Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?

I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you.


Does quantum mechanics mean that there are a finite number of colours?

Forgive me if my reasoning is based on flawed logic and information. I am no physics expert. As I understand it when light strikes an object the energy of the photons is absorbed by the atoms that make up the object. An atom's electrons can only orbit its nucleus at one level or another, nothing in between. When the atom absorbs the photon, the electrons jump up another level before going back down again. When this happens a new photon is emitted by the atom, it's energy dictated by the level the electron fell. Once this photon enters the eye we perceive it as a color prepending on how much energy it has. This is the photoelectric effect. In other words, when I turn on the light in my living room, the light hits my walls and is absorbed by the atoms in the purple paint. They tune the light to their own frequency, in a sense dye the light, and eject it out into the world. This is how we not only see in color but see at all. Atoms that emit photons at very specific levels and only a finite number of levels, like cars have a finite number of gears and are either in one or another. From this line of reasoning, I suspect that means there are a finite number of possible colors. That the spectrum we can see is quantized and not continuous. If light depends on the atoms in the physical matter to give them color and atoms can only emit photons at a fixed set of discrete frequencies based on what element they are, then it would follow there are a fixed, finite number of colors, of shades that could possibly exist in the universe. Is this true? Is every photon that comes off an object the same? Does this apply to monitor too? Is every color we see part of a fixed pallet? Something predetermined and unchangeable? Like a cheap art program where you can only select from a list of preprogrammed colors? Is mixing paints, mixing atoms of various elements together make it continuous or is it still quantized and finite? It is said that color is a wavelength and a wavelength can be any length and there can be an infinite number of differences between 2 points if you make the integer small enough. So there can hypothetically be any wavelength, any color, any shade within the visible spectrum. But how can wavelengths be infinitely variable if they depend on atoms that can only emit wavelengths of certain colours? I write this because I have always been a very creative person and this idea is very upsetting to me. And if it's a vast but finite number of colors it would still upset me. Without going into how human perception works, could you answer my question? This is very important to me so please, if you answer, make the argument intelligent and open-minded. I know that scientists sometimes talk about unproven things as if they are proven. I've never been able to pick up on that so if your answer is based on something that's still theoretical, please let me know because I tend to take things literally and think in absolutes. Someone talks about a theory like it's a truth and I can't help but assume it's already been proven beyond a doubt.


Is there a way or a 3rd party application which would let me 'send' a keyboard input/keystroke to a game (so that it has the same effect as physically hitting the key on the keyboard rather than just repeating the letter) while I hold the key down?  So, for example, I could tell it to hit Q 20 times a second as long as Q is held down?  Simply, I need something like  macOS.  Thank you in advance


Can you remove one community rather than the entire account?

So like, if I have a profile on puzzling.StackExchange.com and StackOverflow.com, can I remove myself from the puzzling.SE community, rather than deleting my entire account?


What is this "unknown device" in my "Additional Drivers"?

I opened Software&Updates > Additional Drivers as I'm looking into some GPU issues, and was surprised to find an "unknown" device listed. I've never encountered that before, but I haven't modified my hardware in a long time.   I have no idea how long this unknown device has been here, or what it might be.  --> How can I determine what this extra device might be?


What is $\lim_{n \to \infty} 1+ 1/2 + 1/3 +\dots +1/n$. What is $\lim_{n \to \infty} 1- 1/2 + 1/3 +\dots +1/(2n-1)-1/(2n)?$ I feel like $\lim_{n \to \infty} 1+ 1/2 + 1/3 +\dots +1/n$ should be equal with 2, but I'm not sure. Any help is hugely appreciated, because I've never done such exercises before and I couldn't find how to approach them.


How to play a sound in a talking dog toy

So, my dog has a 'babble ball', which is a toy ball that plays random sounds when she rolls it around. She loves it, but the sounds are cringe-worthy. I would like to essentially remake this, but playing sounds of my own choosing (in this case, sound snippets from Austin Powers films).  Because it all has to fit in a small plastic ball, space is at a premium, so please bear that in mind - for instance, I -cannot- use a shield. Also, the sound quality doesn't have to be exceptional, given the application.  Currently, I'm planning to use a shake switch to detect when the ball is in motion, and ideally use an arduino chip as the brains. The part I'm struggling with is storing, and playing the audio.  The default Internet suggested option seems to be using pwm to play sound off a microsd card.  I do not want to use a playback chip, as I'm trying to use this as an excuse to learn how to do this.  What I would like to ask, is;  A. Could I store the relevant sound bytes on the arduino itself? Either in the sketch, or some sort of on-board memory? Putting a microsd card in for a couple of seconds max of audio seems overkill.  B. If so, how would one go about doing this?  C. Out of curiosity, how would one play a sound file without the use of a microcontroller? I appreciate it would probably always be easier to use one, but I'm interested if there is some sort of dedicated IC for this purpose.


For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.

Hello I am doing this exercise where we let X and Y be topological spaces and $f:X\to Y$ a function. We suppose that $\mathcal{A}$ is a collection of closed subsets of X, such that $\bigcup_{A\in\mathcal{A}} A = X$. We assume that for every $A\in \mathcal{A}$ the restriction $f_{|A}: A\to Y$ of f to A is continuous. Furthermore we suppose that for each $x\in X$ there exists a neighborhood U of x such that the intersection $A\cap U$ is non-empty for only finitely many $A\in\mathcal{A}$. And I have to show that f is continuous. I know that since $f_{|A}: A\to Y$ is continuous we have that for all open subsets $O\subseteq Y$ the inverse image $f^{-1}(O)$ is an open subset of A. And to show that $f: X\to Y$ is continuous I am thinking of showing that for each open subsets $O\subseteq Y$ the inverse image $f^{-1}(O)$ is an open subset of X, but this would be obvious wouldn't it since for all open $O\subseteq Y$ we have $f^{-1}(O)\subseteq A\subseteq X$?


How to achieve line break in simple $formula$-mode

I want to have inline math text like  Figure \ref{figure:example graph} shows an example of a graph $G = (\{v_{1}, \dots, v_{5}\}, \{(v_{1}, v_{2}), (v_{2}, v_{3}), (v_{1}, v_{3}), (v_{2}, v_{5}), (v_{3}, v_{4}), (v_{4}, v_{5})\})$ with $|V| = n = 5$ vertices and $|E| = m = 6$ edges.   but then, LaTeX messes with the linebreak and the rendered text looks like in the attached screenshot.    Is there any way, I can tell LaTeX to break the formula within simple $'s?


I followed the instructions and got success response but I didn't receive email.  Then I used the id to get Email Status and got 404 error.  Here is my json :  POST :   {     "To": {         "Address": "example@gmail.com",         "SubscriberKey": "example@gmail.com.tw"     },     "Options": {         "RequestType": "ASYNC"     } }   GET : {id}  Please let me know how I can resolve the issue.


Web application Design - using full screen width

With today large screen resolution (1920 screen width rules now), I need to decide between using the full width of the screen (liquid) versus fixed with (padding with white margin over 1366px for example).  Our main a web applications has tables, lists, complex forms and is designed to be used mainly on organisation Desktops.  While using all screen width can be great in terms of complex layouts such as master-detail, many charts and tables, I am aware that elements that are in the far left/right corners can be ignored easily. I see that many web apps goes for the full screen width (slack, Asana, Jira, Salesforce). Any ideas, thoughts or references regards such decision?  Thanks, Iris--


What do I need disk space on a Xbox 360 for?

I've never had an Xbox 360 but I want to get one. I don't want to do any hardcore gaming like Halo, only lighter stuff like the Skate games and Family Guy, Back to the Multiverse. So, in order to decide if the 4GB edition is good enough for me, I'd like to know what does the XBox need the hard drive for? Do games require to be installed on disk perhaps? What about demos or XBLA?


Exception in thread "main" java.lang.NullPointerException in LU Decomposition Method

I Have 2 matrices (lower and upper) from the LU decomposition method, and I am trying to get the variables.   public void getZ() {     for(int i = 0; i < z.length; i++) { // iteration          if(i != nodeApplied) { // first we initialize the z with 0              // unless we reach the node that the force was applied             z[i] = 0;         } else {             z[i] = force;         }     } }  public void getNewZ() {     // lower     int[] newZ = new int[n]; // we create a new int list to save the values of the variables     for (int i = 0; i < n; i++) {         int decrement = 0; // all positions in the row before the diagonal subtracted         for (int j = 0; j < n; j++) {             if (j == i) { // if it is a diagonal                 newZ[i] = (z[i] - decrement) / lu.lower[i][i];             } else { // if is not in the diagonal                 decrement += lu.lower[i][j] * newZ[j];             }         }     }     this.z = newZ; }  public void getVariables() {     getNewZ();     for(int i = 0; i < n; i++) {         System.out.println(z[i]);     } }     Exception in thread "main" java.lang.NullPointerException     at Matrix.getNewZ(Matrix.java:92)     at Matrix.<init>(Matrix.java:68)     at Matrix.main(Matrix.java:118)


Manipulating X key and pointer grabs on the command line

What command line tools exist to list and manage X server grabs? (That's grab as in key and pointer grabs, i.e. restricting the use of a particular key or mouse button to a particular application, or constricting the mouse pointer to remain in a particular screen area.) I'm looking for a hypothetical xgrab utility that would show things like  Key     0x00f00ba5  0x123   0 Button  0x00f00ba5  2        Pointer 0x00abcdef     meaning that there has been a call to XGrabKey(display, 0x123, 0, 0x00f00ba5, ...) and so on with XGrabButton, XGrabPointer, XGrabKeyboard, XGrabServer (if possible). The display format doesn't matter, what I want is some way to see who's grabbing what, and possibly some way of revoking these grabs (if it's possible, I'm not sure if the X11 API allows that).


This falls over on the first elseif. Basically I have a load of dropdowns and I'm trying to work out which filters to select based on if people have selected the dropdown items or not.    An unhandled exception of type 'System.NullReferenceException' occurred in    Based On   private void btnSearch_Click(object sender, EventArgs e)     {         if (ddCompany.SelectedItem.ToString() == null && ddStatus.SelectedItem.ToString() == null)         {             UpdateTicketsList("NO", "NO");         }         else if (ddCompany.SelectedItem.ToString() != null && ddStatus.SelectedItem.ToString() == null)         {             UpdateTicketsList(ddCompany.SelectedItem.ToString(), "NO");         }         else if (ddCompany.SelectedItem.ToString() == null && ddStatus.SelectedItem.ToString() != null)         {             UpdateTicketsList("NO", ddStatus.SelectedItem.ToString());         }     }


What is the importance of the concept of probability space?

We know sample space (S), elementary outcomes and events.  And axiomatically define probability of these events or assign probabilities to these events.  Now event space (F) and the triplet probability space (S,F,P) are defined.  What is the use of probability space and event space - when we are completely done when we define the sample space and and probabilities of the events in it?


Sun the sun and many other stars shine their light outwardly, and light travels very long distances, why is space dark? Why isn't it all lit up due to the stars?


Why do you allow guests to answer questions, but members aren't allowed to participate in open questions by posting comments?

