Ideals and prime ideals in a commutative ring.

Let $A_1$ and $A_2$ be two ideals, and $P_1$ and $P_2$ be two prime ideals in a commutative ring $R$. Assume that $A_1 ∩ A_2 ⊆ P_1 ∩ P_2$. Is there at least an $i$ and $j$ such that $A_i ⊆ P_j$ is true?


How to add a new value to the end of an numerical array?

In PHP I can do like:  $arrayname[] = 'value';   Then the value will be put in the last numerical key eg. 4 if the 3 keys already exists.  In JavaScript I can’t do the same with:  arrayname[] = 'value';   How do you do it in JavaScript?


Cannot flag as duplicate if there is a bounty

I just tried to flag  on AskUbuntu as a duplicate. However, due to it having a bounty on it, I cannot. I just get this error:    Even if the general StackExchange policy is to not close questions with a bounty on them, it should be possible to at least mark them as duplicates and add the flag somewhere. I don't think it's reasonable to have to wait 7 days just to mark it as a duplicate.  In 7 days, I'll have forgotten about this question anyways, I'll forget to mark it and it won't show up as "possible duplicate", just as a "linked question".  EDIT: To clarify: I do not necessarily want to vote to close the question. I'd just like the box to appear just like it does on this post:    And as far as I know, "flagging for moderator attention" does not do this.


how to get concave surface which close to the outer edge point

In qgis, how to generate the blue outer edge (the concave surface close to the outer edge point) in Fig. 2 from the point in Fig. 1. Any suggestion?


How to add metadata and tags to folders in Windows 10?

How could I add metadata and tags to folders? I know that I can add metadata and tags to files supported by File Explorer. For unsupported files, I use , but it seems not supporting adding metadata and tags for folders. I'm using Windows 10.    There's  that's asking about adding files/folders metadata for Windows 7. My question is asking about adding metadata as well as tags specifically for folders on Windows 10.


Find $\displaystyle \int_{0}^{\infty} \dfrac{\ln(x)}{1+x^2}dx$.   How should I change the limits of integration to evaluate this?


$f(z)=f(iz)\forall z$, my question is : is there such $f$ exists?

$f$ be an entire function such that $|f(z)|\le c|z|^3\forall |z|\ge 3,f(z)=f(iz)\forall z$, my question is : is there such $f$ exists?  $f(z)=a_0+a_1z+a_2z^2+a_3z^3+a_4z^4+a_5z^5+\dots=a_0+a_1iz-a_2z^2-ia_3z^3+a_4z^4+ia_5z^5\dots$  $|g(z)|=|{f(z)\over z^3}|\le c\forall |z|\ge 3$ so by Liuvilles $f(z)=kz^3\forall |z|\ge 3$ also $kz^3=-ki z^3$ so $k=0$, so $f(z)=0\forall |z|\ge 3$? so $f\equiv 0$? am I wrong anywhere?


How do I calculate a random color, thats going to be more or less unique to a specific string? Its true that RGB format of (0-255, 0-255, 0-255) will only allow maximum of 16581375 unique colors, while strings are indefinite.  The string can be random like hello123 or bye456.  My goal is to show a control (expander) in a almost unique color by text of the header. Because on other list in GUI there is a reference to that expander, so i want to help the user to find that entry quicker.  So I need to get a SolidColorBrush for background.  Example: The header of one expander is hello123 and the following expander header is bye456. So I want to set the background of each header to a (nearly) unique color.


Why do we take the value of the constant in Coulomb's law as $\frac{1}{4\pi\varepsilon_0}$?


How does a non EU spouse apply for spouse reunification visa for Italy to visit Italian husband?

I am a Canadian married to Italian in Italy. Our marriage has been registered in Italy and everything is legit. I live and own a business in Canada and my husband is planning to join me in the future. He is staying in Italy until his elderly mother passes on so in the meantime I am back and forth because I have more flexibility. I was in Italy for 90 days (consecutively from May to August) and need to return within the 180 days (in December) for his ailing mother.    I am in need to find a way to get into Italy without being stopped at the border.  I am looking to apply for a reunification visa, but I have searched the web for information, but cannot find an actual visa form specifically about a reunification visa. I even emailed back and forth with the consular office he is telling me I don't need a visa, just to register at the Anagrafe, but how do I get into the country to register? Can someone advise if I can just apply for a regular Schengen visa and indicate in the cover letter that I am joining my husband or is there a separate visa form for re-unification?  Thanks to all in advance.


Hydraulic Disk brake piston not fully retracting

My front disk brake's piston doesn't fully retract.  While I can ride the bike, the brake is slightly rubbing.  (IE, if I just spin the wheel with my hand, it'll go around about one and a half times and then stop.) It's definitely slowing me down.   If this fixable?  The advice I got was that it's not worth the trouble and to buy a replacement set.  The current brakes are Avid Juicy 7s that are about 7 years old


How to unable and uncheck other checkbox if one is check using jquery?

<input type="checkbox" class="allCheck" />all  <input type="checkbox" class="checks" />shoes  <input type="checkbox" class="checks" />bag  <input type="checkbox" class="checks" />car   how to unable and uncheck other checkbox if checkbox all is checked?  NOTE: I want to check multiple checkbox EXCEPT ALL if ALL is checked the others must be unchecked and disabled.


How to activate new device without access to other devices and SMS?

I am going to travel to the USA next month and I'm willing to buy a new iPhone. Currently, I have a Mac and an iPad and an Android smartphone. When in the USA, I will have neither my Mac nor my iPad with me, and I won't be able to receive SMS through my Android device.  I have two-factor authentication turn on. I don't see how to turn it off on Apple ID page. Is there any way I set up my new iPhone without carrying, let's say, my iPad with me for the trip?


Is it better to store images in a BLOB or just the URL?

Possible Duplicate:          I was wondering if there's any good reason to still use blob fields in a database. A couple of years ago I worked with a DB with a bunch of images in it, the DB was very slow and I couldn't see any good reason to keep the images inside the DB, so I got the images out and stored the filenames instead.  Was this a smart move? What would you do in my place?


Bring back process after closing terminal

Is there a way to "reopen" a process that is running? I accidentally closed my terminal window and it was running a openvpn. Is there a way to bring that process back to the focus of the terminal? I've tried fg and jobs but since it is a program I don't believe those commands apply.


Breaking ZIP 2.0 encryption without password

I have an old sourcecode backup from my DOS days stored in a ZIP 2.0 encrypted archive, but I lost the password.  The password was written on a paper slip, but I remember that it consisted of 30+ completely random alphanumeric characters with some special symbols in between.  I have read that a GPU cluster will crack old ZIP 2.0 archives almost instantly, and that there is a vulnerability in the ZIP 2.0  encryption allowing an attacker to recover the password instantly if there are multiple files in the archive.  But what if there is only one file in the archive, and the password consists  of 30  completely random characters?  Can I expect fast recovery if I can run the process on a GPU cluster?    Addition: The archive was created with PKZIP 2.04C and there is nothing known about the filename extension and nothing known about the plaintext.  Does it change the calculus that the archiver was 2.04C and not 2.04G?


How can we provide square brackets under regex

I have an api which accepts PIN which shouldnt be anything other than numeric. I am using regex to check if the pin contains any other character. This is my regex  var regex = new Regex("[a-zA-Z!@#$&(){}%^*_=;:?<>\\-`.+,/\"]");   I need to add verification for [] brackets also but whenever i put it inside the expression it doesn't work.  var regex = new Regex("[a-zA-Z!@#$&(){}%^*_=;:?<>[]\\-`.+,/\"]");   Do i need to use any special character for this ?


Tag edits result in a "success" screen instead of the updated post

When editing a post's tags today (directly, via the "Edit tags" link), the tag edits are successful, but instead of returning me to an updated page, I receive something like:  {"success":true,"html":"linux< ... continues ...   This happened to me on U&L, and terdon has confirmed it also occurs for him on ELU.


Where is the code downloaded by apt source stored?

I know how to use apt source but where are the files of apt source stored?


What makes a hash function good for password hashing?

Using a cryptographic hash to store e.g. passwords in a database is considered good practice (as opposed to storing them plaintext), but is subject to attacks on said cryptographic hash, assuming the database is compromised.  Which properties of a cryptographic hash function make it suitable for hashing passwords and the like?  Which functions are secure enough, while still being widely available, without patent issues and not too computationally intensive?


How to uninstall a program that was originally installed on a different drive?

I have a C: drive where I have Windows 7 64 bit installed and I used to have a D: drive on which I installed Paint.NET. This D: drive doesn't exist any longer. When I go to Control Panel\Programs\Programs and Features I still see the entry for Paint.NET, but I get an error after attempting to uninstall it: "The folder path contains an invalid character." I'm assuming that his is the result of the D: drive not existing any longer.    The reason I'm asking this question is because I get a fatal error when trying to install the newest version of Paint.NET.    How can I uninstall the registry entries (and other residual files) of the previous instance of Paint.NET without using any untrusted 3rd party tool?


L:K algebraic and separable then [L:K] $\leq$ n

Suppose that $L:K$ is an algebraic and separable extension, and that for every $\alpha \in L$, the minimal polynomial of $\alpha$ over $K$ has degree at most $n$. Then $[L:K]\leq n$.  I'm having trouble proving this. The material that I am studying uses the following definition of separable:  Separable: an irreducible polynomial $f \in K[t]$ is separable over $K$ if is has no repeated roots in the algebraic closure of K. An algebraic extension $L:K$ is separable if every $\alpha \in L$ is algebraic over $K$ and the minimal polynomial of $\alpha$ over $K$ is separable over $K$.   I think this is to do with the primitive element theorem or perhaps the Tower Law, but I can't puzzle it out. Any help appreciated.


Unclear why warning about low-quality-question is displayed

Not a Duplicate Claim:  Before you flag this question as a duplicate of , please consider that I'm not discussing if such a warning is useful (I fully agree that it's useful), but instead I have problems following the advice given in the warning because I seem to have ran into a special case (deleted questions which I can't see anymore). This topic might need attention from an SE developer.  Question:  When I go to  then I get the warning     Wait! Some of your past questions have not been well-received, and   you're in danger of being blocked from asking any more.   along with some helpful links for resolving this issue.  However, when I go to my profile, I see only one question, and it's currently upvoted with 2. I think that this can't be the reason for the warning, so I don't understand why the warning is there.  Maybe in the past I had bad style questions on android.stackexchange.com which were deleted, but now I barely remember and I can't find them and I can't improve them. So the warning is there for a reason which I can't reconstruct. So ultimately, the warning is almost useless for me, except that it vaguely tells me to do better.  I think that this warning shouldn't be there, or that it should give me more information what I have been doing wrong. Can I switch it off somehow or do something else about it?


