Basis for co-countable topology
What are the basis for co-countable and co-finite topologies
Quickest way to rename files, without retyping directory path I am stuck on the following question:     Find the volume of the torus obtained by rotating the circle $(x-a)^2+y^2=b^2$, where $a&gt;b$, around the y-axis. Zooming to selection in arcpy.mapping and only seeing selected features? I selected data by using select layer by attribute, then I need to only select these selection and zoom in to the selection.  my code is this, it can zoom in base on the scale I set, but I see other adjacent polygon that has other Code_No, why?  Layer = arcpy.mapping.ListLayers(mxd, "lyr", df)        arcpy.SelectLayerByAttribute_management(lyr, "NEW_SELECTION", "Code_NO = '%s'"%mycodeNo)            df.extent = lyrLayer1.getSelectedExtent() df.scale *= 2 How do I perform a redirect to a custom URL after login? I am trying to redirect users to a custom URL after they logged in, but my code doesn't work.  How do I redirect users after they logged in? How to remove app icons in system tray on Ubuntu 18.04 with GNOME How can I remove the apps in right top corner (Google Chrome, flux, TeamViewer)?  Before my update from Ubuntu GNOME 16 these were even more annoying in the left down corner. GUI/Unity crashing in 16.04 LTS after updates 2018-01-04, compiz segfaults TikZ: multiple decorations on a path. Inequality: $x^2+y^2+xy\ge 0$ I want to prove that $x^2+y^2+xy\ge 0$ for all $x,y\in \mathbb{R}$.  My "proof":  Suppose wlog that $x\ge y$, so $x^2\cdot x\ge x^2\cdot y\ge y^2\cdot y=y^3$ (because $x^2\ge 0$ so we can multiply both sides by it without changing the inequality sign) giving $x^3\ge y^3$. Substracting we have $x^3-y^3\ge 0$ or $(x-y)(x^2+xy+y^2)\ge 0$. Since $x\ge y$ we can divide by $x-y$ to get $x^2+xy+y^2\ge 0$.  Is it right?  Thanks for your help! I recall :    It was one that I knew could use a bit more spit and polish, but I didn't have the inclination or energy to edit it myself, so I skipped it.  I wander my way over to  (10K only), and look at the listing...    ...so, when did I approve this again? I skipped the question; that doesn't mean I gave my tacit approval, does it?  Seems like the dashboard needs to agree with the suggested edits view. HTTP webpage is showing "Not Secure" in Chrome I've called GoDaddy a few different times and they said that it looks like it is a problem with my HTML file.  Except, my HTML file is the basic outline of a webpage, nothing fancy at all.    Chrome still says that the webpage is, "Not Secure" with the big red x over it.    I'm not sure what to do to fix it, I don't have any personal information on the site nor am I collecting any information from visitors (it's sort of an information site).  I shouldn't need an SSL certificate because I am not hosting anything privately. Apache doesn't log remoteIP when RemoteIPHeader X-Forwarded-For is present What's the difference about /t̬/ and /d/? From time to time, I need to typeset Welsh. Sometimes, I need to typeset citations and bibliographies in Welsh. I think that last time I did this, I may still have been using BibTeX although I am honestly not sure. In any case, my entire work-flow now uses biber and biblatex...  I found  on changing the names of things, including the names of things used by biblatex. However, that cannot deal with the case of an unsupported language.  Suppose that I want to typeset a document in Welsh:  \documentclass[a4paper,welsh]{article}  \usepackage{babel} \usepackage[utf8]{inputenc}% welsh needs utf8x but biblatex doesn't like it \usepackage[T1]{fontenc}% not great for Welsh but the best pdfTeX can do \usepackage{csquotes}% doesn't like Welsh though biblatex likes csquotes on account of babel... \usepackage[backend=biber]{biblatex} \bibliography{biblatex-examples}  \title{Fy Nogfen} \author{Rhywun}  \begin{document}   \maketitle   \tableofcontents   \section{Cyntaf}   \autocite{westfahl:space}    \printbibliography  \end{document}   There are multiple problems in such a case. (One is that I need utf8x but can't use it on account of biblatex. Another is that I need utf8x at all. Another is that biblatex likes csquotes but csquotes doesn't do Welsh. But these are irrelevant to this question.)  