Experimental proof of gravity propagation?
What is the status of existing measurements of the speed of gravity?
Transforming the dummy values to be able to take logs I have a panel data model with double-log functional form. I have 4 variables, one of which is a dummy. What is the best way to transform the values of 0 for my dummy to be able to take natural logs (since you can't take logs from zero)? I have found 2 options so far, but I dont know which is the best (or perhaps there is a 3rd option).  1) Transform all the values of 0 into a very small value (0.00000000001) and then take the logs. I'm not sure this wouldn't still change the outcome of my model quite a bit. 2) Change the values of 0 into 1 and the dummy values of 1 into e (the base of natural logarithm). The log of this newly defined dummy then takes on the values of zero and one and the interpretation of my betas would remain the same. How to find and replace a string by increasing its numerical part? My input file is,  ami21 ami65 ami67 ami66 ami88 ami76 ami29 ami55  ami54 ami32   Using a single command line I need the output as,  ami22 ami66 ami68 ami67 ami89 ami77 ami30 ami56 ami55 ami33   I used the command  awk -vRS=ami '{$0=$0+1;ORS=RT}++n' inputfile &gt; outputfile   but I got the outputfile as ami21ami65ami67ami66ami88ami76ami29ami55ami54ami32  i.e. all strings are written in same line and without space. Could anyone suggext me some better command line. Atiyah-Macdonald, Exercise 5.4 I was having some trouble with the following exercise from Atiyah-Macdonald.     Let $A$ be a subring of $B$ such that $B$ is integral over $A$. Let $\mathfrak{n}$ be a maximal ideal of $B$ and let $\mathfrak{m}=\mathfrak{n} \cap A$ be the corresponding maximal ideal of $A$. Is $B_{\mathfrak{n}}$ integral over $A_{\mathfrak{m}}$?   The book gives a hint which serves as a counter-example. Consider the subring $k[x^{2}-1]$ of $k[x]$ where $k$ is a field, and let $\mathfrak{n}=(x-1)$. I am trying to show that $1/(x+1)$ could not be integral over $k[x^{2}-1]_{\mathfrak{n}^{c}}$.  I have understood why this situation serves as a counterexample. But I am essentially stuck at trying to draw a contradiction. A hint or any help would be great. what are all the open subgroups of $(\mathbb{R},+)$ How to find relevant and new open research topics? How does "warp drive" not violate Special Relativity causality constraints? I'm talking about this nonsense:   Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here:   But in this case my question is different and more specific. Sweeping all the other problems of constructing such a beast under the rug, wouldn't this violate causality?  SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. (I think we can all agree, can we not, that the threshold should be extremely high before breaking assumptions that we're in a causal universe?)  So how is any scheme to travel faster than light, even if it may locally satisfy the equations of GR, not a blatant violation causality according to SR?  Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? (Pending a serious replicable experiment showing causality to be breakable.) "Much more easy" versus "much easier" Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result I'm currently tutor in an undergraduate course and the students are asked to find how addition and multiplication behave on the field with 4 elements: $\{0,1,x,y\}$. In the solution the teacher gave me, he uses the fact that $(\mathbb{F}_4^*, \cdot )$ is cyclic with order 3 to find that $x$ and $y$ are both generators and that $(\mathbb{F}_4,+)$ is a group of order 4 to deduce that $0=1+1+1+1=(1+1)(1+1)$ and hence, $(1+1)=0$ since a field is integral.   However, I'm not satisfied with this reasoning because this question is asked to student in first year and they juste have been introduced to fields (and this was part of an analysis course so they won't see any result soon). So I tried to find how it behaves by myself, using as few results as possible.  Multiplication is the easy part, $0\cdot a$ and $1 \cdot a$ is trivial for all $a\in \mathbb{F}_4$. Then, $x\cdot y\not = 0$ because it is invertible, and it can't be equal to $x$ or $y$ because that would imply the other element to be equal to $1$. Hence, $x\cdot y=1$. We are left to find what is $x^2$ (and similarly, $y^2$). $x^2$ cannot be $0$, nor $x$. If $x^2=1$, then $y=(x^2)y=x(xy)=x\cdot 1=x$. Contradiction. Hence $x^2=y$ and by the same reasoning, we have $y^2=x$.  It was easy with the multiplication, but I can't figure out any non-trivial result concerning addition. My intuition tells me that distributivity should be used here but I'm feeling like it's just converting a problem into another one because we don't know anything about addition.  Does anyone here have an idea of how addition can be "found" without using any advanced result (or as few results as possible)?  Thanks in advance. Intuitive explanation of convergence in distribution and convergence in probability What is the intuitive difference between a random variable converging in probability versus a random variable converging in distribution?  I've read numerous definitions and mathematical equations, but that does not really help. (Please keep in mind, I am undergraduate student studying econometrics.)  How can a random variable converge to a single number, but also converge to a distribution? I use ps -ef | grep catalina | grep -v grep to print the tomcat process running on the system:  kshitiz   7099     1  0 May11 ?        