting sold as a servant, test with Zulaika, prison, ec.

Yusuf: 90
Indeed, he who fears Allah and is patient, then indeed, Allah does not
  allow to be lost the reward of those who do good."

Their lack of power makes them look like us
If a prophet was all power, then some might start to worship him. Moses split the sea. The prophet split the moon. Jesus brought dead back from life...

Conclusion
Prophets are ranked by servitude, not power. Allah wants to give us the heavens. He needs to test us. He really can't succeed in having a meaningful test if his prophets beat the hell out of all opponents. Because there would be no opponents left. A meaningful test would have some level of difficulty.
The mother of all tests is the test with pride. Even Jealousy (حسد) is rooted in pride. We need to be humble to follow a normal looking person who doesn't have wings and can't summon the dead and can't bring tornados unto his enemies, who can be hit and stoned or killed by others.
Footnotes:

Nahj al-Balaqa, Sermon 192
Comment: Any reason for the downvote?


UIImagePickerController bottom gets cut off when I add an overlay View

Question: Need some help on an issue that is consuming my time. It's probably something really simple and I must be forgeting something. Here it go:
I have an UIImagePickerController in which I add a cameraOverlayView (just an ImageView). The problem is that the bottom bar gets cropped by some pixels. When I remove the overlay it works fine. I have even tried to change the overlay frame so that it fits the screen, the image is just the size of the camera viewport, but this happens even with small images. Here is some code:
UIImagePickerController* cam = [[UIImagePickerController alloc] init];                                                   cam.sourceType = UIImagePickerControllerSourceTypeCamera;
cam.delegate = self;
<code>UIImageView *overlay = [[UIImageView alloc] initWithImage:[UIImage imageNamed:@"silhueta.png"]];
overlay.frame = CGRectMake(0, 0, [UIImage imageNamed:@"silhueta.png"].size.width, [UIImage imageNamed:@"silhueta.png"].size.height);

cam.cameraOverlayView = overlay;

[overlay release];
</code>
Answer: Try to set the contentMode of your UIImageView to i.e. UIViewContentModeCenter.


joomla contact form module

Question: Is there a good free joomla contact us extension that can be used without  much configuration?
Answer: There are several form components that are very good. If the person using the component is pretty technically savvy, then Chronoforms is the way to go. It allows a lot of options including executing code, emailing form contents, saving forms contents to the DB, curl operations, all kinds of stuff.
http://extensions.joomla.org/extensions/contacts-and-feedback/forms/1508
If the user is a little less technical and just needs forms that email results, you should look at BreezingForms or RSForm, both are easier to use, but do not offer as much latitude.
http://extensions.joomla.org/extensions/contacts-and-feedback/forms/4709
http://extensions.joomla.org/extensions/contacts-and-feedback/forms/2265
Answer: FoxContact is probably the simplest and most elegant way to add a contact form to a Joomla website. It offers template changes, multiple contact e-mails, and the form possibilities are endless. Only downfall is the small Branding links on the bottom of the forms which can be removed at a nominal fee.
http://www.fox.ra.it/
or to see in action on my sit
http://cnclinks.com/gcnav/book-a-tee-time
Answer: ChronoForms (http://www.chronoengine.com/downloads/9-chronoforms.html) is a GREAT 'free' form component that works in ALL JOOMLA versions.
It includes a 'easy form wizard' for "drag and drop" form creation. In addition, it easily allows the form data to be passed to pages, sent via email and stored in a database table.
VERY EASY to you and very flexible.
Todd

joomla contact form module


Is there something after Hyper Hexagonest?

Question: After you have finished the Hyper Hexagonest mode, is there an additional mode unlocked? Or is it just the achievement?
Answer: From what I have gathered, the final and hardest mode is Hyper Hexgonest. Once you successfully complete this mode, you will get the "Hexagon" achievement (if you already haven't) and are presented with the ending of the game.
So yeah, no more modes unlocked after this currently.
Answer: Once you last 60 seconds on Hyper Hexagonest, you enter the seventh mode. Dying during the seventh mode gets you the ending. the seventh mode lasts forever, and cannot be selected. you can only reach it by surviving long enough in hyper hexagonest.


Grub2 installation error

Question: I am attempting to install Ubuntu 14.04 LTS server edition on an old Dell xps 410. It has two hard drives in a RAID configuration. I keep getting a fatal error when installing grub boot loader. It is looking for a Device for boot loader installation. How do I determined what command to use? I've tried /dev/sda, /dev/sda1 through 5, /dev/hd00, /dev/hd01, /dev/fd0, /dev/sdb, /dev/sdc. How do I determined what my number one hard drive path is?
Answer: I was able to solve my own problem. I removed the RAID configuration. Not the most elegant solution, but it worked never the less.

Grub2 installation error


How to design IXP with redundancy?

Question: With two route servers, one of them for redundancy, making peering for ISP's Do I have to make peering between the route servers? Despite of each route server would have all the prefixes for each ISP's.
Comment: Did any answer help you? If so, you should accept the answer so that the question doesn't keep popping up forever, looking for an answer. Alternatively, you can post and accept your own answer.
Answer: From a design standpoint, specifically referring to the route servers, the answer is no, they should not peer with each other via an iBGP session [disclaimer: I've never personally attempted to do this, but I might now for fun]. The reason why is because route servers behave similary to route reflectors, only it's eBGP rather than iBGP. The most important part to remember though, is that a route server is not a router, it is a "BGP message broker". This means that to all of its route server clients, it does not participate in any routing decisions. Because of this, route server clients will configure their sessions to the IXP's route servers as a standard eBGP session, however, because the route server does not insert its ASN onto the AS_PATH of NLRI received from its clients before it advertises to its other clients, the client configuring the eBGP session will have to ensure that its eBGP config on whatever device they're configuring allows for a way to disable enforcing the first ASN in a path from an eBGP neighbor (see Cisco IOS implementation notes), otherwise (depending on the vendor of course) the session will not come up, or will come up but no NLRI is exchanged, etc. Keeping that in mind, by creating an iBGP session between the two route servers, every route server client will have to drop an NLRI update message from itself, that was received from one route server, forwarded to the other via iBGP, and then re-forwarded to the route server client that (presumably) has an eBGP session up with both route servers. This will basically cause unneeded headache (in the form of possible CPU and/or memory churn) for the route servers and all of their clients. With that said, yes, it is BCP to operate two route servers (without iBGP between them), and mandate that the route server clients peer with both of them if they're going to peer with them at all, as Leon Weber has already mentioned.
In addition, it should be noted that designing an IXP "with redundancy" does not simply mean "running two route servers." Using AMS-IX as an example again, I suggest taking a look at their design documentation (specifically for 10G customers) for a good example of redundancy in an IXP. Again, just to provide a single example - a discussion on designing for redundancy within an IXP is beyond the scope of the format of this site.
Answer: A common solution is to run two separate route servers and mandate all peers to peer with both of them simultaneously, announcing the same set of prefixes.
See the AMS-IX documentation for an example. They run two redundant route servers:

When peering with the route servers we mandate that routers are set up to connect to both route servers and advertise the same amount and length of prefixes for resilience.
Answer: It would be preferable to peer your two routers using ibgp.
That way, your left hand is in sync with the right hand :-)
Your question doesn't specify if you have two different ISPs connected to your two routers or just one ISP that is connecting you. I would recommend using route filtering so as not to configure your routers to become a transit AS (unless you want to).
A common configuration would see your primary router advertising your AS normally and your backup router advertising your AS using prepending. That is to influence the return path towards packets that have left your network amongst other things.
Other configurations advertises your network to your primary ISP using the longest match while your backup router advertises your network as normal to the other ISP.
For example RouterA is your primary connecting to ISP-A and your backup is Router-B connecting to ISP-B. Your network is 192.168.0.0/16.
RouterA advertises 192.168.0.0/17 and 192.168.128.0/17 to ISP-A;
RouterB advertises 192.168.0.0/16 to ISP-B
Truly there are many ways to manipulate how you advertise your networks and filter/manipulate the routes leaving/entering your network.
Here is a good link towards prepending for your perusal: http://networklessons.com/bgp/how-to-configure-bgp-as-path-prepending/
Don't forget to test your configuration in a simulator like GNS3 first before implementing it on your production systems :-)
Comment: I think the question was more about running a route server instead of routers.

How to design IXP with redundancy?


What does the sentence mean, and is it grammatically correct?

