I was reviewing my flagging history list and i saw a strange number after the question/answer I flagged. Have a look at in the image,        Now such type of number is there in few flag posts, while others don't have it. I just want to know is what this number indicates?

I'm not quite sure what to search for on this, but I noticed a little number on one (and only one, so I couldn't pinpoint a trend) of my flags in my flag history.   The text appears as follows:     title of question [closed] (1)   the flag was marked as helpful, the question was subsequently closed, yet a little (1) remains. I tried to see what that question had that the other questions did not, but moderator shut-down, specific tags, number of votes didn't matter. My only guess would be number of answers to the question? But I have no evidence for that. Does anyone know for certain?


There seems to be quite a few posts about this around google and on stack overflow, however most of them aren't very descriptive and I'm just having a really hard time understanding. Solutions offered all talk about using an external library, which I cannot use.   I have a JavaScript object that looks similar (not exactly) to this:  var test = {[{ "question": "What are you doing?", "id": 1, "answers": [                 { "answer": "Eating some pizza", "correct": true },                 { "answer": "Working on my PC", "correct": false },                 { "answer": "Sitting in a chair", "correct": true }             ]}]}   Obviously that is an array, because usually there will be multiple questions. Now what I'm doing is trying to make a page where I can edit the test, but I want to make sure that changes have been made to the test before sending it off to the backend for processing. There isn't any reason to send a request to the server if the test hasn't been modified. This means that if any character has been changed, a space has been added, an answer was changed from correct to incorrect, a question was added or removed, then this method would return true.  Else it would return false.   The only third party library I'm allowed to use in AngularJS. I've tried the  method and it didn't yield proper results.  One method that I've thought of using, which should have ideally of worked was the following:  function isEqual(obj1, obj2) {     return (JSON.stringify(obj1) == JSON.stringify(obj2)); }    However when a value (Such as a space " ") is added, it will still return true, even though the objects are different. While printing the value, it seems that if the space is at the beginning end of a string it will be trimmed. (The same result as angular.equals) However if a space is added between text, then the check returns false (as expected)  So what is the best way to check an object for equality with pinpoint accuracy?   Would appreciate if all answers are in raw javascript, and not using external libraries.

A strict equality operator will tell you if two object types are equal. However, is there a way to tell if two objects are equal, much like the hash code value in Java?  Stack Overflow question  is similar to this question, but requires a more academic answer. The scenario above demonstrates why it would be necessary to have one, and I'm wondering if there is any equivalent solution.


I see that there is a LaTeX package available for Windows.  I was recommended to install MikTeX on my PC w/ Windows10.  Why would one choose one over the other?

I have been using MiKTeX for a couple of years. I don't know whether it is "wise" to insist on using it. Could you give me a list of advantages of TeX Live over MiKTeX?


Especially looking at sine and cosine here. I'm trying to learn them by heart and it's quite unintuitive for me. If you guys could tell me about your way, be it by drawing up something or a table, I'd be glad to hear you guys suggestions :))

My math professor recently told us that she wanted us to be able to answer $\sin\left(\frac{\pi }{2}\right)$ in our head on the snap. I know I can simply memorize the table for the test by this Friday, but I may likely forget them after the test. So is there a trick or pattern you guys usually use to remember it? For example, SOHCAHTOA tells us what sine, cosine, and tangent really mean.   If not, I will just memorize the table. But just wanted to know what memorization techniques you guys use. I feel this is the perfect place to ask, because I bet a bunch of people in the math stackexchange, also had to go through the same thing freshman year of college.  Oh here is a picture of the unit circle:


I'm trying to generate a series Y that is correlated to series X. I know the data from X, I know the mean and the standard deviation of series Y, and I know the Pearson coefficient between X and Y (0.9). Example: X=[44.69,43.98,43.96,43.02,44.37,43.96,42.74,41.99,43.26,43.17] Pearson=0.9 mean_Y=20 Standard_deviation_Y=4.5 Can you help me somehow in getting the desired series Y? It would be great to have the solution ready to be used in Python. Thank you in advance for your time and help!

For a simulation study I have to generate random variables that show a predefined (population) correlation to an existing variable $Y$.  I looked into the R packages copula and CDVine which can produce random multivariate distributions with a given dependency structure. It is, however, not possible to fix one of the resulting variables to an existing variable.  Any ideas and links to existing functions are appreciated!     Conclusion: Two valid answers came up, with different solutions:   An R  by caracal, which calculates a random variable with an exact (sample) correlation to a predefined variable An R  I found myself, which calculates a random variable with a defined population correlation to a predefined variable     [@ttnphns' addition: I took the liberty to expand the question title from single fixed variable case to arbitrary number of fixed variables; i.e. how to generate a variable having predefined corretation(s) with some fixed, existing variable(s)]


I created a 30GB partition from my C drive. I want to install ubuntu in that partition but in the installation process am not getting the option to install ubuntu alongside windows. When I click on something else the free space I partitioned is saying unusable. How can I Fix this?

I want to dual boot windows 10 and ubuntu but I can't see the option to install alongside windows 10 during ubuntu installation. Yet ubuntu installer recognizes windows 10. My pc has 4 partitions. Please help


When i fill a space, why does it look like this?

While rendering a mesh with smooth shading on, I get a dark region/shadow on certain faces. The effect is more evident when smooth shading is applied to a mesh containing ngons, with the ngons turning black when rendered.   The blackening effect is visible in the viewport too.  How can I solve this problem?


A while ago, I spotted the gold badge, , which carries the description, Zero score accepted answers: more than 10 and 25% of total.  The way I interpret that is that you need more than 10 zero score accepted answers, and at least 25% of your accepted answers need to be zero score.  I'm guessing my interpretation is incorrect, as looking at my own profile, I have:   35 accepted answers with scores 12 accepted answers without scores 47 total accepted answers 12 out of 47 is 25.53% zero score answers   So by my reckoning, I should have that badge.  My zero score accepted answer percentage was higher a week or so ago (I seem to recall it was around 27% or 28%), but has since decreased as I've had some answers accepted recently that had been up voted.  Can anyone explain this? I'm guessing I'm misinterpreting the badge description?

Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a "(retired)" next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type.


I know there are a lot of discussions about this topic in this forum and I read all of them but my situation is slightly different.  I took a class with my professor and I worked in his research lab and I know him for a while. When I asked him for a letter of recommendation he told me send you CV plus draft of your letter of recommendation. In this forum a lot of people said do not do that it is unethical. I understand this and I understand why it is unethical but what should I say to him should I say this is unethical and I cannot do that or should I forget about letter of recommendation from someone who I worked in his lab.

This question is, honestly speaking, probably somewhat opinion-based, but I still want to give a shot.  A professor acceded to my invitation of writing a reference letter for me. Nevertheless, unlike the other professors who also acceded to write a reference letter for me, he asked me to draft it on my own. Originally I did not feel anything "wrong", and I just felt embarrassed to recommend myself. But yesterday a friend told me that a professor would ask you to write her reference letter for you when she does not actually think that you are "worthy" enough for her to write you one on her own.   What is the probability that such viewpoint is true? Any opinion is greatly appreciated!


Consider $\mathbb{N} \times \mathbb{Q}$ as a subspace topology of $\mathbb{R}^2$ with usual topology. Consider the set $A = \{(n,\frac{1}{n}) : n \in \mathbb{N}\}$. Is $A$ closed, open ? What is the boundary of $A$ in $\mathbb{N} \times \mathbb{Q}$?  My Attempt:  The basic open sets on $\mathbb{N} \times \mathbb{Q}$ will be of the form $n \times (a,b)\cap \mathbb{Q}$ where $(a,b)$ is open on $\mathbb{R}$.  So for a fixed $n$, $\{(n, \frac{1}{n})\}$ is a closed subset of $\mathbb{N} \times \mathbb{Q}$. $A$ is a countable union if closed set.  To be open for any point $a \in A$ we shall get a basic open set $B$ s.t. $a \in B \subset A$. It does not hold. So $A$ is not open set.  $\mathbb{N} \times \mathbb{Q} - A = \cup_n [n \times ((-\infty, \infty) - \frac{1}{n}) \cap \mathbb{Q}]$ is a countable union of open sets  $n \times ((-\infty, \infty) - \frac{1}{n}) \cap \mathbb{Q}$. So $\mathbb{N} \times \mathbb{Q} -A$ is an open set and so $A$ is a closed set.  The boundary of $A$ is empty.  Is my attempt correct? Thank you for your help.

The topological space $X=\mathbb{N}\times \mathbb{Q}$ with subspace topology of $\mathbb{R}^2$ the set $S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?  $S^c=\phi\times\{{1\over n}\}^c$ right? but I know $\mathbb{Q}$ is neither open nor closed in $\mathbb{R}$, I am confused here, could any one help me to answer this question?  the boundary of $S$ is $\bar{S}\setminus $ int S. as int S is $\phi$ so boundary is $\mathbb{N}\times \mathbb{R}$?


I have these random solid squares appearing in my pdf files for no reason. I tried to isolate the problem and relate it to a particular type of command. But, I still see them from time to time regardless of what commands I use. Here is an example of a simple TeX input.  \begin{itemize} \item Outer item 1. \begin{itemize} \item The code is easy to read/understand given the comments/documentation. \end{itemize} \end{itemize}   And below is a snapshot of the pdf that is generated. The funny thing is if I make the text sentence in the inner itemize shorter, it doesn't appear in this case.    I am using Tex Live 2015 on OS X, El Capitan.

Under TeX, when I write a line too long, it prints a fat black box at the end of the line.  That is probably a feature, but I dislike it.  How to turn that OFF? Is there a command-line option or something else?   I usually use LaTeX, but I have a complicated file which happens to be plain TeX.


