I recently installed ChrUbuntu onto my Acer C7 Chromebook. I tried running the update manager from the terminal and I keep getting the same message  E: Malformed line 60 in source list /etc/apt/sources.list (dist parse) E: The list of sources could not be read.   Someone help me, I'm so new to Ubuntu.


how to make the tab visible for other users

Household information must only be visible to the director and staff.  Adoption requests are only visible by staff and directors.


hello my var directory is full and i want to add space to directory but i can't. I have a lot of space in the /home and root directory and I want to give it to /var I used GParted as a live CD but it did not allow me to increase or decrease and I do not know what to do and i'm not professional please help me


Convergence of a sequence whose even and odd subsequences converge

Suppose $\{a_n\}$ is a sequence such that the subsequences $\{a_{2n−1}\}$ and $\{a_{2n}\}$ converge to the same limit, say $a$. Show that $\{a_n\}$ also converges to $a$.


For integer $n \ge 3$, is $3^{2^{n-3}} -1 \equiv 0 \pmod {2^n}$

For integer $n \ge 3$, is $3^{2^{n-2}} -1 \equiv 0 \pmod {2^n}$ Here's what I am seeing: $$3^{2} - 1 = 2^3$$ $$3^{4} - 1 = 5\times2^4$$ $$3^{8} - 1 = 205\times2^5$$ $$3^{16} - 1 = 672,605\times2^6$$ I was trying to prove that this is true for all $n \ge 3$ but I am not clear how to do it. How would one establish the inductive step?


Why doesn't tar ask before overwriting existing files?

I lost a couple hundred lines of a Vim plugin I wrote and continue back up every so often because I extracted a tar file containing an older version. I decided not to use source control management when I wrote the plugin, since I only update it periodically.  Why doesn't tar ask before overwriting existing files by default? I'm guessing that there's some rationale behind why the default behavior is to overwrite files silently, since we usually want safety over speed and convenience. For example, we usually use #ifdef NDEBUG, not #ifdef DEBUG; similarly, I would expect tar ask me before overwriting any files, and for it to have some flag which I can use to tell it to overwrite files without asking me. Also, how can make it so that tar does ask me by default, without me having to give it any flags? I'm fine with using tools other than tar, if they support this safer default behavior.  Thank you for your time!


I realize this a difficult issue to solve but still, maybe someone can suggest a good compromise. When designing a website on my system the colors look the way I want but when checking them on the customer displays they look horrible (in some cases). Is there a way to solve this issue? What would be the best approach? Thank you.


How do I recover data from an encrypted Home directory

I opted to encrypt my Home during install, and now I would like to access my data from a LiveCD, unfortunately I'm having trouble following these . I get the error "mounting eCryptfs: [-2] No such file or directory"


What does 'exec {fd}</dev/watchdog' do in Bash

That is literal, {fd} isn't a placeholder. I have a script that does this, and does not source in anything, nor does it reference {fd} anywhere else.  Is this valid bash?  exec {fd}</dev/watchdog


In Clan Wars, what factors are used to determine the opponent clan?

In the clan wars matchmaking, what criteria is used to determine the clan that you are fighting against? Is it based on Clan Total Points (i.e. trophies), or something else?  If you win many wars in a row, does this mean you will get harder opponents?


I'm stuck in proving this statement of division

Can anyone help me prove if n divides a and n divides b, then n divides (ax + by).  I'm not sure if writing in the form of : a = nx and b = ny are still allowed to be used as x and y exists in the definition of the conclusion. I was thinking of using other variables such as: a = nc, and b = nd but I got stuck instead.


Sum of squares of residuals instead of sum of residuals

As I was working my way through my book about statistics, I came across the topic of linear regression. During the chapter the author begins with explaining that you want to minimize the residuals in order to make your y = a + bx as good a fit as possible: I do understand this, but halfway the chapter all of a sudden the residuals change into sum squares of residuals. Why is this done? I have been googling, but couldn't find the right answer. Who would like to help me understand why the sums of squares of the residuals is used instead of just the sums of residuals?  Kind regards, Bas


What is the formula for capacitance of two non parallel plates at an angle with each other?If the plates were parallel then the value can be calculated as (PermittivityX area of one plate)/distance between them.But what happens in case the plates are tilted at an angle?The question came to mind while trying to understand electrostatic separator.What would be the derivation of the formula for capacitance of two non parallel plates placed at an angle? I did get a method from  Equation 6 from the above link above helps but it is independent of the length of the plates which doesn't seem likely.


How to install/upgrade to Windows 8.1 RTM without a Microsoft account

When I installed Windows 8, I deliberately chose not to use a Microsoft account to sign in. I like to keep things separate, and just logon with a traditional local account. Any apps that require me to sign-in with my Live account, will have to prompt me to sign-in.  Now, I just updated to 8.1, but towards the end of the setup process, I was asked to sign-in with a Microsoft account or create one.  Unlike when installing Windows 8, there didn't seem to be any option to skip that step, or otherwise close the sign-in prompt and continue to my updated Windows installation. At least not that I could find.  This is particular annoying, when setting up computers for friends and family, whom I support. They may not have, or have any interest in getting, a Microsoft account and I'm reluctant to use my own.  I realize I can disconnect my Microsoft account after the fact, but is there really no way to install, or upgrade to, Windows 8.1, without being forced to create a Microsoft account? If there is, how does one go about that?


I know in php you are able to make a call like:  $function_name = 'hello'; $function_name();  function hello() { echo 'hello'; }   Is this possible in .Net?


What's the incentive to answer questions?

I am still new to this website but I am curious, what is the incentive for people to answer questions?  It seems like there is a much higher time effort of people to answering versus asking, which surprises me (from a pure utilitarian perspective).  For me the answer has boiled down to a few basic categories:   To gain reputation (this was novel at first and wore off after the first few days of using the site).  Also rep can always be gained by asking questions, with the benefit of also obtaining information. To give back.  I find myself doing this whenever I come to SO to search for/ask a question, and see something on the landing page I can answer. To correct the answer to an existing question.  This happens when I find the answer on SO and after trying it find it to be incomplete/not fully correct. Boredom.   I'm surprised how many people are willing to contribute so much time in answering questions with seemingly minimal reward.  Is it just that the community is that friendly and people are acting out of the goodness of their hearts?


Enable backspace shortcut for back in chrome

It was with disbelief that I noticed Chromium has decided to , a shortcut which has been established almost universally across all browsers for decades.   This really, really irritates me as I navigate 'back' probably hundreds of times a day and backspace is by far the quickest way to do it.  I'm aware there are other options such as clicking the back button, Right click-> Back or Alt+Left, but all seem a little awkward for something as simple as going back.   Is there any way to enable the shortcut? Preferably without an extension?


How to find the name needed to launch app from terminal?

I read several questions similar here, but none answered my question. For example I have Vmware player installed, and I would like to launch it from terminal. vmware + TAB gives me this list:  vmware-authd              vmware-gksu               vmware-license-enter.sh   vmware-rpctool            vmware-user-suid-wrapper vmware-authdlauncher      vmware-hgfsclient         vmware-modconfig          vmware-toolbox-cmd        vmware-vmblock-fuse vmware-checkvm            vmware-hgfsmounter        vmware-mount              vmware-uninstall          vmware-xferlogs vmwarectrl                vmware-installer          vmware-networks           vmware-unity-helper        vmware-fuseUI             vmware-license-check.sh   vmware-ping               vmware-usbarbitrator         So I guess it's one of these I am supposed to launch, right? Some things I tried, but didn't give me good results: locate vmware, whereis vmware.  Is there some kind of general way (using just terminal) on how to find exact name needed to launch certain program? I know usually it's just typing program name, but as you can see in this case it does not work.


Why does the mirror modifier disappear when I merge objects together?

For starters, I started studying blender it's been just a couple of weeks.  So, just for fun, I started modeling a key using a torus, a cylinder and a cube, as you can probably figure out by the images below:        It was all fun and games 'till I tried to merge the objects into one using Ctrl+J, weirdly the result was this:    I've tried changing the sequence of selection when I was merging, but it didn't solve the problem. That little thingy still disappeared. I think this error is due to the mirror modifier I used on the last piece of the key, and maybe when I merged it something wasn't compatible.  I also tried adding the same modifier to the other pieces but the result was the same. The last piece in detail can be seen in the link with the screenshots.  If anyone would kindly explain what's going on and hopefully come up with a solution I would be very much appreciated.


i want to turn an open edge loop into a single vertex, how do i do this

. i know this may have been asked before but isimply can't find it.


Something wrong with the Software center?

I just upgraded to 16.04. I notice that the Software center loads extremely slow. And that a lot of packages aren't there. They're supposed to, but a search gives me 'No application found'.   Is that a bug or feature?


Find an example of a non-surjective field endomorphism

Can we find a field $K$ and an endomorphism $f$ of $K$, such that $f$ is not trivial and $f$ is not surjective? In other words, can we find an endomorphism of $K$ which is not an automorphism?


I've been googling for hours now but can't find a sure or helpful answer. I need to disable high-volume outgoing UDP from my server.  I'm trying to configure APF because of the RAB functionality, but fail because the module ipt_recent is not enabled. No luck with modprobe either.  modprobe: ERROR: ../libkmod/libkmod.c:507 kmod_lookup_alias_from_builtin_file() could not open builtin file '/lib/modules/3.13.0-042stab103.6/modules.builtin.bin' modprobe: FATAL: Module ipt_recent not found.   I have installed Deflate, but it was before the attacks happened so it's probably not working.  Can someone point me in the right direction to either fix the ipt_recent module, or a completely different angle to deny the outgoing UDP flood?


I need help to understand why this piece of code works correctly in python 2 but it doesn't work for python 3.  res = 76460188758730153884232119087179527041998988911761118644170793575 while res > 31:     print(res%31)     res = (res - res%31)/ 31   In python 2 the result of res%31 is: 23, 17, 2, 28, 17, 17  In python 3 the result of res%31 is: 23, 4.0, 17.0, 6.0, 21.0, 22.0, 18.0, 14.0  I'm having problems with long numbers in python3, but I can't solve them.  Thanks in advance,


I want to use OSM data to make network dataset in ArcGIS 10.2. However, this is not installed successfully. It keeps telling me I don't have ArcGIS 10.2 that is exactly what I am using now. I think others have same issues. Anyone help me to resolve this problem? Or is there any way to make network dataset without ArcGIS Editor 10.2 for OSM?  Further information for this issue, I am using 10.2.2 desktop with 64 bit. And this is concurrent user version supported by my school for the researcher.  I can use all of functions and extensions with this privilege. Also, I followed the direction indicated below:   As you can see comments in the website, other people have same issues like me.