I'm just wondering what the rationale was for this decision.  It seems kind of backwards.  It seems to me that you could reduce the number of duplicate questions by allowing members to participate in open questions rather than forcing them to ask duplicate questions.    And yes, I know this is a duplicate question.  Which proves my point!


So I am studying for an exam and was wondering if anyone could explain some of the reasoning being the proofs of the following properties:   Let R be a ring with $a,b\in R$. Then    $a0=0a=0$  $a(-b)=(-a)b=-ab$ $(-a)(-b)=ab$   Proof 1:   $a0=a(0+0)=a0+a0$ hence $a0=0$   I don't really understand why $a0+a0$ proves that $a0=0$


How can I enter this 'F' in LaTeX?   \mathcal{F} looks quite similar to it, but a little bit different.  I prefer not to use additional package if possible.


Executing project in terminal gives NoClassDefFoundError

I got some code using the PDFBox. Executing it with Eclipse no Error. But when I try to use the Windows Terminal it shows:  Exception in thread "main" java.lang.NoClassDefFoundError: org/apache/pdfbox/pdmodel/PDDocument         at PdfReader2.main(PdfReader2.java:15) Caused by: java.lang.ClassNotFoundException: org.apache.pdfbox.pdmodel.PDDocument  Whats the problem?


machine wakes only on local magic packet

I've got a Debian server, which I would like to wake up remotely using a tool like wakeonlan.  I have assigned the server a static internal IP 192.168.0.14 and set up the appropriate port forwarding in the router (which otherwise has a very limited admin interface).  When I am logged in to the same network, I can wake the server using the subnet IP, but I cannot wake the server using the public IP of the router.  What I do not understand: When the server is running and I listen on the server with netcat nc -ulv -p 9, I can see the packet coming in in both cases (both when sending to the subnet IP and when sending to the public IP of the router).  If the packet arrives in both cases, why does the machine wake up only in one of them?


Four cards are face down on a table. You are told that two are red and two are black, and you need to guess which two are red and which two are black. You do this by pointing to the two cards you’re guessing are red (and then implicitly you’re guessing that the other two are black). Assume that all configurations are equally likely, and that you do not have psychic powers. Find the probability that exactly j of your guesses are correct, for j = 0, 1, 2, 3, 4.  I know the answers and calculations for each of the five probabilities: j=0: 1/6, j=1: 0, j=2: 2/3, j=3: 0, j=4: 1/6 but I do not understand where the numbers are coming from. What do the j numbers have to do with anything? Can someone please explain to me the thinking process of solving this problem? I am just extremely confused as to what the js have to do with anything and why the probability is only zero on odd numbers and why j=2 is different than j=0 and j=4.


I would like to change Google spreadsheet header labels. I would like to change A,B,C... to more detailed descriptions. How do I achieve this?


Rounding of decimal number to whole number

I'm having a problem with the result of the average in my UserForm. So, I have 4 textboxes where the user will input the grades then upon clicking the button, it will get the average of it. Here's my code: Dim Total As Double, i As Integer    If IsNumeric(tb_music) Then Total = Total + CDbl(tb_music): i = i + 1  If IsNumeric(tb_arts) Then Total = Total + CDbl(tb_arts): i = i + 1  If IsNumeric(tb_pe) Then Total = Total + CDbl(tb_pe): i = i + 1  If IsNumeric(tb_health) Then Total = Total + CDbl(tb_health): i = i + 1    tb_mapeh.value = Round(Total / i, 0)  I tried to input a grade of 88, 91, 92, and 91. When using a calculator, the result will be 90.5, right? The result of my code above is 90. I need to show the result as 91. Can someone help me? Any help is highly appreciated. Thank you!


Converting symbols from ArcGIS Desktop to QGIS?

How do I export map information display styles from ArcGIS Desktop to QGIS?   I tried exporting MXD to QGS (using mxd2qgs) - but the styles were not saved;Also, when I try to export styles from arcgis to SLD format (using ArcGIS_SLD_Converter) and finally got:     "Index outside the range."   The index should be a positive number, and its size should not exceed the size of the collection Parameter name: index in System.collections.ArrayList.get.item (lnt32 index) in ArcGis_SLD_Converter.Output_SLD.WriteToSLD()"


I am facing certificate error when recording HTTP(S) request in jmeter 2.11.  For testing purpose i am using  but the moment i access the URL after starting proxy server,i get the certification error on webpage.  I have installed the jmeter Root-CA certificate multiple times but still no success. Please advise.


Exponential or logarithm of a dimensionful quantity?

I have a unit measure, say, seconds, $s$. Furthermore let's say I have a dimensionful quantity $r$ that is measure in seconds, $s$. What is the unit measure of $e^r$? ($1/r$ is in $Hz$.)  My question is general, how to find the unit measure of a transformation function $y=f(x)$ where $x$ takes some known unit measure. I give above two functions $f(\cdot)=e^\cdot$ and $f(.)=1/\cdot$.


I need to get the node's view mode so that in the mymodule_page_attachments, I can add libraries conditionally if the node's view mode is set to full or default. I tried the following but not able to get the nodes view mode once I retrieve the$node` object.   How to get node's view mode in hook_page_attachments?  Here is what we tried:  function mymodule_page_attachments(array &$attachments) {   $node = \Drupal::routeMatch()->getParameter('node');   if(is_object($node)) {      // we tried printing but that didn't result any view_mode field.       ksm($node);      // Goal     if($node['view_mode'] == 'full' or $node['view_mode'] == 'default') {        // proceed with my logic.      }   } }


In Pokemon Go how much does a Power Up increase the CP?   In Pokemon Go What are the best, top tier Pokemon?  When using a Power Up do some pokemon gain more CP than others?  How much do they gain?


Let $n = 4k$ or $n = 4k+1$ for non-negative $k$. Prove that there exist a self-complementary graph $G = (V, E)$, where $|V| =n$

Letting $\bar{G}$ be the complement graph of $G$.  I know that if $G$ is self-complementary then $n=4k$ or $n=4k+1$ is true. However, I am having trouble proving the other way around. I have tried to use a proof by induction but at some point in the proof it became too complicated to complete.  We know that self-complementary means that graph $G$ and $\bar{G}$ are both isomorphic and complement of each others.  It is easy to prove that they are complement of each other, but I am finding difficulty proving that they are isomorphic.


sharelatex: PDF inclusion: required page does not exist

I checked the other question similar to this issue yet I could not find a proper solution for the issue I am facing for including an .svg file which is converted using inkscape with pdf+latex option set to ON, and I have also included both the .pdf and .pdf_tex file in the path. Yet I get the above mentioned error.   My code:  \begin{figure}[h!]  \centering \def\svgwidth{\columnwidth} \input{Implementation/Figs/most_changed_from_default_pos_0.pdf_tex} \end{figure}   Full error description:  !pdfTeX error: pdflatex (file /compile/Implementation/Figs/most_changed_from_default_pos_0.pdf): PDF inclusion: required page does not exist <5>   Any help to solve this issue would be really appreciated. I also downloaded the pdf file to check whether it has 5 pages. I could verify it, there were 5 pages in the pdf file.   The file which I want to convert is   I have added the google drive link to the file which I have used for analysis herewith


Help with System of nonlinear equations!

I have post once here about this question but i had some problems and i stopped with solving it. Now i started again and i think i`ve made it better. Here is where i need help.  This is the system of nonlinear equations.  f(x) = 0 where:  $$ \left\{  \begin{array}{c} x_1^5+x_2^3+x_3^4+1 \\  x_1^2*x_2* x_3 \\  x_3^4-1 \end{array} \right.  $$  The right side of the equation is 0.  A) Find manually all the zeroes of the system.  B) Calculate the Jacobian J(X). (Notice that J(x) is singular for x3 = 0)  C) Check this two starting solutions:  1) X0 = {-0.01, -0.01, -0.01}  2) X0 = {-0.1, -0.1, -0.1}  D) Calculate the determinants |J(X0)| and |J^-1(X0)| for the two starting solutions. Notice that Jacobians are almost singular, altough the starting solutions are not so far from the real solutions.  -------------------------------------------------------------------------------  This is the task that i need to solve. I started from here.  From this system we can see that $$ X_3 = \pm 1 $$ So going from this we can make 4 solutions.  $$I:x_3=1, x_2=0, x_1=-1$$  $$II:x_3=1, x_2=-1, x_1=0$$  $$III:x_3=-1, x_2=0, x_1=-1$$  $$IV:x_3=-1, x_2=-1, x_1=0$$  After this i started with the Jacobian. I have made this for the Jacobian matrix.  $$ \left[     \begin{array}{ccc}       5x_1^4 & 3x_2^2x_3^4 &4x_3^3x_2^3\\       2x_1 x_2 x_3 & 1*x_1^2 x_3 & 1*x_1^2 x_2\\       0 & 0 & 4x_3^3     \end{array} \right] $$  After the jacobian i calculate the determinants for all 4 solutions and I have:  I:  the determinant is: 20.  II:  the determinant is: 0.  III:  the determinant is: 20.  IV:  the determinant is: 0.  I stucked on this: When i need to see the two starting solutions C). And when i need to calculate their determinant. The first number that i calculate is 0.00000005 and i said okay its enough i am something wrong.


From a square of unit length, pieces from the corners are removed to form a regular octagon. Find the value of the  removed area.  I got a weird answer, as I considered each side of the removed area will be $\dfrac{1}{3}$ and got $\dfrac{1}{18}$ for area of one triangle. Then I multiplied it by 4, to obtain  $\dfrac{2}{9}$ which I thought to be the answer but I was wrong.


Please allow us to delete our old, subpar, unvoted answers

I'm trying to  when I run into this:     "You have already deleted 5 of your own posts today; further deletes are blocked"      I found conflicting information on this very annoying limit:   This post from May 25, 2010: . This is marked . If this is no longer the case, please edit that question and flag it as . Then , indicates that the problem has risen from the dead -- despite :     Each time that I've seen it (pruning subpar answers), it's been a user who is deleting their own redundant zero-upvote answers. Can you tweak the algorithm slightly so answers with less than one upvote don't count towards tripping this flag?     (Emphasis added.) :     I don't mind it when         cleaning up redundant answers on questions that have multiple alternate good answers   cleaning up old, "less awesome" answers that are no longer reflective of the user's current skill level         (Emphasis added.)     So why do we have barriers in place, to making SO answers less, "less awesome"?      Proposed Solution:  Please let us (¿once again?) delete an unlimited number of our own answers, when they have zero up-votes and are not marked as the answer.  Otherwise, please edit the linked questions to clear up the confusion.


Should we have a designated page for site rules?

This has happened to me a couple of times now. I visit a new Stack Exchange community where I don't normally frequent. I feel like maybe my question belongs there, but I fear it might also fall into the off-topic category based on that community's rules.   Where do I go to view the rules though? Maybe they are buried somewhere in the Meta, where I will find a post that explains some of them, but is that all of them? It seems like this is a grey area.  I know the sites are very different in nature, but I'm imagining something like reddit's “Rules” column. It's specific to each subreddit, and you always know where to look for it. I'm not saying SE should be more like reddit, just offering an example I hope will be easily understood.  So, what do you all think? Would you welcome such a feature? Or does it exist somewhere and I just don't know where? Come to think of it, I'm not even sure if this question is on-topic. But I don't know where to look to check....