Sorry if this is an easy one, but I'm learning and I'm new to python. I have a textbox where you can input some text but I need to remove special characters as it seems to be gumming up some other operations. I've tried different ways of using .replace('"', '') but I'm just getting errors.  here's my code that grabs the textbox input  def setter(self):         self.url = self.url.get()         self.artist = self.artist.get()         self.album = self.album.get()         self.album_artist = self.album_artist.get()         self.genre = self.genre.get()         self.year = self.year.get()         self.textBox = self.textBox.get("1.0", END)         if self.artist or self.album or self.year:             self.folder_name = self.artist + " - " + self.album + " (" + self.year + ")"   The error  "Michael P. Shipley's" ETERNAL Mistake is processing. Exception in Tkinter callback Traceback (most recent call last):   File "tkinter\__init__.py", line 1883, in __call__   File "AlbumWindow.py", line 64, in <lambda>   File "AlbumWindow.py", line 93, in setEntries   File "AlbumWindow.py", line 203, in instructions   File "AlbumWindow.py", line 182, in trackSplitter   File "site-packages\pydub\audio_segment.py", line 780, in export   File "site-packages\pydub\utils.py", line 57, in _fd_or_path_or_tempfile OSError: [Errno 22] Invalid argument: 'mick gordon - doom ost (2020)/"Michael P. Shipley\'s" ETERNAL Mistake.mp3'   Anything with quotes and some japanese characters are making it fail, I need to basically remove all special characters from self.textBox except for :  If I manually remove the " out of the textBox before I submit everything works fine.  Thanks!

I have a string that I want to use as a filename, so I want to remove all characters that wouldn't be allowed in filenames, using Python.  I'd rather be strict than otherwise, so let's say I want to retain only letters, digits, and a small set of other characters like "_-.() ". What's the most elegant solution?  The filename needs to be valid on multiple operating systems (Windows, Linux and Mac OS) - it's an MP3 file in my library with the song title as the filename, and is shared and backed up between 3 machines.


I'm using a Canon Powershot sx510hs which is an advanced point and shoot camera with 30x optical zoom. It has only one focus point at the center. Whenever I am trying to take portraits, having sky as background, the background appears to be over-exposed. The metering I am using is in evaluative mode or matrix metering mode. I would like to know whether there is a process by which I can attain even exposure for darker foreground subject and brighter background in case of outdoor portrait photography.

I took a picture once in a beautiful location with an awesome background, and a cool location to get the shot. The problem is, the location of the subject had substantially less light then the background, giving a silhouette effect. Without using an external flash, and on a low budget, what could I do to improve this picture?  Specifically, I shooting with a DSLR, outdoors. The DSLR has a small pop-up flash. The nearest good light source was maybe 5-10 feet away.   Thanks guys!    How do I avoid a dark subject when there's bright sunlight from windows?  by   I recently shot some photos at a friend's wedding. The location was lovely with lots of light — sometimes too much. The sunlight from the windows and skylights seemed to overpower the shot and the subject/people were very dark. What are some ways to avoid this without using fancy equipment? (I'm just starting out, I'm not a wedding photographer or anything!)  Here is one example I took — and this is after I've lightened it somewhat with Picasa:    I'm using a Nikon D5000 with a standard 18-55mm lens.


After reading , I know how to calculate certain (easy to express with in binary) exponents.  However, I find this method inefficient to calculate on paper.  I have this following problem: 2 ^ 2000002 mod 41  What would be a "good" (efficient, quick, simple) way to approach and solve this type of problems, where the exponent is a very large number?

How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and .


In my Article model, I have 4 different columns: short_effects, long_effects, benefits, and alternatives. They are all text columns.   In my view, I am calling each one in the same basic format:   <% unless @article.short_effects.blank? %>

Short-term side effects

     <% @article.short_effects.split(';').each do |effect| %>
<%= effect.downcase %>
     <% end %>
 <% end %>  <% unless @article.long_effects.blank? %>

Long-term side effects

     <% @article.long_effects.split(';').each do |effect| %>
<%= effect.downcase %>
     <% end %>
 <% end %>  . . .   to eliminate repetition, I would like to create a helper or a partial... however, I do not know which is better for this situation. I know some people frown upon HTML inside of helpers, but since helpers are used to reduce code from views, I feel that may be the best way. Any advice is greatly appreciated.

In a rails application, in which situation would you use a partial and when would you use a helper? I find both very similar, since they represent markup fragments.  Is there a convention around this? which is the 'rails way' of using them?  Thanks!


In Google analytics I freqently experience what I am calling "SEO attacks", where a single visitor or entity visits all or may of the links on my website, but somehow resets the session for each page, making the bounce rate look incredibly high even though I have had a "large amount" of visitors. Even though there are "multiple" visits I know it's one entity (person, machine, company?) because I currently have very low website traffic and when these spikes in activity happen they stand out very strongly. As well, the behavior for each "separate" visit is exactly the same, though they view multiple pages (for example, they all bounce 100%, or they visit the page 3 times, or they all have a 20 second time on page). Screenshot below:  Sometimes it's 20 "sessions", sometimes it's 100, sometimes it's 300. The only semi-solution I have for the problem is to go through and delete every individual user, but that takes a lot of time. Has anyone else had this type of problem? Does anyone else know how to prevent it?

Last months I have lots of referrer spammers in my GA statistics. Their count is ~10x higher than count of legit visitors (my site is not very popular yet). I've turned on an option to hide known spammers in GA settings, but it didn't help at all. It seems these spammers are using scripts to spam directly to GA (i.e. they are not logged in my IIS).  Is there anything I can do to stop these spammers?    UPD 10 months later, and they started spamming using fake target page names... and Google is still doing nothing about it.


I am using ubuntu terminal on my windows 10. I cloned a project, and I have been working on it inside VSC for a week now. I finally closed the program, and when I open it again I could not find my files even in recent. In ubuntu terminal, I found the directory and when I do yarn run dev the website opens with all the changes. I found the path using ls | xargs realpath and but I can not find it in my computer to open it in VSC. this is the path /home/'my user name in github'/'project-name'

I have installed Ubuntu subsystem on Windows 10 (after enabling feature in settings), but where is the Ubuntu file system root directory located in the drive?


To help people make sense of the world, we need to make information crystal clear. Well-placed icons can reinforce meaning and draw the eye quickly to the relevant section on a page. I need to communicate experiences and emotions. Here are some examples:  Emotions   Need Curiosity Desire to change the world Gratitude Motivation Personal satisfaction   Experiences   Public recognition/accolade Interviewing someone Being under-resourced Helping people Drawing Taking a photograph Empathizing/listening   These are difficult concepts to illustrate, and emojis have done the job remarkably well. However, for my business audience, this not the direction I want to go. Ideally, I'd like to find a beautiful library of flat, similar-style icons that are all free. Realistically, though... Let's just say I'm open to whatever the community has to offer.

I'd like to change the style of our Windows Mobile application to follow the Modern UI style (as in Windows 8 or Windows Phone 7). While there are excellent guidelines for layout, fonts and sizes, I'm not able to find suitable icons to use in our toolbar (little images showing the state of the network or the battery). Those are the flaws of the icon packs I already found:   Usually there are just one or two battery icons, whereas I need several to indicate the different states The icons get very blurry when resized to 16x16 pixels (even for vector graphics) A lot of icon sets contain gradients, shadows or gray pixels Most of the icon sets contain only a hundred to five hundred icons   If you have a look at the , they're very clear and sharp. I already know , but the icons get very blurry when resized to 16x16 pixels as well. Currently we're using the icons from , but they don't provide suitable icons for Modern UI applications.  So my question is basically: Where can I find professional, high-quality icon packs with a lot of different icons (either PNG or vector graphics)? They don't have to be free, but must be allowed to be used for commercial applications. What are the major icons vendors and what platforms are available to obtain icon packs from?


If a scalar field $f$ is differentiable at a point $\mathbf{a}$ in $\mathbb{R}^n$, then the directional derivative $f^\prime( \mathbf{a}; \mathbf{y})$ exists for every direction $\mathbf{y}$, and we have  $$ f^\prime( \mathbf{a}; \mathbf{y} ) = \nabla f (\mathbf{a})  \cdot \mathbf{y}. $$  Now my question is, does this formula always hold as long as all the partial derivatives of $f$ exist at the point $\mathbf{a}$? If so, then how to prove this? If not, then what counter-example(s) can we give?   P.S.:  Suppose that $f$ is a scalar field defined on a set $S$ in $\mathbb{R}^n$, let $\mathbf{a}$ be an interior point of $S$, and let $\mathbf{y}$ be any point in $\mathbb{R}^n$ such that all the partial derivatives of $f$ exist at $\mathbf{a}$ and the directional derivative $f^\prime ( \mathbf{a}; \mathbf{y} )$ exist. Now my question is, does the formula  $$ f^\prime ( \mathbf{a}; \mathbf{y} ) = \del f( \mathbf{a}) \cdot \mathbf{a} $$ always hold?   Of course, this formula does hold when $f$ is differentiable at $\mathbf{a}$. This much I know.

During my analysis course my teacher explained the difference between partial derivatives and directional derivatives using the notion that a partial derivatives looks at the function as approaching a point along the axes (in case of of the plane), and a directional derivative as approaching a point from any direction in the plane. He also explained that the existence of directional derivatives is a stronger notion than the existence of partial derivatives exists: if all directional derivatives exist, then the partial derivatives exist too.  I am to show (not necessarily prove) a case where the partial derivatives exist, but not all directional derivatives exist (hence, f is not differentiable).


Let $p_n$ be the $n$-th prime. Is there an elementary way to prove the statement that there exists a polynomial function $P$ such that $$p_n \leq P(n),$$ for all $n \in \mathbb{N}$? (Or, alternatively, for all $n$ from some $N \in \mathbb{N}$ onward?) I know the statement is true, and that $p_n$ "behaves asymptotically like" $n \log n,$ but I'm specifically looking for an elementary proof. (I'd like to show $\sqrt[n]{p_n} \to 1,$ and since trivially $n \leq p_n,$ the result would follow from the squeeze theorem.) Thanks in advance!!!!!!