Nginx includes config files not in order?

Is the order in which Nginx includes configuration files fixed, or random? Apache  wildcard characters are expanded in alphabetical order. With Nginx it seems this does not apply, and .  In my setup, 20_example.com was included before 00_default, which defeats my purpose of defining shared directives (like log formats) there.


Compute factor group $\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}$ - Fraleigh p. 147 Example 15.11

(1.) Why's there a 'great temptation' to set $2 \bmod 4$ and $3 \bmod 6$ to 0?   (2.) Why are you authorized to set $2 \bmod 4$ and $3 \bmod 6$ to 0? $2 \bmod 4 \neq 0$ and $3 \bmod 6 \neq 0$, hence does this even make sense?   (3.) How do you envisage and envision to work with $(1,0) + H = \{(1, 0), (3, 3)\}$?  I know the second paragraph starts with the Fundamental Theorem of Abelian Groups, but my course doesn't include this hence I can't use it. I also know: $| \dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle} | =  6 \times 4 = 24$, order $(\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}) = lcm(4, 6) = 12.$


I'm trying to figure out how to export my blender object to unity while maintaining all of its properties

I'm fairly new to using both blender and unity but my end goal is to have my blender asset in unity just as it appears in blender. So essentially, I have two basic cube mesh's that are scaled to the size I need and both connected together. The bottom cube mesh had a simple black and white material added to it. In the nodes, I displaced it a little to add texture and I also added a color burn to make it gold colored. The top cube had a basic marble material added and a slight displacement along the sides again to add texture. The problem is when I place the object in unity, the textures created from the slight displacement on both objects and the gold coloring from the color burn do not show up. The basic materials are transferring over just fine as does the basic cube mesh. Like I said though, I am new to this so I'm not sure what other information might be helpful but let me know and I will provide whatever info is needed. Thanks in advance for any help.


What is the maximum supported hardware RAM in Windows 32-bit?

I want use 4GB of RAM.  Can I use in Windows XP 32-bit?  Or should I go for Windows XP - 64-bit? Does it support 4GB of RAM?  Does Windows 7 32-bit support more than 4GB of RAM, or is >4GB support only available in Windows 7 64-bit?


I want to have a 9v battery to give a 4.5v - 5v power supply?

I am trying to download a program on to my PIC circuit. As you know the pic isn't supposed to operate with anything larger than 5v. I don't have any access to a battery pack which could hold 3 x AA batteries. What i do have are lods of other stuff, that may be useful. I was thinking that if i used two 330 ohm resistors to create a potential divider then had another battery snap going off from that to the pic circuit. Would that work?  ]


Preventing boredom creep with hobby projects

This question is directed more towards the hobbyist developer rather than professional game developers.  Quite frequently while developing a game I'll get bored staring at the same exact game scene after days or weeks of work (while new features only slowly creep in) that I find myself abandoning projects and starting new ones, never really finishing what I've started.    How do you prevent yourself from getting bored with a hobby or side project?  What tips/tricks/techniques do you use to keep yourself motivated to actually finish a project?


Is Unity Answers associated with Stack Exchange?

seems to have a similar format and style to the stack exchange sites, so I was wondering if they were associated in any way.


A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r>R$, using infinity as the reference point.  My attempt:  From Gauss' theorem we may deduce that $\displaystyle\mathbf{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r'^2}\hat{\mathbf{r}}$ where $r'$ is the distance of an arbitrary point from the center of the sphere provided $r'>R$.  $V=-\int_\infty^\mathbf{r}\mathbf{E}\cdot d\mathbf{l}$  My question: What is $d\mathbf{l}$? Since we are traversing in the direction opposite to $\hat{\mathbf{r}}$, I think it should be $-dr'\hat{\mathbf{r}}$. But when I use it to find $V$, I get a sign error. Please help!


How can I create interchangeable instructions?

document.body.style.backgroundColor="#F00";   This statement styles the body background color as red.  In my original code I have a function that assigns elements by tag name to a global variable element. I've found after calling this function I can do this: element.style.backgroundColor="#F00";  However, there doesn't seem to be ANY way to substitute for the property section of the statement. Below I've produced the most obvious approach, though I have also tried assigning the parameters to variables and various combinations of quotation.    function assignStyle(value) {   document.body.style.backgroundColor = value; }  function attemptStyle(property,value) {   document.body.style.property = value; } button { font-family: monospace; } <button onmouseover="assignStyle('#131519');" onmouseout="assignStyle('#FFF');">   function assignStyle(value){} </button><br />  <button onmouseover="attemptStyle('backgroundColor','#137619');" onmouseout="attemptStyle('backgroundColor','#FFF');"> function attemptStyle(property,value){} </button>     Edit: This question is not a duplicate of . That question contains jQuery, which many people, including myself, know literally nothing about. My question is concerned with basic JavaScript. Also, I want to know how to add a property to an element, and so by means of passing an argument to a function parameter. As far as I'm concerned, variables complicate the question further.


Alphabetical sorting of a sequence of names

I have a long number of people to acknowledge in my thesis, and I was wondering if it would be possible to sort their names automatically, rather than doing it by hand. In other words, I would like a macro, say \sorted, which would take \sorted{Gauss, Carl Friedrich and Riemann, Bernhard and Euler, Leonhard}  and output  Leonard Euler, Carl Friedrich Gauss and Bernhard Riemann  To be clear, I am not looking to sort the items in a list environment. Rather, I would like to output a sentence that contains the various names, in alphabetical order. All names but the last two should be separated by a ,, while the last two should be separated by and.


Complex matrixes $A$, $B$ such that $AB - BA = B$. Prove that $0$ is the only eigenvalue of $B$.

There are complex matrices $A$, $B$ such that $AB - BA = B$. Prove that $0$ is the only eigenvalue of $B$.  I know that $tr(B)=0$. I tried different transformations and I ran out of ideas. Can you please help me?


I was wondering how to add some .sty file that Texlive 2016 doesn't include, in my case, points.sty. I simply copy and paste to the path C:\texlive\2016\texmf-dist\tex\latex, however it seems to not work.


Performance differences between visibility:hidden and display:none

I want to simplify things in my jQuery Backbone.js web application. One such simplification is the behavior of my menu and dialog widgets.    Previously I created the div boxes of my menus at start and hid them using display: none; opacity:0;.   When I needed a menu, I changed its style to display:block then used the jQuery ui position utility to position the div box (since elements with display:none cannot be positioned) and when it was done, finally changed its style to opacity:1.    Now I want to just hide them with visibility:hidden, and when I need one, I use the position utility and then change the style to visibility:visible.  When I begin using this new approach, I will have around 10 div boxes throughout the web application session that are hidden but occupy space, in contrast to the previous div boxes hidden with display:none.    What are the implications of my new approach? Does it effect browser performance in any regard?


I'm having trouble finding the definite integral:  $$\int_{-\infty}^{\infty}\cos(x)\operatorname{sech}(x)dx$$  I know the answer is $\pi\operatorname{sech}(\frac{\pi}{2})$. There isn't an indefinite integral in terms of elementary functions. The indefinite integral given by Wolfram Alpha is in terms of hypergeometric functions, but I wanted to know if you could get the answer without that. Maybe some differentiating under the integral jazz? Or maybe series. Not too sure where to start, but I would appreciate an explanation. Also, I personally don't know Complex Analysis, but if that's the only way, that wouldn't be a bad answer for others on this site.


In Arkham Origins, which I am absolutely loving, I can't find any way to do the classic, and often essential "Disarm and Destroy move".  This is the one where you press X + Y on Xbox, or Square + Triangle on PS3, and you punch a dude, take his weapon (knife, glowstick, shield, gun), and break it. Which means it can't be used again.  It's totally essential to combat, as bad guys become progressively more prepared throughout the game. I can't perform it by default, and there's no unlockable option for it in the Waynetech upgrade screen. I got the Double Special upgrade, which mentions in the description that you can use it with other Specials, but it still doesn't work.  Anyone else having this issue? I feel there's a small change you can't use the ability until the game tells you to i.e. I might play a mission where it will tell me to use the ability, and from there it's unlocked.


How to prevent a coauthor from stealing the article?

Please go through the following incidents to understand the problem.  Mr. A is a Ph.D. student of some institute who was working with Prof. B of another institute on a very interesting mathematical problem since last three years. Recently, they came across a significant solution to it. They wrote a research article to publish in a very good mathematics journal that accepts the online submission.  Prof. B wanted to submit it to the journal by himself. Mr. A agreed.   A few days ago, Mr. A wanted to know about the submission of their article via telephone. Prof. B informed that the article is submitted. But, Mr. A received any confirmation e-mail neither from the journal nor Prof. B forwarded the submission mail to him. Prof. B did not upload it in arXiv, which is a free preprint repository.  Mathematics journals used to take a long duration to review and publish an article. Prof. B told that submitting this article to arXiv will immediately attract community attention. Many researchers will start working in the new direction. As a result, Mr. A and Prof. B may lose their opportunity to work on that problems. Also, the article may be stolen.  Mr. A did not ask Prof. B to forward the submission confirmation mail to him. Prof. might think that Mr. A is suspecting him. It may affect the relationship. Also, Prof. is a very powerful person in the administration, who may prevent an opportunity for Mr. A to gain a job. Again from some of his friends, Mr. A came to know that Prof. had distributed related research problems to his collaborators.  As a consequence, Mr. A is thinking that Prof. has submitted this work in his own name and he has lost his credit as the first author of this article.  Now the question is: How Mr. A may save his credit and his work without hampering his relationship with Prof B?


Add Google as Default Search Provider for Windows 8.1 IE 11

I have been trying with no luck to use Google as the default search provider for IE11 on Windows 8.1  Currently I can only add Google Australia as an "Accelerator" however this does not provide the capability to search Google from the IE11 address bar.  It currently seems that unless your IE11 came with multiple built in search providers, you are pretty much stuck with Bing for now.  Has anyone figured out how to do this?


If we threw a baseball from the ISS, could we deorbit the ball?

Clearly this is a hypothetical question.  Say we bring a star baseball player into NASA, prep them appropriately for a mission in space, and fly them up to the International Space Station. They go on a spacewalk with a baseball, and at the apoapsis (highest, slowest point in the orbit) throw it retrograde as hard as they can. Could they decelerate the baseball enough that its periapsis (lowest, fastest point in the orbit) dips into Earth's atmosphere enough to de-orbit the ball over time?  (Let's assume that the ball must de-orbit within about 10 years or less. 10,000 years is too long. Also, let's neglect any loss in mobility that a space suit might cause.)


