Define $$f(z)=\ln r + i\theta$$ on the domain $\{z:r\gt , 0\lt \theta \lt 2\pi\}$.   This domain is just a punctured disk of radius $\ln r$, correct?  How does one determine whether this is analytic, I can't see how I would take the CREs  $$u(r,\theta) = \ln r$$ $$v(r,\theta) = \theta.$$  Should I convert this back to $x+iy$ form and proceed? How can I do such a thing with what appears to be a punctured open neighborhood?  How do I show that the function is analytic and find its derivatives?

Show that in polar coordinates, the Cauchy-Riemann equations take the form   $\dfrac{\partial u}{\partial r} = \dfrac{1}r \dfrac{\partial v}{\partial \theta}$ and $\dfrac{1}r \dfrac{\partial u}{\partial \theta} = −\dfrac{\partial v}{\partial r}$.      Use these equations to show that the logarithm function defined by   $\log z = \log r + i\theta$ where $z=re^{i\theta}$ with $-\pi<\theta<\pi$ is holomorphic in the region $r > 0$ and $-\pi<\theta<\pi$.   What I have so far:   Cauchy-Riemann Equations: Let $f(z)$ = $u(x, y)$ +$iv(x, y)$ be a function on an open domain with continuous partial derivatives in the underlying real variables. Then f is differentiable at $z = x+iy$ if and only if $\frac{∂u}{∂ x}(x, y)$ = $\frac{∂ v}{∂ y}(x, y)$ and $\frac{∂u}{∂ y}(x, y)$ = −$\frac{∂ v}{∂ x}(x, y)$. So we have $f'(z)= \frac{∂u}{∂ x}(z) +i \frac{∂ v}{∂ x}(z)$. Let $f(z)$ = $f(re^{iθ})$= $u(r,θ)$ +$iv(r,θ)$ be a function on an open domain that does not contain zero and with continuous partial derivatives in the underlying real variables. Then f is differentiable at $z$ = $re^{iθ}$ if and only if $r \frac{∂u}{∂r}=\frac{∂ v}{∂θ}$ and $\frac{∂u}{∂θ}$ = $−r \frac{∂v}{∂ r}$.  Sorry, if this is not very good. I just decided to start learning complex analysis today...


I want the ability to lock my Macbook at my command. I don't want a screensaver or sleep lock. Don't you get tired of repeatedly typing in your password in all day? I don't want to wait for my computer to lock itself in 10 minutes or 1 minute when the screensaver or sleep begins. I don't want to save and close all my apps and documents and logout.  So just let me lock my computer, simple request. Hit a hotkey? Close the lid?    I walk out my door, I lock my door. I get out of my car, I lock my car. Why can't I just lock my computer?    I've been told you can't reconfigure this type of setting in OS X, is this true?

On Windows you can hit the keys Windows+L to lock your computer if you step away.  I don't want to have to remember if sleep currently asks for a password, if there is a time out where my screen isn't locked during a short period. Even with Lion supporting resume of many apps, I don't want to log out.   I do want to be sure data is secure when stepping out for lunch or a smoke break.


I am pursuing masters degree in computer applications. I have no formal Mathematics and Physics background but for masters degree entrance examination I have studied senior high school level Mathematics with some introductory college level Mathematics like multi-variable calculus, advance linear algebra etc but that was 2 years back.  In my personal opinion computer programming is a monotonous work which is making me bored and from past 2 years (after studying mathematics)and I have a strong urge to self learn Mathematics and Physics.  Maths is prerequisite for both computing especially advanced topics (Algorithms, Artificial Intelligence etc) and Physics so I have decided to cover these Mathematical topics first  1. Linear Algebra by using   2. Trigonometry by using   3. Coordinate Geometry (Need Recommendation for book to cover this topic)  4. Calculus (Confused which book to use Thomas' Calculus or Stewart's or some other)   And finally  as my first physics book  It will take a lot of time to cover all this therefore I don't want to make any mistake in selecting wrong text for a newB. Can you help me by recommending some good books which i can use with or instead of books mentioned above and a suitable strategy to attain the goal in parallel with my regular studies.

What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory?  Some subjects off the top of my head that probably need covering:   Differential geometry, Manifolds, etc. Lie groups, Lie algebras and their representation theory. Algebraic topology.


First of all I'm studying machine learning with  Bishop's pattern recognition  I'm stuck with chapter two Gaussian parts. It requires a lot of linear  Algebra and Statistics. which books you  recommending to form the base for Gaussian part?   and this is my second question about chapter 2(Gaussian)   this equation is from gaussian conditional distribution for quadratic equation   $$-\dfrac{1}{2}({\bf x}-{\pmb \mu})^T\Sigma^{-1}({\bf x}-{\pmb \mu})=-\dfrac{1}{2}{\bf x}^T\Sigma^{-1}{\bf x} + {\bf x}^T\Sigma^{-1}{\pmb \mu}+const \qquad{(2.71)}$$  This is called completing the square    How left equation derived to the right equation? what does equation represent? (do not understand the format of the euations and why we use this?)  what does it mean to find the mean and the variance from this equation?    and this is conditional probability for gaussian   and this equation  $$-\dfrac{1}{2}{\bf x}_a^T\Lambda_{aa}{\bf x}_a \qquad{(2.72)}$$  it said take derivative two times and this equations derived. ..... why....  $$\Sigma\_{a|b} = \Lambda_{aa}^{-1} \qquad{(2.73)}$$  why some covariance represent the conditional probability?   if its too hard to explain can you list the "things" I should know for this equations?

I have been trying to derive the posterior distribution in the case of weighted Bayesian regression in the case of multivariate normal distribution for a few days and have been stuck. I am not sure if this is due to lack of my linear algebra skills or if I have done something really wrong.  In my case, the distributional assumptions are:  $$ y = N (B x, W^{-1} \nabla) $$  The parameters $B$ have a normal prior.   $$ P(B) = N (B_0, \Sigma_{B}) $$  The conditional posterior distribution for $B$ is proportional to $P(y|B) P(B)$. This is proportional to:  $$ \exp \big((B - B_0)^T \Sigma (B - B_0) + (y - Bx)^T \nabla (y - Bx)\big) $$  I have seen the textbooks mention something called completing the square which as far as I can tell equates to matching like terms. Even though I could work out for scalar variance terms, I am having trouble figuring out how to deal with the precision matrices and how this can be decoupled.   [EDIT]:  So, I tried to make a run with Glen_b's suggestion and came this far:  Original expression without the exponential (I will simplify notation slightly):  $$ (B - B_0)^T \Sigma (B - B_0) + ( y - Bx)^T \nabla (y - Bx) $$ Expanding:  $$ B^T\Sigma B - 2 B_0^T \Sigma B + B_0^T \Sigma B_0 + y^T \nabla y - 2 y^T \nabla B x + (Bx)^T \nabla Bx $$  $$ = B^T(\Sigma + x^T \nabla x)B - 2 (B_0^T \Sigma B + y^T \nabla B x) + C $$  So I am not sure how to make further progress with the second term. I guess I have to make it in the form 2(some_term)B but not sure how that can be done.


I tried to implement a custom download link in the theme settings, section that will give the users to download there custom settings for the backup. I tried this option   if( isset($_GET['download']) && $_GET['download'] == true ) {              $data = '';              if( $upanel !== FALSE ) {                 $data .= serialize(                         array(                             'theme'=>'theme_name',                              'data'=>$upanel                         )                 );             }               $filename = "theme_settings.txt";               header("Content-Disposition: attachment; filename=".$filename);             header("Content-Type: application/download");             header("Pragma: no-cache");             header("Expires: 0");              echo $data;             exit();         }   This section working fine and the data is downloaded correctly but its also insert the header html code into the text file. Like all the HTML codes.   Its clue less for me, that without inserting in my text file, hows it comes there? How do i rid from the header html codes.   Downloaded sample:   </div>             </div> // Above is unexpected html code from starting // into the theme_settings.txt file //Data that i want only  a:2:s:5:"theme";s:6:"theme_name";s:4:"data";a:52:s:9:"site_logo";s:0:"";s:12:"site_favicon";s:0:"";s:1

I wrote a plugin that displays all products in a woocommerce store in admin settings option, now I want to add a link to download the products as CSV file.  The problem is, when I click the link I get a permission error saying I don't have permission to view this page.  Here's my code:  function extra_tablenav($which) {     if ($which == "top") {         echo '
'         . __('These products are currently in the database:')         . '
' .         '&nbsp;&nbsp;&nbsp;' .         '' . __('Export to CSV') . '';     } }   How can I fix those permissions?


I have been thinking about this for a long time, may I know which step of my thinking is wrong as I do not seems to get the correct answer. If I am not going towards the right direction, may I get some help thanks!  My attempt:  Let $S = 1+3+5+\dotsb+(2n+1)\label{a}\tag{1}.$  Then I rearrange S from the last to first terms:  $S = (2n+1)+(2n-1)+(2n-3)+\dotsb+1\label{b}\tag{2}.$  Adding the two series $(1)+(2)$:  $$2S = (2n+2)+(2n+2)+(2n+2)+\dotsb+(2n+2),$$  I have $n$ copies of $(2n+2)$.  Therefore:  $2S = n(2n+2)$  $S = n(n+1)$.

The question asks to verify that each equation is true for every positive integer n.   The question is as follows:  $$1+ 3 + 5 + \cdots + (2n - 1) = n^2$$  I have solved the base step which is where $n = 1$.  However now once I proceed to the inductive step, I get a little lost on where to go next:  Assuming that k is true (k = n), solve for k+1:  (2k - 1) + (2(k+1) - 1) (2k - 1) + (2k+2 - 1) (2k - 1) + (2k + 1)   This is where I am stuck. Do I factor these further to obtain a polynomial of some sort? Or am I missing something?


$a = '35'; $b = '-34.99'; echo ($a + $b);   Results in 0.009999999999998  What is up with that? I wondered why my program kept reporting odd results.  Why doesn't PHP return the expected 0.01?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


Suppose that n lines in general position are given in a plane. (General position means that no two lines are parallel, and no three lines have a common point.) Into how many regions do they divide the plane?

Show that $n$ lines separate the plane into  $\frac{n^2+n+2}{2}$ regions if no two of these lines are parallel and no three pass through a common point.   I know we start with the base case, where, if we call the above equation P(n), P(0), for 0 lines would be 0.  But I really have no idea how to begin the inductive step.  How do we know what k+1 we're supposed to arrive at?  Thanks!


String theory proposes the existence of extra space dimensions. Very brilliant minds believe in their existence.   Of course, I could appreciate that they are consequences of mathematical consistencies of String theory. Also, Einstein's theory of gravity is consistent with any number of space dimensions, and there is no sane reason why should the universe must be $3+1$ dimensional or cannot have more than $3$ space dimensions. So extra dimensions could really exist. I don't deny that; don't get me wrong.   But I cannot get my head around that if extra space dimensions are really out there, why can't we see them? I never did understand this. The answer often offered is that since these extra dimensions are small we cannot see them. I can understand microscopic objects in $3$ dimensions cannot be seen but I cannot understand how could dimensions themselves cannot be seen.

