Solving Stefan's solidification problem - moving boundary issue
How to solve a system of PDEs with zip condition?
Find the point which is furthest away from existing points while remaining within the convex hull Find the value of $y(1)$ of the ODE $y'+y=|x|$. Let $y$ be the solution of $$y'+y=|x|$$ for $x\in\mathbb{R}$ and $y(-1)=0$. Then the value of $y(1)$ is    $\frac{2}{e}-\frac{2}{e^2}$ $\frac{2}{e}-2e^2$ $2-\frac{2}{e}$ $2-2e$   I don't know what to do with the absolute value function in this problem. So I started like the regular first order equation by calculating integrating factor, and got $$ye^x=\int |x|e^x dx+C.$$ Now I got stuck as how to tackle the absolute value function? Help me to solve this. Thanks! I'm trying to figure out how to use "not only... but also" properly. Basically, my goal is to combine two clauses by using "not only".  For negations, I've figured out two styles that both sound correct:   He knew that if he fractures his finger, not only would he not be able to compete in the water polo tournament, he would not be able to take the SAT on Monday, either. He knew that if he fractures his finger, neither would he be able to compete in the water polo tournament, nor would he be able to take the SAT on Monday.   However, I don't know how to form a sentence that does not include a negation while using "not only". Here are a few possibilities that I've considered:   Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was also given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was also given a full scholarship.   In those four possibilities, I'm varying the usage of "but" and "also" in the last clause.  What is the proper usage of "not only"? How do I make 'X-Axis Mirror' available in Pose Mode? More often that not, while posing an armature, I want to mirror the pose across the X-axis, so that when I move "brow.L", "brow.R" also moves in the same way.  You can copy and paste a mirrored pose, or select both bones prior to performing a transform, but both of these options aren't particularly good workflow wise.  In edit mode, in the tools panel, under options you can enable "X-Axis Mirror" to copy all transforms across the X-axis in real time, but this option is not available in pose mode.  I'm not very experienced with python, but edit source reveals:  col.prop(ob.data, "use_mirror_x")   My understanding is that "use_mirror_x" refers to a boolean property, but I have no idea how to find where that boolean property is defined or if it would be possible to modify it to get the same result in pose mode.  Any advice on this is appreciated. Maybe there's a better way to achieve this?  Thanks. How do I alter a message in the message queue independent of site language? I want to programatically alter a message in the message queue. The message I want to alter is set in the message queue by function comment_form_submit() in comment.module, i.e.:  if ($comment-&gt;status == COMMENT_NOT_PUBLISHED) {   if (!user_access('administer comments')) {     drupal_set_message(t('Your comment has been queued for review by site administrators and will be published after approval.'));   } }   Instead of this, I want the call to drupal_set_message() to be this:  drupal_set_message(t('Your comment will be published when you validate your e-mail address.'));   How do I do this?  Postscript: Based on the answer below by Topsitemakers, I got this working for any language by using array_search() inside a custom MYMODULE_comment_submit to search the message array, and then compare the translated strings to identify the key of the string to alter.  This is the working code I ended up with:  $mm = drupal_get_messages('status', TRUE); $key = array_search(t('Your comment has been queued for review by site administrators and will be published after approval.'), $mm['status']); if (FALSE !== $key) {   $mm['status'][$key] = t('Your comment will be published when you validate your e-mail address.'); } foreach ($mm['status'] as $msg) {   drupal_set_message($msg, 'status'); } What is the best way to explain how to choose between "its" and "it's"? View a man page in a specific section I wanted to access man pages for command chmod.  Command whatis chmod gave this output:  chmod (2)            - change permissions of a file  chmod (1)            - change file mode bits  But I was actually looking for chmod(2).  When I type man chmod, man pages for chmod(1) appears.   Both man chmod(2) and man 'chmod(2)' commands show error.   I tried running info coreutils 'chmod invocation', but output is some kind of documentation which doesn't look like a typical man page. I'm sure everyone is familiar with the Ship of Theseus paradox, basically "If you replace parts of a ship over time until none of the original ship is left, is the end product still the same ship?"  I just read pop philosophy books, so spare me if this is an idiotic question, but could this be applied to the Brain and consciousness? If you were the take individual atoms/neurons, and somehow replace them with its exact copy one at a time, how would the person experience that?   I don't think there would be an interruption of consciousness, but at the end it's a completely separate (but identical) brain from the one you started with. Exactly as if you had just cloned the whole thing, right? But without interruption.  