CSS - Concentric circles
Concentric circles with CSS
How can I prove these are the adjoint operators? How can I utilize the whole terminal, like htop or emacs do? I want to write a program that can "draw" in the terminal the same way as htop or emacs. By that I mean "get rid of the prompt and make the output dependent on the current size of the terminal".   To make this a bit more clear:   I want to use the terminal this way:     in stead of this way: Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.   I've solved this, but I think the proof is a bit weird and I wonder if there's a better one.    My proof:  We can see that $n\neq 1$, $n\neq 2$, $n=3$, $n\neq 4$ and $n\neq 5$.  Let $n&gt;5$. Notice that $5^6$ has $5$ digits, while $\frac{2^6}{9}=7\frac{1}{9}$, so $5^6$ has to have at least $8$ digits in order for the sum of the digits to be able to at least reach $2^6$.  Everytime $1$ is added to the exponent of $5$, the amount of digits $5^n$ gets is at most $1$, while $\frac{2^{n+1}}{9}-\frac{2^n}{9}=\frac{2^n}{9}&gt;3$, so the lowest amount of digits it has to have to reach $2^n$ becomes higher by at least $4$.  When $n=6$, the amount of digits $5^n$ has is already lower than the amount it has to have in order to reach $2^n$, and I've just proved that the amount it has to have in order to reach $2^n$ grows faster than the amount of digits $5^n$ has, therefore $5^n$ will never be able to reach $2^n$ when $n&gt;5$.  Hence the only solution is $n=3$. The strange thing is that opened scripts or newly opened ones are working fine. It's the new created C# scripts that are not working.  With not working, I mean the MonoBehaviour is not in light blue color it's in black color. In this screenshot I took, I marked it with a red circle.    What have I tried so far? I have closed Visual Studio and started over again.  Since it didn't solve it, I closed the unity editor and started it over again, to no avail.  I pressed 'clean solution', I pressed 'rebuild solution', I pressed 'build solution'.  What else can I do ? And why are the other scripts working fine? If I type gameo...it will auto complete it to GameObject but in this specific script it's just not working.  This is a screenshot of the editor. I have in the Hierarchy a Ladder object.  In the Assets I created a folder name Ladder and a script name Ladder. But this Ladder script is not working.    This is the Ladder script and this script was working before but once I created another script inside the ladder folder name Raise empty script the Raise script didn't work and now the Ladder is not working either. But other scripts are working fine.  using System.Collections; using System.Collections.Generic; using UnityEngine;  public class Ladder : MonoBehaviour {     public Transform charcontroller;      private bool inside = false;     private float heightFactor = 3.2f;      private void OnTriggerEnter(Collider other)     {             inside = true;     }      private void OnTriggerExit(Collider other)     {             inside = false;     }      private void Update()     {         if (inside == true &amp;&amp; Input.GetKey("w"))             charcontroller.transform.position += Vector3.up / heightFactor;     } } 'bridges' on a PCB copper layer I've come across a design where each pad was connected using 4 'bridges' to the GND copper layar. What stands behind these 'bridges'? Why not make a full copper layer with only solder-mask defining the pads? Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$? We can prove that there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1$. This leads to the following question:     Is it true that for every pair of primes $p&lt;q$ there are only finitely many integers $n$ such that $p^n-1\mid q^n-1$? Are there two primes $p&lt;q$ and an integer $n&gt;p+q$ such that $p^n-1\mid q^n-1$?Is it true that if $n&gt;6$ then $2^n-1\nmid 5^n-1$?   Edit: Here are some examples: \begin{array}{ll} 2^{36}-1\mid 41^{36}-1, &amp;3^{12}-1\mid 97^{12}-1,\\ 5^{6}-1\mid 37^{6}-1, &amp;7^{4}-1\mid 151^{4}-1. \end{array}  Now I prove there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1.$  Proof: Denote $A=2^n-1$ and $B=3^n-1$. If $n$ is even then $3$ divides $A$ but not $B$, a contradiction.  If $n$ is odd then $A\equiv -5\pmod {12}$. Since every prime greater than $3$ is $\equiv \pm1,\pm5 \pmod {12}$, some prime factor $p$ of $A$ must be congruent to $\pm5 \pmod {12}$. As $p \mid B$, we have $3^{n+1}\equiv 3 \pmod p$. Since $n+1$ is even, we get $(\frac{3}{p})=1$, a contradiction again. I am running 14.04 and have a HP Deskjet 2545 wireless printer which is supported by Ubuntu. I have run HpLIP, the latest version and installed the printer.  The printer is recognised by Ubuntu, printer and network, but LibreOffice do not see the printer. Only a Generic printer.  