I inserted a two-pin header (P1) into this circuit using EasyEDA.  Does the square outline mean that is the positive pin, or is there another meaning?
I have a PCB with documentation. In the documentation, there is referred to specific pins of several jumpers and connectors. On the PCB however, there isn't a label or so for which pin has what number. I need to figure out which pin has which number, so that I know the function of each physical pin.  I noticed all connectors have all pins with a rounded tin pad, whilst one pin (either the first or the last when counting from right to left) has a square tin pad:     Is it some kind of convention which number this pin has? After that, how to count the other pins?
Under the U.S.'s Copyright Law, is it an act of copyright infringement if we changed the color of another artist's image to black and white? I just dropped my Vaporeon off at the gym, but to my surprise, he can still be viewed in my Pokémon list! The buttons are there to level him up, but I'm not gonna be able to get any Eevee candy for a few hours to try. Can I level him up while he's in the gym? Does there exists an Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.  Attempt In my opinion It does not exists.  If there exists such an isomorphism say $\phi :\mathbb{C}^* \to \mathbb{C}$ then, from the fact that Isomorphism takes identity to identity we have $$\phi \left( 1 \right)=0$$  From the fact      Given $\phi:G \to H$ be an isomorphism, then For a fixed integer $k$ and a fixed group element $b$ in $G$, the   equation $x^k=b$ has the same number of solutions in $G$ as does   the equation $x^k=\phi\left(b\right)$ in $H$.   We have $x^4=1$ and $x^4=0$ must have same number of solutions, but the solutions to these equations are 4 and 1 only. How can I recover from deleting the /usr/share/themes directory? Which of $\{J_0,J_1,J_2\}$ and $\{J_0,J_+,J_-\}$ is a generator for the Lie algebra $\mathfrak{su}(2)$? I have just started learning about Lie algebra in the context of quantum mechanics and got confused with this: Some sources say the generators are $J_0,J_1$ and $J_2$ and some use $J_0,J_+$ and $J_−$. Which set is correct? Or if both are correct what key concept am I missing here? My understanding is that if have certain commutation relations then we know that Lie Algebra is such and such. But if we have two such choices then this understanding falls apart? How do I figure out what is $\mathfrak{su}(2)$ Lie Algebra in general? Hat duplicates when info is expanded It seems like there is a bug that is causing a duplicate hat to appear when I expand info, like pressing &quot;(more)&quot; on a suggested edit. This bug does not seem to be specific to the suggested edits review queue though, as others have reported seeing this bug in other places, like code snippet expansion. Steps to repro:  Put on a hat. Navigate to one of your own suggested edits. (You can just also open the Suggested Edits review queue and go to a random suggestion, but there is no guarantee any of those users will be wearing a hat.) Click the &quot;(more)&quot; button to expand the top box.  What should happen: Hat should shift down with the rest of the content. What happens: All the content shifts down, but a duplicate hat remains in the initial place. Before expansion:  After expansion with duplicate hat: Questions on "All Horse are the Same Color" Proof by Complete Induction I'm bugged by the following that's summarized on p. 109 of .     False theorem: All horses are the same color.      Proof by induction:      $\fbox{$P(n)$ is the statement: In every set of horses of size $n$, all $n$ horses are the same color.}$   $\fbox{Base Case or $P(1)$:}$ One horse is the same color as itself. This is true by inspection.   $\fbox{Induction Step:}$ Assume $P(k)$ for some $k \geq 1$.   $\fbox{Proof of $P(k + 1) :$}$   Since $\{H_1, H_2, ... , H_n\}$ is a set of $n$ horses, the induction hypothesis applies to this set. Thus, all the horses in this set are the same color.   Since $\{H_2, H_3, ... , H_{n+1}\}$ is also a set of $n$ horses, the induction step likewise holds for this set. Thus, all the horses in this set are the same color too.         Therefore, all $n +1$ horses in $\{H_1, H_2, H_3, ... , H_n , H_{n+1}\}$ are the same color. QED.   The issue the instructor was trying to point out is clearly valid. For the case $n = 1$, there is only ${H_1}$. So this case says nothing about possible overlapping elements of each set of $(n + 1)$, for instance $H_2$ in the above proof.    But it was proposed in the class discussion that this was the only problem. Had you been able to prove $P(2)$ true, then a proof of the above format would have been fine.    My interpretation is that yes, you could prove all horses are the same color, if you can prove that any set of two horses will be the same color. But this format would not work.  Why not? The problem I see is that the above proof is for the existence of at least one particular pair of sets of horses of sizes $n$ and $n + 1$, such that in each set, all horses are the same color.  Particularly when the set of size $n$ is a subset of the set of size $n + 1$.  