I am watching a UK TV programme called "The Apprentice".  The candidates have to sell guided tours.  Some candidates are terrible at giving these tours.  They fluff their lines, or they haven't researched, or they make up "facts".  Watching their ineptitude cause a feeling of discomfort.  What is the best word for this discomfort?  The German word schadenfreude means roughly "the pleasure derived from the misfortunes of others".  The word I want would be almost an antonym of schadenfreude - "the discomfort derived from the mosfortunes of others".  Except not the misfortunes but the uselessness of others.
When I see someone else being embarrassed / humiliated, for example a singer forgetting their words in a concert, I would say something like "I feel embarrassed for them". But is there a better word to describe this feeling?  I would say it's a mix of:   Empathetic discomfort for someone else's humiliation Tension; hope that spectators will be forgiving Frustration that I cannot help them   Other scenarios I would feel the same emotion:   Seeing someone make a presentation, the slides are all out of order, and their face gets red with embarrassment while there's a tense silence in the room. Seeing someone make an embarrassing social blunder in front of unforgiving people. Seeing a speaker who keeps making a distracting and annoying gesture, and they don't realize that the whole audience is annoyed. Seeing someone be taken advantage of, like seeing someone naively and happily accept a terrible offer on a car. Seeing a person of strong image (for example the CEO of your company) do something like accidentally leave their webcam on after a conference call, and employees see him/her let out a big burp and pick their nose or something.   In these cases it's important that the audience is not forgiving, even if they don't confront the person about it. The person may or may not know they are being humiliated.  "Pity" as proposed in an answer seems very close, but I think it lacks a few components. I think "pity" has a chronic connotation - that you are referring to the general state of things rather than a specific event.  I think "pity" also depends on the subject suffering, but in my example they are often oblivious.  It could very well be that there is no word for this at all.  NOTE: Some people do not feel the same way I do in this scenario, so you may not think this question makes any sense.
Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$ Given $f$ entire show that $$ \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2 $$ I've come close to getting the exact answer by writing $f(z)$ as $u(x,y)+iv(x,y)$ and realizing the Laplacian of f is equal to zero. This leads to a lot of cancellations but I'm still making mistakes in my computations and I can't figure out where. Any help is appreciated. The  doesn't give me much hope, but I'm hoping it's an undocumented (and/or GNU-specific) feature. I have a song that Windows can't play because there is a question mark in the name of the file.  "Where Have All the Cowboys Gone?.ogg" // as an example   So I try to rename it and Windows complains whether I try it in Explorer or from command prompt.  Error I get when trying to copy, rename, or move is:     The Filename, directory name, or volume label syntax is incorrect   Is there a Windows way to force a rename in this case?   Update  I'll keep an eye on this question, but after 13 answers and many attempts (aside form 3rd party solutions) it seems that Windows can't do this (or at least my windows can't, no short names). So I'm accepting the answer which was my original solution anyway of using Linux. It would be nice to see Windows handle this somehow, so don't stop just because I've accepted this answer, the question still stands! What OpenType math fonts are there available for usage in TeX/LaTeX, e.g. with the unicode-math package?  Here is a MWE which you can use to show off the font.  \documentclass{article} \pagestyle{empty}  \usepackage{amsmath} \DeclareMathOperator\Res{Res} \newcommand*\diff{\mathop{}\!