Consequences for a tenured person of not getting grants
If tenured staff are virtually unsackable, why is the drive to find funding so strong?
How can I draw annotated braces over and under math expressions? What LaTeX markup would one have to write to produce a result similar to the image below?    Please excuse my Paint-and-mouse drawing skills. :-) Under what conditions is $AA^T$ invertible? Given a matrix $A$ with dimensions $m \times n$, is $B=AA^T$ invertible if and only if the rows of $A$ are linearly independent?  So far, I've tried writing A as row vectors,   $$A = \begin{bmatrix}v_1\\ v_2\\ \vdots \\ v_m\end{bmatrix}$$  where $B_{i,j} = (v_i v_j) $  The Wikipedia page on the  suggests that the condition I stated above is necessary and sufficient, but does not provide a proof. I have a simple page that has some iframe sections (to display RSS links). How can I apply the same CSS format from the main page to the page displayed in the iframe? We are using .Net to make web service calls the Salesforce API. Is there a way to know for sure that the calls are using TLS 1.2? Are there any API logs or records of the protocol is use in Salesforce we can review to be confident the change is working? A potential customer wants to evaluate our storage system. They run Windows 2008R2 x64 with 4KB NTFS on a virtual test machine they've sent us. They did not seem to know this at hand, so I think it's reasonable to assume that environment was not tweaked. The tests are inserting, indexing, searching, deleting. Tool is not known to me.  Given that the windows NTFS block size is 4KB, and SQL write in 64KB chunks - is it safe to assume that a block size of 64k on the SAN is a good choice?  They run SQL Server 2008, perhaps standard. On the first puzzle of the quest Under Saarthal (the one with the six pillars), I enter the correct combination, but the door still doesn't open, and arrows are still shot at me. I've reloaded the game a couple hundred times, I've left the room, and it still doesn't work. What do I do? Here's a pickle: reference style links in markdown are fantastic. Numbered footnotes, however, can be a pain. Named references are a beautiful solution, but the editor seems to choke on them in certain contexts, throwing an error:  your post appears to contain code that is not properly formatted as code...  I've looked at a  and tested it out quite a bit and I'm pretty sure line breaking isn't the problem, named references are valid , and I can get multi-word named references to work basically every time (in this post, even). Is there a reason for named references to be seen as improperly formatted code in certain contexts? At the risk of being verbose (but for the sake of completeness), here's the source of the specific question I was trying to post when I encountered the problem: I'm trying to build a [Google Apps Script] that integrates with [Trello], the idea being to use it to push information from spreadsheets and forms into the [Trello API] and create cards on a `pending` list on a certain board.  I found this [question] on here that pointed me in the right direction, and added in OAuth based on the [GAS OAuth Documentation]. The problem is I can't post the the board. I run the script, the OAuth prompt fires, and the script completes with no errors. I can also `GET` data from the private board, so I assume the authorization is working properly.  So, what am I doing wrong that prevents my script from `POST`ing to Trello?  Here's the code I'm working with:      var trelloKey = [Trello API key];     var trelloSecret = [Trello API key secret];     var trelloList = [the id of the list we're posting to];      var oauthConfig = UrlFetchApp.addOAuthService('trello');         oauthConfig.setAccessTokenUrl('https://trello.com/1/OAuthGetAccessToken');         oauthConfig.setRequestTokenUrl('https://trello.com/1/OAuthGetRequestToken');         oauthConfig.setAuthorizationUrl('https://trello.com/1/OAuthAuthorizeToken');         oauthConfig.setConsumerKey(trelloKey);         oauthConfig.setConsumerSecret(trelloSecret);      function createTrelloCard() {        //POST [/1/cards], Required permissions: write       var payload = {'name': 'apiUploadedCard',                       'desc': 'description',                       'pos': 'top',                       'due': '',                       'idList': trelloList};        var url = 'https://api.trello.com/1/cards'       var options = {'method' : 'post',                      'payload' : payload,                      'oAuthServiceName' : 'trello',                      'oAuthUseToken' : 'always'};        UrlFetchApp.fetch(url, options);     }  [Trello]: http://trello.com [Google Apps Script]: https://developers.google.com/apps-script/ [Trello API]: https://trello.com/docs/ [other question]: http://stackoverflow.com/questions/18710641/trello-api-how-to-post-a-card-from-google-apps-script-gas [GAS OAuth Documentation]: https://developers.google.com/apps-script/guides/services/external#making_requests_to_services_with_oauth  If I'm being a complete dunce, please let me know. It seems like one of those errors where it's either a hardcore backend bug or a really stupid user mistake and I'm ready to admit to the latter. Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals? I recently started studying set theory and am having quite a bit of difficulty accepting Cantor's diagonal proof for the uncountability of the reals. I also saw a topological proof via nested sets for uncountability which still does not satisfy me completely, given that just like the diagonal it relies on a never ending process. In fact, the nested sets proof sounds very much like the diagonalization proof to me.  