Obscure show or movie from the 80's or 90's
Water Wars: Time Travel TV Show?
Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$ Suppose that we have open sets $A, B\subset \mathbb{R}^2$ such that $A$ and $B$ are simply connected and have smooth boundaries. Furthermore, let us assume that $m(A) = m(B) &gt; 0$, where $m$ is the Lebesgue measure on $\mathbb{R}^2$. My question is as follows: when does there exist an area-preserving diffeomorphism between $A$ and $B$? In this context, an area-preserving diffeomorphism between $A$ and $B$ is a is a $C^{\infty}$-diffeomorphism $\phi : A\to B$ such that $m(S) = m(\phi(S))$ for all measurable $S\subseteq A$. If an area-preserving diffeomorphism doesn't always exist between sets $A$ and $B$ as above, are there any extra conditions we can impose on $A$ and $B$ such that there does exist an area-preserving diffeomorphism?  My thoughts thus far are that we always have a $C^{\infty}$-diffeomorphism between $A$ and $B$: this is a consequence of the . It's also obvious to me that if we can deform $A$ linearly to get $B$, then that deformation will be area-preserving. Furthermore, it seems that aside from this case, there's no reason why an area-preserving diffeomorphism should exist. However, I'm having a hard time proving that there necessarily isn't an area-preserving diffeomorphism between $A$ and $B$ if $B$ is not a linear deformation of $A$. Does anybody have any ideas? Could new users be prompted to edit instead of commenting? It's very common to ask for additional information on a question.  This is perhaps most common with new users who are a little unfamiliar with the need to put all relevant information in their question to start with.  To be blunt, I'm a little tired of explaining to new users that an edit is better than a comment, particularly where we ask "please add the output of..." I note that some users have taken to explicitly asking OPs to edit their question and adding an edit link in their comment.  But still this is missed.  More recently, adding a comment to a new user's question displays a little note saying:     ... is a new contributor. Be nice, and check out our Code of Conduct.   Could there be a similarly formatted note to new contributors commenting on their own question or answer:     If you need to add more information please  your [question][answer] instead of adding a comment. Selecting all objects that have been specified in Modifiers Could anyone help in making a script for selecting all objects that are specified in the different modifiers that an object has stacked? For example if my object has a Boolean modifier and an Array modifier, which both refer to an empty or another object (in the Array modifier there is for example an Object offset you can specify). Would it be possible to select all those object with one click? Thanks. When can you switch the order of limits? Proof of the duality of the dominance order on partitions Could anyone provide me with a nice proof that the  $\leq$ on partitions of an integer $n$ satisfies the following: if $\lambda, \tau$ are 2 partitions of $n$, then $\lambda \leq \tau \Longleftrightarrow \tau &#39; \leq \lambda &#39;$, where $\lambda&#39;$ is the conjugate partition of $\lambda$ (i.e. the transpose of the set of 'dots' which $\lambda$ represents).   I feel like there must be a nice clever and concise/intuitive proof of this, but all I can come up with is an ugly brute force approach based on the definition of sums of the components $\lambda_i$. Could anyone suggest a particularly nice way to obtain this result? Many thanks. AWS dynamodb support for "R" programming language The temperature and pressure everywhere inside the Sun reach the critical point to start nuclear reactions - there is no reason for it to take such a long time to complete the reaction process.  Just like a nuclear bomb will complete all the reaction within $10^{-6}$seconds.  Why does most of the hydrogen of the Sun still not react even though it reaches the critical point, and why take stars billions of years to run out of fuel? I got a brand new Windows 7 machine, installed the operating system, created one account and forgot its password. What can I do?  There is no external CD, the operating system is loaded from somewhere inside the machine.  I already tried to remember passwords and tried all candidates with all possible combinations of caps lock, num lock etc. I am trying to implement  using additive ElGamal.  I am trying to run the full protocol mentioned in Section 3.4 on the following inputs:   $p = 17$ (prime) $g = 6$ (generator) $x = 5$ (private key) $k = g^x \pmod p = 6^5 \pmod{17} = 7$ (public key)   Suppose the clients inputs are 1, 2. Then $P(x) = (x-1)(x-2) = x^2-3x+2$, and therefore the coeffiecients to encrypt are $(1, -3, 2)$. I chose $y = 10$ and so the encrypted values are:   $1$ becomes $(15,12)$ $-3$ becomes $(15, 1)$ $2$  becomes $(15, 4)$.   The Server Side Input Set $S=\{1\}$ and the random value $r0$ corresponding to $\{1\}$ is $r_0=2$.    With the above problem in context, I have some questions:   What does P 0,j refer to in Step 7. Can you please give an example? In Step 8, suddenly variable i is introduced along with j. What does i, j, refer to? In Step 8, ENC() function has a ; in between. How do we interpret ENC(a;b)? How do you get the index of the current iteration of a foreach loop? Is there some rare language construct I haven't encountered (like the few I've learned recently, some on Stack Overflow) in C# to get a value representing the current iteration of a foreach loop?  