Is $K_1$ bipartite?

Question: I'm thinking that it could be trivially bipartite since it only has one vertex and no edges but I am still a little bit unsure about it being trivially bipartite.
Comment: Ummm... what is "k sub 1"?  Do you instead mean $K_1$?
Comment: not only is it bipartite, it is also unipartite
Comment: @DavidG.Stork Yes, did not know how to make it like that in my title. Seemed to fix itself.
Answer: Depends on your definitions. (As pointed out in Matthew Daly's answer, $K_1$ should be bipartite, because it has no odd cycles, so it would otherwise be an awkward exception. But not all definitions will play nicely with this desired property.)
West's Introduction to Graph Theory says

1.1.10. Definition. A graph $G$ is bipartite if $V(G)$ is the union of two disjoint (possibly empty) independent sets called partite sets of $G$.

So under this definition, if $V(K_1) = \{v\}$, then we let $\{v\}$ be one partite set, and $\varnothing$ be the other; $K_1$ is bipartite.
Bondy and Murty write

A graph is bipartite if its vertex set can be partitioned into two subsets $X$ and $Y$ so that every edge has one end in $X$ and one end in $Y$

which still works just fine, setting $X = \{v\}$ and $Y = \varnothing$. They do not specifically point out that $X$ or $Y$ could be empty, but they do not rule it out either. (Elsewhere, Bondy and Murty talk about "nontrivial partitions" or "partitions into nonempty parts", which make it clear that a partition without this qualifier is allowed to have an empty part.)
They are in better shape than Diestel, who has

A graph $G = (V, E)$ is called $r$-partite if $V$ admits a partition into $r$ classes such that every edge has its ends in different classes

with an earlier qualification that the classes of a partition may not be empty. Since $K_1$ should be bipartite by any reasonable definition, Diestel is in the wrong here. (Diestel later claims that all graphs with no odd cycles are bipartite, with no mention of $K_1$ as a special exception.)
If we treat "bipartite" as synonymous with "$2$-colorable", then $K_1$ is happily bipartite, since any function on its vertex set is a $2$-coloring (and also a $1$-coloring).
Comment: Quick question. Lets say we have ={}  and =∅, in reference to Bondy and Murty's definition. Would the edge connecting both subsets have vertices that are the empty set? Ie one empty set from X and the other from Y
Comment: The definition says *every* edge has a certain property; it doesn't say there exist any such edges. Since $K_1$ has no edges, the definition holds.
Comment: Ah, makes sense now. Thanks!
Answer: My graph theory professor spent a while teaching on this, because it's a mess either way.
It probably should be trivially considered bipartite. Otherwise you have to put disclaimers in all of your theorems (like the fact that $K_1$ doesn't contain any odd cycles).  But $\{\{v\},\emptyset\}$ is not a valid partition of the vertex set, since it contains the empty set as a member.
Comment: A reasonable definition of "bipartite" does not run into trouble if one partite set is empty.
Comment: @MishaLavrov On the other hand, requiring the parts of a partition to be non-empty isn't entirely unheard of either. So defining bipartite as a partition of the set of vertices into two can run into issues with $K_1$.
Comment: Yeah, I think that Dr. Schäffer's solution was to have us write in the margin of Bondy and Murty "... or $K_1$".
Comment: But Bondy and Murty are totally fine with empty parts in a partition, as far as I can tell...
Comment: @MishaLavrov As I say, my professor assumed that "partitioned into two subsets $X$ and $Y$" means that $\{X,Y\}$ was a partition of the vertex set, which could not be legally done if one of the sets was empty.  Bondy and Murty clearly either thought that it was okay or they hadn't considered the edge case, but pedantry like that got under my professor's skin.  ^_^

Is $K_1$ bipartite?


Adjust the power of laser diode on both CW and pulsed mode

Question: I am working on my graduation project to build a laser unit, i am supposed to control the power of laser diode when operating in pulsed mode and continuous mode.
firstly, i had the pulses from "Arduino UNO" and connected it to a FET then i have a pulsed laser diode.
secondly, i implemented a current constant driver which include a comparator "OP-AMP" , curent sensing resistor and FET, then i can control the current of laser diode butt it is not pulsed.
The question here is how can i make an accurate constant current driver controlling the laser diode by digitally (by Arduino) with the ability to work in CW or pulsed mode.
Comment: Show the schematics of your circuits, and specify the components you're using.
Comment: Also, you need to specify the minimum pulse width you need to control and your target for the accuracy of your "accurate constant current driver".
Answer: Mosfets are an answer. They do make great current sources and scaling is by size. To be honest I don't know how fast you need to pulse this, but I'm going to give you a part that is both a CC driver and a PWM. You really don't want to make that circuit discretely. CAT4101 from OnSemi. Use a make-before-break digi-pot to change the constant current bias and use pwm for... pwm!


How are User files in Windows 7 protected?

Question: I noticed that I cannot access user files from one account across another. However, if someone took my HDD, hooked it up to another computer, would they be able to see the files? Is there a way to encrypt user files without encrypting the entire HDD? I would like to encrypt my files on my laptop, but only those in my user account. This because I do not want a password prompt on the HDD, as I am using Prey and users need to be able to do Windows gust user logins for Prey to (potentially) track stolen property.
Answer: What you have noticed is ACLs (Access Control Lists), which specify which users can read or write to which files.
This relies on the OS to enforce it; as you suspected, anyone with physical access to the disk can read anything.
You can tell Windows to encrypt files using EFS by right-clicking one or more files or folders, clicking Properties, Advanced, Encrypt these files.
This will encrypt the files using your Windows login password, so that they will not be readable outside your account.
If you forget that password, you will lose the files.
Comment: @Polynomial: That's what I said.
Comment: As Ash noted in his answer, it's trivial to mount the volume on a Linux OS and have the ACLs completely ignored. They're not enforced if the OS doesn't understand them. Conversely, *nix permissions don't work on Windows either. See http://security.stackexchange.com/questions/26041/what-mechanism-enforces-user-permissions-in-unix-linux
Comment: Is the password entered upon user account login, or each time the file is accessed?
Comment: @Zombies: It's entered on login.  From your account, encrypted files work just like regular files.
Comment: @SLaks You said that the OS enforces it, yes; I was just expanding on that. Figured it was worth providing a link to the Sec.SE question.
Answer: I haven't tested this in Win7, but I mount my Vista HDD from Linux all the time. There is no protection, I can make any changes I like. I can only guess that Windows 7 would behave in the same way.
Regarding encryption: Have a look at TrueCrypt if you haven't already. That lets you set up an encrypted file and then mount it as a logical drive (after entering password), which you can then access from the file system like any other drive.
Answer: In Ash's case, either he/she is going over the network (logged in either as the user or the administrator) which means that Windows is still doing all the access (and therefore using Windows security), or if physically mounted, he/she has the special group Everybody granted with full rights on the volume.
I was worried about this on a 1TB portable drive I got for my birthday/Christmas.  But when I checked security, the entire drive had been marked to give Everybody full access.  So when I move the drive to another computer, I will still have full access to all the files, and can add more files that I know I will be able to access on other machines.
Dealing with getting the data off other hard drives from previous machines can be a pain.  You have to grant ownership to the directory (if done through properties, you have to completely get out of the properties dialog to continue making the further changes you need to make, which usually entails setting yourself up with full rights (getting ownership does NOT automatically grant you those right!), and applying them to all the subdirectories that may reside under that directory.
Comment: I physically mount the drive. As a test, I just ran up a Linux Live CD and wrote a file to c:/Windows/System32 with no problem. The Everybody group definitely does not have write access to that directory (after booting back into Windows, confirmed with "effective permissions"). As I said, I only have access to Vista, but I would be surprised if this has changed.


Generate recurrence relation for a hyperbolic equation

Question: I want to generate the recurrence relation for the integer solution of the equation 3m² - 2n² = 1 ; I'm a tenth grader, and so it took me pretty long to at first get out of the normal Quadratic Formula and stuff and realize that there exists things like Cayley-Hamilton Theorem, but unfortunately, I'm inexperienced enough to even try that !! I used Diophantine solving methods, manipulating it but end up messing with the equation ... With reference to Ryan's Generating Integer solution from Hyperbolic Equation , I'd appreciate if one can explain Will Jagy's solution and how he arrived at the recurrence xn+2 =  6xn+1 - xn
Comment: Someone asked one of these yesterday. Where is the question coming from?
Answer: The equation is the same as
$$(3m)^2-6n^2=3$$
which in effect is the same as
$$r^2-6n^2=3$$
as each solution of this has $3\mid r$.
That's the same as
$$(r+n\sqrt6)(r-n\sqrt6)=3.$$
Now
$$(5+2\sqrt6)(5-2\sqrt6)=1.$$
If
$$r'+n'\sqrt6=(5+2\sqrt6)(r+n\sqrt6)$$
then
$$r'-n'\sqrt6=(5-2\sqrt6)(r-n\sqrt6)$$
which leads to
$$r'^2-6n'^2=(r'+n'\sqrt6)(r'-n'\sqrt6)=(5+2\sqrt6)(r+n\sqrt6)
(5-2\sqrt6)(r-n\sqrt6)=3.$$
Then $r'=5r+12n$ and $n'=2r+5n$. If we let $m'=r'/3=5m+4n$
then $n'=6m+5n$ and
$$3m'^2-2n'^2=1.$$
So we can start with $(m_0,n_0)=(1,1)$ and then
recursively define $$(m_{k+1},n_{k+1})=(5m_k+4n_k,6m_k+5n_k).$$
Then
$$m_{k+2}=5m_{k+1}+4n_{k+1}=5m_{k+1}+24m_k+20n_k=10m_{k+1}-m_k$$
and similarly for $n_k$.
Answer: I would expect you to do better with Conway's topograph method. Everything involved here can be done without actual matrices, including the recursion.
I guess I will put some books, including a very good new one, CONWAY and HATCHER. There is also (I bought a copy) a well illustrated new one by WEISSMAN
This time it is
$$ x_{n+2} = 10 x_{n+1} - x_n \; \; , $$
$$ y_{n+2} = 10 y_{n+1} - y_n \; \; . $$
These come from the combined one-step rule
$$ (x_{n+1}, y_{n+1}) = (5 x_n + 4 y_n \; , \;  6 x_n + 5 y_n)  $$
which you get pretty quickly with Conway. Here is a fairly basic version of the topograph for $3x^2 - 2 y^2,$ showing several locations with $3 x^2 - y^2 = 1$ labelled with the appropriate $\left( \begin{array}{c} x \\ y \end{array} \right)$ in green

Then the separation into two rules can be done without matrices, I wrote that out at http://math.stackexchange.com/questions/1786760/recursive-system-solution/1786850#1786850
<code>Mon Apr  2 10:34:50 PDT 2018
 x:  1   y:  1
 x:  9   y:  11
 x:  89   y:  109
 x:  881   y:  1079
 x:  8721   y:  10681
Mon Apr  2 10:34:53 PDT 2018
</code>
Comment: Perhaps !! That's where I'm stuck :( How do you derive the recurrence relation at the first place ?