I don't know what to do anymore and would like to get some good advice Approximation algorithms for min vector subset-sum over GF(2) In  vzn asked about the following problem, which I'll call Vector-Subset-Sum.     Given a set of vectors $v_i$ over GF(2) and a target vector $y$, is there a subset of the $v_i$ summing to $y$?   In the answers, comments, and referenced papers I noted   The decision problem is in P. The natural minimization problem (finding the smallest subset) is NP-hard. It's related to the problem of finding sparse codewords in a linear code.   My question is: are there any known polynomial-time approximation algorithms for the minimization problem in (2)? I know very little about coding theory, so there may be some obvious or well-known approximation-preserving reductions to (3) that I have not seen. What happens when Wild Shape/Polymorph runs out in a space that's too small? Polygon intersection using turf js I have given this code for intersection: function intersectPolyByPolyFC(poly,fcPoly){         var fgp=[];//variable for feature group         var bbPoly=turf.bboxPolygon(turf.bbox(poly));//polygon representation of the bounding box of a reference polygon         for(var i=0;i&lt;fcPoly.features.length;i++){//loop through the feature collection of polygons             var bb=turf.bboxPolygon(turf.bbox(fcPoly.features[i]));//variable bb represents each polygon for feature collection             if(turf.intersect(bbPoly,bb)){//condition to check if the two bounding boxes intersect                 var int= turf.intersect(poly,fcPoly.features[i]);                 if(int){                     int.properties=fcPoly.features[i].properties;                     fgp.push(int);                 }             }         }         return turf.featureCollection(fgp);     }  and the function definition I have given as var bufline=turf.buffer(line,0.05,{units:&quot;kilometers&quot;}); var intBUOWL= intersectPolyByPolyFC(bufline, lyrBUOWL.toGeoJSON()); L.geoJSON(intBUOWL,{style:{color:'red',weight:5}}).addTo(mymap);  When I am drawing a line over a polygon for intersection I am getting this error Uncaught TypeError: Cannot read property 'map' of undefined     at Object.t.collect (turf.min.js:1)     at summarizePointsByLine (buffer.html:440)     at NewClass.&lt;anonymous&gt; (buffer.html:155)     at NewClass.fire (Events.js:190)     at NewClass._fireCreatedEvent (leaflet.draw.js:8)     at NewClass._fireCreatedEvent (leaflet.draw.js:8)     at NewClass.completeShape (leaflet.draw.js:8)     at HTMLAnchorElement.handler (DomEvent.js:92)  How can I resolve this error? The particle number on my settings appear in gray, I don't think i'm able to change the number even thought i need it, how can i make it white again? (Up to / until / by) 50% off I wonder if someone could tell me which choice works in the following sentence and why the others do not work: (From my point of view, all of these choices work in this context.)  They have great promotion till January 5th......50% off. a) up to; b) until; c) by Split a string with delimiters but keep the delimiters in the result in C# What are the most commonly used and basic Apache htaccess redirects? QGIS Processing - Additional Creation Parameter for GdalWarp I am having a hard time getting the "Additional Creation Parameters" to work when using GdalWarp through the processing toolbox.  I am trying to set the nodata value to 0 for the output raster.  processing.runalg("gdalogr:warpreproject","InRaster.tif","EPSG:32736","EPSG:32736",10,0,"-dstnodata 0","OutRaster.tif")   Has anyone used this functionality and managed to get it to work? How to restore Windows 7 MBR without a CD I have been playing with Ubuntu for a few weeks now, and I'd like to revert my computer back to it's original - factory - defaults.   On the computer I have a recovery partition (it's a netbook). I went through the process of recovery and everything seemed fine. However, when I restart the computer I'm presented with   grub rescue &gt;   Now, my understanding is that when I installed Ubuntu "side by side" it replaced the MBR or something like it, with GRUB.   I've read on a slew of forums, that I need to use a Windows Recovery Disk.   Here are my issues:   a) I don't have a recovery disk, I have a recovery partition - it's a netbook. b) I don't have an external cd drive.   What I do have is a USB key that has about 1gb of space on it.   Thanks in advance. Why does an open interval NOT have measure zero? $P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$ Is it true that  $$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$$ has no real root for even $n$ and exactly one real root for odd $n$? I can only prove that the polynomial cannot have any multiple roots. Am stuck , Please Help. Laplace transform of $1/t$ Call to a member function on a non-object