Suppose that $f$ is entire and that for each $z$, either $|f(z)| \le 1$ or $|f'(z)| \le 1$. How can I prove that $f$ is a linear polynomial?  What I have tried: I tried to use line integral to show $$|f(z)| \le A + |z|$$where $A = max(1, |f(0)|)$  However, I was not satisfied with my approach. I am looking forward to hearing how you tackle it.
My question is in the title. I'm a little lost in how to solve this problem. There is a hint associated with the problem that states the following:   Use a line integral to show that $ |f(z)| \leq A + |z| $ where A = $\max\{1, |f(0)|\}$  Thanks for the help.
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$? Can't run "dpkg --add-architecture i386" on 12.04 64-bit to run eclipse ADT This seems to be a chicken-egg problem. The most common task using sudo is installing and removing software.  sudo apt-get purge &lt;appname&gt;   But sudo itself can be removed.  sudo apt-get purge sudo # Do not run this command on production computers!   This is where the fun comes  ubuntu@ubuntu:~$ sudo bash: /usr/bin/sudo: No such file or directory   Although it's obvious that no person in his right mind will purge sudo (other than me), someone can be fooled to run this command (not directly, in its hex mode, or whatever it's called) or a person could SSH in disguised as tech guru and do the mess.  So is there a way of reinstalling sudo? Short science fiction film about a Midwest farmer who builds a bunker after finding a space plant Same gravatar is displayed for different users in stackexchange.com filters Same gravatar is displayed for different users in the stackexchange.com , under the Top Network Askers in the right side bar.   The red circled image's source (&lt;img src=) are from   https://www.gravatar.com/avatar/?s=18&amp;d=identicon&amp;r=PG&amp;s=30                                ^   Seems the gravatar id is missing here in the image source.  For an example from the list, the user  gravatar id should be    https://www.gravatar.com/avatar/66c66c4d97a7bc3859a85253f003e1fb?s=18&amp;d=identicon&amp;r=PG&amp;s=30   but it is mapped with   https://www.gravatar.com/avatar/?s=18&amp;d=identicon&amp;r=PG&amp;s=30   which caused the display issue. Processing time/speed for Mosaic to New Raster I have a question on speeding up “Mosaic to New Raster” or finding an alternative.  After completing a suitability analysis we are trying to define movement corridors.  We used a modified CircuitScape that left 4 folders, each containing 1080 raster tiles across our study area.  We now need combine all 1080 rasters in each folder then combine these 4 combined rasters into a final raster which will be analyzed for paths.  I tried a python script that just wouldn’t work so I went on to Model Builder.  It iterates through the grids in the folder, collects the values (raster names), then mosaics all to a new raster.  It has been running for 5 days now and the results window indicates it is working.  I’m hoping it will conclude in the next day or 2.  But, we still have 3 more folders, each with 1080 rasters, that need to be mosaicked.  So….is there a way to speed up Mosaic to New Raster or is there an alternative I could use to produce the final grid?    The cell size is 270 meters, 540 x 540 columns and rows, 1 band, 32 bit floating. I want to use  to display my CPU-Core temperatures (haswell i7). However the setting:  order += "cpu_temperature 1" #... cpu_temperature 1{         format = "T: %degree °C" } #   doesn't display the correct core temperature. The numbers it shows seem to correspond to the value xsensors shows for temp1, if I change the 1 to 2 above it corresponds to xsensors temp2. Trying 3 or 4 doesn't have any effect. However I want to get the true core temperatures of all 4 cores with i3 status. How can I do this? How to run Wireshark on Ubuntu 17.10 I used to run wireshark on ubuntu 17.04 with  ~/$ sudo wireshark   but now (just after update to 17.10) when I write the same I get an error  ~/$ sudo wireshark      QStandardPaths: XDG_RUNTIME_DIR not set, defaulting to '/tmp/runtime-root'     Invalid MIT-MAGIC-COOKIE-1 keyQXcbConnection: Could not connect to display :0 Norm of adjoint operator in Hilbert space What is the closed formula for finding      $$ \sum_{i=0}^{k} \binom{n}{2i}=?\quad ,k\leq \lfloor{n/2}\rfloor $$   I need summation only up to some intermediate  $k$ where $k\leq \lfloor{n/2}\rfloor$ .  SAY I need a closed formula to calculate $\binom{8}{0}+ \binom{8}{2}+\binom{8}{4} +\binom{8}{6}$  HERE $n=8$ and $k=6$ Why aren't hash values for "nothing" (empty) defined as all zeros? Any decent hash algorithm will produce basically "random like" values for any given input including the empty input.  For example MD5 produces d41d8cd98f00b204e9800998ecf8427e on an empty input.  I wonder, however, why the MD5 algorithm wasn't defined to have a final step where the output is XORed with d41d8cd98f00b204e9800998ecf8427e. This should not affect the cryptographic strength of the hash algorithm, and it would have the convenient property that a hash of all zeros represented a zero input.  Would it simply just because adding that step would slow the hash down a bit? Is $D_n$, the dihedral group of order $2n$, isomorphic to a subgroup of $S_n$ ( symmetric group of $n$ letters) for all $n&gt;2$? Clarifications about Gstreamer I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help I have Solaris 8 OS installed in French.  Is it possible to switch from French to English without reinstalling the OS ? If yes how ?  