For instance, I currently do something like this depending on the circumstances:  int i = 0; foreach (Object o in collection) {     // ...     i++; } Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$ Show that   $$\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$$  this is so confusing. i have no idea how to even start. im thinking integration by parts but that doesnt seem right.  hope you guys can help!! Is there an option to output a manual page in a different language? I don't want to change the computer language completely, but only specific manual pages. For example  $ man -English man Man is a manual program … $ man -Russian man Инструцтия для Unix, BSD и Linux. … Graphing y=x^2 and y=x I want to draw the region bounded by y=x^2 and y=x. Any ideas? I was hoping this would be somewhat simple. I've tried used a similar, with \begin{axis}..\end{axis}, but it doesn't like that. Did I not declare a package or something?   Also, if I wanted to show the solid this region creates by rotating it about the x-axis, is there a way to did this in latex? (If you had cal 2, think volume of a solid rotated about ...). How to modify existing, unpushed commit messages? Most of what I have read about retry operations is that they are vaguely complicated and indepth. I have written the code below which seems to accomplish this without too much confusion - I'm wondering if there are any pitfalls I am not seeing here.   The class uses a top-level schedulable class, which calls a queueable class to make the callout, and if the callout is unsuccessful, it just schedules the top level class again five minutes later. After testing it appears this works indefinitely.   A simple string token, assigned at the first invocation, is also passed between the classes, and I have tested and found that the token does persist, even when runs are scheduled for a later time.   Thanks for helpful thoughts!  public class SelfServe implements Schedulable {      public String Token = null;      public void execute(SchedulableContext ctx) {                  RetrieveMachineDetails Job = new RetrieveMachineDetails();             Job.Token = Token;             System.enqueueJob(Job);      }           public class RetrieveMachineDetails implements Queueable, Database.AllowsCallouts {          public String Token = null;          public void execute(QueueableContext context){                                            Http http = new Http();             HttpRequest request = new HttpRequest();                             request.setEndpoint('https://app.endpoint.com/api');                     request.setMethod('POST');                     request.setHeader('Content-Type', 'application/json;charset=UTF-8');                                      request.setBody('{"query":  "$message_=\'METRIC\' &amp;&amp; $tier=\'customer\' "}');                                                                                                                                                                                    HttpResponse response = http.send(request);                            if (response.getStatusCode() == 200) {                 //do stuff                  }              else { //retry                  DateTime Dt = system.now().addMinutes(5);                                String day = string.valueOf(Dt.day());                                        String month = string.valueOf(Dt.month());                                          String hour = string.valueOf(Dt.hour());                                       String minute = string.valueOf(Dt.minute());                                                       String year = string.valueOf(Dt.year());                                   String ScheduledTime = '0 ' + minute + ' ' + hour + ' ' + day + ' ' + month + ' ?' + ' ' + year;                  SelfServe Job = new SelfServe();                     Job.Token = Token;                 System.schedule('SelfServe Job'+Dt, ScheduledTime, Job);              }         }        }  } Comprehensive Rules for Game of Thrones Lines of Succession I'm three quarters through the third book, "Storm of Swords" right now (so please, no spoilers from too late in the book or any subsequent books).  I just read a part where Tyrion is discussing with Prince Oberyn and they mention the difference between Dornish law and Westerosi law in Line of Succession (ie women can rule under Dornish law).  I'm a little confused trying to puzzle out what the exact LOS rules are.  At first I though it was: at the moment a king/lord dies, to find who holds the title next, you do a depth-first search down the family tree starting with the oldest sibling (ignoring anyone who isn't true-born or has given up their claim ie as Night's Watch or Kingsguard etc.).  Then, for Dornish law you take the first living person and for Westerosi law the first living male person found in this way (so succession can pass through a woman in both cases, but only Dornish law actually allows them to claim the title). If there are no valid living heirs, then you work backwards along the paternal line until you find an ancestor who has living heirs and start from them.  But there were various references to if Sansa's brothers were all dead, then her child would claim Winterfell.  