I have been reading a lot about string theory and the necessity of extra dimensions (particularly as visualized in Calabi-Yau spaces), as "curling-ups" in our apparently 3-dimensional (or 4-dimensional, including time) world. I do not understand, though, how all these "extra dimensions" are actually adding dimensions to our world.  Even if these little multi-dimensional curls are everywhere and too tiny for us to see, how is it still adding extra dimensions? I mean, if our eyes were sharp enough, couldn't one still specify their location according to an $x,y,z$ axis? They will be a certain amount to the "left," a certain amount "high," and a certain amount front or backward (etc). It's still length, width and depth.   What am I missing here?


So I have to manage a listbox that has columns like table and I would like to give each column a fixed width. I wrote this method to convert the strings into a fixed length:  const int nameMaxWidth = 20; int nameLength = name.Length;  if (nameLength < 20) {    while (nameLength < 20)    {       name = name + " ";       nameLength++;    } } else {    name = name.Substring(0, nameMaxWidth); }   but it seems that it does not work since each letter has different size, for example nnnnn is longer than iiiii although both have the same length. I have tried String.Format but it doesnt work either. Is there anything I can do?

A Java version of this question was just answered, and, well, I don't know how to do this in .net.   So how do you calculate the display width of a string in C# / .net?


I have a WPF program that needs to detect if another software is opened or not. If it is opened, my program will connect to it automatically:  private void Window_Loaded(object sender, RoutedEventArgs e) {     if(!DataModel.IsConnected)     {       connect();     } }   However, in this way it can only build connection when that software is opened before I run the WPF window. If I want the WPF program can always detect if the software is open - even if the software is opened after I run the WPF window.

When I get a reference to a System.Diagnostics.Process, how can I know if a process is currently running?


I am using Ubuntu 13.10 and come from Ubuntu 13.04.   First check locahost, It's work fine. PhpMyAdmin is also work fine. I look some related problem . But some similarities with this answer and still I have problem when I write for-example http://localhost/PHP_Work/ in a browser.  Problem  Forbidden You don't have permission to access /PHP_Work/ on this server.   Path of PHP_Work folder is : /var/www/PHP_Work  Following results of line write by using terminal:  conf.d files  zeb@zeb-Lenovo-B570:/etc/apache2/conf.d$ ls  Result:  empty folder  zeb@zeb-Lenovo-B570:/etc/apache2/conf-available$ ls  Result:   charset.conf            localized-error-pages.conf    security.conf javascript-common.conf  other-vhosts-access-log.conf  serve-cgi-bin.conf   Site File  zeb@zeb-Lenovo-B570:/etc/apache2/sites-available$ ls  Result: 000-default.conf  default-ssl.conf  Don't know how and what changes make in virtual host directives. Or what should I do to sort it out , any help would be appreciated.

After upgrading from Ubuntu 13.04 server, the www pages won't display themselves.     Error 403 Forbidden You don't have permission to access / on this server.   I've changed access control saves from apache2.2 to apache2.4, but that didn't work. What else could I do?


I have a positive infinite series $a_n$ and I know that $a_n$$a_{n+1}$ converges to 1 and also that $a_n$$a_{n+2}$ converges to 1.   How do I prove that $a_n$ is a Cauchy sequence (without using limit arithmetics)? How do I calculate $lim_{n->inf}a_n$ = ?   Thanks.

I have a positive infinite sequence $a_n$ and I know that $a_n$$a_{n+1}$ converges to 1 and also $a_n$$a_{n+2}$ converges to 1.  Why does it mean that $a_n$ also converges to 1? How can I prove it?  Thanks.


I am trying to get a query from a database, however, the value I have for bindParam (:name) is not being bound, when I echo $sql and print_r($stmtTwo) the WHERE clause states WHERE :name instead of the string from $wherefinal.  The code I have is:  $sql= "SELECT Species.Species_ID      FROM Species      JOIN (          SELECT Species.Species_ID, COUNT(*) AS mynum          FROM Species_Opt LEFT JOIN Species ON (Species.Species_ID = Species_Opt.SO_Species_ID)          WHERE :name         GROUP BY SO_Species_ID HAVING mynum = 6          ) AS mytable ON Species.Species_ID = mytable.Species_ID"; $stmtTwo = $pdo->prepare($sql); $stmtTwo->bindParam(':name', $wherefinal); $stmtTwo->execute();   with $wherefinal being defined before the sql statement and being defined as:  $where = ""; foreach ($_POST as $k => $v){     $where .= "(Species_Opt.SO_Option_ID = $v) OR ";  }; $wherefinal = substr($where, 0, strrpos($where, " OR "));   And when echoed, $wherefinal displays:  (Species_Opt.SO_Option_ID = 4) OR (Species_Opt.SO_Option_ID = 12) OR (Species_Opt.SO_Option_ID = 17) OR (Species_Opt.SO_Option_ID = 20) OR (Species_Opt.SO_Option_ID = 21) OR (Species_Opt.SO_Option_ID = 32)   $v is from the value of a radio button from a form that is generated via a different SQL statement and smarty.

Why can't I pass the table name to a prepared PDO statement?  $stmt = $dbh->prepare('SELECT * FROM :table WHERE 1'); if ($stmt->execute(array(':table' => 'users'))) {     var_dump($stmt->fetchAll()); }   Is there another safe way to insert a table name into a SQL query? With safe, I mean that I don't want to do  $sql = "SELECT * FROM $table WHERE 1"


Where did I go wrong? (preferably a logical explanation instead of "this isn't how you use (insert name) rule) \begin{align*} &\lim_{x\to 0}\frac{ 1 -\cos x }{x²}\\ =&\lim_{x\to 0}\frac{ 1 -\cos x }{(x-0)\cdot(x-0)}\\ =&\lim_{x\to 0}\frac{\sin x }{x-0}\\ =&\lim_{x\to 0}\cos x\\ =&1. \end{align*}

$$\lim _{x \to 0}{1-\cos x\over x^2}={2\sin^2\left(\frac{x}{2}\right)\over x^2}={\frac{2}{x^2}\cdot {\sin^2\left(\frac{x}{2}\right)\over \left(\frac{x}{2}\right)^2}}\cdot\left(\frac{x}{2}\right)^2$$  now $$\lim_{x \to 0}{\sin^2\left(\frac{x}{2}\right)\over \left(\frac{x}{2}\right)^2}=\left({\sin\left(\frac{x}{2}\right)\over \left(\frac{x}{2}\right)}\right)^2=1^2$$  So we have $$\frac{2}{x^2}\cdot \left(\frac{x}{2}\right)^2=\frac{2}{x^2}\cdot \left(\frac{x^2}{4}\right)=\frac{1}{2}$$  Are the moves right?


At the very end of "Crossroads, Part II", after Starbuck comes back, we see "Earth". At the time, we assume that this is the same "Earth" she has just been speaking about. However, at the end of the series finale "Daybreak", the fleet arrives at a second planet they also call "Earth". This corresponds to the planet we call home IRL. Let's call them Earth 1 and Earth 2.  I always assumed that the "Earth" we saw in "Crossroads, Part II" was still "Earth 1". However, in the episode, one can clearly make out continents corresponding to our real Earth, for example the continent of North America. As "Earth 2" corresponds to our real-life Earth, it presumably has the same continents.  Does this mean that Earth 1 and Earth 2 are geographically the same? Or does it mean that the planet we saw in "Crossroads, Part II" is actually "Earth 2"?  I'm interested in any in-universe or out-of-universe (e.g. interviews etc) explanations.

So in the end of season three I think, when Thrace comes back and says 'I found Earth', the ending zooms out of the galaxy, zooms back in, and I could have sworn I saw Florida, the continental United States, and the gulf of Mexico, all while hearing 'I found Earth and I will take you there'. So when they finally get to the (nuked out) fake-Earth, that is presumably the planet.   So, why does fake-Earth have a Florida and Mexico? (We know the final-Earth was found because in the end when they arrive, we clearly see Africa and Arabia).


I am planning to go on an outdoors day trip with no way to heat up food.  Is it safe to heat up a packaged, fully cooked sausage in the early morning (4:00 AM) and wrap it with bread and store it in a plastic ziploc bag for consumption in the afternoon (2:00 pm)? (around 10 hours)  I am ok with eating cold food.

If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?


When an electron exchanges a virtual photon with another electron or proton, is the virtual photon a real particle or just a mathematical construct? In string theory, the force carrier particles of the electromagnetic, strong, and weak forces are supposed to be open string bound to their d branes. But if virtual particles are just mathematical how can this be?

I have heard  pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate the conservation of energy?


If $X$ and $Y$ are independent random variables, both having the standard normal distribution, then are $X+Y$ and $X-Y$ also independent?  To show this, I was trying to get the joint CDF of $X+Y$ and $X-Y$ but didn't get far. I know they are individually normally distributed.

$X$ is multivariate normal distributed with $\mu = (2, 2)$ and $\Sigma = (1, 0 ; 0, 1)$ and I have 2 vectors $A = (1, 1)$ and $B = (1, -1)$. How can I than show that the linear combinations $AX$ and $BX$ are independent?


Most of my Latex is in regular English, but there are a couple of lines of Cherokee here and there that I want to include. What packages do I need to install? I tried playing around with fontspec and babel but I think I must be using them incorrectly. I also tried minted, but nothing shows up. I'm working in Overleaf!

