How to get mathbb{1} to work in beamer? (or similar alternative)
How do you get \mathbb{1} to work (characteristic function of a set)?
What is the C# equivalent of NaN or IsNumeric? Consider the following figure from Faraway's Linear Models with R (2005, p. 59).    The first plot seems to indicate that the residuals and the fitted values are uncorrelated, as they should be in a homoscedastic linear model with normally distributed errors. Therefore, the second and third plots, which seem to indicate dependency between the residuals and the fitted values, suggest a different model.  But why does the second plot suggest, as Faraway notes, a heteroscedastic linear model, while the third plot suggest a non-linear model?  The second plot seems to indicate that the absolute value of the residuals is strongly positively correlated with the fitted values, whereas no such trend is evident in the third plot. So if it were the case that, theoretically speaking, in a heteroscedastic linear model with normally distributed errors  $$ \mbox{Cor}\left(\mathbf{e},\hat{\mathbf{y}}\right) = \left[\begin{array}{ccc}1 &amp; \cdots &amp; 1 \\ \vdots &amp; \ddots &amp; \vdots \\ 1 &amp; \cdots &amp; 1\end{array}\right] $$  (where the expression on the left is the variance-covariance matrix between the residuals and the fitted values) this would explain why the second and third plots agree with Faraway's interpretations.  But is this the case? If not, how else can Faraway's interpretations of the second and third plots be justified? Also, why does the third plot necessarily indicate non-linearity? Isn't it possible that it is linear, but that the errors are either not normally distributed, or else that they are normally distributed, but do not center around zero? How can I solve this integral using the Residue theorem? $$ \int_{-\infty}^\infty \frac{\sin(x)}{x^2 + 4x + 5}dx$$  What I now is you can use residue theorem, and evaluate this integral  $$ \oint \frac{e^{iz}}{z^2 + 4z + 5}dz$$ and through calculating the residues and using the residue theorem I get that the answer for the above integral is $$\pi e^{-1-2i}$$  However after this I am completely lost.  Any guidance will be much appreciated. I would like to know why I can evaluate the integral as an exponential integral as well. I have recently been thinking about the difference between the two ways of defining an array:   int[] array int array[]   Is there a difference? I'm at roughly 67% completion of the Alola Dex, with ~200 caught, ~290 seen. After scanning QR codes, I've caught a Swinub and Cyndaquil. However, neither were registered in the Pokédex, since neither are Pokémon in the Alola Dex. This brought up the following question:  When will I unlock the National Dex?   Do I need to have seen all the Pokémon in the Alola Dex? Do I need to complete some specific quest, like catching/defeating the Ultra Beasts? MPI Get Processor with Minimum value Finding the perimeter of a right triangle with area given C: pointer to struct in the struct definition How can author deal with late reviews? What happens with No-Maj-Borns? In the Harry Potter series, lots of Muggle parents are introduced to the wizarding world because of their magical children. This is seen with Hermione's parents visiting Diagon Alley and various other moments.   In the 1920s USA world that has been created, rules about fraternising with No-Majs are very strict. Is there any evidence in any of the Pottermore articles or recently published film tie-ins which explain what happens with magical children born to No-Majs around this time? (Clearly certain events in the film suggest that they may have no procedure and that there can be side-effects of this - but I feel that those events must be rare!) How are private keys handed to users in Identity-based Encryption? Alternatives to 'respectively' Often, crontab scripts are not executed on schedule or as expected. There are numerous reasons for that:   wrong crontab notation permissions problem environment variables   This community wiki aims to aggregate the top reasons for crontab scripts not being executed as expected. Write each reason in a separate answer.  Please include one reason per answer - details about why it's not executed - and fix(es) for that one reason.  Please write only cron-specific issues, e.g. commands that execute as expected from the shell but execute erroneously by cron. Question : $$\begin{align}a+b+c &amp;= 0\\ a^3 +b^3 +c^3 &amp;= 12\\ a^5 +b^5 +c^5 &amp;= 40\end{align}$$ Then , $a^4 + b^4 + c^4 = ?$  My try : As a common perspective I just went to find any trick related to it and my first step is as usual as a common man will think $3abc = 12$ and got $abc = 4$ After that I am unable to link it with any other equation Duplicate explanation should encourage improvement of original SELECT permission on view querying table from another database SQL Server 2008 R2 SP1  My company uses the Great Plains (GP) financial system with several customizations.  Our Value-Added-Reseller (VAR) for GP has setup most of these customizations in a separate database from the GP data called DYNCUSTOM.  In the DYNCUSTOM database is a View that is merely a SELECT * FROM a table in the GP company database (called PARTS).  I was approached by a user having problems trying to select on this view.  The error he was getting:  Msg 229, Level 14, State 5, Line 2 SELECT permission denied on object 'BM010415', database 'PARTS', schema 'dbo'   I looked at how his login was mapped and he had a database user in the DYNCUSTOM database belonging to a database role that was granted select on the view.  However, he did not have a database user in the PARTS database.    Usually the intent of a view is so that one can grant select permissions on the view without exposing access to the underlying table.  With SQL Server however, if the view crosses databases does it then change the security context being used?  Therefore, the user would also need a database user in the PARTS database as well as granted select access to the underlying table? What is the difference between Early and Late Binding? What is the difference between early and late binding? How can I download a distribution? Am I right in thinking that the Drupal distributions that I can download from  are a standard Drupal core download with a load of other stuff added at /profiles?  Anyone know if there are any plans to create a dev branch of distributions that would automatically update the core version that the distribution is running on? Currently it seems that the distribution runs on whatever core version its developer has chosen.  And how can I use distributions with Drush? Is there an equivalent to drush dl drupal that will download a specific distribution?  And, finally, is there any difference between an install profile and a distribution? How can I randomize order of elements in a list? Use sub and superscript as [optional] parameters for macro