In order to prove the induction step, don't you need to prove that sets of sizes $n$ and $n + 1$, do not necessarily contain the same, overlapping elements?  You could prove that any horse can be added to a set of 2 horses.  Take the last two, and they must be the same color, and so on.  Wwhatever color the first two happen to be, all other horses must thus be the same color.    Am I misinterpreting the example, or am I making a logical error? Thanks in advance. Lately, I've seen many search results in the form of https://stackoverflow.com/q/&lt;id&gt; and /a/&lt;id&gt; on Google. Why do I see these slug-less permalinks instead of the full URL?  For instance, a search for  gives  instead of :        For the record, it seems that Google has indexed  and . Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura Let $I$ and $J$ be ideals of a Noetherian ring $A$. If $JA_P\subseteq IA_P$ for every $P\in \operatorname{Ass}_A(A/I)$, then $J\subseteq I$.   I'm reading Matsumura's Commutative Ring Theory book on my own. This is exercise $6.4$ in that book, and I fail to prove it. Could you help me with this? Thanks in advance. When does a flying creature start and end falling? Situation:  Alice the Aarakokra sees Bob the Battlemaster coming. She ascends to 605', just out of the 600' range of Bob's longbow.  Bob (Str 14) performs a running high jump 5' into the air and successfully hits Alice with his longbow, despite firing at disadvantage for long range. He spends one of his maneuver dice to perform the Trip Attack maneuver, and succeeds on the contested roll to knock Alice prone.  Alice is now flying and prone, so she falls. Falling does 1d6 bludgeoning damage per 10' fallen, to a maximum of 20d6.  Questions:   When does Alice start falling? It is on Bob's turn as soon as she's knocked prone, or some time else such as the beginning of her own next turn? When does Alice hit the ground? On Bob's turn as soon as she's knocked prone, or some time else?   These answers determine whether anyone can save Alice from her 20d6 of certain doom.   Is a reaction (e.g. casting Feather Fall) on Bob's turn the only hope? Can Alice's ally Charlie swoop in on his subsequent turn within the same round to catch her? Can Alice spend half her movement on her next turn to "stand from prone" and pull out of her involuntary dive? If Alice had expected to be shot down, could she have spent an action to be Ready to "stand from prone" while moving through Bob's airspace? Elliptical orbits of planets As we know, the velocity of the planet changes as it orbits around the sun, both in its magnitude and direction. The centripetal acceleration causes the change in the direction of velocity but I want to know what is the tangential force that acts on the planet to change the velocity by its $magnitude$. The answer normally as to why the speed changes is: If  the  force  that  the  Sun  exerts  on  the  planet increases  (as  the  planet moves closer),  then  the acceleration   of  the  planet must  increase,  resulting  in a  higher  orbital  speed,  and vice  versa. But this force is not along the body but towards the sun. So such a force should only change its direction. Why can't I seem to grasp interfaces? Could someone please demystify interfaces for me or point me to some good examples? I keep seeing interfaces popup here and there, but I haven't ever really been exposed to good explanations of interfaces or when to use them.  I am talking about interfaces in a context of interfaces vs. abstract classes. How do I clone a generic list in C#? Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers How would I show the following.  For all odd integers a,b, and c if z is a solution of $ax^2+bx+c=0$ the z is not rational.  How would I show this? This is what I did  Let a be an odd integer then for a integer k it has the form $a=2k+1$  then $b=2t+1$ for if c integer.  then $c=2r+1$ if s is an integer then I do  $(2k+1)(x)^2+2t+1(x)+(2r+1)=0$  But I find my self stuck on what to do any hint are appreciated. I can show this best by a picture:    This cross also shows when I export it as raster or pdf. What is it and how can I get rid of it?  I am using Qgis 2.4 and the map was done with the help of the Grass plugin AniMove on Linux Mint. Few days ago I got sample of toroidal core from my friend. I don't know any technical details of core just know OD-10cm, ID-6cm, height- 5cm and wet about 1.845 kg(M4 grade CRGO). I want to make toroidal transformer using this core but how to calculate core area and maximum VA capacity of core.I take some photos and attach. Short story from many years ago: the ancient, brilliant, cruel race was Earthlings I'm attempting to modify the Table of Contents in my document. Currently, chapter one in my document is listed as   1   Introduction   What I would like to see is  Chapter 1   Introduction   Seems like an easy enough thing to ask for, but can't seem to find a good way to do this. Any feedback would be most appreciative. What Wording Did Witches and Wizards in Other Cultures Use for Spells? Windows 7 "Waiting for background program to close" I am using Windows 7 Home Premium. When I shut down my computer why does the screen show this:    Before shutting down I'm close all programs.