graph on mobius strip is nonplanar?
"Planar" graphs on Möbius strips
Why won't my computer go to sleep automatically? Windows 8 is set to sleep after 30 mins, and it used to work, but recently it's started refusing to sleep. (I can still manually ask it to go to sleep without any issue.)    I was having issues a while ago, but it was with my network adapter. That's since been disabled, so it's definitely not that:    I've checked to see what devices are able to wake up my machine, but it only appears to be my mouse:    Which is odd, because I haven't recently changed my mouse, and more confusing still: The monitor does go to sleep just fine. If it was actually the mouse keeping my system awake, I'm pretty sure the monitor wouldn't go to sleep.  I've checked my Wake Timers, and nothing:    I've also checked my existing requests...  UPDATE: I found something. What to do with it, I don't know...    Note: Even when /requests says that there's "NONE" under every category, my machine still won't sleep(!).    In short: How can I tell what's preventing my computer from Sleeping?    UPDATE: Ok, so I now have a few more pieces of the puzzle. I came back to my computer and it was ASLEEP! Lawks! It seems that the only times it doesn't sleep is if VLC Player is open, even if a video isn't actually playing.  UPDATE UPDATE: Ok, so it won't sleep sometimes when VLC Player ISN'T running, either. Bah! Expected number of rolling a pair of dice to generate all possible sums A pair of dice is rolled repeatedly until each outcome (2 through 12) has occurred at least once. What is the expected number of rolls necessary for this to occur?  Notes: This is not very deep conceptually, but because of the unequal probabilities for the outcomes, it seems that the calculations involved are terribly messy.  It must have been done already (dice have been studied for centuries!) but I can't find a discussion in any book, or on line. Can anybody give a reference? How to boot from iso with Grub2/Burg boot loader Can ubuntu be installed in intel kabylake 7th gen processor? I am using a 7th generation i5 processor(7200,2.50 ghz).The processor also have intel hd graphics 620 and nvidia geforce 940mx 2gb graphics card. I read previously that only windows 10 can be installed to this specific processor.  Is it true no version of ubuntu can be used with this processor?  If it's possible to install ubuntu using this processor, what additional steps other than the normal installation process should I undertake to get Ubuntu working? Setup SunFire 440 Raid Configuration How can I setup Internal Hard disk RAID5 configuration? I have SunFire 440 machine with 4 internal hard disk. I have never worked on Sun systems except for now and I am exploring google for the above solution. If anyone could help me out. Proof that every repeating decimal is rational "pros and cons", "black and white", "ups and downs". Always in a fixed sequence, is there a word or phrase for these? Is there a word or phrase for two nouns or adjectives joined by a conjunction (usually "and") in a fixed sequence?        alive and well           fast and furious   hat and gloves   pen and pencil   law and order   wit and wisdom   salt and pepper   bacon and eggs   horse and carriage   Adam and Eve   ladies and gentlemen   loud and clear   heads or tails   yes or no   dead or alive Installing Ubuntu with Fake RAID 1 Is there any difference in meaning between 'efficacy' and 'efficiency'? Basis for Skew Symmetric Matrix I'm trying to find a basis for the kernel for the following mapping:  Considering the linear transformation T: $M_{33} \rightarrow M_{33}  $ defined by $T(A) = .5(A + A^T)$. I know that this is basically asking for the basis under the condition that $T(A)=0$ which means that $A+A^T=0$ so $A^T = -A$.  I found that matrices that fit this condition are Skew Symmetric Matrices.  However, I'm not sure how to find the basis for the kernel of these matrices. How do I start a process from C#? Let's say I have a script that will be executed on various machines with root privileges, but I want to execute certain commands within that script without root.   Is that possible? Handler frame_change_pre doesn't work in render this works in viewport but not in render.  