Is there a way to show that $\sqrt{p_{n}} < n$?  In , I show that $f_{2}(x)=\frac{x}{ln(x)} - \sqrt{x}$ is ascending, for $\forall x\geq e^{2}$. As a result, $\forall n \geq 3$ $$\frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}}\leq \frac{p_{n+1}}{ln(p_{n+1})} - \sqrt{p_{n+1}}$$ Also (and as a result), $\forall n \geq 3$ $$ \frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}} > 0$$ Or $$ \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} < \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$  According to  $$\displaystyle\smash{\lim_{n \to \infty }}\frac{\pi (p_{n})}{p_{n}/ln(p_{n})}=1$$ Or, $\forall \varepsilon >0$, $\exists N(\varepsilon )$: $\forall n>N(\varepsilon )$ $$1- \varepsilon < \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} < 1+ \varepsilon$$ Or $$1- \varepsilon < \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} < \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$ As a result $\forall \varepsilon >0$, $\exists N(\varepsilon )$: $\forall n>N(\varepsilon )$ $$(1 - \varepsilon ) \cdot  \sqrt{p_{n}} < \pi (p_{n}) = n$$  But this is not enough.  Interestingly,  is true iff function $f_{4}(x)=\pi (x) - \sqrt{x}$ is strictly ascending ($x < y \Rightarrow f(x) < f(y)$) for prime arguments.  If $f_{4}(p_{n}) < f_{4}(p_{n+1})$ then $$\pi (p_{n}) - \sqrt{p_{n}} < \pi (p_{n+1}) - \sqrt{p_{n+1}}$$ Or $$\sqrt{p_{n+1}} - \sqrt{p_{n}} < \pi (p_{n+1}) - \pi (p_{n}) =1$$  And vice-versa, if $$\sqrt{p_{n+1}} - \sqrt{p_{n}} < 1$$ Then $$-\sqrt{p_{n}} < -\sqrt{p_{n+1}} + 1$$ Or $$\pi (p_{n})-\sqrt{p_{n}} < \pi (p_{n}) + 1 -\sqrt{p_{n+1}} = \pi (p_{n+1}) -\sqrt{p_{n+1}}$$  So, if Andrica's conjecture is true then $\forall n \geq 3$ $$\pi (p_{n})-\sqrt{p_{n}} > 0$$ Or $$\sqrt{p_{n}} < \pi (p_{n})= n$$


Suppose we have the following sequence of functions: $f_n:[0,1]\to \mathbb{R}$  $$ f_n(x)=nx(1-x)^n$$  I need to show this sequence does not converge uniformly to $f(x)=0$  For my definition of uniform convergence I am using:    $f_n,f:I\to \mathbb{R} \\ \qquad f_n \rightrightarrows f \iff \text{if} \enspace \forall \epsilon \enspace \exists n_0 \enspace \text{such that} \enspace \forall n\ge n_0 \enspace \text{then}:$  $$\sup_{x\in I}|f_n(x)-f(x)|<\epsilon$$    What I've done: (I'm not sure if it is correct)  If I fixate n=1, clearly we have $f_1(x)=1-x^2$, in this case, I could say  $$ \sup_{x\in [0,1]}|1-x^2-0|\ge 1$$  Does this show our sequence of functions does not converge uniformly to the 0 function? I guess I'm having trouble taking the negation of the definition of uniform convergence.

Suppose $f_n:[0,1]\to\mathbb{R}$ such that $f_n=nx(1-x)^n$, then I need to show that $f_n$ converges pointwise but not uniformly. I can see that since $f$ is defined on $[0,1]$, the part $(1-x)^n$ is smaller than $1$ and therefore will converge, but what about $nx$? This will go to infinity...  Therefore, I can't even see that it converges pointwise, but let's suppose it converges to some function, how do I show that it doesn't converge uniformly? I should find an $\epsilon$ such that it's not valid for all $n>n_0(\epsilon)$ that $|f_n-something|<\epsilon$, right?


CentOS 5.x  I noticed that someone (presumably another admin) added an entry directly to the bottom of /etc/crontab so it reads like:   SHELL=/bin/bash PATH=/sbin:/bin:/usr/sbin:/usr/bin MAILTO=root HOME=/  # run-parts 01 * * * * root run-parts /etc/cron.hourly 02 4 * * * root run-parts /etc/cron.daily 22 4 * * 0 root run-parts /etc/cron.weekly 42 4 1 * * root run-parts /etc/cron.monthly 00 3 * * 0 root foocommand   Assuming that I indeed want the command to run as root, are there consequences to adding scheduled tasks this way?  I'm more accustomed to using crontab -e to add/edit scheduled tasks.

System crontab:  /etc/crontab   Root crontab:  sudo crontab -u root -e   Which way is preferred? As they all run tasks within administration privilege.


In my experiment, participants are shown 4 images (A, B, C, D) that they have to rate on a 5 point scale. So my data looks like this: particpant1: A 5, B 3, C 3, D 1 p2: A 4, B 3, C 2, D 4 p3: A 4, B 3, C 2, D 4 etc... I want to see if A and B are rated higher by participants, but I am not sure how to do this. I thought I could use a poisson regression, because I have count data. But I'm not sure and wouòd appreciate help.

In my experiment, I asked 50 participants to rank on a 5 point scale which voice they preferred. I summed each particpants' rating for each voice: the total for voice 1 is 95, the total for voice 2 is 186.  Am I correct in doing this? Or should I analyse the raw data?  Which test should I use for this data? Would a t-test work here? Alternatively I thought I could use a chi-square test.   I am interested in seeing if the preference for voice 2 is significant.


I keep geting this error message on every page request:  Fatal error: Allowed memory size of 167772160 bytes exhausted (tried to allocate 36 bytes) in C:\wamp\www\mydrupal2\includes\theme.inc on line 98 Call Stack #   Time    Memory  Function    Location 1   0.0100  142240  {main}( )   ..\index.php:0 2   0.0220  449448  drupal_bootstrap( ) ..\index.php:20 3   0.2050  3025040 _drupal_bootstrap_full( )   ..\bootstrap.inc:2259 4   0.6290  15508712    drupal_theme_initialize( )  ..\common.inc:5144   Increasing memory allowance has not had any effects. I try using drush to disable the offending theme or go back to the last working one, it's the same error message. I can't even use drush for anything else. It reports the same error message. I tried the SQL method on this . Same result.

I've switched from Drupal 7.14 to 7.15 three weeks ago and therefore, I'm encountering a series of very sophisticated (for me) memory limit errors.  Those errors occur any time I'm trying to clear cache in performance or to run update scripts.  My hosting company has increased my memory limit in php.ini up to 126 M, 256 M, 512 M, and even 1024 M. But the errors still occur. I've migrated my site from shared to VPS, But the error incredibly still occurs. I have no way and no idea how to move forward.   Here are the errors:   Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 30 bytes) in /home/example/public_html/sites/all/modules/views/views.module on line 416 Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 108 bytes) in /home/example/public_html/includes/menu.inc on line 2736 Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to allocate 71 bytes) in /home/example/public_html/sites/all/modules/chain_menu_access/chain_menu_access.module on line 59 allocate 64 bytes) in /home/example/public_html/sites/all/modules/views/includes/base.inc on line 93


My friend gave me 3 Lenovo Thinkpads and 3 PSU cables and I'm trying to match them up.  In particular, the most powerful laptop is a Thinkpad X1 Carbon.  On the back it says it requires 20V,4.5A.  However, the most powerful of the PSUs says its output is 20V,3.25A. All of the three laptops and PSUs are physically compatible with each other, ie have the same shaped power plug/socket. Is it generally ok to use a 3.25A PSU with a 4.5A laptop, if the voltage is the same? Does the 4.5 mean that is the maximum current it might need? Will it tend to run slowly as a result of using less current? thanks, EDIT - in the comments below this question is referred to:  That's kind of different to my situation because in that other question the current difference is larger (8A v 5A, compared to 4.5A v 3.25A in my case). EDIT 2 - what's pushing me towards thinking it's ok is that this item on amazon , which claims to be a Thinkpad X1 Carbon Charger, seems to be identical to the 3.25A charger that I have.

I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6 V at 8.0 A. The output on the second laptop's power supply is 15.6 V at 5 A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop?


Question:      Which option is right. In case if both are right- for which case the using is more appropriate or I can use them interchangeably in some cases?   .     1) IN or/and FOR    I haven't seen him in a few years I haven't seen him for a few years      2) IN or/and FOR    I haven't seen him in a seven years  I haven't seen him for a seven years

, the seventh point says I can use the preposition in in an negative sentence. Does it mean I don't have to use the preposition for and still it will be correct?   For example:   I was there for three years. I was not there in three years.   Thanks for help.


if you set a dish filled with soapy water onto a loudspeaker or other vibrator and make vibration, When it oscillates, it is possible to hold small droplets on its surface for a long time. I mean, when the liquid surface starts vibrating, some drops of the same liquid, Spontaneously appear on the surface of the liquid.  What causes this phenomena? Why do the drops appear?  This is different from  . the defference :  In this question some drops will be *created Spontaneously *  But in the other question drops wich are put on the vibrating surface won't coalesce.

if you set a dish filled with water onto a loudspeaker or other vibrator and make vibration, When it oscillates, it is possible to hold small droplets on its surface for a long time. I mean, when you put a droplet of water on vibrating water surface, it doesn't coalesce with the water and bounce on the surface of water.( see this video  )  As we know, drop reaches its minimal potential when coalescing with water ( that's why drops coalesce)  what exactly cause this? why doesn't the drop coalesce with the water?


Like the group "Anonymous," they are not REALLY anonymous since they are all over media outlets. Is there a word for that?   Edit: Autoantonym almost sounds right but that seems to imply it has two meanings like left the airport vs going left. This one doesn't mean well known, it is the complete opposite of the actual word.

Is there a word for a word whose form is contrary to its meaning?  For example, "quotidian" is anything but quotidian.


If $X$ is a topological space and $\sim$ is an equivalence relation on $X$, I want to show that  $\tau: X \times I \to (X/{\sim}) \times I, \; (x,t) \mapsto (\pi(x),t)$ (where $I =[0,1]$ and $\pi: X \to X/{\sim}$ is the quotient map) is an identification.  Obviously, $\tau$ is continuous. But how do I prove that $\tau^{-1}(U)$ is open iff $U$ is open? So far all of my attempts have failed since $\pi$ can't be assumed to be an open map.  Thanks for help in advance.

It is not true in general that the product of two quotient maps is a quotient maps (I don't know any examples though).  Are any weaker statements true? For example, if $X, Y, Z$ are spaces and $f : X \to Y$ is a quotient map, is it true that $ f \times {\rm id} : X \times Z \to Y \times Z$ is a quotient map?