\mathup{d}}  \usepackage{amsthm} \newtheorem{theorem}{Theorem}  \usepackage{unicode-math}  %%% % Set up you text and math fonts %%%  \begin{document}  \begin{theorem}[Residue theorem]   Let $f$ be analytic in the region $G$ except for the isolated   singularities $a_1,a_2,\dots,a_m$. If $\gamma$ is a closed   rectifiable curve in $G$ which does not pass through any of the   points $a_k$ and if $\gamma\approx 0$ in $G$, then   \[     \frac{1}{2\pi i} \int\limits_\gamma f\Bigl(x^{\mathbf{N}\in\mathbb{C}^{N\times 10}}\Bigr)     = \sum_{k=1}^m n(\gamma;a_k)\Res(f;a_k)\,.   \] \end{theorem}  \begin{theorem}[Maximum modulus]   Let $G$ be a bounded open set in $\BbbC$ and suppose that $f$ is a   continuous function on $G^-$ which is analytic in $G$. Then   \[     \max\{\, |f(z)|:z\in G^- \,\} = \max\{\, |f(z)|:z\in \partial G \,\}\,.   \] \end{theorem}  First some large operators both in text: $\iiint\limits_{Q}f(x,y,z) \diff x \diff y \diff z$ and $\prod_{\gamma\in\Gamma_{\bar{C}}}\partial(\tilde{X}_\gamma)$;\ and also on display \[   \iiiint\limits_{Q}f(w,x,y,z) \diff w \diff x \diff y \diff z   \leq   \oint_{\partial Q} f'\Biggl(\max\Biggl\{   \frac{\Vert w\Vert}{\vert w^2+x^2\vert};   \frac{\Vert z\Vert}{\vert y^2+z^2\vert};   \frac{\Vert w\oplus z\Vert}{\vert x\oplus y\vert}   \Biggr\}\Biggr)\,. \]  \end{document}   Here is a similar MWE for ConTeXt.  The images in the answer will only be shown for LaTeX output but the ConTeXt output looks very similar.  %%% % Set up you text and math fonts %%%  \setupmathlabeltext[Res=Res] \definemathcommand[Res][nolop]{\mfunctionlabeltext{Res}} \definemathcommand[diff]{\mathop{}\!\mfunctionlabeltext{diff}}  \defineenumeration   [theorem]   [text={Theorem},    style=italic,    title=yes,    titlestyle=normal,    distance=0pt,    titleleft={(},    titleright={).~},    alternative=serried,    width=fit]  \starttext    \starttheorem[title={Residue theorem}]     Let $f$ be analytic in the region $G$ except for the isolated     singularities $a_1,a_2,\dots,a_m$. If $\gamma$ is a closed     rectifiable curve in $G$ which does not pass through any of the     points $a_k$ and if $\gamma\approx 0$ in $G$, then     \startformula       \frac{1}{2\pi i} \int\limits_\gamma f\Bigl(x^{{\mathbf N}\in\mathbb{C}^{N\times 10}}\Bigr)       = \sum_{k=1}^m n(\gamma;a_k)\Res(f;a_k)\,.     \stopformula   \stoptheorem    \starttheorem[title={Maximum modulus}]     Let $G$ be a bounded open set in $\mathbb{C}$ and suppose that $f$ is a     continuous function on $G^-$ which is analytic in $G$. Then     \startformula       \max\{\, |f(z)|:z\in G^- \,\} = \max\{\, |f(z)|:z\in \partial G \,\}\,.     \stopformula   \stoptheorem    First some large operators both in text:   $\iiint\limits_{Q}f(x,y,z) \diff x \diff y \diff z$   and   $\prod_{\gamma\in\Gamma_{\bar{C}}}\partial(\tilde{X}_\gamma)$;\   and also on display   \startformula     \iiiint\limits_{Q}f(w,x,y,z) \diff w \diff x \diff y \diff z     \leq     \oint_{\partial Q} f'\Biggl(\max\Biggl\{     \frac{\Vert w\Vert}{\vert w^2+x^2\vert};     \frac{\Vert z\Vert}{\vert y^2+z^2\vert};     \frac{\Vert w\oplus z\Vert}{\vert x\oplus y\vert}     \Biggr\}\Biggr)\,.   \stopformula  \stoptext Here is my player code.  Rigidbody rb;  Vector3 currMovement; public float jumpSpeed = 10; public float moveSpeed = 10; public float rotSpeed = 180;  float distToGround;  public float posSmoothTime = 0.5f; float currPos; float targetPos; float posVel;  public float rotSmoothTime = 0.5f; float currRot; float targetRot; float rotVel;  void Start() {     rb = GetComponent&lt;Rigidbody&gt;();     distToGround = GetComponent&lt;Collider&gt;().bounds.extents.y; }  bool isGrounded() { return Physics.Raycast(transform.position, Vector3.down, distToGround + 0.1f); }  void Update() {     Move(); }  void Move() {     // Rotation smoothing.     targetRot = Input.GetAxisRaw("Horizontal") * rotSpeed * Time.smoothDeltaTime;      if (targetRot &gt; 360)         targetRot -= 360;     if (targetRot &lt; 0)         targetRot += 360;     currRot = Mathf.SmoothDampAngle(currRot, targetRot, ref rotVel, rotSmoothTime * Time.smoothDeltaTime);      transform.eulerAngles += new Vector3(0, currRot, 0);      // Movement smoothing.     