Can I delete leftover field_deleted_* tables?

I have a lot of field_deleted_* tables in the database and neither drush cr or running cron is removing them. Is it okay to just remove them from the database? How can I tell Drupal to remove them otherwise?    Edit: Per 4k4 troubleshooting tip:  ➜  default git:(HUHLR-172) ✗ drush ev "var_dump(\Drupal::state()->get('field.storage.deleted'))" array(0) { }   This means:     If this is empty, then you can remove the tables in the database as   well, because Drupal has no chance to guess the hash keys of the table   names without this information.


Show that $f$ has at most one fixed point

Let $f\colon\mathbb{R}\to\mathbb{R}$ be a differentiable function. $x\in\mathbb{R}$ is a fixed point of $f$ if $f(x)=x$. Show that if $f'(t)\neq 1\;\forall\;t\in\mathbb{R}$, then $f$ has at most one fixed point.  My biggest problem  with this is that it doesn't seem to be true. For example, consider $f(x)=x^2$. Then certainly $f(0)=0$ and $f(1)=1 \Rightarrow 0$ and $1$ are fixed points. But $f'(x)=2x\neq 1 \;\forall\;x\in\mathbb{R}$. Is there some sort of formulation that makes this statement correct? Am I missing something obvious? This is a problem from an old exam, so I'm assuming that maybe there's some sort of typo or missing condition.


Baire space $\mathbb{N}^\mathbb{N}$ written as $\mathbb{R}$

I'm writing my bachelor thesis on various topics from set theory and descriptive set theory (mainly topological games), and I just read a paper in which the Baire Space $\mathbb{N}^\mathbb{N}$ is dubbed $\mathbb{R}$. Here is how it justifies it:     Since any two uncountable polish spaces are borel ishomorphic and since many set-theoretic questions are invariant under borel isomorphism it is customary to dub any uncountable polish space $\mathbb{R}$. Also in set theory it is often desirable to deal with a version of $\mathbb{R}$ which is transparent from a combinatorial point of view, so we will work with the Baire space $\mathbb{N}^\mathbb{N}$.   I don't really understand what they mean by "transparent from a combinatorial point of view". I have an intuition on why it is desirable to work with the Baire space. In fact I'd say that it is because it is pretty close to $\mathbb{R}$ (it is homeomorphic to the irrational numbers with the relative topology) and, in a certain sense, it allows to contruct its elements in a much simpler way than in $\mathbb{R}$. This emerges for example in the elegant characterization of continuous functions in the Baire space. So my questions are:   What do they mean by "transparent from a combinatorial point of view"? Is my intuition on the construction of the baire space elements formalizable in some way? It is in some way related with the total disconnection of the space?  If the answer to the previous question is affermative then the reason why the Baire space is desirable can rely also on this consideration (on the element construction)?   Thanks!  EDIT: this is the link to the article I was quoting:  I want to point out that the article doesn't say anything more than the quote I posted in this regard.


I paste a code in WSL but I get only part of it

I use Ubuntu 16.04 (xenial) via WSL.  I copy this code  #!/bin/bash read -p "Have you created db credentials already?" yn case $yn in     [Yy]* ) break;;     [Nn]* ) exit;; esac   When I paste it in Ubuntu I get only part of it:  read -p "Have you created db credentials already?" yn Have you created db credentials already?   Why when it is pasted, it is pasted partially?  Update  I copy the code from GitHub, when the case conditions are indented with tabs and when the code is without a line break in the last line (no extra empty note after the last line).


Extract single file from tar to other folder

I've searched for multiple forums for this questions and have seen different answers but so far, nothing have worked yet even from the ones I've seen here.  I want to extract a single file from a tar to a different directory.  I've tried this:  tar xvf file.tar -C /home/dir/ filename   or this:  tar -x filename -f file.tar -C /home/dir   But got these errors respectively:  x filename, 14826 bytes, 29 media blocks. File -C not present in the archive. File /home/dir not present in the archive.   and:  tar: /dev/rmt0: A file or directory in the path name does not exist.   The first extracted the file but in the same directory, not to the folder I wanted.


I moved postgresql's data directory by following the following steps:   Stop postgres cp -a source_data_directory destination_data_directory export PGDATA=destination_data_directory Changing data directory to destination_data_directory within postgresql.conf pg_ctl start   But when I run: "pg_ctl start" I get the following error. Can someone please help me figure out the error.   server starting postgres@Server:/usr/lib/postgresql/9.1/bin$ postgres cannot access the server configuration file "/home/destination_data_directory/postgresql.conf": No such file or directory


Recently, I've been developing a scheduled apex class to send a csv file to an email. I was using the getContent method from a report page to achieve this. I was doing fine when executing it in anonymous window. But upon scheduling it, I discovered that getContent is considered as callout and cannot be used in scheduled apex. Do someone knows any work around for this without querying the records and putting it in string and converting it to blob? We still want to use the report that was created if possible. Thanks!


I wrote a simple atm machine program, but some inputs cause a 0.01 difference. What's wrong with the code? (Beginner)

banknotes = [200,100,50,20,10,5,1,0.50,0.25,0.10,0.05,0.01]  amount = float(input("Enter an amount: "))  for i in range (0,len(banknotes)):     if banknotes[i] <= amount:         banknote = int(amount // banknotes[i])         amount = amount - banknote*(banknotes[i])         print(banknotes[i],"banknotes:",banknote)  For example when I input 86.74, program acts like its 86.73. But somehow when I input 386.74 or almost any other number, it works correctly. I really can't see where the problem is, and I tried online python compiler to see if my IDE is bugged, same thing happened.


Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$

The complex general linear group is a subgroup of the group of real matrices of twice the dimension and with positive determinant.  Let us decompose complex matrices $M$ as $M=A+iB$, where $A,B$ are real matrices. Now consider the correspondence $$f(A+iB)=\begin{pmatrix} A & -B \\ B & A\end{pmatrix}.$$  If $\det f(M)=|\det M|^2$ for square matrices, then we would have $GL(n,\mathbb C)\subseteq GL_+(2n,\mathbb R)$ with the identification $M\to f(M)$, which is an injective homomorphism. In other words, the complex general linear group would be a subgroup of the group of real matrices of twice the dimension and with positive determinant.  How is $\det f(M)=|\det M|^2$?


Is there an alternative to chromium-browser as a snap

I would like to install chromium-browser, but since it is a snap, I cannot pre-install it.  Is there another option or way to install it the old-school way and will that be deprecated in the future?


How to limit internet access for specific program?

Well, the title says it all. Suppose I have some program, I run it as normal user, and I want it to have no internet access.  P.S. I'm using Arch Linux, but I'm also interested in more general solution.


Ubuntu Bash on Windows - Accessing Windows drive

I just installed Ubuntu Bash on Windows (Windows Subsystem for Linux) on my Windows machine. This is the developer mode through the Anniversary Update.   I would like to access files from my Windows Desktop (or any other subfolder) by Ubuntu command line (accessing Windows drive).  If you can, please point me to the correct reference or guide.  I want to move run code on Ubuntu command-line that will use files in the Windows memory (Dropbox Folder)


Which is the most expensive broom in current canon?

There are many flying brooms in the world of Harry Potter, like the Nimbus series, the Cleansweep series, the Firebolt etc.   However, I didn't find any concrete information about which broom is the costliest of all. I understand that some brooms will be best for some situations or people. But still I want to know which broom is the most expensive.


Can I edit shapefile while using a definition query in QGIS?

Is it possible to edit shapes while using a "definition query" or "query builder" in QGIS? I'm trying to do this in the same way I used to in ArcGIS.  Thanks!


Make a bootable USB stick for MacBook Air, with wifi drivers?

I was able to make a bootable USB stick that I could use on a MacBook Air, except that it did not have the necessary driver for the wifi hardware, meaning I was unable to connect to the network.  I did look at the steps on '', but it didn't indicate any steps to add extra drivers.  The  given for installing the drivers are, in a booted Ubuntu to run:  sudo apt-get purge bcmwl-kernel-source sudo apt-get install firmware-b43-installer   Though, I have no network connection to be able to do this and even then will this stick through reboots?


After exporting an ldraw file from stud.io into blender through TonyLobster's ldraw importer, I went to try to render. It keeps rendering while tinted pink and I cannot figure out why. I know that the pink tint has to do with missing textures, but (that I know of) the importer I used should be getting the textures from the Ldraw parts library that I linked it to. I am using Blender version 2.79.


Multiplication operator has no eigenvalues

Let $X=C([0,1])$ be the space of continuous functions on $[0,1].$  Consider $T:X\rightarrow X$ given by $(Tf)(t)=tf(t).$  Then $T$ has no eigenvalues.  My thought :   Assume that $T$ has an eigenvalue $\lambda$.  Then, $Tf=\lambda f$  for a non-zero $f$  So we have $(t-\lambda )f(t)=0$  Then, $t=\lambda\in[0,1]$  Then, my friend told me that if $ t \neq \lambda$, then $f=0$  And $f$ is continuous, so it forces $f$ to be zero.  But I don't quite understand his argument since $t \in [0,1]$.  So can anyone tell me what I am missing here?  Also, I have found similar posts.      But unfortunately, I failed to understand them, so I'm asking here.  Thank you.


Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$

Evaluate $$\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos(\theta)}\mathrm d\theta$$   This is the final question on my review for my final exam tomorrow, and I will be honest and say that I have no clue how to begin problem. Any hints in the direction of how to solve this would be helpful.  Following from @Adam Hughes,   $-\dfrac{\pi}{2}[f'(0)+Res_2]$When I took the derivative of $f(z)=\dfrac{(z^2-1)^2}{2z^2+5z+2}$ and evaluated for 0, I got $-\dfrac{5}{4}$ Now, $Res_2$


How to factor this algebraic identity used in Lagrange's theorem for polynomial congruences

The question is how to factor an identity.  The identity is shown below but it uses $f(x)$ as defined in Theorem 5.21, so let me show $f$'s definition first.  In the proof, we eventually get to this identity:  We have two equations there.  I'm good with the first.  Just expanding it out makes it obvious.  My problem is on the second equation.  By taking the expansion and factoring $x$ on all non-$x_0$ terms, I get $$x(c_n x^{n-1} + \cdots + c_2 x + c_1).$$ Similarly for $x_0$, $$x_0(c_n x_0^{n-1} + \cdots + c_2 x_0 + c_1).$$ Question.  How can I use these two expressions and get the second equation in the identity? If I let $g(x) = (c_n x^{n-1} + \cdots + c_2 x + c_1)$, then I have $g(x)$ in the first expression above and $g(x_0)$ in the second.  These are not the same, so I'm puzzled as how this is allowed.