I have a XeTeX document in Cherokee, but when it compiles to PDF, all of the Cherokee glyphs show up as boxes.  Here's an example:  \documentclass[12pt,a4paper]{book} \usepackage{fontspec} \setmainfont{Times New Roman}  \begin{document} ᎪᎯ ᎤᎵᏍᏆᎸᏗ ᏕᎨᏌᏗᏒ ᎢᎩᏁᏤᎸ ᎤᏪᏥ ᎤᏮᏔᏅ, ᎾᏍᎩ ᎤᏪᎧᏅ ᎤᏤᎵ ᎢᏳᎵᏍᏙᏗᏱ ᏂᎦᏗᏳ ᏧᏓᎴᏅᏛ, ᎾᏍᎩ ᎾᏍᏉ ᎬᏗᏍᎬ ᎡᎶᎯ ᏚᏬᏢᏁᎢ; ᎾᏍᎩ ᏗᎦᎸᏌᏓᏗᏍᎩ ᏥᎨᏒᎩ ᎤᏤᎵ ᎦᎸᏉᏗᏳ ᎨᏒᎢ, ᎠᎴ ᎾᏍᎩᏯ ᏗᏟᎶᏍᏔᏅᎯ ᏥᎨᏒᎩ ᎾᏍᎩ ᏄᏍᏛᎢ, ᎠᎴ ᏂᎦᏗᏳ ᏧᏓᎴᏅᏛ ᏥᏚᏍᏆᏂᎪᏗᏕᎬᎩ ᏥᎬᏗᏍᎬᎩ ᎤᎵᏂᎩᏗᏳ ᎧᏁᎬᎢ, ᎾᎯᏳ ᎤᏩᏒ ᎤᏓᏛᏔᏅ ᎤᏅ ᎦᎸᎭ ᎢᎩᏍᎦᏅᏨᎢ, ᎤᏪᏁᎢ ᎠᎦᏘᏏᏗᏢ ᎦᎸᏉᏗᏳ ᎨᏒ ᎦᎸᎳᏗ. ᎾᏍᎩ ᎢᎦᎢ ᎤᏟ ᎢᏳᏓᎵᏁᎯᏯᏛ ᎾᎬᏁᎴ ᎡᏍᎦ ᏗᏂᎧᎿᏩᏗᏙᎯ, ᎾᏍᎩ ᎤᏘᏯᏍᏓᏁᏗ ᎨᏒ ᎤᏟ ᎢᎦᎸᏉᏗ ᏧᏙᏍᏙᏗ ᏧᏩᏛᏔᏅ. ᏗᏂᎧᎿᏩᏙᎯᏰᏃ ᎨᏒ ᎦᎪ ᎢᎸᎯᏳ ᎯᎠ ᏄᏪᏎᎶᎢ, ᎠᏇᏥ ᏂᎯ ᎪᎯ ᎢᎦ ᏍᏆᏕᎲᏏ? ᎠᎴ ᎾᏍᏉ ᎯᎠ; ᎠᏴ ᏥᎦᏴᎵᎨ ᎨᏎᏍᏗ, ᎾᏍᎩᏃ Ꮎ ᎠᏯᏥ ᎨᏎᏍᏗ? ᎠᎴ ᎾᏍᏉ, ᎾᎯᏳ ᎢᎬᏱ ᎤᏕᏁᎸᎯ ᎡᎶᎯ ᎤᎾᏄᎪᏫᏒ ᎯᎠ ᏄᏪᏎᎢ; ᎠᎴ ᎾᏂᎥ ᏗᏂᎧᎿᏩᏗᏙᎯ ᎤᏁᎳᏅᎯ ᏧᏤᎵ ᏫᎬᏩᏓᏙᎵᏍᏓᏏ. ᏗᏂᎧᎿᏩᏗᏙᎯᏃ ᎯᎠ ᏂᏕᎦᏪᏎᎭ, ᎾᏍᎩ ᏗᏂᎧᎿᏩᏗᏙᎯ ᏧᏤᎵ ᎤᏃᎴ ᏥᏂᏕᎬᏁᎭ, ᎠᎴ ᎠᏥᎸ ᎠᏓᏪᎳᎩᏍᎩ ᏧᏅᏏᏓᏍᏗ ᏥᏂᎬᏁᎭ. ᎤᏪᏥᏍᎩᏂ ᎯᎠ ᏂᎦᏪᏎᎭ, ᏣᏤᎵ ᎦᏍᎩᎸ, ᏣᏁᎳᏅᎯ, ᏂᎪᎯᎸ ᎠᎴ ᏂᎪᎯᎸ ᏂᎬᏩᏍᏗᏉ; ᎠᏙᎳᏅᏍᏗ ᏚᏳᎪᏛ ᎠᏛᏁᏙᏗ ᎾᏍᎩ ᎠᏙᎳᏅᏍᏗ ᎪᎱᏍᏗ ᏨᏗᎭ ᎾᎿ ᏣᎬᏫᏳᎯ ᎨᏒᎢ. \end{document}   What do I need to do in order to render the Cherokee text correctly?


I am not sure why bash works this way. I am inside the home directory. The filename is automation.sh. If I type the below, automation.sh  I am getting the following error. automation.sh: command not found But if I type the following command, it works: ./automations.sh

Why do we use ./filename to execute a file in linux?  Why not just enter it like other commands gcc, ls etc...


I have a command which needs a math environment to be used.  But sometimes I want to use it in a text environment and so, I need to create the math environment :   words words words \( \myFunction \) words words   How to detect in which environment I am ?   I want to be able to do :  words words words \myFunction words words   and  \( 1+2 = \myFunction \)

I'm using the package braket for my physics notes, and this speeds things up a great deal but I'm constantly writing \ket{\psi} or \bra{\psi}, and because this specific pair of bra and ket appears so often, this gets repetitive and I would like a macro to speed this up.  However since the braket package works only in math mode, my attempt \newcommand{\ketp}{$\ket{\psi}}$ work when I'm writing in text mode, but when I'm writing in mathmode it breaks (unsurprisingly).  Is there any way I can get this command to work in both mathmode and textmode without having to define two different macros, one for each?    Thanks in advance for any help.  P.S. I'm certain this is a very simple question but I could find little to no explanation of this feature.


Following the instructions , I am attempting to install some specific NVIDIA drivers on Ubuntu 18.04. I am doing this as the first thing after a fresh installation of Ubuntu, such that there are no NVIDIA drivers already installed.  The instructions say to run:  sudo apt-get install --no-install-recommends nvidia-driver-418   After doing this, I run apt list --installed | grep nvidia to see what NVIDIA packages it has installed. It prints out 17 package names, including nvidia-driver-418 and nvidia-driver-430.  Then, I run nvidia-smi, and this print out Driver Version: 430.26.  I have also looked at Ubuntu Software -> Additional Drivers, and the checked radio button is for Using NVIDIA metapackage from nvidia-driver-430 (proprietary, tested). Below this is an unchecked radio button for Using NVIDIA driver metapackage from nvidia-driver-410 (open source).  This doesn't seem very consistent to me... My questions are:   Why does installing nvidia-driver-418 actually install both nvidia-driver-418 and nvidia-driver-430? Given that 430.26 is the driver being used by my system (presumably from the nvidia-driver-430 package), how can I tell my system to actually use the 418 version of the driver? It seems that I could use Ubuntu Software -> Additional Drivers, but this lists version 410, not version 418. And I haven't even installed version 410... What's going on?

I just ordered the Nvidia GTX card. I have a dilemma, though. Should I keep using the driver which is available in "additional drivers" in Ubuntu, or should I install the driver from the Nvidia site?  So which driver is the best for me?


( Edit: I understand that a very similar question has been asked before, but in this case I was hoping for: confirming that I was thinking correctly; and get a more clear/concise answer if possible by doing so, since the answers to the other questions about this, although very interesting, seemed to not clearly state: the definition of set is this, and of class is this, and of collection is this)  I am trying to understand the distinction between set, class and collection. I don't know that much about logic, although I am familiar with concepts like first order languages and universes, but not much more than that. By reading other posts here and the appendix of Kelley's General Topology, this is the idea that I got:   Collection is left undefined - it is assumed that we know what it means: a "bunch" of "things". It is the most general concept of these (and maybe of mathematics??) A Set is a collection respecting the axioms of ZFC set theory. A Class is a collection of sets   So in particular a set is a class which is an element of another class, and a class that is not a set is called a proper class. A class that is a set is called a small class. We can now for example talk about the class of all sets, although it must be a proper class, since otherwise we get Russel's paradox.  Questions:   How much of this is incorrect? Can we talk about the "collection of all classes", which will contain in particular the class of all sets? Do some paradoxes arise? Any other things to add to this list or maybe some enlightening comments?

In school, I have always seen sets. I was watching a video the other day about functors, and they started talking about a set being a collection, but not vice-versa. I also heard people talking about classes. What is their relation? Some background would be nice.   It has to do with something called Russell's paradox, but I don't know what that is.   I think that the difference between a family and a set is that the former is a function and the latter is a set. Is this right?


public void synchronized method1(Class_Instance_Variables instanceVar, int classprimitive) public void method2(Class_Instance_Variables instanceVar, int classprimitive)   When passing parameters to method does java creates fresh reference to the methods or  does it use existing reference to pass to the methods ?   Thread-1 get the lock of synchronized method1 and pass "class instance variable" and class instance primitive variable. Thread-2 pass method2 pass same "class instance variable" and class instance primitive variable.  How the references work in this case ? Does it create a new reference for each passing?

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


In an attempt to install cuda, I copy-pasted some apt-get install packages. For unknown reasons the line that I got run in the end is the following:  sudo apt-get install libgtk2.0-   The result was that many packages got removed. Randomly picking a few:  libreoffice-* python-* xfce4-*    The list is huge. A considerable number of system parts have been uninstalled. Now this seems like a serious deviation from what I expect when I run apt-get install.  What is going on?

I was looking for some package (nautilus-terminal), and accidentally did this:  $ sudo apt-get install nautilus- Reading package lists... Done                                                                                Building dependency tree                                                                                Reading state information... Done                                                                                The following packages were automatically installed and are no longer required:                                                                                apturl apturl-common libgail-3-0 linux-headers-4.4.0-57 linux-headers-4.4.0-57-generic linux-image-4.4.0-57-generic linux-image-extra-4.4.0-57-generic                                                                       Use 'sudo apt autoremove' to remove them.                                                                                The following packages will be REMOVED:                                                                                gnome-session-flashback nautilus nautilus-sendto nautilus-share ubuntu-desktop                                                                                0 upgraded, 0 newly installed, 5 to remove and 69 not upgraded.                                                                                After this operation, 2 031 kB disk space will be freed.                                                                                Do you want to continue? [Y/n] ^[[^C                                                                                That's quite dangerous because remove is much harder to mistype than a simple dash from a failed autocompletion.     Is that an equivalent of apt-get remove? I couldn't find any documentation for that. Edit: except for overlooking the man page...


I am a beginner.  How do I print multiple expressions in Python 3 on the same line.  Here is some simple code I wrote for a class exercise in my beginner class:  temp = int (input ("What is the outside temperature? ")) if temp < 70:   print ("Wear a jacket ") else:   print ("No jacket is necessary ") print ("when you go outside.")   If I input 50 degrees, the output says:  "Wear a jacket when you go outside."   whereas I want it to read:  "Wear a jacket when you go outside."

I'd like to do it in Python. What I'd like to do in this example in C: #include <stdio.h>  int main() {     int i;     for (i=0; i<10; i++) printf(".");     return 0; }  Output: ..........  In Python: >>> for i in range(10): print('.') . . . . . . . . . . >>> print('.', '.', '.', '.', '.', '.', '.', '.', '.', '.') . . . . . . . . . .  In Python print will add a \n or space, how can I avoid that? Now, it's just an example, don't tell me I can first build a string then print it. I'd like to know how to "append" strings to stdout.


OK guys I have this problem:  For $x,y,p,q>0$ and $ \frac {1} {p} + \frac {1}{q}=1 $ prove that $ xy \leq\frac{x^p}{p} + \frac{y^q}{q}$  It says I should use Jensen's inequality, but I can't figure out how to apply it in this case. Any ideas about the solution?


So no one knows how to deal damage without instant damage effect, but how can I use it but deal less damage? Instant damage 1 is still way too much damage so how do I use command blocks to do less?

I want to make a datapack where if you touch lime glass, you get damaged 2.5 hearts. I don't want the commands to work for just this specific value. Instead, I want to be able to specify the amount of damage. I can't use the instant damage effect because it's not controllable.


