Let $(\Omega, \mathcal F,P)$ be a probability spaces and $H$ be a Hilbert space. By a random operator $A$ from $H$ to $H$ we mean a linear continuous mapping from $H$ into the Frechet space $L_0^H (\Omega, \mathcal F,P)$ of all $H$-valued random variables. My question is: How Can we define $|A|$ and the adjoint $A^*$?
Let $(\Omega, \mathcal F,P)$ be a probability spaces and $H$ be a Hilbert space. By a random operator $A$ from $H$ to $H$ we mean a linear continuous mapping from $H$ into the Frechet space $L_0^H (\Omega, \mathcal F,P)$ of all $H$-valued random variables. My question is: How Can we define $|A|$ and the adjoint $A^*$?
I've always wondered how to write the "A ? B : C" syntax in a C++ compatible language.  I think it works something like: (Pseudo code)  If A &gt; B    C = A Else    C = B   Will any veteran C++ programmer please help me out? LM393 voltage comparator is not working Sufficient condition(s) for $f'$ to be Riemann integrable Identification card for foreigners in trains in Germany I want to go to Berlin to Gottingen by train. I found that to avail myself of the &ldquo;savings fare&rdquo;, I have to book a ticket at least one day in advance. And I saw a requirement on the Bahn website to have a identification card for online tickets.  I am a foreigner in Germany, so does my passport count as valid identification in German trains? bash if not multiple conditions without subshell? I want to combine multiple conditions in a shell if statement, and negate the combination.  I have the following working code for a simple combination of conditions:  if [ -f file1 ] &amp;&amp; [ -f file2 ] &amp;&amp; [ -f file3 ] ; then   # do stuff with the files fi   This works fine.  If I want to negate it, I can use the following working code:  if ! ( [ -f file1 ] &amp;&amp; [ -f file2 ] &amp;&amp; [ -f file3 ] ) ; then   echo "Error: You done goofed."   exit 1 fi # do stuff with the files   This also works as expected.  However, it occurs to me that I don't know what the parentheses are actually doing there.  I want to use them just for grouping, but is it actually spawning a subshell?  (How can I tell?)  If so, is there a way to group the conditions without spawning a subshell? Which fuels burn the longest in Minecraft? I recently upgraded to Windows 8 from Win 7 64 bit and have started to encounter a strange issue. When I have any program running which plays sound, such as a game or spotify, after a random interval (usually around 5-10 minutes) the program sound will set itself really low.    If I Alt-Tab to the desktop and check the Mixer I can see that the Application volume has automatically set itself really low - the other volume levels (i.e. the Device speakers) stay the same.  I'm able to just set the application volume back to a reasonable level and it stays that way for another 5 - 10 minutes then goes quiet again.  My sound is Realtek High Definition Audio and my machine is an Acer Aspire 5738G if that helps in any way.  Any help much appreciated! '+' and 's' in permission strings If the ls -l command gives me a permission string like  rwsr-s--x   What does the 's' mean? The only sources I found mention that it can be present sometimes but do not elaborate.  What does a '+' instead of a '-' mean? I have found mentions of 'extended permission' but nothing clear. Link button in post editor escapes square brackets in code My input file is,  ami21 ami65 ami67 ami66 ami88 ami76 ami29 ami55  ami54 ami32   Using a single command line I need the output as,  ami22 ami66 ami68 ami67 ami89 ami77 ami30 ami56 ami55 ami33   I used the command  awk -vRS=ami '{$0=$0+1;ORS=RT}++n' inputfile &gt; outputfile   but I got the outputfile as ami21ami65ami67ami66ami88ami76ami29ami55ami54ami32  i.e. all strings are written in same line and without space. Could anyone suggext me some better command line. Does the force of kinetic friction increase with the relative speed of the objects involved? If not, why not? Biblatex handling of Dutch "van" prefix This question has been posed in many different variants, but not exactly as I ask here, so please do not consider this as a duplicate.  I use biblatex with the option useprefix. I would like to have the following automatic behavior:   Name prefixes are rendered before the last name in the bibliography, but always in lower case. The name prefixes are ignored for the sake of sorting of the bibliography. In running text, the name prefix is rendered with a capital letter at the beginning of a sentence, and lower case elsewhere (possible using \Textcite vs. \textcite).   