Is there a way to filter RSS feeds in Google Reader?

Question: I have a number of busy RSS feeds for which I only find a subset of the messages to be of interest to me. Is there a way to configure Google reader to only display certain RSS items that match particular keywords rather than giving me the entire feed?
Comment: Some high-volume sites are now offering RSS feeds for keywords and/or categories. Subscribing to one of those feeds instead would certainly cut down on the clutter.
Answer: I don't know of a way of doing it directly in Google Reader however Yahoo have a particularly nice rss/atom feed processing engine called Yahoo Pipes. This allows you to pull a number of feeds from other places apply translations and filtering to them, and then re-publish the modified feed. You can then set Google Reader (Or any other preferred RSS reader for that matter) to subscribe to the newly published Yahoo Pipes RSS feed. The interface is drag-n-drop. You literally build "pipes". Plus there is a full gallery of other peoples published pipes that you can use as examples, or even as components to your own pipe.
Comment: While the design of Yahoo Pipes is pretty brilliant, I find the implementation a little unreliable. I've been burned too many times by feeds going unrefreshed for days or weeks and then all of the sudden refreshing. I would be more likely to build my own clone service than to use Yahoo Pipes again in the future.
Comment: I have to admit I'm inclined to agree with you Adam. I use a pipe to group a number of the separate BBC news feeds into one, then remove duplicates. And I do tend to get the updates in large batches :-}
Comment: http://webapps.stackexchange.com/questions/357/is-there-a-way-to-filter-rss-feeds-in-google-reader/17518#17518 google alert lets you create own feeds with help of keywords and search operators pretty much like yahoo pipes
Answer: There's a GreaseMonkey script called Google Reader Filter which allows you to specify lists of words to kill - if the word appears in the title, that item gets dimmed.
More info here and here
Answer: Yes!  You can do this in Google reader, but I don't think you can set up as a permanent search.

If you have a group of feeds you want to search through, bundle them together under a single folder/tag. Like group all your tech news feeds you read into "Webtards."
Then you can use the search box at the top of Reader to search for a keyword, and filter it to just the feeds in your tag/label.  So you can search for "Twitter" in your group of feeds "Webtards" to see everything your webtards are saying about Twitter.

Reader also gives you the ability to search within an individual feed, which is also helpful.  So if you subscribe to the TechCrunch feed, you can search for "Twitter" within the feed "TechCrunch" and get back a bunch of articles from MG Siegler, God bless him.
Comment: This isn't technically a way to filter a feed, but it is an interesting alternative
Answer: There is not a way to save a filter within Reader, but you can perform a search (you can search within a folder/tag) that you would like to save and you can copy the url from your browser's address bar or save it as a bookmark.  When you would like to see those results again you can click the bookmark and the same search will be run.
Answer: Take a look at this greasemonkey script from PostRank, http://labs.postrank.com/gr.  It allows filtering of feeds in google reader based on its rankings.  If you don't find their rankings useful, then their greasemonkey script itself may potentially be useful in determining how to create your own script.
Answer: Unfortunately Google Reader is not evolving much.
You'll have to use a third party tool.
I use Feedrinse. It's free and is simple enough.
Answer: http://www.google.com/alerts
You can create a feed out of it. Just put your keywords into it and the site, e.g.
scienceblogs.com evolution biology
Afaik you can use pretty much all google operators for google alerts


Why can I only have one Pokemon in the gym battle, and not have 6 in a row?

Question: I used to go into the gym and it would show six Pokemon who would fight in a row, and when one died the next one would start immediately. Now I can only have one in battle at a time. How can I change this?
Comment: Are you trying to attack a friendly gym? In friendly gyms, you can only use 1 Pokémon, whereas in other teams gyms, you can use 6.
Comment: I understand now. I was mystic and he was valor. That's why. Thanks
Answer: The gym you're "attacking" is controlled by your team - you're training it.
When powering up friendly gyms, you are limited to one pokemon.
Update: As of 0.41.x, powering up friendly gyms are now 6v6.
Comment: When I was fighting there was only one, but my friend who was with me could fight and as the Pokemon died the next one automatically popped up to fight
Comment: is your friend on the same team as you?
Comment: @Susan Then your friend is on a different team. If your team controls it you can use only 1 Pokemon to train. If it is an enemy team then you can use 6 Pokemon to attack it.
Answer: As of the latest update (12th of October) you can use 6 Pokemon while training a gym.

Updated Gym Training: Trainers can now bring six Pokémon to battle at friendly Gyms. The CP of the Pokémon you are battling may be temporarily adjusted lower for your training session.
Answer: Yes, as these guys have mentioned already. Attacking friendly gyms is called "training". You can only use 1 pokemon in the gym battle, but in the end, the pokemon you used will still have 1 hp if you lose.
Attacking a rival gym allows you to have 6 pokemon with you.
Think of it like this. Friendly=duel (1v1), and Rival=war (6v6)
Comment: More like friendly is solo running a gauntlet.


Projective module over $R[X]$

Question: Let $(R,m)$ be commutative noetherian local ring with unity. Suppose $P$ is a finitely generated projective module over $R[X]$ of rank $n$ . Is $P$ free? If not, what is the counter example?
Comment: Well the answear is affirmative by obvious application of serre's conjecture if $(R,m)$ is zero dimensional. In general I expect a counter example. But I am not getting it. thanking you
Comment: @Anjan: the Quillen-Suslin solution of Serre's conjecture actually showed a bit more, and in particular gives an affirmative answer to your question when $R$ is a DVR.  Moreover, it a famous conjecture of Bass and Quillen that your question should have an affirmative answer if you add the hypothesis of **regularity** (since a regular one-dimensional local ring is a DVR, this is exactly what we did above).  So I think you should look for counterexamples among singular one-dimensional local rings.  (I don't know of one off the top of my head, but I also suspect they should exist.)
Comment: According to Wikipedia a counterexample occurs with R equal to the local ring of the curve $y^2 = x^3$ at the origin. It doesn't state what the counterexample is or provide a reference. http://en.wikipedia.org/w/index.php?title=Projective_module&oldid=388883610#Serre.27s_problem
Comment: Another good place to look would be Lam's new(ish) book *Serre's Problem on Projective Modules*.  (I do not yet have a copy, or I would tell you whether a counterexample can be found there.)
Comment: @Pete: If $R$ is a DVR there's a much easier proof (this is from Lam's book you mentioned): Start from Kaplansky's theorem that every submodule of a free module over a left hereditary ring (every left ideal is projective) is a sum of left ideals (see Lam, *Lectures on modules and rings*, (2.24), p. 42). For a DVR $R$ every left ideal $I$ of $R[X]$ is of the form $R[X] \cdot f$ where $f$ is a polynomial in $I$ of minimal degree (by the division algorithm). Since $R[X]$ has no zero-divisors, we have $I \cong R[X]$. Thus Kaplansky's theorem shows that every projective module over $R[X]$ is free.
Answer: Here is some elaboration on the wiki entry in George's comment.
Suppose $R$ is a  domain. $R$ is called seminormal if whenever $b^2=c^3$ in $R$ one can find $t \in R$ such that $b=t^3, c=t^2$.
The relevant thing here is the following fact:

R is seminormal if and only if $Pic(R) \cong Pic(R[X])$

So if $R$ is local and not seminormal then there will be a projective, non-free $R[x]$-module of rank $1$.
As for an implicit example, take $R = k[t^2,t^3]_{(t^2,t^3)}$. One can check that $I = (1-tx, t^2x^2)$ is an invertible (fractional) ideal of $R[x]$ which is non-free.
UPDATE: by request, a reference is this survey, see page 16. I am sure you can find more by googling the relevant terms.
Comment: Is $1-tx$ even in $R[x]$?
Comment: George, it is inside the quotient field.
Comment: Ok, yes, its a fractional ideal (I was forgetting that invertible ideal means invertible *fractional* ideal by definition).
Comment: Can you tell me a reference for the proof of the fact that $R$ is seminormal iff $Pic(R) \cong Pic(R[X])$? Thanks for this nice answer

Projective module over $R[X]$


How do I learn jazz on piano?

Question: I am very interested in learning piano but more specifically jazz. I really like the way people can just improvise. I know that I would not be easy but I would like to know what the best book or specific resource I can learn to learn jazz improvisation. I'm not too interested in playing any specific piece of music. I purchased a 61 key digital keyboard and I am a complete beginner; I know nothing about how to play piano or any instruments.
Comment: Hi Ben. Requests for resources are considered off-topic here, but see the linked question for tips on getting started with piano improvisation.
Comment: Check Facebook marketplace for pianos. People are ALWAYS giving away free pianos. Expect to spend about $100 to tune it. The sooner you get a piano, the better. You have to spend a LOT of money on a keyboard before it'll start to approximate the feel of a piano.
Answer: This is on its way to being closed, but it sounds like you need, first and foremost, a teacher. You say you know nothing about how to play any instruments - piano included.
There's always two distinct parts to learning music on any instrument. There's the instrument itself - how it produces the sounds, and there's the music - a huge subject on its own, which has only some relationship with the instrument concerned.
Since piano is one of few on which chords and melody can be played simultaneously, there's a lot to do before even considering playing jazz on it.
Start simply, by just messing about and learning what a piano is about. It may be that with a 61 note instrument, there's no 'piano' action. In which case, you're looking at changing it quite soon. Learn about triads, developing into more complex chords. learn about pentatonics, and how they will ease you gently into improvising. There's a start for you, but requests for resources themselves are offside on this site.
Answer: You were able to type that question, because you can improvise - in natural language. Written language at least, apparently, but most probably spoken language as well.
The skill of improvisation in music comes the same way as improvisation in natural language: by hearing and mimicing existing expressions. First you just try to copy and repeat what you hear, and then you'll start to make your own combinations and modifications, and the expressions, words, syntax, sentence structure, becomes part of your vocabulary and just knowing the language.
All aspects of music can be improvised: melody, harmony, rhythm. And improvisation of all of those aspects is learned the same way: by repeating existing pieces of music and combining the learned parts in new ways. "Jazzing up" a song means modifying the harmony, melody and rhythm in interesting and creative ways.
Start off by playing simple melodies by ear, in the key of C, so you can start with the white keys only. Then learn to accompany simple songs with chords. Then combine parts of songs and chords in new ways, modifying the songs, making your own variations.
But do try and find a teacher. There is a wide array of skills to obtain, starting from something as trivial as finding where C is on the keyboard. What is a C major chord. Etc.

not too interested in playing any specific piece of music.

