I've recently been getting into Linux (Debian - Gnome shell) and am currently having trouble with my WiFi.  Basically when I reboot the WiFi works fine for about a minute or two, after that it remains connected but I can't ping any external IP (8.8.8.8 is my test IP address). After googling similar issues I tried a few of the tools I saw suggested.  running route -n on boot (when WiFi is working) gives the following:  Destination    gateway        Genmask       Flags  Metric Ref Use Iface 0.0.0.0        192.168.178.1  0.0.0.0       UG     1024   0   0   wlan0 169.254.0.0    0.0.0.0        255.255.0.0   U      1000   0   0   wlan0 192.168.178.0  0.0.0.0        255.255.255.0 U      0      0   0   wlan0   After a minute or so when the internet access cuts out if I run the same command I get:  Destination    gateway        Genmask       Flags  Metric Ref Use Iface 0.0.0.0        0.0.0.0        0.0.0.0       U      1002   0   0   eth0 0.0.0.0        192.168.178.1  0.0.0.0       UG     1024   0   0   wlan0 169.254.0.0    0.0.0.0        255.255.0.0   U      0      0   0   eth0 169.254.0.0    0.0.0.0        255.255.0.0   U      1000   0   0   wlan0 192.168.178.0  0.0.0.0        255.255.255.0 U      0      0   0   wlan0   so I tried shutting down eth0 with: ifconfig eth0 down and voila the internet works again. for another minute or so only for eth0 to somehow come back online and mess it up again.  I really have no idea what's going on being so new to Linux, so if anyone could shed some light on why eth0 keeps coming online and clashing with my WiFi would be appreciated.   ---- EDIT ----- Found the ACTUAL solution for gnome-shell  So all of the solutions I found on the suggested threads (and supposedly duplicate questions) didn't actually help me in the long run. Or they were sub-optimal solutions that forced annoying manual reconfiguration of network devices every time devices are changed.  what I ended up doing was simply removing the eth0 interface from /etc/network/interfaces  so by commenting the following:  # allow-hotplug eth0  # iface eth0 inet dhcp  This allows the network manager that comes with Gnome to take control of eth0 and stops the clashing of the interfaces. meaning the standard GUI networking tools acted as expected.

eth0 has a static IP set in /etc/interfaces  wlan0 gets it IP dynamically  How can I change my routing table and where would I put the command to always make wlan0 the default route so internet access will work?  Right now I can ssh into the box using either eth0 or wlan0 but internet access gets routed through eth0 always which does not work.  Also, are auto and allow-hotplug contradictory options?  Kernel IP routing table Destination     Gateway         Genmask         Flags Metric Ref    Use Iface default         192.168.20.1    0.0.0.0         UG    0      0        0 eth0 192.168.10.0    *               255.255.255.0   U     0      0        0 wlan0 192.168.20.0    *               255.255.255.0   U     0      0        0 eth0  source-directory /etc/network/interfaces.d auto lo iface lo inet loopback auto eth0 allow-hotplug eth0 iface eth0 inet static         address 192.168.20.2         netmask 255.255.255.0         gateway 192.168.20.1 allow-hotplug wlan0 iface wlan0 inet dhcp     wpa-conf /etc/wpa_supplicant/wpa_supplicant.conf allow-hotplug wlan1 iface wlan1 inet dhcp     wpa-conf /etc/wpa_supplicant/wpa_supplicant.conf


In MS Word Mac, is there a native way to save the document I am currently working on as .docx and a .pdf file with one click?  I need the document to be in both formats.  behavior now: first I save it as .docx by clicking cmd + s, then go to save as > pick .pdf from the dropdown > click export  expected: cmd + s results in 2 files, one .pdf and one .docx with current changes.

This question is inspired by my use of LaTeX, where you usually share the generated PDF, not the source file. I want my .docx documents to be source files, with PDFs being the files to share. Thus I would like to have MS Word making a PDF with the same document name every time I save the .docx file. Is there a way to obtain such a behaviour? I'm on a mac, but it'd be nice to be able to do this on a Windows based computer as well.  Example: If I make a new document which I name mydocument.docx, then MS Word makes a copy in the same location named mydocument.pdf. The PDF will be saved and overwritten for each time I change and save mydocument.docx. A somewhat make-like action?


I'm in the sudoers file (username ALL=(ALL) ALL, but am not the root user on a machine.  When I want to install something from Ubuntu Software, or want to execute some other root operation from a GUI, I get the following popup:    This popup shows the root user (name redacted in image), not me. I have the permission to do this operation (I'm in the sudoers file after all), but the popup doesn't give me any option to change the user that should do the operation. How do I solve this? I can of course execute the corresponding command with sudo from the terminal, but I'd like to be able to use the GUI as well.

When I attempt to perform certain actions within ubuntu I am asked to authenticate with a root user, but ubuntu doesn't give me options for which root user, it just specifies it as the user that set up my machine. I was wondering how to go about changing which user it selects to run the authentication?  For instance, if I want to install software from the Ubuntu Software Center I am asked to authenticate with user X and I would like to change that to be user Y globally.  I am also aware that I can just run things with sudo from the command line, but I don't want to have to do that.  I'm using ubuntu 14.04. And user Y is in the sudoers file and as of now user X is not.


Does it matter that the speed of light, $c$, is 299,792,458 meters per second in a vacuum? Would the universe be different if $c$ were, for example, 1 meter per second? Or should things be the same, whatever $c$'s value is?

This is meant to be a generic question of the type that we get repeatedly on this site, in different versions:        Why do universal constants have the values they do? Can we predict their values theoretically? Do they change over time? How would the world be different if a particular constant had a different value?


I have parsed a txt file and as a result I have now a String str = "33 00 9D F2 C9 59 02 0A 00 00 CB 08 01 01 03 01 43 97 B1 02 9D F2 C9 59 1C 01 04 00 10 00 00 16 03 80 05 00 19 00 00 00 4D 00 06 00 45 00 5A A0 47 3E A7 04 D5 08 00 00 00"  now I do str.split(" ") which gives me a String[] containing each of those values from the string. How can I translate each of those 2 char strings to bytes without changing their values?  So basically how to do String[] = {"33", "00", "9D"....} -> byte[] = {33, 00, 9D}?

I am looking for a way to convert a long string (from a dump), that represents hex values into a byte array.  I couldn't have phrased it better than the person that posted .  But to keep it original, I'll phrase it my own way: suppose I have a string "00A0BF" that I would like interpreted as the  byte[] {0x00,0xA0,0xBf}   what should I do?  I am a Java novice and ended up using BigInteger and watching out for leading hex zeros. But I think it is ugly and I am sure I am missing something simple.


OK, so I'm learning probablilites for the first time, and of course I'm having lot of conceptual difficulty (eg How does the outcome depends on how you define randomness, why for example Monty Hall problem is true).  Can you suggest some good probability book which doesn't hand waves these issues, and treats probability from a historical viewpoint, and also readable by beginners ?  (BTW, I have the book ""40 Puzzles and Problems in Probability and Mathematical Statistics"" for intersting and hard exercises, but you can suggest some hard and challenging problem book also as a sidenote)  (Sorta analgous to Hardy's book A course in pure mathematics for learing calculus)

I am doing my research in Functional Analysis, especially in "Generalized inverse of Linear Maps". I have come across Probability by studying only the methods or Distributions(like Binomial, poisson, normal,etc) Now I wish to study the mathematical background and intuitive way of looking on it. Can you suggest some probability text book which explains,  $\bullet$ Geometrical ideas of the Probability Distributions. May be using diagrams, graphs, etc. $\bullet$ Proofs for the distribution functions. $\bullet$ Problems with natural solutions and then generalizations Like, for a binomial distribution(how they are giving the probability mass function).


I currently have a 3.47 GPA at Georgia Tech in Computer Science. I have already withdrew from 6 classes but 4 of those were from a semester I got hospitalized. I'm failing a class right now but I may be able to pull of a C or even an A because the final replaces the course grade.   I want to do a Master's in environmental science or environmental modeling. I want to be a data scientist for the NOAA or any organization working on the acidification of the ocean.   I may even do a PhD if I can. I have research experience.

The chronic medical illness has affected my ability to take the most rigorous schedule and led me to withdraw from one class and also take a year break in my undergraduate education.  I'm wondering how this will affect my grad school chances. I have excellent LOR and GRES, good GPA.  Should the illness be discussed in SOP or elsewhere?


With Yosemite we got handy, growl-like, alert popups from the notification center. It's great but it often hides handy utils which also take the top right position of the screen.  Is there any way change the position of those alerts (via system preferences, plist, or an app)?

Is it possible to change where macOS Notification Center alerts appear on the screen?  They currently appear at the top right of the screen with the menu bar:    Alerts appearing in the top right tend to cover up work I'm doing more often than not. They cover up browser tabs, toolbar icons, and window titles.  I would prefer, say, the bottom right corner of the screen.  If moving the alerts is not possible, is it possible to change the screen on which they appear?


I am working in a form that submits data to my SQLServer database. This form contains 6 fields that will be submitted when clicked on 'Submit' using the following piece of code: $sql_thread = "INSERT INTO threads (thread_id, related_ticket, thread_content, is_internal_note, sent_by, timestamp)  VALUES ('$thread_id', '$related_ticket_id', '$content', '$is_internal_note', '$sent_by', '$timestamp')";  $stmt = sqlsrv_query($conn, $sql_thread); if( $stmt === false) {     echo $sql_thread;     die( print_r( sqlsrv_errors(), true) ); }else{     //if everything went well, redirect back with error code 004     header("Location: ../admin/create-thread.php?errcode=004");  }  The issue is that, if any of the fields contain a ' character, my query gets split into pieces. For example, if I type: you're amazing!, then my query will divided that into two parameters:  you re amazing!  Then I will have seven parameters to inset into the database and not 6 as it is expecting, therefore my query will fail. Is there any way I can modify my query to avoid this from happening? If I submit the form and any of the fields contain a ' character, then this error message is shown:  Thanks in advance, please let me know if any other details are needed to help this!

