Can anyone justify the presence and absence of comma after first in the sentences below?        First we’ll create a screen for the user to log in.   First, we’ll define the AniJS helper and then we’ll declare the before animation function.
If I have a sentence that starts with additionally, finally, consequently, etc. do I always have to put a comma after it? Or is there a different rule?
I have trouble on this question: "Characterize the groups G for which the map $$\iota: G \to G$$ sending $$x \mapsto x^{-1}$$ for all $x \in G$, is an automorphism of $G$." From  post I have seen that $G$ must be abelian. Can anyone propose another characteristic of $G$ that I can derive from the given conditions besides abelian? Thank you so much!! Keeping tables/figures close to where they are mentioned If $g \circ f$ is surjective, show that $f$ does not have to be surjective? How do I prevent "Read more: www.site.com" from being injected with non-Tynt JavaScript into copy-paste actions? There are many sites that insert something like "Read more: www.site.com" into your clipboard when you copy text in your browser.  I find this abominable.  A google search reveals   to stop this if the website happens to be using the service  (by just blocking the Tynt domain), but many websites use home-grown JavaScript.  Is there a general way to block this behavior besides just turning off JavaScript?   I use Chrome but I am interested in all solutions.  EDIT: To be clear, I want to be able to keep the rest of the JavaScript functionality for these websites, since many will break without it.  EDIT #2: Here are two example websites which continue to harass me despite my use of a Tynt blocker:  |   Here are two   and two   which explain ways to implement this shady practice manually without Tynt.  Here is a  describing how hard this turns out to be to block reliably.  Here is the  I could find (March 2013) which offers suggestions on how to block this in Chrome using AdBlock, but it didn't work for me. How to know the model has started overfitting? I originally read this book in the mid- to late '70s.   The premise was a bureaucracy whose job it was to manipulate events in human history by making the smallest possible change that would effect the desired outcome. Not time cops in the sense of going after law breakers.  The intent was to maintain a policy of non-interference as much as possible but when interference was warranted then to make the least possible change and to do so invisibly.  For example, they might take someone's keys off the dresser and put them just out of sight underneath the dresser where they plausibly might have fallen.  The subject would never know of the manipulation but would then be delayed getting out of the house and the ripples grew from there to avert a war or otherwise affect events on a large scale.  After reading that, whenever I would lose something - especially in an improbable way such as dropping a screw at my feet and then finding it on the other side of the room half an hour later - I would take some consolation in the thought that I had just averted some global catastrophe.  I was pretty scatterbrained as a kid (we call that ADHD nowadays) so I experienced this a lot.  Given that I've spent so much time pondering the ideas from the book, I'd love to re-read it. I’m looking for a word I’m struggling to remember that refers to a job or role which is inconsequential and usually created in order to install someone in a company, not based on their merit.  An example would be creating a vague new role for a friend’s son. The word I’m looking for refers to the actual job itself - it’s a noun that would replace the ‘job’ (e.g “they put so and so’s cousin in a ____”).   I believe the word may not be a strictly formal or technical word but I don’t think it was slang. About the semantically related words Google's algorithm uses in mixed language websites Because I'm Latin, sometimes I use a word in English while talking in Spanish.   In a website, for example, I could be interested in ranking for a word as “promoter” inside a page in Spanish, because that is how my public understands that concept.  Does the latent semantic indexing (LSI) (or whatever Google uses for semantic relation) fail to relate “promoter” with the content (because there are not related words in English) and then could that prevent my site from ranking? Allow a user to download a file after submitting their email address I got the Turkey e-visa several times with my schengen visa. In the e-visa form there is a condition      I have a round-trip ticket with Turkish Airlines, Pegasus Airlines,   Onur Air or Egypt Air.   