Some weeks ago I lost access to the email account I had associated with my Stack Exchange account, but as you can see, I still have access to it from the mobile version.  The problem is, I logged in with Google every time I wanted to access the site, but as my email account got disabled, I can't do it any more.  I looked for a way to update my login information from the app, but I didn't find it. Is there another way to recover my account?


Can I batch set the date on Canon RAW files with a tool?

I have just noticed my cameras date has been wrong for the last month. However it is consistently wrong, so if I work out (or guess) the date and time of the first photograph, is there a tool that will work out the correct date/time of the rest of the images?


I know that when you square something you can visualize it as a 2d square.  When you cube it you can visualize it as a 3d cube.    For example:  2^2 -- a 2 by 2 square  2^3 -- a 2 by 2 by 2 cube  I've been puzzling over how something would look when you make it to the power of a fraction.  Is it some shape with 2D and 3D aspects? Or is it just a non-regular 3d shape.  2^(3/2)  It would be nice to have an explanation and maybe some pics :)  P.S.  I didn't really know what tags this should have so feel free to edit.


Is there a term for a section of an article which contains a quote or snippet from the main text?

Sometimes in articles in newspapers / magazines / websites there will be a small section separate from the main body of text that contains a short line - often a quote - which is either representative of the article or an interesting angle.  For example:    Here the quote in the box on the right hand side is an example of what I am looking for a term for.  It could be referred to as a blockquote (but those could be in-line with the text) or a figure (but those could be graphics to illustrate an article) or an excerpt (but those are broad eg a read aloud excerpt from a book, etc).  Is there a term that is specific to these small vignettes that appear with a body of text, but are presented separately to the body of it? Perhaps a technical term used by those in publishing / layout design / journalism?  There is a similar concept of a , for example in a box or panel, but I am interested specifically in a quote being set off from the main body of text.


How to read a multiple string input in form of an function?

I have a task to get user input in this form:  "SEND name1 name2"   The goal is to find the shortest path between the names, but that currently not the problem. I don't know how to read multiple strings form a single input.  The first string would be SEND, but that's the easiest one. How do I read the other two? After getting the names, I'd pass them on to a function to find out the distance between them.


This integral is defined ? $\displaystyle\int_0^0\frac 1x\:dx$

$\displaystyle\int_0^0\frac 1x\:dx$ This integral is defined ? If it define, what is the value ?  Please,step by step


How to efficiently persist uploaded files in JAX-RS / JavaEE?

I need to write a rest service that offers batch validation for pdf documents.   The basic validation workflow is as follows:  Files are uploaded via rest api one file at a time. Documents have sizes between 10- and 150 Megabytes on average. Once a batch is complete validation starts: Every document is successively taken from storage, validated, a report is being generated and the originally uploaded document will get deleted afterwards.  The platform to be used for development is Java EE (Jersey and EJB). Since EJB doesn't allow for saving data directly to disk as a file, I've considered using a database via JPA to temporarily save the files until processing.  Is this a sound choice or would you prefer a different solution that I haven't thought of?   Is using a database for this scenario a bad idea performance wise?  We're expecting batches of up to 4000 documents. I'm especially worried about performance bottlenecks and resource consumption (ram, disk space).....


What are all the other treasures in Odin's treasury?

In Thor Ragnarok, Odin's treasury contains the tessaract, that-big-flame-guy's crown, the eternal fire, and a few other things that Hela walks past. What are those other things?


Shell script ssh to login multiple servers with password passing from a file

Shell script ssh to login multiple servers with passing password from a file   for example: Password file name : password.txt and the password is "test123".  ssh_script:    ssh testuser@testserver   <<< Here I need to get the password from a file >>>   It should read a password from a file and entered into server.


What causes the GPS offset/shift in China?

I've spent close to two full days trying to understand the nature of the infamous GPS shift in China. After sifting through the noise, two recurring symptoms are that:   GPS coordinates (WGS-84) plot poorly on Chinese maps, with an offset ranging from 50 to 1000 meters. Google and Apple Maps in China have severe misalignment between their street maps and satellite imagery ()      make contradictory claims:   Cold War-era regulations mandated introducing random offsets into GPS chips due to security concerns protectionist measures aimed to favor GPS devices manufactured in China  a , and the offsets are not random GPS chips manufactured in China offset the coordinates they return, in order to match approved Chinese maps, which must follow the GCJ-02 datum   What is the actual story? This looks like the type of pervasive problem that merits a Wikipedia page, but I haven't been able to find anything authoritative yet.  The  questions suggested as  duplicates don't answer exactly what the cause is; rather, they describe symptoms.


How can I take screenshots of YouTube videos in full screen?

I am trying to take a screenshot of a YouTube video in fullscreen.  When I pause the video and wait a moment, only the bottom UI bar (play/pause/seek) disappears. The top UI bar (Like/Share/More Info) stays there.  So when I press PrintScreen on the keyboard, the screenshot is polluted by this top UI bar. Is there any way to remove it while the video is on pause?


How to move layers in the Layer Order Panel using PyQGIS?

Related to the following question but looking for a PyQGIS method:      The following is a simple setup containing a group with three layers.    The code I use adds a new layer at the end of this group:  root = QgsProject.instance().layerTreeRoot() group = root.findGroup('Main group')  vlayer = QgsVectorLayer('LineString?crs=epsg:27700', 'vlayer', 'memory') QgsMapLayerRegistry.instance().addMapLayer(vlayer, False) group.insertChildNode(-1, QgsLayerTreeLayer(vlayer))       In the Layer Order Panel, the newly added layer is at the end.       Is it possible to move this to the top without moving the layer in the Layers Panel?


I'm curious to whether you guys have any tips on book concerning classical euclidean geometry. I'd like somewhat of an advanced treatment, around the same level as Coxeter's "Geometry revisited". I'd however want something more comprehensive, therefore I'm asking you for tips!  Hopeful for answers ^^


If $$|x| < 1$$ Prove that  $$\begin{align}\large 1 + 2x + 3x^2 + 4x^3 + \dots = \frac{1}{(1 - x)^2}\end{align}$$


Package dependencies cannot be resolved help

This error could be caused by required additional software packages which are missing or not installable. Furthermore there could be a conflict between software packages which are not allowed to be installed at the same time.  The following packages have unmet dependencies:  steam-launcher: Depends: curl but it is not going to be installed  Depends: libc6 (>= 2.15) but 2.15-0ubuntu10.4 is to be installed   How do I get these? because with out them I can't run Steam


Restricted \write18 enabled entering extended mode error

Hi I am creating pdf on my windows 8 machine. I am using texlive 2019. While giving command pdflatex test.tex I am getting this error.  I have no clue why this error is happening.  This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/W32TeX) (preloaded format=pdflatex)  restricted \write18 enabled. entering extended mode (./test.tex LaTeX2e <2018-12-01> (c:/texlive/2019/texmf-dist/tex/latex/base/article.cls Document Class: article 2018/09/03 v1.4i Standard LaTeX document class (c:/texlive/2019/texmf-dist/tex/latex/base/size10.clo)) No file test.aux. [1{c:/texlive/2019/texmf-dist/fonts/map/pdftex/updmap/pdftex.map}] (./test.aux)  )<c:/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb> Output written on test.pdf (1 page, 9062 bytes). Transcript written on test.log.   Please guide me is there any package I have to install or any settings I need to make.


Blender material button doesn't work for selected object.   As you can see, it worked on the first object, but wont work for the plane, either. Maybe I messed up at the first object"s material, cause I'm new and it just wants me to give up? I tried transparency to the first object and I assume that we wouldn't be able to see that without rendering, since it's not partially transparent in this view.  Thanks in advance.


I tried different methods of integration, but I can not solve this problem.  $$\int \sin^n (x) dx$$


Adding switzerland cran mirror for R in /etc/apt/sources.list

I've got an error while trying to add the R cran mirror for Switzerland to the sources.list file (), even though I followed the instructions from page  (I'm running Ubuntu 13.04) I really can't find what I'm doing wrong... here are my steps:   sudo gedit /etc/apt/sources.list   then, in the source.list file, I added a line like that, at the very end:  #R repositories switzerland  http://stat.ethz.ch/CRAN/bin/linux/ubuntu raring/     then, save and exit and the error appears when typing the sudo apt-get update command:   sudo apt-get update  E: Type 'http://stat.ethz.ch/CRAN/bin/linux/ubuntu' is not known on line 60 in source list /etc/apt/sources.list E: The list of sources could not be read.       why?   Thank you for your answers!


As my client software uses lat/lon coordinates when communicating with my (spherical mercator) postgis database i decided to ST_Transform every geometry to WGS-84.  However i noticed that ST_Distance for WGS-84 returns units as degrees (i need meters). So i decided to use ST_DistanceSpheroid(geom1, geom2, 'SPHEROID["WGS 84",6378137,298.257223563]') but this method seems to be extremely slow.  Therefor i switched back to using spherical mercator again and transforming my input and output to and from wgs-84 as that performs a lot better.  Am i using the correct method or is this a known issue?


For instance trichomania is a love of hair, and trichophobia is a fear of hair. But what suffix would denote a loathing of hair?  Edit: Maybe I'm looking at the wrong end of the word, and I should be considering the prefix "miso-".


Open user profile from meta sites shows wrong title

If you open a user profile from any post on meta sites (not MSE) via Android app, the title, site icon, about section and badges will be from the user's most popular site, but the list of the post from this meta site.  E.g. if you open my profile from any of  (e.g.  can be opened via app) you will see the following:        Here are title, rep and badges from the Stack Overflow in Russian, but list of the posts and about section are from the Meta Stack Overflow (in English).   App Version: 1.0.95 Device Manufacturer: LGE Device Model: LG-H860 OS Version: 7.0 (172342203b663)


How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$?

Problem:   Find the value of $$\sum_{r=0}^{44} \tan^2(2r+1)$$  Note: The angles here are in degrees.    I don't know how to solve this question because trigonometric simplifications didn't get me anywhere. I think there was a method to solve this question using complex numbers which I no longer remember. Any hint/help will be appreciated.


How to use bridge edge loops to make a pipe bend in Blender 2.8/9

I'm trying to bridge two edge loops in Blender 2.8 to make a curved pipe. I was able to do this in 2.79 but I cannot get it work in 2.8.   After setting profile to 0. Setting it to -1 makes it look crumpled. Either way I cannot seem to make a nice arc.   Is there another way to bend a pipe?   Same settings as Robin Betts


I want to get the "mean" value of all Orders from my sharepoint list.  How do i do this?  This is my code so far:  function VisaLista() {     namn = document.getElementById("txtNamn");     var camlQuery = new SP.CamlQuery();     camlQuery.set_viewXml(     "<View>" +     "<Query>" +     "<Where>" +     "<And>" +     "<Eq><FieldRef Name='Title'/><Value Type='Text'>" + namn + "</Value></Eq>" +     "<Or>" +     "<Eq><FieldRef Name='Prioritet'/><Value Type='Text'>Hög</Value></Eq>" +     "<Eq><FieldRef Name='Status'/><Value Type='Text'>Startad</Value></Eq>" +     "</Or>" +     "</And>" +     "</Where>" +     "</Query>" +     "</View>");     listItems1 = list.getItems(camlQuery);     clientContext.load(listItems1);     clientContext.executeQueryAsync(OnSuccessVisa, OnFail); } function OnSuccessVisa() {     var listEnumerator = listItems1.getEnumerator();      while (listEnumerator.moveNext()) {         var currentItem = listEnumerator.get_current();         $("#Kategori1").text(currentItem.get_item('_x0072_zb6'));      } }


A more general definition of branched covering.

