How to create "not less than or greater than" symbol?
How do I create a vertical version of \not?
Reference request: convergence for periodic Markov chains Consider an irreducible but possibly periodic Markov chain on a finite state space with transition matrix $P$. We know there exists a unique stationary distribution $\pi$. If the Markov chain were aperiodic, we would have $P^n_{ij} \to \pi(j)$ as $n \to \infty$. This fails if the chain is periodic, but we have convergence of the Cesaro averages: $$\frac{1}{n}\sum_{k=1}^n P^k_{ij} \to \pi(j) \text{ as } n \to \infty.$$ Can anyone point me to a reference that states this fact? Every reference I've seen only considers convergence for aperiodic chains, or "fixes" periodicity by considering a lazy version of the chain. Alternatively, is there a simple way to obtain this result using the result for aperiodic chains? My 13 year old daughter says she wants to be a boy. This is out of character for her. Is this a phase? My daughter, 13, has said she wants to be a boy. A little background: we moved to a new state a year and a half ago. In her new school, she felt isolated among her peers until she met a girl in art, and became good friends. She joined the drama club, and made  friends with some 8th graders. They joined “the diversity club”. This club is a LGBT club. The kids put on a play they wrote and starred in, which had homosexual connotations. “Romeo and Juliet”, but script  rewritten to include  2 females as the couple, for instance.   My daughter got so wrapped up in it, that her life was as if she was copying the play. She’s no longer friends with the friend from art, but remains close with the 8th grade crowd. They all labeled themselves. One week, my daughter said she was gay, then, changed to bi, then onto pan. (I had to google that one). Now she is emphatic about being disgusted with her body and wants to be a boy. She wants to donate all the “girly” clothes she picked out last year, and tossed out all the makeup she bought a few months ago.   All her life, she was the classic girly girl. She had crushes on boys, and she and this boy were inseparable since first grade. She was sad when it came time to move away. When we settled here, she became sullen and angry, putting herself down. She now sees a therapist who she really likes. We’ve been working on her self esteem issues. She’s wanting us to call her “he” and by a male name. I can’t do that. She’s my daughter. She is female. Had we seen this coming, maybe I could come to accepting. But it happened out of the blue.  Sometimes the old her comes back-I got a makeup sample and she was interested in trying it, looked at me, then quickly put it down and said “ewww, makeup”—just a few months ago, she bought a bunch. She’s now wanting to wear boys clothes and talks of wearing a suit to her prom. She is very impressionable, and seems affected by viral YouTube videos about kids coming coming out to their mothers, and the mothers gleefully embrace with happy tears. She has told me when she’s 18, she’s having her breasts removed.    Nothing seems normal to me anymore-in terms of how she always was-this new situation just doesn’t fit.  My gut tells me this is a phase.  I’m hoping it’s a phase. But with all I’m seeing in the media about this, I’m not sure. I love her; this is too much for me to process. I’m a stay at home mom; we were inseparable. I knew her. Until now.:(  She cut off all her beautiful hair, and wears boys shorts, baggy tee shirts, and bought this awful men’s deodorant spray. Please help me sort this out. I’m at my wits end.  Do you think this is a phase? Is this common? Leading zero in umask 0022 How to scan an entire network using Nmap? Is there a way to scan an entire network using ?   What I want to do is scan my network for all the devices that are currently connected to it. Why does `last` show '{' and '|' in the TTY field? Check if url has domain name and not an ip Some time ago, I baked a cake (Sachertorte to be exact). The taste and texture was fine, so my recipe is okay.  My biggest issue was the shape. In the middle it was really a lot higher than on the sides. I would like to redo it in the near future, but preferably with a flat(ter) surface. (Especially since I put icing on top and I don't want it to drip off this time.)  Anyone knows the cause of my problem, or even better a solution? I think I put enough butter on the side of my springform pan, in case this is an option. Automatically turn on VPN on computer unlock Ubuntu 18.04 When I wake the laptop from the sleep I need to get the VPN state as I left it (turned on). Can't find the setting of autoconnect in VPN settings... Need some easy way to ask the system to autoconnect the VPN when the internet is available.  Edit based on comments:  Ubuntu 18.04 has no option to Always connect to VPN when using using this connection. How to get full query text from performance_schema.threads? According to : Access to the threads table does not require a mutex  and has minimal impact on server  performance. The other sources have negative performance consequences because they require a mutex.   So yes, I want to use threads table to examine running queries. The trouble is, the PROCESSLIST_INFO column does not contain the full query. It just contains a truncated version of the query. There is a flag viz performance_schema_max_sql_text_length which controls how many bytes are allocated for the SQL query. But it seems to affect the events_statements_history_long table. There is no change in the thread table output. There is also the events_statement_current table. But it is not clear if accessing that table affects performance or not. Extrude Faces along Local Normals I am trying to extrude faces of a cylinder along local normals. 3dsmax can do it easy, couldn't find how to do it in blender.  The extrude region option extrudes it as shown in the first example. I want it done like the 2nd example. "I don't know nothing" vs "I don't know anything" Possible Duplicate:             I'm not a native English speaker, and this question may be very basic, but I want to learn English better, so don't hurt me with downvotes.  What is the difference between "I don't know nothing" and "I don't know anything"?  Do they have the same meaning or opposite ones? For a moderately complex query I am trying to optimize, I noticed that removing the TOP n clause changes the execution plan.  I would have guessed that when a query includes TOP n the database engine would run the query ignoring the the TOP clause, and then at the end just shrink that result set down to the n number of rows that was requested.  The graphical execution plan seems to indicate this is the case -- TOP is the "last" step.  But it appears there is more going on.  My question is, how (and why) does a TOP n clause impact the execution plan of a query?  