Question: What does this sentence mean?
And is it grammatically correct?

You will always find a person in your life who enjoys other people suffering.
Answer: First we will break down the sentence to see if it's grammatically correct:

You (subject) will always find (verb) a person in your life who enjoys other people suffering.

With the main subject and verb in a sentence, it can be considered grammatically correct.
How do the other parts (aka non-essential clauses, which means they can be removed and still have a complete sentence) play a role in this sentence:
will always describes when you will find (verb)
a person describes what you will find (verb)
in your life describes where is a person
who enjoys other people suffering describes what a person enjoys

What it means:
A sentence can have different meanings in different contexts. I would think that the most common meaning of this sentence would what it says.
In case you don't understand, this is a way to rephrase the sentence:

In your life, there will always be someone that enjoys seeing other people suffer.

Sorry if it's still not clear, since I would think that is pretty understandable already.


ReferenceError: Drupal is not defined

Question: I am working on a production site, moving settings from a development site for a mobile environment. However, I am receiving the above error. I can not figure out what is causing this error. It does not matter what theme I change my jquery mobile environment too. I've checked all the modules and they seem to be the same versions. The only thing I can see that is different is in the development site I can uncheck/check the block cache, on the production environment I can not do this.
Answer: Sounds like an issue with the ordering of the javascript files. Drupal is defined in
/misc/Drupal.js
var Drupal = Drupal || { 'settings': {}, 'behaviors': {}, 'locale': {} };

Check Drupal.js is added to your HTML source, prior to when that variable is requested.
Comment: Thank you for your answer. I'm not sure if that was the issue or if I was having issues with htaccess. Either way I was able to resolve the issue.
Answer: In drupal 8 you might have to add core/drupal as a dependency of your module.
your-custom-module:
  version: 1.x
  js:
    js/your_custom_module.js: {}
  dependencies:
    - core/drupal
    - core/drupalSettings

Answer: I've experienced the same problem installing a drupal 7 web site from a dump.
The original default folder was provided empty for sizes management.
After pushing in the settings.php file and the files directory the Drupal is not defined error was there.
Originally the developers had two other folders inside the default folder.
When restored this folders the error was solved.
Answer: As mentioned by @David Thomas, this is an issue with file misc/drupal.js. Drupal by default puts it into the correct order. So most likely, the file is not accessible by your web server. Create its URL and try accessing it in your browser, and you will see.
In my case, this was due to using PHP-FPM (which runs with user rights similar to mod_suphp), and forgetting that static files (`png, jpg, css, js etc.) are still served by apache2 in my case. So these needed to be world-readable.

ReferenceError: Drupal is not defined


Entropy of the Ising model

Question: Consider the standard Ising model on $[0,N]^2$ for $N$ large. By that I mean the square-lattice Ising model without external field, inside an $N$-by-$N$ square. What is its entropy for $N$ large? It must behave asymptotically as $c(\beta)N^2$ for some constant $c(\beta)$ depending on the inverse temperature $\beta$. What is $c(\beta)$? Has it been computed?
Comment: Start with the partition function, see e.g. p. 480-1 (search for the page numbers) of http://www.amazon.com/Modern-Course-Statistical-Physics/dp/0471595209/. Then do some thermodynamics.
Answer: To expand on Steve Huntsman's comment, the entropy follows from Onsager's result for the free energy per site, $F=$
$$
-\beta^{-1}\left[\ln 2+ \frac{1}{2}\frac{1}{(2\pi)^2}\int_0^{2\pi}d\theta_1\int_0^{2\pi}d\theta_2 \ln(\cosh2\beta E_1\cosh2\beta E_2
-\sinh2\beta E_1\cos\theta_1-\sinh2\beta E_2\cos\theta_2)\right],
$$
and the thermodynamic relation,
$$
S=-\frac{\partial F}{\partial T},
$$
for the entropy per site.  Here $\beta=1/(k_BT)$ and $E_1$ and $E_2$ are the horizontal and vertical interaction strengths.  If you set both interaction strengths equal to 1 and use units where Boltzmann's constant equals 1, then the critical temperature is $2/\ln(\sqrt2 + 1)\approx2.269$.  If you plot $S$, you should find that it interpolates between 0 at low temperature and $\ln2$ at high temperature, as expected.  At the critical temperature, the graph has infinite slope.
Comment: Thanks for expanded explanation. I need to do some reading before I can make sense of this answer.
Comment: The double integral expression for *F* looks a bit unpleasant, but it's really just some sort of hypergeometric fuction, i.e. a solution to a linear second order ODE.  It just happens not to be expressible in terms of anything more elementary.  Feel free to email me if you have questions.

Entropy of the Ising model


Where does Ubuntu store its library files?

Question: I want to add my own library to use in c compiling, but don't really know where ubuntu stores it.
Comment: It stores in **/usr/lib** & **/usr/include**
Comment: Libraries and headers are different things, /usr/include does NOT contain libraries, it contains headers which are definitions of functions/objects available from libraries. The question should be improved, it's hard to understand what are you trying to achieve.
Comment: i did find my library's in /usr/include how should i go with putting them in? should i just put a header file and a c file near it or should i write the header and the function together in one .h file?
Answer: Depending on library, ubuntu stores its libraries mainly in three locations

/lib
/usr/lib
/usr/local/lib

Following is from File System Hierarchy Standard
/lib

The /lib directory contains those
  shared library images needed to boot
  the system and run the commands in the
  root filesystem, ie. by binaries in
  /bin and /sbin.

/usr/lib

/usr/lib includes object files,
  libraries, and internal binaries that
  are not intended to be executed
  directly by users or shell scripts.
  [22]
Applications may use a single
  subdirectory under /usr/lib. If an
  application uses a subdirectory, all
  architecture-dependent data
  exclusively used by the application
  must be placed within that
  subdirectory.

/usr/local/lib contains local libraries i.e one specific for this system but I can not find references to /usr/local/lib in FHS, it only contains explanation for /usr/local.
Answer: Based on your comments to your question, I think what you are really asking is "How do I install a custom library I wrote and where should I put it?"
In general, things built locally for others on the machine to user are put into the /usr/local tree.  The header file should go into /usr/local/include.  The compiled library should go into /usr/local/lib.  The .c file is not part of the library, it is part of the source and not something normally not installed for the use of the end user.  You will need root access to put files in either of these locations.
To build the library, you will need to build first decide if you want a static or dynamic (shared) library.  More information on creating a shared library can be foundin section 3.4, Creating a Shared Library at http://www.linux.org/docs/ldp/howto/Program-Library-HOWTO/shared-libraries.html.  (They also have recommendation about where to put stuff -- most developers will have an an opinion or three :-) )
Answer: Ubuntu follows Filesystem Hierarchy Standard (http://en.wikipedia.org/wiki/Filesystem_Hierarchy_Standard), regular applications libraries should be stored under /usr/lib .
Please note that developing/managing libraries is not a trivial subject, you should read some more detailed documentation, here is a nice tutorial:
http://www.yolinux.com/TUTORIALS/LibraryArchives-StaticAndDynamic.html
Answer: You should tell the compiler, where it can find your library. Assumed, the path to your library is "/path/to/lib/libfoo.a", you could compile and link your program "hello.c" like this:
gcc -L/path/to/lib -lfoo hello.c

This is not specific to Ubuntu, actually all C-compilers I know support those flags.
Answer: In Ubuntu they are found in /usr/include.
Comment: [*Header* files](https://en.wikipedia.org/wiki/Header_file) are in `/usr/include`. The actual binaries for a library are not stored there. Headers may be considered part of a library, but they have to be installed separately, and they are use to *compile* programs that use a library. Once a program that uses a library has been compiled, it doesn't need or use the header files anymore.


