Say I have the following dataframe:  In [1]: df = pd.DataFrame({ 'one' : [11, 12, 13], 'two' : [21, 22, 23]})  In [2]: df Out[2]:    one  two 0   11   21 1   12   22 2   13   23   Is there any difference between using a colon or not when selecting all colums? e.g.  In [3]: df.loc[ df.two &gt; 22, :] Out[3]:    one  two 2   13   23   vs  In [4]: df.loc[ df.two &gt; 22] Out[4]:    one  two 2   13   23   ?  Thanks
I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$ How do you prove that $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$? I tried to identify the sum as a binomial series, but the $4$ and the $-1/2$ puzzle me. (This series arises in studying the first passage time of a simple random walk.) List of Stored Procedure from Table I have a huge database with 100's of tables and stored procedures. Using SQL Server 2005, how can I get a list of stored procedures that are doing an insert or update operation on a given table. Can i install ubuntu on meizu mx4 android edition like ubuntu edition with iso recovery in this page "  " How to type an inline chi in Latex \( \chi \) produces a letter that is slightly below the row, but I've seen in many papers a chi that is in the same line as the rest of the row) I get it after updating in Synaptic Manager  I recently did a clean install of Ubuntu 17.04 from 16.10.  error message:-  W: Download is performed unsandboxed as root as file '/var/cache/apt/archives/partial/samba-libs_2%3a4.5.8+dfsg-0ubuntu0.17.04.1_i386.deb' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) How many ounces is a British "tin" of tomatoes? If I have a British recipe that lists "1 tin chopped plum tomatoes," how many ounces is that? In British English, does "tin" usually refer to a specific size? In the US, cans generally come in 14 and 28oz sizes - which one is likely closest to what the recipe means? Is there a quick way to set an HTML text input (&lt;input type=text /&gt;) to only allow numeric keystrokes (plus '.')? This is something I'm supposed to be able to prove for an upcoming test, but I can't find anything to help me prove this in my notes or the chapter, which is on cosets and Lagrange's theorem. If all I start with is the group having no proper subsets, then that means any subset is the whole group. By Lagrange's theorem, that means the index is $1$, but that doesn't get me anywhere. Where do I start? Order posts by tags count? I am trying to order posts by tag count. I want to order posts with no tags first and posts with highest count last.  I tried and got posts with no tags only.       $tags = get_tags();     $tag_ids = wp_list_pluck( $tags, 'term_id' );      $args1 = array (        'orderby'          =&gt; 'DEC',        'post_type'        =&gt; 'post',        'pagination'       =&gt; true,        'posts_per_page'   =&gt; '1',        'tag__not_in'      =&gt;  $tag_ids,        'meta_key'         =&gt; '_thumbnail_id',     );   How do I order posts based on the tags count? How to prove that if $\forall x \in (a,b)$ Lebesgue integral $\int_{(a,x)}fd\lambda=0$, then $f(x)=0$ $\lambda$-almost everywhere? Let $f:(a,b)\rightarrow\mathbb{R}$.  The statement to prove is that if $\forall x \in (a,b)$ Lebesgue integral $\int_{(a,x)}fd\lambda=0$, then $f(x)=0$ $\lambda$-almost everywhere.  So if it wouldn't be true then we would have $\forall x \in (a,b):\int_{(a,x)}f_+d\lambda=\int_{(a,x)}f_-d\lambda\neq0$, so every interval contains positive and negative values of the function. It is  such an $f$ so my guess would be that this function is not Lebesgue measurable and we can't take this integral.  Thanks in advance! My online friend is asking for money in order to visit my home country. Is this a legit request or a scam? I use the code below to produce handouts of my presentations.  When I open the resulting pdf with any pdf viewer, it is viewed correctly, but when I print it, it is always printed very small, no matter the program I use (Okular, Evince, Acrobat...). Bonus to anyone that can make the pdf be printed correctly by Okular under Ubuntu! Thanks!  MWE here:  \documentclass[handout]{beamer} \usepackage{pgfpages} \pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] \setbeameroption{show notes on second screen=bottom}  \setbeamercolor{background canvas}{bg=pink}  \mode&lt;presentation&gt; {     \usetheme{Singapore} } \begin{document}   \begin{frame}[plain]     \titlepage   \note{     Notes for the title page } \end{frame}   \section*{Outline} \begin{frame}[plain] \frametitle{Outline}     \tableofcontents  \note{     Notes for the table of contents } \end{frame}   EDIT:   If I place the line "\pgfpagesuselayout{2 on 1}" after the line "\setbeameroption{show notes}" I do not experience the printing problem anymore!! However, the slide preview and notes that appear at the bottom belong to the NEXT SLIDE, instead of to the CURRENT SLIDE!! What is going on with that? Area of a weird ellipse shape. A propeller has the shape shown below. The boundary of the internal hole is given by $r = a + b\cos(4α)$ where $a &gt; b &gt;0$. The external boundary of the propeller is given by $r = c + d\cos(3α)$ where $c - d &gt; a + b$ and $d &gt; 0$.  Calculate the total area of the propeller as shown by the shaded region and calculate the average temperature of the propeller, given by $T (r, α) = C/r$, where $C$ is a constant.     Have absolutely no idea how to solve this. Hide files from root in ubuntu Javascript determine if such object property exists based on a string Why don't my female dwellers give birth to children? I am playing Fallout Shelter on my IPad. There were some women who have already gave birth, but two female dwellers are carrying their babies for about 18(!) hours. I know that this process takes three hours, so this is not normal. What do I do? TestMethod do not support Web service callouts, test skipped Interior of cartesian product is cartesian product of interiors I have to prove that:  $$Int(A\times B) = Int(A)\times Int(B)$$  Where $A\subset M$ and $B\subset N$, both $M$ and $N$ metric spaces.  The problem is that the exercise does not specify the metric, so I need to try to prove it using a generic metric.  If $x\in Int(A\times B)$, then an open ball can be centered at $(x,y)$ such that it is contained in $A\times B$. Therefore, this open ball, $B((x,y),r)\subset A\times B$. It means that $d((x,y),a)&lt;r$ for any $a\in A\times B$ for some $r&gt;0$. I guess that if I can take from here that $d(x,a)&lt;r$ and $d(y,a)&lt;r$ I can prove thhat $Int(A\times B)\subset Int(A)\times Int(B)$, but I still have to prove the other way around.   Any ideas? Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.  If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.  How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument? Tokenizing strings in C I have been trying to tokenize a string using SPACE as delimiter but it doesn't work. Does any one have suggestion on why it doesn't work?  Edit: tokenizing using:  strtok(string, " ");   The code is like the following  pch = strtok (str," "); while (pch != NULL) {   printf ("%s\n",pch);   pch = strtok (NULL, " "); }