Maximal ideal of the ring of all real valued continuous functions on $[0,1]$
Ideal in a ring of continuous functions
PBKDF vs HKDF for pretty long key I'm developing a messenger application with encrypted chats.   In the first version of the app I've used PBKDF2 (10000 iterations, SHA1, random salt) to extend a short user password and generate keys to encrypt (AES256) and sign message (HMAC).  In the current version of the app I generate a random 130-bit key and use it instead of a user password. I think that using PBKDF2 with such a key has some overhead.   I see 2 possible ways to improve the current approach:   Keep using PBKDF2 and decrease iterations to 1 or 10. Don't use PBKDF2 and use HKDF instead.   What are the advantages and disadvantages of each approach? Are there any other options? Are there published predictions that hydrogen could remain metallic at ambient pressure? Below the question  there is a  that directed me to the BBC News summary . In their attempt to balance the skepticism of this particular reported observation with the potential implications of producing metallic hydrogen in a laboratory, the BBC included some far-reaching possibilities:  If that is true - and it is a controversial claim - it fulfills a more than 80-year quest to produce what many have said would be a wonder material. Theory suggests metallic hydrogen could be used to make zero-resistance electrical wiring and super-powerful rocket fuel, among many applications.  At the end of the article:  &quot;The scepticism here is probably a good thing, in that it will drive many groups towards attempting to reproduce this experiment. This publication will certainly incite the field. Again, if it holds up, this is an exciting result. I think in this case time will tell,&quot; he told BBC News.  ...referring to Marcus Knudson from Sandia National Laboratories.  And Jeffrey McMahon from Washington State University concurred: &quot;With respect to the tiny sample amount: Such experiments are performed in small diamond anvil cells. One challenge would be to make a larger quantity (at once); another, perhaps bigger challenge is to recover even the small sample (ie, remove it from the extreme pressures that it is under in the diamond anvil cell). &quot;Whether the latter is possible is an important open question.&quot;  Question: Are there published, peer-reviewed predictions that hydrogen could remain metallic at ambient pressure? A link or reference would be appreciated. If it's still in pre-print form (AeXiv) that's OK too. If it's possible, a little help understanding the prediction would be great as well: I know there are many predicted crystalline forms of water ice at elevated pressures and/or reduced temperatures, and many or most of these have been observed, but I think most of them revert once pressure is reduced to ambient. Also the  comes to mind. If there is such a prediction of the possibility of hydrogen remaining metallic at ambient, is there an analogous example of this with a material I'm more familliar with, or is this something quite new? Is it safe to delete from C:\Windows\Installer? What's the best way to scan in hundreds of pictures? I have thousands of old pictures which were sitting in a photo album. Unfortunately, instead of the photo album protecting the pictures, the plastic coverings yellowed, and the pictures themselves had to be carefully extracted from the books. There is also quite a bit of powdered paper (the backings on the books pretty much fell apart while we extracted the pictures), and the fronts of the images are still a bit sticky.  These pictures are 30+ years old, are often extremely faded, and were originally taken on (what I think is) "110 film" -- they are approximately 2.5" squares.  Anyway, I need to scan all these images in to preserve them from further decay. Unfortunately, it's taking forever -- going through less than 100 images took an entire day, even if one discounts any time spent in Photoshop trying to remove some of the photo album's artifacts on the images.  What I really need is some method of scanning the images in faster. Most automated solutions aren't going to work because they accept 4x6s as their smallest image size, and even if that was not the case, the adhesives still stuck to the prints would probably ruin any such device in 5 seconds flat.  Is there a better way of doing this (i.e. fast scanner?) that wouldn't take so much time? Cut part from video file from start position to end position with FFmpeg I have a video file of 30 minutes, but I want to extract a video from 00:09:23 to 00:25:33.   I can define the startposition with -ss, but I couldn't find one for the end position. Any help please? Does this sentence have too many subjunctives? I would like to have a similar biblatex behaviour as described , i.e. separate bibliographies for different publication types, each bibliography should 1) be prefixed with a corresponding label (C for conference publications, J for journals etc), 2) sorted so that the newest entry is at the top (defined by the publication year) and 3) with reference numbers sorted in descending order per bibliography, i.e. the newest entry should have the highest number.  Journal articles ---------------- [J3]    reference from 2017 [J2]    reference from 2016 [J1]    reference from 2015  Conference publications ----------------------- [C4]    reference from 2017 [C3]    reference from 2017 [C2]    reference from 2016 [C1]    reference from 2015   I currently have the following:  \usepackage[backend=biber,         isbn=true,         giveninits=true,         style=numeric,         maxnames=99,         sorting=ydnt,         defernumbers=true,         autocite=superscript]{biblatex}  \subsection*{Journal articles} \begin{refcontext}[labelprefix=J] \printbibliography[type=article] \end{refcontext}  \subsection*{Conference publications} \begin{refcontext}[labelprefix=C] \printbibliography[type=inproceedings]   Separate bibliographies works fine, labelprefix also works as desired, sorting by year in descending order as well. However, if I try the solution mentioned in the above question I get very high reference numbers (in the 500s).  