Can I make "starter" with active dry yeast?
Baking lots of bread - keeping a yeast starter
This is Baby Rudin exercise 7 of Chapter 3. Prove that the convergence of $\sum{a_n}$ implies the convergence of $\sum{\sqrt {a_k} \over k}$ if $a_n \ge 0$.  Proof:  I will attempt to show that the cauchy criterion is met so $${\sum_{k=n}^m {\sqrt {a_k} \over k}} \le \epsilon $$ for all $n,m \le N_1$. Im disregarding the absolute value since its all positive terms.   Since $\sum{a_n}$ converges, we know that the $\lim \limits_{n \to \infty} a_n =0$ So there exists some $N_2$ such that for all $n \ge N_2$, $$   a_n \lt \ {{(m-n)}^2k^2(\epsilon)^2} $$ I am again disregarding the absolute values because its always positive Let N=max{$N_1,N_2$} then for all $n,m \ge N$ $$\sum_{k=n}^m {\sqrt {a_k} \over k} \le \sum_{k=n}^m {\sqrt {{(m-n)}^2k^2(\epsilon)^2} \over k} \le \sum_{k=n}^m{(m-n)(\epsilon)} = \epsilon $$  Maybe this is just crazy, should I just use Cauchy-Schwarz inequality and forget about this or could I possibly make this method work? How do I set a static IP address in Windows? 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: Root partition size remains same after partition resize with gparted I had resized my root partition from 30gb to 70gb using gparted. But Ubuntu still shows that I have the same old disk size while gparted shows that I acually have 70gb and that the other 40gb is somehow used. How can I fix this?  Output of 'df -h':  Filesystem      Size  Used Avail Use% Mounted on /dev/sda5        30G   16G   13G  55% / none            4.0K     0  4.0K   0% /sys/fs/cgroup udev            1.9G  8.0K  1.9G   1% /dev tmpfs           391M  884K  390M   1% /run none            5.0M     0  5.0M   0% /run/lock none            2.0G  284K  2.0G   1% /run/shm none            100M   48K  100M   1% /run/user /dev/sda6       341G  115G  227G  34% /media/Data /dev/sdb1       932G  459G  474G  50% /media/sidharth/passport   Output of mount:  /dev/sda5 on / type ext4 (rw,errors=remount-ro) proc on /proc type proc (rw,noexec,nosuid,nodev) sysfs on /sys type sysfs (rw,noexec,nosuid,nodev) none on /sys/fs/cgroup type tmpfs (rw) none on /sys/fs/fuse/connections type fusectl (rw) none on /sys/kernel/debug type debugfs (rw) none on /sys/kernel/security type securityfs (rw) udev on /dev type devtmpfs (rw,mode=0755) devpts on /dev/pts type devpts (rw,noexec,nosuid,gid=5,mode=0620) tmpfs on /run type tmpfs (rw,noexec,nosuid,size=10%,mode=0755) none on /run/lock type tmpfs (rw,noexec,nosuid,nodev,size=5242880) none on /run/shm type tmpfs (rw,nosuid,nodev) none on /run/user type tmpfs (rw,noexec,nosuid,nodev,size=104857600,mode=0755) /dev/sda6 on /media/Data type fuseblk (rw,nosuid,nodev,allow_other,default_permissions,blksize=4096) binfmt_misc on /proc/sys/fs/binfmt_misc type binfmt_misc (rw,noexec,nosuid,nodev) gvfsd-fuse on /run/user/sidharth/gvfs type fuse.gvfsd-fuse (rw,nosuid,nodev,user=sidharth) /dev/sdb1 on /media/sidharth/passport type fuseblk (rw,nosuid,nodev,allow_other,blksize=4096) The set of integers $n$ expressible as $n=x^2+xy+y^2$ 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" What to do when visa admission expires during lockdown? How do I "replay" the "Caveats" section from a homebrew recipe I am flying from Doha to Philadelphia by Qatar Airway. While in Philadelphia, I need to change flight to US Airway. But I only have 1 hour and a half before my next flight to Birmingham. Do I have enough time to check out and check in my baggage?  1.Kuala Lumpur (KUL)  Tue, 21 Jul 2015 20:50  2.Doha (DOH)  Tue, 21 Jul 2015 23:20  3.Doha (DOH)  Wed, 22 Jul 2015 01:10   Philadelphia (PHL)  Wed, 22 Jul 2015 07:45   5.Philadelphia (PHL)  Wed, 22 Jul 2015 09:40 Terminal F  6.Birmingham (BHM)  Wed, 22 Jul 2015 11:00 I am a economics major undergraduate student who will apply for grad schools in the coming semester. I think I have quite a strong research experience in mathematical statistics (asymptotic statistics to be specific), but, unfortunately, not much in economics itself. So I am curious if economics departments in graduate schools will care about my research experience in statistics?  Maybe a broader question is if grad schools care about applicants' research experience in a different (maybe even unrelated) field at all? I guess in my case statistics and economics are still quite correlated, but what about other more distant combinations of target departments and previous research experience? Mute conversations on Skype I'm in a conversation and I don't really want to leave because the people there keep adding me back so it's just whatever. But I would like to mute the conversation or something like I do on Facebook so I won't take notifications or anything from there unless I press on the group and see what's going on. Because for now I have my Skype having a new notifications every half a second.  Any solutions to that? Preserve blend mode effect when underneath layers are disabled? (Photoshop) I've heard many times that it's bad to use display: none for SEO reasons, as it could be an attempt to push in irrelevant popular keywords. A few questions:   Is that still received wisdom? Does it make a difference if you're only hiding a single word, or perhaps a single character? If you should avoid any use of it, what are the preferred techniques for hiding (in situations where you need it to become visible again on certain conditions)?   