targetPos = Input.GetAxisRaw("Vertical") * moveSpeed;      currPos = Mathf.SmoothDamp(currPos, targetPos, ref posVel, posSmoothTime * Time.smoothDeltaTime);     currMovement = new Vector3(0, 0, currPos);     currMovement = transform.rotation * currMovement;      if (isGrounded())     {         if (Input.GetButtonDown("Jump"))             rb.velocity += Vector3.up * jumpSpeed;     }      rb.position += currMovement * Time.smoothDeltaTime; }   I have a Rigidbody attached to my player. I think the problem is with my camera script. Here is my camera script.  public Transform player; Quaternion targetLook; Vector3 targetMove; public float smoothLook = 0.5f; public float smoothMove = 0.5f; public float distFromPlayer = 5, heightFromPlayer = 3; Vector3 moveVel;  void LateUpdate() {     CameraMove(); }  void CameraMove() {     targetMove = player.position + (player.rotation * new Vector3(0, heightFromPlayer, -distFromPlayer));     transform.position = Vector3.SmoothDamp(transform.position, targetMove, ref moveVel, smoothMove);      targetLook = Quaternion.LookRotation(player.position - transform.position);     transform.rotation = Quaternion.Slerp(transform.rotation, targetLook, smoothLook); }   }  The player is not an parent of my camera. When I parent the player to my camera the shake stops. But I want a custom smooth camera movement with my custom scirpt, so I can't make the player a parent of the camera. example of not surjective isometry on a bounded not closed set. Is there an example of a bounded not closed set $A\subset \mathbb R^n$ for some $n\in \mathbb N$ and an isometry $f:A\rightarrow A$ ($\forall x,y\in A\space;\space d(x,y)=d(f(x),f(y))$ where $d$ is the euclidean metric) such that $f$ isn't surjective? How to call a SOAP web service on Android I am having a lot of trouble finding good information on how to call a standard SOAP/WSDL web service with Android. All I've been able to find are either very convoluted documents and references to "kSoap2" and then some bit about parsing it all manually with . OK, that's fine, but it's 2008, so I figured there should be some good library for calling standard web services.  The web service is just basically one created in . I would like to have IDE support for generating the plumbing classes. I just need the easiest/most-elegant way to contact a  based web service from an Android-based phone. How to use numpad / on a keyboard without a numpad? I've just got into Blender, and I like it a lot. But as I just switched from a stationary computer to a MacBook, I've got some new problems regarding the numpad. I can use 1-9 perfectly, But I have no idea how to emulate buttons like / (used to enter local view). I've searched the web for an answer, but I can't find any. How to remove the "3D Objects" entry from Windows 10 Explorer? The 2017 Fall Creators Update to Windows 10 added a "3D Objects" folder to the "This PC" view of Windows Explorer:    How can this be removed? Recently I booked a flight using my points. I am  planning to fly to Seattle WA from Indianapolis Indiana.  Stop over is Chicago.  On the day of my flight I am supposed to be in Chicago.   So I was wondering if I can directly board my Seattle flight from Chicago thereby not showing up in Indianapolis.  Is this okay?  Will United airlines cancel my entire journey if I do not show up in Indianapolis? RSA when N=pq and p = q Ubuntu 12.04 boots to TTY1 Alrighty, I have perused the threads already in existence and am finding none of them seem to have the exact combination of variables I've got going.  I'm working on a computer using Ubuntu 12.04. Currently, it boots straight into tty1  Ubuntu 12.04.4 LTS [computer name] tty1  [computer name] login: Password:   Login leads to:  Last login: Wed Mar 19 13:47:11MDT 2014 on tty1  Welcome to Ubuntu 12.04.4 LTS (GNU/Linux 3.2.0-32generic-pae i686   The owner of the computer stated that this issue happened after a recent update, if that gives anyone a hint as to the specific location of the graphics failure.   