Complete reset windows 10 system-wide user keyboards

My Windows 10 system keyboards are messed up since I received this new laptop.  I mean there are 5 keyboards and only 2 are necessary.  Is there any way to completely reset keyboards into two only , ar-sa for Arabic and en-us for English ?? Is this possible through system registry or a system shell command ?


Can't update GCC version from 4.9.2 to 5.4 or 6.2?

I am trying to update gcc version in debian pc, but no luck yet.  I have followed the instruction given in  and changed the last command to apt-get install gcc-5.4 g++-5.4 but it seems no installable package is available for latest gcc verion. Even aptitude search gcc-5 does not list anything.   EDIT  : Adding output of cat /etc/*-release  PRETTY_NAME="Debian GNU/Linux 8 (jessie)" NAME="Debian GNU/Linux" VERSION_ID="8" VERSION="8 (jessie)" ID=debian HOME_URL="http://www.debian.org/" SUPPORT_URL="http://www.debian.org/support" BUG_REPORT_URL="https://bugs.debian.org/"


On Ubuntu 12.04 LTS x64, we'd like to remove the i386 foreign architecture it comes with, but I don't see a dpkg command to do this cleanly.  In , the user is advised to just remove the line from /etc/dpkg/dpkg.cfg.d/multiarch, I can do that (or even remove that file altogether), but I was wondering whether there is a more "appropriate" way to do that.  The reason we want to do that is that we maintain a large number of continuous integration agents using Puppet and want to stick to "pure 64". We install our own Debian packages from our own maintained repository and this fails unless we provide an i386 version of the package. I'm aware that it's possible to override the architecture in the specific repository configuration but it'll be cleaner to just disable the non-64 architecture altogether.


What is the antonym for the phrase "role model"?

"Role Model" is used in a positive light, and thus doesn't fit the sentence below.  Bob saw his incriminated elder brother, and made a ____ out of him.


Rules for Arithmetic with Two Equivalent Infinities

I believe $\infty-\infty$ is indeterminate, but is $\aleph_0-\aleph_0$ zero? In Altar Ego's response to  those two infinities must've had different ordinality or cardinality or whatever measurements of size.   Aleph Null minus itself could be interpreted as the size of the set of all natural numbers minus the size of the set of odd numbers, for example. There's a one to one correspondence between each set since they have the same cardinality, it doesn't matter that one set seems "denser". To me intuitively, no matter the size any exact number minus itself should be zero. Is this an exception and if so why?   What about other arithmetic like Aleph Null divided by itself? (I know, infinity isn't a number but)


Reading HTML Contents Into Javascript String

I have been using   $autoComplete = file_get_contents("stackoverflow.com");   When using PHP, but I now need a Javascript equivalent. Is there one..  I need to read a txt file that is accessed via URL..  I obviously have been googling, but nothing seems to work.  Any help would be great..


I was wondering is it possible to prove 1+0=1(or 0+1=1)? If yes! how does it look like! Does it even make sense to ask for proof here? My google searches didn't turn up anything.  Thanks.


Probability of Various Combinations of Weather

There's a 10% chance it will rain today. There's a 15% chance it will snow today.   What percentage chance is it that it will:   Both rain and snow (it can both rain and snow at the same time)? Neither rain nor snow? -   Raining and snowing are independent of each other.  EDIT: (ADDED)   Rain or snow but not both?


Polymorphism cast doesn't work for my classes

Sorry for asking I believe a repeated question, but I can't figure out the problem here, maybe my understanding of this is not correct. Setup     class Job {     public:         virtual bool createJob() {             return false;         }     };      class Limit {     public:         virtual bool updateLimit() {             return false;         }     };      class Base : public Job, public Limit {     private:         std::string cx;     public:         virtual ~Base() {          }     };      class DerivedJob : public Base {     protected:         std::string ax;         std::string bx;         std::vector<std::string> vx;     public:         bool createJob() override {             return true;         }     };      class DerivedLimit : public Base {     protected:         std::string ax;         std::string bx;         std::vector<std::string> vx;     public:         bool updateLimit() override {             return true;         }     };  Should work?     Base parent;      auto stat = static_cast<DerivedJob&>(base);     std::cout << "JOB: " << std::to_string(stat.createJob());     std::cout << "LIMIT: " << std::to_string(stat.updateLimit());      auto dyn = dynamic_cast<DerivedJob&>(base);     std::cout << "JOB: " << std::to_string(dyn.createJob());     std::cout << "LIMIT: " << std::to_string(dyn.updateLimit());      auto stat1 = static_cast<DerivedLimit&>(base);     std::cout << "JOB: " << std::to_string(stat1.createJob());     std::cout << "LIMIT: " << std::to_string(stat1.updateLimit());      auto dyn1 = dynamic_cast<DerivedLimit&>(base);     std::cout << "JOB: " << std::to_string(dyn1.createJob());     std::cout << "LIMIT: " << std::to_string(dyn1.updateLimit());  I Tried many examples and read many posts, but when I add string and other garbage to my derived classes, it stops working, maybe my fundamental understanding of this is incorrect? Don't be to harsh, I am only a junior in c++ :D Thank you for your time explaining these things to me. Additional question How does dynamic casting work? Example class Device { private:   Base _base; public:   Device(int x) {     if (x == 5) {        DerivedJob object;        object.test = 5;        object.test2 = 1;        _base = object;     } else if (x == 7) {        DerivedLimit object;        object.test = 5;        object.test2 = 1;        _base = object;     } ...   } }


Checking residuals for normality in generalised linear models

uses generalised linear models (both binomial and negative binomial error distributions) to analyse data. But then in the statistical analysis section of the methods, there is this statement:     ...and second by modelling the presence data using Logistic Regression   Models, and the foraging time data using a Generalized Linear Model   (GLM). A negative binomial distribution with a log link function was   used to model the foraging time data (Welsh et al. 1996) and model   adequacy was verified by examination of resi- duals (McCullagh &   Nelder 1989). Shapiro–Wilk or Kolmogorov–Smirnov tests were used to   test for normality depending on sample size; data were log-transformed   before analyses to adhere to normality.   If they assume binomial and negative binomial error distributions, then surely they shouldn't be checking for normality of residuals?


Outside Tokyo: Where for flora, landscape, nature?

As I'm ruling out Tokyo in this post, this doesn't duplicate .  Please recommend where to enjoy picturesque backwoods? Criteria:   No dangerous animals or untamed boondocks. No  or snakes. I won't drive, and must rely on public transport and walking less than 5 km in total.  No shrines, temples or any religious edifice. OPTIONAL: I fancy  , the more  the better.


AES-CBC with zero IV and a unique first block

Is it safe to generate the IV for AES-CBC as the following?   It's like the real IV is all zeros. The first block of data will be a low-entropy but unique data. Once the first block is encrypted, the ciphertext will look like a random sequence of bytes that will automatically serve as IV of the second block   This would allow to save space since we don't have to store a "real" IV in addition to the low-entropy data of the first block that we need to store anyway.  Is it safe to to this thing?


Boot-repair after shrinking Windows partition not successful - boot info says there is no Linux system

I have a VAIO laptop, with a dual boot Windows 10 / Ubuntu 16.04.   I wanted to resize the partitions to increase the disk space allocated to Ubuntu, so I tried to shrink the Windows partition from Windows, using AOMEI partition assistant. After the software was done, the computer rebooted, but I ended on the GRUB command-line prompt, meaning (I think) that it was not able to boot either Windows nor Ubuntu. I tried using boot-repair on a live USB. It said that the repair was successful, but I still cannot boot my computer. It gave me a Ubuntu pastebin address to get help:  I tried to follow the instructions on the following threads:  ,  , but I don't remember on which partitions the two OSs were mounted, and I didn't want to make more damage. Finally I ran GParted from the live USB, here is what it gave me:   The size of /sda4 corresponds to the size that the shrunk Windows partition should have, and the size of the unallocated space corresponds to the size of the space left empty by the resizing of the Windows partition plus the size of the previous ubuntu partition.   Does someone have an idea of what I should do ? From what I can guess the Ubuntu partition has been quite damaged (if I remeber well, it was on /dev/sda7, but there is no such partition any more, and on line 236 of the boot-info file is written that there is no linux OS), but I hope that I am wrong!


CloudFlare CAPTCHAs are blocking CDN content

When I changed my avatar on  a few days ago, it briefly displayed at the top, then after a few minutes disappeared from the toolbar.     Later it disappeared from my questions and profile as well. Further inspection revealed that it was hidden behind an HTTP 403 forbidden result with a CAPTCHA, courtesy CloudFlare. Answering the CAPTCHA restores functionality, for now.  This is the same problem as . Randomly knocking out resources is unacceptable for a CDN. Please address this.


I have a question if anyone of you can help me. Anyone of you know what linux consume fewest possible resources? I have old laptop with:   CPU: T550(it's dual core but have some problem with bios and use just one core) RAM: 2GB GPU: Integration   I want to know which Linux can I put on this laptop.. Because any Linux I already know runs so slowly...  Thanks :D


when taken 5 root of big number gives wrong answere in js

When I take the 5 root of a big number, js gives me a wrong answer   var pow = 5; var A = 133; var B = 110; var C = 84; var D = 27; var E;  E = Math.pow((Math.pow(A, pow) + Math.pow(B, pow) + Math.pow(C, pow) + Math.pow(D, pow)), 1/pow);  console.log(E)    This should give 144 but gives 144.00000000000003 5 root of 61917364224 = 144


Proxied nodejs site not loading over HTTPS in Apache

I have a node server running on a port and I am using Apache to proxy pass to it. I have setup SSL on the virtual host and HTTP works fine but HTTPS times out and says Connection Refused  Config:   <VirtualHost *:80>         ServerAdmin webmaster@test.co         ServerName dl.test.co         ProxyPass / http://localhost:8004/         ProxyPassReverse / http://localhost:8004/ </VirtualHost>  <VirtualHost *:443>         ServerAdmin webmaster@test.co         ServerName dl.test.co         ProxyPass / http://localhost:8004/         ProxyPassReverse / http://localhost:8004/          SSLEngine on         SSLProtocol all -SSLv2         SSLCipherSuite ALL:!ADH:!EXPORT:!SSLv2:RC4+RSA:+HIGH:+MEDIUM          SSLCertificateFile /etc/apache2/ssl/ssl.crt         SSLCertificateKeyFile /etc/apache2/ssl/ssl.key         SSLCertificateChainFile /etc/apache2/ssl/sub.class1.server.ca.pem </VirtualHost>


Declaration of for loop with double greater than operator

I came across this line of code in a reseach paper for "":  for (int d = n>>1; d>0; d>>=1){...}   (int) n is an input variable.  I am familiar with for-loops and c++ in general. So I just could figure out the parts n>>1 and d>>=1. I havent seen this before. Could someone provide a short explanation? Thank you.