Some references I've found so far:       If you're straight-out using CSS to hide text, don't be surprised if that is called spam. I'm not saying that mouseovers or DHTML text or have-a-logo-but-also-have-text is spam; I answered that last one at a conference when I said "imagine how it would look to a visitor, a competitor, or someone checking out a spam report. If you show your company's name and it's Expo Markers instead of an Expo Markers logo, you should be fine. If the text you decide to show is 'Expo Markers cheap online discount buy online Expo Markers sale ...' then I would be more cautious, because that can look bad."   And  on the same article     We can flag text that appears to be hidden using CSS at Google. To date we have not algorithmically removed sites for doing that. We try hard to avoid throwing babies out with bathwater.   Eric Enge      The legitimate use of this technique is so prevalent that I would rarely expect search engines to penalize a site for using the display: none attribute. It’s just very difficult to implement an algorithm that could truly ferret out whether the particular use of display: none is meant to deceive the search engines or not. Let $S = \{ax + by: x,y \in \mathbb{Z}\}$  and let $e &gt; 0$ be the smallest element in $S$. Prove that $e \mid a$, and hence prove that $e = \gcd(a,b)$  I'm afraid I can't provide much of my initial working here because I'm at a loss of how to start.  I suppose that to show $e\mid a$ I would have to show that $eg = a$ for some $g \in \mathbb{Z}$. But I have no idea how I would do this. root@SERVER ~$ df Filesystem  512-blocks  Free    %Used   Iused   %Iused  Mounted on /dev/YXCV   655360      365632  45% 6322    13% / /dev/ASDF   3801088     670648  83% 41759   32% /usr /dev/ASR    1048576     500496  53% 5555    9%  /var   How can I pipe the df command's output to only display lines that have more usage than 80%?  e.g.: it would only display:  /dev/ASDF   3801088     670648  83% 41759   32% /usr Vandermonde Determinant This is an exercise from Ian Stewart's Galois Theory, $3^{rd}$ edition:     If $z_1,z_2,\ldots,z_n$ are distinct complex numbers, show that the determinant $$D=\left|\begin{array}[cccc]  11&amp;1&amp;\cdots&amp;1\\ z_1&amp;z_2&amp;\cdots&amp;z_n\\ z_1^2&amp;z_2^2&amp;\cdots&amp;z_n^2\\ \vdots&amp;\vdots&amp;\ddots&amp;\vdots\\ z_1^{n-1}&amp;z_2^{n-1}&amp;\cdots&amp;z_n^{n-1} \end{array}\right|$$   is nonzero.       Hint: Consider the $z_j$ as independent indeterminates over $\Bbb C$. Then $D$ is a polynomial in the $z_j$, of total degree $0+1+\cdots+(n-1)=\frac{1}{2}n(n-1)$. Moreover, $D$ vanishes whenever $z_j=z_k$ for $k\neq j$, as it then has two identical rows. Therefore $D$ is divisible by $z_j-z_k$ for all $j\neq k$, hence it is divisible by $\prod_{j&lt;k}(z_j-z_k)$. Now compare degrees.   My question is how to do this. I follow the hint and I'm thinking of $D$ as a cofactor expansion; is that the idea? Also, the fact that $D$ vanishes whenever $z_j=z_k$ for $k\neq j$ follows since it would have two identical columns, right? I don't see why $z_j=z_k$ would imply it has two identical rows, as the hint suggests. The fact that it is divisible by $(z_j-z_k)$ is easy since that would make $z_k$ a root for $k=j$, but I'm not quite sure I follow why the degrees would be different. I think the degree of the product would be $1+2+\cdots+(k-1)$, but then add these up for all $k&lt;n$?   I appreciate any clarification that you can provide! Is there a guideline about when to end expressions with semicolons? How do I Parameterize a null string with DBNull.Value clearly and quickly I would like to know if it is possible to enable free shipping with Woo Commerce only if certain items (or items of certain categories / shipping classes) are included in the cart.  The Free Shipping option only activates on the basis of cart value or via a coupon code so I investigated Flat Rate shipping and discovered that it prioritises the most expensive shipping class over the cheaper ones. This means the free shipping class I created never overrides the default charge.  I understand the logic behind this but it's the opposite of what I need as the idea is to incentivise purchases of higher profit margin products by eliminating delivery charges when they're included in an order.  I don't know if what I am trying to achieve is simply not possible within Woo Commerce. A coupon that only applies to certain products / categories seems to be the closest I can get but I'd rather not force users to enter a code at checkout.  Does anybody know if there any simpler ways to give users who purchase certain products free shipping? My Android device screen got broken and I can't see what I'm doing. That's the only wrong thing with my device, the rest is apparently working OK. Is there any way to send my device screen to my computer? I don't want to work blindly anymore!