How to prevent milk overflow from pan?
Can I boil milk unattended (and still keep the pan clean)?
${a^2}{\mid}({b^3} + 1)\;$and$\;{b^2}{\mid}({a^3} + 1)$ Indefinite Integral with "sin" and "cos": $\int\frac{3\sin(x) + 2\cos(x)}{2\sin(x) + 3\cos(x)} \; dx $ Detecting device for debugging (ADB) does not work Are PDO prepared statements sufficient to prevent SQL injection? Let's say I have code like this:  $dbh = new PDO("blahblah");  $stmt = $dbh-&gt;prepare('SELECT * FROM users where username = :username'); $stmt-&gt;execute( array(':username' =&gt; $_REQUEST['username']) );   The PDO documentation says:     The parameters to prepared statements don't need to be quoted; the driver handles it for you.   Is that truly all I need to do to avoid SQL injections?  Is it really that easy?  You can assume MySQL if it makes a difference.  Also, I'm really only curious about the use of prepared statements against SQL injection.  In this context, I don't care about XSS or other possible vulnerabilities. How to convert a list of string to a list of int Displaying row/column of point in raster using QGIS? Is it possible in QGIS to display column and row index of pixel in raster?   I mean something similar to value tool. Finding what's using all the space in *nix Which sequence of commands will tell me which files are the largest starting from a particular directory, including all sub directories? I want to know where all the space went.  Preferably just with regular unix'y commands.  If possible, try to keep it compatible with Sun OS 5.10 (perhaps in addition to regular Linux answers, not as a replacement, to keep it as general as possible.) What do I say to make a new line when using voice recognition? I've found I can make punctuation happen by saying "comma", or "period", but I can't find the word for new line.  I tried "paragraph", and "line break", but it just prints those words. Why do people omit the definite article? I'm used to always hearing or seeing a  before certain nouns.  Yet on certain occasions the article is totally omitted, and it bothers me.  I'm wondering what the justification for omitting the article is, especially when the definite article would seem to be required, or if it is just bad English either on the part of the individual in question or more likely by tradition.  The most frequent place I hear this is at the doctor or dentist's office. In every one I have ever visited, the receptionist or assistant always says things like "Doctor will see you shortly" instead of "The doctor will see you shortly."  The wikipedia article linked above says this: "A definite article indicates that its noun is a particular one (or ones) identifiable to the listener".  In the case of a clinical setting, I know who the doctor is, especially if this is not my first visit.  The people in the office know the doctor even better than I, so it would seem to be inappropriate to omit the article. Even the indefinite article would be incorrect. It further says, under "Zero article":  "In languages having a definite article, the lack of an article specifically indicates that the noun is indefinite."  Since the noun is not indefinite, why are they omitting the article?  Another place I see the article omitted is with the word "bar".  Bartenders apparently don't say "I tend the bar" they say "I tend bar".  Unless a bartender works in multiple bars, it would seem like an article would be required.  Furthermore, "the bar" can mean any bar a person goes to, so even in a case like , it seems like the word "the" should be in the sentence.  The only thing I can think of in this case is maybe the speaker doesn't want to confuse the listener into thinking they work in the legal field.  Is this just a bad habit, a historical corruption or tradition, or is there really a valid reason (or perhaps more than one) for these omissions? In response to  question, I started to think about what it means when a Wild Magic Surge results in a "You cast spell-X".  So, "specific beats general" gives:   You can cast a second spell when you would not normally be allowed to You can cast a spell you don't know If the surge forces you to cast a concentration spell you would lose any concentration spell that you currently had active Subject to what the specific entry says you can target it how you like Unless the specific entry prohibits it you could use metamagic on the spell   I am pretty confident in all of the above but if anyone disagrees please address in an answer.  Here comes the question.  How does this impact on your available spell slots?  "You cast ..." to me suggests that if you have an applicable slot available then you have to use it to cast the spell because that is the general rule for casting spells but if you don't then "specific beats general" and it is cast anyway.  Specific examples:     You cast fireball as a 3rd-level spell centered on   yourself   This must be a 3rd level spell:   if you have a 3rd level slot available you have to use it? if you don't, if you have 5 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?      You cast confusion centered on yourself.   No level specified and confusion is a 4th level spell:   if you have a 4th level slot available you have to use it? if you have a 4th, a 6th and an 8th level slot you can choose which one to use? if you have only a 5th level slot but also 6 sorcery points and a bonus action, you could choose to use the 5th level slot or use the points to create a 4th level slot? if you don't have any 4th level or higher slots but you have 6 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?   