Cell Theory- does the first cell not contradict cell theory

Question: In cell theory, we have cells arise from other existing cell.
But the first cell did not arise from existing cell, and that means there are some other condition which allows cell to be formed.
I understand the chance of forming the cell without other cells has a low probability, but given it is still possible, does that not contradict the statement itself that you must have other cells to form new cells even ignoring the first cell as a special case?
Comment: I think this is mostly a confusion of the meaning of "laws" that govern fields like physics and the "laws" that govern biology. Biology tends to stubbornly break any sort of "law" you try to constrain it with (besides those of physics), but that doesn't necessarily make biological "laws" less useful, it's just that we tend to take for granted how things need not be as they are in biology.
Comment: Can you please clarify what it is about the standard models of [abiogenesis](https://en.wikipedia.org/wiki/Abiogenesis) that you do not understand?
Comment: @jakebeal Thanks - I understand we can create cells from non-living material, but I do not see why we can leave that out in cell theory, and say cells are only created from other existing cells. We can say this is the only way cells are created by living material (ignoring cases which cells arise from non-living material), is from other cells, but then all living materials have cells (from the definition of cell), and so that makes that statement trivial?
Answer: Sometimes the probabilities of events are so low, that we can neglect them for all practical purposes. A classical example in thermodynamics: if we have a gas in a container, there is a non-zero probability that all the molecules assemble in one half of this container, while in the other part we have vacuum. It never happens in practice - the probability of such an event is $\propto 2^{-N_A}$, and if one observes a container, one would have to wait for longer than the age of the universe (which is much longer than our lifespan, the existence of the humankind, and the existence of life). Thus, we can confidently treat it as a law, and claim that the sea had never opened in front of Moses.
Same about the acquisition of the cellular membrane: the event might have happened only once in a few billion years, and in very special conditions, which are not at all common nowadays. It is negligible for all practical reasons, to the precision that makes it possible to consider it a law.
Comment: It's also worth noting that existing life will inhibit the emergence of new life, as existing life will tend to quickly _eat_ anything with the potential to become new life.


Cannot connect to samba member server as local user a few days after AD join and SSSD

Question: Edit: I tried to simplify the question:
=========================================================================
How can I enable a local (linux/samba) user to access a samba share (member server) besides the AD-users, which already have access?
The problem is that my samba always asks the DC for user authentication and never tries to authenticate the user using passwd/smbpasswd.
=========================================================================
Here is the old, long question:
i managed to set up a Samba 4 server on Ubuntu 18.04.
My steps:

Drive is mounted with "user_xattr acl"
Hostname is set to e.g. myserver
ipv6 is disabled
the ipv4 static ip is set correctly with netplan
the only entry in /etc/hosts is "127.0.0.1       localhost"
timesync is configured and working
installed: krb5-user samba sssd sssd-tools
created an AD Group (edit: on the Windows Server 2008 DC) e. g. g_fileserver_rw and joined the AD accounts to the group
/etc/krb5.conf
[libdefaults]
   default_realm = INTDOM.TLD
   ticket_lifetime = 24h #
   renew_lifetime = 7d
# The following krb5.conf variables are only for MIT Kerberos.
   kdc_timesync = 1
   ccache_type = 4
   forwardable = true
   proxiable = true
# The following libdefaults parameters are only for Heimdal Kerberos.
   fcc-mit-ticketflags = true
[realms]
[domain_realm]
   .intdom.tld = INTDOM.TLD
   intdom.tld = INTDOM.TLD

I have a comprehension question here:
Are the parameters "kdc_timesync, ccache_type, forwardable, proxiable, fcc-mit-ticketflags" necessary or adverse here?
/etc/sssd/sssd.conf, mode 600
[sssd]
services = nss, pam
config_file_version = 2
domains = MC.DE

[domain/MC.DE]
id_provider = ad
access_provider = ad

# edit: this is actually not used
override_homedir = /home/%d/%u

# edit: I need this, performance not an issue in my env.
enumerate = true

/etc/nsswitch.conf
passwd:         compat systemd sss
group:          compat systemd sss
shadow:         compat sss
gshadow:        files

hosts:          files dns
networks:       files

protocols:      db files
services:       db files sss
ethers:         db files
rpc:            db files

netgroup:       nis sss
sudoers:        files sss

Domain join with ´net ads join -U email@example.com´ was successfull
´getent passwd´ and ´getent group´ list local and domain users respectively groups
I added a local user (e.g. lu) with this command:
´adduser --home /dev/null --shell /bin/true --gecos "" lu´
then I created a samba user with
´smbpasswd lu´ using the same password
I set up the rights on the shares like that (if you wonder that group has more rights than user, see ´acl group control = yes´ entry in smb.conf below):
chown -R lu:@firstname.lastname@example.com /sambashare/One
chown -R lu:@email@example.com /sambashare/Two
chmod u-w,g+w,o-rwx /sambashare/One
chmod g+w,o-rwx /sambashare/Two

/etc/samba/smb.conf
[global]
   workgroup = INTERNAL
# Entries recommended in Ubuntu-Wiki:
        log level = 0
        client signing = yes
        client use spnego = yes
        kerberos method = secrets and keytab
        realm = INTDOM.TLD
        security = ads
# End of Ubuntu-Wiki-entries
# My entries
restrict anonymous = 2
acl group control = yes
inherit acls = yes
inherit owner = yes
inherit permissions = yes
vfs objects = acl_xattr
deadtime = 15
store dos attributes = yes
domain master = no
local master = no
preferred master = no
os level = 0
idmap config * : backend = tdb
idmap config * : range = 1000-199999
idmap config MC.DE : backend = sss
idmap config MC.DE : range = 200000-2000200000
# End of my entries
   server string = %h server (Samba, Ubuntu)
   wins server = <WINS-Server IP Address>
   dns proxy = no
   log file = /var/log/samba/log.%m
   max log size = 1000
   syslog = 0
   panic action = /usr/share/samba/panic-action %d
   server role = member server
   passdb backend = tdbsam
   obey pam restrictions = yes
   passwd program = /usr/bin/passwd %u
   passwd chat = *Enter\snew\s*\spassword:* %n\n *Retype\snew\s*\spassword:* %n\n *password\supdated\ssuccessfully* .
   map to guest = bad user
[One]
        path = /sambashare/One
        valid users = "lu", @email@example.com
        create mask = 570
        directory mask = 570
        writeable = no
        write list = @email@example.com
[Two]
        path = /sambashare/Two
        valid users = "lu", @firstname.lastname@example.com
        create mask = 770
        directory mask = 770
        writeable = yes

For a week all was working normal, but now the local user "lu" can no longer access the shares. The domain users can access the shares normally. The local rights are still the same: ´drwxrwx---+´ on directories  and ´-r-xrwx---+´ for lu:email@example.com.
Can someone tell me how to enable the local user to access the shares again?
Answer: Well, it was my fault. The config is actually working and it did not stop working after a few days, but I was rather dumb to make this assumption as I saw problems with other machines.
It still worked on the machines I tested it first.
Windows machines, which had an altered security policy (different from the default) could not connect using a local account.
The setting is here:
Under "Security Options" in secpol.msc:
"Network security: LAN Manager authentication level"
it started to work, as soon as I set it to:
"Send NTLMv2 response only"
I'm sorry that I wasted your time.
A mod can remove my question and answer all together, if he considers so.


Animated (anime?) movie with a boy who is transported to another world and meets his backpack as a living creature

Question: Animated (anime?) movie with a boy who is transported to another world by a girl, accidentally. In this world he meets his backpack who is now a cute living creature and learns that he can become anything he can imagine. I think the girl wanted to transport another boy she had an eye on to help and save her world/kingdom from a great threat, but this other boy got summoned instead. He vowed to save it nonetheless. The threat moved to the real world.
Comment: Can you remember when you would have watched this? Was it new at the time? If so could you [edit] that into your question?
Comment: Also the unaccepted answer to https://scifi.stackexchange.com/q/251259/23243
Answer: The Toy Warrior (2005)
The plot synopsis on IMDb matches your description quite well. It mentions saving the world, imagination and the loyal backpack.

The Land Of Toys is a world of pure imagination, ruled by the popular doll Princess Sherbet, but when the mysterious Dark One threatens Sherbet's toy kingdom, she turns to the real world in search of a heroic Warrior Prince... Unfortunately, she ends up with the imaginative trouble-maker Jinoo. When Jinoo accidentally touches Sherbet's magical Warrior Stone, the spunky sixth-grader is suddenly transported to the Land Of Toys to become the powerful Toy Warrior! Aided by the reluctant Princess Sherbet, the transforming Police-bot, R.J., and Jinoo's amazingly loyal backpack, Ping, Jinoo is ready to play Toy Warrior and chase the dark forces across the landscape of imagination. The evil is spreading and now both the real world and the very Well of Imagination itself are at stake! Our only hope is a hero with heart... the Toy Warrior Jinoo!

The Toy Warrior poster - click to enlarge.
It is available online at YouTube but in Hindi. From skimming the video the below appears to be the boy's backpack as a creature in the new land.