If $f:X\longrightarrow Y$ is a holomorphic map between two compact Riemann surfaces, then $f$ is called also a branched covering map. This is because the branched points of $f$ form a finite set $S\subseteq Y$ and the map $f$ restricted on $X\setminus f^{-1}(S)$ is a topological covering map of $Y\setminus S$.  Now I cannot find a standard notion of branched covering for topological spaces, but I think that it should be like the following:     A continuous and surjective map $f:X\longrightarrow Y$ between topological spaces is a branched covering map if there exists a dense subset $S\subseteq Y$ such that $f$ restricted on $X\setminus f^{-1}(S)$ is a topological covering map of $Y\setminus S$.   Some authors say that $S$ should be nowhere dense and others require that $S$ is a finite set. So, what is the more standard definition of branched covering in the topological framework?


Trying to understand Microsoft SQL and Windows Server licensing

I'm trying to understand how many licenses I'm supposed to purchase and check if I have the correct amount of purchased licenses. I have Windows Servers & SQL Servers in virtual environment.  From my understanding:    Windows Server only:  Server with Windows Server – the license is 'Per CPU'.   A Server with 1 CPU & 2 Cores total - need 1 windows license.  A Server with 2 CPU & 4 Cores total - need 2 windows license.  A Server with 2 CPU & 8 Cores total  - need 2 windows license.    SQL Server:  A server with SQL server – The license is 'Per CORE'.  Also needed Windows Server license, amount depends on the number of CPU.  A Server with 1 CPU & 2 Core total – need 2 SQL licenses.  A Server with 1 CPU & 4 Core total – need 2 SQL licenses.  A Server with 2 CPU & 8 Core total – need 4 SQL licenses.  A Server with 2 CPU & 12 Core total – need 6 SQL licenses.    Please let me know if my example is correct, So I can be sure I understand the licensing as needed.  Thank you!


Please show changed titles separately in edit diffs

In an edit diff, when the revision changes the title, removed words are shown struck out in red and added words are shown with a green background. This is fine when there are only removed words, or only added words, but when there are both, the result is difficult to read.        Getting default accessible fields of… No. Getting accessible fields of an object in a Salesforce object… No. Getting accessible fields of a Salesforce object using REST API. Phew. Yeah, ok.        Program causes run. Time error? Oh, Program causes run-time error … when run on specific machine. Yeah, sounds sensible. What was the old title? Oh dear…  Please show both the old title and the new title, one below the other.


when ever I'm logging in, I have set a login password for my account but it is logging in automatically with out asking me for a password. Please tell me what I can do to get rid of this problem.


IP Address of a server's website url in Javascript

I would like to take a url and find it's IP Address using Javascript code.


How can I add a VirtualBox machine to the Unity launcher?

VirtualBox allows me to put a shortcut icon for a virtual machine to the Desktop:    I tried to drag it to the Unity launcher but cannot place it there.   Is there any way to add a desktop shortcut icon of a virtual machine to the Unity launcher?


what is the difference between IBE and ABE schemes

Can somebody explain in simple words. real life example light help and limitations of these schemes etc.


Why does Clipboard.GetText() give no answer?

So I'm making a .Net Application and I have this textbox that is supposed to have the contents of your clipboard in it. But the Clipboard.GetText() does not import anything into the textbox, I've tried replacing it with "Hello World" and it works fine. Code snippet: bool running = true;      public void GetClipboard()     {         while (running)         {             CurrentCopied.Text = Clipboard.GetText();             System.Threading.Thread.Sleep(500);         }     }      public Main()     {         InitializeComponent();          ThreadStart CopyThreadStart = new ThreadStart(GetClipboard);         Thread CopyThread = new Thread(CopyThreadStart);         CopyThread.Start();     }


Is there a way to run Skyrim in windowed full-screen mode, preferably without a border? I usually play in windowed mode but it's a bit sad. I do it to keep Fraps on loop buffer; full-screen cancels loop buffer every time I switch windows.


Was/is Darth Vader the most powerful force user?

In this  when asked why Darth Vader is a favorite character among children George Lucas says;     "... and who is more power than Darth Vader? Some will be attracted to   Luke Skywalker because he is the good guy, but ultimately we know that   Darth Vader is more powerful than he is. As time goes you discover   that he more powerful because he is the ultimate father, who is all   powerful."   Looking at this question  there many answers in the primary canon and Legends canon on who that might be.   Does this quote from Lucas  give us a clear answer that Darth Vader is the most powerful, or is Lucas' quote being given in the narrow field of Darth Vader vs Luke Skywalker? I understand this George Lucas we are talking about... so there might be a contradiction in another interview or something was ret-conned at a later time!  Also, at the time the interview was given I think the answer would be limited to Episodes I-VI. Answers would have to come from G-canon.


Does Euler formula work for complex $z$?

We know Euler formula:  $$ e^{ix}=\cos(x)+i\sin(x). $$  Does this formula work if we replace real number $x$ with complex number $z$?


How Execute Bulk Update with SQLAlchemy ORM (Not CORE) in Python?

SQLAlchemy ORM Mavens,  Using SQLAlchemy ORM (not CORE), how can a bulk UPDATE be configured on an unknown quantity of objects in a manner similar to a SQL UPDATE-SET-WHERE command (such as this one:)?   UPDATE items SET items.price = (items.price * 1.1) WHERE Left(item_id, 4) = "PAX-";   After hours of poring over manuals and docs...all I can find are CORE examples—and hope you'll be so kind as to offer a tip.  Many, many thanks! Planewryter  PS: Using Python 3.7 and SQLAlchemy v1.2.13 on an iMac w/macOS 10.14.1


Help with understanding of proof of no rational points on $x^2+y^2=3$?

In Julian Havil's The Irrationals, he at one point in Chapter 2 supposedly states a proof that there are no points with rational coordinates on the curve $x^2+y^2=3$. He begins:  "Assume that a rational point $(p/q, r/s)$ lies on the circle and so $p^2/q^2+r^2/s^2 = 3$, resulting in $p^2s^2+q^2r^2=3q^2s^2$ and so $(ps)^2+(qr)^2 = 3(qs)^2$ and therefore the existence of positive integers so that $a^2+b^2=3c^2$. Since the sum of two even numbers and the sum of two odd numbers are each even, it must be that one of $a^2$ and $b^2$ is even and the other odd; so..."  and continues. I understand every step other than this - why does the fact that one of $a^2$ and $b^2$ must be even and the other odd from the simple fact about the sums of odd and even numbers?


I was going through one of the topic "Introduction to Formal proof". In one example while explaining "Hypothesis" and "conclusion" got confused.  The example is as follows:     If $x\geq4$, then $2^x \geq x^2$.   While deriving conclusion article said "As $x$ grows larger than $4$, LHS $2^x$ doubles as $x$ increases by $1$ and RHS grows by ratio $x+1/x$".  Thanks in advance.


Proof verification and advice: Prove that an integer is divisible by 9 IFF the sum of its digits is also divisible by 9.


determinant of a matrix with binomial coefficient entries

I trying to prove a statement, which boils down to showing that the determinant of a specific matrix is nonzero. I use the convention that $\binom{n}{k} = 0$ if $k > n$ or $k < 0$. Let $k,l$ be natural numbers such that $k \le l$. Then the $n\times n$-Matrix $A$ is defined to have the entries   $a_{ij} = \binom{l}{k +i - j}$. So it looks like  $A = \left( \begin{array}{cccccc} \binom{l}{k} &  \cdots & \binom{l}{0} & 0 & \cdots & 0 \\  \vdots & \ddots &  & \ddots & \ddots &  \vdots \\ \binom{l}{l} & & \ddots & & \ddots   & 0  \\ 0& \ddots && \ddots & & \binom{l}{0}\\ \vdots&\ddots&\ddots&&\ddots&\vdots\\ 0&\cdots&0& \binom{l}{l} & \cdots & \binom{l}{k}  \end{array}\right)$.  Clearly the cases $k = l$ and $k = 0$ are trivial, since $A$ is then triangular. My first idea was to use the formula  $\binom{r}{s} = \binom{r-1}{s-1} + \binom{r}{s}$ and add columns/rows to each other. But that does not work out that well...   So if anyone has any ideas, or this matrix is known to be invertible, I would be very thankful.


How to process the data which type is BLOB?

I get the following data from MySQL by db_query(). The type of the column is BLOB.     a:2:{s:10:"attributes";a:1:{s:5:"title";s:0:"";}s:8:"langcode";s:7:"zh-hans";}   How should I process it?


"-bash: {}: No such file or directory" using find exec

I'm trying to run find . -name "binaries.tgz.*.gz" -exec gzip -d -k < {} \; (ultimately I'm trying to run find . -name "binaries.tgz.*.gz" -type f -exec gzip -d -k < {} \; | tar tzf - but I'm trying to figure out why the command before the pipe isn't working first), but I get the following error:     -bash: {}: No such file or directory:   [user@host:/data/dionaea]$ find . -name "binaries.tgz.*.gz" -type f -exec gzip -d -k < {} \; -bash: {}: No such file or directory [user@host:/data/dionaea]$ ls | grep binaries binaries binaries.tgz binaries.tgz.10.gz binaries.tgz.11.gz binaries.tgz.12.gz binaries.tgz.13.gz binaries.tgz.14.gz binaries.tgz.15.gz binaries.tgz.16.gz binaries.tgz.17 binaries.tgz.17.gz binaries.tgz.18.gz binaries.tgz.19.gz binaries.tgz.1.gz binaries.tgz.20.gz binaries.tgz.21.gz binaries.tgz.22.gz binaries.tgz.23.gz binaries.tgz.24.gz binaries.tgz.25.gz binaries.tgz.26.gz binaries.tgz.27.gz binaries.tgz.28.gz binaries.tgz.29.gz binaries.tgz.2.gz binaries.tgz.30.gz binaries.tgz.3.gz binaries.tgz.4.gz binaries.tgz.5.gz binaries.tgz.6.gz binaries.tgz.7.gz binaries.tgz.8.gz binaries.tgz.9.gz   What am I doing wrong?


Add the duplicate suggestion feature to mobile theme

I noticed this issue as I tend to view Stack Overflow via the mobile site frequently:   The mobile version does not show possible duplicate questions while you're typing the question/description, while in "full site mode" the suggestions come up just fine.  In my mind, getting the suggestions to show up on the mobile version of the site should not be a hard thing to implement  While I admit it makes me lazy asking for this feature when there is a work around, the full site doesn't display nearly as well as the mobile one so it would make life a lot easier to have this simple change.  Also, what good programmer isn't lazy? :)


In java , let's say I have a reference to an object , and a function: object p = new object(); function(p);  where function is: public void function(object x) { /// }  What actually happens in memory here?I think of x and p as pointers in C++.Will "x" and "p" have the same value,but different adresses in memory , or they will have the same value and adress?Thanks.