And so on ... Prove that a power series $\sum_{n=0}^{\infty}{{a_n}{z^n}}$ which converges for any $z \in \mathbb{N}$, converges for any $z \in \mathbb{C}$. PROBLEM  Prove that a power series $\sum_{n=0}^{\infty}{{a_n}{z^n}}$ which converges for any $z \in \mathbb{N}$, converges for any $z \in \mathbb{C}$.  MY ATTEMPT  Since the power series $$\sum_{n=0}^{\infty}{{a_n}{z^n}}$$ converges for any $z \in \mathbb{N}$, then $$\sum_{n=0}^{\infty}{{a_n}{z^n}}$$ can be considered (?) to be a polynomial in $\mathbb{C}$.  Hence, $$\sum_{n=0}^{\infty}{{a_n}{z^n}}$$ is entire, and therefore continuous in $\mathbb{C}$ (since differentiability implies continuity).  It follows that $$\sum_{n=0}^{\infty}{{a_n}{z^n}}$$ converges for any $z \in \mathbb{C}$.  QUESTION     I am aware that, while I may have (some) ideas for a (general) proof, admittedly there are several grey areas (i.e., gaps) that need to be filled.  Would you be kind enough as to fill in these gaps, by providing useful hints? How to embed fonts in HTML? I'm trying to figure out a decent solution (especially from the SEO side) for embedding fonts in web pages. So far I have seen , which doesn't even work on Firefox, and . The second solution is for titles only. Is there a solution available for full text? I'm tired of the standard fonts for web pages.  Thanks! Story about space explorers who communicate but then decide they must destroy each other I'm looking for a sci-fi story or novel from many years ago where a deep space explorer encounters an alien explorer. The explorers learn to communicate; but on parting, each decides to destroy the other in order to protect his own world. This is about a step in a derivation of the expression for the relativistic Doppler effect.  Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is emitted at frequency $f_s$ and wavelength $\lambda_s$. The frequency $f_0$ and wavelength $\lambda_0$ received by the observer will be different.  Some textbooks now argue that the wavelength received by the observer is given by $\lambda_0=(c+u)T_0$, where $T_0$ is the time period of the wave in the observers frame. The argument given is that the successive "crests" will be an extra distance $uT_0$ apart due to movement of the source. Upon relativistically transforming the time period in the source frame to the observer frame, the correct result $f_0=f_s\sqrt{\frac{c-u}{c+u}}$ is obtained.  But the argument for the wavelength seems reminiscent of the classical Doppler effect for sound. Is it really applicable here through this argument? And is there a way to show the same result for $\lambda_0$ mathematically? Need help finding a good book on Riemann Geometry I remember  due to misuse and I wonder if bots have a part of it. If the bot is POSTing something to my site what are ways I can combat it? I was thinking of setting some cookies and having the cookies changed via JavaScript + timestamp and sign (so yesterday's cookies can't be used today and next week).  I'm sure most people/bots would just use another site instead of enabling JavaScript in their bot.  What else can I do? I'm thinking daily POST limit and a honeypot for generic bots who just randomly post spam. In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$ Let $R$ be a principal ideal domain, and $a, b \in R$ with $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$, and $\gcd(m, n) = 1$. I now want to show that we then already have $a = b$.   I think the statement is easily seen to be true if $a = 0$ (or $b = 0$), since if $a = 0$ and $a^m = b^m$, then $a = b$ since $R$ doesn't contain any nontrivial zero divisors, so $b ≠ 0$ already implicates $b^m = b \cdot b^{m-1} ≠ 0$.  I don't really know how to prove the statement for the general case, where I can't directly apply the fact that $R$ doesn't have any zero divisors except $0$. I most likely have to use the fact at some point that $gcd(a, b) = 1$, but I'm not sure how. Related to Meta Super User efforts:  and Meta Server Fault efforts:  We already auto-remove negatively voted unanswered old questions automatically after 30 days, network wide, with no human intervention required. I was thinking we might extend that to remove old, unanswered zero score questions... based on the following criteria:  fewer than (question age in days * 1.5) views 0 score or lower, or 1 score or lower if the original author is deleted no answers 1 comment or fewer asked more than 1 year ago (thus based on creation date, not last activity date, so , or a user editing it, does not give a doomed question 365 more days of zombie &quot;life&quot;)  See the results of this query on:  (10509) |  (787) |  (650) This query has been refined based on the comments, and this is the final version that will roll out tonight. Every site in the network (except metas) will automatically delete old questions that meet this criteria from this point forward. Open the default browser in Ruby In Python, you can do this:  import webbrowser webbrowser.open_new("http://example.com/")   It will open the passed in url in the default browser  Is there a ruby equivalent? Can I visit the US twice within a 90 day period under the Visa Waiver Programme? 2nd time is only to transfer (change terminal, not airside).