What is Elrond's position/status, as compared to Galadriel's?

In the Lord of the Rings books, Galadriel of Lorien is even more exalted than in the movies.  She is essentially a queen, and the deference shown to her far exceeds that shown to Elrond of Rivendell.  Yet in the films, we see her trying to persuade Elrond to intervene in the battle of Helm's Deep by sending Elf troops to reinforce Theoden's forces.  Eventually, Elrond relents, and orders the Elves into battle.  But the troops in question are Galadriel's, not Elrond's - they are led by Haldir, one of Galadriel's guards; the trip from Rivendell to Helm's Deep (500 miles as the crow flies) is about 2 times longer than the trip from Lorien to Helm's Deep (250 miles as the crow flies), far too long for the reinforcements to arrive in time.  But then Haldir greets Theoden of Rohan by saying he has come bearing a message from Elrond - not Galadriel.     I bring word from Lord Elrond of Rivendell. An Alliance once existed between Elves and Men. Long ago we fought and died together. We come to honor that allegiance.    This seems odd for a few reasons. The troops are Galadriel's, not Elrond's, and they come from Lorien, not Rivendell. She clearly wanted to send them to Helm's Deep - she was cajoling, prodding, and guilt-tripping him into doing just that.  She is also a queen, and could presumably order them into battle regardless of what Elrond says.    So why does she have to talk Elrond into letting her send her own troops into battle, especially when he is too far away to contribute manpower (elfpower) or materiel to the battle of Helm's Deep?  Why not say, "I'm not going to sit here doing nothing while Saruman runs roughshod over Rohan;  you can support me or not, Elrond, but if you aren't willing to help, you can at least get the hell out of the way"?  Why does her aide Haldir "bring word from Elrond" when the troops - and the impetus for sending them - came from Galadriel, and Elrond resisted sending them out for as long as he could?  And again, what is Elrond's official position/status/rank, and why would a queen need his permission to deploy her own troops?


Using terminal escape-sequences within GNU screen

I have a ruby terminal script that I would like to print out hyperlinks. I achieve that like so:  puts("\e]8;;https://example.com\aThis is a link\e]8;;\a")   This works perfectly fine in a "normal" terminal (gnome-terminal btw) window.  But I need to run this script within GNU screen, where the escape-sequence simply has no effect. Other sequences (like colors for example) work fine, the hyperlink one (which according to the  might be a gnome-terminal-only thing) doesn't. (screen is running inside gnome-terminal)  How can I get screen to acknowledge my link sequence and display it properly?


I'm creating a set of enum values, but I need each enum value to be 64 bits wide. If I recall correctly, an enum is generally the same size as an int; but I thought I read somewhere that (at least in GCC) the compiler can make the enum any width they need to be to hold their values. So, is it possible to have an enum that is 64 bits wide?


How to download a whole FTP site using command line?

I need to download an FTP site (a web site source code actually) containing a very high quantity of relatively small files (downloading it with FileZilla took more than a day, but I believe it could be downloaded much faster if many files were downloaded at once). Unfortunately there is no SSH access to the site and no way to archive the files on the server side.  So at least the question is how to download a whole FTP site into a folder using command line tools. A better it'd be if the download could be parallelized by downloading many files simultaneously instead of one by one.


Is $x\sin\left(\frac{1}{x}\right)$ uniformly continuous in $\mathbb{R}$?

Let $f:\mathbb{R}\xrightarrow{}\mathbb{R}$ with rule defined as $$ f(x) = \left\{\begin{array}  xx\operatorname{sin}\left(\frac{1}{x}\right) &\text{  if }x\neq0 \\                       0  &\text{ if } x=0 \end{array}\right. $$ I would like to show that this function is uniformly continous over $\mathbb{R}$. I started out with the $\epsilon-\delta$ definition and tried to manipulate the following expression without success, $$ \left|x \operatorname{sin}\left(\frac{1}{x}\right)   - y \operatorname{sin}\left(\frac{1}{y}\right) \right |\\ =\left|x \operatorname{sin}\left(\frac{1}{x}\right) -x \operatorname{sin}\left(\frac{1}{y}\right) +x \operatorname{sin}\left(\frac{1}{y}\right)   - y \operatorname{sin}\left(\frac{1}{y}\right) \right | \\ \leq \left|x \left(\operatorname{sin}\left(\frac{1}{x}\right) - \operatorname{sin}\left(\frac{1}{y}\right)\right) + (x - y) \operatorname{sin}\left(\frac{1}{y}\right) \right | $$ Also, the function isn't Lipschitz, so I can't go this way too. I've seen some other proofs at mathSE however they try to show things for smallers domains as $[0,1]$.


So I just started using bodegraph but no graph at all. Always from this pdf .  \documentclass{standalone} %    \usepackage[utf8]{inputenc} %%    %    \usepackage{pgf} %    \usepackage{tikz} \usepackage{bodegraph} % per i diagrammi di Bode  \begin{document}              \begin{tikzpicture}[xscale=7/4]             \begin{scope}[yscale=3/40]             \semilog{-2}{2}{-20}{20}             \BodeGraph[asymp lines,samples=100]{-2:2}             {\POAmpAsymp{6}{0.3}}             \BodeGraph{-2:2}{\POAmp{6}{0.3}}             \end{scope}             \begin{scope}[yshift=-2.5cm,yscale=3/90]             \semilog{-2}{2}{-90}{0}             \BodeGraph[asymp lines,samples=100, const plot]{-2:2}             {\POArgAsymp{6}{0.3}}             \BodeGraph{-2:2}{\POArg{6}{0.3}}             \end{scope}             \end{tikzpicture}            \end{document}   but it only show me the empty grid. As @Marijn suggested in a previous post, I tried only with the code for the bodegraph. Still the same...   And the result shoul look more o less like this:    Tanks in advance Fr3d


To display the lengths in millimeters by default

All my length are in millimetres and the command \the\mylength outputs a length in points. Idem with the \layout from the package layout.  How can I display all theses lengths in millimetres (more easily understandable than the points).


In Pokemon Go, is it better to have small defects for Attack, Defense, Stamina, or one big defect and perfect in other areas?

For example, if a Pokemon can have  Attack, Defense, Stamina of  14  14  14   Is that better than  15  15  12   Their perfection scores are the same: 93%, but one is more well rounded and one is perfect in two areas but with a bigger defect in one area.  Similarly, would that be better if it is  13  13  13   as opposed to:  15  15  09   or   14  14  11   ?


I'm no expert in any language, especially English, however..  In all questions lists, there're columns for votes, answers and views. The answers and views make sense, but a positive number in votes shows the sum of positive and negative votes for a question, not the number of votes that one might expect. At least this is what I am assuming since votes can be negative.  How about renaming votes to score or something else that's less misleading?


is a disease of having abnormally large size.  Is there a grammatical rule that says that it should be called "gigantism" and not "giantism"?


Why do they sell Cat 5 Ethernet splitters if you can’t split the signal?

I have tried splitting the cables that go into the router with a Y and it does not work.


dist$(x,A)=0$ if and only if $x\in \overline{A}$ (closure of $A$)

Let $(X,d)$ be  a metric space and non-empty $A\subset X$. The distance from $x$ to $A$ is defined as $$\mbox{dist}(x,A)=\inf\{d(x,a):a\in A\}$$  I want to show that dist$(x,A)=0$ if and only if $x$ is in the closure of $A$.     (=>): dist$(x,A)=0$ implies $\inf \{d(x,a):a\in A\}=0$. Suppose $x\not\in \overline{A}$, then $x\in X\setminus \overline{A}$, which is an open set. Thus $\exists\epsilon >0$ such that punctured open ball $B(x;\epsilon)\setminus\{x\}= \{y\in X:0<d(x,y)<\epsilon\} \subset X\setminus\overline{A}$. But then dist$(x,A)=\inf\{d(x,a):a\in A\}\ge \inf\{d(x,y):y\in B(x,\epsilon)\setminus\{x\}\}>0$. This is a contradiction! Hence, $x\in \overline{A}$.      (<=): Suppose $x\in \overline{A}$. If $x\in A^\circ$ (the interior of $A$) then $\inf\{d(x,a):a\in A\}=d(x,x)=0$.   If $x\not\in A^\circ$ then $\exists $ a sequence $(a_k)_k\subset A$ such that $a_k$ converges to $x$. Then, $\forall \epsilon > 0, \exists N\in\mathbb{N}$ such that $k\ge N\implies d(a_k,x)<\epsilon$.      So that dist$(x,A)=\inf\{d(x,a_k)\}=\lim\limits_{k\to\infty} d(x,a_n) = 0$.   Please let me know if my proof is rigorous / correct. I'm not completely sure, think it's better to check.


My server has rebooted a few times in the past week due to electricity cuts. I would like to know when was the server running.  Uptime only gives me information about the last time it's been on.  Last only gives me information about user login but nobody has logged into the server during this time.  Is there a way to check this with the packages installed by default in Ubuntu server 12.04?


I remember seeing a TV show in the 90s (I am not sure when it was first aired). It...:   Has a medieval setting Has a handful of heroes, all young men and women (ie: mid to high teens)  à la Power Rangers The protagonists use weapons/powers based on the classical elements: Fire, Water, Earth, Air/Wind   Does anyone know what the name of the show?


What is the difference between the following:  Things started to work again. Things started working again.


Is there a common or well understood word for 'a group with no shared members'?

I have two mathematical sets that have no common elements.    In mathematical terms, these are called 'disjoint sets', and together they are called a 'partition'.  What common or well understood word or phrase could I use to explain what these are, when speaking to someone who doesn't know what a disjoint set or partition is?  Edit: I am looking for an alternative to the answer found in . I am looking for a reasonably common word/phrase to replace "disjoint". The other answer found in the linked question, "orthogonal", is much too obscure for my purpose.


What makes a good entry level road bike?

I've been riding a mountain bike for years, but I prefer to go longer distances on paved ground, so I think a road bike would be better. When I ask what is a good bike, I don't need brands or models - more like what components of the bike should I look for, and what should I avoid? Additionally, is it necessary to "go big or don't go at all" as far as spending - getting a real good quality road bike for $500 to a few thousand, or should I cheap out on a $100-200 road bike, as it is my first, then get a better one when I'm more experienced?


Is it ok to remove the intercept in a linear regression model (OLS) if the results are really good?