I am trying to install a software through terminal. It asks  for my password and i have given the correct password but still it says wrong password. Then i removed all kind off password from my login account. but still it asks for the password. i am using Ubuntu 14.04. Can anyone help me please.


Out of memory error java heap space using InputStream. How can I fix this?

I'm trying to read each file in a directory that contains 4000 json.gz files. I'm running out of heap space during execution. I'm unsure how to solve this.         File folder = new File(directoryPath);         String [] files = folder.list();          assert files != null;          for (String file: files) {             String filePath = directoryPath + "/" + file;              if (filePath.substring(filePath.length() - 2).equalsIgnoreCase("gz")) {                                  try (GZIPInputStream gzipInputStream = new GZIPInputStream(new FileInputStream(filePath))) {                     InputStreamReader reader = new InputStreamReader(gzipInputStream);                      Object obj = jsonParser.parse(reader);                      TextFileModel textFileModel = processObject(obj, controller);                     textFileModelList.add(textFileModel);                                      } catch (IOException | ParseException e) {                     e.printStackTrace();                 }           }   UPDATE: I've tried a few of the suggestions but I'm still getting the same error try (InputStreamReader reader = new InputStreamReader(new GZIPInputStream(new FileInputStream(filePath)))){                      Object obj = jsonParser.parse(reader);                      reader.close();                      TextFileModel textFileModel = processObject(obj, controller);                     obj = null;                     textFileModelList.add(textFileModel);                  } catch (IOException | ParseException e) {                     e.printStackTrace();                 }  Error Message: Exception in thread "main" java.lang.OutOfMemoryError: Java heap space     at org.json.simple.parser.Yylex.yylex(Yylex.java:668)     at org.json.simple.parser.JSONParser.nextToken(JSONParser.java:269)     at org.json.simple.parser.JSONParser.parse(JSONParser.java:118)     at org.json.simple.parser.JSONParser.parse(JSONParser.java:92)     at com.sbl.Main.main(Main.java:45)


Why do British people pronounce "idea" with an "r" sound at the end?

Non-rhotic dialects tend to drop "r" sounds, so why is one added here when there is no "r" in the word?


how does python assign value to inner function

Can someone please explain how python assigned the value below to y. I understand how the function works but I do not understand how the function call a(10) assigns its value y.   def outside(x):     def inside(y):         return x ** y     return inside  a = outside(2)  a(10)


Side by side images (Centering subfloats and changing font)

I have the following images produced by the following code:  \begin{figure} [H] \def\tabularxcolumn#1{m{#1}} \begin{tabularx}{\linewidth}{@{}cXX@{}} % \begin{tabular}{cc} \subfloat[Node 3 - Therapy Group 1 (443 patients)]{\includegraphics[width=5.5cm]{3e3}}     & \subfloat[ Node 4 - Therapy Group 0 \& Initial State Group 1 (116 patients)  ]{\includegraphics[width=5.5cm]{3e4}}\\ \subfloat[Node 5 - Therapy Group 0 \& Initial State Group 2 (39 patients)]{\includegraphics[width=5.5cm]{1e5}}     & \subfloat[Node 6 - Therapy Group 0 \& Initial State Group 3 (16 patients)]{\includegraphics[width=5.5cm]{3e6}}\\ \subfloat[Node 7 -Therapy Group 0 \& Initial State Group 34 (8 patients)]{\includegraphics[width=5.5cm]{3e7}}  \end{tabular} \end{tabularx}   How can I 1) Make the caption font smaller 2) get the whole image centered to the middle of the page 3) get the last figure (e) centered with the other above it 4) get them even apart so that the caption would fit in 1 line


I wanted to type an equation in LaTeX. But it is too long to fit into one line. It involves big arrays with many columns so I cannot split it. I wanted to reduce the font size so that it can fit in one line. However, \small doesn't work in the equation environment.


Canonically, can Mjölnir be lifted by brute strength?

I was just watching Ultimate Avengers and apparently, Hulk got really angry and just decided to pick up Thor's hammer... Twice. Now we do know that people other than Thor can wield it as long as they deemed worthy, but I highly doubt that was the case here. So is it canon that Mjölnir has been lifted before just by the Hulk's or any other character's brute strength?


I'm investigating into the angular velocity of a planet in its elliptical orbit.  I have these variables defined:  speed of planet.     speed of planet at perigee and apogee.     length of orbit.     time of orbit.      distance away from center at apogee and perigee.   Is there a way from this data that I can calculate the angular velocity of the planet in this orbit ?.  $\tt\mbox{I need the angular velocities of all the 8 planets.}$  I've already done this all for a circular orbit which is quite easy but I can't figure out how to do it for elliptical orbits. Any help will be appreciated !. Thank you in advance.


Assign points within 150 meter buffer of each other the same unique identifier?

I have a bunch of points on a QGIS map. Each point is a unique sampling event. However, some of these points have been sampled multiple times but there is no common identifier in the attribute data to determine this. The only way we can see this is by looking at the map and seeing points very close to each other.   I am wondering if anyone has a method to assign points within a 150 meters of each other a common identifier?


Rule of thumb for choosing NN parameters in a regression analysis

I am building a simple NN for a regression analysis (0.5 mln rows of data) in Keras. # Define model model = Sequential() model.add(Dense(32, activation = 'relu')) model.add(Dense(32, activation = 'sigmoid')) model.add(Dense(1)) # Define model parameters model.compile(optimizer = 'sgd', loss = 'mse', metrics = [tf.keras.metrics.MeanAbsoluteError()])  I am satisfied with results, but would like to know if there is any rule of thumb or recommendations how to build such models for a regression analysis. For example:  How many layers? Which activation functions? Which optimizer?  What is your state of the art approach, when you start to do such type of analysis? Especially appreciate any academic sources.


I'm playing grand theft auto 5. I needed to earn money from any character of GTA. So how can I earn money easily?


Count discrepancy when flagging and selecting a "vote to close" option

Defect Description Over at , I have enough rep to vote to close questions. I've been using the 'flag' option out of force of habit, but when I select that a question doesn't belong, it takes me to the close panel anyway and allows me to register my vote. However, once I have voted to close, what ends up happening in the UI is it improperly shows the new number of close votes and flags. Example Current Behavior Say I have a question with one vote to close it. Following the process in the defect description, I vote to close it as well. However, the UI takes my close vote, adds it to the existing count (1), then edits the count beside flag (my entry point) to show 2 flags in addition to the previous single vote to close.  Expected Behavior There should be two votes to close.  Additional Information If I refresh the page, the counts show correctly. In other words, the back-end code is fine, but the AJAX callback seems to edit the element I clicked rather than the element that represents the action I actually took.


Is there a sentence that contains every English phoneme?

An example of a sentence with every letter of the alphabet is: "A quick brown fox jumps over the lazy dogs."  Is there an example of a sentence which contains every English phoneme? I realize accents would skew this. I would be happy to see a sentence in American English accent.


matplotlib plt.hline; customized the space between each horizontal lines

I'm plotting horizontal lines using the following  K = 85 space = K plt.hlines(y=np.arange(0,K*space,space), xmin=0, xmax=torch.randn(K))   It gives the plot     While; the argument space location the y-axis; but each line is so close with its neighbor and its very hard to put y-axis labels for each of the horizontal line  I'm more interested in increase the space (distance) between each line so that y-axis labels can be better visualized. Any help ? Thanks


When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$?

Are there specific conditions under which the following is true? E.g., certain distributions, positive RV?  $$\mathbb{E}\left[\dfrac{1}{\sum X_{i}}\right] = \dfrac{1}{\mathbb{E}\left[\sum X_{i}\right]}$$


Why are IID normal random variables spherically symmetrical?

Given a finite sequence of $s+1$ IID normal random variables $X_1, \ldots, X_{s+1}$ They are spherically symmetrical.  This means that the radial projection of the point $(X_1, \ldots, X_{s+1}) $ onto the unit sphere $S^s$ has uniform distribution on $S^s$.  My questions are: what is meant by radial projection and how can I prove that the resulting distribution will be uniform?


/ is full. How do I find out what's taking up space?

I Recently noticed an lightweight app (Sonarr) wasn't running, so when into webmin to find a fidk fill error. '/' was 100% full. I have hunted around and sound a few commands to get a bit of short term space back (down to 96%), but there shouldn't be that much usage. I'm just running Ubuntu Server LTS18 and a couple of apps on a 120GB SSD. But I am seeing the below and cannot (and do no know how to) find where the heavy directories and/or file are in /.  Filesystem                                 Size  Used Avail Use% Mounted on udev                                       7.3G     0  7.3G   0% /dev tmpfs                                      1.5G  2.8M  1.5G   1% /run /dev/sde2                                  110G  104G  4.6G  96% / tmpfs                                      7.3G   12K  7.3G   1% /dev/shm tmpfs                                      5.0M     0  5.0M   0% /run/lock tmpfs                                      7.3G     0  7.3G   0% /sys/fs/cgroup /dev/loop0                                  90M   90M     0 100% /snap/core/7917 /dev/loop1                                  90M   90M     0 100% /snap/core/8039


Which lenses can I use on my Sony Alpha 100?

I have a Sony Alpha 100 and I've bought an adapter M42 for it. I'd like to know, which lenses can I use on my Sony?


University wifi quietly disconnects on AR9285

I have trouble with Ubuntu 13.10 on my university wifi. I connect, and it works fine for five seconds to five minutes, then the connection quietly disappears. It does not indicate that anything is wrong with the network, no "Connection lost", et cetera. It just reports that I am still connected to the network, but doesn't actually work. A solution is to disconnect the wifi, then reconnect, giving me a few moments more of working wifi - horribly annoying.  Wifi stats   WPA(2) Enterprise PEAP authentication - version automatic I have the university .CRT certificate installed; I hear it's unnecessary MSCHAPv2 inner authentication Username ... Password ... Typically three out of four bars signal strength in my dorm room.   Other notes   Lenovo G770 laptop Works fine in Windows 8 Have tried Ubuntu 13.04, Linux Mint, Fedora, all have same problem Have tried other cards:  Atheros RTS5139 USB - same problem   Intel Wireless AC 7260HMW MiniPCIe - same problem AND lagged my PC horribly; removed  My roommate reports similar issues with a Broadcom card I think it worked okay for a month or two when I joined university, only to suddenly begin acting in the mischievous manner I describe, after several fresh reinstalls. I am fairly experienced with Linux and have been using it since Ubuntu 8 or somewhere along those lines.   Do you have any ideas? I've been stuck using Windows and it sucks so bad. I'm desperate enough to consider buying a router and trying some bridge method... if nothing else would that work?  lspci output  02:00.0 Network controller: Qualcomm Atheros AR9285 Wireless Network Adapter (PCI-Express) (rev 01)     Subsystem: Lenovo Device 30a1     Kernel driver in use: ath9k


What unlockable items exist in Shower With Your Dad Simulator's main game mode?