What interests me is the gradual transition of consciousness here, is it possible to know how that would  work?  I think I remember hearing people argue similarly for both the existence of a transcendent soul and also AI consciousness. And the only other discussion I found of this was on a flat earth forum, so I don't know what to make of that.   I hope I articulated my question clearly. Thank you! Chaining the Imperius curse What would happen if a wizard w successfully casts the Imperius curse on a equally powerful wizard a and then order him to cast the same curse back on w?  Follow-up questions.  It is established that casting the curse can be done .  What would happen in the case of a chain of casts that would hit back the original wizard? w-&gt;a-&gt;b-&gt;c-&gt;w  The original wizard could rather command the last wizard c, in the chain, to curse his first target instead. w-&gt;a-&gt;b-&gt;c-&gt;a wich would create a loop of a-&gt;b-&gt;c-&gt;a...  In what kind of limbo would wizards a, b and c exist in?  ( for the sake of simplicity, we can assume that every curse target is not very good at resisting the curse ) Automatically convert quotations in the form of "abc" to become ``abc" $x,y,z$ are independent and uniform random on $[0,1]$.  I know that $P(x \geq yz) = 3/4$ by triple integrating the triple density function.  However, is there a easier way to get this solution? Without triple integration. Aligning multiple points to line in QGIS? I would like to align multiple points to a line, or lines within a layer, using a specified tolerance or buffer around the line objects. Please refer to the sample sketch attached.  For the sake of this example, the points closest to the line in the BEFORE picture are within 5 map units of the line, while the outermost points are over 10 map units away. I would like to snap the closest points onto the nearest line, using a tolerance of 5 map units to achieve the result in the AFTER picture. How to write 1, 2, ... as a subscript to a letter? Formula between wire size and current Is there a mathematical formula between wire size, current, temperature and wire type(Or resistance)? So I'm making this summary of a course where I've only been getting information from one book. Sometimes I want to show what page from the book a statement is taken from but I can't figure out a clean way of doing it.  Basically I would like to have something (in function) similar to:  "Statement[Book p123]"  Do you have any suggestions? I have a file containing two columns and 10 million rows. The first column contains many repeated values, but there is a distinct value in column 2. I want to remove the repeated rows and want to keep only one using awk. Note: the file is sorted with values in column 1. For example:    1.123 -4.0 2.234 -3.5 2.234 -3.1 2.234 -2.0 4.432 0.0 5.123 +0.2 8.654 +0.5 8.654 +0.8 8.654 +0.9 . . . .   Expected output  1.123 -4.0 2.234 -3.5 4.432 0.0 5.123 +0.2 8.654 +0.5 . . . . How do I get attention for old, unfixed bug reports and feature requests without official responses here on Meta? I posted a question here on Meta Stack Exchange, or on a per-site meta, regarding a bug I found in the system. I got no comments, or a few comments stating that this is a legitimate bug (and not by design). However, it's been quite a long time, and no official response was ever posted there.  Or, I had an idea for a new feature, but realized it's already requested, either by searching or posting a request myself only to have it closed as a duplicate of the existing one. It's been a while since the original request was filed, but no official response has been made.   I'm aware that staff members are , but either my post isn't about one of the indicated topic areas for which they're accepting escalation requests for that month, or I already flagged to request escalation but it was declined, so the instructions there don't apply for my post.  What can I do to draw attention to meta questions for the SE team, so they can give an official response, and possibly implement the bug fix or feature?  Note: This is different from other general questions which ask for how to get attention for unanswered questions, since the procedures on meta sites are different, and getting an official response isn't necessarily the same as getting a good answer. How can I find the location of an icon of a launcher in use? passive Vs active or omission of 'which is' What is the part of speech of 'regarded' in the following?     "a quality of beauty and intensity of emotion regarded as characteristic of poems"    Why isn't it "... [which is] regarded ..."?  And in another case:      "a small lizard with wide feet, found especially in warm countries"     And also:      "Words used to describe writing or speech style"    In all these examples, why shouldn't the verbs be in their passive form (e.g. which is found, words that are used)?   I am a ESL learner and I am very confused by these usages! What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that $p=0$ (or similarly $p=1$) and sample size is relatively small, for example $n=25$?