In The Last Jedi, Vice-Admiral Holdo kamakazis' her cruiser by jumping it to hyperspace through the enemy fleet, destroying it in the process. This seems like an enormous plot hole. Why don't the rebels, or anyone else for that matter, just do this all the time? Just mount a hyperdrive on any object and jump it at the enemy. Judging by the effect that cruiser had on an entire enemy fleet, doing this is has the following properties:  ignores shields super laser damage level cannot be dodged cheap and easy  Who needs death stars, super star destroyers, or really any planetary destroying tech, when you can just attach a hyperdrive to an asteroid? Furthermore, doesn't this make any ship bigger than an x-wing immediately obsolete? Any large, slow moving targets could be easily be destroyed by a hyperdrive missile. Apparently, you can mount a hyper drive on an A-Wing. Great, take A-Wing hyperdrive out, tape some scrap to it, and all those AT-AT walkers are toast. Am I missing something here?

This question is related to "The Last Jedi":  The maneuvre that vice admiral Holdo (with the purple hair) uses towards the end of the film seems remarkably effective.   It seems that it would have worked pretty well much earlier. Especially as two other ships were just allowed to run out of fuel and be destroyed.  It seems doing it earlier with different assets would have incurred less losses. Yet nobody seemed to consider it. Any in universe reason why?


Let $P(x)=ax^3+bx^2+cx+d$, where $a,b,c,d$ are real numbers. It is given that $-1 \le P(x) \le 1$ if and only if $-1 \le x \le 1$. Find the maximum value of $|a|+|b|+|c|+|d|$. I believe that the answer should be $7$. I have gotten as far as here:  Let $\lambda = 1$. Sub in $\lambda, \frac{\lambda}{2}, -\frac{\lambda}{2}$ in $P(x)$. We get that $$|\lambda a+b+\lambda c+d|,|\frac{\lambda}{8} a+\frac{1}{4}b+\frac{\lambda}{2} c+d|,|-\frac{\lambda}{8} a+\frac{1}{4}b-\frac{\lambda}{2} c+d|$$ are $\le 1$. Note that $$|\lambda a+b|=|\frac{4}{3}\times(1)-2\times(2)+\frac{2}{3}\times(3)|\le|\frac{4}{3}\times1-2\times-1+\frac{2}{3}\times1|=4,$$ where $(1),(2),(3)$ are the three expressions above. Similarly, $$|\lambda c+d|=|-\frac{1}{3}\times(1)+2\times(2)-\frac{2}{3}\times(3)|\le|-\frac{1}{3}\times-1+2\times1-\frac{2}{3}\times-1|=3.$$ The polynomial $4x^3-3x$ is an example of $7$ being able to be achieved.  However, I do not have the sufficient knowledge to complete the proof from this point.

Consider a polynomial $(\alpha ,\beta >0)$,$f(x)=x^3/\alpha+x^2/\beta+x/\gamma+1/\delta$.  If $|f(x)|\leq 1$ for $|x|\leq 1$ then $\max{(1/\alpha+1/\beta+|1/\gamma|+|1/\delta|)}$ is what?  Intuitively it seems that the value should be within the range $1$ to $10$....just plugged in random values.But I'm not able to solve it....


I have used Datatable to call ajax from servlet and display table on the basis of data received in response. Although API is returning data correctly that is text containing german characters but when it comes to displaying on html in datatable its showing special character like(Gl�ckwunsch, Verk�ufer) Initalizing Datatable: $('#table').DataTable({      'destroy': true,      "sDom": 't',      "bPaginate": false,      "bLengthChange": false,      "bFilter": false,      "bInfo": false,      "bAutoWidth": false,      "language": {      "url": "https://cdn.datatables.net/plug-ins/1.10.19/i18n/German.json"       }});  When calling ajax below is my code. $('#table').DataTable({   'destroy': true,   'ajax': {     "type": "POST",     "url": 'Servlet',     "data": function(d) {       // parameter sent in post     },     "dataSrc": ""   },    'columnDefs': [{       "title": "Column1",       "targets": 0     },     {       "title": "Column2",       "targets": 1     }   ],   "deferRender": true,   "pageLength": 25,   'columns': [{       "data": "Name"     },     {       "data": "desc"     }   ],   'dom': 'Bfrtip',    "language": {     "url": "https://cdn.datatables.net/plug-ins/1.10.19/i18n/German.json",     "decimal": ",",     "thousands": "."   }  });  Response from API [{     "Name": 'ABC',     "desc": "Glückwunsch" }, {     "Name": 'ABC',     "desc": "Verkäufer" }]  Can someone please help me over here. I didn't get anything related to this on google. Thanks in advance

I need to get UTF-8 working in my Java webapp (servlets + JSP, no framework used) to support äöå etc. for regular Finnish text and Cyrillic alphabets like ЦжФ for special cases.  My setup is the following:   Development environment: Windows XP Production environment: Debian   Database used: MySQL 5.x  Users mainly use Firefox2 but also Opera 9.x, FF3, IE7 and Google Chrome are used to access the site.  How to achieve this?


I'm trying to educate my self in key management, how to store them, how to generate them, how to use them properly.  I've been trying to find how you would generate a key for symmetric encryption (say AES-128), there is enough to find for public key crypto but that's not what I'm looking for.  For what I understand so far is that simply generating a 128 bit random number through a crypto-secure RNG would be sufficient, Is this correct? or are there special algorithms for creating an aes key?  The key will probably be generated when we flash our embedded devices, so it will be done on a windows PC.

I need to generate a 256 bit encryption key described by the adjectives in the title. Currently I intend to create the key using this .  Is this a secure manner of creating the key, given that it has the following properties:   Private key for symmetric encryption Used many times (of course with unique IV's)   And given the following facts:   I will literally just get the RNG to produce 32 random bytes not doing anything with (1) SALT (2) Iterations (3) Anything else   Please note that I am only asking if the key, directly after being generated, is secure. Thanks


Just out of curiosity, why was this cheeky badge retired? Was it because it was self-deprecating? Did it encourage no-answer questions?

This is an unofficial list/changelog of new features and various changes to Stack Overflow and the Stack Exchange network.  It is maintained by the community, while a Stack Exchange employee changes the accepted answer to ensure that the latest changes remain on top (given default user settings).  To see the list in reverse chronological order (latest entry on top), .  For those adding new features here: please post only feature changes that affect the whole network and have some global impact. i.e. bug fixes don't belong here, nor do mobile app updates.


I can't notice any differences except welcome message in second case. Also different files in etc/pam.d/ are responsible for different types of login

What is the difference between the following commands:  su sudo -s sudo -i sudo bash   I know for su I need to know the root password, and for sudo I have to be in the sudoers file, but once executed what is difference?  I know there is a difference between su and sudo -s because my home directory is /root after I execute su, but my home directory is still /home/myname after sudo -s. But I suspect this is just a symptom of an underlying difference that I'm missing.


I think that referring to a non-specific indefinite person like everyone, anyone, someone etc. as "they" is grammatical and widely accepted as being natural at least in informal speech. For example, the sentence "Everyone did their best" is grammatical. However, what about referring to a specific definite person? Let's consider the following conversation.  "My friend just got back from the shop." "What did they get?" "They bought furniture for their new apartment." "Are they married?" "Yes, they are."  Are these grammatical? Here's another example. A quote from the novel "A Study in Scarlet" written by Arthur Conan Doyle in 1886.  "What do you think of that?" cried the detective, with the air of a showman exhibiting his show. "This was overlooked because it was in the darkest corner of the room, and no one thought of looking there. The murderer has written it with his or her own blood.  Let's replace "his or her" by "their". Is the sentence "The murderer has written it with their own blood." grammatical in present-day English?

In "The Troubles" of U2, there is this :     Somebody stepped inside your soul   Somebody stepped inside your soul   Little by little they robbed and stole   Till someone else was in control   What I don't understand is why are we using "they" here ? Is this referring to the person that "stepped inside the soul" or is it about other people ? If it is referring to somebody, what are the rules that enables us to use they while it's one specific person that stepped inside the soul, and not multiple people ?


I'm looking for a function that takes an iterable i and a size n and yields tuples of length n that are sequential values from i:  x = [1,2,3,4,5,6,7,8,9,0] [z for z in TheFunc(x,3)]   gives  [(1,2,3),(4,5,6),(7,8,9),(0)]   Does such a function exist in the standard library?  If it exists as part of the standard library, I can't seem to find it and I've run out of terms to search for. I could write my own, but I'd rather not.

I have a Python script which takes as input a list of integers, which I need to work with four integers at a time.  Unfortunately, I don't have control of the input, or I'd have it passed in as a list of four-element tuples.  Currently, I'm iterating over it this way: for i in range(0, len(ints), 4):     # dummy op for example code     foo += ints[i] * ints[i + 1] + ints[i + 2] * ints[i + 3]  It looks a lot like "C-think", though, which makes me suspect there's a more pythonic way of dealing with this situation.  The list is discarded after iterating, so it needn't be preserved.  Perhaps something like this would be better? while ints:     foo += ints[0] * ints[1] + ints[2] * ints[3]     ints[0:4] = []  Still doesn't quite "feel" right, though.  :-/ Related question:


Hopefully this is a quick question. I'm making a simple rock paper scissors game. I make a random computer choice fine, and get the user's choice fine. But when I try to find who wins, it prints the last else in my else if block that is for invalid input.  It prints "Enter a valid choice" when a correct choice has been made.   import java.util.Random; import javax.swing.JOptionPane;  public class JavaApplication4 {      public static void main(String[] args)      {         Random ranNums = new Random();          int comp = ranNums.nextInt(3);         String comp2;         String winner;          String user = JOptionPane.showInputDialog                 (null, "Enter rock, paper, or scissors");         user.toLowerCase();          if(comp == 0)             comp2 = "rock";         else if(comp == 1)             comp2 = "paper";         else              comp2 = "scissors";          //Computer wins         if(comp2 == "rock" && user == "scissors")             winner = "The computer wins";          else if(comp2 == "paper" && user == "rock")             winner = "The computer wins";              else if(comp2 == "scissors" && user == "paper")             winner = "The computer wins";          //Tie game         else if(comp2 == "rock" && user == "rock")             winner = "It's a tie";          else if(comp2 == "paper" && user == "paper")             winner = "It's a tie";          else if(comp2 == "scissors" && user == "scissors")             winner = "It's a tie";          //User wins         else if(comp2 == "scissors" && user == "rock")             winner = "You win!";          else if(comp2 == "rock" && user == "paper")             winner = "You win!";          else if(comp2 == "paper" && user == "scissors")             winner = "You win!";         else             winner = "Enter a valid choice";          JOptionPane.showMessageDialog(null, "You picked " + user + "\n" +             "The computer picked " + comp2 + "\n" +                 winner);        } }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