Here is a simplified version of what is going on in my case:  The query is matching rows from two tables, A and B.    Without the TOP clause, the optimizer estimates there will be 19k rows from table A and 46k rows from table B.  The actual number of rows returned is 16k for A and 13k for B.  A hash match is used to join these two results sets for a total of 69 rows (then a sort is applied).  This query happens very quickly.  When I add TOP 1001 the optimizer does not use a hash match; instead it first sorts the results from table A (same estimate/actual of 19k/16k) and does a nested loop against table B.  The estimated number of rows for table B is now 1, and the strange thing is that the TOP n directly affects the estimated number of executions (index seek) against B -- it appears to always be 2n+1, or in my case 2003.  This estimate changes accordingly if I change TOP n.  Of course, since this is a nested join the actual number of executions is 16k (the number of rows from table A) and this slows down the query.  The actual scenario is a bit more complex but this captures the basic idea/behavior.  Both tables are searched using index seeks.  This is SQL Server 2008 R2 Enterprise edition. Software Tester Skill Matrix with Levels I would like to know if there's a standard Skill set for Skill Matrix for a Software Tester of different levels, like for example, what are the skills needed for an Entry level tester as well as what technologies and responsibilities he needs. And for the Mid Level tester and Senior Level as well.  Note that I am working in a company who designs and develops websites. How to select an index value from a String Array in a JOptionPane Dark color scheme for Eclipse Is Eclipse at all theme-able? I would like to install a dark color scheme for it, since I much prefer white text on dark background than the other way around. Can you be sued for using publicly used images on a blog without copyright permission? Lets say I write a blog post about the new Batman movie or a the new Grand Theft Auto game and i decide to use the boxart/poster or a wallpaper as the main image for the blog post,  can I be sued for breach of copyright on this image?  Im pretty sure Warner Bros are going to be hunting anyone down even if it is legal, but is this actually legal? If i buy the DVD or Game and take a picture of it, is this my copyright? When a trailer gets released and put on youTube, can i take a screenshot of this video and use this as an image?  It seems people can get rightly screwed for this, so I would like to know where i stand on this sort of thing. Dependency is not satisfiable: libtiff4 when trying to install Lightworks on Ubuntu 14.04 I was trying to install Lightworks 11.5.1 (amd64) on Ubuntu 14.04(amd64) but there's a notice: Dependency is not satisfiable: libtiff4. Is there anyway to solve this dependency issue?  Thanks in advance. I recently moved from having a main site like www.example.com with a subdomain associated site yyy.example.com, to moving everything off the subdomain to a subdirectory like www.example.com/yyy/, with the same hierarchy underneath the subdirectory, and now yyy.example.com is just a redirect page to the subdirectory, so yyy.example.com/abc/page-x is redirected to www.example.com/yyy/abc/page-x and so on.  The effect has been that the traffic increased by several times (the total page views are more than ten times at the present rate) what it was to the yyy subdomain. Previously almost all of the traffic to the yyy subdomain was from the www site. This is from monitoring the old yyy site for a year or more.  I'm curious to know if there's any research or results which would indicate whether this is universal (subdirectories beat subdomains) or "just me". SEO preference: does a site with WWW rank better than without WWW? After having read various articles on this site about WWW or Non-WWW website setup, ,  and , and after having setup a correct redirection rule in .Htaccess to at least eliminate duplicate contents (currently the non-www solution (e.g. http://example.com) I have a feeling that my site rank less since I changed this.   My confusion was strengthened by these two opponents:     &amp;     Could the change of www.example.com >> http://example.com have a factual impact on ranking?  say either is better or worse. Are they holding information back?  I am confused fellow folks...  As much as I would like to separate facts from fiction, I am aware that not all the good valid information is written. Not on google webmaster site and perhaps not elsewhere. If so it seems out of date!  Does or does not a WWW domain impact SEO/rank better than its NON-WWW version? (Given that you have setup a proper redirect to avoid duplicates and go with one) What does “the lowest common denominator” mean in the context other than math? In the  (May 31) article under the title, “Stephen Hawking angers Trump supporters with baffling array of long words,” Andy Borowitz wrote;     “Speaking to a television interviewer in London, the theoretical   physicist, Hawking called Trump “a demagogue who seems to appeal to   the lowest common denominator. --- “For a so-called genius, this was an   epic fail,” Trump’s campaign manager, Corey Lewandowski, said. “If   Professor Hawking wants to do some damage, maybe he should try talking   in English next time.”        Later in the day, Hawking attempted to clarify his remark about the presumptive Republican Presidential nominee, telling a reporter, “Trump bad man. Real bad man.”   From the context of Professor Hawking’s remark, I take “the lowest common denominator” as referring to the  “social segment of low educated, unsophisticated people,” but I’m not sure.   I thought  "common denominator" is a simple mathematic term. What does it mean in the context of the above quote?  Mr. Trump’s campaign manager says Professor Hawking should try to talk in English. Is this a farfetched way of using “common denominator” from math to politics?   Did Professor Hawking misuse "the common denominator"? Or does Mr. Trump's campaign manager not understand the meaning of "common denominator", which some call an "everyday-use" English phrase?  P.S.  I found the following definition of 'common denominator' in Oxford Advanced Learners English Dictionary;   2) an idea, attitude or experience that is shared by all the members of group - see also Lowest common denominator.  Readers English Japanese Dictionary at hand, published by Kenkyu-sha, a foreign language, especially English language dictionary specialist publisher in Japan, and rated as the most reliable English Japanese dictionary totally dropped the reference to this paticular meaning.  It was a learning. I told to myself that I should have made more homework on English-to-English dictonaries beforehand.