Prove that if $T,U: V \rightarrow V$ are linear operators on an inner product space, then $(TU)^* = U^*T^*$
How can I prove these are the adjoint operators?
Error when clipping raster in QGIS: "'ascii' codec can't encode character"? I have done it many times (clipping a raster with a polygon layer or by extension) but today I got an error for the first time and I don't know how to solve it. I am always using the same type of raster layers. When running the clipping tool I got the following message:  gdal_translate -of GTiff -ot Byte -projwin 410282.185971 4694950.41162 410783.882475 4694524.96815 -co COMPRESS=DEFLATE -co PREDICTOR=1 -co ZLEVEL=6 -co TFW=YES "C:/Users/FERRAN ALA/Desktop/Justificació Fontanals/QGIS/Topo 1_5000/bt5mv20sd0f283077st1r031.sid" "C:/Users/FERRAN ALA/Desktop/Justificació Fontanals/QGIS/background/image.tif"   GDAL command output:     'ascii' codec can't encode character u'\xf3' in position 201: ordinal not in range(128) See log for more details   Does anybody know what that is? I applied a survey consisting of 12 questions to 120 people and each questions include 4 nominal categories; I want to make comparison of people's answers according to their socio-demographic characteristics such as their educational level or socioeconomic status. All of my comparison criteria consist of nominal categories and number of categories change between 3 to 6. I cannot drop or combine comparisons; categories in other words number of categories are fixed.    My question is when I compare the frequency distribution of people's answers based on their education levels (for example) through chi-squared test, I got a warning that says (for instance) 7 cells have less than count five; minimum expected count is; 43.  I got this warning for almost my all questions - demographic characteristics comparisons.    Shall I underestimate this warning and use my test results or is there a different test I should use? If I should use a different test, which one? I have created a VF page and used "render as pdf"  &lt;apex:commandButton value="Save to Opportunity" action="{!savePdf}"  /&gt;   Its working fine when i am using above line without rerender and oncomplete but when i am adding rerender or oncomplete it is not working.I am able to save the PDF in attachment folder but when i am trying to open its showing  "Unable to load document"  Even if i remove oncomplete and use Rerender then also its saving the attachment in Attachment object and when i view ,it is not loading and says "Unable to load document"      &lt;apex:commandButton value="Save to Opportunity" action="{!savePdf}"  oncomplete="myClose();"/&gt;   Javascript Code  function myClose(){      self.close();     window.opener.location.href="/{!$CurrentPage.parameters.Id}";  }   Class Code  public void savePdf() {      PageReference pdf = Page.GenerateQuotePDF;     pdf.getParameters().put('id',parentId);      Attachment attach = new Attachment();      Blob body;     body = pdf.getContent();     attach.Body = body;     attach.Name = 'Opportunity'+ '.pdf';       attach.IsPrivate = false;     attach.ParentId = parentId;     attach.ContentType = 'application/pdf';     insert attach;     }     Please help.. 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I must know ID of this element to show only that history the element what was clicked fom open menu: Converting FLV to MP4 Using FFMPEG and Preserving the Quality Im trying to use ffmpeg to convert my flv files to mp4 to play them on iOS devices but the converted video has a much worse quality than the original one.  Here is the command i use:  ffmpeg -i input.flv -ar 22050 output.mp4   I would really appreciate if someone could provide me with the best settings for flv to mp4 conversion. How to cite own unpublished work in text and reference? I would like to cite one of my own unpublished work (under review). Is it okay to cite as following?  In text According to author et al. (year of submission)................. In reference authors list, year of submission, title, name of the Journal (status)   How about the results?   How will the reviewer access those results cited here?   Is it okay to provide them as supplements?   If I provide couple of figures as supplements, whether it will violate the copyright of the under reviewed paper? What process created the /var/lib/dpkg/lock-frontend file in Ubuntu? I have just booted my clean Ubuntu 18.04 LTS VM and tried to install some application with sudo apt install.  But got error message:     E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable)       E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend), is another process using it?   What process created the /var/lib/dpkg/lock-frontend file in Ubuntu? How to gently stop it and take manual control on APT? How was Thor able to dent Captain America's Shield? I was reading about Adamantium on the      Proto-Adamantium   This is the original Adamantium created by Dr. MacLain. Proto-Adamantium is the official name for the metal that makes up Captain America's Shield. It has never been recreated and is the absolute most invulnerable item in all of existence.    This lead me to read about      The true shield was once slightly dented by an enraged Odinforce empowered Thor, using Mjolnir, but he later reconciled and pounded out the small dent.    Was the dent caused by Odinforce or Thor's Hammer? Is Mjolnir or Captain America's Shield "the absolute most invulnerable item in all of existence"? Is there an unsubdivide function in Blender? I know that any group satisfying $x^2=1$ for all $x$ is abelian. Is the same true if $x^3=1$? I don't think it is, but I can't find a basic counterexample.