Say a train is moving in the positive $x$-direction at 100 meters per second with respect to the ground frame. Now let's say someone is pushing a large box in one of the cars of that train in the negative $x$-direction and is applying sufficient force to keep the box moving at a constant 5 meters per second in reference frame of the train car.    My intuition keeps telling me that this is like any other problem where the ground frame observer would witness the force being applied over a longer distance compared to the pusher/observer in the train frame, so work done is greater in ground frame,  but isn't the energy dissipated as heat independent of reference frame?   Furthermore, the ground observer would see the box moving forward at 95 meters per second as the train moves forward at 100 meters per second. Correct? The person pushing is doing work and the friction is doing equal work in the opposite direction. From the ground frame we'd see much more work done but how do we account for the dissipated energy such as heat and vibration? I feel like from the ground frame you'd see enough heat to start a fire.  I hope I have articulated my confusion clearly enough.
(This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent pushes a cart of mass, say, $m$, accelerating it from rest to $v_2$, relative to the plane (so relative to the ground, its velocity goes from $v_1$ to $v_1+v_2$). From your perspective, the work done is then $$W = \Delta E = \dfrac{1}{2}mv_2^2$$ but from the perspective of the ground, the work done is $$W = \Delta E = \dfrac{1}{2}m(v_1+v_2)^2 - \dfrac{1}{2}mv_1^2 = \dfrac{1}{2}mv_2^2 + mv_1v_2.$$ Why are these quantities unequal?  I've seen some similar problems, like a body colliding with a wall in different reference frames, but I don't have the physics experience to tell if that question is analogous to this one. So, my apologies if this is a duplicate. :)
Why has Steve Nash moved to the LA Lakers in sign-and-trade deal? Congratulations to Steve Nash on his move to Lakers !  His contract with the Suns has expired so I don't understand why he moved in a sign-and-trade deal.    Why resign and move in trade? Why didn't the Lakers sign Nash without any trade? What if client doesn't like any logo design concept? I'm in a process of creating Graphic Design contract. I've decided to provide each client with 3 logo concepts and 3 rounds of revision. Ideally, I would create 3 concepts and client will chose one, but it happend to me before that client didn't like and concept and I end up with doing 10+ more (yes, I've worked without contract).  How can I prevent this situation? Should I charge hourly for each new concept separately? How can I express my thoughts clearly in a contract (without sounding like 'if you don't like any, you'd have to pay more)? I don't want to scare client and put thoughts into their minds saying that there is a possibility that they won't like me ideas. Determine $4$ specific digits in $34!$ Find the values of $a,b,c,d\in\mathbb{N}$ such that      $$ 34!=295232799cd9604140847618609643ab0000000 $$   My Attempt:  The factorial of $34$ contains a $3$, so the RHS must be divisible by  $3$. Similarly, it must be divisible by $7$, $11$, $13$, $19$ etc.  But I do not understand how can I calculate $a,b,c,d$ in this equation. The label toolbar uses fields in the attribute table of vector layers to fine tune labeling (Data defined labeling). That's the main reason i'm looking for that, but it may have more applications.  I'd like to automatically add some format columns instead of adding them manually every time.   Do you know a plugin or a way to do this manipulation automatically on multiples layers ?  I tried to get the QGIS tool "Add a field to attribute table" into a quick model which works properly, but it creates a new memory layer. And I'd like just new fields.  ##Add_ETIKT_Field=name ##myvlayer=vector ##myvlayer=output vector outputs_QGISADDFIELDTOATTRIBUTESTABLE_2=processing.runalg('qgis:addfieldtoattributestable', myvlayer,'ETIKT_Y',1,15.0,4.0,None) outputs_QGISADDFIELDTOATTRIBUTESTABLE_1=processing.runalg('qgis:addfieldtoattributestable', outputs_QGISADDFIELDTOATTRIBUTESTABLE_2['OUTPUT_LAYER'],'ETIKT_X',1,15.0,5.0,myvlayer)   What I'm looking to automate is :   Open the attribute table Edit button Field Calculator button Add Column + Type + length + Precision   It seems there's some ideas in , but I'd love to avoid coding anything, or at least at minimum go through the modeler.     Adding and Removing Fields       To add fields (attributes), you need to   specify a list of field definitions. For deletion of fields just   provide a list of field indexes.   if caps &amp; QgsVectorDataProvider.AddAttributes:     res = layer.dataProvider().addAttributes([QgsField("mytext", QVariant.String), QgsField("myint", QVariant.Int)])  if caps &amp; QgsVectorDataProvider.DeleteAttributes:     res = layer.dataProvider().deleteAttributes([0]) Automatic reboot after ubuntu freeze? How Can I Do It? In the following setup, does method B run in a (new) transaction?  An EJB, having two methods, method A and method B  public class MyEJB implements SessionBean     public void methodA() {        doImportantStuff();        methodB();        doMoreImportantStuff();     }      public void methodB() {        doDatabaseThing();     } }   The EJB is container managed, with methodB in requires_new transaction, and method A in required transaction. thus:  &lt;container-transaction id="MethodTransaction_1178709616940"&gt;   &lt;method id="MethodElement_1178709616955"&gt;     &lt;ejb-name&gt;MyName&lt;/ejb-name&gt;     &lt;method-name&gt;*&lt;/method-name&gt;   &lt;trans-attribute&gt;Required&lt;/trans-attribute&gt;   &lt;/method&gt;   &lt;method id="MethodElement_1178709616971"&gt;     &lt;ejb-name&gt;MyName&lt;/ejb-name&gt;     &lt;method-name&gt;methodB&lt;/method-name&gt;   &lt;/method&gt;   &lt;trans-attribute&gt;RequiresNew&lt;/trans-attribute&gt; &lt;/container-transaction&gt;   Now let another EJB call methodA with an EJB method call. methodA now runs in an transaction. Will the subsequent call to methodB from methodA run in the same transaction, or does it run in a new transaction? (mind, it's the actual code here. There is no explicit ejb-call to method B) How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$ How can I download an entire website? How can I download all pages from a website?  