Why direction of dipole is from negative charge to positive charge?
An  is defined as $p = q\times d$ (for two point charges $\pm q$ separated by a distance $d$).    What is the physical meaning of this quantity?  Why does the direction of the electric dipole moment go from the negative charge to the positive charge? Another way of saying this, why electric dipole moment is a vector quantity?
Hyphenation of words containing slash How can I tell LaTeX to automatically split up the german word  Kontrast/Rausch-Verhältnis    into   Kontrast/Rausch-|Ver|hält|nis   LaTeX complains that "/" is not a letter. Are there any disadvantages to using your companions for transporting Power Armor After I read that companions don't drain the fusion core of a Power Armor when wearing it, I decided to try giving my armor to Nick so I'll always have it close by if I need it.  But I was wondering if there are any other drawbacks to that. For example, does the Armor get damaged or destroyed when the companion is under fire? How can I make a script run automatically after gdm login and logout? I have a setup where my users log on using ldap and it works just fine.  I want to run a script after my users login (its a script that will detect which groups they are in and map network shares accordingly), and after they logout (umounting their shares).  Both scripts are done and they work.  I want that when the user logs in the box a script runs downloading the mounting script from my server (wget i guess?) and runs it, same thing for logout.  Can it be done? I've been searching the net and had no luck so far. I've managed to make that work on shell login/logout, but my users dont even know what shell is and have no use for it :) How do I modify the options for the power button? When I press the power button a dialog opens, but I want to shutdown the system without receiving "Do you really really want to shutdown?". How can I choose a direct shutdown action on a pressed power button?   I had the same problem with the 11.04 version, but I don't remember the solution and yesterday I upgraded to Ubuntu 11.10. Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction Prove that $2(\sqrt{n+1}-\sqrt{n}) &lt; \frac{1}{\sqrt{n}} &lt; 2(\sqrt{n} - \sqrt{n-1})$ if $n \ge 1$ using induction.  Can someone help me with this problem please. Base case is easily shown, and for the inductive step I know I have to use the inequality for $n\gt1$ to show that it is true for $n+1$, but I am not quite sure how to.   Thanks. How could the human race be saved in Interstellar? In  (2014) the human race seemed to be facing pretty poor odds until they discovered a convenient wormhole placed by an unknown entity expressed as "they". Later in the movie, we discover that       "they" are actually the human race in the future, reaching back in  time to save itself.   The end of the movie gets a little wild on the physics end, and I'm happy to take that ending as is - no need for it to make sense - but one very basic detail does bother me:  How could the human race have gone back in time to save itself from circumstances that would have caused us to go extinct without our own help (the convenient wormhole)? Seeking detailed description of qgs file structure? Is there a detailed description on the .qgs file structure somewhere?   I checked at  and got     The requested URL /qgis.dtd was not found on this server.   and at  which wasn't very detailed. Uniform Continuity implies Continuity Let $f$ be a function from a metric space $X$ to a metric space $Y$. Show that if $f$ is uniformly continuous on $X$ then $f$ is continuous on $X$. Show that the converse is not true.  Uniform continuity definition:  $∀ε&gt;0:∃δ&gt;0:∀p,q∈X:d_{X}(p,q)&lt;δ⟹d_{Y}(f(p),f(q))&lt;ε$  Continuity definition:  $∀ε&gt;0:∀p∈X:∃δ&gt;0:∀q∈X:d_{X}(p,q)&lt;δ⟹d_{Y}(f(p),f(q))&lt;ε$  I wonder if these proofs are correct and if they are formal enough?    Uniform continuity ⟹ Continuity   Let $f$ be uniformly continuous. Fix $ε_{0}$, obtain $δ_{0}(ε_{0})$ (as a function of $ε_{0}$), fix any $p_{0}$ and $q_{0}$ and we know that:   $d_{X}(p_{0},q_{0})&lt;δ_{0}⟹d_{Y}(f(p_{0}),f(q_{0}))&lt;ε_{0}$   If we want to prove that $f$ is continuous at $p_{0}$, we fix $ε_{0}$ and we pick the same $δ_{0}$ as above and fix any $q_{0}$ and we are assured by 1. that   $d_{X}(p_{0},q_{0})&lt;δ_{0}⟹d_{Y}(f(p_{0}),f(q_{0}))&lt;ε_{0}$   Since $p_{0}$ was arbitrary, $f$ is continuous at $X$.     Continuity $\color{red}{\implies}$ Uniform continuity   Let $f$ be continuous. Fix $ε_{0}$, fix any obtain $p_{0}$ and $p_{1}$, obtain both $δ_{0}(ε_{0},p_{0})$ and $δ_{1}(ε_{0},p_{1})$ (not necessarily equal), fix any $q_{0}$ and $q_{1}$ and we know that:   $d_{X}(p_{0},q_{0})&lt;δ_{0}⟹d_{Y}(f(p_{0}),f(q_{0}))&lt;ε_{0}$  $d_{X}(p_{1},q_{1})&lt;δ_{1}⟹d_{Y}(f(p_{1}),f(q_{1}))&lt;ε_{0}$   For $f$ to be uniformly continuous, if we fix $ε_{0}$, obtain $δ$, fix any $p_{0}$, $p_{1}$, $q_{0}$ and $q_{0}$ we must have that:   $d_{X}(p_{0},q_{0})&lt;δ⟹d_{Y}(f(p_{0}),f(q_{0}))&lt;ε_{0}$  $d_{X}(p_{1},q_{1})&lt;δ⟹d_{Y}(f(p_{1}),f(q_{1}))&lt;ε_{0}$   But those two implications need not hold for the same $δ$ as shown above. Suppose we pick $δ_{0}$ and w.l.o.g. we suppose $δ_{0}&gt;δ_{1}$. Then it could be the case that   $δ_{1}&lt;d_{X}(p_{1},q_{1})&lt;δ_{0}$  but we cannot conclude ⟹$d_{Y}(f(p_{1}),f(q_{1}))&lt;ε_{0}$.  