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I've seen a few different solutions but I can't seem to make them work. The solution I attempted is based on this question:. I'm not seeing a distinguishable difference between the answer provided for that question and my own.  Here's the link for the jsfiddle that they used also:   Dynamically created element:
190563
   Javascript to add hover:          $(".deckCardListCard").on({             mouseenter: function() {                 $("#deckCardDisplay").css("background-image", "url('images/cards/" + $(this).attr("data-cardID") + ".png')");             },             mouseleave: function() {                 $("#deckCardDisplay").css("background-image", "url('images/layout/back.png')");             }         });   ** EDIT **  I have selected an answer from below but the question is more why what I have doesn't work when the apparent same thing works here:

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Suppose you’re on a game show, and you’re given the choice of five doors: Behind one door is a car; behind the others, goats. You pick a door, and then the host, opens two of the doors, which guaranteed have goats. He then says to you, “Do you want to switch to other door?” What is the probability of winning if you decide to switch

I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$) doors, one with a car and the other three (or $n-1$) with a goat each (I want the car).  We need to choose any one of the doors. After we have chosen the door, Monty deliberately reveals one of the doors that has a goat and asks us if we wish to change our choice.  So should we switch the door we have chosen, or does it not matter if we switch or stay with our choice?  It would be even better if we knew the probability of winning upon switching given that Monty opens $k$ doors.


I am currently reviewing my questions to see if there are any answers that should be accepted, any outdated things that could be revised etc. But there does not seem to be a good way to do it for all sites combined.   The network profile lacks basic information, for example if there is an accepted answer to a question. The profiles on the subsites work well, but only show the content of the subsite. I would like to have a "combined" profile that shows all questions and answers together in a combined profile view. The network profile currently does not achieve that. For my purposes, formatting it like the other profiles (with green vote count showing questions with accepted answers) would already help.

I'd like to see all my questions waiting for me to accept an answer, across the network, in one overview, possibly on my network profile page.  Rationale  I have a couple of "core" stacks I visit frequently. Most other stacks are "drive by" stacks, where I've asked the occasional question.  I know  I've asked where I could have but have not accepted an answer — per site. I've also seen .  But what I'd like to see is one single overview of questions that are still waiting for me to accept an answer. This would preferably find its home on my user profile or my network profile.


My setup: I use Ubuntu 14.04 to perform a range of tasks. These tasks are performed whenever I execute a bash script. When it has finished the tasks the computer is automatically shut down (I don't want to suspend or hibernate).  My Question: What is the most convenient way of scheduling booting my computer? I want the computer to boot 2 times per weekday (let's say 9am and 5pm) and execute my script at startup.  I guess that combining rtcwake and crontab is necessary but I am not sure how to do this properly. I am powering of my computer with a python script but I could also execute rtcwake commands in this script if necessary. Also note that my computer cannot rely on wake-on-LAN.  edit: I have seen  but it does not address my question. I know how to boot my computer at a specific time. I would like to know how I can schedule my booting time two times a day only on weekdays.  edit: I have done it myself. I've written a python script that reads the weekdays, hours and minutes from a csv file and computes the number of seconds until the next entry of the list occurs based on the current time. I feed this number to rtcwake and execute the whole thing with python's subprocess module. I am thus able to boot my computer at arbitrary times if I power off my computer with this script. Unfortunately, this question is marked as duplicate. As long as this remains, I want make an effort to provide details.

Usually BIOSes have an option to schedule a time to which to boot at. Is there a Unix/Linux interface to specify the scheduled boot?


I read this novel a very long time ago, so the details are hazy, of course.  All I clearly remember is that the main character has to sleep in the body of a dead dragon (to escape inclement weather, maybe?) and ends up acquiring powers because of it.  I seem to remember that it was a girl, though that may be wrong, and I believe there was something about rainbows.  I also think, for some reason, that she was a slave, but again that could be wrong.   Any help would be greatly appreciated!

I'm trying to remember the name of a series of books about a boy who works with dragons.  Dragon's blood (or maybe it was slobber?) is acidic, and the children who wrangle these dragons often end up with deep pock marks.  On this world, days are like ours but nights get very cold, requiring anyone stuck outside to find a shelter until dawn (not the false dawn)  The other thing I remember is that in one of the books by slicing open a dragon and spending the night, the character emerged with special dragon powers.


What is the difference in meaning between the above words? Are they interchangable? I have seen several instances where efficacy has been used where it seems that efficiency is the correct term. Please forgive me if this question has been asked elsewhere. If anyone could point me in the direction of an explanation I'd be very grateful.

I feel that there is a subtle difference in meaning between 'efficacy' and 'efficiency', but I couldn't find any authoritative sources that could help me confirm or refute this. Is there any difference between the two words, especially in scientific context?


I am trying to proof the following expression (without a calculator of course).  $\log_{12}{18}\times\log_{24}{54} + 5(\log_{12}{18}-\log_{24}{54})=1$  I know this isn't a difficult task but it's just killing me. I have tried many things, among which was base transformation to 12 and expressing every logarithm in terms of $\log_{12}{3}$ and $\log_{12}{2}$ but every time I try to do it, I mess up something. I don't know if my concentration is terrible or  I'm doing something wrong.   Thanks ;) ( if there are more levels to this task, I'd like a hint, not a complete solution)

$X = \log_{12} 18$ and $Y= \log_{24} 54$. Find $XY + 5(X - Y)$  I changed the bases to 10, then performed manual addition/multiplication but it didn't yield me any result except for long terms. Please show me the way.  All I'm getting is $$\frac{\lg 18\lg54 + 5 \lg18\lg24 - 5\lg54\lg12}{\lg12\lg24} $$


I've got the following question that I have very little idea on how to approach proving:   I was wondering if someone could send some hints/starter lines so that I actually know where this proof is headed? I'm unsure what exactly we're meant to do here :S

Prove that if $f:[a,b] \rightarrow \mathbb{R}$ is integrable, then so is $|f|$ and $\left|\int_{a}^{b}f(x)dx\right| \leq \int_{a}^{b}|f(x)|dx$   I already proved that |f| is integrable, but how do I show that $|\int_{a}^{b}f(x)dx| \leq \int_{a}^{b}|f(x)|dx$   ?


sudo apt install apache2 Reading package lists... Done Building dependency tree        Reading state information... Done Package apache2 is not available but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'apache2' has no installation candidate  sudo ufw app list Available applications:   OpenSSH  I am trying with this command root@mydate:~# sudo apt-get install apache2 Reading package lists... Done Building dependency tree Reading state information... Done Package apache2 is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'apache2' has no installation candidate     root@mydate:~# sudo apt update Ign:1 http://archive.ubuntu.com/ubuntu trusty InRelease Get:2 http://archive.ubuntu.com/ubuntu trusty Release [58.5 kB] Ign:3 http://rpms.litespeedtech.com/debian focal InRelease Get:4 http://ppa.launchpad.net/ondrej/php/ubuntu focal InRelease [23.9 kB] Err:4 http://ppa.launchpad.net/ondrej/php/ubuntu focal InRelease Couldn't create temporary file /tmp/apt.conf.BLogEL for passing config to apt-key Get:5 http://rpms.litespeedtech.com/debian focal Release [1,646 B] Get:6 http://archive.ubuntu.com/ubuntu trusty Release.gpg [933 B] Ign:6 http://archive.ubuntu.com/ubuntu trusty Release.gpg Get:7 http://rpms.litespeedtech.com/debian focal Release.gpg [836 B] Ign:7 http://rpms.litespeedtech.com/debian focal Release.gpg Reading package lists... Done W: GPG error: http://ppa.launchpad.net/ondrej/php/ubuntu focal InRelease: Couldn't create temporary file /tmp/apt.conf.BLogEL for passing config to apt-key E: The repository 'http://ppa.launchpad.net/ondrej/php/ubuntu focal InRelease' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. W: GPG error: http://archive.ubuntu.com/ubuntu trusty Release: Couldn't create temporary file /tmp/apt.conf.eRadTX for passing config to apt-key E: The repository 'http://archive.ubuntu.com/ubuntu trusty Release' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. W: GPG error: http://rpms.litespeedtech.com/debian focal Release: Couldn't create temporary file /tmp/apt.conf.2NAiA5 for passing config to apt-key E: The repository 'http://rpms.litespeedtech.com/debian focal Release' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.      root@mydate:~# sudo ufw app list Available applications: OpenSSH root@mydate:~#     root@mydate:~# sudo systemctl status apache2 ● apache2.service Loaded: not-found (Reason: Unit apache2.service not found.) Active: failed (Result: resources)  Jan 19 06:48:21 mydate systemd[1]: Stopped The Apache HTTP Server. Jan 19 08:25:00 mydate systemd[1]: apache2.service: Failed to run 'start' task:> Jan 19 08:25:00 mydate systemd[1]: apache2.service: Failed with result 'resourc> Jan 19 08:25:00 mydate systemd[1]: Failed to start The Apache HTTP Server. Jan 19 08:26:21 mydate systemd[1]: apache2.service: Failed to run 'start' task:> Jan 19 08:26:21 mydate systemd[1]: apache2.service: Failed with result 'resourc> Jan 19 08:26:21 mydate systemd[1]: Failed to start The Apache HTTP Server. Jan 19 10:35:01 mydate systemd[1]: apache2.service: Failed to run 'start' task:> Jan 19 10:35:01 mydate systemd[1]: apache2.service: Failed with result 'resourc> Jan 19 10:35:01 mydate systemd[1]: Failed to start The Apache HTTP Server. lines 1-14/14 (END)

There are now errors when updating and I cannot install most software due to a corrupted  /etc/apt/sources.list   file. Is there a copy I can download to replace it?  The file would be for Ubuntu 12.04 (Final Beta) in the United States.


I am trying the following code          \begin{equation}         \bm{F}=\bm{F}_{vol}\={\bm{F}}     \end{equation}   But it's some errors. I think the error might be because I cannot use macron in math environment. how can I resolve this?

$$ = \sum_{e \in A} w(e)    = \sum_{e \in A} w(e)+ \sum_{e \in \{(r,v)| v \in V(G)\}} w(e)     = w( \~{A} ) $$   I get the following error message:     Error: Please use \mathaccent for accents in math mode for the following code   I'm not sure what's wrong with it. I'm in math mode by using $$  $$, am I not?


Very difficult question. Can't make sides equal after multiple manipulations.This one is lost on me. Help a fellow human out. Thank you.

I would like to construct a formal proof of the following:  $$(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$$  Let $a∈A$ be an arbitrary element, we will show that $a\in A \cap \overline B \cap \overline C$.  For LHS, since $a\in A$, we have that $a\in (A \cap  \overline C) \cap  (\overline B \cap \overline C)$. This is equivalent to $a\in (A \cap  \overline B) \cap \overline C$.    For RHS, since $a\in A$, we have that $a\in (A \cap  \overline B) \cap \overline C$  $\therefore lhs \equiv rhs$ and this concludes the proof  I would be grateful for any feed back on this element chasing proof. Is it flawed or where should improvements be made?  Thanks


I have Windows 10 and now I want to install Ubuntu using VirtualBox. While installing Ubuntu, I'm getting a warning saying that to install I need to erase the disk, which will automatically will delete all the files and documents in all operating systems. So, how can I install Ubuntu while keeping all my files & documents safe?