Your path to learning improvisation will consist of playing specific pieces of existing music, or at least parts of existing pieces, because that's how you build your musical vocabulary.
Answer: It's a long road. I'll just add some points that helped me (note each of these are long topics, I'm just give my short thoughts on them):

You need to understand basic music theory. If you can take a basic music theory course or go through a book chapter by chapter, that will help. There's a lot of information here that musicians take for granted, what the notes are, what chords/triads are. What the major scale is. Part of this is learning to read music. There are a lot of great musicians that don't read music, but learning to read music will make everything much easier imo.

Think of music as melody, rhythm and harmony. This may seem trivial but it was a bit of a revelation to me. Before I realized this I used to think of music more as a bunch of different polyphonic lines that magically worked together (like Baroque music). But for improvisation, it really helps to divide music into melody, rhythm and harmony. Now this basically means that you have a melody line (the part you sing) and you have a "chord" behind it. So a song is a sequence of chords in the background, with a melody in the front.

On the piano this (very basically) translates to a chord in the left hand and a melody in the right hand. Then you can eventually add a third element... a bass line which acts as part of the harmony and rhythm.
So you have these 3 parts... a melody, a bassline, and chords. But you only have 2 hands. The art of solo jazz piano is to get these 3 parts work together with your two hands. Sometimes you leave out the chords, sometimes you leave out the bassline. It's all a matter of taste.

Eventually you want to take a simple tune like 'Happy Birthday' and play it on the piano with a chord in the left hand the melody in the right hand.

Get used to singing melodies, and improvising around them. Take simple tunes like Happy birthday or mary had a little lamb... Improvisation is basically singing lines "in your head" while playing them on the instrument. The easiest instrument to start out with is your own voice.

If you can improvise by singing around the melody of Happy Birthday, then go back to the piano. Again play the chord in the left hand and the melody in the right. But this time try improvising around the melody in the right hand.

To get into jazz you need to learn chords beyond triads. Mainly 7th chords (major 7th, minor 7th, dominant 7th).

Eventually get a "fake" book eg: the Real Book. These are notated with chords and the melody. These books are really suited for jazz players/improvisers. They don't give note for note instructions to the player. You take the chords and melody and play them in the way that suits you.

The technique of the instrument. You need to learn proper fingerings so that you can play fluidly... learning the proper fingerings of scales really helps. But different people have different sized hands, so you may have to find something that isn't the accustomed fingering that suits you. You want to minimize stress on the hands and shoulders etc. You want to minimize any tension.

Listening to the original songs of jazz standards first before they are "jazzed" up, so that you know the melodies. Then listen to jazzed versions from the 20s and 30s. Why I say from the 20s and 30s is because the improvisation isn't too complex for the ear. In the 40s we get Bebop and the improvisation (imo) takes a quantum leap.

How do I learn jazz on piano?


Choosing the "right order" of approximation in Taylor Series

Question: I was evaluating the following limit using Taylor series, $\lim_{x \rightarrow 0}(2 \frac{e^x-1-x}{x^3}-1/x)$, and I wrote the exponential function as $e^x=1+x+\frac{x^2}{2}+ \frac{x^3}{6}+o(x^4)$ and got that the limit is $\frac13$. But, if I had written $e^x=1+x+\frac{x^2}{2}+o(x^3)$, I would have obtained a different result, so how do I choose correctly at which order I'm supposed to stop when writing a Taylor series to evaluate a limit?
Comment: Use a backslash "\" when in doubt, in MathJax - placing backslashes before a standard expression such as $\lim$ will usually be rendered properly: e.g., `$\lim$`, `$\sin$` render as $\lim$ and $\sin$ instead of $lim$ and $sin$
Comment: Since the limit has one distinct answer, it would be very useful for your question if you showed *how* you obtained $\frac{1}{3}$, and how using a different little-o would supposedly lead to a different answer
Comment: @FShrike if I use the first series I worte, I get that the function within the brakets in the limit becomes $\frac{x^2+\frac{x^3}{3}+o(x^4)}{x^3}-1/x$ and when I do the division, I get $1/x+1/3+ o(x^4)/x^3-1/x$ which goes to 1/3 as x approaches 0. If I stop at $o(x^3)$, I don't get the 1/3 term because I simply have $o(x^3)/x^3$ which is 0
Answer: $$\lim_{x\to0}2\frac{e^x-1-x}{x^3}-\frac{1}{x}=\lim_{x\to0}\frac{1}{x}+\frac{1}{3}+\frac{1}{12}x+\cdots-\frac{1}{x}=\frac{1}{3}$$
However, if you choose to use little-o notation, recall that the definition of little-0 is that:
$$f(x)\in\omicron(g(x)),\,x\to0\iff\lim_{x\to0}\frac{f(x)}{g(x)}=0$$
Whereas the definition of big-O notation is:
$$f(x)\in O(g(x)),\,x\to0\iff\lim_{x\to0}\frac{f(x)}{g(x)}\lt\infty$$
So we notice that:
$$\frac{x^3}{6}+\frac{x^4}{24}+\cdots\in O(x^3)$$
But is not little-o of $x^3$ - this is because the remainder terms divided by $x^3$ leave you with $\frac{1}{6}$ and some other terms that go to zero, leaving $\frac{1}{6}\neq0$ as the limit.
So in fact $e^x=1+x+\frac{x^2}{2}+O(x^3)$, not little-0!
Now:
$$\begin{align}\lim_{x\to0}2\frac{e^x-1-x}{x^3}-\frac{1}{x}&=\lim_{x\to0}2\frac{\frac{x^2}{2}+O(x^3)}{x^3}-\frac{1}{x}\\&=\lim_{x\to0}2\cdot\frac{O(x^3)}{x^3}\end{align}$$
Which is an ambiguous expression that is not necessarily (and not actually, in this case) equal to $0$. If we replaced $O(x^3)$ with: $\frac{1}{6}x^3+o(x^3)$ however, that would be correct, as the remainder terms when divided by $x^3$ are $\frac{1}{24}x+\frac{1}{120}x^2+\cdots$ which do go to zero as $x$ does.
To demonstrate the proper use of these notations, this is what you should be doing:
$$\lim_{x\to0}2\frac{e^x-1-x}{x^3}-\frac{1}{x}=\cdots=\lim_{x\to0}\frac{1}{3}+\frac{o(x^3)}{x^3}=\frac{1}{3}$$
Since $o(x^3)/x^3\to0$ by definition.
Comment: Now I understand, thanks!


How can I determine the monitor refresh rate?

Question: Is there a cross platform way to get the monitor's refresh rate in python (2.6)? I'm using Pygame and PyOpenGL, if that helps.
I don't need to change the refresh rate, I just need to know what it is.
Comment: What are you going to use the refresh rate for, if I might ask? If you are writing a game loop or something, you generally don't need to use the refresh rate.
Comment: When my app is running in full screen, v-sync is enabled which caps the fps at the refresh rate. V-sync isn't enabled in windowed mode, and the fps is many times faster. I want it to run at the same speed in windowed and fullscreen, so I want to set the maximum fps as the refresh rate of the monitor.
Comment: You should not tie your game logic and your render rate together as much as you have. Look here for some alternative game loop constructions: http://dewitters.koonsolo.com/gameloop.html
Answer: I am not sure about the platform you use, but on window you can use ctypes or win32api to get details about devices e.g. using win32api
import win32api

def printInfo(device):
    print((device.DeviceName, device.DeviceString))
    settings = win32api.EnumDisplaySettings(device.DeviceName, -1)
    for varName in ['Color', 'BitsPerPel', 'DisplayFrequency']:
        print("%s: %s"%(varName, getattr(settings, varName)))

device = win32api.EnumDisplayDevices()
printInfo(device)

output on my system:
\\.\DISPLAY1 Mobile Intel(R) 945GM Express Chipset Family
Color: 0
BitsPerPel: 8
DisplayFrequency: 60

Answer: I recommend switching to the community edition of pygame. Their website https://pyga.me/. Long story short, the pygame former core developers had challenges contributing to the original development upstream, so they forked the repository and moved to this new distribution that aims to offer more frequent releases, continuous bug fixes and enhancements, and a more democratic governance model (The magic of Open Source). You can easily switch to it by running pip uninstall pygame and then pip install pygame-ce --upgrade. They have the same API as the original pygame (so you still use import pygame and everything remains the same).
They have many nice new features and bug fixes, including methods to get the monitor's refresh rate in the display module:
import pygame

pygame.init()
screen = pygame.display.set_mode((1280, 720))
clock = pygame.time.Clock()
running = True

print(
    "Screen refresh rate for current window:", pygame.display.get_current_refresh_rate()
)  # Must be called after pygame.display.set_mode()
print(
    "Screen refresh rate for all displays:", pygame.display.get_desktop_refresh_rates()
)  # Safe to call before pygame.display.set_mode()

while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    screen.fill("purple")

    pygame.display.flip()
    clock.tick(60)  # limits FPS to 60

pygame.quit()

On my computer, this prints
pygame-ce 2.3.2 (SDL 2.26.5, Python 3.11.4)
Screen refresh rate for current window: 144
Screen refresh rate for all displays: [144]

which is indeed correct.
Answer: On macOS, you can use pyobjc to query the refresh rate of all the attached displays.  You'll need the Cocoa (i.e. "AppKit") framework for this:
$ python3 -m venv screen-res
$ . ./screen-res/bin/activate
$ pip install pyobjc-framework-Cocoa

then, in Python:
from AppKit import NSScreen

for each in NSScreen.screens():
    print(f"{each.localizedName()}: {each.maximumFramesPerSecond()}Hz")

On my system, this produces:
LG HDR WQHD+: 120Hz
Built-in Retina Display: 120Hz

(Which is correct, my displays are indeed both set to a 120Hz refresh rate.)
On Linux, you can use python-xlib:
from Xlib import display
from Xlib.ext import randr
d = display.Display()
default_screen = d.get_default_screen()
info = d.screen(default_screen)

resources = randr.get_screen_resources(info.root)
active_modes = set()
for crtc in resources.crtcs:
    crtc_info = randr.get_crtc_info(info.root, crtc, resources.config_timestamp)
    if crtc_info.mode:
        active_modes.add(crtc_info.mode)

for mode in resources.modes:
    if mode.id in active_modes:
        print(mode.dot_clock / (mode.h_total * mode.v_total))