In the main game mode, you can unlock items such as a Razor and Soap. What other items can you unlock, how do you unlock them, and what do they do?


For any integers $a, b$, let $N_{a,b}$ denote the number of positive integers $x<1000$ satisfying $x\equiv a\pmod{27}$ and $x\equiv b\pmod{37}$. Then find $N_{a,b}$.    progress:  $x\equiv a\pmod{27}$ and $x\equiv b\pmod{37}$ implies $x=27m+a$ and $x=37n+b$ for some integers $m,n$. For common sosultion, $27m+a=37n+b\implies 27m-37n=b-a$. Now $\gcd(27,37)=1$ sow there exists integers $u,v$ such that $27u+37v=1$. Is it possible to solve using this relation ? Thank u in advance


Can I visit UK a month before my visa expires?

I'm from the State of Kuwait and hold an Eritrean passport. I'm planning to visit UK in October but my visa will expire in November.    Is it OK to make a journey in the last month of my visa, provided that I make sure that I book my plane back before expiring date?


How do I use method overriding in this case?

So this is my class and I just learned a little bit about inheritance. I heard about overriding methods but how do I do it in this case?  class Game {     string consoleName;     int gameID;      public Game(string name, int id)     {         this.consoleName = name;         this.gameID = id;     }     public string displayGame()    {         return consoleName + " is the console I am playing";    }   Here is my child class.  class RolePlayingGame : Game {     int level;      public RolePlayingGame(string name, int id, int lv) : base(string name, int id)     {          this.level = lv;     }      // override method for displaying. meant to display what the game class displayed and "I am level " + level }


Is it possible to have 2 git repositories in one directory?  I'd think not, but thought I'd ask.  Basically, I'd like to check in my home directory config files (e.g. .emacs) which should be common across all of the machines I work on, but have a second repository for local files (e.g. .emacs.local), which contains machine-specific configurations.  The only way I can think of to do that is to have the local config in a subdirectory and ignore that subdirectory from the main git repository.  Any other ideas?


Will a key light, a back light, and white reflector as fill achieve a white background for portrait photography?

Good evening experts. I have a Nikon D5200 with 50mm f/1.8 lens.  Shooting fashion photography, and trying to get a white background.  Would 3 point lighting with a white reflector as fill give me a good result ?


Verb meaning "to present a fact/the facts"

I need a verb meaning "to present a fact/the facts".  E.g. "If you cannot lie you must word here".  I know using multiple words is easy but I need it to be one word.  I do not mean "to speak honestly" because that is too vague and unlike this word, it would not fit.  E.g.    If someone asks "How many people watched the 1966 FIFA World Cup Final: England v West Germany?"  If you said "I don't know." you would be speaking honestly but you would not be presenting the "truth/facts" about it.  If you said "32.80 million rounding to the nearest 10,000. You would be presenting the facts"


in Ubuntu, what is the difference between en_US:utf8 and en_US: when setting LANGUAGE

related question:     for setting  my existing Ubuntu 12.04 server has LANGUAGE as en_US: And I can set it to en_US:utf8 as well. What is the difference ?  existing configuration is, which i found by typing locale    LANG=en_US.utf8 LANGUAGE=en_US: LC_CTYPE="en_US.utf8" LC_NUMERIC="en_US.utf8" LC_TIME="en_US.utf8" LC_COLLATE="en_US.utf8" LC_MONETARY="en_US.utf8" LC_MESSAGES="en_US.utf8" LC_PAPER="en_US.utf8" LC_NAME="en_US.utf8" LC_ADDRESS="en_US.utf8" LC_TELEPHONE="en_US.utf8" LC_MEASUREMENT="en_US.utf8" LC_IDENTIFICATION="en_US.utf8" LC_ALL=   EDIT: right now LANGUAGE is en_US:. notice the colon at the end


I have to send out my passport for visa processing, can I fly with my expired driver's license and a photocopy of my passport

What it says on the tin: I'm a U.S. national adult and I need to send my passport out for visa processing this week. On August 10, I'm flying to San Francisco from Chicago and my passport is the only currently valid form of id I have.   Will I be able to get away with using my (expired) driver's license in combination with a photocopy of my passport?   Thanks!


How do we go about calculating a posterior with a prior N~(a, b) after observing n data points? I assume that we have to calculate the sample mean and variance of the data points and do some sort of calculation that combines the posterior with the prior, but I'm not quite sure what the combination formula looks like.


How much disk space do I need to upgrade Xcode on macOS Big Sur?

I'm on macOS Big Sur (11.2.3).  I would like to upgrade my Xcode to the latest version and have this disk space available $ df -h / Filesystem      Size  Used Avail Use% Mounted on /dev/disk1s5s1  234G   15G   30G  33% /  However when I go into the app store and attempt to upgrade, I get this message ...  Is this message a false flag?  Do I really need more then 30 GB to upgrade Xcode?


How do I get Markdown source code during a pending edit?

When trying to answer a badly formatted question, I tend to click "edit" to view the raw Markdown text, as this tends to be better formatted than the displayed text.  But during a pending suggested edit, I can't view this, so I can't see, for example on Stack Overflow, the correct format of the data layout.  Is there a way around this?  The following image illustrates this:


How can I pass file using javascript/jQuery/JSON/Ajax to Insert into database as a blob?

I'm Using front-end angularjs, there is a file upload option. When I upload a file it will pass to back-end Java Web services and It will insert into database. So this is the flow I have to do.  My problem is, How can I pass the file using JSON AJAX to the web services, Please let me know further any questions required.  Thanks in Advance.


Interpreting markedly large Logodds in logistic regression?

I am running a logistic regression in R and for some reason, some of my outcome variables o a ridiculously high log odds (ie -14), which corresponds to a p value of 0.9. But this does not make sense to me as e^-14 is an odds close to 0, which is well below no difference in odds. Can someone explain what is going on and why this is happening? I do notice that the ones that this occur on seem to be those with a very low in one group (ie: 22/22000), but still does not help me with interpreting this. Call: glm(formula = as.factor(Y) ~ BMI_NUM + SEX + AGE + RACE,      family = "binomial", data = df)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -0.6620  -0.1430  -0.1188  -0.0987   3.4692    Coefficients:                                 Estimate Std. Error z value Pr(>|z|)    (Intercept)                    -18.58551  549.85748  -0.034  0.97304    BMI_NUM                          0.02014    0.01187   1.697  0.08964 .  SEXmale                         -0.15877    0.16449  -0.965  0.33443    AGE_90ormore                    -0.43949    0.21364  -2.057  0.03967 *  AGE30_39                        -0.03423    1.02629  -0.033  0.97340    AGE40_49                         0.14823    0.61841   0.240  0.81056    AGE50_59                        -0.37233    0.41475  -0.898  0.36934    AGE60_69                        -0.30675    0.25620  -1.197  0.23119    AGE70_79                        -0.45086    0.20601  -2.189  0.02863 *  AGElessthan30                  -13.84406  783.82263  -0.018  0.98591    ######This One RACEAsian                       -0.64351    0.71603  -0.899  0.36880    RACEBlack                        0.67466    0.27934   2.415  0.01573 *  RACEOther                      -13.74345  540.78513  -0.025  0.97972    ######And this one


Monty Hall and conditional probabilities

I am a bit confused. I thought after Monty opens the door with the goat, conditional probabilities kick in and our sample space shrinks down to 2 doors instead of 3, and since they were all equally likely, the two doors now have probabilities of 1/2. But apparently, we are not supposed to use conditional probability here?  Thanks in advance


Show the limit of the sequence is $\sqrt{\alpha}$

Given: $\sqrt{\alpha}<x_1, \alpha >0, x_{n+1}=\frac{1}{2}\left(x_n+\frac{\alpha}{x_n}\right)$. Show $\lim_{n\to \infty}x_n=\sqrt{\alpha}.$ I have already shown the this is a monotonic decreasing function. Intuitively, I see in the end I get $\frac{1}{2}\left(\sqrt{\alpha}+\sqrt{\alpha}\right)$ but I'm not sure if I should keep going using $\lim$ notation or if I should switch to the definition of converging sequence.


Do I need a visa to travel to South Africa with an Australian convention travel document?

When travelling on an Australian travel document for refugees, do I need a visa to enter South Africa?


I'm trying to compile Alephone on Ubuntu 14.04, but I'm getting the issue that -lGL isn't found. Running whereis libGL.so returns nothing, even though I've installed libgl1-mesa-dev, mesa-common-dev, freeglut3-dev, and freeglut3. This started after installing the proprietary drivers for the AMD Radeon 2400 HD pro. Due to an error with the installation, though, I removed it, and I think that's the culprit. How do I get the library back?


How to draw a line linking two elements on HTML page?

I want to draw a line on HTML web page dynamically to connect two html elements, which can move on html page.  This action is something like connect two Rectangle's angle, like this:   Is there any way to achieve this?


About the 1.6x crop factor on a crop body

I have a 600D and a 7D and I use the kit lens  " EF-S "18-55mm  and the 55-250 mm , and I am thinking of buying a 24-105mm f4 IS USM L... so does the EF-S suffer from the same 1.6x crop factor as the EF? For example, the 24-105 IS USM L on an APS-C sensor is like 33mm to 168mm, and the 18-55mm has is equivalent to 28.8-88mm?


-24 Google Play Error on installing eBay

Whenever I try to install the eBay app from the play store I get a -24 error code: "unknown error when installing application". I have googled the error and I cannot find anything relating to this. Anyone know what this error is and how to fix it?  I can install other apps. I have an S4 on Kit Kat (4.4.2). I have forced stopped the play store and cleared the data on play services and play store.


What is the intuition behind the formula for the average?

Why is the average for $n$ numbers given by $(a+b+c+\cdots)/n$? I deduced the formula for the average of 2 numbers which was easy because its also the mid point, but I couldn't do it for more than 2 numbers.


Can lightning be used as a source of energy?

Is it possible to use lightning or thunder as a source of energy, with the help of dielectric breakdown and splitting?


Why do cockroaches burst from soapy water?

(careful, disturbing!)  I was experimenting with some stray cockroaches that ended up falling in my bath tub overnight (there is currently an infestation undergoing in my apartment building) and I found out that they are very easily killed by simply soaking them in soapy water.  I read that soap blocks some pores in insects' bodies which leads to suffocation, which appears to be the cause of death for my test cockroaches. But what I don't get is why about a half of them died with their innards bursting from their tail end. The water wasn't too hot to make them boil. Is it that they suffocate so hard that attempting to breathe they blow out their insides? Or is it the soap's reaction with the cockroach's bodily materials? Or is something else causing this?  I remember watching a documentary on injecting various insects with hydrogen peroxide which caused much more dramatic explosions, but it's not like I was injecting cockroaches, I just sprinkled them with soap water.


