Why does the SSR have 1 degree of freedom in simple linear regression?
Why does the degree of freedom of SSR equals 1 in simple linear regression
Includepdf causes an error message from pgfplots externalization I have a file test.pdf which I include in a document containing also an externalized pgfplots picture.  When I compile the following code, I get the error message Sorry, the system call pdflatex ... did NOT result in a usable file.  In order to make my code work, I first need to remove the includepdf statement, compile (to create the externalized figures) and then compile again with the includepdf statement.  I suppose that it is a bug, or is there any possibility to solve it ?  Of course, the file test.pdf is totally independent from the externalized pictures from pgfplots.  \documentclass{scrbook}   \usepackage{pgfplots}  \pgfplotsset{compat=1.8}  \usepgfplotslibrary[external]  \tikzexternalize[shell escape=-enable-write18]  \usepackage{pdfpages}   \begin{document} \includepdf{report_test-figure44}   \begin{tikzpicture}  \begin{axis}[  xlabel=Cost, ylabel=Error]  \addplot[color=red,mark=x] coordinates {  (2,-2.8559703) (3,-3.5301677) }; \end{axis}  \end{tikzpicture}   \end{document} Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains?  I heard many reasons, but I'm not sure which is true.   Some say it's just a matter of beauty, so Lagrangians are more beautiful because they don't break/separate the space-time variables (so space-time is a single variable, like in the Klein-Gordon Lagrangian and Hamiltonian).  Some say that Hamiltonians are not always Lorentz invariant.  Could someone explain in a little bit more details? First, if you have a better suggestion for title I'm really opened to suggestions, but it is the best I came up with.  If I touch an electric line and the earth, I will get electrocuted.  However, if I touch the positive of a car battery, people told me the same thing won't happen...why is it?  It seems I need to touch the battery positive and the battery ground. Trigger Task Scheduler in Windows 7 when computer wakes up from sleep/hibernate I don't want task scheduler or whatever to wake the computer, but when I open the laptop back up and the machine wakes I'd like that to be the trigger that task scheduler or something uses to run an app. I am trying to understand the derivation of the stars and bars formula. I understand how a problem can be converted to the stars and bars format, but I am confused about how the problem of choosing all the different ways to put k stars in n sections can be written as ${n+k-1 \choose k}$. Generally "n choose k" is for counting the number of combinations of k objects we can get given n distinct objects right? That I understand since we're doing permutation divided by the number of orderings for each group since order doesn't matter. I need help figuring out how stars and bars fits into this. My primary router has trouble extending wifi coverage to some bedrooms in the house so I am planning to add a second router to extend the wifi network using the wired Ethernet ports in one of the areas of poor coverage. Basic layout -   The ISP's router is in my family room downstairs (fiber connection) and the internet connects to the fiber via a box in an upstairs closet.   I purchased and installed an unmanaged Ethernet switch/splitter. In the upstairs closet where all of the Ethernet wires meet, the family room Ethernet cable was plugged into the ISP's box. I disconnected this wire and replaced it with a CAT5 cable running from the ISP's box in the closet to the Ethernet switch's port 1.  I think connected the family room Ethernet cable to port 2 and did the same in order for all the remaining Ethernet cables to various bedrooms.   So far, the switch is working fine.  I have wifi working with internet coming off of the router in the living room so I believe the switch is installed correctly otherwise that wifi should not have internet coming off of the living room jack.   Here is where things go awry - I took my second wifi router and connected the WAN/Yellow port to the Ethernet wall jack in another bedroom.  I then connected a lap top to one of the Ethernet ports on this router and found "no internet" after connecting.  On a whim, I changed the connection so that the router was connected to the Ethernet wall jack in one of the white ports but with the same results.   I don't think this counts as cascading and I don't really need a new network since I do not share the connection with any non-family members.  