Therefore, continuity does not imply uniform continuity. When is an elected moderator shown as "departed" on the election page? On Philosophy, one of the elected moderators has since deleted their account, and they're shown as "Departed" on :        However, , one of the elected moderators still has their "previous" flair shown in place, despite the fact that they've already resigned and left the Network completely in the wake of the recent events.        , the same happens (old flair remains), but without the clickable &lt;a&gt; around the image, and with a noticeable :        This looks inconsistent, so when exactly will a placeholder image showing "Departed" replace the flair for a departed election winner? Why is pressure in a liquid the same in all directions? I'd like answers both in the more intuitive side an on the more precise side.   Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a  triangular prism, yield different results. Will this fact, then, be dependent on the format of the molecules of the liquid ?  I've heard of the rotational symmetry of liquids. What is its precise statement ? Why is it true ? I heard about nautilus-gksu and would like to install it. Unfortunately, when I try, I get this:  glemi@XPS:~$ sudo apt-get install nautilus-gksu Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package nautilus-gksu   How and where can I get this package? This might be a stupid question, but why exactly is work a path function?  In school, my teacher said it’s because it depends on the path. She gave an example of walking up a mountain, and said the work you expend depends on the path you take (straight path up or circling up around the mountain). But isn’t the work expended just equal to $E= mgh?$ I noticed with the holiday patch that there are new trees and shrubs that spawn on my land.  One popped up today, being specifically an X-Mas tree - which costs 25,000 gold to remove.   Is there any benefit to removing this X-Mas tree?  Is there any benefit to leaving it there?    It is noticeably the most expensive obstacle to remove yet. Einstein equation  where $E$ is energy, $m$ mass, and $c$ the speed of light in vacuum. So does it mean objects without any mass does not posses energy for eg lights photons does not have mass but how can they posses energy If $a_{ij}=\max(i,j)$, calculate the determinant of $A$ I'm trying to determine the best way to truncate or drop extra decimal places in SQL without rounding.  For example:  declare @value decimal(18,2)  set @value = 123.456   This will automatically round @value to be 123.46, which is good in most cases.  However, for this project, I don't need that.  Is there a simple way to truncate the decimals I don't need?  I know I can use the left() function and convert back to a decimal.  Are there any other ways? Dropbox: ext4 isn't ext4 I know I can set the render border with Ctrl+B and dragging a box.  But is there  a way I can exactly specify the border dimensions? Equation for a smooth staircase function I am looking for a smooth staircase equation $f(h,w,x)$ that is a function of the step height $h$, step width $w$ in the range $x$.   I cannot use the unit step or other similar functions since they are just one step. I have been experimenting with various sigmoid curves and while I can get a single smooth step I cannot get to realize the staircase shape. The closest staircase function I have found is given in  in equation (18) and depicted in Fig. 4 and it is a close example of what I want (i.e generate a staircase in the range $x$ for arbitrary step heights and widths) but it is not smooth at all.  Regarding smooth steps, a likely starting point I found is  but it gives a smooth function of just a single step. I have been unable to modify the equation to make it into a staircase. I would like to specify arbitrary step heights and widths and generate a smooth staircase in the range $x$ specified.    Edit (Extra info): The smooth function I mention above has the problem that the upper, horizontal line is not equal in length to the lower, horizontal line which is why I have been unable to adapt it into a staircase function   Edit 2 Including some pictures     Edit 2 Plot of $s$ with a steep slope showing a different width on the first horizontal line I have quite a bad habit of copy-and-pasting my packages from one LaTeX document to another. Is there any way we can detect unused packages (i.e. \usepackage commands) so that they can be removed from the LaTeX document?