What is the difference between"energy saving" and "energy savings"?

When I read the papers, I sometimes see the phrases energy saving and energy savings. I don't understand how they are different. Compare these sentences:     1) However, the maximum energy saving obtained by the OTMR scheme depends on appropriate speed setting for the processing units, which in turn is determined by the system power characteristics.       2) As we discussed earlier, the processing speed for the ﬁrst two processing units in OTMR systems is critical in energy savings.      3) However, if it is possible to reduce the voltage at all by running slower, then there will be a net energy savings per cycle.   How are they different?


How is "interpretation" used differently in propositional vs. first-order logic?

I am confused on the usage of the word "interpretation" and/or "model" when it comes to propositional logic versus first-order logic because there are so many conflicting / unclear notions that I would like to clear up.  My current understanding is as follows and I would like any corrections / elaborations on where I am confused:  I am using the definition of a "model" being an interpretation that satisfies a formula / set of formulas. In the case of a theory we can treat its axioms as a set of formulas, and so a "model of a theory" meaning any interpretation that satisfies the set of axioms of that theory.   In propositional logic an "interpretation" is an arbitrary assignment of true/false values to all the atomic propositions in the alpha set. For example $p_0 = T, p_1 = F, p_2 = T, p_3 = F, ...$ and so on. This tells us which row of any given truth table we should look at when evaluating the "truth value" of any fixed proposition.   But then in first-order logic, it seems like an "interpretation" is no longer some specific assignment of values to non-logical terms, but rather entire number systems like "the natural numbers," which would also be a "model" of, for instance, peano arithmetic, which satisfies its axioms.  Why is this? Why wouldn't we say "boolean variables" model propositional logic then? Why wouldn't we say some specific assignment of values satisfy first-order logic / PA / etc?   Why is interpretation seemingly being used differently in both cases? If an interpretation is what we'd call the specific T/F assignments in propositional logic, then what do we call the choice of a boolean system in the first place?  And more of a side question, but then what of propositional logic systems like natural deduction which have no axioms at all? What models "satisfy" it if there's no set of axioms to represent the theory?


If an electric charge suddenly appears will an electric field be present everywhere instantaneously?

This question has been asked many times in conjunction with a suddenly disappearing sun. The common reaction to this is that it takes a while for the spacetime curvature to be changed around it. In accordance with special relativity, so it is said. An instantaneous change from curved to flat by means of a disappearing mass doesn't mean though that information is traveling faster than light. Why not? Simply because you can't remove a mass instantaneously. This renders the question meaningless maybe, but you can do it in the imagination. If the mass suddenly is not there anymore, there will not emerge a gravitational wave. Only when you move it this will happen. Which is needed to transmit information. If I move the mass fast to and fro, a wave will emerge, so you can convey information with it. But not if the mass suddenly ceases to exist. In connection with charge and the electromagnetic field surrounding this charge, I've read about experiments to uncover if the change in the field surrounding the charge is instantaneous. This means that there is a doubt for that case. The same arguments I gave above can be applied to the electromagnetic field. Will an electromagnetic field instantaneously appear if charges appear in the creation of a positron-electron pair (or disappear when they annihilate)? See also  article (written in 2006 by W. Engelhardt, retired from Max-Planck-Institut für Plasmaphysik, D-85741 Garching, Germany), in which it is written:  the instantaneous transmission of both energy and information over macroscopic distances is feasible by using the quasi-static fields which are predicted by Maxwell’s equations.  I don't think that the conclusion drawn there (or by me) is correct though (information can't travel at the speed of light). Even if you could create single electrons (contrary to an electron and a positron, appearing at a point), and the field of that electron would be present at the same time everywhere, you could use them to transmit information: when I create one electron per second it's an A, when I create two per second, it's a B, three per second a C, etc. but is Engelhardt mistaken too? Is it because he's retired..., maybe?


Why is a polynomial defined the way that it is defined?

For instance, why are only non-negative integer powers of a variable allowed within the scope of the definition of a polynomial? I am thinking there must be some reason within the developmental context of the definition but I am not sure what it is.


E/Var of a random variable on three events

E, F and G are independent events with probabilities $\frac12,\frac14,\frac15$   of occurring. Let $X$ be the number of events that occur.      A. Describe $X$ and calculate its expectation and variance.   B. The same, but this time assume the events are mutually exclusive.   I really don't know how to proceed. I have tried to set the support of $X$ as $\{0,1,2,3\}$ and then write the probability of each event as $P[E](X=1)=\frac12$ but I don't think it's the real solution.


Why did Euler use e to represent complex numbers?

From Euler we've learned that $z=re^{i\theta}$.  And it's easy to see that $|z|^2=r^2$, since $re^{i\theta}\times re^{-i\theta}=r^2$.  Why must we use e to represent these numbers correctly? It seems that I could arbitrarily choose a different exponent $z=r\pi^{i\theta}$ and get the same size for $z$ as I did before: $|z|^2=r\pi^{i\theta}\times r\pi^{-i\theta}=r^2$  What did I miss?


Pros and cons of cheap studio strobes vs. hotshoe/speedlight flash for portraits?

Not so long ago, AC-powered studio lights were the only option for serious studio photography, and low-cost starter sets like  this ¹ were a fixture in every neighborhood camera shop. With the digital revolution and explosion of consumer photography, speedlight-style² portable flash is increasingly sophisticated, cheap, and powerful.  If I'm building up a new portrait studio, what are the advantages and disadvantages of cheap "monoblock" studio strobes like those in that kit vs. speedlights? In what situations would one choice have an advantage over the other? I assume the AC-powered strobes are much more powerful than a typical³ speedlight; how much more powerful — and when does it matter?  What about as we go ? Do the pros and cons change if I have a lot of money to spend? Are there advantages that expensive studio lights have that the low-end kit doesn't offer?  Fundamentally, if you're buying a digital camera, buying a cheap  (perhaps used and out-modeled) interchangeable lens camera gets you into a whole different level of system, better for really learning photography than than a fully-automatic point and shoot which might even cost more. Do studio strobes offer similar advantages in what you can do, or is it a different situation?    1. Chosen at random. Not an endorsement. / 2. We sometimes  hotshoe flash, but in this case they might be in a cold shoe controlled wirelessly. / 3. Extra question: products like the GN80 bare-bulb, separate-power-pack yet hotshoe mount  seem to blur the lines; how do this and similar products fit in?


How would the Compton Effect be if an electron absorbs 100% of the energy of the incident photon?

How can I prove that the relativistic energy and the impulse cannot be conserved if an electron, which is essentially free, absorbs all the energy of the incident photon?


How to split multiple lines into equal parts or overcome split tool limitation using Basic or Standard license?

I would like to split multiple lines into equal aproximately 10m lengths. (Line length / 10m = number of segments) The split tool can only split one selected feature at a time. To overcome this I can merge multiple lines into a single multigeometry feature then run the split tool on the merged line. Works fine until I run into what seems to be a limitation - the split tool can only split into a maximum of 999 equal parts. When I enter a higher number the OK button goes dim.   Is there a workaround to overcome this limitation or another way to split mupliple lines into equal parts?  Basic or Standard licence only.   Figure 1 - Split Tool dialog showing 999 equal parts:     Figure 2 - Split Tool dialog showing 1000 equal parts:


JUnit 4: Set up things in a test suite before tests are run (like a test's @BeforeClass method, just for a test suite)

I want to do some functional testing on a (restful) webservice. The testsuite contains a bunch of test cases, each of which performs a couple of HTTP requests on the webservice.  Naturally, the webservice has to run or the tests will fail. :-)  Starting the webservice takes a couple of minutes (it does some heavy data lifting), so I want to start it as infrequently as possible (at least all test cases that only GET resources from the service could share one).  So is there a way to do set up me the bomb in a test suite, before the tests are run like in a @BeforeClass method of a test case?


MODIS-Sphere to WGS84 coordinate system in ArcGIS

I want to overlay two global raster datasets on land use which use different coordinate systems (MODIS-Sphere & WGS84) using ArcGIS Desktop. There seems to be no direct transformation option from MODIS-Sphere to WGS84. It seems to me that I would have to use a custom transformation. However, for that I would need some sort of transformations dialogue/script which I don't have. Or am I missing something?!  Does anyone have any idea on which steps to take?  The dataset I want to transform is   Format: ESRI GRID Projection: Goode's Homolosine Equal-Area Projection Geographic Coordinate System: MODIS-Sphere  I want to transform this dataset so that it matches the other one (which uses GCS_WGS_1984 as spatial reference and D_WGS_1984 as datum)


We have seen that Madara had awakened his left eye to a Rinnegan. But Nagato's both eyes have Rinnegan when they are transplanted.  How did Madara Uchiha give his Rinnegan to Nagato?


Entire non-constant function $f: \mathbb{C} \rightarrow \mathbb{C}$ such that $f(cz) = f(z)$

I would like to find an entire, non-constant (complex) function $f$ with $f(cz) = f(z)$ $\forall z \in \mathbb{C}$ for some $c \in \mathbb{C}$. This is pretty straightforward if $|c| \neq 1$, but I am going to establish a few properties of $f$ first: Because $f$ is entire, we know that it is continuous on the unit disk $B_0(1)$ and thus bounded on $B_0(1)$. Because $f(cz) = f(z)$ for any $z$, we can repeatedly plug in $cz$ in to the right side and get $f(c^k z) = f(z)$ $\forall k \in \mathbb{N}$. Suppose $|c| > 1$ and let $z_0 \in \mathbb{C}$. Then $|z_0| < |c|^k$ for $k \geq N$ because $|c|^k$ diverges. This can be rearranged to $|\frac{z_0}{c^k}| < 1$, so $\frac{z_0}{c^k} \in B_1(0)$ and with the second property $f(z_0) = f(c^k \cdot \frac{z_0}{c^k}) = f(\frac{z_0}{c^k})$. This means that for any $z_0$, $f(z_0)$ corresponds a value on the unit disk (whose values are bounded) and thus $f$ is bounded. Since $f$ is entire and bounded, Liouville's theorem tells us that $f$ is constant. So for any $c$ with $|c| > 1$, there is no non-constant function $f$ with this property. The case $|c| < 1$ follows analogously with $|z_0| < |\frac{1}{c}|^k$ for $k \geq N$. Now suppose $|c| = 1$. Write $c$ in polar coordinates: $c = e^{\varphi i}$ with $\varphi \in [0,2\pi)$. If $\varphi \in \pi \mathbb{Q} := \{\pi \cdot q | q \in \mathbb{Q}\}$, we can again write $c = e^{\frac{p}{q}\pi i}$ with $p,q \in \mathbb{N}$ and $\text{gcd}(p,q) = 1$. One can now take $f(z) = z^{2q} \in \mathcal{O}(\mathbb{C})$ (meaning $f$ is entire) and with this $f(cz) = (cz)^{2q} = (e^{\frac{p}{q}\pi i})^{2q} \cdot z^{2q} = e^{2p\pi i} \cdot z^{2q} = z^{2q} = f(z)$ so $f(z) = z^{2q}$ is of the desired form. The case that gets me stumped is when $\varphi \not\in \pi \mathbb{Q}$ or if there is a much easier way that I am overlooking. In any way, I am interested if there are any more such functions with the properties I want (but especially for the case that is still missing). For orientation, I am an undergraduate that has just taken his first complex analysis course this year. Any help is appreciated!