While installing Ubuntu in VirtualBox, the installer indicated it was going to erase all existing data on the disk. Does this only refer to the area I have allocated during setup or my entire hard drive. It seems obvious but it's quite a mistake to make since I'm not sure. Help.


Let $S$ be a subring of $\mathbb{Q}$ containing $\mathbb{Z}$. Prove that it is a principal ideal domain.  So here is what I tried. Take any ideal $I\subset S$. Take any two elements, say $a=p/q, b=r/s$ in $I$. Rationalize denominators (we can do that since $\mathbb{Z}\subset S$. Now we have $aqs=p=K(r)=K(bqs)+R$, that is, just apply the Euclidean Algorithm. Now, $a-Kb=R/qs\in I$, so take the set of all such remainders $R/qs$.   There are two possibilities. Either this set has a smallest positive element, or it does not.   Suppose it has a smallest such element, call it $x=m/n$. Let $a=p/q\in I$. We show $a=lx$. For suppose not. Rationalizing denominators with $n, q>1$, $p=Lm+Z$, so then $Z<m$ so $Z/qn<m/n=x$, giving a contradiction.   Now though, I am stuck on the case where there is no such smallest element :(  Any thoughts?  EDIT: For those marking it as a duplicate: The first answer in the linked question, as mentioned in the comments, feels somewhat unnatural and requires all this extra machinery. On the other hand, the second answer given is incomplete: The poster says "Now show that the ideal generated by $t=\frac{t}{1}$ in R is the ideal you started out with." But if $\frac{r}{s}\in I$, then there exists $k$ such that $r=kt$, so $\frac{r}{s}=\frac{k}{s}\cdot \frac{t}{1}$, but $\frac{k}{s}$ is not necessarily in $S$.

Let $A$ be a PID and $R$ a ring such that $A\subset R \subset \operatorname{Frac}(A)$, where $\operatorname{Frac}(A)$ denotes the field of fractions of $A$. How to show $R$ is also a PID?   Any hints?


The question tells me that i can use $x=(x+y)-y$  and $|x+y|≤|x|+|y|$ to prove. But i don't know where to use  $x=(x+y)-y$.  Till now,i only get that $-|x|-|y|≤|x+y|$ from the use of $|x|≤A$,$-A≤x≤A$

I've seen the full proof of the Triangle Inequality  \begin{equation*} |x+y|\le|x|+|y|.  \end{equation*} However, I haven't seen the proof of the reverse triangle inequality:  \begin{equation*} ||x|-|y||\le|x-y|. \end{equation*} Would you please prove this using only the Triangle Inequality above?  Thank you very much.


Hi i am trying to send form using enter button usually by default when i click enter the form will submit but in this oage i am unablr to proceed to form submit when i press enter button.  i can submit the form only by using mouse click on "login" i am sending with ajax  hi this my llogin form:  <form  class="form-horizontal" id="loginForm" >
         <input type="text" class="form-control" placeholder="Email" name="login_email" id="login_email">

         <input type="password" class=" form-control" placeholder="Password" name="login_password" id="login_password">

                         <input type="button" name="login_button" id="login_button" class="btn btn-default btn-block btn-primary" value="LOG IN">

           Forgotten account Password?

             CREATE AN ACCOUNT
 </form>

Well I am trying to submit a form by pressing enter but not displaying a submit button. I don't want to get into JavaScript if possible since I want everything to work on all browsers (the only JS way I know is with events).  Right now the form looks like this:  <form name="loginBox" target="#here" method="post">     <input name="username" type="text" /><br />     <input name="password" type="password" />     <input type="submit" style="height: 0px; width: 0px; border: none; padding: 0px;" hidefocus="true" /> </form>   Which works pretty well. The submit button works when the user presses enter, and the button doesn't show in Firefox, IE, Safari, Opera and Chrome. However, I still don't like the solution since it is hard to know whether it will work on all platforms with all browsers.  Can anyone suggest a better method? Or is this about as good as it gets?


Find the number of non negative integer solutions to $$x_1+x_2+....x_k=n$$ with the additional constraints $$x_i < s,  \forall i \in [1,k], i\in Z$$  This is how I tried.  The number of non negative integer solutions to $x_1+x_2+....x_k=n$ without the constraints is: (Call it $A_0$)  $$ n+k-1 \choose k-1 $$ This can be found using standard ball & stick argument.  We need to apply Inclusion Exclusion Principle Now:  Let $P_i$ be the property that the $i^{th}$ $x_i$ violates the constraints. Then let $A_i$ be the set of non negative integer solution of $x_1+x_2+....x_k=n$ with the additional constraint $x_i < s$ does not hold. i.e $x_i \geq s$ Then |$A_i$| is $n-s+k-1 \choose k-1$ (Is this correct?)  The number of required solution is then: $$|A_0| - |A_1 \cap .... \cap A_K|$$  Then by Inclusion Exclusion Principle: $|A_1 \cap .... \cap A_K|$ can be calculated   Now how to proceed from here? How do I get my final answer in terms of $n,k,s$

Let $n,k,r$ be positive integers. The number of all nonnegative solutions of the Diophantine Equation $x_1+x_2+\dots+x_k=n$ is $\binom{n+k-1}{n}$. Is there a general formula for the number of solutions of the equation $x_1+x_2+\dots+x_k=n$ with $x_i\le r$ for every $i\in \{1,2,\dots,k\}$?  If one defines $A_i$ to be the number of solutions with $x_i>r$ then the answer will be $\binom{n+k-1}{n}-|A_1\cup\dots\cup A_k|$. I think it can give a complicated formula. What is the formula?


My codes asks for the age but how do I make it so that the age will always be a valid number and not words.      while True:          test = int(input("What is your age? "))         if test > 0:            print("has to be a number")

What is the best possible way to check if a string can be represented as a number in Python?   The function I currently have right now is:  def is_number(s):     try:         float(s)         return True     except ValueError:         return False   Which, not only is ugly and slow, seems clunky. However I haven't found a better method because calling float in the main function is even worse.


What would be the equivalent for  for Windows? Task Manager isn't enough for me.

Is there a utility for Windows that operates similarly to iotop for Linux?  I'm looking for simple tool that can tell me what applications are writing to disk and how much they're actually writing.


Perhaps this applies to more than just bash, but I am confused about the role of brackets in if-statements. Most  seem to have the following format  if [ expression ]; then     #do stuff fi   But this doesn't always work for me. For example I have the following script test.sh:  #!/bin/bash  flag=False if ! $flag; then     echo "No brackets: Flag is $flag" fi if [ ! $flag ]; then     echo "With brackets: Flag is $flag" fi echo "The end."   Which prints  $ ./test.sh No brackets: Flag is False The end.   So the statement using brackets is either ignored or it evaluates to False. Why does this happen? What do the brackets do?  I've also seen double brackets. How are those used?   --  Edit: the questions claimed as duplicates ( and ) answer only a small part of this question. I'm still unclear why the syntax with brackets would fail (it seems to me that test ! false should evaluate to true) and why the syntax without brackets succeeds (although, as @ilkkachu mentions in the comment, it seems like it should actually fail as well?).

I am a little bit confused on what do these operators do differently when used in bash (brackets, double brackets, parenthesis and double parenthesis).  [[ , [ , ( , ((   I have seen people use them on if statements like this :  if [[condition]]  if [condition]  if ((condition))  if (condition)


I am trying to completely remove a label boundary/border (bubble) that by default appears when using my labels of a point GeoJSON layer.   The layer I have is defined as below:  var points_layer = new L.geoJson(points, {     onEachFeature: onEachPointFeature,     pointToLayer: function (feature, latlng) {          return L.circleMarker(latlng, labelMarkerOptions);     } });   the options for the label are  var labelMarkerOptions = {   opacity: 0,   fillOpacity: 0,   fillColor:'black',   fill: 'false',   interactive: false   };  the oneachFeature function  is  function onEachPointFeature(feature, layer) {   if (feature.properties) {      layer.bindTooltip(feature.properties.v2_number.toString(), {permanent: true, className: 'labelstyle'});    } }   using the style below I was able to remove almost all of the borders around the label text but a small white triangle remains next to the label which I cannot get rid of. This somehow seems to be a svg path or something (but can determine what it really is fully or where it comes from exactly).    How can I accomplish this?  .labelstyle {       all: revert;     color: green;     font-size:14px;     font-weight: 700;     fillColor: none;     fillOpacity: 0;     background-color: none;     border-color: none;     background: none;     border: none;     box-shadow: none;     margin: 0px;     cursor: none;     direction: 'center';     interactive: false;     fill: false; }   Below is how the remaining border of the original bubble is currently looking. The White triangles to the right of the green labels is (what is there by default) and what I would like to get rid of    I do not think that this is a duplicate of   because that is where I started using the tips in there but still could not get the white triangle styled at all.   Anyone has insight how to alter my css to make the triangle disappear ?

I'd like to override the default style of Leaflet 1.0.0 tooltips, especially the bubble/frame. I don't see any options or methods for this. How do I hook into the CSS? I want to change layers individually, so I need to select each layer's tooltips individually with CSS.