So I've gone through this  and all the answers where the general consensus is that you should never remove the intercept of the linear regression model. The most upvoted answer says:     The shortest answer: never, unless you are sure that your linear approximation of the data generating process (linear regression model) either by some theoretical or any other reasons is forced to go through the origin. If not the other regression parameters will be biased even if intercept is statistically insignificant    However, I'd like to know if it's a good idea to remove the intercept if you  get better prediction results (Adjusted r-squared: 0.82) ? I've trained the model without specifying the intercept ( extra details: used OLS regression in python statsmodels package) and then tested the results.     I cross checked the results and saw that the predicted values and actual values was real close (+/-2 difference in average). So is it a good enough reason as to foresake the intercept?


Can I receive an email notification when someone submits a form?

I would like to receive an email notification when someone submits a form. I am on the free version.


Can spells from the Magic Initiate feat be swapped out for different ones?

For example, a character takes the Magic Initiate feat at level 4, picking spells from the Wizard spell list, because they have been researching and learning all they can about magic (such as a Sorcerer studying their inborn magic or a High Elf expanding on their Cantrip feature). It stands to reason that they would continue their research of magic over their next 16 levels, which indicates that they should learn new spells.  At any point, can the spells chosen through the Magic Initiate feat be swapped out for other spells, according to the same Magic Initiate spell selection rules of two cantrips and one 1st-level spell?


Why are trailing line breaks stripped when used as an argument (for echo)?

When I run this…  echo "              fdsfsd dsfsdf    "     I really get the output of all these lines.  However, if I use this output as an argument for echo again…:  echo "$(echo "    fdsfsd dsfsdf    ")"   …I do only get the leading new lines, not the trailing ones:  (4 empty lines)       fdsfsd dsfsdf   So: Why does this happen? (Note I explicitly quoted the output of the $(), so I thought that would prevent such things.) And how can I prevent this?  (tested with zsh)  BTW, same result if I use printf instead of echo – although the former obviously always misses the last line break echo would usually add.


Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$

This may seem like a silly question, but I just wanted to check. I know there are proofs that if $f(x)=f'(x)$ then $f(x)=Ae^x$. But can we 'invent' another function that obeys $f(x)=f'(x)$ which is non-trivial?


How can I parse numbers written in English words into their numeric equivalent in F#?

What's the easiest way in F# (in a functional/recursive style) to, given a number in words, convert it to it's numeric equivalent?  I'm looking at only English for now. E.g:  let parseNumber (s : string) =     match s with     | "One" -> 1     | _ - failwith "Cannot parse"  let result = parseNumber "One Thousand Two Hundred" // result should be 12000   Is there any way of doing this that doesn't involve a massive look-up table?


What if we get an answer in user comments?

I asked a question on Stack Overflow, . For that question I got answered by Gintas K's comments, but I can't accept that comment as the accepted answer. So I wrote that comment as an answer and accepted it. How do I accept a comment like that as the accepted answer?


This question had a sequel to the question just below.   Thanks to WS2's reply and link I draw my conclusion for the phrase 'blow me down.' But to my surprise I think I have reached a different answer than you.  Here are examples that you presented in your link.        I'm absolutely blowed if I know what to do.         I think this sentence means that I would be shocked if I know what to   do. That is, I think I have no chance of knowing what to do.          Blow me tight if ever I saw such a thing in my life before.         I would be shocked if I saw such a thing in my life before. There's no   chance of my seeing such a thing in my life before. That is, that's my   first time that I saw such a thing in my life.         Blow me if I do!         I would be shocked if I do.  That is, there's no chance that I do   (it).   Am I right in my description of the three sentences above?  And on the sentence in question, I draw my comprehension based on your explanation.        "Blow me down if she didn’t just run off!"         I would be shocked if she didn’t just run off! There's no chance that   she didn’t just run off. That is, she must have just run off. If not,   I would be shocked.   The last line is my conclusion that I drew on your explanation.  Here is your sentences. "When she just ran off, you could have knocked me over with a feather!" "She's run off ? - well blow me down!"  These two sentences implies that I am shocked because she runs off. That means the speaker didn't expect she would run off.  If that is your thought, that's just the opposite of mine.


Set nomodeset in usb installation (efi loader with iso)

I'm working with  to creating a live USB on OS X. I managed to get Ubuntu booted but the screen looks like a corrupt/glitch image. I can just about make out the clock on the bottom right and a few icons. I've been told that this is easily fixed and that nomodeset needs to be set for the graphics card. But all the solutions I find are for Ubuntu systems installed to hard drives. Where you can cd in and edit the grub file - how do you do this is if it's in an iso?


Could I ask for help in the following homework question?     Given any metric space $(M, d)$, show that the metric $\rho = d /(1 + d)$ is always uniformly equivalent to $d$ but that there are cases in which the inequality $d < C \rho$ may fail to hold.   Does equivalent imply uniformly equivalent?


Has any author ever attempted to explain Magneto's fitness and longevity?

Many superheros have their origins in/around world war 2 or older events, Wonder woman was a nurse, captain america was a soldier, but other these characters very super powers explain their lack of aging and general fitness. Other characters who have a defined back story, like Batman or the Flash, rely less on real-world dateable events.  Magneto on the other hand, in the year 2019, is getting a bit old for his backstory -- which is integral to his character motivations. Having survived the holocaust he wants to prevent the same thing from happening to mutants. Even assuming he were born in the last year of WWII, he'd be 75; more likely at least 80 given he was old enough to remember it.   To my knowledge he has no powers that would keep him from aging or showing infirmity, yet he's generally shown as middle aged or slightly older and still very fit. Has any author attempted to explain this away in universe?  (Obviously the out of universe explanation is he's recognizable with a relatable story and marvel wants to keep cashing in)


I'm reading a group theory book and the author gives the following definition for cycle type:  If $\sigma \in S_n$ is the product of disjoint cycles of lengths $n_1,n_2,\ldots ,n_r$ with $n_1 \leq n_2 \leq \cdots \leq n_r$ (including its 1-cycles) then the sequence of integers $n_1, n_2, \ldots ,n_r$ is called the cycle type of $\sigma$ where $S_n$ is the symmetric group of degree n.  I'm curious about the significance of the cycle type. If two elements of $S_n$ have the same cycle type are they somehow related?


I'm building an Online Food Ordering website, where users can order food from their favourite restaurants. I'm confused in selecting the colors for the website, can any one help me with it.    Which colors should I use for website background or should I put delicious food images? Which colors to use for the text?   I have read some article that Red, Green, Oranges are good options for food related websites.


Generating unique random numbers except from a specific one in C

I was wondering, how can I generate unique random numbers except from a specific one. For example, if I want to generate numbers in range 1 to 10 except from 3, the output should be something like this:  7 6 1 2 4 9 5 8 10


Do I have to inform the hotel about my lateness for check in?

It's my first time to personally book a room, and I'm a little bit confused with the notion of "check in".  Let's say I am supposed to arrive at the hotel on Aug. 15th @ 01:00 am (the room is fully paid for all of planned night) whose check in time is 03:00 pm. Then, if I doesn't book Aug. 14th, I have to wait 14 hours till the check in time (!); however, if I book Aug. 14th, as well, then I can directly get to the hotel at 01:00 am.  But I do not know whether I must inform the hotel about this plan or not, because some people say if you don't be at the hotel some time around the check in time (say mostly one hour later), they will maybe give your room to another one.  Is it true?! I mean, I have already paid the price for Aug. 14th; why do I have to inform the hotel about my lateness?


Travel Visa-Free stopover Guangzhou, multi-city

Does anyone know if the following itinerary is valid for a visa-free stopover in Guangzhou?  Brisbane, Australia -> Singapore -> Guangzhou -> Brisbane?  If I buy the tickets multi-city will this work? Will it not work if I book it all on Singapore Airlines since technically I'm going through Singapore in order to arrive back home?


Insert variable into global namespace from within a function?

Is it possible to write a function which inserts an object into the global namespace and binds it to a variable? E.g.:  >>> 'var' in dir() False >>> def insert_into_global_namespace(): ...        var = "an object" ...        inject var >>> insert_into_global_namespace() >>> var "an object"


MicroSD card is set to Read-only state. How can I write data on it?

I have a MicroSD card reader in my notebook. When I insert a MicroSD memory card into it, I can't write any data on it - it's read-only. The same thing happens when I try to do it under root. And I can't change the permission policy for it. This problem happens for all microSD cards (I've tested 2 cards). I've encountered it on Ubuntu 12.04 LTS, now I'm on Ubuntu 12.10, the problem is still on it's place. When I try to insert such a "read-only" card in my mobile phone, everything's OK and I can write data on it. So, can anybody tell me, how can I write a data onto the card?  UPD: here's fdisk -l output:  Disk /dev/sdc1: 2013 MB, 2013135360 bytes 62 heads, 62 sectors/track, 1022 cylinders, total 3931905 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x00000000   Device Boot      Start         End      Blocks   Id  System   The file system of the card is msdos. As to me it's weird.   UPD2: I've found a small "lock" switch on my card adapter, and it turns out, that when I insert it in my notebook, it switches on. Perhaps, I have to find some glue or something to get that switch stuck...  UPD3: There was no glue near me, so I've decided to buy another card-reader.


W: An error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: http://deb.playonlinux.com precise InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 73F0D6E88E3D6C3A W: Failed to fetch http://deb.playonlinux.com/dists/precise/InRelease  The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 73F0D6E88E3D6C3A W: Some index files failed to download. They have been ignored, or old ones used instead.


How do you text people from your number and not from your Apple ID email?

I've recently went to an Apple store and the guy reset all my settings. Lately, whenever I text people with iPhones, they tell me that I don't text from my number anymore, but from my Apple ID email. I tried going into Settings and changing some things, and texting some of my friends to see if it's changed but they keep saying I'm still texting from my email. How do I reverse this or text from my regular number?


Terminal states gparted is already installed but I cant find it in my apps menu

when I tried to install gparted in the past using a command it worked without any problem.  But now when I tried to install the gparted in my newly installed Ubuntu with the same code it stats that gparted is already installed.  How is that even possible when I installed it for the first time.  Moreover there is no gparted in the apps menu ....  sudo apt-get install gparted Reading package lists... Done Building dependency tree        Reading state information... Done gparted is already the newest version (0.25.0-1). 0 upgraded, 0 newly installed, 0 to remove and 454 not upgraded.


Can anyone tell me that actually What vector multiplication is?