What I Think I Know: Hydrophilic and hydrophobic things repel each other. Since the cell membrane contains hydrophobic tails, it is difficult for hydrophilic molecules to pass through the cell membrane.  Question: Why don't the heads of phospholipid bilayers repel hydrophobic molecules? In other words, if the phospholipid membrane has both hydrophilic and hydrophobic portions, why do only the hydrophobic portions act as repellents?  Stipulation: I need a quotation from a textbook, university, or other credible source.  Evidence of Prior Research:  : This question has a comment that links a graph from a textbook. I can't understand the graph by itself. There are no other references.  : All references discuss the topic, but none answer the question.  I understand that this topic is addressed quite frequently, but the question I'm asking is never answered. Texts tend to say something like, "Ions can't get through the core because of their charge" and completely gloss over the concept of lipids getting through the heads. Please don't dismiss this as a homework question that I didn't take the time to research. This is my second try asking this question (on this site); I have spent hours trying to find an answer.


I can't overstate the significance of "instantly"! I'm trialling a working process that makes very heavy use of spaces. Heavy enough that any delay when switching spaces is making it essentially unworkable.  I made a change — turned "Reduce Motion" on — which I think sped things up, but nowhere near enough. I need the delay to be as little as it is when, for example, switching windows within the same app+space i.e. instant.  To demonstrate the issue, open a few applications across a couple of spaces, then try to cmd-tab between a) apps on different spaces b) apps on the same space. Note that, even with "reduce motion" enabled, switching is much faster within a space.  Is there any setting I can change, or third-party app, that will totally eliminate the delay? Failing that, can anyone familiar with macos programming weigh in on whether this is even possible or not, or whether its something imposed by the OS which there is no chance of changing at all (without hacking the os binary!)  I'm running a MacBook Pro Retina Mid-2014, macOS 10.13.3, with 10 workspaces configured.  My preference would be for the animation to be totally eliminated for every switch-spacing mechanism. However, my main method is going to be using Ctrl+[1-0] to switch between 10 workspaces.


US domestic flight without passport for a foreigner

I’m a foreign student and I lost my passport. I’d like to travel from Chicago to New York by plane. Can I use a copy of my passport or my student card as an ID?  I checked the TSA website already.


Is a measure for a sigma algebra determined by its values for a generator of the sigma algebra?

If the value of a measure on any subset in a generator of a sigma algebra is known, will the measure for the sigma algebra also be uniquely determined? Thanks!


I want to prove that every normal planar graph has a straight-line embedding.   First, I assume that the planar graph $G$ is maximal planar, i.e the number of edges is $3n-6$ for $|G|=|V(G)|\ge3$. If the graph is not maximal planar I simply add some edges until it is maximal. I also know that all faces form triangles.  Now I want to prove the result with induction with respect to $n$.  $n=3:$ This case is trivial, it is just a triangle.   $n-1\rightarrow n$. I assume I know that the embedding works for a graph with $n-1$ vertices. I do not know hot to conclude. Intuitively it is clear to me because it is nothing more than some triangles which I clue together.  Maybe you can help me.


How long does it take to render a 10 sec long YouTube intro in Blender?


Finding the expectation of $\hat \theta$, if $\theta = \max(X_1, ..., X_n)$

I am trying to make $\hat \theta$ an unbiased estimator for a uniform distribution on $(0, \theta)$. So I am given the fact that $\hat \theta$ is the MLE for $\theta$, but I need to show that if I choose $c_1$, then the estimator becomes unbiased. What gets me stuck is the fact that $\hat \theta = \max(X_1, ..., X_n)$.   Basically, how do I deal with the "max" part of the problem given that I want to show that $\hat \theta$ can be unbiased if we choose $c_1$ such that $E[\hat\theta]$ = $\theta$.   ie. I need to find $c_1$ such that $\hat \theta = c_1 \max(X_1, ..., X_n)$ such that $\hat \theta$ is unbiased (aka $E(\hat \theta) = \theta)$  Thanks!


Obtaining an object's type in an extension method on compile-time for generic type usage

I have the following extension method in order for down-casting, mapping parent's properties to child with AutoMapper  using AutoMapper; /**/  public static TChild Downcast<TChild, TParent>(this TParent parent) {      var config = new MapperConfiguration(c => c.CreateMap<TParent, TChild>());     var mapper = config.CreateMapper();      return mapper.Map<TChild>(parent); }   It works pretty well as expected (sample usage):   var parent = new Parent{ Name = "Bob" };  var child = parent.Downcast<Child, Parent>();  ...  Assert.AreEqual(parent.Name, child.Name);   What I'm curious about is, I feel like there should be some way to actually have information about the compile time type of parent, without supplying it, after all, the class is where I call from, and it is-(should be) known at compile time.  So are there any way that I'd simplify this into something such:  public static TChild Downcast<TChild>(this TParent parent) where TParent : caller {      var config = new MapperConfiguration(c => c.CreateMap<TParent, TChild>());     var mapper = config.CreateMapper();      return mapper.Map<TChild>(parent); }   And use it such:  var child = parent.Downcast<Child>();   Thank you for your time.


Ubuntu MATE freeze on logout/shutdown/reboot when running on Intel graphics card

I have installed Ubuntu MATE 16.04 on a new Alienware 13 machine. My problem is that shutdown/reboot/logout stopped working properly and the system freezes one I try to do shutdown. The problem started after I tried to suspend the system and it lead to a freeze too. After extensive searching I found that this freeze on shutdown only happens when the system is switched to Intel card (it shuts down fine when Nvidia is on). Does anybody know the fix for this?


Distribution of $\mathbf{v}^{\top} \Sigma^{- 1} \mathbf{v}$, when $\mathbf{v}$ is a multivariate normal with covariance $\Sigma$?

What is the distribution of the quadratic form $\mathbf{v}^{\top} \Sigma^{-1} \mathbf{v}$, when $\mathbf{v}$ is a multivariate normal with covariance $\Sigma$ and zero means? I suspect this is related to the . In general there is no simple closed form expression for the distribution of a quadratic form of this type. But here the quadratic matrix is constructed with the inverse covariance matrix, which I hope makes the result simple.


On my Windows 7 system I installed via  from Fonts.com:   The font does not appear in C:\Windows\Fonts. However, it shows up in certain desktop applications, for example  as: Sabon Next Com Display  My intention was to use the font in a LaTeX document test.tex:  \documentclass{article} \usepackage{polyglossia} \setromanfont{Sabon Next Com Display}  \begin{document} Hello World! \end{document}   Unfortunately, xelatex test.tex fails:  […] Couldn't find `Sabon Next Com Displ.cfg' miktex-maketfm: No creation rule for font "Sabon Next Com Display".   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! fontspec error: "font-not-found" !  ! The font "Sabon Next Com Display" cannot be found. !  ! See the fontspec documentation for further information. !  ! For immediate help type H <return>. !...............................................    l.4 \setromanfont{Sabon Next Com Display}                                            % Sabon Next Com Display, SabonNex...  ?    Can XeLaTeX even work with fonts installed via SkyFonts? If not, what could be a workaround?


I just wondering if this promising feature has been evolved or is evolving to GA    Any info about current status or roadmap?


Is there a formula for $\displaystyle\sum_{n=1}^{\infty}\frac{n^k}{n!}$ in terms of $k$?  What about  $\displaystyle\sum_{n=1}^{\infty}\frac{(n-1)^k}{n!}$?


Is it safe to cast array of chars to int in C?

Imagine the following situation:  An array of 4 elements of type uint8_t is given that represent 32 bit integer, byte by byte. The goal is to address the whole array as a 32 bit integer.  int main( void ) {     uint8_t array[4] = { 0, 0, 0, 12 };     uint32_t * ptr = ( uint32_t * )array;     printf("%d", *ptr);     return 0; }   Forget about endianess for now, it is not relevant to the question (I do not think).  Now the C standard says that casting a pointer to a type with more strict alignment is undefined behavior.   Some examples of compliant and non-compliant code are given here:   The code above compiles and gives expected result on latest GCC and IAR compilers I've tried.   The question is whether this code is safe in general?  I imagine the following situation on the architecture where integer type is self-aligned. My logic is that since array will inherit the alignment specification of its most strict type - char it can be placed anywhere in memory. For example:  Memory | Value | integer can start here ....            0x20   |       | yes 0x21   | 0     | no   <- array begins, uint32_t ptr 0x22   | 0     | no 0x23   | 0     | no 0x24   | 12    | yes ....   In this scenario if we dereference a uint32_t pointer we may potentially crash on some architectures.  Did I miss something here? Obviously this code works on major compilers and I would imagine that cases where it fails are very specific, more related to legacy architectures and compilers. Nevertheless, is such code safe and portable as according to C standard?  If I made incorrect assumptions or interpreted something incorrectly, please let me know.


How to log original value of $remote_addr when using Real-IP

My environment has user requests passing through a number of systems:  [Client] --> [ELB] ---> [nginx] --> [web]  (ELB = AWS Elastic Load Balancer)  Thanks to this , I have nginx determining and passing the correct client IP address to the upstream servers (web) with the X-Forwarded-For and X-Real_IP headers. The relevant nginx config:      real_ip_header      X-Forwarded-For;     set_real_ip_from        10.0.0.0/8;     real_ip_recursive   on;     proxy_set_header X-Real-IP $remote_addr;   My problem is this, the Real IP module in nginx replaces the existing $remote_addr variable with the result of its X-Forwarded-For calculations. This gives me the originating client IP, but I'm losing the IP address of the system that actually sent the request to the proxy (i.e. the ELB).  Overall, having the client IP is more important to me, but I would like to be able to log the full chain of requests so I can understand (and debug) how traffic is flowing. Currently, I can only have nginx log the client IP, its own IP, and the upstream server IP. I would like to be able to log the ELB IP as well.  I see  asked the same  in 2013, with little luck. Has anything changed or improved since then?


