references as a subsection
Can we create a subsection of the References Cited section with different reference numbering?
What is the name of an anime from 80s-90s movie/series in which there is a scene, maybe the end, where a girl (who has an​ armor) exchanges age with a dying man in a beach, so the man transforms into a baby and the girl grows to a woman? Suppose $K/F$ is an extension field, and $E_1$ and $E_2$ are two intermediate subfields of finite degree. Let $E$ be the subfields of $K$ generated by $E_1$ and $E_2$. I'm trying to prove that $$ [E:F]\leq[E_1:F][E_2:F].$$  Since $E_1$ and $E_2$ are finite extensions, I suppose they have bases $\{a_1,\dots,a_n\}$ and $\{b_1,\dots,b_m\}$, respectively. If $E_1=F$ or $E_2=F$, then the inequality is actually equality, so I suppose both are proper extension fields. I think $E=F(a_1,\dots,a_n,b_1,\dots,b_m)$. Since $\{a_1,\dots,a_n,b_1,\dots,b_m\}$ is a spanning set for $E$ over $F$,  $$[E:F]\leq n+m\leq nm=[E_1:F][E_2:F]$$ since $m,n&gt;1$.  Is this sufficient? I'm weirded out since the problem did not ask to show $[E:F]\leq [E_1:F]+[E_2:F]$ which I feel will generally be a better upper bound. When to use LinkedList over ArrayList in Java? I've always been one to simply use:  List&lt;String&gt; names = new ArrayList&lt;&gt;();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa? Wrap text at any point if normal hyphenation not possible I have data (generated from a database, not manually typed in) that mostly fits into a table cell with fixed width, but sometimes overflows because there are long words for which no hyphenation is found.  The problem can be demonstrated with the following example:  \documentclass{article} \usepackage[utf8]{inputenc} \begin{document} \begin{tabular}{|p{1cm}|p{4cm}|} 1 &amp; Cell where normal hyphenation is possible ÄÖÜ \\ 2 &amp; CellwherenormalhyphenationisnotpossiblebutshouldwrapinsteadofoverflowÄÖÜ \end{tabular} \end{document}   My requirements are:   Text never overflows the cell (assuming some minimum width such that at least a handful characters have place) First priority measure to achieve 1. is the normal hyphenation If 2. fails, it is allowed to break the word at any character, so fill the line and break just before overflow would happen (disregarding normal hyphenation rules)   In the example, the overflow in cell 1 is prevented by measure 2., the normal hyphenation. The second cell overflows. I would like to have this cell treated by measure 3.  For the answer please consider:   Package seqsplit didn't help me The custom macro \wrap proposed in the answer to  comes near my wish, but can't handle the non-ascii characters ÄÖÜ (independent if they are input with utf8 input encoding or with \"A\"O\"U) As the text comes from a database, no manual editing of the cell content is wanted.   One of my ideas was to insert \linebreak[0] after every character, to tell LaTeX that a break can be made if no better opportunities exist. But this doesn't work like intended.  Thanks for your suggestions! Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number I'm trying to understand the following proof of why      No two Fermat numbers have a common divisor greater than $1$.   Hardy and Wright show the following proofs:   If $x = 2^{2^n}$, we have  $$\frac{F_{n+k} - 2}{F_n}(\circ) = \frac{2^{2^{n+k}}-1}{2^{2^n}+1} = \frac{x^{2^k}-1}{x+1} = x^{2^k-1} - x^{2^k-2} + \ldots -1$$  The main issue I'm having is the $\circ$ part. I don't understand how they get that. The rest of the proof makes sense but the first part is really confusing me. Can someone please explain where they get that fraction?  Thanks a bunch! I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself.   Does anybody have a recommendation for a textbook on time series analysis that's suitable for self-study? In Java is there a way to check the condition:  "Does this single character appear at all in string x"  without using a loop? Let's say I have the domain johnsmith.com and I want people to reach me via email, what is the best email username to use?  Some examples:   john@johnsmith.com - redundant john.smith@johnsmith.com - redundant and looks kinda stupid mail@johnsmith.com - makes sense, but looks very "technical" me@johnsmith.com root@johnsmith.com - for the geeks among us ;-)   Of course, technically I can simply say that I will be able to receive *@johnsmith.com, however, for a better user experience I still just want one email address for public presence (website, business cards, etc.).  Any suggestions? What are the 'types' of parametric down conversion? I saw a video of Johann Cruyff , isn't that against the rules? Show that $xy=0$ is a variety but not a manifold When I format a drive to NTFS under Windows and plug it into the Ubuntu machine it is perfectly usable, but when I format it under Ubuntu using Disks (delete all partitions and create one single partition with NTFS) it does not show up when plugged into the Windows machine. Please note that in both cases the USB drive contains only one, primary partition formatted to NTFS, for example: /dev/sdb - the actual device /dev/sdb1 - the only, primary partition I've observed this behaviour both with a solid state USB pen-drive as well as an external USB magnetic HDD. How to (re)format a USB HDD or a stick to NTFS under Ubuntu so it is usable under Windows? How to switch 7 wires with a single on/off slide switch I am working on a project, where I want to build a raspberry pi into a nintendo 64 console, and be able to switch between with a single switch. By that I mean, I want to be able to use a single slide switch to either switch on the raspberry, or the n64.   I already figured the most stuff out, but I need help with wiring the controller port.   I have a n64 to USB controller adapter, which is connected to the raspberry. Each controller has 3 pins, VIN, GND and Data. I have 2 ports I need to switch. I also need to switch the usb Power for the raspberry.   So, I need a single switch, which has 2 states (ON, OFF), to switch the n64 controller ports to either the n64 console, or to my USB adapter. It also needs to switch the 2 wire power for the raspberry. I made some pictures to visualize it better:  So here is how it should be for to work with the regular N64. The controller ports are wired to the n64 console, and the raspberry power is not connected.    Then, when you switch it over to work with the raspberry, the n64 controller ports should go to the USB adapter, and the raspberry power is connected.    Now, my problem is I don't know how to achieve that. I know there are slide switches with enough pins, but they have multiple possibilities, not only two.   I also need something small, since the n64 case is small and doesn't have a lot of space.   Any ideas? Do numbers exist independently from observers? Truncate (not round) decimal places in SQL Server 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? How many "Recommend Close" votes is too many? Serana disappeared during dawnguard questline. Which is correct: "has died" or "died"? To me, using Present Perfect form means the event can occur again. So, saying      someone has died   may not be grammatically correct.  Also, I noticed (it might be just coincidence):     passed away   is used more often than     has passed away   Is using Present Perfect correct here? Symbol for “such that” (not in set) 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"