Click image to enlarge.

I found this by Googling the new title of the post but specifying it must include backpack: Animated (anime?) movie with a boy who is transported to another world and meets his "backpack" as a living creature. This then gave me a Movies & TV question and answer about the work back from when they accepted story identification questions.


Is it correct to avoid starting sentences with subordinating conjunctions in technical writing?

Question: I work on a team where everyone has decided that it is incorrect to start a sentence with a subordinating conjunction period. For example they will change the sentence:
Based on the system-wide risk assessment, the societal risk for the Lateral is low.
to
The societal risk for the Lateral is low based on the system-wide risk assessment.
They believe that in technical writing (oil and gas) it is incorrect to start a sentence with words like 'if', 'during' 'due to' etc. Is this correct, or preferred?
Comment: I don't follow you. Your first example starts with the verb "based", not a conjunction
Comment: Sorry that may be incorrect i was trying to figure out what those words are called and I thought they were called 'subordinating conjunctions' or 'adverbial conjunctions' - basically they have a list of words we are NEVER to start a sentence with such as: based, however, if, due to, where as, etc.  Basically always put the independent clause first and the dependent clause second in the sentence. I'm trying to justify why it is okay to do the opposite but struggling to articulate the rationale.
Comment: I don't see anything incorrect with your example "Based upon....", but in this example, I'd just follow the guidelines (or the whims) of my workplace; they are not wrong either.
Answer: It seems that the choices given miss the point of technical writing.
The idea is to be clear and concise.  This usually means following standard subject verb object word order.  As far as I know, it is not incorrect to begin with a dependent clause, provided the meaning of the sentence is clear.
So my short answer is no, it is not automatically wrong if the sentence does not begin with the independent clause.


What would happen if two electrons fuse?

Question: Two electrons repel each other naturally; however, if protons can be forced to fuse, can electrons technically fuse too? What would be the product if two electrons fuse?
Comment: @Sofia this argument is not correct because the electrons could have opposite spin states.
Comment: Conservation of charge and other quantum numbers basically require that in the end you end up with two electrons.  Lots of other stuff can come out of the energy of the collision too but overall it will be uninteresting.
Comment: You can't make two electrons to fuse because of the Pauli repulsion. Two identical fermions cannot have the same position and linear momentum.
Comment: Protons are bound together via the (residual) [strong nuclear force](https://en.wikipedia.org/wiki/Strong_interaction). There would be nothing to bind two electrons together.
Comment: OP what do you mean by "fuse"? There is no bound nucleus consisting of two protons?
Answer: First of all, two isolated protons cannot fuse to form a bound state. The nuclear force between nucleons depends on their spin orientation. It is too weak to bind two nucleons with anti-aligned spins and two identical nucleons (two protons) cannot be bound with identical spins because of the Pauli exclusion principle.
The nuclear force is a residual of the strong force between the quarks that make up nucleons. It is perhaps analogous to the van der Waals forces between atoms.
Fusion-type interactions cannot occur between electrons because there is no analogy to the nuclear force between electrons. Electrons (as far as we know) are point-like particles with no substructure, experiencing only the electromagnetic and weak forces.
The electromagnetic force between two electrons is clearly repulsive and cannot bind them. The weak force is much weaker than the electromagnetic interaction unless one could get the electrons to separations of $\leq 10^{-18}\ m$, which would require particle energies many orders of magnitude higher than in the centre of the Sun for example.
My (limited) understanding is that even then, the weak force cannot result in a bound state for isolated leptons (if anyone has a simple explanation that would be good here).
Electrons that are not isolated can form bound states - part of the basis for superconductivity - through long range electron-phonon interactions.
Answer:
if protons can be forced to fuse, can electrons technically fuse too

I'm not aware of any known mechanism by which two electrons can 'fuse'.
It is possible, however, for two electrons to form a Cooper pair which is the basis for superconductivity.
However, this cannot occur between two otherwise isolated electrons.
Comment: There is no analogous bound state of two isolated protons either.
Answer: Two protons (or more) protons can stay together because of the effects of the residual strong nuclear force. It's called the "strong" force because it's extremely strong - about 100 times as strong as the electromagnetic force. Without it, protons would fly apart.
The strong force is mediated by gluons, the force's bosonic carriers. In order for electrons to interact via the strong force, they would presumably have to interact via gluons. The problem? There have been no observations of electrons interacting via gluons. In fact, if they did, they would interact with other particles that feel the strong force - such as protons and neutrons - in ways that are different from what has been observed.
So now you have to invent a whole new force, and explain why it hasn't yet been observed.
A nice summary of the strong nuclear force's role in the nucleus can be found here.

What would be the product if two electrons fuse?

Here we have to consider some conservation laws. Quantities that are relevant here that would have to be conserved are

Electric charge
Angular momentum (in the form of spin)
Lepton number
Linear momentum
Energy (including mass)

In this case, you could not have one resultant particle, because that would violate conservation of lepton number. You would need more. So now you're not really "fusing" two electrons but are instead describing a complex interaction. And that doesn't even take the other laws into account.
Comment: But two protons cannot form a bound state?
Answer: The process of 'smashing' electrons on electrons is called Møller scattering. Essentially, you'll get two electrons again (but with potentially different direction). Since there is no attractive force between them, you will not get what is called a bound state, i.e. they will not stay 'close' to each other.
Answer: Using energy arguments, even if you get two electrons moving towards each other at (or very very near) the speed of light, the minimum distance they can reach is the Compton radius.Even an electron and a positron can't get nearer than this due to radiation losses in the process. see https://en.wikipedia.org/wiki/Classical_electron_radius


Do Summon's kills count towards unlocking Limit Breaks

Question: To unlock limit breaks in FFVII you need to score a certain number of kills, if I summon, do the kills the summon gets count towards this total?
Comment: I don't know the answer, but since the summon animations are long and can't be skipped you can rack up kills much faster by not using them and just mashing the circle (attack) button.
Comment: @RossRidge Well the kills I'm doing are for Aeris :/
Comment: You'd still be better off with combat spells, maybe even regular attacks. As measured by the actual time they take, summons have terrible DPS,
Answer: Unlocking new limit breaks is different for each character, depending on how many limit breaks they have, how many levels they have, and how many of each pre-requisite needs to be met to unlock the next limit break, or the next level.
For example, everyone (except Cait Sith and Vincent) have a total of 7 limit breaks. Each Limit Level has two Limit Breaks. To unlock each Limit Break, the character either has to have killed a certain number of enemies, or used (a) limit break a certain amount of times.
Eg; to unlock the third Limit Level, Cloud either needs to have killed 320 enemies, or, used 7 limit breaks. Vincent, on the other hand, is not reliant on limit breaks, and only needs to have killed 40 enemies.

Then, once a character reaches their final Limit Level, a mini-quest to find their final Limit Break "Manual" appears.
Now, as to whether or not summons affect this - yes they do. They rack up on the kill count, therefore they will help unlock the next limit level.

Source
Comment: "Eg; to unlock the third Limit Level, Cloud either needs to have killed 320 enemies, or, used 7 limit breaks." - This part is incorrect. Only killing 320 enemies will unlock the 3rd level. Using 7 level 2 limit breaks will unlock his second level 2 limit break, but it will *not* unlock level 3.
Comment: Brill, that's what I needed to hear :)


Pair production and recombination with a more energetic beta particle

Question: Can gamma particles with sufficient energy for pair production gain energy by recombining their positron with a more energetic beta particle than the one they produced? If yes, is this something that would happen to any significant degree in a sample of radioactive material decaying with high energy gammas and betas eg. Na24?
Answer: Pair production with a gamma ray

Feynman diagram of electron–positron pair production. One must calculate multiple diagrams to get the net cross section

needs a field to  interact with, in the diagram the charged field of a nucleus, for momentum conservation in the center of mass of the final electron-positron pair. A  gamma has mass zero, the pair at least two electron masses, so a single gamma cannot decay to a pair.
Once the pair is produced the original gamma disappears. The positron of the interaction will have an energy momentum vector certainly smaller than the incoming gamma. If the positron interacts with an electron two fresh gammas will be produced (at the low nuclear energy levels your question assumes).  If the electron has high energy, it will be distributed according to the probability of the interaction, on the two new gammas.
At the level of nuclear physics it is not possible energetically to get one of the two  outgoing gammas to have higher energy than the  original incoming one.