Associating the appropriate screen index number with the place you want your PyOpenGL window to open up on is left as an exercise for the reader :).
(I won't duplicate Anurag's answer for Windows here, especially since I can't test it, but that's how you would do it on that platform.)
Answer: You can use DEVMODEW, but this only works on Windows Machines.
Install 'wmi' using pip with "pip install wmi"
import ctypes
import wmi
from time import sleep

class DEVMODEW(ctypes.Structure): # Defines the DEVMODEW Structure
_fields_ = [
    ("dmDeviceName", ctypes.c_wchar * 32),
    ("dmSpecVersion", ctypes.c_uint16),
    ("dmDriverVersion", ctypes.c_uint16),
    ("dmSize", ctypes.c_uint32),
    ("dmDriverExtra", ctypes.c_uint16),
    ("dmFields", ctypes.c_uint32),
    ("dmPosition", ctypes.c_int32 * 2),
    ("dmDisplayOrientation", ctypes.c_uint32),
    ("dmDisplayFixedOutput", ctypes.c_uint32),
    ("dmColor", ctypes.c_short),
    ("dmDuplex", ctypes.c_short),
    ("dmYResolution", ctypes.c_short),
    ("dmTTOption", ctypes.c_short),
    ("dmCollate", ctypes.c_short),
    ("dmFormName", ctypes.c_wchar * 32),
    ("dmLogPixels", ctypes.c_uint16),
    ("dmBitsPerPel", ctypes.c_uint32),
    ("dmPelsWidth", ctypes.c_uint32),
    ("dmPelsHeight", ctypes.c_uint32),
    ("dmDisplayFlags", ctypes.c_uint32),
    ("dmDisplayFrequency", ctypes.c_uint32),
    ("dmICMMethod", ctypes.c_uint32),
    ("dmICMIntent", ctypes.c_uint32),
    ("dmMediaType", ctypes.c_uint32),
    ("dmDitherType", ctypes.c_uint32),
    ("dmReserved1", ctypes.c_uint32),
    ("dmReserved2", ctypes.c_uint32),
    ("dmPanningWidth", ctypes.c_uint32),
    ("dmPanningHeight", ctypes.c_uint32)
]

def get_monitor_refresh_rate():
    c = wmi.WMI()
    for monitor in c.Win32_VideoController():
        return monitor.MaxRefreshRate
    return None

refresh_rate = get_monitor_refresh_rate()
if refresh_rate is not None:
    print(f"Monitor refresh rate: {refresh_rate} Hz")
else:
    print("Cannot Detremine the Monitor Refresh Rate.")
sleep(10)

Answer: You can use the pygame clock
fps = 60
clock = pygame.time.Clock()

At the end of the code:
clock.tick(fps)
Comment: the question is about getting the monitors refresh rate, not setting the game's frame rate.


Why are the days evil?

Question: In Ephesians 5:16 NLT

Make the most of every opportunity in these evil days.

Why are the days evil?
Comment: _... few and evil have the days of the years of my life been,_ (Genesis 47:9). Up-voted +1.
Comment: ... because we are evil and surrounded by evil and sin everywhere.  Rom 3:10-18.
Comment: [James 5:1-3 ESV] Come now, you rich, weep and howl for the miseries that are coming upon you. Your riches have rotted and your garments are moth-eaten. Your gold and silver have corroded, and their corrosion will be evidence against you and will eat your flesh like fire. You have laid up treasure in the **last days**.
Answer: The days are evil because Satan is the god of this eon.  It is called the present evil age.

in whom the god of this present age has blinded their unbelieving minds. 2Corinthians 4:4

4who did give himself for our sins, that he might deliver us out of the present evil age, according to the will of God even our Father, 5to whom [is] the glory to the ages of the ages. Amen. Galatians  1:4

in which once ye did walk according to the age of this world, according to the ruler of the authority of the air, of the spirit that is now working in the sons of disobedience,  Ephesians 2;3

The majority of people living today are blinded by the god of the eon.  He is the one that is working in the sons of disobedience which are the majority of this world right now.
The world governments are definitely influenced by Satan.
It's a dark world because of the spirits  that are ruling over it now.

10Therefore, my brethren, be strengthened in our Lord and in the force of his power. 11And put on all the armor of God, so that you can stand against the strategies of The Devil. 12Because your fight has not been with flesh and blood, but with Principalities and The Rulers and The Powers of this dark world and with wicked spirits which are under Heaven.  Ephesians 6:10
Answer: It simply refers to the evil days or terrible end times aka abomination of desolation, that they were living in. Keep in mind that the whole NT has the apocalyptic theme in which at least 6 million Jews were killed during those few years of "evil days" of persecution. The phrase is just like anyone saying today, that we are living in bad times, pointing out to the increased sin, perversion and persecution. I came across a sermon video of David Wilkerson preaching this generation is worse than Sodom and Gomorrah, he is pointing out the perversion in his nation in general, by saying how evil are the days we live in. The same phrase can be said by people in various nations in all the times, however the NT writers knew well about their end times, so it suits their context best.
Craig Keener in IVP commentary writes:

Eph 6:13. The "evil day" could refer generically to any time of judgment or testing (cf., e.g., Amos 5:13; 6:3; 2 Maccabees 1:5; Sirach 51:11-12; Eph 5:16), though some scholars think it applies specifically to the period of intense tribulation Jewish people expected prior to the end of the age (cf. Dan 12:1), which some scholars believe Paul elsewhere regarded as present (cf. Rom 8:22-23).

To quote those references from Catholic Public Domain Version 2009,

Sirach 51:11-12 Then I remembered your mercy, O Lord, and your works, which are from the very beginning. For you rescue those who persevere for you, O Lord, and you free them from the hands of the Gentiles.
Amos 5:13 Therefore, the prudent will be silent at that time, for it is an evil time.
Amos 6:3 You have been set aside for the day of disaster, and you approach the throne of iniquity.
2 Macc 1:5 May he heed your prayers and be reconciled to you, and may he not forsake you in the evil time.
Ephesians 5:16 but like the wise: atoning for this age, because this is an evil time.
Ephesians 6:13 Because of this, take up the armor of God, so that you may be able to withstand the evil day and remain perfect in all things.
Answer: God is perfect.
Matthew 5:48
Therefore you are to be perfect, as your heavenly Father is perfect.
God is light.
1 John 1:5
This is the message we have heard from Him and announce to you, that God is Light, and in Him there is no darkness at all.
The 'days are evil' because there is darkness and imperfection in this world. Sin can be explained by describing anything that is not of God. As a lie is a distortion of the Truth.
God is truth.
Isaiah 65:16-17
"Because he who is blessed in the earth
Will be blessed by the God of truth;
And he who swears in the earth
Will swear by the God of truth;
Because the former troubles are forgotten,
And because they are hidden from My sight!
"For behold, I create new heavens and a new earth;
And the former things will not be remembered or come to mind.
Answer: The Epistle of Paul to the Ephesians was written in the later time of Paul, while he was imprison in Rome at around 60-62AD. This seemed to be the final chapter of his preaching, in which he emphasized the word "mystery", which had been used nine times in six chapters.
The mystery of Gospel, revealed by the Holy Spirit to Paul, that "The Church is the body of Jesus Christ". The purpose of the church, as revealed in 3:10-12 (NIV);

10 His intent was that now, through the church, the manifold wisdom of God should be made known to the rulers and authorities in the heavenly realms,
11 according to his eternal purpose that he accomplished in Christ Jesus our Lord.
12 In him and through faith in him we may approach God with freedom and confidence.
We became Christian, forming the church, saved by Grace, not by our good deeds. As before we were Christian, we lived following the ways of the world, and the disobedient spirit, Satan. (Ephesus 2:1-2 NIV - As for you, you were dead in your transgressions and sins, in which you used to live when you followed the ways of this world and of the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient). By definition, everyone were dead until we believe in Jesus, saved by His Grace and reborn again.
The Epistle of Paul to Ephesians was written to his fellow Christians. Chapter 4-6 are focus on "Living a life of Holy". His words were mostly encouraging us to follow, rather than warning us if failed. We must be careful not all Christians are eventually saved, many so called Christian haven't been reborne, still living a life of transgression and disobedient. When reading Epehsus 5:16, better include 5:14-17 (NIV)

14 This is why it is said:
"Wake up, sleeper,
rise from the dead,
and Christ will shine on you."
15 Be very careful, then, how you live—not as unwise but as wise,
16 making the most of every opportunity, because the days are evil.
17 Therefore do not be foolish, but understand what the Lord's will is.
Sleeper were those Christian who still lived their life messy. If they died tomorrow, they missed their own salvation, the only opportunity to be saved. Foolish were those who do not understand the Lord's will: "Reborn and live a life of Holy".
Answer: The phrase "the days are evil" refers to the challenging and tempting situations that we encounter in the world, such as temptation to sin, the influence of worldly values, or the presence of suffering and injustice.
These challenges can lead us away from God's goodness and love if we are not prepared to resist them, if we don't follow the teachings of Christ and the guidance of the Holy Spirit.
Therefore, the apostle Paul urges us to put on the "whole armor of God" (Ephesians 6:11-17) in order to withstand the attacks of the evil one and remain steadfast in our faith, even in the midst of a world that is often hostile to the Gospel.

Why are the days evil?


Can I use weather stripping inside a shower?

Question: We are installing a shower base and there is a little gap between the drywall and the shower base. I did some research and the TrimLux from Sealux is perfect for our problem. The only problem is that I can't get it. But I saw a similar profile on a weather stripping. Is it possible to use weather stripping to cover the gap?
Comment: How big is the gap?  Photos?
Comment: The gap is about 1/8" wide. I would love to send photos but we're putting in tile right now. I'll show photos as soon as we're done tiling.
Comment: I added the picture above. Hope that helps
Answer: Caulking is the standard method for shower/baths. 100% silicone mildew resistant caulking.
I do not think the weather striping is going to eliminate water from wicking up from the bottom.
Is there going to be something installed over the the drywall?
Comment: Yes, there will be tile over the weather stripping. Although, i put a bead of silicone i underneath the weather stripping, in between the gap of the base and the wall. Im just using the weather stripping for added protection and as a means for the tile to drop on to
Comment: Usually the product  that you are  mounting the tile to, cement board or denshield or whatever it may be will be, is sitting out further than the shower base or tub so that when you put the tile on the tile comes down over the tub lip or shower base lip.  IE: the base runs up behind the tile. It seams in your case you are going to but the tile up to the base, if so the the weather strip may get in the way or be visible and not look good. ??
Comment: Yeah, thats what it should be. But my dad did it the way it is now. Its looking okay now though. Im just concerned about the weather stripping degrading because it'll be in the shower.


How to direct devices by hacking a router changing the DNS settings?

Question: If I hacked a router's admin panel outside my network, is it possible to direct all devices in that network to any website I want by DNS settings? If it is possible, how?
Comment: Although your context is hacking, this is more of a DNS basics question than a security question. Do you know how DNS works?
Comment: i haven't much experience about networks but i want to know if it is possible to do somthing like that?
Answer: If:

the devices have not cached the IP of the domain locally
the devices are configured to use the router for DNS
the devices can access the website you want them to go to
the original site (Facebook, Google, a bank, etc.) does not use TLS settings that prevent this sort of tampering
the router allows you to edit the DNS table to enter your own settings
the router does not override your new entries from authoritative entries from another DNS server

Then maybe.
As for how, you just create DNS entries.