Problem to show image. Error Bounding Box

I'm trying to add some images, but When i compile it, an error is shown, and in the PDF the images are not showed.  Code I have used:  \begin{figure}[!h] % h-here, t-top, b-bottom \begin{center} \includegraphics[width=0.9\textwidth]{figs/Captura1.jpg} \caption{Figure 1: Screen-shot of a Wireless Follow-me-MP3 Controller} \end{center} \end{figure}   The libraries:  \documentclass{llncs} \usepackage{llncsdoc}         % the original package lncs \usepackage[dvips]{graphicx}  % for images   And the error that returns:    Thanks for all


We want to prove that $$\sum_{k=0}^n (-1)^k{n \choose k}^2=\ \Bigg\{                 \begin{array}                  \ \hspace{2mm}0 \hspace{20mm}\text{ if n is odd} \\                   \ (-1)^{\frac{n}{2}} {n \choose \frac{n}{2}}\hspace{6mm}\text{ if n is even}                 \end{array}$$ The odd proof is pretty easy by creating a bijection between odd and even subsets, but I cannot figure out the even proof. Any help would be significant!


Dynamically make div fill remaining space based on sibling height

I am trying to dynamically make a div fill remaining space in the window based on sibling height.   The idea is that if the header div changes height the page-wrapper will dynamically  change its height based on the remaining space. (avoid overflow if the header div changes height)   Header.sass  .header {   display: flex;   flex-direction: column;   width: 100%;   margin-bottom: 2rem; }   index.html

           ...

         div will fill remaining space

       Current solution  i understand i can achieve this using cal() however this will involve changing the hard coded value for $headerHeight if the header height changes  .page-wrapper {    height: calc(100vh - #{$headerHeight});    background-color: red; }


How to get the wifi password off a school wifi without going up to the router

I have an iPad for school and I want to see the password for the wifi so I can put it into my android phone but I'm not able to go up to the router unless I want to get suspended please help.


$x+1/x$ an integer implies $x^n+1/x^n$ an integer

Suppose that $0\neq x\in\mathbb{R}$ and $x + \frac1x\in\mathbb{Z}$. Prove that, for all  $n\ge1$, $x^n + \frac1{x^n}\in\mathbb{Z}$.  I can't figure out and understand the question. Can you give me some hints ?


WILL Ubuntu 18.10 operate on Toshiba Satellite-L505D

So far I'm at the boot up and creating user name smooth right now but I have not run browsers which is all I really want to do. I have 3gbs of RAM and I believe this is 2.12ghz have to look again. Anyone else running this? This was a PC the customer never came back to pick up.


People typically prefer the Lasso or other methods to stepwise regression.  What are the main problems in stepwise regression which makes it unreliable specifically the problems with forward selection , backward elimination and Bidirectional elimination?


I have hidden input type=file field, and i want to open its select dialog with javascript. I tried to fire click event on this element, but without luck.  Im using mootools.  $('input_id').fireEvent('click');   This is possible at all?


"...programs that each perform..." vs "...programs that each performs...": which is correct?

A source says that the word "each" should always be followed by a singular noun, but however I look at it in this sentence it just doesn't seem to fit:     foo [comprises] multiple binary programs that each performs a single task.   Should it be "performs" or "perform"?


How can i set domain name on my localhost?

I run Apache on my Ubuntu system in local network. there is more than 100 systems in the network so i want to set domain name on this system. How can i do this?  Thanks A lot.


I'm having a hard time to do this exercise. I'm using the definition for convolution but I'm stuck at the integral. Thanks in advance.  For $t>0$ consider $f_a(x)=\frac{1}{\sqrt{4 \pi a}}e^{-\frac{x^2}{4a}}$. Show that $f_a*f_b=f_{a+b}$  By definition: $(f*g)(x)$= $\int_{-\infty}^{+\infty} f(u)g(x-u) du$ One computes, $(f_a*f_b)(x)=$ $\int_{-\infty}^{+\infty} \frac{1}{\sqrt{4 \pi a}}e^{-\frac{u^2}{4a}} \frac{1}{\sqrt{4 \pi b}}e^{-\frac{(x-u)^2}{4b}} du$ $=\frac{1}{\sqrt{4 \pi a}}\frac{1}{\sqrt{4 \pi b}} \int_{-\infty}^{+\infty} e^{-\frac{u^2}{4a}}e^{-\frac{(x-u)^2}{4b}}$ I can't solve this integral. I tried using Gaussian Integral but still cant solve it.


Sci-fi story about a planet with a strange religion that makes people want to merge with a parasite and die

What's the name of a classic sci-fi short story about a planet where their religion makes people willingly merge with a parasite in a cave and die?   Outsiders can't understand why anyone would do such a thing, and when off-world visitors start joining the religion and committing suicide, two humans (a couple) with psychic abilities are sent to get their impressions.  They discover the reason everyone happily merges with the parasite is that, by merging (and slowly dying), in return they join a joyous mental community of every previous person who has joined, with overwhelming feelings of happiness--ecstasy, really.  All the psychic love is nirvana for the very sensitive female partner. She joins the religion and merges. She asks her partner to join the parasite as well but he refuses.  The male leaves the planet with the realization that their love for each other couldn't compete with the parasite-mediated mass love and happiness on the planet.  After finishing the story it brings up thought-provoking ideas on whether you would join such a community, about the ties of your love to your own family,and does organized religion gain our interest by similar promises of eternal happiness?


How to scale down Princes of the Apocalypse for a 3-adventurer party?

I recently just finished DMing Lost Mines of Phandelver with a 3 player party and it went great. Just removed a couple of enemies here and there and it was smooth. I ordered PotA and have started reading the handbook and I realised that the higher level encounters have extremely tough enemies!  I just don't want them to get to the Prophets or the Princes of Elemental Evil and getting absolutely crushed. I can remove enemies from encounters but:  To what point will I have to scale down the encounters so I don't get a TPK after 10 minutes of starting the adventure? How do I scale down a very powerful enemy so 3 players can handle it?   Related:


Why is that the all planets move in the same plane?(correct me if I'm wrong)  Why not some of them in anticlockwise direction and others in clockwise direction?


Why does Stolz- Cesaro fail to evaluate the limit of $\dfrac{n + n^2 + n^3 + n^4 + \ldots + n^n}{1^n + 2^n + 3^n + 4^n + \ldots +n^n}$,

I need to find the limit of the sequence  $\dfrac{n + n^2 + n^3 + n^4  + \ldots + n^n}{1^n + 2^n + 3^n + 4^n + \ldots +n^n}$,  My strategy is to use Stolz's Cesaro theorem for this sequence.  Now, the numerator is given by :  $x_r = n^1+ n^2 +n^3 + \ldots +n^r$, so $x_{n+1} - x_{n} = n^{n+1}$  Similarly for denominator $y_r = 1^n + 2^n + 3^n +\ldots +r^n$, so $y_{n+1}- y_{n} = (n+1)^n$  Using Stolz Cesaro, this limit is equivalent to   $\displaystyle \lim \dfrac{n^{n+1}}{(n + 1)^n}$, which diverges to $ +\infty$,  However ans given to me is $\dfrac{e-1}{e}$, Can anyone tell where is the error in my solution ?  Thanks.


When 0 is multiplied with infinity, what is the result?

Any number multiplied by $0$ is $0$. Any number multiply by infinity is infinity or indeterminate. $0$ multiplied by infinity is the question. Answer with proof required.


How would I change the ownership of a recently made file to root user ownership from its original owner? Every time I type in the following (below), I get a message saying that  it can't change the ownership.   For Example:  touch myfile chown root myfile


Bernoulli's equation and reference frames

So I was thinking about this while driving home the other day.  I've never been quite clear on why when you drive with the windows down air rushes into your car. I thought this might be explained by Bernoulli's equation for incompressible flow, but I ran into what seems to be a contradiction. If we consider the problem from the reference of the car, the air in the car is stationary and the air outside the car has a certain velocity. Then, Bernoulli's equation implies the pressure outside the car is lower than that inside the car. However, if we take the reference frame of the road, the air in the car is moving and then the pressure in  side the car is lower. Intuitively, this second situation seems to be correct since air apparently flows into the car (from high pressure to low pressure). However there seems to be a contradiction, as the pressure gradient depends on reference frame. So my question is what has gone wrong here? Is this a situation in which bernoulli's principle simply isn't applicable? Did I make some sort of mistake in my application of the principle?


Where can some worked problems in classical mechanics (and more specifically the Lagrangian and Hamiltonian formalisms) be found?

I've been looking for a textbook in classical mechanics that's readily available (like can be found in the library of James Cook University of Townsville, Australia) and full of fully-answered questions in the Lagrangian/Hamiltonian formalisms yet I can't find any. My first port of call was the Schaum's Outlines and Demystified series but the only member of these series I could find that was relevant was  which is difficult for me to track-down in real-life.   It would be particularly helpful if one could point me to a free eBook with this material.


Let $A,B$ be complex valued square matrices. If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute.   of this statement can be an easy application of the Cauchy product rule and the binomial theorem.   that this statement doesn't hold, if we restrict ourselves to $t = 1$.  So far I have been trying to use the fact, that $A$ and $B$ are infinitesimal generators to the semigroups $\{\exp(tA)\}$ and $\{\exp(tB)\}$ but I have had no success. Do you have any other hints?    Based on the idea of @Did, I came up with the following:  Series expansions give me: $$ \sum_{n = 0}^\infty \frac{t^n(A + B)^n}{n!} = I + tA + tB + \frac{t^2(AB + BA)}{2} + \sum_{n = 3}^\infty \frac{t^n(A + B)^n}{n!}  $$ and $$ \left(\sum_{n = 0}^\infty \frac{t^n(A)^n}{n!} \right) \left(\sum_{n = 0}^\infty \frac{t^n(B)^n}{n!} \right) = I + tA + tB + \frac{t^2A^2}{2} +  t^2AB +  \frac{t^2B^2}{2} + \sum_{n = 3}^\infty t^n c_n, $$ where  $$ c_n := \sum_{k = 0}^n \frac{A^k B^{n - k}}{k! n!}. $$  The comparison of both expansions gives $$ \frac{t^2(AB + BA)}{2} + \sum_{n = 3}^\infty \frac{t^n(A + B)^n}{n!}  = t^2AB + \sum_{n = 3}^\infty t^n c_n. $$ Division by $t > 0$ yields: $$ \frac{(AB + BA)}{2} + \sum_{n = 3}^\infty \frac{t^{n-2}(A + B)^n}{n!}  = AB + \sum_{n = 3}^\infty t^{n-2} c_n. $$ But I can't quite see, why the two sums $\sum_{n = 3}^\infty \dots$ should go to $0$ for $t \to 0$ yielding the desired equality $$ \frac{(AB + BA)}{2}   = AB . $$


Run multiple virtual machines on a virtual server

Is it possible to run multiple virtual machines on a virtual server? I am on a project and I want to run an Intrusion Detection System as distributed using many ubuntu virtual machines. Is it possible to be done on a virtual server which runs Ubuntu?


I think I might've accidentally removed the main Ubuntu repository after trying to remove a different repository. In the attached screenshot it shows what repositories I have, am I missing any? If I am, what would be the command to add it back?