Hook up a light designed for car into a wall socket or battery source

Question: I'm attempting to hook up the Infrared LED LED Light Bar - 54W to either a wall socket or a battery source. I'd like to know what hardware and what wiring I need to accomplish this. Any embelishment on the parameters that are important would be appreciated so I can solve this type of problem in the future. Thanks. -Rik
Comment: I'm voting to close this question as off-topic because it really isn't a home improvement question. It's pretty simple for an electronics question, but I'd still suggest the Electronics SE.
Answer: You simply need a plug-in AC/DC converter (transformer) of 12-28 volts that provides enough current for the 54 watt consumption.
Divide 54 watts by the voltage of your selected transformer to calculate the amperage draw, and allow a 30% buffer or so. For example, 54 watts / 12 volts = 4.5 amps, so you'd want a transformer that provides at least 6 amps or so. The higher the transformer's voltage, the lower the current draw.
The power bar has a simple wire pigtail for connection, so you'll need to use appropriate crimp connectors or some other safe, insulated method.


Why are Nevada pink sheet stocks particularly risky?

Question: I understand that pink sheet stocks are a lot more risky than those on stock exchanges, but I was told that Nevada pink sheet stocks are the riskiest of them all. I was told that these companies can "go dark" and legally withhold financial information from their shareholders. Is this correct? Is Nevada alone in this, or are there other "bad" states where this can happen?
Answer: The relationship between corporations and their shareholders is, in most respects, governed by the laws of the state in which they are incorporated. Some states afford greater rights to the management of the corporations while others give more power and rights to the owners (shareholders). The differences between states in most respects is small as they tend to follow each other's lead, but there are differences. It's entirely possible that Nevada has weaker shareholder protections and disclosure requirements than some other states.
The SEC also governs some aspects of corporate governance and investor relations. Those aspects will be the same in every state, but the SEC doesn't micromanage every little thing.
EDIT: Note that, according to Wikipedia, Nevada has particularly strong protections for corporate executives (they are not easily sued for the actions of the firm) and weak disclosure requirements. They also have strong protections for executives against takeovers. Moreover, at this time only Nevada and Texas do NOT have information sharing agreements with the IRS. Perhaps this is what your source was concerned about. From what I'm reading, Nevada is particularly friendly to corporate executives and unfriendly to investors.


How to integrate Chainlink Fast Gas oracle

Question: I am trying to estimate the gas fee in USD for a function call. I came across the term "Chainlink Fast Gas oracle" but I couldn't find any documentation on how to use this in a smart contract? There is this website but nothing else: https://data.chain.link/ethereum/mainnet/gas/fast-gas-gwei
Answer: On your link you have the contract address, which is 0x169e633a2d1e6c10dd91238ba11c4a708dfef37c

And you have this specific function that you can call to get the current gwei:
function latestRoundData()
    public
    view
    virtual
    override
    returns (
      uint80 roundId,
      int256 answer,
      uint256 startedAt,
      uint256 updatedAt,
      uint80 answeredInRound
    );

It will returns something like this:

You can call this function from your smart contract if needed, if you want the USD price, you can do the same process by multiplying ETH/USD price by GWEI, ETH/USD
Comment: in the example above the price is expressed in `wei`, so 37 gwei.
On rinkeby it shows `40189528044` which is ~40 gwei
You can check all the conversions here: https://eth-converter.com/extended-converter.html
Comment: I guess the `answer` is the price of 1 GWEI (or wei? what is the unit?) in USD. I've tried this with the Rinkeby test network oracle address (`0xCe3f7378aE409e1CE0dD6fFA70ab683326b73f04`) and it returned this: `344162968520`.  If this is the price of 1 GWEI in USD, it is too high (344.16296852 USD). I am confused.
Comment: One last thing: I guess there is no gas fee oracle deployed for the polygon network, right? I am looking here: https://docs.chain.link/docs/matic-addresses/
Comment: Only on Ethereum for now
Answer: I had a similar question and needed more step by step approach.
I read this blog and it helped.
https://dev.to/costamatheus97/web3-how-tos-interacting-with-external-smart-contracts-in-solidity-3of1
Then, I mocked it up on REMIX.  I used two contracts to simulate the current LINK fast gas contract.  One to represent the current contract and a second one to represent any future contract for gas (or if LINK changes address in future).
In both contracts, I used block.timestamp as a return value in  but offset the time by A LOT of seconds so I could verify the contract update function and then see I got a different return value.
Since Chainlink uses int256 on their fast gas contract "latestAnswer" (the value I am looking for), I type casted the block.timestamp response to int256 to mimic the response I should get from Chainlink more closely.
That way, if you need to flip it back to uint256 for calculations or comparisons in your own contract you can see how to do that too.  Maybe a better way, but I'm a hack so YMMV.
Chainlink Fast Gas contract 1
pragma solidity ^0.8.15;

contract CHLK_FastCash_1 {

    function latestAnswer() external view returns(int256){
        uint256 datetime = block.timestamp;
        int256 converttype = int256(datetime);
        return converttype;
    }
}

Chainlink Fast Gas contract 2
pragma solidity ^0.8.15;

contract CHLK_FastCash_2 {

    function latestAnswer() external view returns(int256){
        uint256 datetime = block.timestamp - 10000;
        int256 converttype = int256(datetime);
        return converttype;
    }
}

My Contract
pragma solidity ^0.8.15;

interface Interface_CHLK_FastGas {
    function latestAnswer() external view returns(int256);
}

contract my_Contract {

    address _CHLKFastGasAddress;

    function get_External_Contract_data() external view returns(int256 latestGasFeeWei) {
        Interface_CHLK_FastGas CHLK_getCurrentGas = Interface_CHLK_FastGas(_CHLKFastGasAddress);
        (latestGasFeeWei) = CHLK_getCurrentGas.latestAnswer();
        return latestGasFeeWei;
   }

   function setChainLinkFastGasContractAddress(address _address) external {
    _CHLKFastGasAddress = _address;
   }
}

In case you are new and wondering like I did...  What do I do with the above?
Go to remix.ethereum.org (aka REMIX), create 3 contract files with solidity code above.  Compile all 3 contracts.  Deploy the first two contracts to mimic chainlink fast gas.  This will give you their contract addresses.
Then deploy "my_Contract".  Once you have all 3 deployed, you can copy the contract address of the first contract and paste/apply that in the "my_Contract" function 'setChainLinkF...' section.  This will set the variable to the first contract address for mock Chainlink contract 1.

Once you do that, you can call the get_External function (press the button) from the first chainlink contract in the "my_Contract" deployed contract.
Make note of the ordinal time value you receive.

When you are ready to switch to the second chainlink contract, you can copy the second deployed contract address, paste/apply that into the "my_Contract" function function 'setChainLinkF...' input area (and press button to push this to contract).
This will change "my_Contract" to use contract 2's address.  Then, when you press the 'get_External...' button you will read the older timestamp value in contract 2.
Make note of the ordinal time value you receive.  It will be ~1000 less than the first value.
HTH
S_Z


What is a double shutter camera?

Question: I did a google search and came up with nothing for this question. A scientific PIV paper referenced to a double shutter camera, but there is no explanation on what this is. Any help is appreciated. Thanks.
Answer: From the description here and the schematic diagram here, it seems that it's a camera that's capable of recording two images separated by an extremely short (e.g. 5µs) delay. You can see from the schematic that the first image is read out of the device at the same time that the second image is being exposed, so it seems likely that the sensor itself probably incorporates a latch on each pixel that stores the value until it can be read, allowing the entire image to be saved and enabling the very short delay between the end of the first exposure and the start of the second.
The goal of particle image velocimetry (PIV) is to analyze the flow of a fluid by tracking individual particles suspended in the fluid. It's important to be able to take two images in rapid succession so that you can match the particles in the second image to those in the first before they move too far.
Comment: What do you mean by saying the sensor incorporates a latch? I dont see how an image could be read out at the same time as a second image is exposed, so i will look into this. Thanks for the answer!
Comment: @DanZ *Latch* is a digital electronics term that describes a circuit that stores an input value and keeps it stable even though the input might change. By *analog latch* I meant to invoke that same behavior, i.e. the sensor must store the voltages at all the photosites so that the values can be read while the sensor is exposed the second time. It turns out that a better name for this type of circuit in the analog world is [*sample and hold* circuit](https://en.wikipedia.org/wiki/Sample_and_hold).