Let's consider the following inclusion chain of topologies on space $X$: $\tau_1\subset\tau_2\subset\cdots\subset\tau_n\subset\cdots$.  Let $\tau=\bigcup_{n=1}^\infty \tau_n$. Is $\tau$ a topology?  Obviously , the intersection of any two sets from $\tau$ belongs to $\tau$. However, it is not clear whether $\bigcup_{n=1}^\infty A_n\in\tau$ where $A_n\in\tau_n$. I think, in general $\tau$ is not a topology but cannot find a counterexample.

Let $\lbrace \tau_n:n\in \mathbb{N}\rbrace$ be an ascending chain of topologies on a nonempty set $X$. Then is $\bigcup\limits^{\infty}_{n=0}\tau_n$ a topology on $X$?   I have a strong notion that it may not be a topology. But I am not getting the proper counter example. Please help. I know this must be a topology if the collection is finite.


I see "share this link to earn the publicist badge"  Where exactly do I share the link?

Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a "(retired)" next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type.


I'm using cycles render for glass shader. I'm using GPU compute for faster rendering in the viewport. I have bumped the samples to 100000, and still getting fireflies on the glass. I have tried various set ups from YouTube tutorials, but the fireflies insist showing on the glass sphere.  Q: How to get rid of the fireflies in this case?

I often use Cycles' built in Glass BSDF shader to achieve realistic refraction effects, but in many cases, it seems that Cycles' glass caustics creates an unfortunately large number of fireflies (pixels that are abnormally bright relative to their surroundings). In some models of mine, even when I render for 3000 or more samples/pixel, my final image is still covered in fireflies. While I can improve this in many cases by increasing the total amount of light available in the scene, this loses a lot of the potency of the refractive effects I'm looking for, especially in scenes with low light levels.  So my question is, how can I reduce the amount of fireflies while using Cycles' caustics without sacrificing the quality of the refractive effects?  Note: I am aware that Cycles' caustics will perform much better once Cycles has full support for bidirectional path-tracing, but it looks unlikely that that will become , unfortunately.


Is it possible to change to boot animation in 12.04? I know it was possible on 11.10...  if it is, how do you do it?

With regards to Plymouth --  Are there alternative boot screens available?  What's the easiest way to change the boot screen?


(I'm aware treating photon as particle and talking about its position is not exactly, conceptually right but I think it makes sense, at least in the point of view of a beginner. Please just assume photons carry fields and they exist like particles for the moment,or call them anything else if you think it fits better.)  When I study maxwells electrodynamics, I always end up seeing the following image. However I do not really understand what meaning should I make of it. I would really appreciate if you can briefly mention any experiments measuring this electric and magnetic field property, in case its relevant to your answer.    (here is the image I encounter)  1- Does it mean a single photon moves and carries fields of varying magnitude? Therefore we experience different electrical and magnetic field depending on at which position we encounter the photon? So by chance, if a point object is just at the place where E=B=0, photon may just pass through without doing anything? I tried to draw it as follows, in case I cannot make myself clear by words.   (picture 1)  2- Or does it mean, photons travel in groups and their sequence forms a sinusoidal shape. And the whole group goes with c, as in the following clumsy drawing (of course it is drawn discrete but I mean if this image was continuous):  (picture 2)  I think that all notes I encounter mean the 'picture 1' I have drawn. But it just do not feel right to me with my current knowledge, since varying fields of single photon means effect of a photon to a point charge depends on which phase photon meets the charge although photons were supposed to have a constant energy to give off. And also, if we look at the field distribution with a ray of photons, that would make the field move even faster than c, since photons carry their wave with c but the wave they carry also seems like propagating as it changes with time. Would you explain this mechanism to me, what proof do we have to say this actually happen instead of picture 2 I have drawn? Why do we rule out possibility of picture 2?  (the question is not duplicate specifically because this part, and that it tries to relate photons propagation with it)  I know I should be violating some basic concepts but I am trying to learn by questioning and I have already read the existing lecture notes so please bear with me. I am really dying to make a sense out of this electrodynamics but I just cannot do it since no one even attempts to talk about what would a particle correspondence of wave theory would be. I would really appreciate any insights, explanations, corrections or experimental information. Thanks in advance.

At the end of this nice video (), she says that  is a chain reaction of electric and magnetic fields creating each other so the chain of wave moves forward.  I wonder where the  is in this explanation. What is the relation between electromagnetic wave and photon?


I reference figures this way: \label{fig:hello} and then just \ref{fig:hello} but the latter returns only the number without the word "Figure". How can I get the word Figure such as "Figure 1"?

Is there a package that automatically inserts the ToC level of the reference I inserted?  Section 1.1 \label{a} Subsection 1.1.1 \label{b} Subsection 1.1.2  \label{c}   So that the text:  Blah \superref{a} and \superref{b} and \superref{c}   becomes:  Blah Section 1.1 and Subsection 1.1.1 and Subsection 1.1.2   So that it automatically adapts if I change the level of a label?


I'm new with Python and for some needs I am trying to figure out how to work with list of lists of lists.  Here's what am I doing:  segment_coef = [[list()]*4]*17  print segment_coef segment_coef[0][0].append(1) segment_coef[1][0].append(2) segment_coef[2][0].append(3) print segment_coef   After first print I have :  [ [ [],[],[],[] ] , ... 14 more time ... , [ [],[],[],[] ] ]   After these three append commands I'd like to have smth like:  [ [ [1],[],[],[] ] , [ [2],[],[],[] ], [ [3],[],[],[] ] ]   But I've got:  [ [ [1,2,3],[1,2,3],[1,2,3],[1,2,3] ] , [ [1,2,3],[1,2,3],[1,2,3],[1,2,3] ], ... up to the end ]   What am I doing wrong?

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


I would like to create a user which can only access and administer a particular folder via SSH situated in webroot of the server. Been through many blogs..none of them helped. I am using ubuntu server 16.04.  Thanks in advance

I want to give a client access to my server, but I want to limit those users to their home directories. I will bind-mount in any files I want them to be able to see.  I've created a user called bob and added him to a new group called sftponly. They have a home directory at /home/bob. I've changed their shell to /bin/false to stop SSH logins. Here is their /etc/passwd line:  bob:x:1001:1002::/home/bob:/bin/false   I've also changed the /etc/ssh/sshd_config to include the following:  Match Group sftponly         ChrootDirectory /home/%u         ForceCommand internal-sftp         AllowTcpForwarding no   When I try to log in as them, here's what I see   $ sftp bob@server bob@server's password:  Write failed: Broken pipe Couldn't read packet: Connection reset by peer   If I comment out the ChrootDirectory line I can SFTP in but then they have free rein over the server. I have found that ChrootDirectory /home works, but it still gives them access to any home directory. I have explicitly tried ChrootDirectory /home/bob but that doesn't work either.  What am I doing wrong? How can I limit bob to /home/bob/?  ----EDIT-----  Okay so I just had a look at /var/log/auth.log and saw this:  May  9 14:45:48 nj sshd[5074]: pam_unix(sshd:session): session opened for user bob by (uid=0) May  9 14:45:48 nj sshd[5091]: fatal: bad ownership or modes for chroot directory component "/home/bob/" May  9 14:45:48 nj sshd[5074]: pam_unix(sshd:session): session closed for user bob   I'm not entirely sure what's going on there,  but it suggests something is wrong with the user directory. Here is the ls -h /home output:  drwxr-xr-x 26 oli      oli      4096 2012-01-19 17:19 oli drwxr-xr-x  3 bob      bob      4096 2012-05-09 14:11 bob


In      Six questions to ask yourself before making a decision   ... is "before" a preposition because it is the beginning of a prepositional phrase? Or is it an adverb since it's followed by a verb? (Or is "making" even a verb, or is it a gerund?!)

I need to know the word type of "before" in constructions like the following:     Before going home, I had a beer.   I do know the word types before can be in general, so no need for lengthy responses ;).


I have 32GB server running a SQL Server instance and  I have  set the max server memory to 22 GB which is 75% of the total memory. What is the reason for SQL Server to exceed its allocated max server memory setting? Here is the screenshot of of top 5 allocation list.  When I add all of this up it seems it is almost near to 22 GB. That is why I am wondering: What is the reason my SQL Server is utilising 81% of the server memory, instead of just 75% as per my configuration?

SQL Server is consuming 87.5 % of my server RAM. This recently caused a lot of performance bottlenecks such as slowness. I researched this issue. One common solution I could find on the internet is to set the maximum limit for SQL Server. This was done and much improvement is gained. I want to know why if the maximum memory value is not set why SQL Server keeps consuming the resources


I'm trying to prove that if $f\colon\mathbb{R}\to\mathbb{R}$ is continuous function and there is a sequence of polynomials $p_n$ that converges uniformly to $f$ on $\mathbb{R}$, then $f$ is a polynomial itself.  It smells like somewhat near the Weierstrass approximation with polynomials, but I have no idea how to use uniform convergence on the entire real line, since this statement is wrong on any bounded interval.  Any hint or solution will be appreciated.

Let $f:\Bbb R\to \Bbb R$ be a function which is the uniform limit of polynomials. I want to show that $f$ is a polynomial.   I mean this seems a bit trivial...  If it's the uniform limit of the set of polynomials doesn't that guarantee it's a polynomial?   If I define $f$ to be the set of all polynomial do I define a uniform limit $L$ s.t $d(f,L)<\epsilon$?  or approach via contradiction?   any help would be great


Is it possible to search for all messages by a particular user in the chat search, at ? I tried searching with the 'search for' field empty, but got no results... and with '*', the same.

Here's the situation: I'm investigating a user's behaviour in a couple of chat rooms because I find the overall patterns concerning, and may need to direct some official attention their way discreetly. They haven't spoken there often, and I suspect a high % of their activity will be of interest.  Is there some way I can find the various instances of someone's activity in a room? Either their messages, or the days on which they have spoken, would be useful.  The best I can think of is to open up the Transcript and search it for very common words, but "the" turns up no results, and "you" isn't picking up much. I also tried Google ({username} site:chat.stackexchange.com/transcript/{roomnumber}), but that digs up a lot of false positives, and doesn't turn up incidents I know are there (I was there for them).


Often I will work out of the root of a rails directory where I find my self navigating the same path twice every time I would like to move a file:  mv app/views/layouts/application.html.erb app/views/layouts/application.html.haml   The haml is just one of may examples where I need to change the file name without modifying the directory it currently lives in and without changing directory.  Is there a way to achieve  this?

I know how to rename files in Unix:  $ mv ~/folder/subfolder/file.txt ~/folder/subfolder/file.sh       ^-------this part------^    ^------this part-------^   It takes too long time to repeat ~/folder/subfolder/file twice.  Is there a quicker way?