I'm a little confused about which is better or correct to declare a function in "for" & "member function" in a class. I think the best way is trying not to make these cases... Here are some examples. template<typename K> class Bigger { public:     bool operator()(const K& a, const K& b) const {     int aa = a.getValueJ() * a.getValueK();     int bb = b.getValueJ() * b.getValueK();      return aa > bb;     } };  template<typename K> class Bigger { public:     bool operator()(const K& a, const K& b) const {       return (a.getValueJ() * a.getValueK()) > (b.getValueJ() * b.getValueK());     } };  =======================================  for (auto i : time1) {   int t = t.getValueJ() / t.getValueK();       cout << t << " "; }  for (auto i : time1) {      cout << t.getValueJ() / t.getValueK() << " "; }  It seems like a very novice question. Could you give me a little advice for them? Have a nice day~

Is it more efficient for a class to access member variables or local variables? For example, suppose you have a (callback) method whose sole responsibility is to receive data, perform calculations on it, then pass it off to other classes. Performance-wise, would it make more sense to have a list of member variables that the method populates as it receives data? Or just declare local variables each time the callback method is called?  Assume this method would be called hundreds of times a second...  In case I'm not being clear, here's some quick examples:  // use local variables class thisClass {     public:         void callback( msg& msg )         {             int varA;             double varB;             std::string varC;             varA = msg.getInt();             varB = msg.getDouble();             varC = msg.getString();              // do a bunch of calculations          }  };  // use member variables class thisClass {     public:         void callback( msg& msg )         {              m_varA = msg.getInt();              m_varB = msg.getDouble();              m_varC = msg.getString();               // do a bunch of calculations         }      private:         int m_varA;         double m_varB;         std::string m_varC;  };


I am writing some SQL queries (which I'm pretty new at) for a SQLite DB using Python 3.3 and sqlite3. I have 2 tables that are relevant to this query Bins and Shelves. I ask the user for some input to create a bin and place it on a shelf. Then the query takes the name of the shelf from the user and uses it to get the shelf_id. Then the data the user entered to create the bin (just a name at this point) is used alongside the shelf_id to create a new record (the bin table contains bin_id, name and shelf_id columns).  Now I have this working with these queries but I don't want to query the DB twice if I can do it in one shot:  results = cur.execute('SELECT shelf_id FROM Shelves WHERE name = ?', [n_bin_shelf]) shelf_id = results.fetchone() cur.execute("INSERT into Bins (name, shelf_id) VALUES (?,?)", [n_name, shelf_id[0]])   So I wrote this to do it all at once:  cur.execute(             "SELECT             shelf_id s_id             FROM Shelves s             WHERE s.name = ?;             INSERT into Bins (name, shelf_id) VALUES (?,s_id)", [n_bin_shelf, n_name]         )   The problem is the alias s_id isn't preserved after the semi-colon. It executes fine if I substitute the literal for the shelf_id instead of the alias.  How can I preserve the alias across the semi-colon to execute this query successfully?   UPDATE: What I ended up using that worked perfectly and is much cleaner:  cur.execute(     "INSERT INTO bins ( name, shelf_id ) VALUES(?, (SELECT  shelf_id s_id FROM Shelves s WHERE s_id = 1))",     [n_name] )

I am trying to INSERT INTO a table using the input from another table. Although this is entirely feasible for many database engines, I always seem to struggle to remember the correct syntax for the SQL engine of the day (, , , , and ).  Is there a silver-bullet syntax coming from an SQL standard (for example, ) that would allow me to insert the values without worrying about the underlying database?


Sometimes I need to login on my Linux Mint 19 PC remotely via ssh. To make this more secure I try to switch to use Public Key authentication (as I already use it on my raspberries).  Basically the authentication works. But only if I logged in via GUI previously. After a fresh start of the system, the ssh server denies the public key authentication.  What could be the issue here?

I can't do ssh public key login to my server and I think this issue is related to the fact my home is encrypted. I chose the option "encrypt my home folder" under the Ubuntu install setup. The permissions on /home/MY-USER are 700.  I've tried another workstation and everything works fine. I would be glad if someone help me to get out this without removing the encryption.


It would make it a lot easier for people to do stuff like post a link to Puzzling, and then spoiler-tag some discussion about the answer in chat without ruining it for others who want to look.

Stack Overflow allows spoilers in the form:  >! SPOILER   Example:      SPOILER   Why doesn't chat support them? They would be quite useful, especially for rooms that are frequently off topic and often have dicussions about movies etc.  Many other sites, like Arqade, would make even better use of spoilers.


How can I calculate my take home pay in Sacramento area in California?  I have an offer of USD 95,000 per year in Sacramento. After searching multiple sites for tax calculations, I understood that it depends on the number of dependents as well.  I have a spouse not working, and one child of 4 years.  Can someone please suggest, how much take home pay I can expect?

In some months, I'll start working in the United States. I come from a country where calculating the net salary is REALLY complicated, and where the various taxes are paid at multiple stages (e.g.: some are paid by my employer before the money arrives into my bank, others are paid by me at the end of the year, ...).  The system of income tax in the U.S. looks to me really simple, and I wanted to be sure that I correctly understood it, so here I am.  Suppose that my gross salary (as specified on the contract) is 100k USD. The standard deduction is 6,300 USD. The taxable income is 100k - 6,300 = 93,700 USD. Suppose I don't qualify for any exemption.  This puts me in the 28% tax bracket. I'm single, so I have to pay a federal tax consisting of 18,481.25 + (93,700 - 90,750) * 28% = 19,307.25 USD (the numbers come from ).  That's all I have to pay. I'm not interested in knowing whether the numbers are exact, rather I'm interested in knowing if there are other taxes that I have to pay (e.g. state taxes).  Also, an important question: I will personally pay the federal tax every year and my employer will send me the gross salary, right?


I just upgraded the packages on my 18.04 machine and after reboot I see a new symbol in my top right that looks like a shield with a red "denied" symbol on it.   After further investigation this turns out to be the icon for the "livepatch" feature. It is notifying me that "livepatch" is off, and urges me to register to enable it.  I have zero interest in livepatch. I never opted to install this feature. I guess if I don't do something this shield will stay annoying and in-my-face 24/7-365?  Anyway I need help to remove it permanently like it never existed in the first place. Like completely deleted from my OS. Any help is much appreciated.  EDIT-1: Clarification in case you think I want to simply hide the notification. I actually want to COMPLETELY OBLITERATE IT and leave behind only unlinked inodes.  EDIT-2: I don't have livepatch installed. In fact look at this screenshot:

After updating Ubuntu packages today, I see a new livepatch indicator in the top-panel:    How can I hide it? I tried running sudo apt remove indicator-livepatch, but there's no such package. When I go to livepatch settings, I don't see an option to hide the indicator, just a button for sign-in.


This is a long shot but I am looking for a movie I saw in the early 90's.  It involved a ship sent to research an abandoned ghost ship.  They go through "hyperspace" and find the ship.  The ship they find looks like pole with a ball on the end and it is spinning.  They dock with it and and find computer terminal and restart the computer.  I believe by pressing some crystals on the console.  They ask it some questions and get answers, form a bond but seem uneasy.  Eventually they crew of the rescue ship finds out the planet/star close by is about to implode and they do not have enough fuel to escape.  They end up using the abandoned ship as a booster to get away but not before the computer in the abandoned ship finds out and questions it. They proceed regardless, detaching after fuel is spent in the abandoned ship.  They escape, but the abandoned ship gets destroyed when the planet implodes.  This might be a TV movie, I am not sure.  I saw it when I was around ten so some details may not be 100% but I am pretty sure it is.

Some years ago, I saw a scifi movie from the 70s/80s and I remember the following scene: It's the future, two astronauts (a Russian and an American) are floating above the Earth in a space station. They receive a spoken message from Earth that their nations are at war effective immediately and therefore the astronauts must not see or talk to each other.  I know that this is a very vague description, but I remember that I liked the whole style of the movie. Can anyone remember the name of this movie?


Suppose you're at the center of a circular field of radius 100 ft and there is a guard dog on the perimeter of the field. If the guard dog runs 4 times faster than you but cannot leave the perimeter, how can you avoid the guard dog and escape from the field?  This is an interesting problem and you may want to solve it first if you haven't already seen the solution.  Two questions:  Is there a speed multiple at which the guard dog will always be able to catch you and if so what is the multiple?   Given that the dog runs m times faster than you, what is the shortest path to escape from the field?

A famous problem:  A lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of the lady is to come to the ground without meeting the monster, and the goal of the monster is to meet the lady.  Under some conditions on $v_m,v_l$ the lady can always win. What if these conditions are not satisfied?  Edited: the monster cannot swim. If the conditions are not satisfied, then monster can always perform a strategy such that the lady will not escape the lake. On the other hand this strategy is not desirable for both of them because they do not reach their goals. As there was mentioned, this deals with undecidability of the problem. On the other hand, if you imagine yourself to be this lady/monster, you can be interested in the strategy which is not optimal. What is it? If there are such strategies in the game theory?  Edited2: My question is more general in fact. If we have a game with one parameter $v$ when two players $P_1, P_2$ are enemies and if $v>0$ then for any strategy of $P_2$ the player $P_1$ wins. If $v\leq 0$ then for any strategy of $P_2$ there is a strategy of $P_1$ such that $P_2$ does not win and vice versa. I am interested in this case. From the mathematical point of view as I have understood the problem is undecidable since there is no an ultimate strategy neither for $P_1$ nor for $P_2$. But we are solving somehow these problem IRL. Imagine that you are a lady in this game - then you would like to win anyway even while knowing that your strategy can be covered by the strategy of the monster. On the other hand, the monster knows that if he will cover all strategies of the lady she will never reach the shore and he will never catch her. I mean they have to develop some non-optimal strategies. I hope now it's more clear.


I am almost brand new to programming. I am in my second college course. I have spent hours looking online and on here looking for help. I have to sort the salaries by year and add them together. I thought I could make an if statement to sort the salaries into different arrays, but it does not appear to be working. As you can see by the code output, it shows invalid year, but it also pops up that the year is 2014. The file that I am reading from follows this format: 2014 Employee Smith,John 2000 0 (this is one line and there are 9 more like it). Thanks for any help and advice.  public class JohnSummersProject1 {  public static void main(String[] args) {      int count = 0;     String[] year = new String[10];     String[][] employeeType = new String[10][2];     String[][] name = new String [10][2];     String[][] monthlySalary = new String [10][2];     String[][] micellanious = new String[10][2];     String line = "";     String splitBy = " ";     BufferedReader inputStream = null;     String[] input = new String[5];     String year2014 = "2014";       try {         String x = (args[0]);         inputStream = new BufferedReader(new FileReader(x));         while ((line = inputStream.readLine()) != null && line.length()!=0) {             input = line.split(splitBy);             year[count] = input[0];              employeeType[count][0] = input[1];             if(year[count] == year2014){             name[count][0] = input[2];             monthlySalary[count][0] = input[3];             micellanious[count][0] = input[4];             System.out.print(year[count] + " ");             System.out.print(employeeType[count][0] + " ");             System.out.print(name[count][0] + " ");             System.out.print(monthlySalary[count][0] + " ");             System.out.println(micellanious[count][0]);             }             else if(year[count] == "2015"){             employeeType[count][1] = input[1];             name[count][1] = input[2];             monthlySalary[count][1] = input[3];             micellanious[count][1] = input[4];             System.out.print(year[count] + " ");             System.out.print(employeeType[count][1] + " ");             System.out.print(name[count][1] + " ");             System.out.print(monthlySalary[count][1] + " ");             System.out.println(micellanious[count][1]);         }             else{                 System.out.println("Invalid year");             }             count++;          }     }      catch (IOException io) {         System.out.println("File IO exception" + io.getMessage());         System.exit(0);     } finally {         try {             if (inputStream != null) {                 inputStream.close();             }         } catch (IOException io) {             System.out.println("Issue closing the Files" + io.getMessage());         }     }     for(int i = 0; i <year.length; i++){      System.out.println("Year " + year[i] + " Employee type = " +        employeeType[i][0] + " Name: " + name[i] + " Monthly count = " +              monthlySalary[i][0] + "extras: " + micellanious[i][0]);     } }   }

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?