import bpy from math import *  def frame_handler(scene):     z = scene.objects['Lift'].location[2]     scene.objects['Text'].data.body = str(floor(z / 4.0) - 2)  bpy.app.handlers.frame_change_pre.clear() bpy.app.handlers.frame_change_pre.append(frame_handler)   How to get it working in render? I've read  and changed from "bpy.data.objects" to "scene.objects" as already seen in the script. What am I missing? Blender v. 2.81.16  Edit. Tried that depsgraph thing mentioned in comments and changed to frame_change_post:  import bpy from bpy.app.handlers import persistent from math import *  @persistent  # maybe not relevant but doesn't harm anything? def frame_handler(scene, depsgraph):     z = scene.objects['Lift'].evaluated_get(depsgraph).location[2]     scene.objects['Text'].data.body = str(floor(z / 4.0) - 2)  bpy.app.handlers.frame_change_pre.clear() bpy.app.handlers.frame_change_post.clear() bpy.app.handlers.frame_change_post.append(frame_handler)   Now the Text doesn't show up at all in rendered (but works in viewport). To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 ... (2n-1)\over 2.4.6...(2n)$ How can I show   $\lim_{n \to \infty} a_n = 0$  $a_n = {1.3.5 ... (2n-1)\over 2.4.6...(2n)}$  I have shown that $a_n$ is monotonically decreasing. I thought to shown sequence is bounded from below then it automatically would converge and hence my question will be solve. But I'm unable to show its boundedness... Or there maybe another method to prove this. Thanks Tabs in output file written by xelatex and pdflatex are different Downloading files instead of opening directly I have kept files in site assets and created hyperlinks to the files (which may be PDF or word ). When i click on the link it opens up in the browser. How do i force it to download ? Is the following correct, or is there more to it?  "I forgot his name" — I knew his name, but I forgot it.  "I forget his name" — I keep forgetting his name. Where using "forget" basically means that you tried to remember this information before as well, but you couldn't then either. How to use st_buffer? I would like to calculate a buffer of 5km around country polygons. However, I somehow always get a warning and an error. Here is a reproducible example code.   library(sp) library(sf) library(tmap)  library(rnaturalearth) countries_sp &lt;- ne_countries(scale = 10)  countries_sp &lt;- countries_sp[(countries_sp@data$geounit %in% "France"), ]  proj4string(countries_sp) &lt;- CRS("+init=epsg:4326")   countries_for_buff &lt;- st_as_sf(countries_sp, crs ="+proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +units=m +no_defs ")  countries_buff_5km &lt;- st_buffer( countries_for_buff, 5000)   here the warning:  dist is assumed to be in decimal degrees (arc_degrees). Warning message: In st_buffer.sfc(st_geometry(x), dist, nQuadSegs, endCapStyle = endCapStyle,  : st_buffer does not correctly buffer longitude/latitude data   Then   tm_shape(countries_sp) +   tm_polygons() + tm_shape(countries_buff_5km) +   tm_polygons()   gives the error   Error in if (all(tiny) &amp;&amp; show.messages) warning("all relative area sizes are below thres.poly",  :     missing value where TRUE/FALSE needed   What am I doing wrong? I guess there is something about the projection that does not quite work out the way it should. Delete or remove all history, commits, and branches from a remote Git repo? Jordan normal form and invertible matrix of generalized eigenvectors proof Struggling to find a place to start with this proof- just began learning about Jordan normal.  Given a 2-by-2 matrix $A$ and a Jordan normal form matrix $J_{\lambda}$, there exists a matrix $S = [v1, v2]$ s.t. $$S^{-1}AS = J_{\lambda}$$ That is, $J_{\lambda}$ is similar to $A$.  WTS: $$(A - \lambda I)v_{1} = 0 $$ $$(A - \lambda I)v_{2} = v_{1}$$    I was going to try to start with the similarity condition and work into producing the two statements below.  Transform the similarity condition to: $$(A = SJ_{\lambda}S^{-1}) * v_{1}$$  Rewrite our first statement to prove as: $$Av_{1} = \lambda I v_{1}$$   Substitute: $$\lambda I v_{1} = SJ_{\lambda}S^{-1}v_{1}$$  But I've been continually getting stuck.  Tried a few ways other than this.  What intuition am I missing?