What is a double shutter camera?


Can I use waste water from kitchen for plants?

Question: Can I use the waste water mixed with dish washing liquid from kitchen for watering my garden?
Comment: What sort of dish washing liquid are you using?
Comment: *Most* hand-dishwashing soaps are OK. I'd look at the ingredient list of a machine washing detergent **hard** before putting it on my tomatoes. A small scale test on a potted plant such as basil might be a good way to proceed.
Answer: Even if you remove all the solids first after washing your dishes as they might attract flies and rodents, you may still have a problem with sodium being added to your soil. So the type of liquid detergent is important.
http://ecologycenter.org/factsheets/greywater-cleaning-products/

Household Cleaners / Dish Soap / All Purpose Liquid Cleaner:

Recommended:
Oasis dishwash/all-purpose cleaner for handwashing dishes, body & shampoo
Ecos: Creamy Cleanser; Parsley Plus; Furniture Polish; Window Kleener; Floor Kleener; Carpet Shampoo

Limit:
Bon Ami (it is biodegradable and has no perfumes, dyes, chlorine, or fragrance, but does contain sodium carbonate)
Ecos: Shower Kleener (sodium gluconate, sodium citrate)
Dr. Bronners: Sal Suds (sodium laurel sulfate)
Citra Dish (sodium chloride)
Ecover Dishwashing Liquid (sodium laureth sulfate, sodium chloride)

Avoid:
Ajax (sodium carbonate, bleach, fragrance, color);
Comet (bleach, +?);
Ajax (?);
Ivory (?);
Palmolive (?);
Joy (?);
Dawn (?)


Using symmetric-key cryptography

Question: A group of 30 people who wish to establish pair-wise secure communications using symmetric-key cryptography. How many KEYS need to be exchanged in total?
Comment: Is this a trick question or extreme laziness? ... 435
Comment: To explain exactly the part you have trouble with (meaning, without rewriting the whole book), it might help if you describe your problem a bit more. What did you try and why, where are you stuck? And/or do you not know what some word means? And/or ...
Comment: It might help to make it simpler; suppose there are 3 people (Alice, Bob, Carol) who wish to establish pair-wise secure communication; how many KEYS need to be exchange in total?  Once you have that, how about 4 people?  Once you see how it works in the small, ramping it up to 30 should be easy...
Comment: No, it's a real question out of a text book and I am very confused and looking for some help.
Answer: Let's start off with the fact that there are $n\cdot n$ ordered pairs of (person, person). Now we assume that nobody needs encryption to talk to themselves, so we subtract the $n$ pairs where the person is the same, to get $n\cdot n-n=n(n-1)$. Next, we note that the same secret key can be used to send messages on the route (A,B) as on the route (B,A) (with proper care taken to avoid reusing the same nonce, etc). So we divide by two to get $n(n-1)/2$. Finally, we plug in $n=30$ to get $30\cdot 29/2=15\cdot 29=435$.
Answer: For symmetric pairwise, the minimum would be 435 unique keys.  (N * (N-1)) / 2 unique connections between nodes.
For asymmetric, it would be 30 keys.  Which is one reason asymmetric encryption is so useful.
Also see https://stackoverflow.com/questions/13730546/how-to-prove-max-number-of-connection-between-n-nodes-is-nn-1-2

Using symmetric-key cryptography


Recommendation for testing a website or web application in python

Question: I am working for an eCommerce travel portal which is written in Java. So apparently i am very comfortable with Python language i am looking for a framework in python which could test the website and give us the complete information as where is the issue on which step. So i was wondering is there anything which could accomplish this task.
Answer: You could have a look at the Robot Framework, which allows extensions in either Java or Python. We've used it at work and it works pretty well, escpecially the test reports are very comprehensive and easy to examine.


Editing theme's less files doesn't reflect in the website

Question: I'm new to Magento. I have recently purchased a Magento theme from Themeforest, I found that there are no .css files there, instead there are only .less files, so I edited them but nothing happens in the website, nothing at all! Is there any specific command I have to run?
 And what is the right way to edit theme's stylesheet in Magento?
- Magento v2.2.3
- Mode: Default Mode.
Answer: yes there are few commands to run in order to reflect the changes :
in comamnd line on your magento root run below command :
rm -rf ./pub/static/frontend ./pub/static/adminhtml ./var/view_processed/pub

php bin/magento setup:static-content:deploy -f

Comment: It says : NOTE: Manual static content deployment is not required in "default" and "developer" modes.
  In "default" and "developer" modes static contents are being deployed automatically on demand.
  If you still want to deploy in these modes, use -f option: 'bin/magento setup:static-content:deploy -f'
Comment: Should I run it with (force mode?)
Comment: yes, i have updated command
Comment: The deployment ran successfully but nothing happened.. Changes did not reflect.
Comment: in which file are you making changes ? this command will compile your less file code
Comment: I'm making changes in the less file code
Comment: which less file is it ? could you name it.. because command provided here should compile all less, unelss you are making changes in wrong less..
Answer: To reflect the changes of css files you have to do following steps.
Install node.js to any location on your machine.
Install Grunt CLI tool globally. To do this, run the following command in a command prompt:

npm install -g grunt-cli

Install (or refresh) the node.jsproject dependency, including Grunt, for your Magento instance. To do this, run the following commands in a command prompt:

cd  npm install npm update

Add your theme to Grunt configuration. To do this, in the dev/tools/grunt/configs/themes.js file, add your theme to module.exports like following:
module.exports = { ... <theme>: { area: 'frontend', name: '<Vendor>/<theme>', locale: '<language>', files: [ '<path_to_file1>', //path to root source file '<path_to_file2>' ], dsl: 'less' ... },

Where the following notation is used:
<theme>: your theme code, conventionally should correspond to the theme directory name.
<language>: specified in the 'code_subtag' format, for example en_US. Only one locale can be specified here. To debug the theme with another locale, create one more theme declaration, having specified another value for language
<path_to_file>: path to the root source file, relative to the app/design/frontend/<Vendor>/<theme/>web directory. You need to specify all root source files of the theme. If your theme inheritsfrom a certain theme, and does not contain its own root source files, specify the root source files of the parent theme.
(Optional) If you want to use Grunt for "watching" changes automatically, without reloading pages in a browser each time, install the LiveReload extension in your browser
There are grunt commands which will useful.

grunt exec: grunt less: PHP bin/magento s:s:d - f
Comment: http://devdocs.magento.com/guides/v2.0/frontend-dev-guide/css-topics/css_debug.html refer this for more in detail
Comment: I'll follow this answer and let you know what happens. Thanks


is it possible to brand a sharepoint online site and also use sharepoint inbuilt apps like, Hero, weather forecast, etc after branding it?

Question: I am new to SharePoint. My boss wants me to make a certain template for our client (which will be completely custom made), and he also wants to use the Sharepoint webapps and webparts after the branding. However from what I know by my limited knowledge is that branding can be done only in Publishing website and
publishing websites does not support OOTB SharePoint webapps and features. But i would like to confirm from more experienced people if it really is so, before telling my boss its impossible.
Thank You.
Answer: No, the branding can be done on the websites not only publishing site.
The publishing site supports the OOTB SharePoint webapps and features.
It is possible to brand a SharePoint online site and also use SharePoint inbuilt apps like Hero, weather forecast and so on.
The SharePoint inbuilt apps like Hero and weather forecast can be added in the SharePoint modern page. They have nothing to do with the publishing feature.
More reference:
Branding guidance for SharePoint Online portals.
Updated:
You could create the site page in the site pages library, then edit the site page and add the Hero web part and weather forecast web part in the site page.

More reference:
Using web parts on SharePoint pages.
Comment: can you tell me how to add em. I can only see 'web-parts' where you can upload photos and such. perhaps can you redirect me a tutorial?
Comment: I have updated my reply
Comment: The first link redirect me to Search Center in SharePoint instead of branding. Can you please update the correct link?
Comment: Sorry for giving your confusion. I have updated the first reference with correct link.


Auto creating accounts

Question: I'm wondering if there is any way to configure Ubuntu or install special software which could allow to automatically create user account when user login first time (without any special privileges, only standard user).
The scenario is to allow any user which has physical access to computer to login on it (with GUI). Using guest session is not enough because each user should has it's own profile and folder.
I know there is a way combined with LDAP authentication for creating accounts and home folders for valid users. I would prefer to not use LDAP mechanism because I want skip process of setting up accounts for each user on LDAP server.
I do not expect full solution (but if someone accidentally has sth like that it could be nice:)) maybe some tips what tools or system modules could I use/modify to achieve this.
I will be grateful for any help.
Thanks in advance.
Answer: Linux isn't meant for that, it would require modifying login scripts. Easiest way would be to make www site with option to add users.