The router has been reset to factory settings to clear out any old instructions - but I still can't get it to connect to the internet or access the router to change the settings even - it's a netgear and the routerlogin.net will not let me access the router even when I am on the working WIFI for internet and have a cable running from the laptop to the netgear router.   I could use some help - just trying to extend the wifi range and it seems like it should be much less complicated. Tried following instructions in several other posts and they did not work for me - because I cannot access the router to change any settings. Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$ Let $\phi: R \to S$ be a surjective homomorphism. Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$ for an ideal $J$ of $R.$  Obviously, $S \cong R/ \ker \phi$(first isomorphism theorem) and $\phi(J)$ is an ideal of $S$, since $\phi$ is surjective( $\forall s \in \phi(J), s = \phi(j)$ for some $j \in J, \forall s' \in S, s' = \phi(r)$ for some $r \in R$, so $ss' = \phi(j)\phi(r) = \phi(jr) \in \phi(J)$, and $ss' = \phi(r)\phi(j) = \phi(rj) \in \phi(J)$ ).  However, I'm having trouble with going on. If it's important, I mean a unitary ring by a ring. GeoJSON does not appear on my Leaflet map I'm a beginner in Leaflet and I need help to deal with GeoJSON files.  I succeeded in creating a Leaflet basemap. I can add markers without troubles but I cannot manage to show a GeoJSON layer.  Here is the code I picked up from Leaflet Tutorials website  :  var geojsonFeature = {     "type": "Feature",     "properties": {         "name": "Coors Field",         "amenity": "Baseball Stadium",         "popupContent": "This is where the Rockies play!"     },     "geometry": {         "type": "Point",         "coordinates": [-104.99404, 39.75621]     } }; L.geoJSON(geojsonFeature).addTo(map);   Unfortunatly, the GeoJSON does not appear in my map.   Can you tell me where I missed something ?    Alright, you're fine Francisco, this part was OK. I changed the whole script and it works !  However, would you know how to load a GeoJSON from an external source ?  I tried this :   var geojsonLayer = new L.GeoJSON.AJAX("foo.geojson");        geojsonLayer.addTo(map);   from   but this definitely does not work.  Any ideas ?    I am not skilled enough to understand your advice.  Here is the whole code I am using to create my map :  &lt;!DOCTYPE html&gt; &lt;html&gt; &lt;head&gt; &lt;title&gt;data&lt;/title&gt; &lt;meta charset="UTF-8"&gt; &lt;link rel="stylesheet" href="https://unpkg.com/leaflet@1.0.3/dist/leaflet.css" /&gt; &lt;script src="https://unpkg.com/leaflet@1.0.3/dist/leaflet.js"&gt;&lt;/script&gt; &lt;script src="https://code.jquery.com/jquery-3.1.1.min.js"&gt;&lt;/script&gt;   &lt;script type="text/javascript" src="http://maps.stamen.com/js/tile.stamen.js?v1.3.0"&gt;&lt;/script&gt; &lt;script src="/js/leaflet-0.7.2/leaflet.ajax.min.js"&gt;&lt;/script&gt; &lt;script src="htdocs/webmap101/leaflet.ajax.min.js" type="text/javascript" &gt;&lt;/script&gt; &lt;style&gt;    #map {width: 960px; height:700px;} &lt;/style&gt; &lt;/head&gt; &lt;body&gt;   &lt;div id="map"&gt;&lt;/div&gt; &lt;script&gt;   // create map var lat = 44.933331; var lon = 4.9;  var map = L.map('map',{center: [lat,lon],zoom: 6});   // basemaps var base = L.tileLayer('http://{s}.tile.osm.org/{z}/{x}/{y}.png',   {attribution: '© &lt;a href="http://osm.org/copyright"&gt;OpenStreetMap&lt;/a&gt; contributors'  }); var toner = new L.StamenTileLayer("toner"); var watercolor = new L.StamenTileLayer("watercolor"); var landscape = L.tileLayer('https://tile.thunderforest.com/landscape/{z}/{x}/{y}.png'); base.addTo(map);   // markers  var mark1=L.marker([lat,lon]) mark1.addTo(map)    // layers panel  L.control.layers({"base": base, "water": watercolor, "toner": toner , "landscape" : landscape}).addTo(map);    // geojson files var geojsonFeature = {     "type": "Feature",     "properties": {         "name": "Coors Field",         "amenity": "Baseball Stadium",         "popupContent": "This is where the Rockies play!"     },     "geometry": {         "type": "Point",         "coordinates": [-104.99404, 39.75621]     } }; L.geoJSON(geojsonFeature).addTo(map);    //ajax  var geojsonLayer = new L.GeoJSON.AJAX("foo.geojson");        geojsonLayer.addTo(map);  &lt;/script&gt; &lt;/body&gt; &lt;/html&gt;   I know it's a bit messy but this is actually my very first HTML script... I guess I did not include in a proper way the AJAX library.    