I am a high school student. Yesterday I attended a lecture on vector multiplication (first time). There was something I was not able to understand. The only concept of multiplication I had before is 2x3=6, means that if we write '3' 2 times we'll get 6.  But now there are two types of multiplications:   Dot product Cross product   Dot product  What I understood is that dot product of two vectors is a scalar quantity, But how?   Here if we multiply projection of A on B (A cos0) with B, finally that product would be in the direction of B?, am I right or wrong?  Secondly please specify the difference between this dot product and ordinary multiplication which I stated above (2x3=6)?  Cross product:    By Cross product I understand that it's the product of the 'length of perpendicular produced for projecting A on B' and 'B'?   What is the purpose and meaning of this product?  And After multiplication product is multiplied by unit vector n, which perpendicular to the A and B.  Why the cross product is always perpendicular to the given vectors?  And if I am right that Cross product is the product of the 'length of perpendicular produced for projecting A on B' and 'B' then why that projection is not shown in this diagram of cross product (which is taken from wikipedia)?


MIXED_DML_OPERATION, DML operation on setup object is not permitted after you have updated a non-setup object

I've written a trigger that will add users to a public group but can't seem to get my test class to work. I have 100% code coverage but the test keeps failing with the Mixed DML Operation error.   Trigger:      trigger addintoPublicgroup on User (after insert, after update) {     AddUser.AddToGroups(trigger.newMap.keySet()); }   Class:  //This class is refrenced in the apex trigger Add to Group in order to add users automatically to public groups. public class AddUser{  @future public static void AddToGroups(Set<Id> userIds) {  //Get the groups that the user should be added to Group g=[select Id from Group Where DeveloperName='Coordinators']; Profile p =[select Id from Profile Where Name = 'Sesaco Coordinator'];   List<User> users=[Select Id,Name from user Where Id IN :userIds and user.ProfileId=:p.Id];   List<GroupMember>listGroupMember =new List<GroupMember>();    // loop the users that have been created  for (User user : users){       GroupMember gm= new GroupMember();        gm.GroupId=g.id;       gm.UserOrGroupId = user.id;       listGroupMember.add(gm);     }   insert listGroupMember; } }   Test Class:  @isTest public class addintoPublicgroup_Test {      static testMethod void AddToGroups(){      County__c cty = new County__c();         cty.Name = 'Whitman';         cty.State__c = 'WA';         cty.Planting_Area__c = '1';         insert cty;      Account act = new Account();         act.Name = 'Test Account2';         act.Account_Status__c = 'Active';         act.BillingCity = 'Pullman';         act.BillingState = 'WA';         act.BillingCountry = 'US';         act.Description = 'Go Cougs';         act.County__c = cty.Id;         insert act;      Contact con = new Contact();         con.FirstName = 'Test User';         con.LastName = 'Number One';         con.Email = 'testing222111@sesaco.com';         con.AccountId = act.Id;         insert con;          Profile p = [Select Id from Profile WHERE Name = 'Sesaco Coordinator'];          User usr = new User();         usr.FirstName = 'Test User';         usr.LastName = 'Number One';         usr.Email = 'testing222111@sesaco.com';         usr.Username = 'testing222111@sesaco.com';         usr.Alias = 'tester';         usr.ContactId = con.Id;         usr.ProfileId = p.Id;         usr.TimeZoneSidKey    = 'America/Denver';         usr.LocaleSidKey      = 'en_US';         usr.EmailEncodingKey  = 'UTF-8';         usr.LanguageLocaleKey = 'en_US';           try {             insert usr;         } catch (Exception e) {            System.debug('An error occurred');         }        } }   I believe I need to use a combination of System.RunAs and @future in my test class but am unfamiliar with either of those uses in a test class. Any help is appreciated!


The Android app crashes when trying to upload a picture from my phone

When trying to upload a picture from my phone, the Android app crashes a few different ways, depending on whether I select the Gallery or Photos image source. (Uploading by manually entering a URL works perfectly.) The problem occurred using beta versions 1.0.63, 1.0.71, 1.0.72, and now 1.0.73, on a Samsung Galaxy S4 running Android 4.1.2.  These are the steps which I've used:   Open an Ask/Answer a Question window, enter a sentence. Click on the picture icon, which opens a "Choose Image Source" window. Select "From Device," which opens a window offering a choice of "Gallery" or "Photos."   If I select Gallery, when the pictures open, choosing one causes the app to immediately crash. The circle goes around for about 15 seconds (see picture on left below), then re-opens to the Ask a Question window, where the original text is still visible. The camera icon isn't live (it's grayed-out), so trying to post again in that window is not an option.   If I select Photos, when the pictures open, I can choose one. It pauses, which I interpret as an effort to post. After about 10 seconds, however, the app crashes to the feed screen, and an error message in a black box appears which says "Unfortunately, the process com.stackexchange.marvin has stopped." (See picture on right below.) There are Report and OK options under the error message. Initially I was able to get a screenshot, however the message disappeared before I could select Report, then the app crashed. However, on 8/11/15, and a few times since, I've been able to submit a report before the crash.  Update 9/2/15: With version 1.0.72, the error message varied, and many tries produced a picture a few times. There was no indication as to when or why it would happen, and each of those times, the picture posted sideways. With version 1.0.73, the error message has returned to the original, and fifty tries have not produced a posted picture from either Gallery or Photos. I'm updating this report in the hope that others are experiencing the same problem, or to be notified if the developers are aware of it. Thanks!


Are there nontrivial vector spaces with finitely many elements?

I have only seen infinite vector spaces and the one finite vector space i.e the trivial vector space $\{0\}$. Is there any other finite vector space?


Prove that $n$ factorial is larger than $n$ cube if $n$ is large enough

I try to solve it by Mathematical Induction. However I don't know how to prove that $(k+1)!>(k+1)^3$


Which loss function is correct for logistic regression?

I read about two versions of the loss function for logistic regression, which of them is correct and why?  From  (in Chinese), with $\beta = (w, b)\text{ and }\beta^Tx=w^Tx +b$: $$l(\beta) = \sum\limits_{i=1}^{m}\Big(-y_i\beta^Tx_i+\ln(1+e^{\beta^Tx_i})\Big)  \tag 1$$  From my college course, with $z_i = y_if(x_i)=y_i(w^Tx_i + b)$: $$L(z_i)=\log(1+e^{-z_i}) \tag 2$$    I know that the first one is an accumulation of all samples and the second one is for a single sample, but I am more curious about the difference in the form of two loss functions. Somehow I have a feeling that they are equivalent.


How to efficiently get the length of linestrings intersecting a huge raster file?

I have a huge shapefile (roadnetwork of Europe) and a raster file (Europe, 100x100m resolution). I want to calculate the length of the roadnetwork for each raster cell, resulting in a new raster layer. The problem is that the number of raster cells is huge and the roadnetwork is very large. My current approach in R is to build 60x60 sub-raster (using the SpaDES-package, convert each sub-raster to polygons (using stars and sf) and then intersect the polygons with the road network. The problem is that this takes very long. Parallelizing the prozess does not work because of memory limitations (st_intersects/st_intersections cause doParallel to make copies of the whole road network for each thread). Is there a more efficient way to perform the task? Is there some software with which this taks can be done efficiently? Thanks!


Cyclic vector implies commuting linear operator is a polynomial

Let $T$ be a linear operator on the finite dimensional vector space $V$. Suppose $T$ has a cyclic vector. Prove that if $U$ is any linear operator which commutes with $T$, then $U$ is a polynomial in $T$.


Determining the characteristic of a field

If $\mathbb{F}=\{ 0,1,x,y\}$ is a field with four elements, why is the characteristic 2?   In a field with four elements, the characteristic is 2 or 3(since it has to be a prime). Is there any way to determine precisely the characteristic of this field, and in general any finite field?


R model developing & validating - Open to Discussion

Throughout my R journey I have noticed the way we can use given data to develop and validate a model.   Assume that you have given data for a problem   train.csv test.csv   Method A  Combine train+test data and develop a model using the combined data. Then use test.data to validate the model based on predicted error analysis.  Method B  Use train data to develop the model and then use test data to validate the model based on predicted error analysis.  Method C  Sub divided 75% as training data and 25% test data on train.csv file and use new training data for developing the model. Then use new test data to validate the model.  After that use initial given test data to double check the performance of the model.   I have identified 3 methods so it is bit confusing which one to use.  Are there any other methods other than these methods?  I need opinions from R experts on   What is the best practice? Does that depend on the scale of the problem (smaller data or big data)? a) Confusion matrix is the only way that can we use to check the performance of a model?   b) Is there any other matrices to check the performance?   c) Does it depend on the type of the model(lm(),glm(),tree(),svm() etc..)?  d) Do we have different matrices for different models to evaluate the model?


Calculate number of solutions for $\sum_{i=1}^k i\cdot x_i = n$

Is there a general method to find the number of non-negative integral solutions for $$ \sum_{i=1}^k i\cdot x_i = n $$


How to securely delete files stored on a SSD?

From a (very long, but definitely worth to read) :  When you delete a file in your OS, there is no reaction from either a hard drive or SSD. It isn’t until you overwrite the sector (on a hard drive) or page (on a SSD) that you actually lose the data. File recovery programs use this property to their advantage and that’s how they help you recover deleted files. The key distinction between HDDs and SSDs however is what happens when you overwrite a file. While a HDD can simply write the new data to the same sector, a SSD will allocate a new (or previously used) page for the overwritten data. The page that contains the now invalid data will simply be marked as invalid and at some point it’ll get erased.  So, what would be the best way to securely erase files stored on a SSD? Overwriting with random data as we are used to from hard disks (e.g. using the "shred" utility) won't work unless you overwrite the WHOLE drive...


i am looking for an application that is like dropbox. i simply would like to synchronize my music folder (which is 100 GB) via LAN between my desktop & laptop. (you can see why i cannot use dropbox for there is the size restriction and it will try to upload a bus load of files to its central server)


Cannot change drive letter in command prompt (cmd) other than C:\

Not sure what might have triggered this but I have noticed that while using the command prompt in windows 10 I am unable to change the drive using the cd command for any of the drive letters other than C:. I have also noticed that the autocomplete function works just fine when trying to change directory into a specific folder from the target drive but the change in the directory just doesn't happen. Screenshots of the Disk Management tool and actual cmd prompt commands will follow:   This behavior does not apply to PowerShell so I can successfully change the drives.


When & How often do 4e Monster powers recharge?

How often should I roll power recharge rolls and at which point in the monster's turn do I re-roll them?  I'm trying to find the official definition of the recharge mechanic in the online compendium and I'm not seeing it there.


strange java string array null pointer exception

This problem came up in a practice test:  create a new string array, initialize it to null, then initializing the first element and printing it.  Why does this result in a null pointer exception?  Why doesn't it print "one"?   Is it something to do with string immutability?     public static void main(String args[]) {         try {             String arr[] = new String[10];             arr = null;             arr[0] = "one";             System.out.print(arr[0]);         } catch(NullPointerException nex) {              System.out.print("null pointer exception");          } catch(Exception ex) {             System.out.print("exception");         }     }   Thanks!