The output is as follows:    Note that the use of the English citation is just so this is easy to reproduce. Obviously, the content of the reference might well be in Welsh. (Though it might be in English, too.)  As can be seen, while elements of the document controlled by babel are handled correctly, those under the control of biblatex are not. However, I cannot simply modify the solution offered by lockstep for changing strings to customised English variants. That is, I can't just use a Welsh version of  \DefineBibliographyStrings{english}{%   bibliography = {Works Cited},   references = {Works Cited}, }   because biblatex has never heard of it.  What is the most appropriate way to configure biblatex for use with an unsupported language? If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$. If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.   I want to use induction to prove this:  It is trivial when $G=p(n=1)$, assume $G=p^n$, $N$ is a normal subgroup in $G$ with order $p$. Since $G$ is p-subgroup, $G$ has a normal subgroup $H$ with order $p^{n-1}$,according to assumption, $N \subset C(H)$. But I don't know how to go on, is $C(H)=C(G)$?Can induction work in this case? creating a csv file from two csv files I have two csv files:  sub_compiler.to_csv('sub_compiler.csv') sub_compiler.head()     and   sub_opt = pd.read_csv('sub_opt.csv') sub_opt.head()     and what I would like to do is to create a csv file where I have something of the form   compiler, opt   How could I do this? I need to do this to make a submission.  Thank's in advance.  [EDIT] Thank you for the answers. Now I have obtained :    don't understand why I have the columns called unnamed.   My objective is to get a csv file that contains only the columns compiler and opt. How could I do this? Thank's again.  [EDIT 2] I have solved my problem but if I open the csv file manually, so just click on the file, I have the following:    s it contains only 11 lines, but it contains 3000 lines in jupyter. Is it there something wrong?  [EDIT 3] I tried to to the following:  import pandas as pd  test = pd.read_csv('1495927.csv') test   and I have:    where 1495927.csv is the csv file I have created and that is in the image where I have 11 elements. What's the difference between the work function and ionisation energy? What is the plural of the abbreviation of "multiplicity automaton", "MA" or "MAs"? The "multiplicity automaton (MA)" is a model in compute science and its plural is "multiplicity automata". Should the plural of the abbreviation be MA or MAs?      is not a duplicate as it is focused on cases like "ATMs" where the expanded form "automated teller machines" has a regular plural ending in "s." Unlike "machines," the word "automata" has an irregular plural that does not end in "s." It's unclear from the linked answers how abbreviations that end in words like this should be pluralized. A high-ranking  mentions "VIPs," but a high-ranking  says     VIPs' is a strange one. It could be argued that the expanded acronym,   when pluralized, should be 'Very Important People' rather than 'Very   Important Persons'. Using this argument, 'VIP' could be used as a   singular or plural noun. "The VIP has arrived." "The VIP have   arrived." I'm not sure anyone else would agree with my logic, though. How do I join a Windows Active Directory? We have a "mix-mode" Lab. and we want to migrate to Ubuntu, from Windows.  In this process, how do we add Ubuntu workstations to a Windows Domain / Active Directory ('AD') setup? I'm looking for a way to reinterpret an array of type byte[] as a different type, say short[]. In C++ this would be achieved by a simple cast but in C# I haven't found a way to achieve this without resorting to duplicating the entire buffer.  Any ideas? Let $R$ be a UFD. Then for any two elements $a,b \in R \setminus \{0\}$ $ab \sim \gcd (a,b){\operatorname{lcm} (a,b)}$.   My attempt :  Let $d = \gcd (a,b)$.Then $d|a$ and $d|b$.Then $\exists x,y \in R$ such that $a = dx$ and $b = dy$.Now it is to be shown that $c = dxy$ is the lcm of $a,b$.Which I find difficulty to show.It is clear that $a|c$ and $b|c$. Now if $u$ is any common multiple of $a$ and $b$.Then $dx|u$ and also since $y|b$ we have $y|u$ i.e. $dxy|u^2$ $\implies c|u^2$.But I have to show $c|u$ to complete the proof which I fail to prove.Please help me to complete the proof.  Thank you in advance.