I'm looking to identify a story about a young woman who needs to go to a Big Baddie's castle to retrieve something, a book, I think.  Along the way she meets a young man who at first she doesn't get along with, but who ends up being a love interest.  She also discovers how to use magic, which she uses by traveling down a "web" in her mind. At the end of the book, her fight with the Big Baddie leaves her "web" burned out.  Some more details, I believe the book has a scene where the Main Character takes care of her leather boots and bag by oiling them.  I think when she and the young man arrive at the Big Baddie's place, the Baddie is manipulative and actually has them stay there for a bit (maybe under the pretense of teaching the young woman magic?). The young man is more suspicious of the Baddie than the young woman.  It's a pretty grounded story. There's not much more to it than the woman going on her quest to the tower, arriving, beating the Baddie and getting the object she was questing for. It did end in a way that made me think there'd be sequels.  I read this in the early 00's but I'm guessing it was published in the 90's.  I know that's not a ton of info to go off of, and I may have mixed some details from another story, but I appreciate your help. It's a book I think my wife would really enjoy.

I read it as a paperback around 2009ish. There are at least two books in the series. In the first book, we learn that the protagonist lives up in the mountains. Her people are distrusted by the people in the plains, and I think have either dark or olive skin. She leaves home to learn magic, something I think is rare in the world she lives in. When she arrives, there's a crazy power-hungry man at her destination and she has to hide who she is because otherwise he'd have her killed to prevent her from surpassing him. At some point, she winds up in a set of chambers set into the mountain where she finds a pool of water and carvings about dragons. Somehow, this leads into her learning to become a dragon, I think perhaps after meeting one. I want to say that the sequel got into her having dreams that turn out to be partly prophetic and partly communication.  One of the reasons the book sticks out in my memory is that, despite the mentions of the protagonists dusky skin, the cover depicts a fair-skinned blonde girl, I think holding a glowing globe of light.


I'm very unfamiliar with the color profile settings in InDesign. Most of the images in what I'm trying to export were pulled from the web. (Clearly, I'm not the most advanced user).  When I export the document as a PDF, the colors don't show up how they show up in InDesign. When I look online, I find a lot of information about how to make Photoshop compatible with InDesign and have the colors show up the same in both places.  I understand that InDesign is production-level software, but is there any straightforward way to export a PDF that looks like what I see on the screen in InDesign. Whenever I try different "destination" color profiles in the export window, some images show up fine, and other colors are distorted worse than before.   Other information:  Color settings:   Even colors on the same page don't show up the same (that's the same shade of blue in both):

Basically, I've designed a booklet on Photoshop CC. It's an informational booklet so it's quite vibrant with lots of colours and pictures in it.   I've finished it and exported all the files into PDF format. Upon doing this, the PDF's are much "duller" for use of a better word. Now I'm not a designer and the whole thing was a learning process but now I'm reading about CMYK and RGB colour models and conversions etc. I designed the whole thing RGB (because CMYK looked duller obviously. The PDF's aren't disastrous, red is still red, black is still black but it's nowhere near as visually appealing anymore.   Is this just because of the monitor and the models each program uses or when I send my brochure to be printed, am I doomed for a much duller booklet? There's obviously a way around it otherwise all print would be dull.


Let $S$ be an equilateral triangle, and $f$ is a continuous function such that for any point $O$ inside $S$, with distances $x,y,z$ from vertices of $S$, $f(x)+f(y)+f(z)=0$. Prove that $f$ is identically zero.

I was told this question by a friend, who said that their friend had thought about it on and off for six months without any luck.  I have then had it for a while without any luck either.  It is in the style of a contest question, but it is unlike any other, as really nothing seems to gain any ground.  Here's the question:  Let $f:[0,1]\rightarrow \mathbb{R}$ be a continuous function satisfying the following property:  If $ABC$ is the equilateral triangle with side lengths 1, we have for any point $P$ inside $ABC$, $f(\overline{AP})+f(\overline{BP})+f(\overline{CP})=0$ where $\overline{AP}$ is the distance from point P to vertex $A$.  (Example: by taking $P=A$ we see $f(0)=-2f(1)$.)  Prove or disprove: $f$ must be identically zero on its domain   Notice that continuity is critical since otherwise I could just take the function $f(x)=0$ whenever $x\in (0,1)$ and $f(0)=1$, $f(1)=\frac{-1}{2}$.


Say I have the following string:  test tester tested testing   I wish to match every word that begins with test, but not the word tester. The pattern test\w* does most of the job, but I have no idea how to add that tester should not be matched. A working pattern should give 3 matches on the string.

I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "<Regex for 'doesn't contain hede'>" input   Desired output:  hoho hihi haha


Is it possible to Integrate Salesforce Directly to an SFTP Server? Has anyone already implemented this?

I have requirement wherein a csv file should generate with some users data and need to place the same file in a SFTP path without using any external tool. Can I have an alternative approach to proceed with the same. A sample code would be much appreciated.


Consider the following example class file  \NeedsTeXFormat{LaTeX2e} \ProvidesClass{myclass} \RequirePackage{kvoptions}  \DeclareBoolOption{foo}  \ProcessKeyvalOptions*  \ifmyclass@foo \def\@title{foo} \else \def\@title{bar} \fi  \ProcessOptions\relax  \LoadClass{article}   And the document  \documentclass[foo]{myclass}  \begin{document}  \maketitle \end{document}   It correctly produces a document with title "foo", so the class is actually using the option I gave. However, LaTeX says:  LaTeX Warning: Unused global option(s):     [foo].   Apparently processing a given option is not enough. How can I mark an option as "used" in order to avoid that warning?

I am struggling to understand how option processing works in classes. As a MWE  foo.tex:  \documentclass[draft,figures]{foo} \begin{document}   \includegraphics{example-image} \end{document}   foo.cls:  \ProvidesClass{foo} \RequirePackage{foo} \LoadClassWithOptions{article} \RequirePackage{graphicx}   foo.sty  \ProvidesPackage{foo} \RequirePackage{etoolbox} \newbool{foo@figures} \DeclareOption{figures}{\booltrue{foo@figures}} \ProcessOptions\relax \ifbool{foo@figures}{\PassOptionsToPackage{final}{graphicx}}{}   When I process foo.tex with pdflatex the log shows     LaTeX Warning: Unused global option(s):       [figures].   but I also see the graphic, which means that I am passing the final option to the graphicx package. Why does LaTeX think the figures option is unused?  Moving \LoadClassWithOptions to before the package is loaded gets rid of the warning. In my real use case, the class that is being loaded, loads the graphicx package and therefore I need to load the package before loading the class.


Which of the following sentences is correct?        What medicine should I take for neck pain?   Which medicine should I take for neck pain?

What are the grammatical rules determining whether to use which or what?  I usually go by intuition. It's "What car are you looking at?" and "What bicycle do you like most?" but "Which song did you sing?" Quite often, I don't know whether to use what or which.  How can I tell?


I was recommended an old book (read around 1985, must be older than that) but they didn't remember the title. All I know (might be inaccurate) is:  A traveler finds a spaceship. This spaceship contains "all" knowledge, so he goes around and offers to help planets in need.  One of those planets is a planet plagued by overpopulation. He solves that problem repeatedly with improved nutritional methods until he gives them one last food that makes them infertile.

I recall reading a book where the nondescript quirky captain of an independent starship was hired to take a group to a possible lost starship. The ship was a giant ecological repository and contained tech which had since been lost. Everyone tried to board, running afoul of various creatures and defenses. The independent captain (thought least likely to survive) wound up somehow managing to become recognized by the ecological ship as its new captain-owner, and spent the rest of the book providing its services, on his terms.  Part of this story also appears as a short story in an Analog magazine.  I probably read this in the late 80s, early 90s.


There is some event which leads to a general loss of knowledge, and the story involves (or at least includes) a person or a group relearning such knowledge, mostly math and physics. I heard about it in the 90's but it's probably much older than that (though surely 20th century). Edit: sorry about the lack of details (although I think Michael got it right; I'll mark it as the correct answer). It's a written, most likely short story, which a teacher described to me a couple of decades ago. I realize it was very little to go by but this had been nagging me for years.

Many years ago I remember reading a short story about an advanced civilization at war that rediscovers how to do math mentally. The reason I remember it is the guy tells it to government officials who are delighted because it means they can put people inside bombs or missiles instead of computers, which were thought to be more valuable.  I believe this is one of those stories I read in a science fiction anthology my father brought home on one of his business trips in the sixties or seventies.


I got this problem:  Is it true or not that for every matrix $A\in M_2( \mathbb C)$ there is a matrix $X\in M_2( \mathbb C)$ such that $X^2=A$? prove the answer.  I know that we can pass to Jordan form, and I proved that this claim is true for all the Jordan forms except  $$         \begin{pmatrix}         0 & 1  \\         0 & 0  \\         \end{pmatrix} $$ any suggestions what to do with this matrix? and also, there is a general version of this problem? thanks for helpers!

True\False?  For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$.  I know that every complexed matrix has a Jordan form matrix $J$ such that $P^{-1}CP=J$, But it's not diagonalizable for sure.  Thanks


If $S_1$ and $S_2$ are both subsets of some arbitrary set $A$, then how do I prove that $f(S_1\cup S_2) = f(S_1) \cup f(S_2)$ for ALL cases  I understand that it is true, but I don't know how to prove it.

$f(S \cup T) = f(S) \cup f(T)$  $f(S)$ encompasses all $x$ that is in $S$ $f(T)$ encompasses all $x$ that is in $T$  Thus the domain being the same, both the LHS and RHS map to the same $y$, since the function $f$ is the same for both.  Can you post the solution?


I am making the "cgboost" apple bownl tutorial. my fabric goes inside the bowls faces,not just on that.how to solve the problem?

I have two chairs, a cloth piece falling on it and then a helmet falling above the cloth on one of the chairs. Whatever the setting I'm trying I cannot get the helmet fall nicely on the chair and interact naturally with the cloth. Right now I have following:    the helmet is falling down  the cloth is falling down  the cloth is interacting with the chairs naturally  in the process of falling the helmet gets pushed by the cloth piece far away (as if it would be very hard surface).       I also read that soft body physics might be a solution, but it didn't work in my case and the rendering times are getting expanded.  The cloth has settings: 5/M, 10/s, 15/b, (here I tried almost everything) rigid body is off,  Collision physics is off  Helmet settings:  Right body active, mass 10, all other physics are off.  Right now almost all the other settings (except cloth physics) are default.  Would be glad to get some help!    Edit : Amended the Rigid Body Collision shape to 'Mesh' and this helped with allowing the helmet to collide with the cloth but now the cloth is being forced through the chair.