How to find the length of a remaining line?

I'd like to put some lines on a page where a student can answer a question, and I'd like that line to go from the prompt to the right edge of the text. The most simpleminded and (therefore?) unsuccessful of doing so is with the following MWE:  \documentclass{article}  \begin{document} \begin{enumerate} \item Prompt: \underline{\hspace{\linewidth}}  \underline{\hspace{\linewidth}} \end{enumerate} \end{document}   The problem is that the first line extends into the right margin. What I need is to find an expression that tells the first line how much space is left from the insertion point (right after "Prompt:") to the left margin.  The second line is exactly the right length.


I need to think of an example of a ring R with ideals I and J where I is an ideal of J and J is an ideal of R, but I is not an ideal of R.


Does a Patronus take form of an animal only?

So far what I can remember from books, I have encountered Patronus of a form belonging to Animal Kingdom only. Here's the list:   Harry Potter / James Potter: Stag Hermione Granger: Otter Ron Weasley: Jack Russell Terrier Albus Dumbledore: Phoenix Lily Potter / Snape: Doe Ginny Weasley: Horse Luna Lovegood: Hare Nymphadora Tonks: Jack Rabbit Remus Lupin / Nymphadora Tonks: Wolf Minerva McGonagall / Dolores Umbridge: Cat Kingsley Shacklebolt: Lynx Arthur Weasley: Weasle Cho Chang: Swan Seamus Finnigan: Fox Ernie Macmillan: Boar Aberforth Dumbledore: Goat   I know that a Patronus is unique to a person and it can change because of emotional upheaval.  But, what exactly is the rule of creating Patronus form? Can I create a Patronus of a form X-wings or R2-D2 or Millennium Falcon or USS Enterprise-E or TARDIS?


I got a secret hat "Chameleon hat".    I wonder what it is for.  I am confused between two possibilities:   Multiple Stack accounts Change in Display picture   What is it for exactly?


I created this table, but i want to increase the height of the rows so that the text would be centered and not hitting the horizontal lines.  I have this code:  \begin{document} \begin{center} \begin{tabular}{||c | c | c | c||}  \hline  & EUROSTOXX50 & Nikkei225 & DAX30 \\ [1ex]  \hline\hline $R_{adj} ^2$ & 0,389  & 0,233  & 0,663 \\ [1.9ex]  \hline $\hat{\theta}$ & 0,623 & 0,157 & 0,482 \\[1.9ex]  \hline $\hat{\alpha} $& 0,165 & 0,133 & 0,497 \\[1.9ex]  \hline  \end{tabular} \end{center} \end{document}


Can I install 12.04 using Wubi without an internet connection?

Do I need an active internet connection to install ubuntu 12.04 using wubi even after downloading the entire image file of the os.


Expansion of $x\mapsto\left(\frac \pi 2 + \arcsin x\right)^2$ in powers of $x+1$

Recently in these pages we have had occasion to see the trigonometric identity $$ 2\arcsin\sqrt x = \frac \pi 2 + \arcsin(2x-1). $$ From this we can immediately deduce that $$ \sqrt x = \sin\left( \frac \pi 4 + \frac 1 2 \arcsin(2x-1) \right) $$ This suggests that the arcsine function near the left endpoint of its graph is shaped  very similarly to the square root function. Part of this is obvious: it has a vertical tangent and is concave downward.  Sorry ‒ there was a typo in the question. What I intended is what the FIRST paragraph of the question was about; the second paragraph failed to be consistent with that since I left out the π/2 term. I've fixed it now.  But it makes me wonder about $x\mapsto \left(\frac \pi 2 + \arcsin x\right)^2$ near $x=-1.$ Is there anything interesting to say about an expansion of that function in powers of $(x+1)\text{ ?}$


Understanding derivative as slope to the curve

I am a novice in calculus and have been learning differentiation lately. I read many books and saw you tube videos. There I noticed that to find the slope of a point in a curve,people take a point $P=(x+h,f(x+h))$ and determine the slope $\frac{f(x+h)-f(x)}{h}$. Now to find the slope more accurately, they take the point $P$ close to $(x,h)$ and say that it boils down to a tangent line. But the tangent by definition will intersect the curve at only one point,in that case shouldn't $h=0$? I know that gives indeterminate form and the people use limits by taking $h$ close to $0$. My question is how is that line a tangent? Even if it is close to $0$,it is still not a $0$,right? So that line still intersects. In that case isn't the derivative an approximation instead of an exact answer. I may be wrong,so please forgive me if I made any mistake.


Exchange 2013 has stopped indexing mail on a specific date

A problem has recently occured where no ones mail is being indexed any more. Everyone can search their mail up until early December and then it just stopped.  When you go to the Indexing options on someones Outlook it recognises there are messages to be indexed as everything is still being received correctly but it refuses to budge.  This happens on both the web app and Outlook itself and I just don't know exchange well enough to diagnose the problem so anything that may point me in the right direction would help as i have seen this question:  but am unsure if it applies.  Running Exchange 2013 + Windows Server 2012 Datacenter  So far:   Checked Index status with Get-MailboxDatabaseCopyStatus -Server | FL Name,Index Mailbox database Index was corrupted, others saying Reseeding required Stopped Search Host and Search Services Renamed folder, restarted services Mailbox status "Healthly" but others still on reseeding required Indexing seems to have got stuck around a particular date, namely, early December, and it doesn't seem to be crawling anymore Mailbox now shows Failed: Internal error has occured For the Database or Index   I just had a quick dig through some files an old technician moved before Christmas and I've possibly found something. Space on the server was low and they moved some of the .log files you find in the Mailbox folders as well as some of the database (.edp) files. Though I assume if we were actually using them we wouldn't be able to see the mail either but I wonder if it has something to do with it, because there's definitely some missing .log files.  Edit..(I've lost count) : The other databases are in use, it seems they were moved and they're still updating on the other drive, found the index folders for them (not in the normal hieracrchy) and working on reseeding those now with above solution.  Final Edit: Problem solved, answer is to make sure you check where all your DB's are and follow the procedure outlined in this question


Using the Mac terminal whenever I hit enter, regardless of shell it outputs the line with square brackets. The issue doesn't occur in iTerm2.   Dan@Mac ~                                                            [10:32:55]  [> $                                                                            ]  Dan@Mac ~                                                            [10:36:11]  [> $                                                                            ]  Dan@Mac ~                                                            [10:36:11]  > $        So above is what there term looks like, input goes at > $ however on enter it shows with [> $.  Any advice appreciated, let me know if you need any other details.   edit: To clarify as this was marked duplicate of another thread which asks the functionality/purpose of mark, when posting this I did not know what mark was or that it existed.


Why are 32.786Khz crystal cans soldered to PCB?

Every development board I have ever used that includes a 32.786Khz crystal has always had its can soldered directly to board.  What is the reason for this ? Is this to minimize radiated energy from the crystal during its operation (assuming that the pad its soldered to is ground) ?  If the can was not soldered to the board, what would be the effect ?  Added  If you look at this image, the crystal has 3 solder points. Two for the legs, and one for the case/shell/can (green arrow).   My question is about the reason for soldering the case/shell/can to the board.


How long does it take for an excited electron to return to ground state?

During a mock Cambridge interview, one of the questions was about how small a computer could theoretically be.The way I approached it was in terms of what something must be to be considered a computer.  I eventually made some progress, but I made a point that I am quite doubtful about. I said that one can use the photoelectric effect as a timer.  When you shine light on an atom and promote an electron to a higher energy level, there is a time delay before it returns to ground state (or at least there is a time delay between light being absorbed and light being re-radiated), which ought to be constant. I know this point may not really relate to the interview question.  Nevertheless, is what I said true? Is there a (measurable) time delay between the absorption of a photon and the re-radiation of a photon?


Prove that $a^2 > b^2$ ; if $a > b \geq 0$.

Problem: Hi, I'm trying to solve the following proof:  If $a > b \geq 0$, Prove that $a^2 > b^2$.  But I'm a bit new with proofs and I don't manage to write a proper one. I would be very grateful if someone could explain me which are the steps required to demonstrate the proof. Thank you.


How can I detect whenever a  is resized using javascript/jQuery

I know about  $(window).resize(function () {.....}); but this only works whenever the window is resized.   I tried attaching this event to a  e.g. $("#some-div").resize(function () {.....}); and it won't work.  Is there some other method using pure Javascript or jQuery?     Thanks


Physically Identify the failed hard drive

So, let's say your server had 6 healthy hard drives.  A drive fails (will not mount/detect, drops out of raid with errors) or is failing (SMART getting worse, etc).  You need to swap out the bad drive.  When you open the case you see.. six identical hard drives.  How can you tell which one is no longer healthy/mounting/functioning?  System would be linux, most likely ubuntu server, using at most simple software RAID.  The hard drives would be SATA and connected directly to the motherboard. (no raid controller)   I don't want to randomly disconnect drives until I pick the correct one.  The drives all appear identical to me; I imagine there is some common way to identify which drive is which that I am unaware of.  Does anyone have any pointers/tips/best practices?  Thanks!  EDIT: I had wanted this to be 'generalized' in a hand-wavy sort of way, but it just came off as 'incomplete' and 'horrible'.  My bad!


Why time slows only for moving object and not stationary observer? How the "stationary" & "moving" are decided?

Explanation for the questions in the title: According to the the (special theory of) Relativity, if an observer is stationary and sees a fast moving object then time runs faster for the observer compared to the mover.  For example, persons 'A' & 'B' are somewhere far away in universe standing on a platform. There is nothing nearby for several light years. Hypothetically assume that 'A' is standing on the platform and 'B' boards the rocket and flies away with a significant % of light speed. Due to which the time runs 1.67 faster for 'A' compared to 'B'. When 'B' returns to see 'A' after 10 years, 'A' has already passed 16.7 years. This is the premises of Relativity.      Now, my confusion starts here. Why only 'A' is considered "stationary" and 'B' as "moving"? Simulate the situation in other way for the same event. With respect to 'B', rocket is stationary and 'A' moves away with platform. And finally 'A' "returns" to see 'B'. In such case, 'B' should have grown older by 1.67 times.  But neither that happens nor both 'A' & 'B' age equally. It's just that 'B' remains younger. On the funny note, the premises of relativity here should be who travels relative to other and not who burns the fuel! :-) I have referred few questions in this forum, but couldn't get the answer.