When locale -a i have this :  POSIX common en_US.UTF-8 C iso_8859_1 en_CA en_CA.ISO8859-1 en_US en_US.ISO8859-1 en_US.ISO8859-15 en_US.ISO8859-15@euro fr_CA fr_CA.ISO8859-1 iso_8859_15 th th_TH th_TH.TIS620   Even when I try to edit /etc/default/init with :  LANG=en_US.ISO8859-15 LC_COLLATE=en_US.ISO8859-15 LC_CTYPE=en_US.ISO8859-15 LC_MESSAGES=en_US.ISO8859-15 LC_MONETARY=en_US.ISO8859-15 LC_NUMERIC=en_US.ISO8859-15 LC_TIME=en_US.ISO8859-15 LC_ALL=en_US.ISO8859-15   and reboot : nothing happens.  To verify the result i always use date and when i reboot : i also have the date in french.  P.S : I have to do this configuration in a computer which isn't here in my office, so i have to this manipulation in a an another computer here in my office and if it works, i'll do it to the other computer.  So the computer here is configured in English and i have to switch it to French. Here is the content of my ~./dt :  C                     errorlog              sessionlogs Desktop               errorlog.old          sessions Trash                 errorlog.older        simulateur.dtwmrc appconfig             help                  startlog appmanager            icons                 startlog.old asr.dtwmrc            outils.dtwmrc         startlog.older bin                   palettes              tmp bookmarks             sdtfonts              types dtwmrc                sdtpcaction.conf      wsmenu en_US.ISO8859-15      sdtpcaction.conf.bak   Thanks I'm trying modeling things like this using oracle:  An account can have 1~5 members  So I'll have a account table and a member table with a FK of account. But is that possible to check if the account have less than 5 members?  I've tried constraint and trigger but oracle doesn't allow sub queries in constraint or condition of trigger like  CHECK( SELECT ...) or IF count(*) &gt;= 5  which make things getting hard. JSON.parse: unexpected character Some doubts about photons In which order should I play the Borderlands series? I have been trying to create a function that does basically the same thing that the QGIS "dissolve" function. I thought it would be super easy but well apparently not. So from what I have gathered around, the use of fiona with shapely should be the best option here. I just began to mess around with vector files so this world is pretty new to me and python as well.  For these example, I am working with a county shapefile founded here  So here are some piece of code I gathered but can't find a way to make them work together  For now my best method is the following based on : . It works fine and I get a list of the 52 states as Shapely geometry. Please feel free to comment if there is a more straight forward way to do this part.  from osgeo import ogr from shapely.wkb import loads from numpy import asarray from shapely.ops import cascaded_union  ds = ogr.Open('counties.shp') layer = ds.GetLayer(0)  #create a list of unique states identifier to be able #to loop through them later STATEFP_list = [] for i in range(0 , layer.GetFeatureCount()) :     feature = layer.GetFeature(i)     statefp = feature.GetField('STATEFP')     STATEFP_list.append(statefp)  STATEFP_list = set(STATEFP_list)  #Create a list of merged polygons = states  #to be written to file polygons = []  #do the actual dissolving based on STATEFP #and append polygons for i in STATEFP_list :      county_to_merge = []     layer.SetAttributeFilter("STATEFP = '%s'" %i )      #I am not too sure why "while 1" but it works      while 1:         f = layer.GetNextFeature()         if f is None: break         g = f.geometry()         county_to_merge.append(loads(g.ExportToWkb()))      u = cascaded_union(county_to_merge)     polygons.append(u)  #And now I am totally stuck, I have no idea how to write  #this list of shapely geometry into a shapefile using the #same properties that my source.   So the writing is really not straight forward from what I have seen, I really just want the same shapefile only with the country dissolve into states, I don't even need much of the attribute table but I am curious to see how you can pass it on from the source to the new created shapefile.  I found many pieces of code for writing with fiona but I am never able to make it work with my data. Example from  :  from shapely.geometry import mapping, Polygon import fiona  # Here's an example Shapely geometry poly = Polygon([(0, 0), (0, 1), (1, 1), (0, 0)])  # Define a polygon feature geometry with one attribute schema = {     'geometry': 'Polygon',     'properties': {'id': 'int'}, }  # Write a new Shapefile with fiona.open('my_shp2.shp', 'w', 'ESRI Shapefile', schema) as c:     ## If there are multiple geometries, put the "for" loop here     c.write({         'geometry': mapping(poly),         'properties': {'id': 123},     })   The problem here is how to do the same with a list of geometry and how to recreate the same properties than the source. For example, in a novel, if someone is so powerful that no one can stop him, something like this would be said:     He [insert word] in the continent [or some other location].   "Moved unhinderedly" somewhat fits it, but it doesn't really seem like the right term.  The word I'm looking for describes a few things:   Should have an implication that the person himself is powerful That person can go wherever he wishes to, and cannot be stopped because of his strength That person can do whatever he wishes to, and like above, cannot be stopped because of his strength   The other word I have is "swept", i.e.:     He swept through the continent.   I used "swept" because when you sweep the floor, nothing stops you and everything is swept away, similar to the example. However, the dictionary definitions don't match up, so that isn't the word either.  Any suggestions?