QUESTION: On a Windows/Linux dual-boot system, is there a way to tell grub to automatically alternate between the defaults, like that every other boot go to Windows, and every other boot go to Linux? WHY: I have a dual-boot computer with Windows and Linux (Mint) side by side. By default grub boots to Linux with a 30 second waiting time. I have set up remote control software (earlier TeamViewer, now I am using AnyDesk) on both OSes so that I can control the computer remotely, no matter if it is booted to Windows or Linux. The remote control software becomes active at OS login, so it is possible to boot the machine and log into it remotely. However, naturally I can't see the grub boot menu remotely as the remote control software is not yet active at that point, so basically I cannot remotely decide to boot to the other OS, only to the default one that GRUB offers. EDIT: It occurred to me though that I could partly achieve what I want by making Linux the default grub OS, and if I want to boot to Windows, I change the GRUB default to Windows while in Linux, before booting the machine. However, if the grub change is permanent, then I can't boot back to Linux anymore? Is there a way to make the grub default change only temporary? I would still prefer the "automatically alternating default" as that is less manual work in case I want to switch OS remotely. EDIT: I'll have to test at home whether this is the solution:

I'm not sure I'd actually do this, but is there a way to make GRUB automatically select the boot option I didn't use last boot? i. e. If I booted into Windows last boot, it selects Ubuntu. If I booted into Ubuntu, it selects Windows. I was just wondering because I often find myself rebooting to switch OSes, as I have different games that I run on each (though with my new rig I don't need to run stuff on Ubuntu just for lower OS resource usage), and I was wondering if I could make it so that every time I pressed "restart" from either OS I wouldn't have to change selections. In practice this would also affect non-restart startups, so then I might have to boot twice to get the OS I was using last time.


Is there a simpler expression for $f(f(f(...f(x)...)))$ (total n '$f$') ?   Thank you.

If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use?  For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is important especially since I am trying to couple this with a limit toward infinity.


I am extremely new to D&D and I'm filling out a 5th edition character sheet for the first time. I chose my race as elf and it says, "You have proficiency in the Perception skill." What's proficiency? How do I fill it out, what do I write? And also how would it be used in combat..?  Just explain it to me as if I am five years old. A scenario would be nice.. Sorry for the trouble, first time with RPG games as well

I am reading the 5e rules, and I keep seeing how you can add proficiency bonus to attack rolls checks with weapons you are proficient in and skill checks in skills you are proficient in, but I can't find anything on what this bonus actually is. How do you determine what the numerical actual bonus you add to your roll is? And at what times is it used?


I do not understand how this theory (the theory of general relativity) would work because gravity is what makes things heavy and weight is what bends things. All of the proof makes it hard to question strongly though (with light bending and all) so simply put my question is how does the earth, sun and everything else "bend" space without gravity to pull it down into space? And if this is so  how does the earth's bending of space attract us to the earth?

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?


I installed a package by "pip inatall " and I want to find where the package is located on my disk.   I found these post:   and , but they didn't answer my question.   My terminal doesn't know the commands 'lsvirtualenv' or 'workon'. The function site.getsitepackages() returned:      ['/usr/local/lib/python2.7/dist-packages',   '/usr/lib/python2.7/dist-packages']   None of these directories included 'okcupyd'.

How do I find the location of my site-packages directory?


I faced a strange function  I installed ubuntu 13.10 and all the time the number pad on the right of my keyboard is typing number without pressing Num Lock and when I turn it on It does the job when Num Lock is normally off .   does anyone have this problem ? and any idea how to fix it ?

I am trying to force numlock to be on upon initial boot at the login screen on Ubuntu 12.04. The only solutions I have found so far switch numlock on only after initial login.  I'm looking to force numlock to be on when the login screen is displayed, and before the user has logged in. Can anyone assist?


I wanted to wrap following line as function which takes parameter as a template type (to replace ConnectionManager for any other type):  std::shared_ptr<ConnectionManager> client = ConnectionManager::createClient<ConnectionManager>(broker, service_url);   So I created function that takes template parameter:  template<typename ClientType> std::shared_ptr<ClientType> createClient(const std::shared_ptr<thrift::TServiceBroker>& broker, std::string url) {         std::shared_ptr<ClientType> client = ClientType::createClient<ClientType>(broker, url);         return client; }   when I try to compile I get following error:  error: expected primary-expression before ‘>’ token  std::shared_ptr<ClientType> client = ClientType::createClient<ClientType>(broker, url);   Kdevelop suggested following change:  template<typename ClientType> std::shared_ptr<ClientType> createClient(const std::shared_ptr<thrift::TServiceBroker>& broker, std::string url) {     std::shared_ptr<ClientType> client = ClientType::template createClient<ClientType>(broker, url);     return client; }   After this change code compiles and works.   createClient is defined in ConnectionManager parent as follows  template<class IMPCLASS> static inline ::thrift::shared_ptr<IMPCLASS> createClient(const ::thrift::shared_ptr< ::thrift::TServiceBroker >& broker, const std::string& address)   I have two questions:   I don't understand why I got compilation error I don't even know syntax that fixed the error   Please explain.

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I need to find   $$ \int \sqrt{1-\sin (2x)} dx $$   I have a doubt in this: the square root is equal to $|\sin x-\cos x|$ can we integrate this without knowing the limits?

I want to solve the following integral without substitution:  $$\int{\sqrt{1-\sin2x}} \space dx$$    I have: $$\int{\sqrt{1-\sin2x}} \space dx = \int{\sqrt{1-2\sin x\cos x}} \space dx = \int{\sqrt{\sin^2x + \cos^2x -2\sin x\cos x}} \space dx$$    but this can be written in two ways: $\int{\sqrt{(\sin x - \cos x)^2}} \space dx$ or $\int{\sqrt{(\cos x - \sin x)^2} \space dx}$ and it seems to be pretty far from what the real result is:   Can I get any hints?  EDIT:  Thank you for your answers! So as you all showed, we have: $\int{\sqrt{1-\sin2x}} \space dx = \cdots = \int{\sqrt{(\sin x - \cos x)^2}} \space dx$ or $\int{\sqrt{1-\sin2x}} \space dx = \cdots = \int{\sqrt{(\cos x - \sin x)^2} \space dx} = \int{\sqrt{(-(\sin x - \cos x))^2} \space dx}$    combined: $\int{\sqrt{1-\sin2x}} \space dx = \cdots = \int{\sqrt{(\pm(\sin x - \cos x))^2} \space dx}$  so we actually have: $$\int{|\sin x - \cos x|} \space dx$$    I drew myself a trigonometric circle and if I concluded correctly, we have: 1. $\int{\sin x - \cos x} \space dx$ for $x \in [ \frac{\pi}{4} + 2k\pi , \frac{5\pi}{4} + 2k\pi ] , \space k \in \mathbb{Z}$ 2. $\int{\cos x - \sin x} \space dx$ for $x \in [ -\frac{3\pi}{4} + 2k\pi , \frac{\pi}{4} + 2k\pi ] , \space k \in \mathbb{Z}$    ... which means: 1. $x \in [ \frac{\pi}{4} + 2k\pi , \frac{5\pi}{4} + 2k\pi ] , \space k \in \mathbb{Z}$ : $$\int{\sqrt{1-\sin2x}} \space dx = \int{\sin x - \cos x} \space dx = -\cos x - \sin x + C$$ 2. $x \in [ -\frac{3\pi}{4} + 2k\pi , \frac{\pi}{4} + 2k\pi ] , \space k \in \mathbb{Z}$ : $$\int{\sqrt{1-\sin2x}} \space dx = \int{\cos x - \sin x} \space dx = \sin x + \cos x + C$$


I have have string  in php as follows:  shows that he/she is a firm believer in “If it ain’t broke, don’t fix it” or “leave well enough alone”        when I print this string it output something like this:  shows that he/she is a firm believer in â€œIf it ainâ€™t broke, donâ€™t fix itâ€ or â€œleave well enough aloneâ€  How can i print this exactly as the first one? is there any solution?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


In modern Western culture we think of numbers typically in base 10. By "we" I mean the vast majority of the public. For some reason this is easy, and I'm not sure why or how to pinpoint it down to some concrete reason for its success. The only thing I can think of is we have 10 fingers so we can count on them, and 10 divides pretty "easily" whatever that vague term means.  But we can think of extremely large numbers down to a very low level of precision using this system. For instance, you can think of the number $171,129,412$, which goes down to describing "two" at the scale of 100 million+. But it's as if in your head you can visualize every element in that set, even though you really aren't, but you get the sense that you can understand its size.  You start to lose track a little if the number is too big though: $12,918,274,182,183,182,874,371,173$. It's pretty much impossible now to know how big this is down to the $173$ scale at the end. I have no idea why but it just seems this way.  But you can get into the millions an billions down to the scale of 1, using our numbers represented in base 10 system.  We can use the base 10 system differently and do scientific notation to create orders of magnitude with it as well, leading to thinking of huge numbers at a broader scale / level of detail. Like $10^{30}$ is pretty large, but you can get a sense of it's relative size to $10^2$.  We can also use the base 10 system for decimals to a good degree, where we can go 9 or 10 decimal places in and still feel we are understanding the value's accuracy.  Given all this, I'm wondering if there are any other systems that work equally as well, or close to as well, or even better, when compared to the base 10 system.  Some common base x systems are base 2 for binary, base 16 for hex, base 60 in the past seems like it was popular. However, I personally can't easily look at one of these numbers and get its value down to an accuracy of 1 right away. TBH, I don't get any sense of value of it all all. I'm not sure if I could with practice, or there is something inherent about 10 that makes it simple and intuitive.  My question is, if there is anything other than base 10 that lends itself to easily understanding large and small numbers at any scales, in the same or similar way that the base 10 system does (as described above). In particular, wondering about base 2, base 3, base 4, base 5, ... base 16-ish, and then any arbitrary number after that that lends itself to understanding would be interesting. But mainly wondering if any of these smaller numbers have good properties for understanding like base 10.  One system that is interesting to consider is Roman numerals. Instead of going $1, 2, 3, 4, \cdots$, where it's 1-digit numbers, followed by 2-digit, followed by 3 digit, ..., you instead have $I, II, III, IV, V, \cdots$, so that was $1, 2, 3, 2, 1, \cdots$. So it's an interesting way to represent it while still keeping it base 10 or whatever base. This fits into the category of things I'm asking about in some way.