I know this is more of a general question,  I would like to get some details on the websites that I could use to do automation testing for learning purpose. I'm looking to a website which have complexity.

I want to learn Selenium, but I don't know what to code. Sure, I can throw Google some queries, I can fill out some forms, press buttons, find divs and links, etc. But I think this stuff is pretty basic.  What would be more "advanced" ideas to try out? Can you give real-life examples?


I am using Mac OSX and when compiling using TeXShop I get the error ! LaTeX Error: File 'slashbox.sty' not found.  I have downloaded slashbox.zip from CTAN and placed it in my ~/Applications/Tex folder where all my Tex files including TexShop are located but still receive the same error.  How do I get slashbox.sty to be recognized / found?

I've searched online, but I have not found any clear instructions how to permanently add .sty files to my TeXShop installation. I'm using a Mac with OSX (TeXShop is a mac only program).  What is the best way of doing this? The one comprehensive set of instructions I found .   I've got as far as extracting the files (running LaTeX on the .ins and . dtx files) but after that I don't know what to do. I also don't understand how to update the index of my distribution, and whether there are particular OSX specifics (the instructions are for Windows).


The above quote is often attributed to Einstein, though according to  it does not originate from him. My question is: isn't the quote completely untrue, as quantum mechanics & nuclear decay completely disprove it, as in both there are examples where doing the same action can lead to completely different outcomes.

We know quantum mechanics gives a random result when we observe a particle that's in a superposition, but why is it random? One of the explanations I've heard is that because light comes with those discrete energy packets called photons, when a photon is passing through a polarized filter, it must either all pass through or all be blocked. You can't let a fraction of the photon pass through while others are blocked. Is it correct? It seems reasonable, but I couldn't find any proper source about this statement.


I got the source code of a webpage and  I want to get a word after the vi-buybox-watchcount">.     After the vi-buybox-watchcount"> has 152 number. I want to extract it..  I know only split keyword to do it.But i cannot use  '>' to split it because that source code has so many '>' with digits..  So i try to split it as following but it is getting errors...  for (int i = 0; i < Convert.ToInt32(idlist.Length); i++)         {             string url = "http://www.ebay.com/itm/" + idlist[i];             HttpWebRequest request = (HttpWebRequest)WebRequest.Create(url);             HttpWebResponse response = (HttpWebResponse)request.GetResponse();             StreamReader sr = new StreamReader(response.GetResponseStream());             // richTextBox2.Text += sr.ReadToEnd();             string a = sr.ReadToEnd();             sr.Close();             string source = null;             source = string.Join(Environment.NewLine,            a.Split('vi-buybox-watchcount">') // this is getting errors                 .Where(m => m.All(char.IsDigit)));   Please suggest me a method to extract this number

I'm looking for a library/method to parse an html file with more html specific features than generic xml parsing libraries.


I have a problem. After I modelled objects in Blender I textured them and textures are as I need them to be - with saturated colors.    However, as soon as I export it to the .FBX format and put them on the Unity scene, the textures become pale.    I suspect this is related to some Blender options but I can't be sure as I'm novice. I searched answer in the internet and didn't find it, how is possible to fix it.

I used node textures in a mesh I exported to .FBX.  I then imported it into Unreal Engine 4 and it didn't import any textures; I clicked the Upload Textures option in Unreal Engine.  Is there something I'm doing wrong or is it Blender?


Suppose  $$a_1 , a_2 , ... , a_n$$ are given real numbers that are greater or equal than $1$.  Prove that $$\sum_{k=1}^n \frac{1}{1+a_k} ≥ \frac{n}{1+\sqrt[n]{\prod_{k=1}^{n} a_k}} $$ I tried using Bergstrom but the it results the opposite inequality(less or equal). And I tried writing them as $$a_1 = x_1 + 1$$ so I can work on positive real numbers but it gets really complicated.  Please help. Thanks!

If $x_1,x_2,\ldots,x_n$ are real numbers larger than $1$, prove that $$\dfrac{1}{1+x_1}+\dfrac{1}{1+x_2}+\cdots+\dfrac{1}{1+x_n} \geq \dfrac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$$   Attempt  AM-GM doesn't work here since we will get an upper bound. I don't see Cauchy-Schwarz working either. Thus, I think a substitution might work, but I am unsure of which one to use.


I would like to make sure all these bones are in a single armature so I can select them all in edit mode.  Thanks

I put together an armature for a four legged creature, but I had to make each leg armature separate. I now want to combine them into one armature. Is there an easy way to do this?


Numerical evidence from Wolfram seems to indicate this. Is this just a numerical coincidence, and if not, can someone explain it?  Another interesting, if unrelated numerical coincidence: Wolfram's approximation of the integral of $x^{-x}$ from $0$ to $1$ is the same as its value for the sum of $n^{-n}$ from $1$ to infinity.

This integral is very closely related to the sophmores dream that states  $$ \int_0^1 x^{-x}\mathrm{d}x = \sum_{n=1}^\infty n^{-n} = 1.27\ldots $$  For example here   Now I want to bound the integral, and showing that is less that 2.  For the interval $[0,1]$ a good bound is rewriting it to $\exp(x\log x)$ and using the expansion   $$ 1 - x \log(x) + \frac12 (-x \log(x))^2$$  but how does one handle $[1,\infty)$ ? In this answer here     gives bounds to the integral, but they are not tight enough.. So to taste my question again, how does one prove that   $$ \int_0^\infty \frac{\mathrm{d}x}{x^x} \leq 2 $$


I started by integration of 3D formula for sphere volume. Not good or? The closed sphere has a centre $(0,0,0,0)$ and a radius $a > 0$ in the $4$-dimensional space: $x^2 + y^2 + z^2 + w^2 \le a^2$.

I want to express the volume enclosed by a hypersphere of radius $1$ with a quadruple integral, in four dimensions. I know that the equation of the sphere is $x^2 + y^2 + w^2 + v^2 \le 1$. However, I don't know how to proceed and I'm having trouble with the limits.  Note: I don't want to find the volume; I just need the starting point.


Okay, so in Blade Runner 2049 we know Wallace wants to be able to create new Replicants with the ability to reproduce. We also know that the Resistance wants freedom for the Replicants.  Then why is Freysa's movement not helping Wallace to create these new Replicants to develop Replicants' technology even further, and worse, is trying to stop Wallace by asking K to kill Deckard?  As we can see, even the Nexus-9 like K can eventually disobey human orders, so it cannot be because she feared the new Replicants would merely be slaves.

In Blade Runner 2049, Wallace wants to capture the replicant child so that he can dissect it, study it, and create replicants capable of breeding.  Meanwhile, the replicant rebels want to use the child as proof of replicant reproduction, arguing that replicants should have the same rights as normal humans.  This seems counterproductive.  Wouldn't it serve the replicant rebellion's interests if Wallace were able to create more replicants capable of breeding?


Given the irrationals are an uncountable infinity, (on, say, (0,1),) the intervals between the irrationals which partition the interval (0,1) must also be an uncountable infinity. However, on each interval between any two irrationals, we know that there lies at least a countable infinity of rationals.  Since there are an uncountable number of intervals, each with at least a countable infinity of rationals on them, how can there only be only a countable infinity of rationals?

I've been told that the rational numbers from zero to one form a countable infinity, while the irrational ones form an uncountable infinity, which is in some sense "larger". But how could that be? There is always a rational between two irrationals, and always an irrational between two rationals, so it seems like it should be split pretty evenly.


Suppose that, in a deleted neighborhood of 0, f is differentiable with $f'\neq 0$ and that $\lim_{x\to0}f(x)=0$. Prove that if $\lim_{x\to0}{\frac{f(x)}{f'(x)}}$ exists, then it must equal 0.  This question is included in L'Hospital Rule's section, but I don't know how to apply the rule here.  It seems to me that if f is differentiable with $f'\neq 0$, then $\lim_{x\to0}{\frac{f(x)}{f'(x)}}$ is not a form of $\frac{0}{0}$. Then I don't know what to show now. Any hints?

Suppose the function $f:[0,\delta) \to \mathbb{R}$ is continuous, differentiable in $(0,\delta)$ and $f(0)=0$.  If the limit $\displaystyle \lim_{x \to 0+}\frac{f(x)}{f'(x)}= L$ exists, then is it always the case that $L = 0$.  This seems to be true both for functions with well-behaved derivatives such as $f(x) = x,$  $$\lim_{x \to 0+} \frac{f(x)}{f'(x)}=\lim_{x \to 0+} \frac{x}{1}=0,$$  as well as functions with "bad" derivatives such as   $$f(x) = \begin{cases}x \ln x &\mbox{if }x>0 ,\\0  &\mbox{if } x=0,  \end{cases},$$  where  $$\lim_{x \to 0+} \frac{f(x)}{f'(x)}=\lim_{x \to 0+} \frac{x \ln x }{1+ \ln x}=0.$$  Is there a simple proof or counterexample?


When I use the setspace package, then the vertical distance from the text to the page number changes. This happens only on the page with a section title. After this page, the distance between the footer and text normalises. Does someone know how to fix the vertical distance?    I'm using the following code:  You've to insert text for two pages after noindent.  \documentclass[12pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \usepackage[left=1.00in, right=1.00in, top=1.00in, bottom=1.00in, footskip=0.5in]{geometry} \usepackage[onehalfspacing]{setspace}  \usepackage{fancyhdr} \pagestyle{fancy} \fancyhead[C]{\itshape\nouppercase\leftmark} \fancyhead[R]{} \fancyhead[L]{} \renewcommand{\headrulewidth}{0pt}  \begin{document}  \pagenumbering{arabic}  \section{}      \subsection{}          \noindent   \end{document}

My LaTeX file compiles fine. However, in reading my .log file, I see many repeated instances of  Package Fancyhdr Warning: \headheight is too small   Looking for it in google, I found some 'fixes', but first I'd like to know what the error is about.  What is fancyhdr? What is \headheight? What does the error mean?


I'm 18 with no credit (a collector has been disputed off) I want to get a personal loan of only a couple hundred but I need it to go towards my credit while I'm paying it back. I also want to take out a secured loan. However I want the lowest interest possible. What would be the best type of product to get for this this?