Should I pay off my HELOC or continue to save/invest?

I currently have a $560k mortgage and took out an additional $105k HELOC piggy back loan to make up the 20% needed for the Jumbo loan last year. I've been saving for the past year and a half and now have $100k in savings. Should I be paying down the HELOC early or investing/saving the money? the HELOC is variable with a current 5.95 APR


What is the difference between meta and meta stack?

I've been participating in stack overflow for a while and for some reason just realized today that there are (at least) two meta sites for stack overflow:     This might be a dumb question, but what is the difference between these two and what belongs on the stack site versus the exchange site?


Codelite 13.0 can't be installed in Ubuntu 18.04

XXXXX-T480:~$ sudo apt install codelite Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  codelite : Depends: libstdc++6 (>= 9) but 8.3.0-6ubuntu1~18.04.1 is to be installed             Recommends: lldb (>= 3.4) but it is not going to be installed             Recommends: clang-tools but it is not going to be installed E: Unable to correct problems, you have held broken packages.


Why did Sméagol turn into a 'creature' when addicted to the ring, but not Bilbo Baggins?

Why did Sméagol turn into a 'creature', but not Bilbo Baggins?  Déagol found the ring in a river, Sméagol stole it and then turned into a weird creature. Bilbo did not turn into a creature when he found the ring.


Provided an action: $$S[A_\nu] = \int\left(\frac{1}{4\mu_0}(A_{\gamma,\mu}-A_{\mu,\gamma})(A_{\zeta,\alpha}-A_{\alpha,\zeta})\eta^{\gamma\zeta}\eta^{\mu\alpha}+\frac{1}{2}\nu^2A_\mu A_\gamma -\beta A_\mu J^\mu\right)\sqrt{-\eta}~dtd^3x,$$  How would one go about finding the field equations for the same? I do understand that using the Euler-Lagrange method is how one should start out.   Does it tell us what kind of field we're looking at, at a glance?


I am confused about Magnetic force whether it does work or NOT because i think that the battery does the word and the magnetic force only redirects the work done by battery into some displacement etc. but somewhere i read that work done by magnetic force is taken into account . so I want to ask whether it does some work or not???


How can I substitute a variable number inside a bash loop range?

This works as intended:  for rcount in {0..10}; do     echo "${rcount}" done   But I have a variable that I want to use as a loop range:  var1=10  These don't work:  Trial 1:  for rcount in {0..var1}; do     echo "${rcount}" done   Trial 2:  for rcount in {0..${var1}}; do     echo "${rcount}" done   How can I do this?


Does Google consider as duplicate percent encoded URL with different cases (upper and lower)?

We have the following two URLs:    https://example.com/%D1%82%D0%B5%D1%81%D1%82  https://example.com/%d1%82%d0%b5%d1%81%d1%82   Both are identical except the the case (upper vs lower).  Will Google consider them to be duplicate URLs or it does not matter?


How can I unapply a subdivision surface modifier?

I accidentally applied a subdivision surface modifier, but I don't want that. I tried to undo it, but that is not working. Is there any other way to do this?


Can't ask questions - But only three minorly downvoted questions asked?

I have only ever asked six or seven questions, but three of them were "unclear" (although I thought them clear enough) and got downvoted once, with the exception of one being downvoted twice. That is a fairly low number. In the Help Center it says "One or two bad questions won't get you blocked". But three? Really? It's impeding my work progress on things I am required by deadline to get done.


python os.walk file.endswith is searching case sensitively. How can I remove this restriction?

I have the following:  for root, dirs, files in os.walk(pathToSearch):             for file in files:                 if file.endswith(fileTypeToSearchFor):   It works well, it searches through and brings back files.  What I'm struggling with though is if fileTypeToSearchFor is 'JPG' it misses all the 'jpg' files and vice versa.  It's fully case sensitive.  Is there a way that os.walk can retrieve a file list with endswith where it's not case sensitive?  Thanks a tonne...


SObject row was retrieved via SOQL without querying the requested field in controller extension

I have written this controller extension:  public with sharing class PopupController {     ApexPages.Standardcontroller cont;     public Request_Change_Reseller__c req{get;set;}      public PopupController(ApexPages.StandardController cont){     this.cont = cont;     req=new Request_Change_Reseller__c();     req.PartnerUserId__c = ((Lead)cont.getRecord()).Assigned_to_Partner__c;      }      public PageReference save(){      return null;     }  }   My visualforce page is:   <apex:page standardController="Lead" extensions="PopupController" sidebar="false"> <apex:form > <apex:pageBlock > <apex:pageBlockSection columns="1">   <apex:outputField label="Lead" value="{!Lead.Name}"/>   <apex:inputField label="Assign To Partner" value="{! req.PartnerUserId__c}" /> <apex:commandButton value="Submit" action="{!save}" /> </apex:pageBlockSection> </apex:pageBlock>   </apex:form> </apex:page>   I created a custom button in the  lead layout. When I click on it a new window opens and I get this error:  SObject row was retrieved via SOQL without querying the requested field: Lead.Assigned_to_Partner__c .   Can I not access all fields in a controller extension? Will I have to make a soql query?


Blender import has armature without bones

I'm new to blender and imported this mesh of a monitor and wall mount. The monitor appears to have an armature attached to it but bone as far as I can tell no bones. It does have these blue lines around the mesh in edit mode. Can someone tell me what these are? Are they a part of the armature? I should be able to swivel the monitor in the obvious points. I know this exact model was used to swivel the monitor before in a different program but how can I make it work here? Also, side question, In object mode this mesh has a light blue color and the screen has a light orange color. Some other objects I imported have seemingly random colors. Can someone tell me what these are?


I want to use ubuntu 16.04 with windows 8.1 (dual boot) . But after installing ubuntu it only boots with a USB. after booting in the grub page it shows 4 options . they are  :-  try ubuntu without installing.  install ubuntu  odx installation (for manufacturers)  check for drive errors. I am now using the 1st option because after installing ubuntu this is the option that I find suitable for using.   I have installed ubuntu 2 times but nothing is working out for me. then I saw a post which instructed me to write some codes in the terminals. the result I got after I tried the below codes:- $ ls -l /dev/disk/by-label/ total 0  lrwxrwxrwx 1 root root 10 Apr 27 15:46 RECOVERY -> ../../sda5     lrwxrwxrwx 1 root root 10 Apr 27 15:46 UBUNTU\x2016_0 -> ../../sdb1     lrwxrwxrwx 1 root root 10 Apr 27 15:46 Windows -> ../../sda4     lrwxrwxrwx 1 root root 10 Apr 27 15:46 WINRE -> ../../sda1    $ sudo grub-install /dev/sdb Installing for i386-pc platform. grub-install: error: failed to get canonical path of `aufs'.  Even I am not able to access any files in my pc through Ubuntu. it shows the error :- unable to access "windows".   Error mounting /dev/sda4 at /media/ubuntu/Windows: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=999,gid=999" "/dev/sda4" "/media/ubuntu/Windows"' exited with non-zero exit status 1:    Blockquote  I am not able to understand what is wrong and I am not able to find a solution for it. I am a new to Ubuntu so do give a bit of explanations.


The narrator, in the quote, said that things turned out to be   horrible.   According to the question I previously posted, this parenthetical prepositional phrase "in the quote" is made possible by whiz deletion. But when I applied whiz deletion to it, it turned out to be a disaster.     The narrator, who was in the quote, said that...   Surely, what I was trying to say was that narrator said something in the quote, not that narrator was PHYSICALLY in the quote.  Here is another example.     They, (who were) after so much thinking, finally decided.   Now it is just not right.   So my another interpretation was that there was an absolute phrase with "being" deleted, but it brought about the same result. You can see what I mean if you substitute who was/were for being.   So, why is it possible to use parenthetical prepositional phrase in the middle of sentence? Is there anything deleted?


Capital gains tax and HMRC. What is the definition of a lodger and is there a difference between a friend staying a few months and a lodger?

I have two friends living with me and they only pay bills (no rent) and I wondering if I would be liable for CGT on the period they live there?  I don't take any rent from them at all and they are just friends staying in my house.  So, in HMRC's eyes, what is the definition of a lodger and specifically does it ever differ from a friend staying rent free in my house?  Also, in the definition of a lodger, if I let a room to a couple on one room lodger agreement does that count as one lodger or two?  (This has extremely large implications on CGT because having two lodgers makes the time they live there liable to CGT)


How to fit maximum likelihood estimates of normal distribution using subset of dataset in R?

I have dataset of numbers given as  $Y = x $ if $ x >= 5 $ and $x<=9$  and $x$~$N(\mu,\sigma^{2})$. Or we can say that we have the data-set as subset of normally distributed data-set.  Now for the given data(histogram given below), how do i estimate those unknown parameters $\mu$ and $\sigma^{2}$ using MLE in R?


Is it possible to prove that planets should be approximately spherical using the calculus of variations?

Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical?  Let's assume that a planet is 'born' when lots of particles of uniform density are piled together, and constrained only by the Newtonian gravity of the $N$ particles with no external gravity.    My question is: Is it possible to use the variational calculus starting from this situation to prove that planets should be spherical?


Is sentence No3 a fragment that needs to be attatched to No2?

Have you seen the movie "Dirty Dancing"?  It's a 1987 American romantic drama, a feel‐good film for people of all ages.  Is the above sentence now a comma splice?


show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$

On the metric subspace $S = [0,1]$ of the Euclidean space $\mathbb R^1 $, every interval of the form $A = [0,a)$ or $(a, 1]$ where $0<a<1$ is open set in S. These sets are not open in $\mathbb R^1$   Here's what I attempted to show that $A$ is open in $S$. I have no idea how it is not open in $\mathbb R^1$.  Let $M = \mathbb R^1$, $x \in A  = [0,a)$ . If $x = 0$, $ r \leq \min \{a, 1-a\}, \\\  B_S(0; r) = B_M(0,r)\cap[0,1] = (-r, r) \cap[0,1] = [0,r) \subseteq A $  If $x \neq 0, r \leq \min \{x,|a-x|, 1-x\},  \\B_S(x; r) = B_M(x,r)\cap[0,1] = (x-r, x+r) \cap[0,1] \subset (0,x) \text{ or } (x, 1) \subset A$


I wound call this Curtain slider. What's the proper name for this component?


How to buy tickets for country to country within Europe

I've been reading some sites on train travel and it's very overwhelming. I'm still not sure what I need to do. I understand that within a country in Europe, its best to purchase from respective sites, but I've no clue what to do between countries. I also don't know if it's advisable, or even possible, that I use the same train pass (the one for getting from country to country) for train passes within the country.  Over the course of 2.5 months, I need to go from Italy to Austria to the Czech Republic, to Germany, to Sweden, then Belgium, and finally France.  What do I do for the train rides between countries?