Most people use base 10; it's obviously the common notation in the modern world.  However, if we could change what became the common notation, would there be a better choice?  I'm aware that it very well may be that there is no intrinsically superior base, but for the purposes of humans, is there a better one?  I've heard from sources such as  and  that base 12 is better, from  that base 8 is better, and, being into computer science, I would say that base 16 is the most handy.  Base 12 does seem to be the most supported non-base 10 number system, mainly due to the following reason pointed out by George Dvorsky:     First and foremost, 12 is a highly composite number — the smallest   number with exactly four divisors: 2, 3, 4, and 6 (six if you count 1   and 12). As noted, 10 has only two. Consequently, 12 is much more   practical when using fractions — it's easier to divide units of   weights and measures into 12 parts, namely halves, thirds, and   quarters.   And, on top of that, previous societies considered very advanced used other systems, such as the Mayans using base 20, and the Babylonians using base 60.  So, summarized, my question is: Is there an intrinsically superior base? If not, is there one that would be best for society's purposes? Or does the best base depend on the context it is being used in?


Do I need to place a comma before -but- in this sentence? I suppose not, because there is no independent clause after but. Or am I wrong? And which option is, stylistically, preferable?  According to the Explanatory Memorandum, the Act equips disputing parties with an auxiliary tool to refrain them from commencing legal proceedings on the merits of the case but instead helps them to negotiate an out-of-court settlement. According to the Explanatory Memorandum, the Act equips disputing parties with an auxiliary tool to refrain them from commencing legal proceedings on the merits of the case but helps them to negotiate an out-of-court settlement instead.

Am I correct to include a comma before "but instead" in the following example? I am not sure if the latter part of the sentence could be considered a main clause because there is no subject, so I am not sure if I am right or not.     The manual holds that women must not choose a programme themselves, but instead wait to be assigned to a module.


When we change the number of electrons in an atom of an element, it constitutes an ion. When we change the number of neutrons of an element it constitutes an isotope. But when we change the number of protons of an element, the change is so drastic that it constitutes a whole new element.  Why is it so?

My question might sound convoluted but my mind is twisting right now so my apologies in advanced.   Why is it that when I have one proton and one electron it is Hydrogen a clear flammable gas, and when I have say, twelve, it is carbon the driving force of life as we know it and then we end up with 239 and we have uranium a radioactive element.   How does the amount of protons affect what matter will be? Why does the amount of these particle things magically make one thing air and another cyanide?  If I have one pebble it is a pebble, if I have 13 its just more of the same pebbles. What makes protons different?  Sorry this is so convoluted,  any reply is appreciated


When I was wondering about if Constant Functions were even or odd, I thought about the function:  f(x) = 0 , It's simultaneously odd and even,  f(3) = 0 , f(-3) = 0, f(1) = 0 , -f(1) = 0,  (It's Indeed a counter-example) I'm pretty sure I haven't solved the profound paradoxes of math. Is what I have concluded right?, Has anyone heard of it?   P.S ( I was taught it can't be both, so YEAH)

I woke up this morning and had this question in mind. Just curious if such function can exist.


Recently I've seen many people on Twitter use "of" instead of "have". Eg. Ben Stokes tweeted after the world cup final, " So proud to of represented my country in a world cup final"  I don't want to generalise, but I think I've seen this used by primarily British people. Is it slang or are my basics weak?

We short men are in big trouble because if we want a shoe that feels decent we feel short and you can’t put in lifts, if you get a shoe with lifts it doesn’t feel comfortable I feel really trapped, that why I cannot believe that there is a god because if there was he wouldn’t of don’t this to me and made me only 5.4″ he or it would of made me to be at lease the regular American height which is 5.8” or taller , its a disaster to be short for a male.   The text is written by a native English speaker. It is the first time I face a usage in which would of + verb is used. Is it grammatically correct? What is the meaning of the parts I have shown in bold?


How can I encode or encrypt a PHP source code?   I've tried this one , the problem is that it is easy to decrypt for someone who knows it. For a stronger encryption I use this one , but if I encrypt some PHP code my page doesn't work.   Which is the best method? I don't want to use Ioncube or Loaders.

Has anybody used a good obfuscator for PHP? I've tried some but they don't work for very big projects. They can't handle variables that are included in one file and used in another, for instance.  Or do you have any other tricks for stopping the spread of your code?


On macOS Catalina 10.15.3, I am getting the below error message while running npm run dev or npm run watch. It seems like something to do with nodejs but no idea know how to resolve it.     “fse.node” cannot be opened because the developer cannot be verified.   macOS cannot verify that this app is free from malware.

I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks.


I'm kinda new to programming, but I can't figure out how to use a String Scanner to see if it is present in an Array (If Array contains "Apple" and the Scanner returns "Apple", Print "Present"). I'm using Eclipse Mars 4.5.0, and the code I have up to now is as follows:  public static void main(String[] args) {       String answer = "null"; //Initialize "answer"     String[] Fruit;         //Array of Strings called "Fruit"     Fruit = new String[10]; //"Fruit" has 10 spaces     //Strings saved in "Fruit":     Fruit[0] = "Apple";     Fruit[1] = "Banana";     Fruit[2] = "Mango";     Fruit[3] = "Pear";      //The actual programme:     @SuppressWarnings("resource")     Scanner input = new Scanner(System.in);     System.out.println("Please enter a fruit:");     answer = input.next();                                                             //If the answer is 'Fruit[0]'     if (answer == Fruit[0] || answer == Fruit[1] ||         //OR 'Fruit[1]' OR etc,         answer == Fruit[2] || answer == Fruit[3]) {         //Print "available"         System.out.println("This fruit is available.");     }                                                             //If the answer isn't 'Fruit[0]'     else if (answer != Fruit[0] && answer != Fruit[1] &&    // AND not 'Fruit[1]' AND not             answer != Fruit[2] && answer != Fruit[3]){      //etc, Print "not available"         System.out.println("This fruit is not available right now.");     } }   However, it always returns "not available", same goes for a While-loop: it somehow doesn't seem to check whether it is even present in the Arraylist or not.  Does anybody know how to fix this? I'd love to know because I couldn't find any similar question anywhere on the internet.  EDIT: Odd, I searched for it quite a number of times, guess I missed one, sorry for duplicating!

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Trying to prove by induction that  $\sum^{i=n}_{i = 0}$$n\choose i$$=2^n$  So obviously, I prove for some arbitary number, i.e $n = 2$  I then go on to show what the n = k terms look like for the first 3 terms  Then I realise to show that it is the same for $n = k+1$, I need to show that:  $2\times(n=k)\equiv (n=k+1)$  Yet when I try and work out the algebra I keep coming excruciatingly close but to no success, am I going about this proof the wrong way or? I've redone my calculations multiple times so there are no errors in my algebraic simplification.  Could it be that I need to go about this another way instead of trying to show it is $2\times n=k$

Prove by induction that for all $n \ge 0$:  $${n \choose 0} + {n \choose 1} + ... + {n \choose n} = 2^n.$$  In the inductive step, use Pascal’s identity, which is:  $${n+1 \choose k} = {n \choose k-1} + {n \choose k}.$$  I can only prove it using the binomial theorem, not induction.


Does java.util.List.isEmpty() check if the list itself is null, or do I have to do this check myself?  For example:  List<String> test = null;  if (!test.isEmpty()) {     for (String o : test) {         // do stuff here                 } }   Will this throw a NullPointerException because test is null?

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I use C# Windows Form. I seem need convert to string. How I can do this?  byte[] data = new byte[256];

How can you convert a byte array to a hexadecimal string, and vice versa?


I need to show that $H$ is a subgroup of $GL(2,R)$ where $H=\{A\in GL(2,R)\mid AA^T=I\}$. I think I can show that $H$ is non-empty because $I$ is the identity of all $n\times n$ matrices in $GL(2,R)$ but, how do I show that it is closed? I have that $AA^T=I$ and $BB^T=I$ but can I show that $AB=I$. Is that even how I do it?

I am studying orthogonal matrices and I am not sure if to show if a set of orthogonal $n \times n$ matrices forms a group under multiplication. We must check each of the group axioms. I found that the axioms are:  Closure Associativity Existence of identity matrix Existence of the inverse matrix.  I edited my question, since I was able to find more information about this topic. This group is called $O(n)$. To check the four axioms I did: Let $A \text{ and } B \in O(n)$, denoted as orthogonal matrices and assume that $C=AB$, then, Closure :  To prove that $C \in  O(n)$ we must prove that $C$ is a real $n \times n$ orthogonal matrix with uni-modular determinant. Since A and B are real $n \times n$ matrices, $C$ is also a real $n \times n$ matrix so, $C^TC=(AB)^T AB=B^T A^T AB = B^TB=I$  Associativity :  Matrix multiplication is associative, so the law holds for $O(n)$ group elements.  I am not sure if this is enough to prove associativity. Identity element :  The $n \times n$ identity matrix $I_{n \times n}$ represents the identity element.  In this case I am not sure if this is enough to prove the identity element. Inverse element :  Let $A^{-1}$ be the inverse of $A$, then we need to prove that  $A^{-1} \in  O(n)$ since $(A^{-1})^T=(A^T)^{-1}$. We have that: $(A^{-1})^T A^{-1}=(A^T)^{-1} A ^{-1}=(AA^T)^{-1}=I^{-1}=I$  Can anyone check if what I did is correct? I also would like to know if I can prove the associativity and the identity element in a better way. thanks


\documentclass[12pt]{beamer}   \usepackage{pgfplots}   \usepackage{tikz}    \begin{document}   \begin{figure}%     \begin{tikzpicture}[scale=0.8]       \begin{axis}[axis lines=middle, xtick={-3,-2,...,5,9},         xticklabels={-3,{}, -1, 0, 1, {}, {}, {}, 5, $k$},         extra x ticks={-2, 2, 3, 4},         extra x tick labels={$-2$, $2$, $3$, $4$},         extra x tick style={           xticklabel style={yshift=0.5ex, anchor=south}},         xmin=-5,xmax=11, ytick={\empty}, yticklabels={},         ymin=-5, ymax=6, axis on top]         \addplot+[ycomb,black,thick] plot coordinates         {(-3,3) (-2,-2) (-1,1.5) (0,4) (1,1.5) (2,-1.5) (3, -3)           (4,-1) (5,4) (9,5)};       \end{axis}       \node at (5.1,3.5) {$\cdots$};       \node at (0,3.5) {$\cdots$};       \node at (0.8,4.5) {\tiny{$x[-3]\delta[n+3]$}};       \node at (2.7,4.8) {\tiny{$x[0]\delta[n]$}};       \node at (4.2,5) {\tiny{$x[5]\delta[n-5]$}};       \node at (6,5.5) {\tiny{$x[\alert{k}]\delta[n-\alert{k}]$}};       \node at (6.8,2.2) {$n$};       \node at (2.7,5.7) {$x[n]$};     \end{tikzpicture}   \end{figure}   \end{document}   After some more searching in this forum, I have come up with this code and the associated plot.  The positioning of the things I want is a kludge.  Questions: All the positioning is manual (by trial and error). Even the x- and y-axis labels I had to locate by trial and error.  Can this be automated?  When I change the fontsize for the x-labels (e.g., \footnotesize), their alignmens get messed up.