Saw a bright orange object in the sky. What was it?

Question: Some friends and I were backpacking in the mountains, and at night we saw a very bright orange object in the sky. It looked brighter than Venus. After a couple minutes we realized it was moving horizontally very slowly. Its movement wasn't noticeable unless looking at it next to a reference point like a tree. This was way brighter and slower than any satellite I've seen. Anyone know what this was?
Comment: I'm voting to close this question as off-topic because this is a (very vague) UFO report and we do not generally make guesses about these things.  In general Astronomy SE deals with objects that are far outside Earth's atmosphere and with the exception of LEO satellites (which your object is apparently not) we don't deal with them.
Comment: The description is consistent with the planet Mars. A time and direction would be helpful.
Comment: I think it's a perfectly reasonable astronomy question. It's not a UFO report (no mention of "flying object"), and the answer is useful in describing how stars and planets low on the horizon can be seen to move very slowly. I too was amazed how bright and orange the object (Mars) was.
Comment: @Chappo I live in Ireland - I am generally amazed if we can see the sky for all the cloud we normally get ! :-)
Comment: Possible duplicate of [Star like light moving in the sky, what could it be?](https://astronomy.stackexchange.com/questions/11634/star-like-light-moving-in-the-sky-what-could-it-be)
Answer: If the bright orange object was low in the southeast around midnight, it may have been Mars.
In late July and early August 2018, it will be only 0.39 AU away from Earth and shine with apparent magnitude -2.7, slightly brighter than Jupiter.
This is not as bright as Venus but may stand out more strongly in a midnight sky than Venus does in twilight.
For most of Mars's 2.1 year synodic period, it is farther from Earth and appears fainter.
As the Earth rotates, celestial objects appear to move about 1/4 degree per minute from east to west.
For observers in the northern hemisphere, objects near the southern horizon appear to move horizontally left to right.
Comment: On the weekend Mars was low in the northeast sky 2 hrs after sunset (southern hemisphere) and was the biggest, brightest and most orange I'd ever seen it. Quite a feast for planet watchers, with Venus brilliant in the northwest and Jupiter and Saturn high in the sky.
Answer: I came here to ask the same question on July 8 but I found you had asked already 3 hours ago. So I waited for answers. When Mike G assured it's mars, I felt better, because when I saw the object I felt it's never a satellite or UFO like something. But we are in different Geo location, right? So how can that answer be authentic?(although, Mike has provided some technical info for Geo locations, but I'm a bit lazy to measure and find that way) So I had to search for any reliable source.
Yesterday, searching on google, I found https://www.fourmilab.ch/cgi-bin/Yourhorizon
I corrected Latitude and Longitude with my location( the city I lived), which I found in wikipedia or you can use google maps( but that case you have to convert the decimal coordinates to degree). And then Updating the data with real time, it's just almost accurate (with eye level measurement) for the red planet and else. Yes, it's mars. But wait, there are more, I found Saturn, Jupiter- I was blown away, identifying them as what they are for the first time in my life. (planets are shown with symbols- the legends you can find on https://www.fourmilab.ch/yoursky/help/icons.html)
I think as it's relative with Geo location, you can get the actual answer, trying this site, the way I found my answer.
Thanks


SMS registration and login

Question: I want change default wordpress login/email/passwords registration to sms/otp (where sms will be the login (for example) and otp is a password). As well as restore passwords will be by sms only. Does anything existing solution here? or may be some have expiriences or advices how to realise it.
Answer: OTP Verification plugin verifies Email Address/Mobile Number of users by sending verification code(OTP) during registration. It removes the possibility of a user registering with fake Email Address/Mobile Number. This plugin checks the existence of the Email Address/Mobile Number and the ability of a user to access that Email Address/Mobile Number.
I have not used this plugin but may be with some modifications overriding the plugin helps convert the plugin in to your needs.
Hope this plugin helps!

SMS registration and login


georeferencing raster data with unknown CRS

Question: I'm new to QGIS and georeferencing raster data. I have a raster dataset with unknown CRS. The coordinates for goerefencing the raster data with reference points (x = 589 Y = 1483 / x = 500 Y = 1500) from an archaeological digging raster. The digging site is in Switzerland. I should georefernce that raster data, how do I have to set the proper CRS? I tried several time but failed and I have no clue how to proceed.
Answer: Archaeological digs usually use a localized grid, that while it may be originally based off a national grid, is customized to fit the local demands. these grids might be orientated to fit the archaeological architecture, topography, and sometimes to force only positive values of east/north in order to make measurements easier.
Georeferencing this raster should probably be done based on a high resolution aerial image of the dig site. the 0/0 location of the grid might be a prominent landmark surveyors used to plan out the grid.
the CRS itself can be a default custom meter grid, with the datum either WGS84 or ETRS89. The relatively small scale of the site means you don't have to worry much about deformities.


Do any Ubuntu-based distributions ship with Unity?

Question: I like distributions like Mint and Pinguy because they include most stuff I want to install out of the box. Are there any such Ubuntu spin-offs that use Unity by default?
Comment: The normal java (sun-java-6) will be removed from any Linux machine soon(ish). Ubuntu uses OpenJDK as default but all others will most likely have to remove it too since Oracle changed the license making it non-free.
Comment: OP, You know this was an over blown exaggeration? you can still have JAVA support, you can still install JAVA from the Oracle site, you have OpenJDK there is no Need for a spin off with Unity nor anything that drastic. As i sense that was your concern, not having Java anymore thus you couldn't use Ubuntu because of that.
Answer: What would be the need of an Ubuntu spin off with unity if Ubuntu 11.10 come shipped with unity by default? Of course, you can install gnome, and personlize it at the max, since this is Linux, but there is no need to make a spinoff for something that is already included in the OS by default ^^
Comment: And then install [ubuntu-restricted-extras](https://apps.ubuntu.com/cat/applications/oneiric/ubuntu-restricted-extras/) for almost everything you need.
Answer: Sabily
http://www.sabily.org
It is an Islamic Linux Distribution based on Ubuntu...... come with Unity & Gnome-Shell, have Java & Codecs installed by default........ also available in 64 bit Version.
Answer: Released 24/02/2012 is DreamStudio

ArchLinux has the ability to install the Unity-Shell - according to their wiki - this ability is unsupported by their developers but they include two repositories for the ArchLinux user to install from.
Fedora had mentioned there was a possibility of a Unity shell - but that development seems to have gone quiet.
The LinuxMint community also have the ability to install the Unity Shell:
Comment: My personal experience has been that Unity doesn't seem to work too well on Linux Mint; and similarly, the only Mate desktop worth having is Linux Mint's.


How to cartographically represent active faults, without using geological symbols

Question: I would like to ask how to cartographically represent active faults, without using geological symbols. I don't want to make a geological map, that's why I don't use that kind of symbology. I don't have the ages of faults, but I do have the type. I saw how the United States Geological Survey (USGS) made similar maps, but they used "age" instead of "type" (of faults).
Comment: What have you tried so far?  If you don't want to use geological symbols, then the sky's the limit.  Faults are typically represented by different colour lines.  Just choose different colours based on type.  Do you have an example of what you'd like it to look like?  A google search on ["active faults map"](https://www.google.com.au/search?espv=2&biw=1920&bih=1115&tbm=isch&sa=1&q=active+faults+map&oq=active+faults+map&gs_l=img.3...0.0.0.25218.104.22.168.0.0.0.0.0..0.0....0...1c..64.img..0.0.0.l_kn8y4E2r8) yields a lot of different results.
Answer: Active faults are generally represented with a continuous line. You could use different colours for the active and inactive faults but the same linetype (e.g. continuous red line for active and continuous black line for inactive). Also fault extensions or possible faults are represented with a dashed line. In the case that you want to create a greyscale map and not a coloured one, using different linetypes is the only way. If you want to play by the book, you should use a linetype that symbolizes the hanging and foot walls of the fault (but since you do not need the geological information you can stick with the aforementioned).
Regarding the USGS symbology you mention, you could also group the faults by ages, since the inactive faults are characterised so based on the geological period they gave their last movement. If I remember correctly a fault is regarded as inactive if it was last active during the Neogene System.
Comment: thank you for your reply! i wanna make a coloured one and not a greyscale map.. one last question, what kind of colors you suggest me to put for the faults? i was thinking red (red shade)..
Comment: I would use mars or crimson red for the active faults and maybe amber for the inactive faults. It doesn't really matter. Just make sure to put a legend on your map that explains everything.


Jenkins does not display the current config

Question: I am currently figthing with Jenkins. I use Ubuntu Server 12.04 and installed from the official apt-repository (package jenkins). Everything went fine and I can access the GUI.
When I started to configure the system (e.g. /configure) I noticed that the system seems to not store the values I configured. I then checked the configfiles. It turned out that Jenkins is storing the correct config but is always displaying the default config.
I have checked the logfiles in /var/log/jenkins but did not find any hint.
I am thankfull for any help.
Take care,
Alex
As I am not allowed to answer my own question at the moment:
It seems as if I have solved the problem. What I did:
1. apt-get purge jenkins
2. Checked that everything is deleted
3. Add Jenkins Repository (http://pkg.jenkins-ci.org/debian-stable/)
4. apt-get update
5. apt-get install jenkins

I am not sure why but this solved my problem. It might be as well a distubring browser cache which prevented the GUI from updating...
Cheers, Alex
Answer: As answered by AlexWerz himself:
"It seems as if I have solved the problem.
What I did:
1. apt-get purge jenkins
2. Checked that everything is deleted
3. Add Jenkins Repository (http://pkg.jenkins-ci.org/debian-stable/)
4. apt-get update
5. apt-get install jenkins

I am not sure why but this solved my problem.
It might be as well a distubring browser cache which prevented the GUI from updating...
Cheers, Alex"


Accessibility question. Company has secondary brand color (orange) that doesn't pass any requirements. Only option change color?

Question: The company I work for uses dark blue as the main primary color and orange as the secondary color. They have used it for years. It doesn't pass any accessibility requirements. We can't go darker since it looks rust and again isn't the secondary brand orange. I suggested gold which works as a replacement. Has anyone ran into similar issues? Is there another way to approach this?
Answer: A color is never an impediment, but an opportunity for a good creative development
The answer is very simple

If the secondary color does not pass any of the accessibility requirements, do not use them in elements where those requirements are
essential.
If the company has these corporate colors and has used them for years, there is no impediment for it to continue doing so, unless a corporate image restructuring study requires it.