I have a credit card with a $700 limit and I am curious how to optimize credit gain with it. Right now, I use it once a month (usually on something small like a drink from a convenience store or something) and pay it off immediately. I am basically using it like a once-a-month debit card for tiny purchases.  I do this because I always hear that loading up your credit card to its limit looks bad (as if you "need" to use it, and are therefore more risky). Is what I am doing optimal or can I improve my credit in other ways?  This card also has an annual fee (something like $30) so part of me also wonders if I am wasting money. I don't particularly use/need credit cards, but I don't want to lose out on building credit, either, in case I want a house someday. I have student loans but I don't know how much those actually help.  I pay off all my debts each month otherwise.


Yo! I'm a newbie to Linux and need some easy to understand help on trying to fix my login loop after attempting to install NVIDIA drivers on my dual booted system. Most of my attempts at trying to solve this issue got me nowhere. Help?  My system dual boots to W10 (taking up 1.6 TB) and Ubuntu (400 GB), with both OS's being 64 bit.   IMPORTANT NOTE:  I can only connect to the internet through my Android phone tethering as of right now, so I don't know whether that can cause issues or not in downloading stuff.

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


How can I show attribute value of shapefile in geodatabase?    <title>OpenStreetMaps and GeoServer</title> <meta http-equiv="content-type" content="text/html; charset=ISO-8859-1">  <link rel="stylesheet" href="http://localhost:8080/geoserver/openlayers3/ol.css" type="text/css">
Text

I have a map a at the link below:    I added one of my GeoServer WMS layers to the map, now I try to add the attributes window pop up on click. I found to examples on the OpenLayers 3 homepage, but I cannot put together a working code...      Is there any chance to have a working sample somewhere?


I want to evaluate this limit :   $$\lim_{n\to \infty}\frac {\left((2n+1)(2n+2).....(2n+n)\right)^{1/n}}n$$  What I did was that I bought the $\frac 1n$ inside and divided throughout by $n^n$ which left me with the answer as $2$. But the correct answer is $\frac {27}{4e}$. How?  PS : forgive me I dont know MathJax or LaTex so :P

If $\displaystyle f(n)=\frac1n\Big\{(2n+1)(2n+2)\cdots(2n+n)\Big\}^{1/n}$, then $\lim\limits_{n\to\infty}f(n)$ equals: $$ \begin{array}{} (\mathrm{A})\ \frac4e\qquad&(\mathrm{B})\ \frac{27}{4e}\qquad&(\mathrm{C})\ \frac{27e}{4}\qquad&(\mathrm{D})\ 4e \end{array} $$ I couldn't get the right way to start off with this problem. But, as the options include the constant $e$ I think I will have to work out with logarithms.   So, this is what I did.  $$ \lim_{n \to \infty} f(n)\\ =\mathrm{exp}\left(\ln\left(\lim_{n \to \infty} f(n)\right)\right)\\ =\mathrm{exp}\left(\lim_{n \to \infty}\left[\ln\left(f(b)\right)\right]\right)\\ =\mathrm{exp}\left(\lim_{n \to \infty}\left[\frac{1}{n^2}\left(\ln(2n+1)+\ln(2n+2)+\ldots+\ln(2n+n)\right)\right]\right) $$ I'm not able to proceed further. In case my method is correct please give me hints on proceeding further and in case it is wrong give me the same on another method.


I  signed the variable bubbleL1 to 1, but why the first variable in the bubbles list, which is bubbleL1 still shows undefined? I know this maybe a stupid question, but I really don't know why.      let bubbleL1, bubbleL2, bubbleL3, bubbleR1, bubbleR2, bubbleR3;     let bubbles = [bubbleL1, bubbleL2, bubbleL3, bubbleR1, bubbleR2, bubbleR3];      bubbleL1 = 1;     console.log(bubbleL1) // 1     console.log(bubbles) // [undefined, undefined, undefined, undefined, undefined, undefined]   What I want is a list with a specific name for each item in it (for the declared reason, I really don't just use bubbles[0], bubbles[1]...)  Let's say we have a list named bubbles, and we also have six variables called bubbleL1, bubbleL2, bubbleL3, bubbleR1, bubbleR2, bubbleR3. I want to put all these six variables into the bubbles list, so later I can assign values to each variables that in the list, like this:  bubbles.forEach((bubble) => {   bubble = "something"; })

The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this?


Hello! I am considering the motion of particle in a central field and appear to derive inconsistent equations of motion when the Euler Lagrange equations are applied directly to (1) the Lagrangian  $L(r,\dot r, \dot \phi)$ and (2) when conservation of angular momentum is used eliminate $\dot \phi$ to write $L(r,\dot r)$:  Method 1: The Lagrangian for a particle in a central field is $$ L = \frac{1}{2}m\left(\dot r^2 + r^2 \dot \phi^2\right) - U(r)$$ Langrange's equation, ${\rm d}(\partial L/\partial \dot q)/{\rm d}t = \partial L/\partial q$, for $q=\phi$ yields conservation of ang. momentum:   \begin{align} &\frac{{\rm d}}{{\rm d}t}(mr^2\dot \phi) = 0 \quad \Rightarrow \quad  mr^2\dot \phi = \text{constant} = M (\text{say})\\ \end{align} Langrange's equation for $q=r$ becomes  \begin{align} m\ddot r = mr\dot \phi^2 - {\rm d}U/{\rm d}r = \frac{M^2}{mr^3} - {\rm d}U/{\rm d}r \end{align} where the second equality holds from conservation of ang. momentum.   Method 2: Now if we use conservation of ang. momentum $\dot \phi = M/(mr^2)$ to eliminate $\dot \phi$ from our original Lagrangian we have $$ L = \frac{1}{2}m\dot r^2 + \frac{M^2}{2mr^2} -U(r)$$  Lagrange's equation for $r$, ${\rm d}(\partial L/\partial \dot r)/{\rm d}t = \partial L/\partial r$, gives $$m\ddot r = -\frac{M^2}{mr^3} - {\rm d} U/{\rm d} r$$  Compare this to the radial momentum equation of method 1. Note the difference in sign of the term $M^2/(mr^3)$!!  Any ideas of how to resolve the disparity?  Resolution of Disparity. Ref:  in particular the answer by @Craig J Copi. Essentially when computing $\partial L/\partial r$ in method 2 one must remember that although $M$ is a constant of the motion ($\dot M = 0$) that $\partial M/\partial r = 2mr\dot \phi = 2M/r \neq 0$

A mass of point performs an effectively 1-dimensional motion in the radial coordinate. If we use the conservation of angular momentum, the centrifugal potential should be added to the original one.     The equation of motion can be obtained also from the Lagrangian. if we substitute, however, the conserved angular momentum herein then the centrifugal potential arises with the opposite sign. So if we naively apply the Euler-Lagrange equation then the centrifugal force appears with the wrong sign in the equations of motion.   I don't know how to resolve this "paradox".


I recently had my computer brought to the the Genius Bar, and they installed a copy of OS X Snow Leopard onto my computer. However, I was previously running Lion. So I went over to the Mac App Store to try and reinstall Lion, and it keeps telling me that the item I've requested is not available in the U.S. Store. Is there any way I can resolve the issue? I've tried switching stores and had no luck.

I have a MacBook model A1181, 2GHz Intel Core 2 Duo, 2GB memory. It's running Snow Leopard, and running fine including speed wise. I want to upgrade to make use of iOS simulator and XCode 4. Saw that App Store has only the newest 10.8 Mountain Lion for upgrade, and saw a few reviews saying it slowed down their Macs, even w/ 16GB memory, wonder what it will do to my machine.  I would prefer to get 10.7 Lion. Any way to get that anymore, maybe at Apple Stores? Or am I out of luck and have to go to 10.8 if I want to upgrade? Too bad I should have upgraded sooner when 10.8 wasn't out yet.  Update: looking around online, looks like my Mac may not even quality for requirements for 10.8, but 10.7 should be ok.


The sequence $f_{n}(x)=\frac{nx}{n^{2}x^{2}+1}$, for $x\in[0,1]$, pointwise converges function $f(x)=0$.    Is $\left\{f_{n}(x)\right\}$ Cauchy with the norm $||\cdots||_{\infty}$?

My Approach. To prove the given statement it is sufficient to show that $$\exists \epsilon > 0, \exists x \in [0,1], \forall N \in \mathbb{N}, \exists n > N $$ $$ \Rightarrow | f_n(x) - f(x)| > \epsilon$$    Let $\epsilon = \frac{1}{10}, x = \frac{1}{n}, n =N+1$. Hence $| f_n(x) - f(x)| = \frac{1}{2} > \epsilon = \frac{1}{10}$. Hence, we have shown for every $N \in \mathbb{N}$, how to choose $n$ such that $| f_n(x) - f(x)| > \epsilon$. Thus, $f_n(x)$ does not converge uniformly on $[0,1]$.    Is there any logical flaw or wrong steps in my proof. Any help would be appreciated.


Is the use of "are staying" in this sentence correct? I think it should be "stayed" because it is already past tense.     The loan specialist personally visited the house where Mr. A and Mr. B   are staying to let the latter sign the documents.

In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct?


I want to show:     If $f(x) \in F[x]$ is a poly of degree n, then the splitting field of $f(x)$ over $F$ in $\bar F$  has an extension degree less or equal to $n!$.   I think $n!$ has something to do with permutation but I cannot proceed further.

Is it possible to prove that if $P$ is a polynomial of degree $n$ then the degree of its splitting field is no greater than $n!$ without using notion of Galois group?