I would like to plot several discrete signals with pgfplots. So far, I've done the following     \documentclass[border={10pt}]{standalone} \usepackage{tikz,pgfplots,filecontents,amsmath} \pgfplotsset{compat=1.5}  \begin{filecontents}{data.dat}  n   xn  -5   0.0 -4   0.0 -3   3.0  -2   2.0   -1   1.0    0   0.0    1   1.0    2   2.0    3   3.0    4   0.0   5   0.0 \end{filecontents}   \begin{document}  \begin{tikzpicture} \begin{axis} [%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     axis x line=middle,     axis y line=middle,     every axis x label={at={(current axis.right of origin)},anchor=north west},     every axis y label={at={(current axis.above origin)},anchor= north west},     every axis plot post/.style={mark options={fill=black}},     xlabel={$n$},     ylabel={$\boldsymbol{x[n]}$},     xtick={-7, -6,-5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8},     ymin=0,     ymax=5.5, ]%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \addplot+[ycomb,black,thick] table [x={n}, y={xn}] {data.dat}; \end{axis} \end{tikzpicture}  \end{document}   The first question is that changing xtick doesn't seem to affect the appearance of the axis, how to expand the xtick? The second question is some signals may have negative values, therefore, the lines will overlap the ticks. My question is is there a way to place the xtick above the axis?


I am refactoring an older application, it was using dynamic in-line SQL, pulling data from a large Oracle database.  I created a stored procedure (PL/SQL) which works fine.  Since it is only one row (datarow) I left it returning a datarow.  This class resides in the DAL.    As I am refactoring things I thought I would isolate the database (in the DAL) from the business layer (use linQ). My first thought was create an object to contain the returned datarow.    One of my coworkers recommended Anonymous types, which I am not familiar with.  In the reading I've done so far it looks simple enough.  I just don't see the value in it if I have still have to put the fieldnames and field types using the anonymous types.    Am I missing something?  Would there be more value to using Anonymous types if I was returning a dataset/datatable?

I've seen lots of descriptions how anonymous types work, but I'm not sure how they're really useful.  What are some scenarios that anonymous types can be used to address in a well-designed program?


Is there a word that describes an important question that is difficult to answer? I'm attempting to get permission for something big.

I am about to coin the word 'conundrous' because I needed it (and I think it deserves a place in the dictionary)!  I would like comments on what you think about that (in the context of a serious article, or I wouldn't have to ask), but the question is as stated — if you can supply one or more adjectives that are synonymous with such an adjective, that's the answer for me. :)  If there are none, I will be happy to accept close synonyms — the Merriam-Webster definition (of the noun) is here:   I'm after the "difficult problem" (but not the "pun") synonymity. It's used to describe a word from an ancient text which is seemingly not in the dictionaries; hard to find information about.  There's enigmatic, but it's just a mystery for the moment; it's not something that is by definition mysterious.  There's elusive, but I think that carries the connotation of forever escaping one's reach.


I was wondering if it is possible to create a backup of a Web Application or (top level) Site Collection and restore it without the contents (documents) in order to preserve only the site structure (and features).  The gist is to create a copy of the production environment without the documents for a new development environment.  Thank you in advance.

Is it possible to perform a backup (either SharePoint backup or sql backup) without any items that are in man-made lists and libraries?  I saw a feature in Metalogix tools where you can copy a site collection without items (howerver lists and libraries will be copied so site structure in good shape).  Can someone please suggest a powershell or codeplex tool or their own custom tool that they created?


Given that a number $n \equiv\{1,3,7,9\} \pmod{10} $ show that there is a multiple of $n$, $q$ that is a string of consectutive $1$s.

How can I prove that every prime except 2 and 5 divide infinitely many of the following integers $11, 111, 1111, ...$ ?


Sorry, I'm still a newbie to blender, but why are some edges visible only in edit mode, but not in wireframe view? is it a bug or am I missing something here?  edit mode: Edges visible. Object mode, wireframe view: Pooff, they're gone. what can i do to fix this? / thanks

The wireframe on the right looks correct, but in object mode on the left, you can see that the upper and lower vertices are not connected, while the "box" to the right is fine.  I tried Fill and Merge Vertices, but both do not result in a correctly looking model. In wireframe mode, it looks great, but in object mode it does not.  I have uploaded my model here:    Does anybody see what causes this weirdness?  Thank you for the help!  Here is another image: It shows that the 2nd "box" is not correct (it has greyish faces), while the 1st and 3rd are correct.


If you have an electric charge somewhere and you make a new  electric charge right now when do these electric charges start to interact with each other? is it immediately or it take some time ? how much time does it take?

Consider two circuits containing a battery, bulb, switch and conducting wires but of length 1 meter in one case and 1000KM in other. When switched on at the same time both the bulbs glow instantaneously. I think it is because, electric filed travels from positive terminal of battery to negative terminal through wire almost instantaneously.  My question is there any speed for this electric field? If yes, what is it? By any modification in this circuit is it possible to induce any delay in glowing the bulb?


I like to use the abbreviations "w/" for "with" and "w/o" for "without" on my powerpoint slides and also in emails. According to this discussion  the meaning of these abbreviations is well known in English speaking countries.  Recently, a colleague pointed out that these abbreviations do not look very professional on slides presented at some conferences. Since we are both non-native speaker, I'd like to know your opinion on using them on slides, does that look awkward or non-professional to native-speakers?  (I am working in natural sciences, if this matters)

I remember when staying a few months in the US years ago that I saw some people using the abbreviations below. However, I can't exactly remember in which contexts I encountered them, (whether I saw my teachers using them when writing something on the board, in papers or in personal notes etc.)  So my question is: Are those abbreviations below commonly used and in which contexts is it okay to use them (e.g. formal texts, personal notes,... or better only used in personal note taking?)         w/o without   w/ with   b/c because      PS: Are there similar abbreviations that are commonly used?


When I open Konsole the settings in .profile are not executed, and it means the ~/bin is not added to the PATH.  Is there a way to get Konsole to do that?  PS. Is there a way to tell whether Konsole is running bash or dash

Problem  I have an Ubuntu 11.04 Virtual Machine and I wanted to set up my Java development environment. I did as follows   sudo apt-get install openjdk-6-jdk Added the following entries to ~/.bash_profile  export JAVA_HOME=/usr/lib/jvm/java-6-openjdk  export PATH=$PATH:$JAVA_HOME/bin  Save the changes and exit Open up a terminal again and typed the following  echo $JAVA_HOME   (blank) echo $PATH        (displayed, but not the JAVA_HOME value)  Nothing happened, like if the export of JAVA_HOME and it's addition to the PATH were never done.   Solution  I had to go to ~/.bashrc and add the following entry towards the end of file  #Source bash_profile to set JAVA_HOME and add it to the PATH because for some reason is not being picked up . ~/.bash_profile   Questions   Why did I have to do that? I thought bash_profile, bash_login or profile in absence of those two get executed first before bashrc.  Was in this case my terminal a non-login shell? If so, why when doing su after the terminal and putting the password it did not execute profile where I had also set the exports mentioned above?


Whenever I look at a question on Stack Overflow, once I spend maybe 30 seconds on that page, or sometimes even if I click edit, the box where it says "posted 10 minutes ago", will automatically switch to "posted 2 hours ago", no matter when it was actually posted.  It seems to happen rather randomly, but it happens on both my laptop and my desktop, which both use Google Chrome.  Is anybody else experiencing something like this?    This actually happened to this question right as I was about to add another comment.  Another Edit: Now when I refresh the page, it says "asked 14 minutes ago"

On Stack Overflow, the time shown for answers and comments is incorrect. When the post is just 20 mins old, the comments and answers say that they are 12 hours old. I have seen this mistake in more than one post. What is the problem with the clock / time display?  Please, take a look at that.


When calculating $\sin x$, $x$ needs to be radian to calculate it. so for example when solving Uniform Circular motion, $x(t)$, $y(t)$ can be expressed $$x(t)=R\cos(ωt) [m] $$ $$y(t)=R\sin(ωt) [m]$$ and when we differenciate it $$v_x(t)=-Rω\sin(ωt) [rad*m/s]$$ $$v_y(t)=Rω\cos(ωt) [rad*m/s]$$ how do you interpret rad in this way? furthermore $$a_x(t)=-Rω^2\cos(ωt) [rad^2*m/s^2]$$ $$ a_y(t)=-Rω^2\sin(ωt) [rad^2*m/s^2]$$ do we just ignore $$[rad],[rad^2],[rad^n] $$to see the unit as [m/s]? or is there a meaning in it when the unit is written with rad? also for $e^{iωt}$ I heard ω needs to be $rad/s $ does that mean $e^{\text{blank}}$ the blank needs to be [rad] to have the meaning?