And a third question/answer, this is on a personal level:
Question: Is there any color that without having passed the accessibility requirements is prohibitive for corporate use?
Answer: no, absolutely all colors are functional, you just have to know how to use them.
Here are some examples of companies using orange as their corporate color:
ING, Nickelodeon, Fanta, Gulf Oil
Comment: These are good examples I can show stakeholders. Unfortunately it is up to them if they want to go 14 bold to keep the orange as is. These are useful. I came to this site with the issues already in place. Thank you for the links.
Comment: *"If the secondary color does not pass any of the accessibility requirements, do not use them in elements where those requirements are essential."*.  I would be cautious of that statement. While I like the suggestion of not using questionable color contrast on essential elements, that does not give you liberty to use low contrast on non-essential elements. Doing so can still cause WCAG failures which could potentially lead to an ADA lawsuit.
Comment: *"If the company has these corporate colors and has used them for years, there is no impediment for it to continue doing so."*  I'm not sure I understand that statement. If something has been used for years and has been inaccessible for years, it's ok to keep doing so? I don't think that's what you're saying.  That would be dangerous.
Comment: ... unless a corporate image restructuring study requires it. I don't think a DEV can freely change the corporate colors of a company just to fix accessibility issues.
Comment: Indeed, I wouldn't advise a dev or designer to change corporate colors. That's a much larger discussion. But that doesn't mean the existing corp colors passes accessibility regardless of how long they've been used.
Answer: The rule of thumb in this situation is to use the accessible dark blue color for the elements that need accessible contrast (like buttons) and use the orange for decoration. Your secondary buttons don't need to be orange just because it's your brand's secondary color; they can be white with the brand blue as an outline.
Your orange color could provide pops of color where you'd want to draw the eye. Like Danielillo said, it's an opportunity to be creative.
Comment: I agree. All I can do is make the suggestions. Thanks again. This all helped.
Comment: To be clear at Normal Text WCAG AA

Does 12px text bold at Foreground: #FFFFFF
Background: #F76300 pass AA small text or it has to be minimum of 14 bold?
pass 4:5:1
Comment: @Keano That would fail at 12px and pass at 14px.
Comment: I believe that would fail to no? I read here:https://webaim.org/articles/contrast/
 web pages 18 points maps to 24 pixels and 14 points to approximately 18.67 pixels.
Comment: Have you checked out https://webaim.org/resources/contrastchecker/ ? They define large text as 14px and bold.
Comment: Hi I did that's where the info came from. I thought it was 14px also but it is pt. They wrote "Large text is defined as 14 point (typically 18.66px) and bold or larger, or 18 point (typically 24px) or larger."
Answer: Do you have examples and specific RGB values for the orange?  Most shades of orange will pass accessibility contrast if used with black or dark colors.  For example, black text on an orange background for a button.  Depending on how dark the dark blue is, it might also pass.
Here are a few examples.
<button style="background-color: #F76300; color:black">foo</button>
<button style="background-color: #F76300; color:darkblue;">foo</button>
<button style="background-color: #F76300; color:white">foo</button>

The first one is black text (#000000) on an orange background (#F76300).  The minimum contrast required by WCAG is 4.5:1.  (14pt bold or 18pt normal can have a lower contrast of 3:1).
Foreground: #000000
Background: #F76300
The contrast ratio is: 6.7:1

The next one uses darkblue for the text (#00008B) and also passes the WCAG minimum.
Foreground: #00008B
Background: #F76300
The contrast ratio is: 4.9:1

The last one uses white text (#ffffff).  This does not pass WCAG for normal size text but does pass WCAG for "large" text (14pt bold or 18pt normal).
Foreground: #FFFFFF
Background: #F76300
The contrast ratio is: 3.1:1

The values of your specific dark blue and orange will have different contrast values but there's a good chance they'll be ok.
Comment: So, researching I see that 14pt bold or 18pt normal at 3.1 equals 24px and or 18px or bold. I thought it was pixels. too. What is small text considered at 4.5.1. I am researching and was thrown by the points.
Comment: Though this shows: https://a11y-guidelines.orange.com/en/articles/font-size-and-colors/
For standard texts:

size less than 24px: contrast of 4.5:1 minimum
size greater than or equal to 24px: contrast of 3:1 minimum
For bold texts:

size less than 18.5px: contrast of 4.5:1 minimum
size greater than or equal to 18.5px: contrast of 3:1 minimum
Comment: I'm not sure I follow your comments. The guideline for [WCAG 1.4.3 Contrast (Minimum)](https://www.w3.org/TR/WCAG21/#contrast-minimum) seems pretty clear. It says the text foreground and the page background must have a 4.5:1 (minimum) contrast **except** in a few cases. One of those cases is "Large Text" which is defined at https://www.w3.org/TR/WCAG21/#dfn-large-scale and which I refer to in my answer. Large text is **either** 14pt bold **or** 18pt normal (or larger, in either case). Apologies if I wasn't clear on that. Feel free to ask additional questions.


Are custom moderator flags really 1.5 months behind?

Question: I have a flag from Dec 25th of last year, that still hasn't been tended to. Maybe it's perhaps time to bring on some new moderators?
Comment: We do not need more moderators at this time. Flags are about 6 months behind, but these are low priority plagiarism flags that are not so easy to handle.
Comment: @Blue Lots of the plagiarised content is already *years* old. A few more months isn't going to hurt anything.
Comment: Huh. My custom flags typically are handled within 24 to 48 hours, but often in less time than that… no need to say who/what, but is your flag about something super complicated? Also, is it just one flag or do you have a bunch that have been pending for a while?
Comment: Related: [We need a dedicated plagiarism flag](https://meta.stackexchange.com/questions/381806/we-need-a-dedicated-plagiarism-flag)
Comment: @Blue plagiarism is notoriously slow to handle. Flags getting handled and *plagiarism flags* being handled are different average times.
Comment: idk @Dharman, telling me you've got flags 6 months behind doesn't exactly scream to me that moderators are on top of things. How does one deem these to be "low priority"? People coming into the site are viewing plagiarized content with no attribution while they're sitting in some queue for months waiting to be looked at.
Comment: @VLAZ how does that work? Do you have to choose yourself to go hunt after them?
Comment: @Gimby how raising plagiarism flags works or how handling them works? For raising - you do have to make a conscious effort. If you find a post that you suspect is plagiarised (and that's quite hard to even get a feeling for), you should probably investigate and cast a custom flag like "I think this is plagiarised from ". Or similar with your reasoning/evidence. How mods handle this, AFAIK, is that they would verify and also check other submissions by that user, as plagiarism is often enough not a singular occurrence. That follow-up check is what takes a long time.
Comment: I'm not familiar with that meme, @Gimby, but I am familiar with [this one](https://www.reddit.com/r/stackoverflow/comments/c6sw60/community_managers_explain_how_they_manage_stack/). To be fair, things have changed in the last 4 years: IPS has been added back to HNQ, and many/most of the beta sites have been graduated.
Comment: Just one flag regarding plagiarism.
Comment: I think it may be time for a system to help identify plagiarism and help escalate these posts to non-diamond moderators.
Comment: It's *long* past that time. I'm told it's being worked on, or at least evaluated by staff. As you implicitly concede, throwing more moderators at the problem is not the solution.
Comment: @CodyGray so many managers are doing the looking away meme right now.
Comment: @CodyGray that one is great :) If you type "looking away meme" (or "monkey looking away meme") into google images, you can't miss it.
Comment: Possible duplicate: [Custom mod flag for plagiarism still in queue after 2 months - necessity for new flag type?](https://meta.stackoverflow.com/questions/421312/custom-mod-flag-for-plagiarism-still-in-queue-after-2-months-necessity-for-new)
Answer: So the answer to your question is yes, but also no.
Stack Overflow gets an enormous amount of flags. We work very hard to handle these flags, but part of handling flags at this volume involves prioritising the things that require immediate attention over those things that can wait. Technically the oldest "in need of moderator intervention" flag is from Jul 19, 2022. However, this does not mean that we're "7 months behind" in flag handling; we've handled plenty of flags that were raised after that one.
A flag might spend more time pending for several reasons:

the flag is low priority (read: not something that requires immediate intervention), and/or
the flag requires a SME to evaluate, and/or
there have been a significant number of higher priority flags raised in the interim, and/or
the flag will take a significant amount of moderator effort to handle, and/or
we're waiting for a follow up from staff, and/or
we've notified the user and are waiting for a response from them, and/or
we've started the process (e.g. redaction) and are waiting for it to complete, and/or
...any number of other reasons.

That's the thing that's different about "in need of moderator intervention" flags, they can be about anything that requires a moderator. As opposed to a standard flag, like "Not an answer," which is localised to a single post, a single mod flag can involve looking through hundreds of posts or user accounts. For this reason, any flags that involve an investigation are more likely to spend time pending until a moderator can adequately handle the concern.
In this particular case, your flag hits several of the reasons why a flag might spend more time pending:

Your flag raises an issue on a post that had been live on the site for over 5 years at the time of flagging; it's probably going to be OK letting it stay on the site for a bit longer.
This issue will require investigation of a user who has dozens of answers.
Your flag (raised on December 25, 2022) was raised during a time when we were being swamped by a significant volume of ChatGPT answers which resulted in a significant number of flags. These flags were also given higher priority because the longer it took to handle them the more content that was dumped onto the site.

So, while the issue you raised is something that will need to be handled (and will be handled eventually) it's not something that is likely to be handled quickly.
As for needing more moderators, we are making significant progress with the flags in the queue. In November, prior to the most recent election, the flag queue contained well over 2000 flags; with the inclusion of the 3 new moderators, we're now down to under 400 flags and that number is continuing to trend downward.
Comment: Thanks for your response. I think I just saw my most recent flag, and was kinda discouraged seeing as how my other flag was in queue for so long. It's a bit frustrating when someone copies your work word for word and posts it as their own.


PublicKey/Pem file Authentication for SSH in Pantheon Files

Question: Is it possible to connect to ssh server using pantheon-files with public key or .pem file, i really need this integration.
The GUI now only show server, surname and password field i cant see a way to select a ssh key
Answer: You should submit an "wishlist" issue on Github about this ( at https://github.com/elementary/files/issues). This is not something that is currently implemented within Files.
Answer: You could try like this:

Set your config file in ~/.ssh
Define your host as follows:
Host some.mydomain.com
  HostName mydomain.com
  Port 22
  User myuser
  IdentityFile ~/.ssh/my_id_rsa

Next, in Pantheon Files just set your SSH host as some.mydomain.com with no username and password.
Connect and have fun.
Answer: It actually works if you use the default id file (~/.ssh/id_rsa). You need to enter the server name like user@host and leave user name and password fields blank. Then, there comes a pop-up asking you to enter the id file password and all works.