Python: differences in search for regex and replace via regex

I'm writing a small script for auto-correcting interwiki translation links with . I look for the existing links and want to rewrite them in a standard format with links to all pages.  The text I'm looking for looks either somewhat like   {{Trad|EN=Under Spring|FR=Sources Interdites|DE=Verbotene Quellen}}    or multiline somewhat like   {{Trad |DE=Urwurzeln |EN=Prime Roots |ES=Raíces Primarias |FR=Primes Racines |RU =Изначальных Корней |H  =  |palette=primes }}    I manage to find these two instances in a wiki page source via   reg_strg = '{{trad([\w\s\|\=]*)}}' rex = re.search(reg_strg, text, re.IGNORECASE | re.MULTILINE)   That yields me the heart of the templates like (for the 1st case)  |EN=Under Spring|FR=Sources Interdites|DE=Verbotene Quellen   and similarily as multiline-string for the 2nd.  However, I now use the same reg_strg in a replace command, it fails to do any replacement, text remains unmodified, new_strg is created from what was read to constitute a replacement string. But the result is independent of whether new_strg is a multi-line string or just a simple "flobberigoo"  text = re.sub(reg_strg, new_strg, text, re.IGNORECASE | re.MULTILINE)   So obviously there is some difference between re.search and re.sub - however I fail to find that in the documentation (even though I am aware of the difference between re.search and re.match, I understood it such, that re.sub should behave like the first).  What do I miss? How can I replace the mentioned regex which I find in the pages with a string?  For completeness sake, this is the complete function including the debug prints:  def replace_translation_template(self, text, translations):     """     @param text The page text to look through     @param translations dictionary of translations     """     reg_strg = '{{trad([\w\s\|\=]*)}}'     rex = re.search(reg_strg, text, re.IGNORECASE | re.MULTILINE)      print("Replacing:")     try:         print(rex.group(1))         strgs = rex.group(1).split('|')         print(strgs)         new_strg = ""         for lang,pagename in translations.items():             if pagename is None:                 pagename = ""             new_strg += '|' + lang.upper() + '=' + pagename + '\n'          #print("New_strg: ", new_strg)          for lang in translations.keys():             for (n,str) in enumerate(strgs):                 if lang.upper() in str:                     strgs.pop(n)          for s in strgs:             if len(s) > 2:                 new_strg += '|' + s + '\n'         print(new_strg, '\n')         print('\n with \n \n')         text = re.sub(reg_strg, new_strg, text, re.IGNORECASE | re.MULTILINE)         print(text)      except:         print("no text matched:", rex)


I'm trying to add the Mirror modifier to a cube. I'm in Object Mode, I click add Modifier. When I click apply, the modifier disappears.  In Edit mode I can't add the modifier at all.   Am I doing something wrong?


Windows 10 64-bit requirements: Does my CPU support CMPXCHG16b, PrefetchW and LAHF/SAHF?

I'm currently trying to find out whether or not it would be a good idea to update my slightly dated notebook (Windows 7, 64-bit) to Windows 10. The problem is that Microsoft states in their  that to use the 64-bit version of Windows 10, a processor which supports CMPXCHG16b, PrefetchW and LAHF/SAHF is needed. I know that my processor is 64-bit (Intel Core i5-2430M @ 2.40 GHz) but I don't know how to find out whether it supports CMPXCHG16b, PrefetchW and LAHF/SAHF, and I have no idea what these mean.  I tried using Google and got no results that made sense to me, only some comparison of my i5 and a similar AMD processor. I also checked Intel's ARK website. If somebody could point me to where I can get more info I would be really grateful.


I found a sentence in the dictionary: 'He walked off in a most bizarre fashion.' I found in the grammar books, it is a rule to use 'the' before superlative degree.  Now, I'm confused when I should use article 'a' before 'most'.


Sum of the first $n$ triangular numbers - induction

Question:  Prove by mathematical induction that $$(1)+(1+2)+(1+2+3)+\cdots+(1+2+3+\cdots+n)=\frac{1}{6}n(n+1)(n+2)$$ is true for all positive integers n.  Attempt:  I did the the induction steps and I got up to here: $$RTP:\frac{1}{6}n(n+1)(n+2)+(1+2+3+\cdots+n+(n+1))=\frac{1}{6}(n+1)(n+2)(n+3)$$ Where do I go from here?  Thank you very much.


What to do with random effects correlation that equals 1 or -1?

Not so uncommon occurrence when dealing with complex maximal mixed models (estimating all possible random effects for given data and model) is perfect (+1 or -1) or nearly perfect correlation among some random effects. For the purpose of the discussion, let's observe the following model and model summary   Model: Y ~ X*Cond + (X*Cond|subj)  # Y = logit variable   # X = continuous variable   # Condition = values A and B, dummy coded; the design is repeated  #             so all participants go through both Conditions   # subject = random effects for different subjects    Random effects:  Groups  Name             Variance Std.Dev. Corr               subject (Intercept)      0.85052  0.9222                              X                0.08427  0.2903   -1.00                      CondB            0.54367  0.7373   -0.37  0.37                X:CondB          0.14812  0.3849    0.26 -0.26 -0.56 Number of obs: 39401, groups:  subject, 219  Fixed effects:                  Estimate Std. Error z value Pr(>|z|)     (Intercept)       2.49686    0.06909   36.14  < 2e-16 *** X                -1.03854    0.03812  -27.24  < 2e-16 *** CondB            -0.19707    0.06382   -3.09  0.00202 **  X:CondB           0.22809    0.05356    4.26 2.06e-05 ***   The supposed reason behind these perfect correlations is that we have created a model which is too complex for the data that we have. The common advice that is given in these situations is (e.g., Matuschek et al., 2017; ) to fix the overparameterized coefficients to 0, because such degenerate models tend to lower the power. If we observe a marked change in fixed effects in a reduced model, we should accept that one; if there is no change, then there is no problem in accepting the original one.  However, let's presume that we are not interested only in fixed effects controlled for RE (random effects), but also in the RE structure. In the given case, it would be theoretically sound to assume that Intercept and the slope X have non-zero negative correlation. Several questions follow:   What to do in such situations? Should we report the perfect correlation and say that our data is not "good enough" to estimate the "real" correlation? Or should we report the 0 correlation model? Or should we maybe try to set some other correlation to 0 in hope that the "important" one will not be perfect anymore? I don't think there are any 100% correct answers here, I would mostly like to hear your opinions. How to write the code which fixes the correlation of 2 specific random effects to 0, without influencing the correlations between other parameters?


After removing all URLs and resubmitting to google search engine. Iv'e not been indexed!

I'm fairly new to websites, earlier this year I started with a static website just submitting .html files to learn seo well. Eventually, I decided to get into wordpress and start fresh with the same domain.  I removed all my URLs from google search console but forgot to change the robots.txt and the sitemap. So basically the google crawler kept checking for URLs that doesn't exist. This went along for about 2 or 3 weeks till the wordpress site was ready and I found out about it and saw many 404 errors. I marked all as fixed and  -----I changed the robots.txt to this.-----  User-agent: * Disallow:  Sitemap: http://www.exampleDomain.com/post-sitemap.xml Sitemap: http://www.exampleDomain.com/page-sitemap.xml Sitemap: http://www.exampleDomain.com/category-sitemap.xml   -----and my sitemap to this.-----  <?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="//www.exampleDomain.com/main-sitemap.xsl"?> <sitemapindex xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">     <sitemap>         <loc>http://exampleDomain.com/post-sitemap.xml</loc>         <lastmod>2017-11-24T02:25:35+02:00</lastmod>     </sitemap>     <sitemap>         <loc>http://exampleDomain.com/page-sitemap.xml</loc>         <lastmod>2017-11-22T02:42:54+02:00</lastmod>     </sitemap>     <sitemap>         <loc>http://exampleDomain.com/category-sitemap.xml</loc>         <lastmod>2017-11-24T02:25:35+02:00</lastmod>     </sitemap> </sitemapindex>   I thought it could be the .htaccess but when I took a look at it. It was populated already by W3 Cache plugin. So it can't be that.  Just to note the new sitemap is reading properly as well as the robots.txt on Google console.  There hasn't been any virus attacks plus the domain is mine from the beginning.  This all happened when I removed all URLs and tried to resubmit the fresh website with the same domain. I don't understand why am I not being indexed already? It been about two days.  Could it be that I need to wait a while like at the beginning when I first submitted to Google search? It takes a good few days, if I'm not mistaken or is it something else.


Best way to get InnerXml of an XElement?

What's the best way to get the contents of the mixed body element in the code below?  The element might contain either XHTML or text, but I just want its contents in string form.  The XmlElement type has the InnerXml property which is exactly what I'm after.  The code as written almost does what I want, but includes the surrounding <body>...</body> element, which I don't want.  XDocument doc = XDocument.Load(new StreamReader(s)); var templates = from t in doc.Descendants("template")                 where t.Attribute("name").Value == templateName                 select new                 {                    Subject = t.Element("subject").Value,                    Body = t.Element("body").ToString()                 };


Is it a bad practice to use implicit wait in Selenium Webdriver? Should one use only explicit wait?

I was reading up on implicit and explicit waits and found the following two statements:     Implicit wait is not considered a good practice because different browsers have different loading times and implicit wait will cause   different results in different browsers.   I have tried to find the blog where I read this, but couldn't find it. But, a similar view is expressed in  article.  Next quote is from :     When compared to Explicit wait, Implicit wait is transparent and   uncomplicated. The syntax and approach is simpler than explicit wait.   Being easy and simple to apply, implicit wait introduces a few   drawbacks as well. It gives rise to the test script execution time as   each of the command would be ceased to wait for a stipulated amount of   time before resuming the execution.   Question: Is it a bad practice to use implicit wait? Should one use only explicit wait?  Note: From the Selenium Documentation, it is clear that one should not use both the waits together. I am asking only about implicit wait.


What is the meaning of the third derivative of a function at a point

(Originally  by AJAY.)  What is the geometric, physical, or other meaning of the third derivative of a function at a point?  If you have interesting things to say about the meaning of the first and second derivatives, please do so.


I'm comparing two list given in the list to see if the item.name exists in both for loop. If not then add into a list to show the error for the missing names.  set<id> setAssetIds = new set<id>(); list<Asset_Store__c>  assets = [select id,name......]; for(Asset_Store__c item : assets ) {     setAssetIds.add(item.id);  }   list<Meter__c>  meters = [select id,name......where id in : setAssetIds];  //now comparing the two lists for(Asset_Store__c a : assets) {    for(Meter__c m : meters)    {      if(a.Name != m.Name)      {        //not matched...        break;      }     } }   the problem with the above approach is that, its not finding the correct name.


I'm curious about some of the hearthstone rules, specifically about when the game is considered a tie.  So, for example, what happens in the following scenarios?   If a warlock plays hellfire when both heroes are at 3hp or less. If your opponent has 5hp, and you have 3hp. You play a leper gnome, and then hellfire.   So, what happens in such occasions? A tie? Both opponents lose? or what else?