I booted Debian from a USB and installed but unfortunately was using the wrong version for my computer so wasn't completely successful.   I removed the incomplete installation, using the windows disk manager to delete the linux partitions.   On restart, the computer went into Grub rescue mode and I used windows 10 USB and diskpart to repair the MBR.   Currently, when booted into the UEFI menu has three options, a functioning Windows, a non-functioning Windows, and a non-functioning Debian.   My understanding is that each of these is meant to point to the given OS info on the hard disk, but the two non-functioning options aren't found because I deleted them, while the functioning one was created by the windows repair tool.  How can I go about "fixing" the boot menu to remove the bad records? Could I just leave them?  Sub-questions (Please just delete these if they need to be separate questions, thanks) :  I intend to reinstall Debian correctly once I get my boot menu squared away. Is there anything else I should check about the set up of the system before installing again?   edit:   I didn't find  due to the lack of any sort of windows tag. This question is specific to windows.  the two answers recommend using third party tools ,where as  uses native windows tools.

After installing fedora and Centos and other OS now I have them all showing in my Boot menu [F2] on start up not the menu form the OS even after deleting them and reinstaling other OS - Ubuntu -so It just shows one when the OS starts but when I go to UEFI setting I still find all the old ones they instruct you to use DEL to take them out but that does not work


I read on some sites that [ ... ] (with backslashes before the brackets) should be used, rather that $$...$$  what is the difference between both? If you compare the output, the result is the same.

I've heard that you should use \[ ... \] for displayed equations instead of  $$ ... $$, but why is that?  I'd assumed that it's so that you can more easily tell which are starting and which are ending delimiters, but if I always use a syntax-highlighting text editor, I can see that easily based on the color of the symbols.  Is there any reason for this suggestion?


I want to use a word that means "live life happily and enjoy every second and every moment."

My friend wants to get a tattoo in English. He's very specific about what he wants it to express, but for both of us English is a foreign language and we're not quite sure how to say that using a short but aesthetic phrase. The closest I can get as far as the meaning is concerned is this:     Live for the moments that make life worth living   but that's too long and I guess not very elegant. Is there a good succinct way to express something like that in English?


I have this portion of code in my javascript file  function insertRespuesta(id, attach) {     document.getElementById(attach).value += " #" + id + " ";     document.getElementById(attach).focus(); }   My html file:  <textarea name="textoConversacion" id="textoConversacion" class="mensaje-mensajeria"></textarea> <a href='#' class='decoracion-link' onClick="insertRespuesta('<?php echo $cada['contador']; ?>','textoConversacion');">#<?php echo $cada['contador']; ?>   So if I click the link it will be focused on the textarea but the textarea cursor will be in the last position I had, and I need to put in the last cursor character + 1.  I preffer not using jquery.

Does anybody know how to move the keyboard caret in a textbox to a particular position?  For example, if a text-box (e.g. input element, not text-area) has 50 characters in it and I want to position the caret before character 20, how would I go about it?  This is in differentiation from this question:  , which requires jQuery.


The change in speed of a photon with respect to time is 0 as photons travel at $c$ forever. If no change in speed exists, how can photons have momentum and acceleration? I guess they don't work like classical mechanics particles.

As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects being affected by gravity. However, momentum is the product of mass and velocity, so, by this definition, massless photons cannot have momentum.  How can photons have momentum?   How is this momentum defined (equations)?


I have 3 entities which are similar, but have different ways of doing certain things.  I use interfaces often and find them very useful, but here I chose a base class design for this approach, because the 3 share plenty of common code.  Only one method is public, and this sits on the Spender base class as the 'gateway':  public void SpendAmount(int budget)   My colleagues say I should create an interface for this base class, ISpender, with just the one method.  My question is - why? I've already achieved:   Polymorphism Reduced repetition Encapsulation (only the one method is callable)   I can't see why anyone would benefit from mocking ISpender for testing.  The design is open for extension (a new type of spender can inherit from Spender)  What's the real added benefits of also incorporating an interface into this design specifically?

When should I use an interface and when should I use a base class?   Should it always be an interface if I don't want to actually define a base implementation of the methods?  If I have a Dog and Cat class. Why would I want to implement IPet instead of PetBase? I can understand having interfaces for ISheds or IBarks (IMakesNoise?), because those can be placed on a pet by pet basis, but I don't understand which to use for a generic Pet.


I have a production database and staging database, they contain the exact same data, the production database was backed up and restored as the staging database. A particular operation (API call) always runs in about 200ms when connected to the Staging database but in production it always takes around 1700ms. I thought the indexes might need reorganizing in production and in staging they could be in better shape because it was restored from a backup but when I ran sys.dm_db_index_physical_stats(NULL,NULL,NULL,NULL,NULL) ddips  the index fragmentation is pretty much the same between both databases. I can try restarting the database server late at night and see if that brings up the performance but i'm really puzzled as to why one database would be so much different to the other in query performance when they contain the same data.

[Salutations]  (check one)  [ ] Well trained professional, [ ] Casual reader, [ ] Hapless wanderer,   I have a (check all that apply)  [ ] query [ ] stored procedure [ ] database thing maybe     that was running fine (if applicable)   [ ] yesterday [ ] in recent memory [ ] at some point    but is suddenly slower now.  I've already checked to make sure it's not being blocked, and that it's not the victim of some long running maintenance task, report, or other out of band process.  What is the problem, what should I do, and what information can I provide to get some help?  [*Insert appropriate closing remarks*]


Overview  I built a simple linear regression model to understand if Universal Healthcare Index predicts suicides. My independent variable is Universal Healthcare Index (scale from 1 to 100). The variable name in my data is called "Trans_uhc". In order to meet the normality assumption, I used a sqrt(max(x) - x)) transformation to normalize a negative skew. My dependent variable is suicides per 100k population. In order to meet the normality assumption, I used the sqrt(y) transformation to normalize a positive skew.  Simple Linear Regression Output  Help Needed As you can see from the above output, my predictor variable is significant. However, how would I interpret this outcome? For example, if the data was not transformed, I would be able to interpret the linear relationship as "when Universal Healthcare Index increases by 1 point, suicides/100k people decrease by .18879." However, I cannot do that because of the transformation. Any help would be greatly appreciated. Thank you!

In OLS regression, what does a one unit change in X represent in terms of a beta-related change in Y when the outcome variable has been transformed to $1/\sqrt(Y)$?   (Transformation was done to ensure linearity in the model. My predictor variables are 0-1 dummies.)  I've consulted the following useful posts, but I still don't know what is the answer:


I cannot save a php file in var/www/html and my computer shows error "Permission denied".   How to change permission to save file here?

I want to stop having to use sudo everytime I work in /var/www. How can I do that? I simply want to put all of my sites into this directory and work with them without too much pain.


This code print all the bash history but i have to print last 20 bash history.How can i do that?  import fpdf  pdf = fpdf.FPDF(format='letter') pdf.add_page() pdf.set_font("Arial", size=14)  for history in open('.bash_history'):     pdf.write(8,history)  pdf.output("bash.pdf")

I'm writing a log file viewer for a web application and for that I want to paginate through the lines of the log file.  The items in the file are line based with the newest item at the bottom. So I need a tail() method that can read n lines from the bottom and support an offset.  This is hat I came up with: def tail(f, n, offset=0):     """Reads a n lines from f with an offset of offset lines."""     avg_line_length = 74     to_read = n + offset     while 1:         try:             f.seek(-(avg_line_length * to_read), 2)         except IOError:             # woops.  apparently file is smaller than what we want             # to step back, go to the beginning instead             f.seek(0)         pos = f.tell()         lines = f.read().splitlines()         if len(lines) >= to_read or pos == 0:             return lines[-to_read:offset and -offset or None]         avg_line_length *= 1.3  Is this a reasonable approach?  What is the recommended way to tail log files with offsets?


I know this question was asked many times but I have some specific questions. I know the usual recommendations but I am afraid of going for Rudin because I've read many reviews that said it wasn't good for self studying. I remember in one review I read the guy said " As you go through the book you get excited about some cool theorems and results only to find that Rudin gives a proof that only does the job and leaves out much of the intuition for you to either find on your own or look for elsewhere".  I don't like this type of texts because when the proof is too directed it becomes unsatisfactory. By directed I mean that the result is already established and we're just trying to make it formal by looking for arguments that just verify the fact without , for example , mentioning how one would first consider these arguments and how they would come up while trying to prove the result.   That said , There are other suggestions such as Barry Simon's comprehensive course in analysis. This is a new text which isn't reviewed a lot. The description says it may be suitable for a graduate level course but others say it gives a good introduction to the prerequisites but I'm not sure.  Any other suggestions ?  Edit : thanks for your answers

Does anybody know of a good book in real analysis for self study for a beginner? What about Analysis 1 by Terence Tao?


I'm trying to show that the following is a tautology, without using truth tables. $$[(p\to q)\wedge(q\to r)]\to(p\to r)$$    I've tried this: $$ \neg [(\neg p \vee q) \wedge (\neg q \vee r)] \vee (\neg p \vee r)$$ $$\neg (\neg p \vee q) \vee \neg(\neg q \vee r) \vee (\neg p \vee r)$$ But I'm not sure what to do after this. I've tried distributing the negation operator using DeMorgan's law, and I've also tried FOILing the results, but no luck.

I am looking for a way to prove that the statement, $[(p \to q) \land (q \to r)] \to (p \to r)$, is a tautology without the help of the truth table. By using only Laws and Theorems like De Morgan's Law, Domination Law, etc. Also, I can't use the rules of inference. Please help, thank you.


At the end of Star Wars Episode VI: Return of the Jedi we see Anakin Skywalker's Force ghost join Obi-wan and Yoda. Given the comments made by Kylo Ren in Episode VII: The Force Awakens when he asks for his grandfather to 'show him again, the power of the dark side', can a Force ghost exist of Darth Vader when there is already one of Anakin or has Snoke been tricking him to keep him a loyal subject?

In Empire Strikes Back and Return of the Jedi we see Yoda, Obi Wan and Anakin reappear as a Force Ghost/Spirit.  The overall objective of the Sith was the achieve immortality, this was one of the reasons why they detached themselves from the Jedi Order.  Immortality seems achievable on the light side of the Force, yet not on the dark side, or at least in canon. Have there been any Sith who achieved this?


When I try to enter the following data into the database, these characters create problems: & (\u0026) and ' (\u0027)   {       "Id":5507542,"Name":"Port \u0026 Company® - Youth 50/50 Cotton/Poly T-Shirt",     "Description":"Cover you kids in the best threads by Port \u0026 Company®. This youth T-shirt is something they\u0027ll always run back to! It\u0027s made of 5.5 oz., 50% cotton / 50% poly (with up to 5% recycled polyester from plastic bottles).      They\u0027ll stay visible in the Safety Green and Safety Orange colors because they\u0027re compliant with ANSI/ISEA 107 high visibility standards for background color. Imprint your company name to this top and let the clients come to you!",     "ShortDescription":"50/50% Cotton/Poly T-Shirt.", }   The PHP code:  <?php       $host="localhost";      $user="root";      $password="";      $db="db";        $connect =  mysqli_connect($host,$user,$password,$db) or die('Database Not Connected. Please Fix the Issue! ' . mysqli_error());        $id = $content['Id'];         $name = $content['Name'];       $description = $content['Description'];       $shortDescription = $content['ShortDescription'];       $query = "INSERT INTO result_tab(id,name,description, shortDescription) VALUES('$id', '$name', '$description', '$shortDescription')";       if(!mysqli_query($connect,$query))     {         die('Error : Query Not Executed. Please Fix the Issue!  ' . mysqli_error($connect));     }      else{             echo "Data Inserted Successully!!!";      } ?>    The error:  Query Not Executed. Please Fix the Issue! You have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near 'll always run back to! It's made of 5.5 oz., 50% cotton / 50% poly (with up to 5' at line 1

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


I have a HP ENVY ah0044TX having realtek alc285 sound card. I only get audio from the two back speakers and not the front one's. I researched quite a bit, hopped several distros with different kernel versions. The problems seems to be a common one with no concrete solution. Currently running Ubuntu 19.04. Please help!