Mosaico Extension Disabled in CiviSpark Pro

Question: I just set up CiviCRM Spark Pro, which says that it comes with Mosaico. However, when I go to create a new mailing, the option is not there. When I go to Administer > Settings > Extensions, Mosaico is listed as disabled. How do I enable it? If I click update, I'm only given the option to cancel, not to update.
Answer: Welcome to SE!  For Spark issues, you may find the spark channel on https://chat.civicrm.org is more responsive.


What solder specs are safe to use when soldering wires to an Mk2a heat bed?

Question: I've already asked which wires I should use, and I believe I have that covered now, but I was also wondering what solder / specs on the solder are considered safe when attaching my wires to my heat bed.  I have some solder here at the house, it's quite new (never been opened) it's Radio Shack 64-008 E 60/40 Standard Rosin-Core with 0.062 diameter...
Answer: Old-style lead/tin solder has a melting range of about 180 to 250 degrees (the transition solid to liquid is spread out). This ought to be fine for the bed (even at the hottest hotspot) but wouldn't be good in the hotend.
Modern electronics lead-free solder varies since there are several different compositions, but is typically a bit higher in melting point (by some 10s of degrees).
Special high melting point solder transitions around 300C, but you would only need to use this in very specific scenarios.
Answer: That solder sounds like it should be fine.
Any solder should work, the only difference you might find is some of the older solder will include lead. if you were overly concerned about safety you might want to check your solder doesn't contain lead. However, for the amount you are doing, even a solder that contains lead isn't going to be an issue.
Comment: Lead-free solder has some pretty significant disadvantages. It's much harder to work with, and over time may form "whiskers". On the other hand, lead is pretty darn bad for you.


Conditions for forming a stationary wave?

Question: Does it only require two waves of the same frequency / wavelength travelling in opposite directions? My teacher says that one wave needs to be reflected and then superimpose with this reflection for a stationary wave to form. Also, aren't stationary waves only formed at resonant frequencies?
Answer: All a "perfect" reflection does for you is to guarantee a wave which is travelling in the opposite direction to the incident wave and also having the same frequency/wavelength and amplitude (which you missed) as the incident wave.
Even if the reflector is not perfect there will be variations in amplitude at different positions but there will be no positions of zero amplitude.
The idea of resonant frequencies crops up with waves which are bounded and the amplitudes of the standing wave of particular wavelengths (frequencies) which are produced are large.
At the boundaries certain conditions have to be satisfied eg node at the end of a clamped vibrating string, displacement node (pressure antinode) at the closed end of a tube and displacement antinode (pressure node) near the end of the open end of a tube, . . . . etc.
So you have to ensure that the standing wave "fits into" these boundary conditions which in turn means that the wavelength (frequency) of the wave can only have certain values.
The losses of energy at the reflecting surfaces and elsewhere can be made up by the energy supplied by a driver eg a bow, musician blowing air, etc and this will maintain the standing wave.
Comment: Thank you for your answer. But you say that resonant frequencies are only related to waves which are bounded, but they are also used if we have a medium with two open ends ( which I assume is unbounded ). Also, a reflection makes the wave undergo a 180 degree phase shift at the point of contact, which is generally not the case with 2 waves travelling in opposite directions with the same freq/wavelength/amplitude.

Lastly, in general, resonance is associated with increasing amplitudes, but in this case, the amplitudes are constant, are they not?
Comment: An open end is a constraint and hence I consider that as a boundary condition.  The reversal of phase corresponds to a node. For a given driver amplitude the response of the system (amplitude) is a maximum at resonance.
Comment: I see... so in general, we will always have a stationary wave if two waves are travelling in opposite directions with the same parameters, but if they are in a bounded medium, then resonance comes into play?
I'm not clear about resonance.. if we push a swing at the resonant frequency, then the amplitude approaches infinity, not merely a high value.
Comment: There is usually a frictional force acting.
Comment: Hold on. When you say "reflected wave", how does it necessarily indicate that it's the same wave, but just travelling in the opposite direction? For instance, if you have a rigid boundary causing reflection, the equation of the reflected wave would be asin(kx-wt+ pi) and not asin(kx+wt) if the incident wave is asin(kx-wt) .
Comment: It will be a reflected wave travelling in the opposite direction with the same amplitude and wavelength/frequency.
Answer: two progressive wave of same amplitude and freqency moving in opposite direction superimposed at a point


Best way to determine power consumption of a microcontroller

Question: What is the best way to determine the power consumption of a microcontroller? Need to select the right voltage regulator to supply 3.3V for PIC32MX795F512H.
Answer: Microcontroller current consumption is dependent on the software so if you actually want to know it, you need your software first.
But if you just want to size a regulator then the current consumption for various clock speeds and generalized configurations should be listed somewhere in the datasheet under electrical specifications.
In this case, it is on table 31-5:
Comment: Well, that would be one item to consider when sizing the regulator. But I would also assume that the MCU isn't the only thing powered by it. The OP has left a great deal out of the question, sadly.
Comment: @jonk True. But the OP asked for the MCU so I answered for the MCU. As long as he can add and repeat the process of finding current consumption for other components in datasheets, he should be fine.
Comment: Yup. Rinse and repeat, I suppose. I am mostly pointing out that the OP didn't say enough to allow anyone to provide useful help. Too much is left unsaid.
Answer: There are standard power estimation tool boxes from MCU vendors (ST has STM Cube MX). You can find one for your microcontroller from MCU websites. I would say it is better to start with those tools to get a fair idea in least amount of time.
The current consumption depends on
 the clock frequency you operate at. Type of instructions that is being executed, the mode of operation (active, low power,sleep etc), the external loads attached such as sensors or LEDs, number of peripherals enabled (ADC, UART, WDT, Timers, Comparators, Opamps, ECC, etc).
The current consumption also varies depending on the operating temperature and schedule of the tasks.
So, estimating the MCU power consumption takes a decent amount of time, software knowledge and operating conditions.
If the regulator is only supplying the MCU then, you can choose the one which can supply the 120% theoretically estimated maximum current.
Choosing a slightly higher capacity LDO won't harm if you have advantage of reusing the existing LDO or in terms of leakage current.


Command Line Tool to Batch Convert .EML/.EMLX/.MBOX to Searchable PDFs?

Question: I need to convert about 500k emails into searchable PDFs. By 'searchable' I mean that macOS will be able to scan them for specific words rather than simply treating them as an image. My searches, thus far, for a tool to do this have ended in proprietary database apps and over-priced sketchball x-to-pdf converters which basically perform the built-in macOS functionality of Print To PDF. Is there a single tool or two complementary tools that could be used together in Terminal to just batch convert all the emails to searchable PDFs?
Comment: Mac Mail lets you export either one message at a time, individually, which is not feasible for this quantity of documents, or by merging a folder of emails into one pdf, which is also not desired. The add-on that allowed Thunderbird to batch export individual emails as pdfs has broken, according to user reviews. I haven't used Outlook in years, but would prefer to not convert all the messages an additional time to be readable by Outlook. Also, Date Created Metadata is important to conserve for this scenario.
Comment: are those all Windows emails
Comment: No, they are not. Some of them are very old Outlook for Mac and Thunderbird files. The majority are Mac Mail files spanning from about 1995 to today.
Comment: just asking, since Thunderbird lets you export as PDF, so does Outlook, so does mac Mail.
Comment: I just tried in Mac Mail and selected 50 email and exported them all at once as individual pdf's
Comment: where do you have the .EML and .EMLX files anyway ? on your hard drive ?
Comment: Well, that's good and surprising news! I'll give it a try. All the mail & related database files, old and newer, are on an 8TB drive thunderbolted to my Mac Mini. I think I may have wrecked some of them a year or so ago with an ill-advised rmlint command and I may find that I need to try to dig up copies of some of those zerokb mboxes from other old drives, but I think *almost* everything is ready & available.
Answer: I had to do this with ~180 emails, and I used a command tool I found on GitHub that converts .eml to .pdf via .html: https://github.com/nickrussler/eml-to-pdf-converter
It takes a little while to convert each .eml file - 22 minutes for 186 emails with lots of images - so it's probably not helpful for a 500k email task. (Maybe if you're reeeally not in a rush and not afraid of multiprocessing!) If it is helpful for you or anyone else, though, here's how I got it to work in the bash command line:

git clone the repo
Install the wkhtmltopdf tool from binary (installing with pip is insufficient) from here: https://wkhtmltopdf.org/downloads.html
From within the cloned repo, generate the email converter .jar file: ./gradlew shadowJar
Run for loop to convert every file in the .mbox (or a directory of .eml):

for file in /path/to/mailbox.mbox/*;
do
   java -jar ./build/libs/emailconverter-2.0.1-all.jar "$file";
done

Comment: Very useful, thanks! On macOS, a simple `brew install wkhtmltopdf` worked perfectly
Answer: I recently came across How to open eml files? on AskUbuntu.
It suggests using munpack, which is part of mpack. It can convert an eml to html or plain txt. There are several tools to convert html to a pdf. WeasyPrint is one of them. You can install it via pip.
mpack is also available in Homebrew. Assuming you have Homebrew installed, it's easily installed via:
brew install mpack

Then run
munpack -t <my.eml>

Comment: Nice find. Might be worth adding at least one way on how to get from HTML/TXT to PDF from the commandline.
Comment: Fair point. I added a tool. It will all require a little bit of scripting. But with these building blocks it should be doable.


This deformations appeared in this 3D round model that I'm trying to create

Question: After creating a 3D sphere, and stretching it out. I also created spaces with the boolean method for the wheels using other round shapes. Immediately after creating these spaces, these deformations started to appear. What should I do?
If possible, I would like to receive a simpler explanation, since I'm still a beginner. But if its not possible, it would still be very much appreciated if you help me.
Answer: You are probably using the "Subdivision modifier" applied to the car mesh.
You should learn how to control this modifier (it's one of the most complex things in 3d software). Here some basic info: https://docs.blender.org/manual/en/latest/modeling/modifiers/generate/subdivision_surface.html#control
The easiest way to go on with your work is to disable the subdivision modifier and work in a "low poly / flat / shade flat" way.
Once you mastered basic modeling, you can try experimenting also the "subdivision" things (here one of many tutorials you'll find on youtube: https://www.youtube.com/watch?v=xmIIIcCUm8E)
Comment: I will look into this better. Thank you for the explanation!


