How to write these equations I want to typeset these equations :
What are good learning resources for a LaTeX beginner? Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see .
The first homology group $ H_1(E(K); Z) $ of a knot exterior is an infinite cyclic group which is generated by the class of the meridian. Using Iterator with ModelBuilder for clipping and splitting in ArcMap? Chrome address bar no longer shows protocol or www subdomain A couple of days ago I noticed that for all websites, chrome omits from the address bar the protocol and the subdomain if it is www. My co-workers report that they are not seeing this. Chrome version is 67.0.3396.87.  For example, if I type into the address bar https://www.google.com (without the quotes), Chrome immediately displays the chip "Secure" followed by google.com. See attached screenshots.      I have looked in vain for Chrome settings that affect this, plus the chrome://flags page and chrome://net-internals page.  I did not do anything consciously to make this change.  Any ideas?  EDIT: Suggestion from MrWhite that Ominbox UI Hide Stead-State URL Scheme and Trivial Subdomains had become enabled: good suggestion, except that the setting is still at “Default.” See screenshot:    However, as a shot in the dark, I am going to play with the setting to see what happens.  First I set it to “Disabled.” That restored the previous behavior of the address bar, which is to not to hide the protocol and “trivial subdomains.” Then I changed it back to “Default,” and it was hiding them again. One would suspect that somehow the default has been changed, except that co-workers are not reporting this issue.  Oh, well. I’ll just leave it as Disabled for now.  I would be ready to accept the answer from MrWhite, because it provides a workaround. Yet will leave it open for a bit longer, because it does not really answer why this behavior has changed, and why it has to be overridden.  EDIT 2: Chrome version is 67.0.3396.87. How do I upgrade from 14.04 LTS to 16.04.1 LTS? So, today is July 21st and . gives me an option to download 16.04.1 LTS. However, attempting to upgrade gets me this message -  $ sudo do-release-upgrade Checking for a new Ubuntu release No new release found   What is wrong? Does it matter that I am running apt-get update behind apt-cacher-ng?  Note: Commenting out the files in apt.conf.d that used apt-cacher-ng did not make a difference.  Edit: Explanation for possible duplicates:  deals with upgrade from 12.04LTS to 14.04LTS. My question is specific to 14.04 LTS to 16.04.1 LTS upgrade. Old answers, while good for archival purposes are less relevant in a fast changing package like ubuntu. Moreover none of the answers answer what is wrong. The link  pointed out is mentioned in one of the comments. This Q &amp; A is more helpful for people upgrading today than the work around mentioned in "". How to split strings into text and number? I'd like to split strings like these  'foofo21' 'bar432' 'foobar12345'   into  ['foofo', '21'] ['bar', '432'] ['foobar', '12345']   Does somebody know an easy and simple way to do this in python? Why do all SSH-RSA Keys begin with "AAAAB3NzaC1yc"? June 13th 2017 Microsoft blocked handling HTML markup in SharePoint calculated fields - how to get the same functionality back On June 13th 2017 all SharePoint calculated columns with HTML markup stopped working.   Basically the fields now render text (regardless of setting the data type to number). The gist of the notice from Microsoft () is:     In Microsoft SharePoint lists and libraries, calculated fields that   are running in the classic UI mode can be used to display results   based on Excel-like formulas. This is a long standing capability, and   is documented in Calculate data in lists or libraries.      Some users have added HTML markup or script elements to calculated   fields. This is an undocumented use of the feature, and we will begin   blocking execution of custom markup in calculated fields in SharePoint   Online from June 13, 2017 onwards. We are also providing this as a   configurable option for on-premises in SharePoint Server 2016 and   SharePoint Server 2013 via the June 2017 and subsequent Public   Updates.   As we don't have on premise SharePoint (online), we have to find an immediate work around, given that this impacts our processes and thus, business.   Is anyone aware of third party applications that will allow for HTML, script markup (that works with SP online)? Is named indexer property possible? How can I sync the new "people" (face recognition) metadata across devices in Photos (iOS 10 and MacOS Sierra)? The new Photos updates for iOS 10 and MacOS Sierra includes a much more powerful and integrated approach to organizing photos by who's in them.  It's built around powerful, on-device facial recognition.  But once it does its automated thing (finding the faces it thinks are the same person), there's still a lot of manual merging and labeling to be done if you have a lot of photos and are as obsessive about organization as I am.  For example, if you have, say... three thousand photos of your daughter, Photos will find almost all of them, but may guess they're 5 or 6 different people.  So you have to merge the buckets that all are one person, assign them a name (so you can search by it), etc.  But unlike other changes (edits, deletions, organization into albums, etc.), manual changes to "people" data don't seem to sync at all by default.      Is there really no way to do this?  It seems bizarre that one of the flagship features Apple's touting in this Photos update doesn't play at all with what was Photos primary selling point over iPhoto - everything synced on all your devices. If I design a PC for use as an NPC, how much XP should he give when killed? As part of an early quest, my PCs are likely to face off against a wizard.  The problem here is that the stat block for Mage NPCs listed in the Basic Rules has a Challenge Rating of 6, while the PCs are going to be five Level 1s. So, instead of messing with the stat block and risk weakening it too much/too little, I'm choosing to create a Level 1 Wizard PC and use it as an NPC for this quest.  The problem with that is that, as far as I can tell, there aren't any designated rules for assigning either Challenge Ratings or XP values to a PC. So, should I just give the wizard a Challenge Rating equal to his level (and thus have him give 200 xp when killed), or is there a better way to do this?  (This is different from , because he's asking for a way to assign a level to an NPC, while I'm asking for a way to assign an XP value/Challenge Rating to a PC (for use as an NPC). Similar questions, but different.) Are delphi variables initialized with a value by default? I'm new to Delphi, and I've been running some tests to see what object variables and stack variables are initialized to by default:  TInstanceVariables = class   fBoolean: boolean; // always starts off as false   fInteger: integer; // always starts off as zero   fObject: TObject; // always starts off as nil end;   This is the behaviour I'm used to from other languages, but I'm wondering if it's safe to rely on it in Delphi?  For example, I'm wondering if it might depend on a compiler setting, or perhaps work differently on different machines.  Is it normal to rely on default initialized values for objects, or do you explicitly set all instance variables in the constructor?  As for stack (procedure-level) variables, my tests are showing that unitialized booleans are true, unitialized integers are 2129993264, and uninialized objects are just invalid pointers (i.e. not nil).  I'm guessing the norm is to always set procedure-level variables before accessing them? Show alert popup on standard page layout on click of standard button "Save" How to wrap lines correctly inside algorithmic I am having problems displaying algorithms. The wrapping is really ugly and I can't, for the life of me, find a fix that doesn't involve manually tweaking the hell out of everything, to the point that I might as well scrap the crappy algorithm packages and write everything out in TeX.  Is there any way to properly indent the following  \documentclass{article} \usepackage{algorithm} \usepackage{algpseudocode} \begin{document} \begin{algorithm}    \caption{My pseudo code.} \begin{algorithmic}[1]    \While{this line is sooooooooooo long and boring and too much for algorithmic to handle}       \State look at this state, this state is just too long for algorithmic to display it properly        \While{again this line is sooooooooooo long and boring and too much for algorithmic too handle}          \State look at this state again, this state is just too long for algorithmic to handle, I'm just going to switch to Word       \EndWhile    \EndWhile \end{algorithmic} \end{algorithm} \end{document}​     so that the output is similar to Penguin Brainteaser : 321-avoiding permutations There are $k$ penguins, $k\ge 3$. They are all different heights. How many ways are there to order the penguins in a line, left to right, so that we cannot find any three that are arranged tallest to shortest (in left to right order)? The penguin triples do not have have to be adjacent.  This problem is courtesy of someone I know only as "DaMancha." How do I find out which version and derivative of Ubuntu is right for my hardware in terms of minimal system requirements? For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements? My windows directory is huge I have always had problems with my windows directory's growing to a huge size.  It started with windows 95 then 98 then 2000 and xp.  Windows 7 however is absolutely huge.  The windows folder itself with out program files is 21.4 gigs...add the program files and other windows files and it is a whopping 32 gigs.  My question is why is it so large and what can I do about it.  At the rate this is going I will be out of space in now time. I need to calculate the following indefinite integral:  $$I=\int \frac{1}{\cos^3(x)}dx$$  I know what the result is (from Mathematica):  $$I=\tanh^{-1}(\tan(x/2))+(1/2)\sec(x)\tan(x)$$  but I don't know how to integrate it myself. I have been trying some substitutions to no avail.   Equivalently, I need to know how to compute:  $$I=\int \sqrt{1+z^2}dz$$  which follows after making the change of variables $z=\tan x$. I am looking for a device that can track my location (lat,long) and speed all day long. Perhaps, I need GPS and accelerometer data bundled together.  What I want to do is to log my daily activities. I spend time walking, running, driving, taking a bus, staying in a building, etc., just like any normal human-being :) I am willing to carry the device with me at all times and would like to see every place I go into and my speed at certain positions.  My requirements are that the location and speed data should be recorded at least every ~20 seconds. I would also like the device to timestamp (date+time) each record. It would be enough if timestamp is precise to nearest minute and the location can go off about a maximum of 10-15m. (30-50ft.)  What I want is a portable device so I can carry all day long for about 2-3 months. I will only use it during casual, daily activities.  I don't want real-time tracking. I can collect the data from a storage later on. Profile Bug - Reputation Summary Not Displaying All Lines NOTE: I am not interested in calling /secur/logout.jsp since it ends all the active salesforce sessions.  I am developing a web application that is registered on salesforce as a connected app, so I am using salesforce credentials to authorize the user.  Application is developed in REST API and the communication with salesforce is happening in restful manner.   Auth url:   Authorization:  Method 1: If there is no salesforce session active, The user is taken to salesforce login page, where he enters his salesforce details to be authorized and after which he is taken to home page of my web application.  Method 2: If there is already a salesforce session active in another tab, the user is directly authorized and is taken to home page of my web application.  Now I am trying to implement logout button for my application, such that the following scenarios are covered,  Scene 1: The user is authorized using method1, and the user press the logout. Upon trying to logback the user is prompted for credentials.  Scene 2:  The user is authorized using method2, and the user should use logout to logout of the web application (not from active sessions). Upon login, the user should be again able to login using method2.  Can someone help me on how to implement the logout button such that it covers scenario 1 &amp; 2.  Thanks in advance.