Homeomorphism between the Unit Disc and Complex Plane

Show that the function  $$\phi (z) = \frac{z}{1 - |z|} $$  defines a homeomorphism between the unit disc $D_{1}(0)$ and $\mathbb{C}$.  Now this is obviously bijective, as   $$ \phi^{-1} (z) = \frac{z}{1 + |z|}$$   gives an inverse function, as  $$ \phi^{-1} \circ \phi (z) = \frac{\frac{z}{1 - |z|}}{1 + \left| \frac{z}{1 - |z|}\right|} = \frac{z}{1 - |z| + |z|} = z$$  Noting that $| \ 1 - |z| \ | = 1 - |z|$ as $|z| < 1 $ always.   Similarly, we have $$ \phi \circ \phi^{-1} = \frac{\frac{z}{1 + |z|}}{1 - \left| \frac{z}{1 + |z|} \right|} = \frac{z}{1 + |z| - |z|} = z$$ Noting that $| \ 1 + |z| \ | = 1 + |z|$ as $1 + |z| > 0$ always.   I am assuming continuity follows from the fact that both $\phi$ and $\phi^{-1}$ are compositions of continuous functions? Furthermore, how do I know that the range of the first is all of the complex plane, and the range of the second is just the unit disc? That is,  $$ \phi (D_{1}(0)) = \mathbb{C} \quad \text{and} \quad \phi^{-1}(\mathbb{C}) = D_{1}(0)$$


How to solve $ \lim_{n\to\infty} \frac {(n!)^\frac{1}{n}}{n} $?

I need to find the limit for:   $ \lim_{n\to\infty} \frac {(n!)^\frac{1}{n}}{n} $  I know the answer is $\frac {1}{e}$ but I have no idea how to get that answer. I'd appreciate some help.


Tag name overflow on "top tags" section of user profile if tag name is long

On the user profile page in the «Top tags» section there is a block for each tag, which contains:  Tag name  Score  Number of posts   If tag name is long, then the tag name may overflow, and parts (2) and (3) are not showing at all. It can be viewed in profiles of many users (all screenshots are from stackoverflow.com, but the error relates to all Stack Exchange sites):


Finding inverse of polynomial in a field

I'm having trouble with the procedure to find an inverse of a polynomial in a field. For example, take:     In $\frac{\mathbb{Z}_3[x]}{m(x)}$, where $m(x) = x^3 + 2x +1$, find the inverse of $x^2 + 1$.   My understanding is that one needs to use the (Extended?) Euclidean Algorithm and Bezout's Identity. Here's what I currently have:  Proceeding with Euclid's algorithm:  $$ x^3 + 2x + 1  =(x^2 + 1)(x) + (x + 1) \\\\   x^2 + 1 = (x + 1)(2 + x) + 2$$  We stop here because 2 is invertible in $\mathbb{Z}_3[x]$. We rewrite it using a congruence:  $$(x+1)(2+x) \equiv 2 \mod{(x^2+1)}$$  I don't understand the high level concepts sufficiently well and I'm lost from here. Thoughts?  Wikipedia has a page on this we a , but it's still not clear in my mind.  Note that  has almost the same title, but it's a level of abstraction higher. It doesn't help me, as I don't understand the basic concepts.  Thanks.


Hacking cloudera virtualbox vm to run on 32 bit windows os

Cloudera provides 64 bit VirtualBox vm to play with hadoop tools. I have a personal laptop which hosts 32 bit Windows OS. Is there any hack to run the 64 bit virtualbox vm to execute on my Windows 7 32-bit.  The VirtualBox i am using is a 32 bit. The Cloudera VM is 64 bit. The VT-x is enabled and also i have changed my chipset to ICH9. Enabled I/o APIC.  But when i boot my cloudera VM i am getting the below issue.    Configuration details.    This question is very specific to cloudera as cloudera ia not providing any 32 bit VM's.


So I had these two functions and the following exercise:  $f(x)=x^3-2x^2$ $g_p(x)=px$ Determine all values of $p$ for which $f$ and $g_p$ have three points in common.  Whats a good way to tackle this? I tried equaling them to each other but that doesn't seem to work. Any good methods? (No hints please).


Whenever I create a document in Microsoft Word, it complains about a lot of my sentences being in passive voice. But, when I read that sentence aloud, it sounds fine to me. I am not sure if it is just me and will a statement in passive voice sound strange to a native speaker?  So, my question is, is it considered bad form to use passive voice generally? Or in some specific cases like written communications only?  Edit: If it is ok to use passive voice, then why does MS-Word complain?


Why does this camera generated JPEG look better than the software generated one?

I was post-processing some photos on Nikon's Capture NX-D I had taken during holidays with a B700 camera and noticed some chromatic aberration in a picture. When I compared the post-processed photo and the camera generated one I found the latter to be actually better, even when I used the same configurations.  The camera generated photo (detail):   Same image generated by Capture NX-D without changing any configurations (I  believe it should give the same result as the camera):   Now the same image, but with axial chromatic aberration correction enabled (doesn't help very much...):   Does the Nikon camera just do a better job at processing its own images than Nikon's software? Well, if that's the case, there is no point in shooting RAW....


There are 21 members in MY clan. I'm the leader. I have been the leader of this clan for a year and never left the clan. But I still can not participate in the league war.  One of my co-leaders started a league war and it is only allowing 15 members in the war and they can't be exchanged for any other people including me. I have been in this clan the whole time so I couldn't have been in a different clan or anything. Why can I not be in the war? Its telling me I'm a spectator. I am high enough rank as well so it doesn't make sense.... please help. Thank you!!


What is difference between people and peoples?

Would anyone like to comprehensively explain? I am not sure peoples word exist or not. Kindly request to you all please explain about this.  Thanks.


Why black screen after Ubuntu installed?

I have just installed Ubuntu using ubuntu-16.04.4-desktop-amd64.iso. I had Endless OS on my lepton and I decided to overwrite it by Ubuntu.  Now, when I start my laptop, I first see "acer" logo, then, for a second I see a purple screen and then black screen.  What can I do to bring my new laptop back to the operational state?


I am a little bit confused about which is really the energy operator. During the lectures, the professor told us that the energy operator is simply the Hamiltonian $\hat{H}$ and that the eigenvalues represent the energy of the system. On Wikipedia [1], though, there is written that the energy operator is  $$ i \hbar \frac{\partial}{\partial t}. $$  On this website I rode that $\hat{H}$ and $\hat{E}$ are the same thing so now I do not understand which one is the right energy operator.  [1]


Show that if $p$ is a prime number $> 3$ then $24 \mid p^2-1$

Hi guys can someone help me with this ?(Without using Modular arithmetic)  Show that if $p$ is a prime number $>3$ then $24$ $\mid$ $p^2-1$


why does it do this when initializing a 2d list

when I initialize an array in python like so and then assign an element to a different value and then print out the 2d list  dist = [[0]*3]*3 dist[1][1] = 1   It gives me this  [[0,1,0],[0,1,0],[0,1,0]]   Can someone explain to me why the whole column has changed instead of just the specific element?


Optimise pathfinding failure - can I reduce the number of sweeps?

I've got pathfinding working on a simple 2D grid map. NPCs can now move around the board and avoid areas they cannot travel. This works well, and is carried out by a single sweep of the board to calculate the path.  If there is no path to the destination, I want the entities to move as close as possible. I have also accomplished this, and have been able to reuse my pathfinding code for this purpose. Essentially, if the initial sweep fails to find a path, the reverse sweep is carried out, which essentially identifies every area which is reachable by the entity. The distance from each cell to the intended destination is already calculated by the pathfinding algorithm. So then I just sort the array of accessible cells by their distance from the destination, and the first one is the closest to the destination. Then I use the pathfinder function again to calculate a path to that closest point.  This does work flawlessly, but it seems inefficient. The process of a failed path find in summary is:   Sweep the board for a path to the destination (which fails) Sweep the board a second time to find all cells accessible by the entity Sweep the board a third time to calculate the path from the entity to the cell which is closest to the destination   I suspect the answer is that this is the only way to accomplish what I want; I need to calculate all three pieces of information ((1) whether a path exists, (2) which cell is closes, and (3) how to get to the closest cell), but I'm far from an expert on these algorithms so if there is a better way I would love to know!


I'm setting up a child theme in WordPress and I can't make add_action to be fired within functions.php.  Functions.php is called and I can run code from within. Any idea on what I'm doing wrong?  $debug_msg = "Hi there!";  function test_function() {     error_log($debug_msg, 0);  } add_action('init', 'test_function', 20);


Why is it that Harry Potter is the only one who should defeat Voldemort?

In the Harry Potter universe, I understand there is this prophecy by Sybill Trelawney:     The one with the power to vanquish the Dark Lord approaches... born to those who have thrice defied him, born as the seventh month dies... and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not... and either must die at the hand of the other for neither can live while the other survives... the one with the power to vanquish the Dark Lord will be born as the seventh month dies...   Harry Potter and the Order of the Phoenix, The Department of Mysteries.   My question is why Harry or Neville?  Albus Dumbledore is the most powerful wizard in the Harry Potter universe, having defeated Grindelwald in 1945 and gained control of the Elder Wand. I understand very well, he never became the 'Master of Death', the Master of Deathly Hallows, also he accepted his death and death could not conquer him and Dumbledore calls him the 'true Master of Death' in Deathly Hallows. Is this a possible reason why Harry is the one who can defeat Voldemort?  I mean: Dumbledore defeated Grindelwald in an epic duel without any Deathly Hallow? He could have destroyed all the horcruxes, much before Harry Potter was born and defeated Voldemort. He wouldn't have known about it, true..and maybe after Harry was born he'd have to kill Harry because he unwittingly was a horcrux, but one death is nothing compared to what Voldemort would have done in power, right?  I feel in a duel with Voldemort and Dumbledore, Dumbledore would eventually win because Voldemort always feared him and Dumbledore knows how to take him down.  I mean I understand in Lord of the Rings, none of the 'Wise' could destroy the One Ring because by even accepting the ring they could become a next Dark Lord, and hence it had to be Frodo, Sam, and Gollum because they had qualities different from Men, Elves, Wizard, Dwarves etc.  Why is Harry so important?


I have an Acer Aspire One netbook which has Windows 7 starter. I have done the recent Windows updates, and says my windows 7 is all up to date. My dad has the same netbook but received the "Windows 10 icon at the bottom tray". My question is, why haven't I received the icon yet through the Windows updates? Which file contains that KB3035583?