It seems to me that that's only true if somebody else doesn't get it first.  In other words, if Sansa's brothers are killed before she has a child (even if she's already married), doesn't that mean Winterfell would pass to the nearest cousin along her father's line (whomever that may be)?  And then because that cousin has already held Winterfell, when they die the next in the line of succession starts from them so Sansa's children's family would not have claim to Winterfell again unless that cousin has no valid heirs.  What am I missing here? Is there some exception?  Are there no valid cousins? How do I explain current and voltage to a lay man? A man asked me this question in suburban train when I told him that I am an electrical engineer. Of course I replied him that current is the flow of electrons and in order for the current to flow there should be a potential difference between them. But the man didn't know what electron or potential difference was either. Spatial query to return multiple values I have a woodland scheme advice layer that has a polygon for each area of advice (brown layer in the picture). I also have a polygon layer of UK local authorities (red boundary layer in the picture). I would like to perform a spatial query which returns the local authority name for each woodland advice scheme. This would work fine if each woodland advice scheme was found in just one local authority boundary. However many are found across a boundary of two different authorities. For instance, one scheme sits across the boundaries of the authorities of Fife and Angus. The scheme is the yellow selected polygon in the picture and the red line is the authority boundary. How do I get the spatial join to return a value of Fife; Angus (or something similar to identify two values) instead of just Fife or Angus. How do I search events between two set dates inside WP? If all motion is relative, how does light have a finite speed? I've often heard that Einstein shattered the notion of absolute motion (i.e. all things move relative to one another) and that he established the speed of light as being absolute. That sounds paradoxical to me; I cannot understand how the two concepts can be reconciled.  Before going further, I'd like to say: 1) Over the years, I've seen many layman's explanations on these topics (including the nice YouTube video by Vsauce, ). I understand everything that's said (or, at least, I think I do). Just nothing I've found seems to address this apparent contradiction. 2) More recently, I've tried to find the answer on my own. That includes searching the posts on this site. Some come close (), but nothing I've been able to find seems address specifically what I'm asking.  Back to the question: Relativity shows us that there is no universal frame of reference by which to judge motion, so object A might be reckoned as moving at 10&nbsp;m/s relative to object B or as stationary relative to object C. This is fine for me. I can grasp that the universe has no intrinsic coordinate system, that we only think that way on Earth because we have the ground to move over.  Then there's the speed of light (in a vacuum). The speed of light is the ultimate "speed limit," it's often said. But if there is no universal frame of reference, how can there be any such speed? The very idea only make sense if there is a universal frame.   If one object is moving (uniformly) at 60%&nbsp;c and another object is also moving at 60%&nbsp;c, but in the exact opposite direct, then from the perspective of either one (if they could still see each other) the other would appear to violate that speed limit. All these spacetime bending consequences used to explain why nothing can move past this speed only seems to enshrine the concept that there is some ultimate speed standard. If there is only relative speed, then the concept of light having a specific speed in the vacuum should be a nonsensical one since it having speed (x m/s) would only make sense when measured against some other body.   Since I was very young, it has always sounded to me like motion is only mostly relative, that until you get close to the speed of light, the effects of an absolute frame of reference are negligible. Perhaps that there is an actual fabric of space which everything moves relative to, which is why there is something to expand between galaxies (faster than light can propagate) in the metric expansion of space. Growing up, I always thought this would just start makes sense with time. Now I'm up to a first year (college) level in physics, I even know basic calculus, yet I'm still hopelessly confused.  EDIT:  Thank you to whoever suggested this may be a duplicate of . It and others are very much related and at least partially answer my question. Unfortunately, explaining that distances become shorter and time becomes slower as a way to stop you from exceeding the speed of light does not explain how that speed is not an absolute.  By my reckoning, if all speed is relative, then no matter how fast you go light should always race away from you at the same apparent speed. I.e. there should be no speed limit. For there to be a speed which you cannot exceed or you would catch up (and make time irrelevant) requires the very concept of some external speed by which light can travel and nothing else can reach - thus my logical paradox continues unabated.