I know it is defined as $ dP \wedge dx  $ or explicitly,  $$ \frac{\partial P }{\partial y } dy \wedge dx   . $$  The question is, could it be $dx \wedge d P $?  Or  $$  \frac{\partial P }{\partial y }  dx \wedge dy ?    $$
I know it is defined as $ dP \wedge dx  $ or explicitly,  $$ \frac{\partial P }{\partial y } dy \wedge dx   . $$  The question is, could it be $dx \wedge d P $?  Or  $$  \frac{\partial P }{\partial y }  dx \wedge dy ?    $$  I know the question must be very naive or even stupid. But I am indeed confused.
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative. to infinitive as direct object?! (as in : I promised to get there in time.) I'm a passionate Korean English-learner, and I would like to ask you a question about grammar.   It was 3 years ago when I first started to study the to-infinitive as studying grammar with Grammar In Use series and English Grammar series by Longman, having been exposed to English for 3 years. There wasn't any mention of the author saying that the usage of the to-infinitive is as an (direct) object. And for me also, the times I have encountered sentences in which the usage of the to-infinitive, so to speak, as direct objects were used, I've read them as some kind of obligatory adverbial that shows what the verbs are about, not as objects, which means they are noun phases! 100% of Korean textbooks say the usage is as a direct object, but I doubt it. I think it's some kind of obligatory adverbial that shows what the verbs are about.    I thought it was better for me to ask Americans themselves. Do you read this usage of to-infinitive as a noun phrase or an adverbial? Requesting review of technically inaccurate answers verbatiminput and fontsize How can I change media volume when no media is being played? Sometimes I want to play games in (near) silence, and don't like the background music to disturb people. If I use the volume buttons, the ringtone volume is changed instead of media volume. When I'm already in the game, the volume buttons do change the volume of background music, but it's kinda too late.  Is there a way for me to change the media volume to a level I like, from the home screen, before starting apps/games? When is the past perfect exactly needed? I have never had this problem before. But after seeing some questions posted on ELU, I started to doubt. I have been through links1, pages of grammar books2, a lot of questions3 posted here and ELU. I now still can't seem to understand how the past perfect is exactly used. The references sometimes even contradict each other.  What I had understood so far was      The past perfect is not necessary if we are not 'going back' to the earlier past, and simply moving from one event to another.   but I then saw a lot of other 'rules' including      If the sequence is clear, the past perfect is not needed.   which is slightly different, less 'narrow' and can be applied in more situations than the first ruleA, and      The past perfect is optional only when talking about an action at a specific time.   This is confusing. Can anyone here clarify things out please?    A For example, for  Doing the survey [completed] -&gt; Showing the result      We showed the result of the survey we did.      If the second rule is applied, the sentence above is fine (the sequence is clear), but not if the first rule since we are not moving from any event to the next and possibly even going back.    1  and   2 Practical English Usage (2005) by Michael Swan, Collins Cobuild Student's Grammar (1991). Upper-Intermediate Cutting Edge.  3 including , , ,  etc. Stripping seasoning from cast iron After reading , I want to try to re-season a skillet with flaxseed oil; I'm fairly certain I did a terrible job when I seasoned the skillet several years ago. Is it possible to do this with steel wool or vinegar? (I don't have a self-cleaning oven, so that method is out.) My Minecraft app now only has the option of "play" and there is no "play on realms" to be found!  I downloaded - and paid for - the multiplayer app, but there doesn't seem to be a way to get to any realms on that app either. Cookie blocked/not saved in IFRAME in Internet Explorer I have two websites, let's say they're example.com and anotherexample.net. On anotherexample.net/page.html, I have an IFRAME SRC="http://example.com/someform.asp". That IFRAME displays a form for the user to fill out and submit to http://example.com/process.asp. When I open the form ("someform.asp") in its own browser window, all works well. However, when I load someform.asp as an IFRAME in IE 6 or IE 7, the cookies for example.com are not saved. In Firefox this problem doesn't appear.  For testing purposes, I've created a similar setup on  .  example.com uses cookie-based sessions (and there's nothing I can do about that), so without cookies, process.asp won't execute. How do I force IE to save those cookies?  Results of sniffing the HTTP traffic: on GET /someform.asp response, there's a valid per-session Set-Cookie header (e.g. Set-Cookie: ASPKSJIUIUGF=JKHJUHVGFYTTYFY), but on POST /process.asp request, there is no Cookie header at all.  Edit3: some AJAX+serverside scripting is apparently capable to sidestep the problem, but that looks very much like a bug, plus it opens a whole new set of . I don't want my applications to use a combination of bug+security hole just because it's easy.  Edit: the P3P policy was the root cause, full explanation below. I am trying to sniff on a custom SPI-like bus protocol, which uses a unified bidirectional data line instead of separate MISO/MOSI. To make sense of the communication, I need to split it up into unidirectional lines before feeding them to my logic analyzer. Otherwise I wouldn't be able to see which device is responsible for which part of the signal. Since my devices won't talk to each other unless the protocol is carried out correctly, it's obvious that the bus splitting device has to be transparent to the actual agents communicating.  