Do all proofs of the uncountability of the reals involve diagonalization? Are there any other proofs I can look at to understand? I couldn't find any on searching stack exchange. Thanks. How can I install Minecraft? I have tried many tutorials but none of them are clear enough. I have also tried installing it using Wine but it won't update and Wine goes gray and stops working.  Does anybody know an easy way to install Minecraft though the Java file without using Wine? What's this? What is it? but not What's it? - Why? Can anyone give a cogent, simply described explanation of why the verb BE in:  What is it?  ... doesn't seem to be able to be contracted with the subject:  What's it? *  Compare the sentences above with:  What's this? What's that?  These are perfectly fine. In fact, the contractions here should be expected in almost all examples of spoken English. Answers with references to authoritative vetted sources would be greatly appreciated. What makes a chewy brownie? I've tried many different brownie recipes and most of mine bake to a cake-like consistency. The brownie holy grail for me is crusty top chewy brownies. What can I add/remove/do that will make my brownies chewier? Why are comments overlapping the sidebar? On , the comments are overlapping the related questions sidebar. Is this something to do with the weird formatting of the first comment?    Browser: Mozilla/5.0 (Windows NT 6.0; rv:16.0) Gecko/20100101 Firefox/16.0 Can I get a postdoc in China more than 3 years after having received my PhD? I've just finished running my first session with only one player, and it felt pretty different from running a session for a group.  Could someone with more experience in this talk about what one should do differently in that situation?  I'm not referring to mechanics like encounter-building, but just how to handle the change to the social dynamics. Why "?v=hash" is added to my URLs? I'm new to wordpress, I set up everything, but there's something that bothers me: on every single URL or link, there's a "?v=hash" appended everywhere (example.com/?v=d21feabed96b).  I tried to see inspect every plugin, I don't understand how this parameter is added.  It looks like it's added in js, because if I see the source, there's no trace of this hash, but I can see in firebug live source.  Plugins installed:   jetpack sumome wp-piwik wp super cache woocommerce   Theme: Storefront  I tried to disable everything, but still I get this hash, does anyone knows how and why it's added?  I'm also using cloudflare How do I change the "Selected Items" color? I was trying to change the selected items color from the default orange to something else, however, the option isn't there, as it used to be in the Appearance properties in previous versions of ubuntu. Any idea where it could be in the beta? What is the right first step to take when integrating $1/(2+ \sin x + \cos x)$? I want a hint on this following integral. I don't know the first step, do I do $u$-sub. or do I use trig. sub or something?  $$\int \frac{1}{2+ \sin x + \cos x} ~\mathrm{d}x$$ "I didn't realize it was him." What is crop factor and how does it relate to focal length? I'm examining a proof I have read that claims to show that the Cartesian product $\mathbb{N} \times \mathbb{N}$ is countable, and as part of this proof, I am looking to show that the given map is surjective (indeed bijective), but I'm afraid that I can't see why this is the case. I wonder whether you might be able to point me in the right direction?  Indeed, the proof begins like this:  "For each $n \in \mathbb{N}$, let $k_n, l_n$ be such that $n = 2^{k_n - 1} \left(2l_n - 1 \right)$; that is, $k_n - 1$ is the power of $2$ in the prime factorisation of $n$, and $2 l_n - 1$ is the (necessarily odd) number $\frac{n}{2^{k_n - 1}}$."  It then states that $n \mapsto \left(k_n , l_n \right)$ is a surjection from $\mathbb{N}$ to $\mathbb{N} \times \mathbb{N}$, and so ends the proof.  I can intuitively see why this should be a bijection, I think, but I'm not sure how to make these feelings rigorous?   I suppose I'd say that the map is surjective since given any $\left(k_n , l_n \right) \in \mathbb{N} \times \mathbb{N}$ we can simply take $n$ indeed to be equal to $2^{k_n - 1} \left(2l_n - 1 \right)$ and note that $k_n - 1 \geq 0$ and thus $2^{k_n - 1}$  is both greater or equal to one so is a natural number (making the obvious inductive argument, noting that multiplication on $\mathbb{N}$ is closed), and similarly that $2 l_n - 1 \geq 2\cdot 1 - 1 = 1$ and is also a natural number, and thus the product of these two, $n$ must also be a natural number. Is it just as simple as this?  I suppose my gut feeling in the proving that the map is injective would be to assume that $2^{k_n - 1} \left(2 l_n - 1 \right) = 2^{k_m - 1} \left(2 l_m - 1 \right)$ and then use the Fundamental Theorem of Arithmetic to conclude that $n = m$. Is this going along the right lines? The 'implicit' definition of the mapping has me a little confused about the approach.    On a related, but separate note, I am indeed aware that if $K$ and $L$ are any countable sets, then so is $K \times L$, so trivially, taking the identity mapping we see trivially that this map is bijective and therefore that $\mathbb{N}$ is certainly countable (!), and thus so is $\mathbb{N} \times \mathbb{N}$. Hence, it's not really the statement that I'm interested in, but rather the exciting excursion into number theory that the above alternative proof provides.