I'm capable of booting into the GUI utilizing startx, but am frankly at a loss of where to go from here. Years of Windows has molded me into a GUI heavy kinda person, so, if possible, work off the assumption that I've no idea what you're talking about and break it down to the simplest of steps.  Thanks! By viewing the polynomials as a difference of two squares, factorise the following polynomial: $$x^4+x^2+1.$$ I searched but couldn't find a way to solve this  Edit: By using Hans Lundmark hint, I get:  $$(x^2+1)^2-x^2$$   Is it fully factorized? I am trying to show that how the binary expansion of a given positive integer is unique.  According to this link, , All I see is that I can recopy theorem 3-1's proof?  Is this polished enough of an argument. Thanks Can you please check my Cesaro means proof I wanted to prove the following:  if $x_n \to x$ then $y_n \to x$ where $$ y_n = {x_1 + \dots + x_n \over n}$$  Please can you tell me if my proof is correct? My proof is this:  Let $\varepsilon &gt; 0$. Fix $N$ such that $n &gt; N$ implies $|x_n - x| &lt; {\varepsilon \over 2}$.   Then $\left |{1 \over n} \sum_{k=N+1}^{N + n} x_k - x \right | &lt; {\varepsilon \over 2}$. Now let $M$ be such that ${|x_1 + \dots + x_N | \over M} &lt; {\varepsilon \over 2}$ and $M &gt; N$. Then  $$ \left | \sum_{k=1}^M {x_k \over M} - x   \right | \le  \left | \sum_{k=1}^N {x_k \over M}   \right | +  \left | \sum_{k=N+1}^M {x_k \over |M-N|}  - x   \right | &lt; \varepsilon $$ Here the proof is finished. But one can observe:  It is possible that $y_n$ converges even if $x_n$ doesn't: If $x_{2n} = 0$ and $x_{2n + 1} = 1$ then $x_n$ does not converge but $y_n \to {1 \over 2}$. How to replace spaces with newlines/enter in a text-file? I have simple text file named "example".  Reading with terminal command: cat example  Output:  abc cdef ghi jk lmnopq rst uv wxyz   I want to convert (transform) into following form: (expected output from cat example)  abc cdef ghi jk lmnopq rst uv wxyz   How can I do this via the command-line?   (This is only an example file, I want to convert word's position in vertical-column) Make Firefox save new bookmarks in the Bookmarks Menu (not Other Bookmarks) Recently, Firefox has changed the default folder for newly created bookmarks (using Ctrl+D) from the Bookmarks Menu to "Other Bookmarks".  Is there some way to change that back? Or some alternate method instead of Ctrl+D?  EDIT  A native way to do this (without an add-on) would be best. Do I need to apply for a visa to enter South Korea as a tourist on an Australian passport? Do I need to apply for a visa to enter South Korea as a tourist for a few days when travelling on an Australian passport? Or will I be able to get one on arrival? Why doesn't the tilde (~) expand inside double quotes? According to  and my own understanding, the tilde expands to the home directory:  $ echo ~ /home/braiam   Now, whenever I want the shell expansion to work, i. e. using variable names such $FOO, and do not break due unexpected characters, such spaces, etc. one should use double quotes ":  $ FOO="some string with spaces" $ BAR="echo $FOO" $ echo $BAR echo some string with spaces   Why doesn't this expansion works with the tilde?  $ echo ~/some/path /home/braiam/some/path $ echo "~/some/path" ~/some/path Why CAN we see the new moon at night? I understand that the Moon's phases are determined by its position in orbit relative to the Sun. (See: ). The "shadow" is not cast by the Earth (a common misconception - this is actually a lunar eclipse), but by the moon's body itself.  It would appear that, in order for the moon to be a new moon, it would have to be somewhere between the Earth and the Sun. However, it would seem that, if we were looking at a new moon, we'd necessarily be looking at the Sun as well.  Why, then, can we sometimes see a new moon at night? Why doesn't it vanish at night for a half-month every month, between its last/first quarters?