I'm trying to install bang and olufsen drivers, or HP hd audio driver, as only 2 of the 4 speakers work and the 2 amps don't work in ubuntu  lspci -v | grep -i audio 00:03.0 Audio device: Intel Corporation Broadwell-U Audio Controller (rev 09)     Subsystem: Hewlett-Packard Company Broadwell-U Audio Controller 00:1b.0 Audio device: Intel Corporation Wildcat Point-LP High Definition Audio Controller (rev 03)     Subsystem: Hewlett-Packard Company Wildcat Point-LP High Definition Audio Controller   The volume is terrible. Is there any way to fix this?  The speakers work perfectly on the pre-installed Windows 8.


Hashirama Senju, a reincarnation of one of the sage of six paths son (Asura) and the only kage who Madara didn't ignore is one of the most overpowered characters in Naruto. Being so powerful (the authors had to make it so that) he had to die of a disease (as anyone who could beat him would have to be stronger than Madara). This is not just a theory as it is confirmed further by one of the data books, can someone help me find where exactly that is stated and what exactly was his disease?

The wiki says that Hashirama died shortly after the creation of Konohagakure.  Do we know how he died?  I mean, he was powerful enough to stand up to Madara, so I feels like it would be no small thing that could kill him.


I read about the  in Wikipedia, and got confused about whether it holds when the domain of the function is non convex. On one hand, convexity is explicitly mentioned as a pre-condition. On the other hand, they say that it holds also for domains that are homeomorphic to a disc, and there may be such domains which are not convex (e.g. a concave quadrangle). So, what is the largest family of sets of $\mathbb{R}^n$ on which the BFPT holds?

Brouwer's fixed point theorem:     Every continuous function $f$ from a convex compact subset $K$ of a Euclidean space to $K$ itself has a fixed point.   I am wondering why the word "convex" is in there.  It seems to me that it is necessary and sufficient for $K$ to have no holes, which is a weaker condition than convexity.  Necessary: if $K$ has a hole, then the continuous mapping that simply rotates points around this hole has no fixed point.  Sufficient: A unit disk in any number of dimensions has a Brouwer fixed point.  Any compact, hole-less set $K$ is homeomorphic to the unit disk in some number of dimensions.  If we map $K$ to the unit disk $D$ with a homeomorphism $h$, then consider the function from $D$ to $D$ given by $h \circ f \circ h^{-1}$.  This is a continuous function from the unit disk to itself (which is convex and compact), so it has a Brouwer fixed point $x$.  Then $h(f(h^{-1}(x))) = x$, so $f(h^{-1}(x)) = h^{-1}(x)$, so $h^{-1}(x)$ is a Brouwer fixed point of $K$.  What's wrong with this argument?


All my previous backup disks are either ext3, ext4, ntfs or fat32. I am having tremendous difficulty accessing my files easily from my mac (even with tools such as Tuxera). I did not expect an OS to not support access open file systems!  So now comes the time to format a new external hard disk where I will keep copies of some of my files (no time machine, just copies of some of my files and maybe an rsync partition). I need to be able to read this disk easily from any linux machine. I suppose FAT32 would work, but it would not support large files. What is the best solution here?

I would like to buy an external hard drive that I'll use on Mac OS X and on Windows, but I don't know the best file system for it (reading and writing on the both system).  I know I can used FAT32 easily, but I have files bigger than 4 GB so I can't use this file system.  So, I think for NTFS or HFS, but I know I can use on the two systems with software, but I don't know the fastest one to transfer files. Also, I don't know if I can use ext3 or ext4.  If someone knows one of the best way to use an external drive on Windows and Mac without used FAT32, please tell me.


For the domain of a standard parabola, we would write, in bracket notation: $(-\infty, \infty)$.  So, I was wondering if you could also write the domain of a parabola as $-\infty < x < \infty$.  Likewise the domain of a function $f(x)$ could be, in bracket notation: $(4,2)$. This is the equivalent of $4 < x < 2$.  So can you write the domain of a parabola as $-\infty < x < \infty$?

I was just wondering if it would be applicable to write the domain of a parabola is:  -∞ < x < ∞


I'm kinda new to the whole aspect of programming and might have f***d up my installations/paths and dont know how to properly fix things. I hope you can help me. I want to start using pycharm which expects python 3.8 from /usr/local/bin/python3.8 as Interpreter but my .bash - console tells me my python version is 3.7.6 and when i do julian$ which python  in my console (on macOS Catalina 10.15.6 btw) the output shows /opt/anaconda3/bin/python  How do I change the path my console chooses to the above mentioned /usr/local/bin/python3.8  such that I can install packages there manually?

Questions about    setting environment variables the PATH   are very common here, and in most cases the answers are very similar to each other. In the future it would be nice to have a good Q/A for this.  So the question is: What are environment variables, like the executable PATH, and how can I change and use them on major operating systems?  A good answer would include a simple explanation of what environment variables and especially PATH mean to the OS, as well as simple guidelines on how to set and read them accordingly.


I've had a PayPal account associated with my main e-mail address for years, but I didn't create this account. For this reason I don't know the details like secret questions and stuff like that and I'm unable to reset my password and close my account because of that.  Communicating with PayPal's support has been unfruitful.  Is there a Stack Exchange site on which I could give a detailed description of what's happening and ask for help on how to close my account?

On which Stack Exchange site can I ask questions like        When will [some new feature] for [some product] be released?   Where can I download an update for [some product]?   I'm getting errors when accessing the customer portal for [some company] – how can I fix this?   Why was I banned for doing [some action] on [some platform]?   Why is [some company] discontinuing [some product]?   Why is [some company] giving away [some product] for free?   What's the price for [some product]?      or any other product support/customer service questions?  It's not a product related to programming (or I've read  on Meta Stack Overflow) so I know Stack Overflow isn't the right place. Which other site in the network will take these kind of questions?


I am using a shared workstation. Typing free -h returns me                total        used        free      shared  buff/cache   available Mem:            31G         30G        232M        292M        1.0G        608M Swap:          2.0G        997M        1.0G   How do I check what processes or who is using the memory?

Ubuntu has been crashing on me recently. I think its because it runs out of memory so I ran the free -m command and found that my memory usage was really high. So then, i ran top to find the culprit, but the displayed processes were using less than 1.5% of memory. How do I know which program is making ubuntu crash/run out of memory? Below is the output:  shafee@shafee-pc:~$ free -m              total       used       free     shared    buffers     cached Mem:          3824       3714        110          0        978       1954 -/+ buffers/cache:        780       3044 Swap:           99          0         99  shafee@shafee-pc:~$ top top - 02:12:14 up  1:24,  2 users,  load average: 0.16, 0.42, 1.49 Tasks: 182 total,   1 running, 181 sleeping,   0 stopped,   0 zombie Cpu(s):  2.9%us,  1.9%sy,  0.3%ni, 79.3%id, 15.5%wa,  0.0%hi,  0.2%si,  0.0%st Mem:   3916708k total,  3803848k used,   112860k free,  1002308k buffers Swap:   102396k total,        0k used,   102396k free,  2001852k cached    PID USER      PR  NI  VIRT  RES  SHR S %CPU %MEM    TIME+  COMMAND              4200 root      20   0  289m  53m  38m S    2  1.4   1:06.45 Xorg                 5590 shafee    20   0 19348 1368  956 R    2  0.0   0:00.01 top                     1 root      20   0 24124 2136 1264 S    0  0.1   0:02.05 init                    2 root      20   0     0    0    0 S    0  0.0   0:00.00 kthreadd                3 root      20   0     0    0    0 S    0  0.0   0:24.23 ksoftirqd/0             6 root      RT   0     0    0    0 S    0  0.0   0:00.00 migration/0             7 root      RT   0     0    0    0 S    0  0.0   0:00.00 migration/1             9 root      20   0     0    0    0 S    0  0.0   0:00.11 ksoftirqd/1            11 root      RT   0     0    0    0 S    0  0.0   0:00.00 migration/2            13 root      20   0     0    0    0 S    0  0.0   0:03.89 ksoftirqd/2            14 root      RT   0     0    0    0 S    0  0.0   0:00.00 migration/3            16 root      20   0     0    0    0 S    0  0.0   0:00.16 ksoftirqd/3            17 root       0 -20     0    0    0 S    0  0.0   0:00.00 cpuset                 18 root       0 -20     0    0    0 S    0  0.0   0:00.00 khelper                19 root       0 -20     0    0    0 S    0  0.0   0:00.00 netns                  21 root      20   0     0    0    0 S    0  0.0   0:00.01 sync_supers         shafee@shafee-pc:~$   Or is it normal to have 110mb of free memory and is my issue related to something else?


I am trying to get the distinct values from below code .But I find no luck to move further.  Can any one let me know what's wrong in my below code. Because I am trying to group the information to get distinct values.

  Title Values	  Month Values

          <select id="drbprogrames" class="select">         <option selected="selected">Select</option>         </select>     	         <select id="drbmonths" class="select">      <option selected="selected">Select</option> </select>

Hi I have a list with two fields "Regions" & "Countries" I am using a rest api to retrieve the list of just regions like so: http:mysitename/_api/web/lists/getByTitle('TaxTool')/items?$select=Region  In the results there are lots of duplicates and I was wondering how to return unique values.


I understand the analytical proof given here.     But in that case since $Y=F(X)$, say where $F(X)$ is the cdf of a standard normal distribution $N(0,1)$ the plot of which is not rectangular but rather S shaped.  I fail to understand. Could someone please help?

How does the inversion method work? Say I have a random sample $X_1,X_2,...,X_n$ with density $f(x;\theta)={1\over \theta} x^{(1-\theta)\over \theta}$ over $0<x<1$ and therefore with cdf $F_X(x)=x^{1/\theta}$ on $(0,1)$.  Then by the inversion method I get the distribution of $X$ as $F_X^{-1}(u)=u^\theta$.    So does $u^\theta$ has the distribution of $X$?  Is this how the inversion method works?  u<-runif(n) x<-u^(theta)


We are thinking to make a backup of all our AWS data (RDS and S3) to some other cloud sources, because there is a possibility that a developer of company AWS account get hacked. The hacker could then can delete everything from AWS. So I have two question here:   Is my assumption correct regarding deletion of entire data by someone? What is the best way to curb this? Basically, I can only think of using some other service as data backup apart from AWS, if anyone has done something like this, it would be very nice to know how they achieved it.