Does the faction of your armor/clothes affect character interactions in Skryim?

So I've killed off some well equipped Imperials, looted their bodies and want to equip their armor.  Does the game take into consideration that I look like an Imperial when I interact with pro-Imperial or anti-Imperial characters going forward?


A question regarding independence of $\min{\{X,Y\}}$ and $X-Y$ when $X,Y$ follows iid geometric distribution

THE PROBLEM :     Let $X$ and $Y$ be independent and geometrically distributed with parameter $p$. Prove that $U=\min\{X,Y\}$ and $V=X-Y$ are independent. (This property characterizes geometric distributions.)   What I did was a brute-force computation of $P(U \leq u) \times P(V\leq v)$ which came out to be $$(1-q^u) \times \left(1-\frac{q^{v+1}}{1+q}\right)$$  However, computation of $P(U \leq u, V\leq v)$ is messier with lot of cases depending on the values of $u$ and $v$. I cannot get to the end. Is there any clever, nice way to solve the problem (without getting into messy calculations)? Thanks in advance.


Is there a path to Stack Exchange's markdown converging with GitHub's?

The markdown used on Stack Exchange and the one used on GitHub are fairly similar, but have some subtle differences. For example, on GitHub, you can add ``` before and after a set of lines to format them as code, but that doesn't work on Stack Exchange.  As someone who writes markdown on both sites, I find these subtle differences inhibit the development of muscle memory (e.g. I often type ``` on Stack Exchange, only to realize (again) that it doesn't work and erase and correct it).  Is there any plan /  path forward to converge these two flavours of Markdown?  Note: I gave ``` as an example, but I'm asking about general convergence between the two flavours, rather than one particular extension.


Prove for every two sets $A$ and $B$ that $A − B$, $B − A$ and $A ∩ B$ are pairwise disjoint.  I've been looking at this problem and keep thinking it isn't true every time I think I make progress.  My main issue is that $A$ and $B$ can be any sets, including themselves. If $A = B$ then $A-B=\{\}$ but also $B-A=\{\}$ so they can't be disjoint.  Obviously, I'm missing something, probably will feel dumb after I figure it out.


Proof: $X$ is Hausdorff if and only if the diagonal $\Delta$ is closed in $X\times X$.

Prove that $X$ is Hausdorff if and only if the diagonal $\Delta$ is closed in $X\times X$.  This exercise appeared on a previous exam in my course, and also in Munkres. Here's my attempt:  First I want to show the implication starting with assuming that $X$ is Hausdorff. Consider $(X\times X)\backslash \Delta$, then for any tuple $(x_1, x_2) \in (X\times X)\backslash \Delta$ we know $x_1\neq x_2$. Then there are neighbourhoods $U,V$ of $x_1,x_2$ respectively such that $U\cap V = \emptyset$. The set $U\times V$ is a basis element of $X\times X$ so it's in the product topology. So any tuple $(x_1, x_2) \in (X\times X)\backslash \Delta$ lies in an open set of $X\times X$, thus $(X\times X) \backslash\Delta$ is open which makes $\Delta$ closed in $X\times X$.  Now I assume that $\Delta$ is closed in $X\times X$. Then $(X\times X)\backslash\Delta$ is open in $X\times X$. Unless I'm mistaken, every open set $A\times B$ in $X\times X$ will be a subset of $(X\times X)\backslash\Delta$. Then $A\cap B = \emptyset$ because otherwise we would have $(x_1,x_1)\in A\times B \subseteq (X\times X)\backslash\Delta$ for some $x_1\in X$, which is a contradiction. Thus $X$ is Hausdorff.  I'm simply wondering if my argument is correct.


A word or phrase that can be used to describe what is only good-looking but has almost no practical value.?

Any word or phrase that can be used to describe someone or something that is only good-looking but has almost no practical value?     Peter's massively bulking muscles do him a big help in chasing girls,   but they are actually ____ when he has to confront a real fighter like   Mike Tyson.


I only have the bin folder in my .minecraft folder

So I deleted my .minecraft folder thinking, "oh yeah it'll all just Re-Download when i start minecraft up". I was wrong. I looked in my .minecraft folder and all that is in there is the bin folder and the last login file. I have no idea what to do... Can someone help me with this?  Just letting you know that I emptied my recycle bin after I deleted it. I also have a premium account and it worked fine for the past year.


Exercise :     Prove that :   $$\frac{|a+b|}{1+|a+b|} \leq \frac{|a|}{1+|a|} + \frac{|b|}{1+|b|}$$   for $a,b \in \mathbb R$.   Methods I have tried so far include: Using the triangle inequality on the numerator on the left side, but I got an expression which was sometimes too big, so it's impossible.  Using a similar method on the right side, but I got a pretty nasty expression so I don't think that's the way.  Going case by case for every pair of a,b but this is also very long.  Can someone give a hint?


Will my software work on the next version of Windows

I have some software and I'd like to know if it works on the next version of Windows (Windows 10).


How to check significant change in the actual population, not sample

I'm trying to understand how I would decide whether a policy actually had a meaningful impact by comparing the population itself, not samples.  An example that comes to mind is comparing the number of accidents on a specific road during $n$ months prior to enacting a law to reduce the speed on that road, to $n$ months after enacting this law.  I would think that I could use a paired t-test using biased standard deviation, since I'm looking at absolute values of the actual population, not samples, but I see a few problems with that: how would I calculate the Standard Error for the t-value if there is no error because I'm looking at the population itself? How would I calculate standard deviation, if there is no mean?  What I'm really trying to understand is: say in my pre-test I get an $x$ number of accidents and in the post-test I got a $y$ number of accidents where $0 < x < y$. How could I know if this change was statistically significant? If someone could just point me to the right direction I can study the subject. I just don't know where to look.


Why is there whitespace below a center environment, but not when using \centering?

I am trying to typeset some content to the top of the page and some to the bottom of the page and both should be centered. Initially I tried this:  \documentclass{scrbook} \usepackage{showframe} \begin{document} \begin{center}     Top     \vfill     Bottom \end{center} \end{document}   However this leaves whitespace between the word Bottom and the actual bottom of the page:    If I am using \centering instead I acheive my result, but I don't understand why and I thin the environment would be the more logic approach, then the \centering switch.  \documentclass{scrbook} \usepackage{showframe} \begin{document} {\centering     Top     \vfill     Bottom  } \end{document}   Result as expected:    The same is true for flushleft and I therefore think it might be expected behaviour, but would like to understand how to prevent it and use the correct approach.


I'm trying to convert this Ã¼ to ü in php.  I want to get this kind of characters to correct format. this is Germany characters format. somehow the database recode is like this. but it's not a correct format.  here is my code,  //Germany $text = "Italienische GemÃ¼sesuppe"; setlocale(LC_ALL, 'de_DE');  $trans_sentence = iconv('UTF-8', 'ASCII//TRANSLIT', $text); //correct format should be like this : Italienische Gemüsesuppe   But this is not working as expected.  How do i do it ?


$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$

Consider $C([0, 1])$, the linear space of continuous complex-valued functions on the interval $[0, 1]$, with the norm  $$\displaystyle\lVert f\rVert_1 = \int_0^1 \lvert f(x)\rvert \,dx.$$  I have to show that $C([0, 1])$ is not complete with respect to this norm. I have found the following example from a book.  Let $f_n \in C[0,1]$ be given by  $$f_n(x) := \begin{cases}  0   & \text{if $0 \le x \le \frac1{2}$}\\  n(x-\frac{1}{2}) & \text{if $\frac {1}{2} < x \le \frac {1}{2} + \frac {1}{n}$}\\  1              & \text{if $ \frac {1}{2} + \frac {1}{n} <x \leq 1 $} \end{cases}$$  How to prove that $f_n$  is a Cauchy sequence with respect to $\lVert \cdot\rVert_1$?   If I use basic definition then I have to prove that $\lVert f_n - f_m\rVert_1 < \epsilon$ $\forall n, m > N$. But I am finding it difficult to prove this.  Please help me to understand how to prove that $f_n$ is Cauchy sequence in $C([0, 1])$.  Thanks


How do I change Wi-Fi Hotspot settings in Ubuntu with GNOME 3?

How do I manage my hotspot connected devices or change the hotspot password? I can only see the Network Name, Security type and the Password but I can't seem to manage users or the network properties.


Why did my desktop background changed and why pictures were opened, if I did nothing to do so?

This is what happened:   My desktop background changed 3 times at different times.   The change picture (every x time) option is disabled and I have always had it in that way.   When I selected a picture to be open, two more pictures were opened too.   I perfectly remember that I only choose one picture to be open. As a matter of fact, this event had never happened to me in my life. Also, think about this, what a "coincidence" that the same day that pictures are opened without requesting is the same day that my desktop background changes too.      There must be a reason because things don't happen just like that.   NOTES.   All the time when this happened, my mac didn't have connection to internet. Every once in a while I see a message on the upper RHS (in the corner of the screen) telling me that I should update something related to the system but I always click on later and then the message vanishes. User Allan said that , then what could possibly have happened?   Please tell me.  I think there must be a reason because things don't happen just like that.


Review Audits confusing Questions and Answers

Failed another high quality  (for trying to ).  However, I discovered something interesting. It would be a good idea if the the there was a match between question and answer.


Seasonality estimation without knowing the number of observations per seasonal cycle

I'm trying to detect if there's any pattern (seasonality) between login attempts on a machine using python. After researching a little bit i stumbled upon the library pmdarima, providing statistical tests such as the Canova-Hansen test to estimate the seasonal differencing term. All the tests however requires knowing apriori the parameter m which indicates the number of observations per seasonal cycle. However data are observed all the time every millisecond therefore one day i could have 500 logins, another day i could have 70 logins and another one none at all. let's say i want to test seasonality in one month period, or one week period,how should i go about selecting the coefficient for the test? Thanks in advance


List of images used in the document latex

I have written a book and inserted a lot of illustrations. All illustrations are input in my document as:  \begin{center} \includegraphics [scale=1]{image/1_12.pdf} \end{center}   I have about 500 images/illustrations  I would like to have the list of all inserted images/illustration, something like:  1_12.pdf  1_23.pdf  test.pdf  and so on. Is it possible to do that? Thanks a lot for the answer.