Actually, I just want a solution to replace the lines where I create the GeoJSON by something that tells javascript to load the GeoJSON stored locally in my folder. This :  var geojsonFeature = {     "type": "Feature",     "properties": {         "name": "Coors Field",         "amenity": "Baseball Stadium",         "popupContent": "This is where the Rockies play!"     },     "geometry": {         "type": "Point",         "coordinates": [-104.99404, 39.75621]     } };   should be transformed into something like (I don't know if it exists) :  var geojsonFeature = [foo.geosjon]   where "foo.geosjson" is a file like :  { "type": "FeatureCollection", "name": "abies", "crs": { "type": "name", "properties": { "name": "urn:ogc:def:crs:OGC:1.3:CRS84" } }, "features": [ { "type": "Feature" Verbatim environment that can break long lines? I want to generate a PDF of user-submitted text using LaTeX. To handle crazy user input, I first thought about using the verbatim package, but of course it doesn't break up too long lines. Is there some package that works similar to verbatim (i.e., accept any input) but formats the text nicely? How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$? Calculating with Mathematica, one can have $$\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}\,\mathrm dt=\frac{\pi}{4}.$$   How can I get this formula by hand? Is there any simpler idea than using $u = \sin t$?     Is there a simple way to calculate $$ \int_0^{\pi/2}\frac{\sin^n t}{\sin^n t+\cos^n t}\,\mathrm dt $$ for $n&gt;3$? Could anyone come up with a reference for this exercise? Let $A$, $B$ be two reduced $k$-algebras. Then if an element of the form $$\sum a_{i}\otimes b_{j}$$ is nilpotent, we can compose it with any $k$-homomorphism $f$ from $A$ to $k$ to get a homomorphism from $A\otimes B$ to $B$. This map's image is $$\sum f(a_{i})\otimes b_{j}$$must be nilpotent as well. So if we assume $b_{j}$ is linearly independent in the first place, we may reason that $f(a_{i})=0$. This showed that $a_{i}$ are in the Jacobson radical of $A$. However, we only know $\mathrm{Nil}(A)=0$, and it is not clear to me how to pass from the Jacobson radical to the nilradical without using some commutative algebra machinery.   Here is what I think that might work. If $A$ is of finite type, then by Nullstellensatz we can assert the above is true. But if $A$ is not of finite type, then I can write $A=k[x_{1},...,x_{n}][X]$, where $n$ is the transcendence degree of $k(A)$ and $k[X]$ is finite over $k$. Then I should be able to pass from $k[X]$ to $A$ by inductive argument on the transcendental degree of $k(A)$, since prime ideals are maximal in a UFD (I am working with $k[x]$ by introducing $[x]$).   The proof I have for the case of finite type is not satisfying. Given $I\subset k[X]$, using Nullstellensatz one can show that $$I_{X}V_{X}[I]=\sqrt{I}$$ where $V_{X}[I]$ is the set of all points in $X$ on which $I$ vanishes, and $I_{X}(V_{X}[I])$ be the ideal in $k[X]$ which vanishes on $V_{X}[I]$. Granting this, let $I=(a_{i})$, then we want to show $I=0$, which is $V_{X}[I]=X$. This follows since if $U\subset W$, then $V_{X}[U]\supset V_{X}[W]$. Since $V_{X}[I]\supset V_{X}[m_{x}]$ for all maximal ideal corresponding to points, it must be $X$. This proof is unnecessarily winding by using the ideal-variety correspondence. Ideally I should be able to construct a pure algebraic proof.   The thing not clear to me is whether the above strategy really works. Namely I am not sure if I can really induct on the transcendental degree of $k(A)$. To make matters simple assume we showed the statement holds for $A$ with transdental degree $&lt;n$. For $A$ with transdental degree $n$ we can thus write it as $k[A'][x]$. Then any maximal ideal $m'$ of $k[A'][x]$ must correspond to a maximal ideal $m=m'\cap k[A']$ in $k[A']$. But it seems not possible to show that any prime ideal is maximal. Indeed considering the simple example of $k[x,y]$, where $(x)$ is a prime ideal but not maximal since $k[x,y]/(x)=k[y]$ is not a field. The problem is in the inducting process the base ring is not neccessarily a field, and so this strategy cannot work.   