Auto creating accounts


android multiplayer gam

Question: I am trying to develop multiplayer turn based android game which will be coordinated using a remote server. I want to use couchbase nosql server with java sdk. I do not understand how data will be moved from mobile to database and back. Could you please help me ? Do I need to use jetty or tomcat ? Is there any other way ? Mostly I have worked on client side only so I am not able to figure this out.
Answer: You need to get started with  socket programmming in java , the most primary thing you should know when developing a network app.
Answer: You should consider a REST-ful interface between the client and server instead of sockets, especially if it's a slow paced game (like Words with Friends or Draw Something)
The basic idea is that the mobile devices post data on various pages you have set up using a server:
http://mygame.com/mobile/api/submitMove?id=123&player=1&move=KnightA4
the server will then read the arguments, figure out if it's valid using a database, and respond back accordingly.
Comment: I have worked on client side only so I am not aware about server side. Could you please refer me a good tutorial ? Do I need to learn using jetty or tomcat ?
Answer: If you want to learn about servers and develop the server from scratch, I can relate to that BUT as a client developer it may take you a lot of time to configure, develop, test, run, host, maintain, scale the server side (and ofcourse it may cost you a great deal of money). If you are looking to release your game as quickly as possible I would propose another solution. I am from Skiller and we have SDK that should shorten the time it will take you to get your game on the market. You can use built in turn based simple API to create or join existing game, challenge players, send messages and much more...
Check our wiki pages or our Skiller website for more info.
Will be glad to get your input.

android multiplayer gam


In Revelation 5:10, how should "βασιλεύουσιν ἐπὶ τῆς γῆς" be translated?

Question: In Revelation 5:10, should βασιλεύουσιν ἐπὶ τῆς γῆς be translated "They will reign on the earth", or "They will reign over the earth"?
Comment: In order to keep my question simple, I have answered my own question below to provide background information as to why this is a question to begin with. I present evidence for translating the preposition as "over", however since almost all translations render the preposition as "on", maybe I'm overlooking something significant.
Answer: The ESV is representative of the vast majority of English translations in rendering the preposition ἐπὶ as "on", understanding it to describe the location from which the saints will reign.

and you have made them a kingdom and priests to our God, and they
shall reign on the earth." (ESV)

I could only find two English translations that render the ἐπὶ as "over", those being the Aramaic Bible in English on Biblehub.com and the NWT produced by Jehovah's Witnesses.
I'm assuming that the former is not a translation from the Greek, based on its title (I could find nothing about this translation online), and that the latter might have some sort of theological motivation.
However, I believe "over" is ultimately a better translation.  I draw this conclusion based on the following evidence.
Evidence from BDAG
BDAG's first definition for ἐπὶ is:

marker of location or surface, answering the question 'where?' on,
upon, near.

The first example is, in fact,

ἐπὶ (τῆς) γῆς on (the) earth

This would seem to indicate that BDAG supports translating ἐπὶ as "on" in Revelation 5:10, since ἐπὶ τῆς γῆς is the exact phrase found there.
However, notice definition 9:

marker of power, authority, control of or over someone or someth., over a. w. gen...βασιλεύειν ἐ. τινος (Judg 9:8, 10; 1 Km 8:7) Rv 5:10.

It is clear that BDAG believes "over" is the correct translation for ἐπὶ in Revelation 5:10
Evidence from LXX
The phrase Βασιλεύειν ἐπὶ τῆς γῆς is also found in 2 Kings 11:3 and clearly means "over".

και ην μετ' αυτης εν οικω κυριου κρυβομενος εξ ετη και γοθολια
βασιλευουσα επι της γης
And he was with her in the Lord's house, hidden for six years, and
Gotholia was reigning over the land. (NETS)

In fact, Βασιλεύειν ἐπὶ occurs commonly throughout the LXX and usually means to "reign over".
Contextual Evidence
It seems strange to me if the purpose of Revelation 5:10 were merely to inform the reader of the location from which the saints reign.
This is not to say that they do not reign on the earth, but that the purpose of the verse more likely is to inform the reader that they will reign over it.
This would indicate the fulfillment of God's will for Adam and mankind, who was to rule over the earth. (Gen 1:26) That he was to rule on the earth is self evident and doesn't need to be stated.
The saints ruling over the earth is also the realization of God's promise to Abraham that his seed would inherit the earth, and is the ultimate fulfillment of the land promises to God's people (Matt 5:5). While inheriting the earth might include being located on it, the primary idea is possession and ownership of it.
Answer: The key to this matter of whether it's 'over' or 'on' the earth, might need to include another point in Revelation, in addition to the very good points raised by the OP.
As I'm often inclined to say in questions about two possible, alternative translations of a word, it need not be "either", "or". It could be both. This is what context might indicate in this instance.
The book of the Revelation gives prophetic visions about a progression of events in time from Christ's ascension to his return at "the last day". Increasing plagues are poured upon an increasingly godless world, causing all but the saints to curse God all the more-so, and to refuse to repent of their sins and abominations. The culmination comes when Christ suddenly returns to start the Day of Resurrection and Judgment. This also brings about the spectacular, total destruction of the old heaven and the old earth. After that, God creates a new heaven and a new earth (Rev. 21:1).
Well, if the view is taken that Christ's return to heaven in glory marked the start of deceased saints thereafter being raised to go to sit with him in heaven on thrones, ruling as kings and priests with him, then for the duration of that part of the Revelation, they would be said to be ruling over the earth - the old earth. They would not, and could not, be on that old earth. Revelation 5:10 explains the situation in heaven after the Lamb (the glorified Christ) begins to open the seven seals in the book God held. Four (symbolic) living creatures and 24 (symbolic) elders fall down before the Lamb and cry:

"Thou are worthy to take the book, and to open the seals thereof: for
thou wast slain, and hast redeemed us to God by thy blood out of every
kindred and tongue, and people, and nation; And hast made us unto our
God kings and priests: and we shall reign on the earth." (Rev. 5:9-10)

Notice that those redeemed people are not yet reigning on the earth? They speak of a future time when they will, and 'on' is the correct translation. But at that time, they are not on the earth; they are in heaven, before the throne of God. At that time, the outpouring of the things in the seven seals have still to come down on to the earth. At that time, the old heaven and earth are in existence. All those yet to be martyred for the faith of Christ are still to be killed while they are on the earth, then to find their souls under heaven's altar, to wait till the full number of the saints will be killed (Rev. 6:9-12). That is what the fifth seal reveals, when opened in its proper sequence. But in 5:10 that exclamation comes before even the first seal is opened (Rev. 6:1).
When the view is taken that "the thousand years" reign of Christ started at his ascension back to heaven, and is a symbolic number, to continue until the time when he spectacularly returns, then it is easily seen that there is a reigning over the old earth until the new heaven and the new earth replace the old one. Then those redeemed ones can reign on the new earth. Then their location might change, but not while the old, sinful world keeps going.
That is not "easily seen" by those who have a doctrine of those kings and priests never returning to earth but staying permanently in heaven, to rule over the new earth from there. That is why, despite the Greek text they use (in their K.I.T.) having 'upon' in vs. 10 and also in vs. 13, they translate it as 'over' in vs. 10 but 'on' in vs. 13 as that makes it look as if that doctrine is correct, which includes billions never getting to heaven but staying on a paradise earth to be ruled over by a tiny number in heaven. When there is such inconsistency in translating the same word within three verses, suspicions must be aroused.
Comment: Thank you for your answer. I particularly appreciated your point " Notice that those redeemed people are not yet reigning on the earth? They speak of a future time when they will, and 'on' is the correct translation."
Answer: Sorry to be difficult here, but I think that this one of the extremely rare occasions where the NWT translation is broadly correct, but only because it agrees with BDAG (epi #9).  HOWEVER, I also think that "on" or better, "upon" is also correct.
Therefore, I would render this passage:

"reign upon/over the earth."