Can't figure out what is taking up so much space

When I cd /; du sudo du -h -d1 I get a total of about 160 GB (this is on a 256 GB drive). However, when I look at Disk Utility or About this Mac -> More Info -> Storage it looks like I'm using a solid 230 GB.  This is on a late 2013 Macbook Pro Retina, OS X 10.9.2.  I suspect the problem may be with mobile backups (I'm not hooked up to an external hard disk for backups).  I've tried, several times, running sudo tmutil disablelocal but that doesn't appear to fix the problem.  Here is the output of df -h after disabling local backups  /dev/disk1      233G  212G   21G  92% /  After re-enabling:  /dev/disk1                         233G  212G   21G  92% / localhost:/ebh4eOBPvo122KL1TUyqlO  233G  233G     0 100% /Volumes/MobileBackups  Output of ls -l /Volumes/MobileBackups/Backups.backupdb/MyComputerName  total 1 drwxr-xr-x 3 root wheel 102 Jul 16 17:55 2014-07-16-175518 lrwxrwxrwx 0 root wheel   0 Jul 16 17:55 Latest -> 2014-07-16-175518  Output of sudo tmutil delete 2014-07-16-175518  Deleting: /Volumes/MobileBackups/Backups.backupdb/MyComputerName/2014-07-16-175518 Error (-36) deleting: /Volumes/MobileBackups/Backups.backupdb/MyComputerName/2014-07-16-175518 Error (642) re-linking Latest for machine directory: /Volumes/MobileBackups/Backups.backupdb/MyComputerName Total deleted: 237.4K  Any ideas?  I know very little about Macs, if that's not obvious.


Build long mesh along bezier curve while using different meshes

So how would you go about making a long piece of pipe and use different meshes along the way.  For example I have one perfect straight piece, one with a dent and another just like the first but with different UV map.   I know you can have caps but can you in some way build it from different pieces?  Ideally I'd like to have a bezier curve to control the placement and then Array+Curve modifier on the mesh to extrude it along the Bezier. But how do you add variation to that other than do it manually? Is there a way to add and align multiple bezier curves one after another?  I thought about vertex groups but bezier curves don't support them?


When enabling a systemd-service why it isn't started?

When running systemctl enable my-service  it gets correctly enabled (the link is created into the right WantedBy-target in /etc/systemd/system) but it is not started. However, when rebooting the machine systemd starts the service. What do I need to do to have systemd start the service when enabling the service? For reference, here's my unit-file: [Unit] Description=WebSocket-server-application  [Service] ExecStart=/usr/bin/ws-server.app Restart=always  [Install] WantedBy=multi-user.target  (A little bit of background: systemctl enable is called during package-installation. I need to have the service started once the package has been installed.)


Inverting direction of mouse scroll wheel

Is there a way to make a mouse scroll wheel invert its direction? I'd like to scroll upwards and have that action scroll downwards and vice-versa. There is no setting on the Mouse control panel that makes this possible.   Any pointers to a hack or a particular mouse model that has such a setting would be appreciated. I am using Windows 7.


Let's define $e$ as the number $a$ such that $\frac {d}{dx} a^x = a^x$.  I'm trying to prove that this $a$ has to be $e$.  I don't see any way of proceeding from here except by the limit definition (I'm not assuming I know what the $\ln$ function is, or else there'd be a much easier definition of $e$ to be had).  $$\frac {d}{dx} a^x=\lim_{h\to 0} \frac {a^{x+h}-a^x}{h}=\lim_{h\to 0} a^x\frac{a^h-1}{h}=a^x\left(\lim_{h\to 0} \frac{a^h-1}{h}\right)$$  So clearly $e$ must be the number that makes that limit on the far right equal to $1$.  I'm not sure how to evaluate this. Using L'Hopital's rule, I just get $\lim_{h\to 0} \frac {d}{dh} a^h$, which doesn't particularly help.  So my question:     How can I prove that there is a unique number such that $\lim_{h\to 0} \frac {a^h-1}{h}=1$?


What is the word for someone who ignores others and does what they want to

This could be in a positive or negative way. So someone ignores people telling them to murder or someone ignores someone telling them to stop being rude. Basically how can you describe someone who just follows their gut in everything they do.


How determinate the torsion subgroup and the normal maximal $\pi$-subgroup of $\mathbb{R}/\mathbb{Z}$?

Let $\mathbb{R}$ and $\mathbb{Z}$ the real numbers and the integers, respectively. Consider $G =\mathbb{R}/\mathbb{Z}$. Find  $O_{\pi}(G)$ - ie, the (unique) normal maximal $\pi$-subgroup of $G$; $T(G)$ - ie, the torsion subgroup of $G$.


Permissions issues for shared directory on a server

The setup is we have a VPS running Debian Squeeze, and I've set up a shared directory for us to share files.  So far I've followed this guide:    I've also set the umask to 002 correctly (see the comments on that guide), so we can both now create files and directories directly on the server and we both have read/write permissions on them.  The only problem is that a lot of our files are created on our local machines (both running Ubuntu 10.10), and then dumped on the server.  This results in only the creator of the file/directory having write permissions on, and the other member of the group I set up for sharing this folder only having read access.  My next thought would be to change the default umask on our local machines, but it seems a bit extreme to have to do that, and I don't know if it's a security risk.  Can someone tell me if there's a better solution to what I'm trying to achieve, or if this really is the way to go?  Many thanks in advance


Fallout 4 is there a hight limit for buildings in settlements

In fallout 4 on the ps4 I have been finishing up on a original 3X3 house that holds up to 15 beds each floor (thats if you really dont want to  get though the door once its built). This desing however is designed to go infinite floors (each floor being 1 wall high). I was wondering if there is a hight limit for how many floors you can place so I know before I go resource farming so I can make a rough estimate for how much wood steel and cotton I will need.


I'm designing an I/O module by using optocouplers for the inputs and outputs which I want to control by a microcontroller.   Here are my questions:   In the datasheet of optocoupler's output current (per channel) is 50mA, and for the output port(figure 1) Relay nominal operating current is 16.7 mA. By knowing these can I calculate how much current will I need for the system. Which parameters do I know?   There are 12 relays, 20 optocouplers (5 module) in total. 3 Opto module for output, 2 for input ports     By directly connecting the GPIO pin and output of the optocoupler to the switches (as input), Can I control the inputs shown in the figures. For the input ports, I don't know how to make the connections. What should I connect to the collector pin?


Can I get involuntarily bumped from a flight even though I already have a boarding pass with an assigned seat?

I am at Newark airport right now, waiting to board a flight to MCO (Orlando, FL) with United Airlines.   They are announcing that the flight is overbooked by 7 passengers and that they need volunteers to be bumped from the flight for a (measly) 150$ compensation.   I cannot afford to be bumped since I have a cruise tomorrow morning and they obviously won't wait for me...   I have checked in for the flight online and received my boarding pass with an assigned seat.  Furthermore, (if that matters) I'm a frequent flyer for the airline. I have booked this ticket 6 months ago.   So, I ask you, can they just bump me in these circumstances?


I have finally managed to get iReports working under Ubuntu 18.04. To start it I need to go to a command window, cd to /opt/iReports5.6.0/bin, and then type ./ireports. Why, I have no idea? If I type ireportes.exe in the bin directory it doesn't start. Regardless it took countless hours to get the correct version of java (1.7) to run instead of 1.8, which was a sticking issue. In Windows I would just create a shortcut to a batch file that would change the directory to /opt/iReports5.6.0/bin/ and then execute ./ireports. And I would then drop the shortcut onto the desktop.   Is there anything analagous in Ubuntu 18 world?


Having problems watching Facebook videos

I am unable to watch any kind of Facebook live videos or any kind of videos on Facebook. But I am able to watch Youtube Videos. I am using Mozila Firefox on Ubuntu 20.04. I have tried video codec. I have also installed Flash Player. But the problem still isn't fixed.


Help me understand this example about FTL = time travel

Searching for clear explanations of why FTL equals time travel I found this  Go at the bottom, when he draws the blue lines. He says that those are the lines of costant time and they are parallel to the space line of the relativistic ship. This imply that the time line is perpendicular to the space line. But before he had said that the time line of the ship was the one named "space ship time" that is skewed towards the space line. So it seems to me that there are two time lines for the ship: the "space ship time" line and the one perpendicular to the space line that isn't drawn.  To say it in other words: if we have a relativistic ship its space and time lines should both be skewed towards the light line, right ? Because light speed is costant for any observer. This means that the light line should always be at the same distance from both the time and the space line.  But when the blue lines are drawn the time line is said to be perpendicular to the space line. This means that the light line would be closer to the space line that the time line. Thus meaning that light would be faster for that observer.  The problem is that if we consider the "space ship time" line as the correct time line there is no time travel.  EDIT: I think I'm starting to understand. In other examples I found online they suggest to rotate the graph, so that the time line of the space ship is pointing towards high. That makes evident the FTL communications between Earth and AC are distorted from the point of view of the ship, with the ones sent from AC to Earth arriving before they are sent. If the ship can sent messages at near istantaneous speed those messages would be a line perpendicular to their time line, but these lines woldn't be perpendicular to the time lines of Earth and AC, arriving after or even before they are sent. So to avoid time paradoxes you have time lines of different reference frames to always make an acute angle. If they were to make a dull angle (by going FTL) that would mean they are going in the past of each other. In fact you could rotate the graph to make on of them your y axis and see that the other is going down (towards the past). Is this correct ?  EDIT 2: Graph I made  In the horrbible graph above we have Earth and AC time lines (black), the realtivistic ship time line (blue) and near istantaneous FTL communications (purple). The first message is sent from AC to Earth, from their point of view is istantaneous, but from the point of view of the ship is going back in the past. When they receive it they sent a message back to AC (purple line perpendicular to blue line). Again this message is istantaneous from their POV, but from AC POV it arrives before it is sent. So AC receive an answer to a message that they haven't sent yet. What did I do wrong ?


Creating directory in bulk using mkdir in shell script

I am trying to create directory in bulk using mkdir through shell script below is the script  #!bin/bash mkdir /tmp/report*/testfolder*/testdoank   when i run it i got an error  -bash: ./makefolder.sh: bin/bash: bad interpreter: No such file or directory   what is wrong?


"there is insufficient memory on the device"

Well my dad just bought some phone for me "x-touch ocean" and I've beeeeeen trying to download apps but it keeps saying "insufficient memory on the device" I tried deleting apps I already found in the phone but still.. I got a new memory card with nothing in it but it still says the same thing over and over.. I haven't downloaded anything at all by the way. And I tried to move apps to the memory card but none of them can be moved unfortunately. Please some one help  #frustrated 15 year old #


Why is : $ \mathrm{dim}_{ \mathbb{C} } V(d,n) = \binom{d+n-1}{n-1} $?