Is the above behaviour possible at all and, if yes, what is the most elegant solution using current biblatex etc.?  Thanks a lot in advance! How often should I remove the charger from my rMBP? I want my battery to remain healthy. I used to charge it full then remove the charger after it's done, then put it back on when it goes down to 10% .. However this is becoming hectic and I was wondering if I can keep it plugged in the whole day and probably remove just an hour or so before going to sleep.  What is the best way to charge and discharge my Retina Macbook Pro while keeping the battery healthy ? Why are doctors addressed as Mr. in the UK? In the US most physicians, surgeons and dentists are addressed as "doctor". Very few other professionals receive the same title.  In the UK, however, surgeons and dentists seem to prefer to be referred to as Mr. If that is true, why?  And who is addressed as Dr. in the UK?  Those who hold doctoral degrees only? Alignment of equals sign in multiple align environments Disable automatic activation of Gnome Shell activities on mouse over How can Kitty Pryde achieve time travel with her phasing abilities? In X-Men: Days of Future Past, how does Kitty Pryde suddenly get the power to send people's minds back in time? Initially she was only able to phase through objects and could extend this power to other people. The explanation of this cited molecular spaces.  How does she go from there to time travel all of a sudden?? Can it be proven that : If $a_n&gt;0$ and $\sum a_n$ converges then $na_n \to 0$ (without assuming $a_n$ is decreasing)  Please note This question does not require $a_n$ to be decreasing as condition,  Is it possible to prove $na_n \to 0$ without requiring $a_n$ to be decreasing? I keep thinking that $a_n&gt;0$ and $\sum a_n$ converging then that implies that $a_n$ must be decreasing anyway(not monotonically decreasing necessarily )  Is it possible that $a_n&gt;0$ and $\sum a_n$ converges then $na_n \not \to 0$?  There are already answered questions that assume $a_n$ to be decreasing as a requirement: (this question does not assume $a_n$ is decreasing)       was the post that made me ask this question, a counter example of monotonoic decreasingness of $a_n$ was given in comments by the OP. How is Leibniz's rule for the derivative of a product related to the binomial formula? Possible Duplicate:          The  describes the expansion of the $n$th power of the sum $(a+b)$:  $$(a+b)^n = \sum_{k = 0}^n {n\choose k}a^kb^{n-k}$$  In calculus, there is a generalization of the product rule called , which describes the expansion of the $n$th derivative of the product of two functions $f$ and $g$:  $$(fg)^{(n)} = \sum_{k = 0}^n {n\choose k}f^{(k)}g^{(n-k)}$$  It's not difficult to prove using the product rule and induction, what I'm really trying understand here is why the formula is true. Is there a way to prove it using the binomial formula? How are these two formulas related? Is there a combinatorial proof for Leibniz's rule like there is for the ?   I understand this question is a bit vague, but I hope you'll agree that these two formulas look so similar it just feels like there should be some relation between the two. Of course this is not necessarily true, but I'm hoping it's not just a crazy coincidence. Cannot install vim How to install import_3dm add-on properly? What would have happened if Voldemort had won Priori Incantatem before Nagini had been decapitated? As wielder of an elder wand that belonged to Harry, during Voldemort’s Last Stand, there are two instances of Priori Incantatem occurring, back to back.  Basically, the current order of events makes total sense. Since Nagini was the last horcrux, when the body died, the fragment of Voldemort’s soul locked in it was released. This disrupted the first instance of Priori Incantatem, and Voldemort was now significantly weaker than Harry – so Harry won. Naturally, the Elder Wand’s killing spell was reflected back on Voldemort because of Priori Incantatem outcome.   But, if Voldemort was just told by Harry that the Elder Wand wouldn’t work against Harry because it belonged to Harry, and was a wand that would win any duel for its master, why would Voldemort willingly try and continue to use it? This is doubly so, since after he had cast the killing spell on Harry once it had only torn Voldemort’s soul from Harry’s body – wouldn’t that even imply that the Elder Wand would realistically refuse almost any attempted direct harm against its owner?  Also, wouldn’t a first refusal of the Elder Wand to kill it’s own master also imply an additional refusal even if Voldemort had won either of the Priori Incantatem matches (in which case, the worst that could happen in this line of thinking is, Voldemort has Harry’s wand since Harry’s spell is Expelliarmus)? How can I show or hide boot messages when Ubuntu starts? Is there a way to easily turn on/off showing the boot messages (loading the services) when Ubuntu starts? Is it something in Grub2?  I am running 10.04. Correctly typesetting a tilde How do I set the tilde (~) character correctly in LaTeX?  There’s a  on Stack Overflow, with a lot of answers. But dare I say it? They all suck:   \textasciitilde is too high, \texttildelow is too low. $\sim$ can be tweaked to look more or less acceptable: {\raise.17ex\hbox{$\scriptstyle\sim$}} – but even that is a hack and uses the wrong symbol.   The point is – the tilde character is definitely an existing glyph in any font I am tempted to use. How can I just access and typeset that character, please? Without resorting to some other, similar-looking glyph that first needs to be nudged into place using a cunning combination of font size and raised boxes?  There must be a possibility to access that glyph directly from the font definition.  To demonstrate, look at this screenshot which attempts simply to display a C++ destructor of a type T (~T):    Compare this with the symbol we get in the browser: ~ – that’s what I want. Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$ I need a hand in showing that $$ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$$   Thanks in advance for any help.