I am thinking maybe I can show $m'=m[f(x)]$ with $f(x)$ some irreducible polynomial in $k[A'][x]$. Because we know $k[A'][x]$ is noetherian by Hilbert's basis theorem, so in particular $m'$ must have a finite generating set. And we can reduce the number of irreducible polynomial to 1 since $m'$ is a maximal ideal. But I still do not know how to use this to finish the proof. I have an unlocked North American (Canada) iPhone 5s, where can I buy a data only SIM card in Japan ? I'm not interested in renting nor in a voice plan, I'll be staying for 4 weeks.  I'll be landing in Tokyo, so preferably around there. Can I get them from the airport somewhere ? I'm assuming I won't have problems with the network/frequencies, am I correct ? Windows update doesn't progress beyond 0 KB 0% Why could centering independent variables change the main effects with moderation? Pressing Enter should not refresh the page Unbiased estimator for geometric distribution parameter p Here's what I am trying to do:  1) User creates record A.  2) Time-based workflow sends an email to the Record A creator based on a date field in the record.  3) The email template has a URL link.  4) The URL links to a Visualforce page that is basically a form with fields to be filled out (this Visualforce page is in a managed package) and a save button that creates a new User record.  5) When the User clicks the URL link in the email, the Visualforce page opens in a new window.  6) I would like to pass the values of the fields in record A to pre-fill the Visualforce page fields.   Here's my link:  &lt;a href="https://cs19.visual.force.com/apex/CloneThisUser?Desktop=true&amp;Id={!Pending_User__c.User_to_CloneId__c}&amp;formGroupInputSmall={!Pending_User__c.First_Name__c}   And here's the code from the relevant section of the Visualforce page:  &lt;div class="form-group form-group-sm"&gt;       &lt;!-- &lt;apex:outputLabel styleClass="col-sm-2 control-label" for="formGroupInputSmall"&gt;First Name&lt;/apex:outputLabel&gt; --&gt;       &lt;div class="col-xm-11 col-sm-12"&gt;           &lt;apex:inputField html-placeholder="First Name" styleClass="form-control FirstNameInput"  value="{!u.FirstName}" id="formGroupInputSmall"/&gt;       &lt;/div&gt;     &lt;/div&gt;   I have only included the first field I would like to pass the parameter to, in order to keep this post simple.   The link passes the User_to_Clone_Id__c just fine but does not fill in the "First Name" field with the value of the First_Name__c .  What am I doing incorrectly? Thanks. Is adjoint of singular matrix singular? What would be its rank? Should we allow adding rep to bounties to extend their duration? There are a few variables here that I was thinking about:   Spend rep to extend a bounty for a certain amount of time Allow the rep spent to extend duration to add into the original bounty Create minimums on the amount necessary to extend dependent on how long it has been up   These are just ideas and can be tweaked as necessary, but the idea in whole is to encourage people to spend more on rep and avoid "wasted" rep because there wasn't a good answer to a question while minimizing the amount of possible abuse. This was part of the idea to spend a small amount of rep to extend duration without adding to the rep so that you wouldn't have to spend the whole amount over again for a couple more days.  The typical use case that I am thinking of is when you create a bounty and it still gets no attention. I think it would be cool if you could then add onto it to turn it into a higher bounty instead of having those points completely gone.  Possible abuses:   Keeping bounty questions alive for inappropriately long times. There is already an answer but the author does not want to award the bounty.   For 1, you can resolve this by increasing the amount necessary to keep a question alive exponentially similar to what is already in place. You could also halve the amount of extended duration per extension. For 2, this is a problem with the existing system as well, but the author does not have a positive incentive not to award the points since he himself still cannot get them back. We are currently working on a windows based application where users capture data. Some data is captured in a table where other data is captured in text blocks. Im currently faced with the dilemma of how to align contents specifically decimal values.  Editable cells in a grid are indicated with a pencil icon which disappears once in edit mode. You will notice that the table consists of various field types, decimals and text. So what should I do and why?  A> right align all cell content  B> left align all cell content  C> right align only decimal values in cells  D> Whatever else you can suggest