Multiple fission and spore formation

Question:
I came across this question today. In the B diagram, zoospores of chlamydomonas is given. Now my doubt is, are the zoospores formed by multiple fission or spore formation? If it is by spore formation, isn't spore formation and multiple fission the same thing when it comes to unicellular organism i.e chlamydomonas? If it is the same thing, why isn't option c correct in the question I attached?
Comment: I will answer later, so I can provide a good ref. The issue is whether this shows the result after fission (asexual)  or meiosis (sexual). Showing 9 daughter cells is a bit unfair..2,4,8,16 would be better. After meiosis the 4 daughter cells can also continue to divide by mitosis before release.
Comment: But zoospores are produced asexually, so meiosis isn't possible. Also is multiple fission produced by mitosis or amitosis?
Answer: All the organisms shown in the figure reproduce asexually. (A) is Penicillium in which non-motile conidia are produced singly or in chains. Organism (B) is Chlamydomonas in which reproduction occurs by zoospores. In Hydra (C) and yeast (D), asexual reproduction takes place by budding.
Mutliple fission and Spore Formation are two distinct processes where in:

Multiple fission can be explained with the following diagram:

Multiple fission is a process of asexual reproduction in which a single organism splits up into multiple organisms or daughter cells of similar type under favourable conditions like availibity of food and suitable environmental conditions.

Spore formation can be explained with the following diagram:

Spores are tiny microscopic hard unicellular sexual bodies which are always suspended in air. Under suitable environmental conditions they settle down and grow into new plants. Above given is a structure of rhizopus(bread mould) reproducing through the process of spore formation. Each rhizopus consists of a globular structure at the top known as the sporangium which consists of spores. When the favourable conditions arrive then the sporangium bursts and the spores get suspended in the air. Soon they settle on the moist bread particles, leading to the formation of new rhizopus plants.

Multiple fission and spore formation


Why is Stack Exchange run by the community?

Question: I've been told everywhere (including the help center!) about the fact that Stack Exchange is run by the community. Why is this?
Comment: I'm curious what the phrase means to you. I happen to think it's clearly the best way to operate but maybe we understand it to mean different things.
Comment: Actually, we'd be even better off if we could, say, fix the Triage queue Requires Editing help text ourselves instead of being dependent on the company to care about Triage again.
Comment: @JeffreyBosboom Funny how that Triage queue Required Editing thing keeps coming up. Shameless plug: https://meta.stackoverflow.com/questions/321895/change-triage-guidelines-for-requires-editing/
Answer: Well... Who else would run it?
The staff is pretty small, so expecting them to do everything on all ~170 different sites would be a big ask. Alternately expecting them to increase the staff so that they could have enough people on staff to do it would be extremely expensive. There are over 500 volunteer moderators on the network, moderating between one and seven sites each. While they're obviously not full-time, replacing them would require a good number of staff.
But that's only a very minor part. Most of the actual "running" of a site is done by normal users like you... Users who have attained privileges due to the reputation they have earned by asking and answering questions.
That's millions of people who are editing, closing, deleting, flagging... and many other tasks involved with "running" the sites.
It'd be impossible to do it any other way and still have the same level of quality that we have now. And the users seem to like that degree of control. We enjoy being able to help improve our communities and being self-sufficient is a reward. It grants a feeling of ownership and community that just answering or asking and voting would create. This is good!
Comment: Well, _I'm growing_. Not sure that helps run the sites much, however.
Comment: Well, I suppose it makes your actions *more weighty*
Comment: What numbers? The number users - absolutely - of sites - yes... slowly. And with them, moderators. The staff, not so much.
Comment: and aren't those number still growing?
Answer: Stack Exchange is run by Stack Exchange Inc in the USA. But they give a significant freedom of your votes and a relatively lenient moderation mechanism.
The system is clearly tuned to motivate you to contribute as much good content as you can. In exchange, you have an above average protection from the flood of crap everywhere on the Internet, and from the individual childish power misuses of the "good old boys" of their sites.
The important thing is: they are mainly using their voting system to reach these goals by statistics and professional community control. In this sense, yes Stack Exchange is run by the community.


Tools to help me write SOPs for graduate school

Question: I am in the process of applying to several graduate school, so I need to write several Statements of Purpose (SOP). English is not my first language and my writing skills are average at best. Are there any tools online that could help me improve my writing either by suggesting alternative words/phrase or correct my grammar? Ones I have found so far that looks good is Grammarly. Would you recommend the premium version or are there an alternative that works better?
Comment: I expanded SOP because it also stands for Standard Operating Procedure.
Answer: If you use Grammarly, take it with a grain of salt. Software can be useful, but it is by no means a replacement for a human eye trained to read a language. Reviews of Grammarly tend to not be very favorable.
If you must use software, either Grammarly or LanguageTool will work.
You say you're applying to graduate school. Did you go to undergrad in an English-speaking school? If so, see if you have a writing center of some sort available to you. They will be able to go over your statement of purpose, and give it a more thorough critique.
Answer: I would recommend you to hire the proofread service, or exchanging language with native friend. Human are far better than machines, at least now.


How can iPhone Nibs be Unit Tested using Logical Tests?

Question: Unit Testing View Controllers seems to be very important part of iPhone Development (see this Article). This, however, requires initializing the Controllers from a Nib, which I found impossible to do properly in a logical test.
Loading Resources from a Bundle (see this Question) in a logical test works fine. Even loading Nibs is possible like this:
<code>    UntitledViewController* controller = [[UntitledViewController alloc]initWithNibName:nil bundle:[NSBundle bundleForClass:[self class]]];
</code>
. It, however, only works as long as the nib only containts UIViews. Other views (I tried UITableView and UISwitch) result in otest failing with code 138.
Is it possible to test my Nibs using logical tests, and if so, how?
Answer: It depends on what you're trying to test. If you want to verify that your bindings are set up correctly, read Chris Hanson's article on unit testing your Cocoa interface. I personally think this is overkill, and leads to a proliferation of test code that's not very useful. But that's just my 2 cents.
If you actually try to interact with those interface elements in your test, you'll eventaully run into lots of otest errors, as you've found, particularly with UIActionSheets and UITableViews.
But your goal should be to unit test your controller's behavior, not the behavior of apple's UI objects. What I've found works best is to use OCMock to mock the UI elements and verify that the controller makes the expected calls on them. Here are a couple of examples:
<code>  -(void)testClickingAButtonHidesAView {
     //setup
     id mockViewToHide = [OCMockObject mockForClass:[UIView class]];
     [[mockViewToHide expect] setHidden:YES];
     [controller setSomeView:mockViewToHide];

     // hideButtonClicked is an IBAction that is the hide button's target
     [controller hideButtonClicked];
     [mockViewToHide verify];
  }

  -(void)testActionSheetPublishClick {
     // ModelManager is the controller's dependency, which publishes Items
     id mockModelManager = [OCMockObject mockForClass:[ModelManager class]];
     [controller setModelManager:mockModelManager];

     // this doesn't really need to be mocked, but it's a convenient way to create
     // a reference you can validate in expect:
     id mockItem = [OCMockObject mockForClass:[Item class]];
     [controller setCurrentItem:mockItem];

     // when the user clicks "Publish" (the first button on the action sheet),
     // the controller should publish the current item
     [[mockModelManager expect] publishItem:mockItem];

     // stub object so I know which action sheet was clicked
     id mockPublishActionSheet = [OCMockObject mockForClass:[UIActionSheet class]];
     [controller setPublishConfirmation:mockPublishActionSheet];

     // simulate action sheet click
     [controller actionSheet:mockPublishActionSheet didDismissWithButtonIndex:0];

     [mockModelManager verify];
  }
</code>
Answer: Use application tests instead and drive/inspect your UI on the device.


Why, if I bind to an NSPathControl, is it grayed out?

Question: I have bound the value of an NSPathControl through a value transformer that converts strings to URLs to my model (a NSMutableArray of NSMutableDictionaries). I have the control's target/action set up.
With the binding in place the control works, showing the path from my model as my table selection is changed. However, it is grayed out and does not accept clicks. Why is this?
If I explicitly set the path control to enabled to YES in code, it makes no difference.
If I remove the binding, it shows whatever path I give it in IB, it is not grayed out, and clicks are accepted and run my action.
I am not using the Enabled binding of the path control. Should I be?
I'm using Xcode 4 and 10.6.
Answer: The answer turned out to be that Conditionally Sets Enabled was turned on (the default). Turning that off appears to have fixed it. Chalk another one up for bindings opacity.


How to fit the size of a font to fit a PDF fillable box

Question: More of a pdf editing question.
A lot of PDF forms restrict you to put 1 letter in each box when filling them
Something like this:

Has anyone found a way to fill these forms via computer ? Very hard to try to change the font size to fit these
Answer: I wasn't aware of that, but apparently Adobe Acrobat reader (free) has this feature and it works amazingly well.
Open the document, then click "Fill and Sign" and hover over the boxed input element, it will fill it automatically within the borders


How to get music back in Undertale

Question: So I completed Undertale a few days ago and whenever I load the game, the ending music plays (reunited) but when I see people go back and play it, the normal music for each area plays. Am I being stupid? How do you fix it? I want to know because I want to find secrets, mess around etc but I want the normal music back. Thanks!
Comment: So you can play the game like normal, walking around, bossfights, dialog, etc., but the "Reunited" track plays the entire time instead of the different other tracks?
Comment: Just to be sure: how did you complete Undertale? And how did *they* complete Undertale?
Comment: Fabian Roling- yes. I completed the game pacifist route and then when I reopened the game Flowey had his little speech about resets then I pressed continue but all the music is 'reunited'.                                                       Zeta- I believe we both played the pacifist route
Comment: https://youtu.be/xXBP3DFBX3Y This is the video I'm referring to. We both did the pacifist run but I don't understand how he gets normal music and I don't
Answer: The OP has linked the following video in the comments to describe what they are talking about:

Observe that at 2:32, and again at 6:25, Sans can be seen. But at the end of the game, Sans hangs out with the others right next to the exit, and can't be found anywhere else. Therefore, the YouTuber did a true reset.
In general, it is not possible to prevent "Reunited" from playing throughout the game's areas after defeating the True Pacifist final boss, unless you reset the game. Normally, the option to do this is labeled "true reset" (and Flowey will give you an earful about not using it the first time you reopen the game). A true reset erases almost everything, with a small number of exceptions, including the following:

True reset will not undo the effects of the Genocide route, because there is no in-game way to undo that.
The secret door (see video above) is never resealed once opened.

In particular, a true reset will erase Flowey's memory, allow you to choose a new name (or re-enter the same name, if you prefer), and prevent any character from experiencing déjà vu as they do in a regular reset. For most practical purposes, it's equivalent to starting the game for the first time.
If you reset after defeating the True Pacifist boss, but before completing the game by exiting the Underground, then it will be a "regular" reset instead of a "true reset." This option is lost once you complete the game, as "true reset" replaces "reset." Like the true reset, a regular reset will prevent "Reunited" from playing everywhere.
(Curiously, Flowey is a bit confused in the "regular reset after final boss" scenario, and advises Frisk to "make friends with everyone this time." He seems entirely unaware of the final boss battle, which suggests this possibility is a bug rather than an intentional design decision.)

How to get music back in Undertale