What if I am traveling from another country to Turkey or using another airlines like Nile Air form Egypt? "Naturally occurring" non-Hausdorff spaces? It is not difficult for a beginning point-set topology student to cook up an example of a non-Hausdorff space; perhaps the simplest example is the line with two origins. It is impossible to separate the two origins with disjoint open sets. It is also easy for a beginning algebraic geometry student to give a less artificial example of a non-Hausdorff space: the Zariski topology on affine $n$-space over an infinite field $k$, $\mathbf{A}_{k}^{n}$, is not Hausdorff, due to the fact that polynomials are determined by their local behavior. Open sets here are in fact dense. I am interested in examples of the latter form. The Zariski topology on $\mathbf{A}_{k}^{n}$ exists as a tool in its own right, and happens to be non-Hausdorff. As far as I'm aware, the line with two origins doesn't serve this purpose. What are some non-Hausdorff topological spaces that aren't merely pathological curiosities? What is "step size" in LASSO regression? Replace links with the current question title in comments In questions, links get converted into question titles (see )  Can the same functionality be added to comments? Cardinality of equivalence relations in $\mathbb{N}$ I came across this long proof on this site:    But I would like to know whether my direction can work.  Say we want to find the cardinality of all equivalence relations in $\mathbb{N}$. Since it is a subset of all relations in $\mathbb{N}$, I conclude it has a cardinality smaller or equal to $\aleph$. Now, define an injective function from $P(\mathbb{N})$ to the set of equivalence relations by matching each subset of $\mathbb{N}$ with the identity relation (which is an equivalence relation in $\mathbb{N}$.  Therefore the cardinality of all equivalence relations in $\mathbb{N}$ is greater or equal to $\aleph$ and using CSB we get the desired result.  Seems legit? Comment deletion notification I think you should be notified if anything of yours is deleted or even flagged, preferably with some explanation (even if it's a simple categorisation like #rude, #irrelevant, #incorrect) and who did it.  Recently, a couple of comments of mine vanished without warning or evidence afterwards. I'm fine with deletion, but I think it should be used sparingly and be based on democratic decisions. What's the harm of letting a comment simply sit with no up-votes or responses rather than outright removal? Or allow downvoting and then negatively voted comments are hidden by default?  I get the impression that anything I post could be deleted. Very few people want to be unpopular or do the wrong thing. It takes time to understand what something is about and how best to use it (this site). Whether or not what I posted deserved to be deleted is irrelevant because I got no feedback. No-one can learn without feedback. The number of frivolous comments with many upvotes I've seen shows how inconsistently the rules are applied. A community that gives too much power to highly rated users won't grow but turn stagnant.  Sorry if this was rude, inappropriate or pathetic. I'm aware that similar discussions have occurred. In any case, I'll continue to use the site and move on... Why we can't implement AES 512 key size? Out of curiosity why we can't implement AES 512 key size?    Please explain somehow i can understand! I'm not an expert. What is the standard way to add N seconds to datetime.time in Python? Given a datetime.time value in Python, is there a standard way to add an integer number of seconds to it, so that 11:34:59 + 3 = 11:35:02, for example?  These obvious ideas don't work:  &gt;&gt;&gt; datetime.time(11, 34, 59) + 3 TypeError: unsupported operand type(s) for +: 'datetime.time' and 'int' &gt;&gt;&gt; datetime.time(11, 34, 59) + datetime.timedelta(0, 3) TypeError: unsupported operand type(s) for +: 'datetime.time' and 'datetime.timedelta' &gt;&gt;&gt; datetime.time(11, 34, 59) + datetime.time(0, 0, 3) TypeError: unsupported operand type(s) for +: 'datetime.time' and 'datetime.time'   In the end I have written functions like this:  def add_secs_to_time(timeval, secs_to_add):     secs = timeval.hour * 3600 + timeval.minute * 60 + timeval.second     secs += secs_to_add     return datetime.time(secs // 3600, (secs % 3600) // 60, secs % 60)   I can't help thinking that I'm missing an easier way to do this though.  Related On citing "common knowledge" statements I am an undergraduate student with no experience at all.  If you are writing a research paper, that you are planning to submit for publication, how do you state that a particular statement/fact is commonly known to all and it's dicoverer/inventor is not known, and that there exists no research paper that introduced the concept but there do exist various books/websites that discuss the very concepts and a few derivatives of the concept?  I am not able to cite a particular statement/bunch of statements as I am not able to find any research paper related to that at all.  The particular thing in question is:   What should I do? Is there a way to change the environment variables of another process in Unix? derivative of a determinant of matrix Let $A,B\in M_{n\times n}(\mathbb{R})$, prove that $$(\frac{d}{dt}\det(A+tB))_{t=0} = Tr(cof(A)^{T}\cdot B), $$ where $cof(A)$ is the cofactor matrix of $A$. I tried expanding it using row expansion, but it gets messed up. Any help?