The reason for this is simple.  The words following "the earth" are genative and can be rendered as BDAG as either "on/upon".  However, the fact that someone reigns on/upon the earth does not necessarily imply that they reign over the earth.
Equally, the fact that someone reigns over the earth does not necessarily mean that they are upon the earth; indeed, God is in heaven but reigns over the earth!
The primary purpose of this passage appears to me as a promise to restore the governorship of the earth to mankind that was lost by Adam.  Compare Gen 1:28 vs Gen 3.  If this is true, then humans will both reign over the earth (as Adam should have) and reign upon the earth.
The context (Rev 5:9, 10) makes this clear - this rulership handed to the saints is on the basis of Jesus sacrifice and the fulfillment of the covenant promise to make them a kingdom of priests and rulers:

Ex 19:5, 6 - Now if you will indeed obey My voice and keep My
covenant, you will be My treasured possession out of all the
nations—for the whole earth is Mine. And unto Me you shall be a
kingdom of priests and a holy nation.'
1 Peter 2:9 - But you are a chosen people, a royal priesthood, a holy
nation, a people for God's own possession, to proclaim the virtues of
Him who called you out of darkness into His marvelous light.
Rev 5:9,10 - And they sang a new song [to the Lamb]: "Worthy are You
to take the scroll and open its seals, because You were slain, and by
Your blood You purchased for God those from every tribe and tongue and
people and nation. You have made them to be a kingdom and priests to
serve our God, and they will reign upon the earth."
Answer: I defend an allusion and contextualization between the story of Athaliah and the great whore of Revelation, with Jehoash referencing the story of Jesus' birth.
(2 Ki. 11:3 BGT) ... καὶ Γοθολια βασιλεύουσα ἐπὶ τῆς γῆς
(2 Chr. 22:12 BGT)  ... καὶ Γοθολια ἐβασίλευσεν ἐπὶ τῆς γῆς
(Rev. 5:10 BGT)  ... καὶ βασιλεύσουσιν ἐπὶ τῆς γῆς. (Simple Future)

Its tail swept a third of the stars out of the sky and flung them to the earth. The dragon stood in front of the woman who was about to give birth, so that it might devour her child the moment he was born. She gave birth to a son, a male child, who "will rule all the nations with an iron scepter." And her child was snatched up to God and to his throne. (Revelation 12:4-5 NIV)

the Root of David (Rev. 5:5)
Upon hearing the news of Ahaziah's death, Athaliah seized the throne of Judah and ordered the execution of all possible claimants to the throne, including the remnant of her Omri dynasty. However, Jehosheba, Ahaziah's sister, managed to rescue from the purge Jehoash, a grandson of Athaliah and Jehoram of Judah, who was only one year old. Jehoash was raised in secret by Jehosheba's husband, a priest named Jehoiada. Wikipedia
Athaliah - Revelation 17  Babylon, the Prostitute on the Beast
For some years before, the prophets Elijah and Elisha had already announced the end of the Royal House of Ahab.   Platts, John. A New Universal Biography, Vol.I, p.156, Sherwood, Jones and Co., 1825
Vide Revelation 11 "The Two Witnesses"

So he got up, took the child and his mother during the night and left for Egypt,  where he stayed until the death of Herod. And so was fulfilled what the Lord had said through the prophet: "Out of Egypt I called my son." (Matthew 2:14-15)

Luke 1:33 καὶ βασιλεύσει ἐπὶ τὸν οἶκον Ἰακὼβ εἰς τοὺς αἰῶνας καὶ τῆς βασιλείας αὐτοῦ οὐκ ἔσται τέλος
"and he will reign over Jacob's descendants forever; his kingdom will never end"... Luke 1:33 NVI
Similarly, Athaliah did not fully reign, she never reigned over the house of David.
This differentiation is perceived in the addition of πᾶσαν
Zechariah 14:9 καὶ ἔσται κύριος εἰς βασιλέα ἐπὶ πᾶσαν τὴν γῆν (Zech. 14:9 BGT)
This is implied by the 3rd, 6th, and 13th verses of the 5th chapter of Revelation.
I understand in this way that the translation of "βασιλεύουσιν ἐπὶ τῆς γῆς" is "They will reign on the earth"
Comment: Welcome to Bible Hermeneutics and thank you for your contribution. You mention a few reference works, please [edit] in citations for these. Also, when you get a chance, please take the [tour] to understand how the site works and [how it is different than others](https://hermeneutics.meta.stackexchange.com/questions/653/how-can-we-educate-new-users-about-our-site-distinctives/803#803).
Comment: Very interesting first answer. I don't necessarily agree with it but it is well researched and insightful.

In Revelation 5:10, how should “βασιλεύουσιν ἐπὶ τῆς γῆς” be translated?


Why do coefficients become exponents in the speed equation when dealing with elementary reactions

Question: In school, while studying chemical kinetics, we were learning about the speed law and equation for different chemical reactions. We learned that in general, the exponents of the concentration of reactants in the speed equation must be determined experimentally. However, earlier this week, we learned that if we are talking about basic elementary reactions, the coefficients of the reactants become the exponents in The equation. This puzzled me. Can anyone explain why the coefficients would become exponents? Thanks in advance
Answer: A reaction occurs when its reactives are in the same region of the space. If you have an elmental reaction of the form $a A + b B \rightarrow $, for the reaction takes place it is needed that $a$ molecules of $A$ and $b$ molecules of $B$ collide. How probably is this event? Well, if you only need one molecule of $A$ ($a=1$), the probability that an $A$ molecule be in this specific place (at some time) is proportional to the $A$ concentration. If $(a=2)$ we need another $A$ molecule, as the probability for a second molecule being in that space region (at some time, in particular at the same time) is independent, the probability of finding two $A$ molecules in the same space region (at the same time) is the product of the two individual probabilities (is like throwing a dice two times). In general, for the mixture the probability of the encounter is proportional to $[A]^a [B]^b$.
The probability of encounter is proportional to the number of encounters in some time interval. And the later to the reaction velocity.
Comment: This sort of made sense but you made it seem as though the concentration is the probabillity of finding a particule at that soace. Is this true?
Comment: It is not the probability, but it is proportional to the probability. Proportionality factor depends on temperature and volition radii. Also, once the volition takes place, there is another probability for the collision be reactive
Comment: Volition = collision after spellchecker
Comment: Ok, so say the coefficient of one of the reactants is 3 and at a particular moment in the reaction its concentration is 2 moles/ liter. I would think that since the reaction requires 3 of these molecules to collide at the same time, it would be less likely than if it only needed 2 and thus the reaction would take longer. However, the value of 2 cubed is larger than 2 squared wich leads to think the reaction would take less time, where is my logic flawed?
Comment: In the omission of proportionally coefficient, if it is small enough to make the product between it and concentration smaller than 1, then the cube will be smaller that the square


Get time & date independent to the local time of client pc

Question: How to get the Exact time and date of the client area, without depending to the local time & date of client's pc. Even if the time and/or date of that pc is set to a wrong time, I want to show the exact time and date of that timezone at my webpage.
May I calculate it using the server time and timezone of client pc and how? Or any other way to do this?
I want any solution with php, mysql, js or jQuery...
Thank you so much...
Answer: If you do it with any server side language like php, it will display server time independent of client's computer. Only client side scripts will display client pc time
like php time()
Comment: That will give you the *server* time, not the *client* time, though.
Answer: What you need to do is to guess the clients timezone. You can only make a guess. There are services where you can send the clients IP address to have it guess the geographic location, and from that figure out the timezone. But they are not reliable. The best is if you ask the client what timezone he is in.
You can then use the jstimezonedetect JS library to make a guess and let the user confirm that. Once you then know the clients timezone, you need to convert your servers time to the client time. How to do that is answered here.


Thunderbird + ldap write support

Question: Is there anyone aware of someone seriously working on thunderdbird to get write support on ldap shared addressbook?
Comment: Probably no one since that isn't working since Netscape Communicator got the ability to read LDAP trees for address books 20000 years ago.
Comment: you are right but in this way there is noway to get a shared and writable addressbook. Isn't it weird? Mail clients like Claws and Evolution have write support since ages while Thunderdbird, which is the only one working well on Windows, still lacks this feature.
Comment: Bad things happen in a bad world. It's open source. So you can make it a better world.
Comment: I wish I could, but I can't. Not enough skills ...
Comment: Then pay someone to do it.
Answer: https://bugzilla.mozilla.org/show_bug.cgi?id=86405 tracks work in progress on this feature.  Apparently the backend is already done, but UI is not.

Thunderbird + ldap write support