To achieve this, I can have three author fields for each concerned entry, with the following scheme:  author = { {v}an Dijk, A.} shortauthor = { van Dijk, A.} sortname = {Dijk, A. van}   Is there a simple way to automate this? Ideally, such a way could also allow for easy changing of the system. mail -s "subject" xxxxx@gmail.com &lt;test.html works, but only for plain text email.  What is the correct way to send HTML email using the Linux command mail? Notification email from stackoverflow contains "<3" after zip code round() doesn't seem to be rounding properly How is The Wall bypassed? How to read and understand the java stack trace? If $a_{ij}=\max(i,j)$, calculate the determinant of $A$ Titles should be stand-alone summaries of questions *without* depending on tags Titles should be completely independent of tags.  A good title tells an expert whether they want to read the full question all by itself. I know this has come up multiple times before, before, but in each case, the discussion has seemed to have turned into a different question.  For example,   really asks, &quot;Don't we need tags in titles to help with SEO&quot;? So, &quot;no, we don't, because we add the top tag (or two, in some cases) to the crawler results,&quot; is correct, but it appears that people are interpreting that to mean that people generally can (or should) omit key terms from their titles if they exist in the tags.  To be clear:  I agree that we should never force a tag into a title if it's not helpful;  should NOT have &quot;[Baking]:&quot; jammed into the title, because it adds nothing to a reader's understanding of what it's about, BUT...  Nothing should be left out of a title just because it exists in the tags.   Trilogy examples:   , ,   examples: , , , The problem with all of these is that without a language, OS, or game title, they fail to convey whether you care to read the question, because you need to read the tags to even figure out if you work with the language or own the game in question. A term being in a tag in no way reduces the need for it in the title.  Tags are great for filtering, but a title is supposed to function like a headline. This is a good headline:  This is not very good headline:  Titles, like headlines, are BIG AND BOLD on the front and other pages.  So you can browse and stuff.  Tags are small, and kind of low contrast.  So they don't, you know, distract you from the headlines. Bear in mind that on non-technical sites, new visitors, even new experts, don't necessarily even know what tags are. The title test:  If you assume the reader can't even see the tags, is your title a good, stand-alone summary of the question for an expert on that topic?  I'm sticking with gaming examples because they're more broadly accessible than some topics:   does not need, &quot;in Starcraft&quot; added, because it's impossible to be interested in the answer and not know that a zergling question relates to Starcraft.  but...  , absolutely needs &quot;...in Starcraft 2&quot; added to it, because without the tags, it's currently useless as a way to decide if you want to read it.  This is really no change from :  In the wake of that comment, people seemed to mostly hear:  &quot;stop forcing a word you don't need in just cuz it's a tag&quot;  ... which is right, but what it really says is,  &quot;most of the time, some tags will naturally belong in a title that effectively summarizes the question&quot;.  EDIT: Some folks felt this was (an unduly public) way to call out gaming specifically. It's not - I think this is a problem to varying degrees on a number of sites, but used examples from gaming because they're easy for most readers to follow. Sincere apologies to anyone in the Arqade community who felt I was using a network-wide forum to criticize a gaming practice - I wanted to clarify the best practice for all the sites that encounter this at least sometimes, including SO, where you still see people stripping languages from titles in edits sometimes. How do I fix these M4 macro errors? I am trying to compile  but when I run ./autogen.sh the script terminates with these errors  Checking for required M4 macros...   libtool.m4 not found   glib-gettext.m4 not found   intltool.m4 not found   pkg.m4 not found   gtk-doc.m4 not found   yelp.m4 not found ***Error***: some autoconf macros required to build mate-desktop   were not found in your aclocal path, or some forbidden   macros were found.  Perhaps you need to adjust your   ACLOCAL_FLAGS?   What do I need to do to get rid of these errors? I tired installing the latest versions of inittool, glib, gtk, yelp, etc... but I still get the macros errors.