00:02:29 /usr/lib/jvm/jdk1.8.0/bin/java -agentlib:jdwp=transport=dt_socket,suspend=y,address=localhost:38156 -Dcatalina.base=/home/kshitiz/Documents/workspaces/ggts/.metadata/.plugins/org.eclipse.wst.server.core/tmp1 -Dcatalina.home=/opt/tomcat-7.0.42 -Dwtp.deploy=/home/kshitiz/Documents/workspaces/ggts/.metadata/.plugins/org.eclipse.wst.server.core/tmp1/wtpwebapps -Djava.endorsed.dirs=/opt/tomcat-7.0.42/endorsed -Dfile.encoding=UTF-8 -classpath /opt/tomcat-7.0.42/bin/bootstrap.jar:/opt/tomcat-7.0.42/bin/tomcat-juli.jar:/usr/lib/jvm/jdk1.8.0/lib/tools.jar org.apache.catalina.startup.Bootstrap start   Then I use ps -ef | grep catalina | grep -v grep | awk -F' ' '{print $2}' to extract the process id:  7099   But when I alias the whole command alias tomcat_id="ps -ef | grep catalina | grep -v grep | awk -F' ' '{print $2}'" and use it via alias, it prints the whole text and awk doesn't seem to work.  type tomcat_id gives:  tomcat_id is aliased to `ps -ef | grep catalina | grep -v grep | awk -F' ' '{print }'' I have written a small script to count number of occurrences of logs in a particular file. The following is my code:   #!/bin/sh count=1 while read line do     found=$( grep M $line )     OCCURENCE=$( grep M /log.txt)     if [ "$OCCURENCE" ]; then         echo $count")" $line &gt;&gt; filesave.txt     fi     count=$((count+1)) done &lt; log1.txt   but I am getting this error:  ./count.sh ./count.sh: syntax error at line 10: `found=$' unexpected How to control fan speed? What were the rules for capitalising nouns in the 17th and 18th centuries? It seems to have been common practice in the 17th and 18th centuries in English-language sources to capitalise the first letters of nouns, as in  At which Time he prov'd himself the Noah's Dove, that finding himself no Rest anywhere, was receiv'd again into his own Ark, and brought a peaceable Olive-Leaf in his mouth. —  (1685)  Most original sources I can find on the web have used modern rules for capitalisation, so I have a few questions:  Was the practice used for all nouns (Note mouth isn't capitalised in my quotation above.)? When did this practice begin? When and why did it end? Flatten an irregular list of lists Lowering elevation of lake using QGIS I am in QGIS. I have a raster layer of mountains and a lake. I have a vector layer (shapefile) of the lake. It sits nicely where it supposed to be over the raster level. I am going to convert this height map to an STL so that I can cnc this out of wood, so I'd like the actual lake to be something like 200 feet lower than it shows on the raster layer so that I can fill it with blue epoxy. I have read a lot of clipping and everything else, and I am lost. Novel about a dragon lord who has to wear gloves at all times I read this novel when I was young. It is probably a children's or young adult novel. I think I read it in 1997 or earlier. I remember very much enjoying it, but the title and most of the details are unfortunately quite hazy for me. Here is what I have:   The main character was a girl in her early teens (I think) She was sent to live with a man who was some sort of master of dragons She may have been related to this man (his niece, perhaps), but I also may have made that up The man wore gloves at all times. When he removed them and touched someone he could see something about them. Their future, I think?   Sound familiar to anyone?   Update: Thinking back on it some more, I think I remember that the dragon lord guy and the heroine ended up in some kind of romantic relationship (making it less likely that he was her uncle). Also, he did at one point take off his gloves and touch her, seeing her future (I think).  'nother Update: It's possible that I'm confusing dragons with volcanos. Or, there may have been both. And I think they lived on an island, or a coastline? I'm trying to find a discontinuous linear functional into $\mathbb{R}$ as a prep question for a test. I know that I need an infinite-dimensional Vector Space. Since $\ell_2$ is infinite-dimensional, there must exist a linear functional from $\ell_2$ into $\mathbb{R}$. However, I'm having trouble actually coming up with it.   I believe I'm supposed to find an unbounded function (although I'm not sure why an unbounded function is necessarily not continuous; some light in that regard would be appreciated too), so I thought of using the vectors $e^i$, which have all entries equal to zero, except for the $i$-th one. Then, you can define $f(e^i)=i$.  That'd be unbounded, but I'm not sure if it'd be linear, and even if it is, I'm not sure how to define it for all the other vectors in $\ell_2$.   A friend mentioned that at some point the question of whether the set $E=\{e^i:i\in\mathbb{Z}^+\}$ is a basis would come up, but I'm not sure what a basis has to do with continuity of $f$.   I'm just learning this topic for the first time, so bear with me please.   The space of sequences that are eventually zero (suggested by a few people) turned out to be exactly what I needed.  It also helped to cement the notions of Hamel basis, not continuous, etc. Let $G = (\mathbb{C} - \{0\}, \cdot)$, a subgroup $U = \{x+yi \mid x^2 + y^2 = 1\}$. Use the Fundamental Theorem to show that $G/(\mathbb{R}_{&gt; 0},\cdot)$ is isomorphic to $U$ where $\mathbb{R}_{&gt; 0}$ denotes the positive reals.  I am struggling to find the correct mapping from $G$ to $U$ that results in the the kernel being the nonnegative reals under multiplication. I'm hoping to get help with this mapping then I can show it is a homomorphism and onto and can use the Fundamental Theorem. I am trying very hard to install Canon LBP2900b Printer in Ubuntu 13.10.  I have searched and googled a lot for the solution over fortnight but none of the site / link gave me the simple solution for me. How can accomplish my goal? IBM Slack links broken