I tried to construct a bus splitting device, but failed as described . Since this question was maybe too specific and has not been answered, I want to ask more generally: Is there a bidirectional bus splitter that is able to split  into four wire SPI? Where could I buy such a device? (This seems similar to  question, only that I'm not talking about two really different protocols, so the answer does not apply). In principle only getting one direction would also suffice, since I could just subtract it from the full signal in order to retrieve the other half. And I'm also only interested in the master side of the communication.    The  seems to be a good candidate. Although it's advertised for use with I2C, it seems to be agnostic to the actual protocol on the lines. (As it does not even differentiate between DATA and CLOCK line for I2C.)     Splits I2C-bus signal into pairs of forward/reverse Tx/Rx, Ty/Ry signals for interface with opto-electrical isolators and similar devices that need unidirectional input and output signal paths.   As my devices operate on SPI mode 3 (polarity 1, idling on HIGH), the implementation of the receive pin should work:        sense the voltage state of the I2C-bus pin Sx (or Sy) and transmit this state to the pinTx (Ty respectively), and   sense the state of the pin Rx (Ry) and pull the I2C-bus pin LOW whenever Rx (Ry) is LOW.      But I am still puzzled on how this would actually work in sniffing this bidirectional bus. I could connect one device with the I2C line and grab its MOSI at Tx and MISO at Rx, but I would eventually have to connect both lines before feeding it to the other device, therefore making it impossible to separate the signals at my logic analyzer again. How can I connect the Tx/Rx for the slave while still being able to read them separately with a third device?  Edit: I now think this is actually not helping at all, since it leaves me with the same splitting issue as with out the device. I already have separate master and slave lines, I just don't know how to join them while still retrieving the separate directions.    I also stumbled upon the . It seems like this is a device designed for sniffing on buses, but I don't think it can help me in my case. Is there a mode where I can use it as a bridge on a bidirectional line and grab unidirectional signals off of it simultaneously?    Edit: I found this  which seems related to the issue. This does supposedly split the bidirectional line to feed it to two unidirectional isolators. The question is: Does this work for my setup? It describes the I2C lines being open-drain, whereas my lines are open-collector and also I'm not entirely sure if I could just leave out the isolator part and grab the signals from the lines or if these would have to be also hooked up to some transistor or be pulled high. In my native language, double negations "cancel out". I have been trying to learn English using movies and such things, but double negation confuses me. I see instances when double negation cancels out, and some when they do not.  For example, "I haven't got no money" is interpreted as "I have no money." "There wasn't anyone who didn't enjoy the party" is interpreted as "Everyone enjoyed the party."  Is this context dependent? If so, how does one decide which interpretation is correct? How can a structure have infinite length and infinite surface area, but have finite volume? So I know umask can restrict privileged users, using this format umask ugo.  I understand that the read = 4, write = 2, and exec = 1. However, when I type umask, it returns 4 digits which is 0022 or 0073. I have no understanding of how does this work now because there is an extra digit. What is that extra digit and what does 0022 mean? Is there a way to target the arrow from an OP bow via command block? I am trying to make an effect trail for a specific weapon in MC, a bow with power 120.  I want to use a command block to target any arrow with the damage it should be doing (63) and summon a trail of splash potions.  I also want to kill any arrow entities that have inGround=True  Is there any way to do this or do I have to come up with something else?  Attempt:  /execute @e[type=Arrow,damage=63,inGround=0] ~ ~ ~ summon ThrownPotion ~ ~ ~ {Potion:{id:potion,Damage:8197}} /kill @e[type=Arrow,inGround=True]   Each unfortunately just affects all arrows.  Is this even possible? Shouldn't rep gains from old questions & answers eventually stop (or at-least reduce)? I've recently decided that I just have to finally learn C/C++, and there is one thing I do not really understand about pointers or more precisely, their definition.  How about these examples:   int* test; int *test; int * test; int* test,test2; int *test,test2; int * test,test2;   Now, to my understanding, the first three cases are all doing the same: Test is not an int, but a pointer to one.  The second set of examples is a bit more tricky. In case 4, both test and test2 will be pointers to an int, whereas in case 5, only test is a pointer, whereas test2 is a "real" int. What about case 6? Same as case 5? The problem of counting the solutions $(a_1,a_2,\ldots,a_n)$ with integer $a_i\geq0$ for $i\in\{1,2,\ldots,n\}$ such that $$a_1+a_2+a_3+....a_n=N$$ can be solved with a stars-and-bars argument. What is the solution if one adds the constraint that $a_i\leq r_i$ for certain integers $r_1,\ldots,r_n$?  e.g. for $n=3$, $N=6$ and $(r_1,r_2,r_3)=(3,3,2)$, the tuple $(a_1,a_2,a_3)=(2,3,1)$ is a solution, but $(2,1,3)$ is not a solution because $a_3=3&gt;2=r_3$. Prove that $(x^2 + x+2)$ ideal is a maximal ideal in $F_3[x]$ ring.  I know the theorem about factor rings and fields     B ideal from A ring is maximal iff A/B factor-ring is a field   How can I use the theorem here? Is there any way of making a Minecraft server lower than the current version? So me and my friends manged to make a server in Minecraft for us to play on and we would like to add mods. But the mods we want to add are a few versions lower than the updated version. Is there any way of making a server with a lower version of Minecraft that people can still play on? Can you use the /testfor command in minecraft 1.8 to find out if a player has died ?  I need it for my map, where 2 players (Only) are pitted against eachother. I want it so that when one of them dies, it will detect the death and declare the victor.