I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've been writing a  (the specifics of which are out of scope), which has me thinking about the problem because I decided to handle angle units as dimensioned quantities, which seemed natural to enable the unit conversion with degrees. The overall purpose of the library is to disallow operations that don't make sense because they violate the rules of dimensional analysis, e.g. adding a length quantity to an area quantity, and thus provide some built-in sanity checking to the computation. Treating radians as units made sense because of some of the properties that dimensioned quantities seemed to me to have:  The sum and difference of two quantities with the same dimension have the same physical meaning as both quantities separately. Quantities with the same dimension are meaningfully comparable to each other, and not meaningfully comparable (directly) to quantities with different dimensions. Dimensions may have different units that are scalar multiple (sometimes with a datum shift).  If the angle is treated as a dimension, my 3 made up properties are satisfied, and everything "makes sense" to me. I can't help thinking that the fact that radians are a ratio of lengths (SI defines them as m/m) is actually critically important, even though the length is cancelled out. For example, though radians and steradians are both dimensionless, it would be a logical error to take their sum. I also can't see how a ratio of something like (kg/kg) could be described as an "angle". This seems to imply to me that not all dimensionless units are compatible, which seems analogous to how units with different dimensions are not compatible. And if not all dimensionless units are compatible, then the dimensionless "dimension" would violate made-up property #1 and cause me a lot of confusion. However, treating radians as having dimension also has a lot of issues, because now your trig functions have to be written in terms of $\cos(\text{angleUnit}) = \text{dimensionless unit}$ even though they are analytic functions (although I'm not convinced that's bad). Small-angle assumptions in this scheme would be defined as performing implicit unit conversions, which is logical given our trig function definitions but incompatible with how many functions are defined, especially since many authors neglect to mention they are making those assumptions. So I guess my question is: are all dimensionless quantities, but specifically angle quantities, really compatible with all other dimensionless quantities? And if not, don't they actually have dimension or at least the properties of dimension?


class User {   constructor(firstName, lastName, age, eyeColor) {     this.firstName = firstName;     this.lastName = lastName;     this.age = age;     this.eyeColor = eyeColor;     this.changeName = function(name) {       this.lastName = name;     };   }    login() {     console.log(this.firstName, "just logged in");    }  }   var user1 = new User("james", "morrison", 23, "blue"); user1.login();   I have the changeName method inside the constructor, what is the difference between this and the login method?

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


In the RSASSA-PKCS-v1_5 signature scheme, the first step is to perform an encoding on the hashed data. (0x00||0x01||PS||0x00||T). Is this encoding important for security ? What happens if the hash is directly encrypted without encoding ?

As we know, Textbook RSA is not enough safe to use because of the following issues;   Guessable plaintext problem  Small $e$ issue   I want to know how PKCS 1.5 solved these problems.


If I have a list like this [C, B, A, B] and I want to get all possible solutions to remove duplicates: [C, B, A], [C, A, B] How can I get this result in pure python?

Is there a built-in that removes duplicates from list in Python, whilst preserving order? I know that I can use a set to remove duplicates, but that destroys the original order. I also know that I can roll my own like this:  def uniq(input):   output = []   for x in input:     if x not in output:       output.append(x)   return output   (Thanks to  for that .)  But I'd like to avail myself of a built-in or a more Pythonic idiom if possible.  Related question:


I have a scene with a lot of objects which can clutter the outliner very quickly. Is there a shortcut to find the selected object? Basically, if I select an object, I would like to have a shortcut to move my outliner view to include that in the displayed portion of the outliner.

How can I jump to the selected object in the out-liner, I've got over 200 objects in my scene, all named cube.___ ... and I can't seem to find my selected object. How can I jump to it?


Given a normed space $X \neq \{0\}$ and $P, Q : X \rightarrow X$ linear such that $$PQ - QP = \mathbb{1}_X$$ Prove that at least one of P and Q is discontinuous.  Hint: Prove and use that $PQ^n - Q^nP = nQ^{n-1}$.  I was able to prove the hint, but I'm not able to use it. My idea was to try to prove this by contradiction, assume that both P and Q are bounded, then try to calculate the norm of Q by using the hint and recursively replacing the $Q^n$s in hopes of coming up with some non-converging series using the 'n terms', but this only leads to a mess. Can someone give some help please?

The Wikipedia article on  claims, without a proof or reference, that there does not exist a (unital) Banach algebra $B$ and elements $x, y \in B$ such that $xy - yx = 1$. This is surprising to me, but maybe the proof is straightforward; anyone have a proof and/or a reference?   More generally, I would have naively thought that I could embed any ring into a Banach algebra. I guess there are actually serious restrictions to doing this; are these issues discussed anywhere?


So... I had the silly idea to extend Knuth's up-arrow notation so that it included zero and negative arrows. It is normally defined as $$\begin{align*} a \uparrow b & = a^b \\ a \uparrow^n b & = \underbrace{a \uparrow^{n - 1} (a \uparrow^{n - 1} (\dots(a \uparrow^{n - 1} a) \dots ))}_{b\text{ copies of } a} \end{align*}$$ so, basically the hyperoperation sequence starting from exponentiation. For now, I will only consider $a,b > 0$.  If we try to go backwards from $a \uparrow b$, the "trivial" extension (letting down arrows represent negative up arrows, because why the heck not) is: $$\begin{align*} a \;b & = a \cdot b \\ a \downarrow b & = a + b \\ a \downarrow \downarrow b & = \text{see below} \end{align*} \\ \vdots$$ But I had trouble coming up with an expression for $a \downarrow \downarrow \downarrow b$.  Maybe it doesn't exist. Alternatively, maybe there is a way of defining $a \; b$ (zero arrows) such that it does exist. So my question is: Is there an extension of Knuth's up-arrow notation such that $a \downarrow^n b$ exists for all $n \geq 3$?  Edit: Welp, I messed this question up. I initially thought $a \downarrow \downarrow b = a + 1$ was correct, but it is actually $b + 1$. So I thought I had an example of an extension when I did not. I have modified the question accordingly.  An extension would define $a \uparrow^n b$ for each $n \leq 0$ which satisfies the recursive definition of the notation.    Edit 2: Okay, turns out $a \downarrow \downarrow b = b + 1$ isn't correct either, as this would imply $a \downarrow b = a + b - 1$. For example, $4 \downarrow 3 = 4 \downarrow \downarrow (4 \downarrow \downarrow 4) = 4 \downarrow \downarrow (4 + 1) = (4 + 1) + 1 = 6 = 4 + 3 - 1$. But it is really close; perhaps we need an exception, such as $$\begin{align*} a \downarrow \downarrow b = \begin{cases}b + 1 & \text{if } a < b \\ b + 2 & \text{if } a = b \end{cases}\end{align*}.$$ The case $a > b$ does not show up when evaluating $a \downarrow b$, but it will be need to be defined if we try to extend further to $a \downarrow \downarrow \downarrow b$. For instance, we could abuse the fact that the case $a > b$ is allowed to be anything, and let $$a \downarrow \downarrow b = b + 1 + \left\lfloor \frac{a}{b} \right\rfloor,$$ but finding $a \downarrow \downarrow \downarrow b$ may be intractable as a result.

I here define the hierarchy of basic mathematical operators and their respective "inverse" operation (see ).  $$ \begin{array}{c|c|c|}   & \text{Operator} & \text{"Inverse"} \\ \hline \text{Incrementation} & a+1 & a-1 \\ \hline \text{Addition} & a+b & a-b \\ \hline \text{Multiplication} & ab & \frac{a}{b} \\ \hline \text{Exponentiation} & a^b & \sqrt[b]{a} \\ \hline \text{Tetration} & ^ba & \sqrt[b]{a}_s \\ \hline \text{} \vdots &   \vdots & \vdots \\ \hline \end{array} $$  Now, it is clear that each "level" is simply the previous one except the process is done several times.  Adding two integers is like incrementing one integer many times.  Multiplication is addition of the same number many times.    My question is: does anything precede incrementation?


I am animating the textures of a model, but when I scrub through the frame timeline the texture is displayed as a still image. I am making an animation were the textures are of eyes and they keyframe different textures to perform a blinking animation, but the only way I can see it is when I render the animation. How do I see the texture keyframes while scrubbing through the timeline instead of them appearing as still images?

I'm creating an educational video, and for efficiency, I'm using a Cyclic repeater to repeat an on-page/off-page effect.  Every loop, I have the texture channel switch to the next image, rather than duplicating all the objects/animations. This works properly and appears when rendering the animation, but does not appear in the viewport. It sticks to the original UV image that was mapped.  Is there a way to have this change appear in the viewport?


I'm trying to install Ubuntu (13.10) on the Lenovo IdeaPad y510p, but all I'm getting is a blank screen after I select Install/Try Ubuntu. Is there any way to fix that? (fn+up has no effect)  EDIT: After removing my second videocard  (appears linux doesn't support SLI, it crashes with second card present) and disabling "quiet" and "splash" it now crashes with "divide error: 0000 [#1] SMP"

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I'm in the process of starting a new company, and am trying to create the brand guideline document, so I'm having to learn all about RGB, CMYK, and Pantone from scratch, so apologies if this is a stupid question.  I'm using a document from an existing company as guidance for creating my own document, and my main issue is that the colors given for RGB/CMYK/Hex don't match what Pantone suggest.  Unfortunately I don't have a color bridge book, and am instead using the site;   as reference.  According to the document I have, the main color is defined using the following figures;    Pantone 303 Hex 003145 RGB 0/49/69 CMYK 100/15/0/80 RAL 5011   Now according to the above link, the figures should be:   Hex 002a3a RGB 0/42/58 CMYK 100/47/22/82   Is there any particular reason why these figures would not match?   Why would a Pantone color be specified if the conversion provided by Pantone is not being used?

I am a bit of a newbie with using pantones and the pantone color guide. I am currently working on a branding project where we will have print material in both pantone and cmyk, and also on screen rgb colors. I would like these colours to match as closely as possible. I used the Pantone color Manager program to help me find the cmyk and rgb references from my chosen pantone colors.  My problem is that there seems to be large discrepancies between the colors when going from the pantone to cmyk to rgb. , the grey pantone 431U is slightly blue which I like and of course want to preserve but when I use the cmyk reference it looks way more blue on screen when both of them are side by side.  I looked online for other convertors and I found other references that seem closer on screen then the one found in the Color Manager program. I am a bit confused and I would like to know the best way to achieve the right colors, as I won't be able to test print with the printer.  Thanks Fred


So I am trying to make a header, but what I see is this:   So I was trying to vertically align the text (the image is out of frame) and I mostly just see Link1-5 all jumbled up together. Is there a simple fix to this?  <!DOCTYPE html>
                          Link             Link             Link             Link             Link

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...