Let $ V(d,n) $ be the vector space over $ \mathbb{C} $, of forms of degree : $d$ , in $ \mathbb{C} [X_1 , \dots , X_n ] $.  How to show that : $ \mathrm{dim}_{ \mathbb{C} } V(d,n) = \binom{d+n-1}{n-1} $ ?  I think $ \mathrm{dim}_{ \mathbb{C} } V(d,n) = \mathrm{Card} \big( \{ (i_1 , \dots , i_n ) \in \{ 1 , \dots , n \}^n \ | \ i_1 + \dots + i_n = d \} \big) $ but, why is : $ \mathrm{Card} \big( \ \{ (i_1 , \dots , i_n ) \in \{ 1 , \dots , n \}^n \ | \ i_1 + \dots + i_n = d \ \} \big) = \binom{d+n-1}{n-1} $ ? This is in reality a combinatoric question, so we need to take in account repetition, without order. but, i still not understand why it's equal to : $ \binom{d+n-1}{n-1} $.  Thank you in advance.


Travelling as unmarried couple in Indonesia

My girlfriend and I are travelling to Jakarta, Yogyakarta and Bali this month and we will share the same room throughout the trip. We are both Chinese citizens. Recently I have seen news reporting that Indonesia is finalising a new criminal code that will criminalise unmarried couple living together.  I have googled relevant information but haven't found anything regarding when the new criminal code will be in effect. All I found were some pieces of news in early 2018 reporting the finalisation of the new legislation, but I have no idea whether the new criminal code is in effect or not. Can anyone advise me when the new criminal code will be carried out and if this will be a concern to our upcoming trip? Do we need to use two separate rooms in a hotel in Indonesia?


LaTeX source code listing with less space between characters

I want to write shell Code in my LaTeX document. I'm using the listings package, with a code sample adapted from :  \documentclass{report}  \usepackage{color} \usepackage{xcolor} \usepackage{listings}  \usepackage{caption} \DeclareCaptionFont{white}{\color{white}} \DeclareCaptionFormat{listing}{\colorbox{gray}{\parbox{\textwidth}{#1#2#3}}} \captionsetup[lstlisting]{format=listing,labelfont=white,textfont=white}  % This concludes the preamble  \begin{document}  \begin{lstlisting}[label=some-code,caption=Some Code]    NETWORKING=YES  HOSTNAME= f e −19. l o c a l d o m a i n  } \end{lstlisting}  \end{document}   The problem is that there is some extra space between every character when I generate a PDF. I would like the code without this space. The extra space is visible in the the part HOSTNAME=.


If $x \geq 2$ prove that $\sum_{ n \leq x} \frac{1}{\phi(n)} = \mathcal{O}(\log(x))$.   This problem is from Apostol's analytic number theory book in the chapter 3 exercises. I am stuck on this problem as I am simply not sure how to do it.  I know from the previous chapters that the following relation exists  $$\phi(n) = \sum_{d \mid n}\mu(d) \frac{n}{d}$$  So I have $\sum_{n \leq x} \phi(n) = \sum_{n \leq x} \sum_{d \mid n}\mu(d) \frac{n}{d}$, where $\mu(d)$ is the Möbius function.  Can anyone offer some information on how to proceed or use this relation?


In the principle of Mathematical Induction, why do we take the base case as $P(1)$ only?

I kinda understand the logic and motivation behind the proof, but what bothers me is the fact, why is the base case (the first statement that we write) is always $P(1)$ when we are proving a proposition is true for all $\mathbb{N} $? Why can't it be anything other than $1$? What about $P(5)$ or something? Does it change anything?


What's going on with "compact implies sequentially compact"?

I've seen both counterexamples and proofs to "compact implies sequentially compact", and I'm not sure what's going on. Apparently there are compact spaces which are not sequentially compact; quick googling and wikipedia checks will turn up examples floating around; they tend to be variants of $[0,1]^{[0,1]}$ with the product topology.  Here's a demonstration(?):  $[0,1]^{[0,1]}$ is compact by Tychonoff's theorem.  So, we demonstrate failure of sequential compactness. Choose a unique binary representation for each $x\in [0,1]$. For each $n\in\mathbb{N}$, let $f_n : [0,1]\to[0,1]$ (an element of $[0,1]^{[0,1]}$) be the function which maps each $x$ to its $n$-th place digit in its binary expansion. Let $f_{n_k}$ be a subsequence of this sequence. Let $x'\in [0,1]$ be such that the $n_{2m}$-th digit is $0$ and the $n_{2m+1}$-th digit is $1$, for all $m\in\mathbb{N}$. Then $f_{n_k} (x')$ does not converge (it alternates between $0$ and $1$), and hence $f_{n_k}$ cannot converge. Thus we have found a sequence in $[0,1]^{[0,1]}$ without any convergent subsequence and so it is not sequentially compact.  (Aside: this is apparently based off of an example in Steen's Counterexamples in Topology, according to  ) Nevertheless, there's also some proofs(?) floating around that compactness of a space implies sequential compactness, along these lines (this proof(?) is of the contrapositive):  Suppose $X$ is not sequentially compact. By definition, this means there is some sequence $(x_n)$ over $X$ with no convergent subsequence. If any $x\in X$ had for each of its neighborhood $U$ infinitely many $n$ for which $x_n \in U$, then we could define a convergent subsequence of $(x_n)$, contradicting our assumption.  (Presumably this is done by choosing for each neighborhood a sufficiently-large-indexed term in that neighborhood.) Thus, for each $x \in X$ we can select an open set $U_x$ such that $x\in U_x$ but with $x_n \in U_x$ for only finitely many $n$. The collection $\mathcal{U}=\{U_x : x\in X\}$ is clearly an open cover of $X$. If $\mathcal{U}$ had a finite subcover $\{U_1, \dots, U_k\}$ then the union $U_1 \cup \cdots \cup U_k$ would contain all of $X$ but only contain $x_n$ for finitely many $n$, which is impossible. Thus $X$ is not compact, since we have found an open cover without a finite subcover.  (Aside: this proof is essentially the same as the proof appearing in Rudin's Principles of Mathematical Analysis for Thm 2.37 that infinite subsets of compact spaces have limit points.) So, what's going on here?  It can't be that what both the counterexample and the proof are telling us is correct.  Is there some subtle (or more embarassingly for me -- glaring) flaw in the proof?


How to solve "The repository does not have a Release file"?

Whenever I run sudo apt-get update I get The following error:  Ign:1http://ppa.launchpad.net/cpug-devs/ppa/ubuntu bionic InRelease Ign:2http://dl.google.com/linux/chrome/deb stable InRelease                    Hit:3http://in.archive.ubuntu.com/ubuntu bionic InRelease                      Hit:4http://dl.google.com/linux/chrome/deb stable Release                      Err:5http://ppa.launchpad.net/cpug-devs/ppa/ubuntu bionic Release                404  Not Found [IP: 91.189.95.83 80] Hit:6http://security.ubuntu.com/ubuntu bionic-security InRelease               Hit:7http://in.archive.ubuntu.com/ubuntu bionic-updates InRelease Hit:9http://in.archive.ubuntu.com/ubuntu bionic-backports InRelease Reading package lists... Done                       E: The repositoryhttp://ppa.launchpad.net/cpug-devs/ppa/ubuntu bionic Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   I understand that  E: The repositoryhttp://ppa.launchpad.net/cpug-devs/ppa/ubuntu bionic Release' does not have a Release file.   is the error. So how do I fix it?  [Edit]  I have found the problem is solved(I just removed the problem causing repo ).


How to use a retail Windows 7 Professional license key to upgrade an installed Windows 7 Home Premium machine

I purchased a retail version of Windows 7 Professional and installed it on a computer.  That machine has died, and I replaced it with a new computer which came with Windows 7 Home Premium already installed.    I'd like to have Professional, not Home Premium, on the new machine, and I don't want to pay for an "Anytime Upgrade" because I already have a valid Windows 7 Professional license (for the dead computer).  Is there a way to legally upgrade using my Professional license key?  I've already installed programs, data, etc on the new machine, so I don't want to reformat and start from scratch.


I'm an Indian citizen, holding a valid Canadian visitor's visa. I'm traveling from Canada through Dublin to another destination. Does Dublin require a transit visa?


Failed installation of Virtualbox 5.1 on Ubuntu 16.04

I followed this  to install Virtualbox, but it failed eventually and I get this error message      Kernel driver not installed (rc=-1908)      The VirtualBox Linux kernel driver (vboxdrv) is either not loaded or   there is a permission problem with /dev/vboxdrv. Please reinstall the   kernel module by executing      '/sbin/vboxconfig'      as root.      where: suplibOsInit what: 3 VERR_VM_DRIVER_NOT_INSTALLED (-1908) - The   support driver is not installed. On linux, open returned ENOENT.   When I ran this command # sudo /sbin/vboxconfig I get this     vboxdrv.sh: Building VirtualBox kernel modules. vboxdrv.sh: Starting   VirtualBox services. vboxdrv.sh: Building VirtualBox kernel modules.   vboxdrv.sh: failed: modprobe vboxdrv failed. Please use 'dmesg' to   find out why.      There were problems setting up VirtualBox.  To re-start the set-up   process, run   /sbin/vboxconfig as root.   and here's the last three lines of dmesg output:  [   44.698246] wlo1: Limiting TX power to 20 (20 - 0) dBm as advertised by 00:18:0a:79:2c:79 [  163.080255] capability: warning: `VirtualBox' uses 32-bit capabilities (legacy support in use) [ 2349.627558] [drm:intel_pipe_update_end [i915_bpo]] *ERROR* Atomic update failure on pipe A (start=142454 end=142455) time 484 us, min 1073, max 1079, scanline start 1061, end 1095   I tried to re-install dkms sudo apt-get install --reinstall virtualbox-dkms I get this error and nothing changes .     vboxpci.ko: Running module version sanity check. Error! Module version   5.0.24_Ubuntu for vboxpci.ko is not newer than what is already found in kernel 4.4.0-47-generic (5.1.10). You may override by specifying   --force.   Any help will be appreciated. Thanks in advance.


Every once in a while an error pops up, so there's this dialogue box which asks if one would like to inform Ubuntu about it. Upon confirming, where does this report go? Can it be followed up? If it is followed up, is there a fix that is provided later? Or is there some place where the solution is provided, which one can check and sort ot out?


I am sure it's just your eyelashes creating a filtering effects, but if you look a a bright(ish) light source such as a lightbulb while squinting, if looks like you are seeing straight light rays emitting from the lightbulb, I assume you can't see an individual ray of light like this?


I realised that I may need more space for Linux as kind it is shifting towards being my primary workspace, hence I decided to extend its size. I un-alloacated a chunk of memory from windows'(  ) partition and tried merging it to the Linux's but I could not. I am using Gparted. My OS is Ununtu Budgie. Attached is a screenshot of my partitions.