Currently our system runs entirely inside AWS. We do rolling snapshots of our EBS and often practice running restores.  What keeps me up at night is having all our eggs in one basket. Here are the scenario's:   Our Amazon zone has some massive event that destroys the data centre Someone gains access to our AWS account, terminates our instances and deletes all our snapshots   To mitigate these risks I'm thinking about moving snapshots periodically to another AWS account (with different credentials) in another region.  My question is this, is this an adequate level of precaution or should I be looking to offsite backups that are completely removed from Amazon?


I know that when referring to myself and a friend, it is proper to say "John and I", as opposed to "me and John". But when referring to ownership, I can't figure out whether this still applies. For example, "John and I's car" certainly sounds more incorrect than "me and John's car", since "I" cannot be pluralized. What is the proper way of phrasing this?

I just stumbled upon a :     My wife and I's seafood collaboration dinner. How does it look?   Sure enough, the top comment immediately points out that it should be "my wife's and my". However, a cross-post to the Grammar subreddit produced :     It's fine as it is written. "my wife and I" is a noun phrase, functioning as a subjective pronoun in the singular and made possessive with the apostrophe. It is exactly the same as "our".      It seems weird because you would never use "I's" on its own but it is not on its own here - it is part of a noun phrase.   That's a rather intriguing argument. Does it hold any water?


I'm pretty certain that the answer to the question in the title is a no, but I don't understand why.  I have some basic misunderstanding of quantum processes that I’d like clarified in the form of asking questions about a hypothetical scenario.   So, let’s say we have a pair of entangled photons…  1)  Is it possible to prepare an entangled pair such that it can be known that, for example, the photon going down a certain path will be measured 25% of the time to be horizontally polarized and 75% likely to be vertically polarized?  I guess this would be some sort of quantum decoherence? Partial collapse?  2) If that is possible, then would it also be possible to measure that photon’s diagonal polarization in order to "reset" the horizontal-vertical probability back to 50-50? I've seen a trick done where you take some polarizing filters and stack them horizontal on top of vertical, so that no light gets through.  But when you slide a diagonally oriented filter between them, some light does get through, because the horizontal/vertical polarization information gets "reset" when measured against the diagonal filter.  3) If these two things are possible, then wouldn’t it be possible to send information along the entangled pair?  If you sent bursts of 1000 photons and were able to measure them all, and found that the first burst had ~750 vertically polarized photons but the second burst had ~500 vertically polarized photons, then wouldn’t you know that the second burst had their diagonal measurements taken?  Or would that not work because the extra measurements "break" the entanglement..?   4) Along with that, how many times can the photon pairs be measured before there are no longer entangled?  Just once?  Or maybe just once per state/qubit/aspect (such as polarization angle)?  I understand that measuring the photon would necessarily change it (like with the polarization filter trick), but then how do scientists measure the polarization angles of two photons like in experiments of Bell’s inequality?  I know that somewhere along the line, what I've described cannot be possible.  If it were, then you could easily send information faster than light.  E.g., say you had a photon-entanglement-generator-and-probability-fixer station in between two planets, 1 light year from the planet Foo and .99 light years from the planet Bar.  After a year's time, after the photon stream has propagated to both planets, scientists on Bar could measure diagonally polarization of 1000 photons to encode a 1 or not measure to encode a 0.  Then scientists on the planet Foo could measure vertically polarity and decode the 1s and 0s based on the statistical readings.  The Bar scientists could encode that such a message and the Foo scientists would "instantly" receive the message.  Except it would actually be from the past, since Foo is 1.99 years outside the Bar light cone.  So since this is impossible, what am I misunderstanding?  Thanks for answering, and thanks for putting up with yet another clueless but curious layman.

It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect the state of the entangled partner.  For example, if Alice and Bob share an entangled pair of electrons and Alice measures her spin in the $x$ direction, then Bob's spin will also end up spinning in that direction, and similarly if she measures in the $z$ direction. Moreover, the effect will be instantaneous, regardless of the spatial distance between the two particles, which seems at odds with special relativity.  Can I use a scheme like this to communicate faster than light?


Below  are some code  var Foo=function(){    this.doSomething1=function(){        //do something     }  }; Foo.prototype.doSomething2=function(){       //do something };   if I change it to  var Foo=function(){   }; Foo.prototype.doSomething1=function(){    //do something }; Foo.prototype.doSomething2=function(){    //do something };   the second block of code almost can do any thing same as the first one. but it has very clear inherit relationship on prototype chain.  What is the advantage for the first code block?  Your comment welcome

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


For any question I can view questions linked from/to it by from the url of the form: https://meta.stackexchange.com/questions/linked/id where id stands for the number of question. If some question has many linked posts, then this link is even available - by clicking on "see more linked questions..." at the bottom of linked questions list.  When I get the list of linked questions, I can choose from the tabs: hot, newest, votes, active, unanswered. I occasionally use this list ordered by recent activity if I am curious about something like this: Why were there recently upvotes on this relatively old post of mine? Did somebody link to it recently? Was something interesting related to this  topic posted recently?  Today I noticed that when I left the list open in one tab, and did something in another one, the number indicating new questions appeared.  It seemed a bit surprising that several posts would be linked to quite old post in such a short period. When I got back to this tab, I saw the gray banner: "3 questions with new activity". After clicking on it, new questions appeared on list. (It seems to be the recently active question on the given site.) After refreshing the page, this new questions disappeared and only questions which are really linked to the original one were shown again.  I should add that probably people will be using links like this very seldom and it can be corrected by refreshing the displayed page, so it is definitely not much of a problem. But I guess it is still a bug worth reporting.    I will add screenshots showing this behavior on this question:  (This is where I observed it. I tried this both in Mozilla Firefox and Google Chrome.)  Here is what I saw after coming back to the tab:    Here is screenshot after clicking on the gray banner:    After refreshing the page it all went back to normal.  When I tried the same thing with two questions from the same site opened in two tabs (namely  and ) I noticed that the same questions appeared in the list. I do not know why, but in this case it took much longer time before I saw this happening. I do not know whether this might depend on the size of the site, or on what I was doing in other tabs, or something else. But for the questions I tried, it seems to take much longer on meta.SE than on math.SE. Based on what I tried so far, it seems that questions which are shown are the recently active questions of the site. In the other words, if I wait a bit, the beginning of the pages  and  (replace any question id here) and will become the same.

When a question got many other questions linked from/to it, there is a special page showing list of all those questions, e.g.   I just noticed while leaving it open, that the live refresh is active in there and showing "x questions with new activity" whenever there is new activity, even if in a question not linked to/from the original question.  I think the live refresh should be disabled while in that view, or filtered to load only questions actually being linked.


I'm preparing for my exam and I came across this question:      Let $X_1, X_2, ...,X_n$ be iid with PDF $f(x)=\frac{2x}{\theta^2}$ for $0 \leq x \leq \theta.$ Find the MLE of $\theta$   So this is what I did:   $L(\theta)= \prod\frac{2x_i}{\theta^2}I(0 \leq x \leq \theta)$  $= (2n \bar{x})(\frac{1}{\theta^{2n}})I(0 \leq min (x_i)\leq max(x_i) \leq \theta) $  $=(2n \bar{x})(\frac{1}{\theta^{2n}})I(0 \leq X_{(1)}\leq X_{(n)} \leq \theta)$  In order to find MLE, I need to maximize $L(\theta)$, by choosing a small $\theta$. However, $\theta$ can't be smaller than $ X_n$. Thus I conclude that:  $\hat{\theta}= max(x_i)$  Is my calculation and conclusion correct?

Assume the standard situation, that is, let $X_1, \ldots , X_n$ be independent and identically distributed with $X_k ∼ P_\theta(x; \theta)$ , where $P_\theta(x; \theta) = 2x/\theta^2$  if $0\le x \le\theta$ and $0$ otherwise. It is required to estimate $\theta$. Show that the maximum likelihood estimator for $\theta$ is $\hat{\theta} = \max{[X_1, \ldots , X_n]}$ and then show that the cumulative distribution function of $\hat{\theta}$ is $F_\theta(z) = z^{2n}/\theta^{2n}$. Here's what i did so far: Maximum Likehood estimator: $L_x(θ) = \prod_{i = 1}^{n} P_θ(x_k)$ Here we have $P_θ(x_1,...,x_n;θ) = P_θ(x_1,θ).P_θ(x_2,θ)...P_θ(x_n,θ)$ Likehood = $L_{x,θ}(θ) =P_θ(x_1,θ).P_θ(x_2,θ)...P_θ(x_n,θ)= 2x_1/θ^2. 2x_2/θ^2.. 2x_n/θ^2 = [2^n.\prod_{i = 1}^{n}x_i]/θ^{2n}$ Log-likehood: $\sum_{i = 1}^{n}log(P_θ(x_1,...x_n;θ))= \sum_{i = 1}^{n}log(2x_i/θ^2)$ Is this correct so far? Im still not sure how to get to $\hat{θ} = max{[X_1, . . . , X_n]}$ As for the the cumulative distribution part to show $F_θ(z) = z^{2n}/θ^{2n}$: $F(z) = P(max({x_k})<z) = P(x_1<z).P(x_2<z)..P(x_n<z) = 2x_1/θ^2.2x_2/θ^2...2x_n/θ^n = 2^n.\prod_{i = 1}^{n}x_i/θ^2n$ Not sure if this is correct. Would really appreciate some help. Edit: From the answers below, we can deduce the the estimator is biased. What estimator would be unbiased? How can i find it?


Just this morning, I accidentally created a hdd filesystem without a partition table.  I didn't even know it was possible but it happened.  Now the issue is to undo it or leave it alone.  For this particular case, I don't want multiple partitions so having no partition table is no problem for me. Indeed, in terms of sysadmin, it's actually  convenient.  But I don't know if there is any loss of functionality with linux.  And I posting to get some guidance on that.   What functionality (other than adding and resizing partitions) am I loosing by not having a partition table.  What about portability or compatibility with future system upgrades (staying within linux)?  How about interoperability between Linux, Windows and OS X?

I ran into something a couple of weeks ago that I'd never seen before: A filesystem (ext3 I believe) installed to a storage device without a partition. In essence /dev/sdb was the entire filesystem. I know many filesystems can be extended into empty space, so doing this allows extending without dealing with LVM or some other kind of volume manager, but are there any other advantages for setting up storage this way?  The specific case I saw was as the ephemeral data volume for a number crunching server, the boot and root volumes were traditional partitions on a different storage device entirely. -


It seems that Google cuts my page title on search results. Is there a best practice to provide titles?  The page www.currenttime.tv/content/article/27236953.html should have this title: Кто такой 'бог Кузя'? Все что вы хотели знать о задержанном лидере секты.  And here's the title on Google:

I'm just wondering how it is possible that IGN.com has this in its title tag:      Video Games, Cheats, Walkthroughs, Game Trailers, Reviews, News, Previews & Videos at IGN   while on Google its title is simply "IGN".   How can one achieve such a thing? Does it use some special meta tag I can't see?