I have a little problem in Latex, which can be easily corrected, but nonetheless I'd like to understand what is going on. Briefly, the problem is that in any document, if I include the abstract, all the main text turns to small size.   Here it is the MWE (BTW, the problem is not because of changing the font family, but font sizes are better distinguished this way):  \documentclass[a4paper, 12pt, notitlepage]{article}  \usepackage[english]{babel}  \usepackage[utf8]{inputenc} \renewcommand*\rmdefault{ppl}  \begin{document}  \abstract{Donec vel lacinia tellus, vel feugiat massa. Proin orci nibh, eleifend vel velit quis, semper faucibus purus. Vivamus ultrices urna eget orci feugiat, vitae elementum mi sagittis. Praesent dignissim mauris lacus, in rhoncus quam posuere sit amet. In hac habitasse platea dictumst. Nullam et interdum ante. Proin accumsan erat quam. Nunc nunc eros, tempor quis ante id, pharetra porttitor dui. Sed at enim lobortis, sagittis odio nec, ullamcorper nunc. Aenean varius vel mi ac dictum.}  \newpage     \section{Introduction}  {\small Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus lobortis iaculis gravida. Suspendisse et dapibus justo. Mauris faucibus massa augue, non placerat nunc faucibus vel. Suspendisse imperdiet sed tortor sed elementum. Nullam at purus imperdiet, dapibus nunc nec, tincidunt diam. Curabitur placerat nulla eu purus volutpat, id porta ipsum gravida. Suspendisse mi odio, euismod nec nulla at, convallis eleifend metus. Curabitur ac cursus nisi.}  Donec vel lacinia tellus, vel feugiat massa. Proin orci nibh, eleifend vel velit quis, semper faucibus purus. Vivamus ultrices urna eget orci feugiat, vitae elementum mi sagittis. Praesent dignissim mauris lacus, in rhoncus quam posuere sit amet. In hac habitasse platea dictumst. Nullam et interdum ante. Proin accumsan erat quam. Nunc nunc eros, tempor quis ante id, pharetra porttitor dui. Sed at enim lobortis, sagittis odio nec, ullamcorper nunc. Aenean varius vel mi ac dictum.  {\normalsize Maecenas a est accumsan, tempor mi nec, lacinia nisi. Morbi eleifend odio et mauris facilisis ultricies. Praesent ipsum magna, malesuada vitae euismod non, finibus ac magna. Sed tempus est eu libero hendrerit malesuada. Sed facilisis quam tristique, dignissim enim non, finibus felis. Integer ultricies ligula sit amet nulla bibendum, eget cursus sem fermentum. Duis auctor libero sed arcu pharetra, a ultrices orci pulvinar. Sed varius vehicula dolor non tincidunt.}  \end{document}   If I compile the code as it is, the page would look like this:    But if I comment out or delete the line of the abstract, it looks like this:    Anyone knows why is this happening?  Thanks!

In the article class, it seems that using the abstract environment has an effect to the rest of the document. More precisely, it seems that it redefines the \linewidth, which equals \textwidth without abstract, is smaller with the abstract. My feeling is that \linewidth is redefined for the abstract environment, but the value is not reseted at the end of the abstract.  Here is a minimal example:  \documentclass{article} \begin{document} \abstract{This is an abstract. This is an abstract.}\bigskip  This is text. This is text. This is text. This is text. This is text. This is text.\\  \rule{\textwidth}{3em} \rule{\linewidth}{3em} \end{document}   The output is not the same if you comment the \abstract line or not.  Do you have the same problem as I do when you compile (if not, I will upload some PDF files to show)? Is this a (known) bug in LaTeX2e? How can we circumvent the problem?  Note: I compile with the pdflatex command, and I use pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian).


I remember aliens watching the tribe to know what humans eat. Hunters captured a rat, so after capture of the tribe, aliens gave them rats as food.  Some of humans were chosen to be implanted knowledge. After returning from one of procedure, human started teaching  others ("this is a triangle").  There was a simulation of flying small craft. In the first attempt s pilot decided to kill an alien by hitting the ground (but it of course was just a simulator).  Some time later humans found military planes(?). They trained fighter pilots in full-cabin simulators. I remember scene with those planes hovering behind bridge or something to hide from alien fighters.  Film ended with one of humans sacrificing himself by teleporting on top of a nuke to the alien home planet. Somehow explosion caused chain reaction that destroyed all atmosphere on that planet(?).

I saw this movie a while back. I don't remember how it starts, but from where I remember watching it, it may have not been too far from the start. Apparently, Earth has been conquered by some alien empire or something and humanity are basically cavemen being used as slaves. From what I remember, the main antagonist alien is seen taking one of the slaves to a room where a machine is used on him to make him smart; this is apparently a big no-no so the main antagonist and his sidekick have to keep it quiet. The idea was that by making one of the slaves smart, it could increase the work output of the others. Apparently the antagonist is using the slaves on Earth to gather gold bullion  which is apparently still very valuable to the aliens but he's doing it illegally (not the slave labor; that's apparently ok). The protagonist who had the machine used on him becomes the intermediary between the slaves and the aliens and begins teaching the other slaves. I remember him teaching them mathematics and I remember him saying that it was universally accepted (I think he may have been referring to algebra or trigonometry). At some point he becomes aware that they are slaves and organizes a plan to free not only his fellow slaves but the Earth. Some escape and find an old museum which has old flight simulators, and shows that humanity wasn't always a slave race and that it may have been modern times in which Earth was invaded (i.e. no lasers or starships). I think they also find Fort Knox as there is a huge collection of gold bricks and weapons. The protagonist comes up with a plan to destroy some sort of teleporter the aliens use to transport stuff to and from Earth, however that alone wont be enough as they could fight back, which will be bad for humanity, which is still undeveloped. So the plan also includes using the teleporter before destroying it to to transport and detonate a nuclear warhead on the alien home world which apparently cripples any attempt to immediately send a fleet but also as a show of strength. After executing their plan, the main antagonist is captured by the humans and as an insult is locked in a cage surrounded by the gold he sought. If I recall correctly the place is set to detonate as to destroy the precocious gold and that will be used against the aliens should they mobilize a fleet in the future (i.e. attack us and we destroy Earth's supply of gold). The antagonist's side kick for some reason I remember as a big black man from whom the antagonist had removed his hand at some point and also apparently the antagonist was cruel to him. After the antagonist is locked up, he is trying to appeal to his sidekick's loyalty, however the sidekick takes the humans' side, I'm also getting an image that apart from treating him kindly the sidekick's missing hand was restored.


I need to build a Java application that I will install on a Linux server.  When people will install they just would need to install this application, launch it, and nothing more. But we have some data to save.   I said no to MySQL, because it needs a server.  I said no to XML because there will be really a lot of data to save and manipulate.   So I'm looking at SQLite which is the best I think. Indeed (stop me if i'm wrong), SQLite doesn't need any server? (just install the final application and SQLite works fine in my application?)  Then I checked at  and I'm really a little bit confused.    What is the difference between a Wrapper and a Driver? Plus I see there exists  a "pure java implementation": SQLJet is it more or less optimized? Finally what would you use in my situation?

I'm attracted to the neatness that a single file database provides. What driver/connector library is out there to connect and use SQLite with Java.  I've discovered a wrapper library, , but are there other more prominent projects available?


Consider an ideal $I$ in $\mathbb{C}[x_1, x_2, x_3, x_4]$ such that $I$ is generated by $x_1x_3, x_2x_3, x_1x_4,$ and $x_2x_4$. I think this ideal cannot be generated by two elements, but can't give a rigorous proof.    Can anyone suggest a proof?

Can $(X_1,X_2) \cap (X_3,X_4)$ be generated with two elements in the ring $R=k[X_1,X_2,X_3,X_4]$? Can it be generated with three elements? (Here $k$ is a field.)    Thanks for any help.


tldr: My MacBook Pro (10.13.6) is broken but I can retrieve files. I got the Notes database files from ~/Library/Containers/com.apple.Notes/Data/Notes and moved them into the corresponding location on another Macbook Pro with the same OS. Only 2 of my dozens of notes are available. What else can I do?    I have a 2016 MacBook Pro running 10.13.6. I took dozens of notes with the Notes app. It's never been connected to iCloud, so everything is stored locally. Now my computer is nonfunctional due to what tech support believes to be a permanent hardware failure, but I can still boot into recovery mode and transfer files off. I'd like to retrieve my notes (I thought they were being backed up, but my backup solution wasn't working the way I thought it was).   Following the process from , I went to ~/Library/Containers/com.apple.Notes/Data/Notes which contains the following:  -rw-r--r--@ 1 zipslime  staff   192K Dec 14 11:58 NotesV7.storedata -rw-r--r--@ 1 zipslime  staff    32K Dec 14 22:49 NotesV7.storedata-shm -rw-r--r--@ 1 zipslime  staff   2.7M Dec 15 08:45 NotesV7.storedata-wal   I copied these files and put them on another MacBook Pro that's running the same OS and that never had any notes taken on it. When I opened Notes on that computer, it showed only the demo note that appears on a fresh installation of notes. After a reboot, it started showing two of my old notes, but there's no sign of the rest.   If I manually examine NotesV7.storedata-wal it's mostly human-unreadable but I can see fragments of some of my old notes, including ones that are not appearing in Notes now. Additionally, I know that my notes were accessible up to the moment the original computer kicked the bucket, so I have no reason to believe the content would be corrupted or otherwise irretrievable. Is there anything else I can try?

I'm using a company-issued MacBook where we cannot use iCloud to backup notes. But I would like to have a way to create backups of the notes, since they are not included in the company backup software. Is there a way to do this by hand?   I tried copying the folder:  $HOME/Library/Containers/com.apple.Notes  but when I copied that one to a new Mac, the notes didn't show up when running Notes.app.


I find it extremely annoying (and ultra lame) that Windows Explorer will only generate thumbnails for those files whose names are visible in the window.  If I open a folder full of photos and walk away for an hour, why the heck wouldn't it generate the thumbnails in the background, so that when I come back I can quickly scroll through the folder and find the photos I want?  Sure, I could import all of the photos into Picasa, but that's not the solution I am looking for.  I really want to find out if there is a way to force Windows Explorer to load all thumbnails in a folder.

Is there some way to get explorer to generate thumbnails without actually having to navigate and scroll through every folder?  All I could get was a command prompt script that would load an explorer window for all subfolders, however only images that were visible would have thumbnails created.


Hi  I am using codemirror for textarea. I want to copy conent of textarea to clipbord, i want to javascript or jquery scipt support for all major browser.  <textarea name="code" id="text_1" cols="30" rows="10"></textarea> <script> $("#text_1").click(function(){      // required code for copy text in  clipbord  });

What is the best way to copy text to the clipboard (multi-browser)? I have tried: function copyToClipboard(text) {     if (window.clipboardData) { // Internet Explorer         window.clipboardData.setData("Text", text);     } else {         unsafeWindow.netscape.security.PrivilegeManager.enablePrivilege("UniversalXPConnect");         const clipboardHelper = Components.classes["@mozilla.org/widget/clipboardhelper;1"].getService(Components.interfaces.nsIClipboardHelper);         clipboardHelper.copyString(text);     } }  But in Internet Explorer it gives a syntax error. In Firefox, it says unsafeWindow is not defined. A nice trick without using :


I'm using Lubuntu in my laptop and I have an e-book reader. (Sony Reader PRS-T2)  However, my e-book reader struggles to open several pdf files with links in it, such as webpage I saved using Google's chrome build-in print-to-pdf tool.  Is there any software (CLI or GUI) that can remove those links from my PDF files?  I have have tried "flattening" function from PDF Chain and PDFTK but they do not work.  P.S. I have tried the solution in  but for some reason it doesn't work.

Are there any Open Source Tools to Remove PDF links in Ubuntu.  I use PDFtk and i am not able to find any internal links in it. Due to the Internal links my python script that uses PyPdf to merge the PDF files into one file fails.