Any platform is fine. Can we prevent titles with an unnecessary tag in them? So we have lots of questions that are titled like this:  Specifically, questions that have one of their tags in front of their title. Thankfully, these silly users usually use a hyphen or a colon afterwards, which makes it really easy to . Can we clear up this clutter?  Perhaps with a filter that strips off the excess when posting? EDIT: As an added bonus, see  for another style of question title that bugs the heck out of me. Are both try to save the file and try saving the file grammatically correct? If so, is there any difference in meaning? Is normal extension of normal extension always normal? Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$ Find the following sum : $\sum_{n=1}^{\infty} \frac{\ln n }{n(n- \ln n)}$  I couldn't find any way to solve.   I just want a hint, how to initiate? How do I prove that a graph is a topological manifold I'm having problems with that:  Prove that M is a topological manifold.  $f:U \to \mathbb R^k$, U $\subset \mathbb R^{n}$ open, f continuous  M = $\{\left(x,y\right)\in \mathbb R^{n+k} \mid x \in U, y=f(x) \}$  Can anyone help me please? I've been trying to develop an intuition based understanding of Bayes' theorem in terms of the prior, posterior, likelihood and marginal probability. For that I use the following equation: $$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$ where $A$ represents a hypothesis or belief and $B$ represents data or evidence. I've understood the concept of the posterior - it's a unifying entity that combines the prior belief and the likelihood of an event. What I don't understand is what does the likelihood signify? And why is the marginal probability in the denominator? After reviewing a couple of resources I came across this quote:     The likelihood is the weight of event $B$ given by the occurrence of $A$ ... $P(B|A)$ is the posterior probability of event $B$ , given that event $A$ has occurred.   The above 2 statements seem identical to me, just written in different ways. Can anyone please explain the difference between the two? pdf of a quotient of uniform random variables Suppose $x_1, x_2$ are IDD random variables uniformly distributed on the interval $(0,1)$.  What is the pdf of the quotient $x_2 / x_1$? How to prove that homomorphism from field to ring is injective or zero? Possible Duplicate:          $f:K\rightarrow R$ is a homomorphism from field to ring. To prove is that it is injective or zero. Capitalizing "the" when mid-sentence in a company name? Consider a company called:     The Association of Examples Ltd.   When you refer to this company, should you have to capitalize "the" when it's mid-sentence and would have been used even if it wasn't in the name?   It looks odd to me:     In other news, The Association of Examples announced that...      Sarah is the founder of The Association of Examples and has...   But I imagine it's the correct way.  For the grammar-conscious, why or why not?    To give you context, I am asking also when branding ones own company like that. The Economist did it (as did ) and , but I can imagine it can cause confusion. What to conclude from this lasso plot (glmnet) Following is the plot of glmnet with default alpha(1, hence lasso) using mtcars data set in R with mpg as the DV and others as the predictor variables.  glmnet(as.matrix(mtcars[-1]), mtcars[,1])     What can we conclude from this plot regarding different variables, especially am, cyl and wt (red, black and light blue lines)? How would we phrase the output in a report to be published?  I thought of following:   wt is the most important predictor of mpg. It is negatively affecting the mpg. cyl is a weak negative predictor of mpg. am may be a positive predictor of mpg. Other variables are not robust predictors of mpg.    Thanks for your thoughts on this.  (Note: cyl is the black line which does not reach 0 till very close to it.)  Edit: Following is plot(mod, xvar='lambda') which shows x-axis in order reverse of above plot: Nth max salary in Oracle i have a tiny little problem with xslt, js and html entities, eg. within a template:  &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     for (var i = 0; i &amp;lt; 5; i++) {         //            ^^^ js error     } &lt;/script&gt;  &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     for (var i = 0; i &lt; 5; i++) {         //            ^ xslt error     } &lt;/script&gt;  &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     // &lt;![CDATA[     for (var i = 0; i &lt; 5; i++) {         //            ^ becomes &amp;lt;     }     // ]]&gt; &lt;/script&gt;   &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     for (var i = 0; i &lt;xsl:value-of disable-output-escaping="yes" select="string('&amp;lt;')"/&gt; 5; i++) {         // works of course     } &lt;/script&gt;   does anyone have an idea where my problem could come from? i always thought the xslt processor would leave the content of a &lt;script/&gt; element unescaped when using the html output method ...  i run libxslt2 version 1.1.24 on OSX which was installed using macportsports ...