I am using Ubuntu 10.10 ,when I use apt-get install I am getting error as Some index files failed to download, they have been ignored, or old ones used instead.

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


Everyone knows that there are at least three functions whose derivative is the function itself, namely $e^x, \  0$ and $-e^{x}$. ( are there more?)  I was drawing some polynomials and their derivatives and noted that sometimes it was almost like the inverse. This lead me to ask this question: is there a function whose derivative is the inverse of that function?  Well, I figured that at least some kind of answer can be found to be of the form $a x^b$.  Lets solve this:   $f(x) = ax^b, f'(x) = abx^{b-1}$. Then $$f \circ f'(x) = a^{b+1}b^bx^{(b-1)b}=x=a^b b x^{(b-1)b}=f' \circ f (x).$$  Thus $b(b-1) = 1 \iff b^2-b-1=0 \iff b = \phi \vee 1-\phi,\ \phi = \frac{1+\sqrt 5}{2}$  We also see that $ab^{b-1}=1$, because both the multipliers must be one. Thus we get $a= \frac{1}{b^{b-1}}$. If $b=\phi$, we get $a=\phi^{\phi-1}$. If $b=1-\phi, \ a=(1-\phi)^{\phi}$  Thus two functions that satisfy the condition are $\phi^{\phi-1} x^\phi$ and $ (1-\phi)^{\phi}x^{1-\phi}$.  I would like to know if there are more functions like these, and do these functions have any 'interesting' properties, like exponential function, apart from this one condition about inverse being the derivative?

What are some good examples of a function  $f : \mathbb{R} \to \mathbb{R}$ where its derivative is equal to its inverse? I attempted to find a monomial that satisfied it by starting with $f(x) = ax^b$ and showing that $f^{-1}(x) = f'(x) \implies b-1=\frac{1}{b} \implies b=\phi$ and got $$f(x) = \frac{x^\phi}{\sqrt[\phi]{\phi}}$$ Which seems to work according to WolframAlpha, but I'm having trouble double-checking it. Any other ideas?


Isn't there anything you can do to get her back? Isn't there something you can do to get her back?  Are these equally natural and used interchangeably?  Which one sounds more frustrated on behalf of the person who the speaker is saying this to?

It's not like there's anything else to do.   Shouldn't the speaker say: "There's something else to do." ? so what's the meaning of the sentence and what's the difference between the two of them? Thank you,


I'm from India and I was wondering how to get around the situation, when I am going for a travel trip to a country (any country for that matter) abroad, but haven't booked a hotel as I am planning to do a couchsurfing. The period of stay could vary between 5 days to 1 month, out of which, suppose I received confirmation of stay for an initial couple of days from a couch surfer.   1)In such a scenario, how do I clear the interview by the immigration officer when asked to provide my accommodation arrangements? Will simply telling the truth about relying on couchsurfing be wise to get clearnce by the officer? 2)Is it even an option to book a hotel through websites in advance and cancel the booking after I get clearance from the immigration officer? In that case, will I be liable to pay cancellation charges- or-the whole booking amount gets deducted from my credit card account?  The questions might sound silly to many, but I am seriously looking for your guidance on this as I will be planning visit to different countries depending mostly on couchsurfing for accommodation. Thanks in advance.  Additional Notes: Currently I hold a B1 valid for 9 more years. I have visited UK and USA once and twice respectively on business purpose- if this info helps. And I'll be planning for travel trip to USA/UK/Europe/south east Asia

Can one use CouchSurfing to prove accommodation for a Schengen visa to Iceland from India?


I'm searching a way to append a World in blender Python. I read the reference in  but that is for group append. is there a way to make that work for world append.  sorry for rip english

I'm searching a way to append a group in Python.  It should behave exactly like the Append function (ShiftF1) works, all objects should be local and editable. The idea is to append a character (with rig etc.) via Python and not Link it (to be able to modify it without making everything local one by one).  Thanks


Let $(E,d)$ and $(F,d')$ be metric spaces and consider $f:E\rightarrow F$. Prove that:  $f$ is uniformly continuous in $E$ $\iff$ for every  $A,B\subseteq E$ such that $d(A,B)=0$, it follows that $d'(f(A),f(B))=0$.  Where $d(A,B)=inf\{ d(x,y)|x\in A, y\in B\}$  The $\implies$ direction is easy from the definition but in the other direction I'm lost. Any help will be gratefully received.

I have the following exercise: Let $(X,d)$, $(Y,e)$ be metric spaces.  This is the definition of distance of sets used in the exercise:  $d(A,B)=inf\{d(a,b)\colon a \in A, b \in B\}$  $d(f(A),f(B))=inf\{e(f(a),f(b))\colon f(a) \in A, f(b) \in B\}$  The exercise is:   Prove that $f\colon X \rightarrow Y$ is uniformly continuous if and only if, for all non empty sets $A$,$B$ in $X$ such that $d(A,B)=0$ we always have that $d(f(A),f(B))=0$.  If we suppose that $f$ is uniformly continuous, the implication is easy. But the converse is very hard for me. Let me show you what I have tried:  Suppose that for all non empty sets $A$,$B$ in $X$ such that $d(A,B)=0$ we always have that $d(f(A),f(B))=0$, and for the sake of a contradiction suppose also that $f$ is not uniformly continuous.   Then there exist $\epsilon_0>0$ such that for all $\delta>0$, exist $x_\delta$, $y_\delta$ in $X$ such that $d(x_\delta, y_\delta)<\delta$ but $e(f(x),f(y)) \geq \epsilon_0$.   In particular, for all $\delta=\frac{1}{n}>0$ there exist $x_n,y_n$ in $X$ such that $d(x_n,y_n)<\frac{1}{n}$ but $e(f(x_n),f(y_n)) \geq \epsilon_0$  Then $A=\{x_n \colon n \in \mathbb{N}\}$ and $B=\{y_n \colon n \in \mathbb{N}\}$ are such that $d(A,B)=0$.   Then by hypotheses, we have that $d(f(A),f(B))=0$. Then, in particular for $\epsilon_0>0$, there exist $x_n,y_m$ in $X$ such that $e(f(x_n),f(y_m))<\epsilon_0$.   But I get a contradiction if $n=m$ but I don't know how to proceed in case that $n\neq m$.   Any help would be appreciated.


I want to prove that $\sin(x)$ is continous in $\mathbb R$, the definition that I have of $\sin(x)$ is the definition of the Spivak's book (the geometric one), but maybe using some other definition would make   the prove easier?

How do I prove $\sin x$ is uniformly continuous on $\mathbb R$ with delta and epsilon?   I proved geometrically that $\sin x<x$ and thus, $$|f(x_1)-f(x_2)|=|\sin x_1 - \sin x_2|\le|\sin x_1|+|\sin x_2|<|x_1|+|x_2|$$   But this doesn't help me much finding a delta...   Thanks for any help!  P.S. I'm only at the beginning of calculus so I can't use many theorems and derivation  (because they haven't been regorously proven).


Consider  $$ P(X) = X^{n+1} - aX^{n} +aX -1 $$ with $a \in [-1;1]$.     Show that the moduli of the roots of $P$ are $1$.   What I tried is   I've noticed if $z$ is a root then $\frac{1}{z}$ is a root as well.  I've checked:   $X-a+aX-1 = (1+a)(X-1)$ $X^{2} - aX -1 +aX = (X-1)(X+1)$ $X^{3} - aX^{2} +aX-1$ is more subtle.   I don't how far this question could lead us but I know compelex analysis and basic algebra.

I gave an exercise to a student the other day, thinking I had a simple solution for it, but it seems that my solution was just bullshit (at least, not conclusive). Well, at least, I warned her I wasn't sure of my solution :-)  Here it is : $a\in[-1,1]$, show that all roots of polynomial $P=X^{n+1}-aX^n+aX-1$ have modulus $1$ (I try different ways of expressing the problem, tell me which one is better english...).  It is easy to see that    roots of $P$ are $1$, $-1$ for some special cases, and complex not real roots $z_i$ such that $\overline{z_i}$ is also a root, as $P$ is kind of reciprocal, $z$ root implies $\frac1z$ is also a root$.   All the other things I tried are not conclusive. For example, $a\in[-1,1]$ may be translated as $a=\cos\theta$ for some $\theta\in\mathbb R$, but I don't see how to use this. I tried some rewriting, but nothing seems to work. I tried to work on the modulus of a root, tried the relations roots-coefficients...  I'm quite stuck here. Could you help me please ?  Thanks.


We know: $\sum^n_{i=1}(x_i - \bar{x})^2 = \sum^n_{i=1} x_i^2 - n(\bar{x})^2$ But I don't understand how we can go from this relation to the result in the title. Thanks for any help.

Show that $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^{n} (x_i - \bar{x})(y_i)$. I fell into this hole where I keep finding that $$\sum_{i=1}^n (x_i - \bar{x}) = \sum_{i=1}^n x_i - \sum_{i=1}^n \bar{x} = n\bar{x} - n\bar{x} = 0$$ This seems true, but I know that I am missing something, since this implies that covariance is always zero, which is obviously not true.


I'm using CSV class to read a csv file with Ruby.  Here is my code  CSV.foreach('../../../db/data/xxxx.csv') do |row|   # ...   row[0].to_i   # ... end   File '../../../db/data/xxxx.csv' surely exists. row[0] returns "1". So I expect row[0].to_i to return 1, but row[0].to_i returns 0. I thought it is encoding matter of row[0].encoding, but it returns #<Encoding:UTF-8>.  row[0] #=> "1" row[0].class #=> String row[0].encoding #=> Encoding:UTF-8 row[0] == "1" #=> false   Does anyone help me?

I'm consuming a data feed that has recently added a Unicode BOM header (U+FEFF), and my rake task is now messed up by it.  I can skip the first 3 bytes with file.gets[3..-1] but is there a more elegant way to read files in Ruby which can handle this correctly, whether a BOM is present or not?


I've just started picking up blender for some projects at work, and am hitting a stumbling block. I'm building a fairly mechanical object and as such have been creating it in layers, using extrusions from paths. All this seems to have worked fine however when I'm now trying to use a boolean to "cut" holes into them, it leaves open holes into the object. Attached are some images to try and illustrate what I mean.        My overall Object/project Here you can see me selecting my boolean modifier Here we have the result. Weirdly, it seems to add it So I go ahead and delete the extra faces, and I've got holes aplenty   You can see on the front of the first image a boolean that I used to cut away a cruve from a block that worked fine, so I'm stumped.  I wonder if it has something to do with my objects being blue rather than grey, but I don't know if this even means anything.

I have a cube that is scaled about 10 times on the Z axis. I added a plane, rotated it 45 degrees on the Y axis, and placed it just below the top of the cube. I applied a boolean difference modifier to the cube, and it cut off the bottom. How can I invert the boolean operation to cut off the top of the cube instead? The plane should be deleted after the cutting.