I have a very long SQRT() equation, that doesn't fit in a line. I couldn't simplify  it, since it involves terms in addition. Is there an alternative way to represent a root as 'SQRT{some function}' ?  \documentclass{article} \begin{document} \begin{equation}     \Delta\sigma_{V,ij} = \sqrt{\Delta\sigma_{x,ij}^2 + \Delta\sigma_{y,ij}^2 + \Delta\sigma_{z,ij}^2 - (\Delta\sigma_{x,ij}\cdot\Delta\sigma_{y,ij} + \Delta\sigma_{y,ij}\cdot\Delta\sigma_{z,ij} + \Delta\sigma_{z,ij}\cdot\Delta\sigma_{x,ij}) + 3 \cdot (\Delta\tau_{xy,ij}^2 + \Delta\tau_{yz,ij}^2 + \Delta\tau_{zx,ij}^2)} \end{equation} \end{document}
How can continue the equation of the rectangle red in next line?   \documentclass[11pt,a4paper,twocolumn]{article}  ...  \begin{equation*}     \left| \dot{r} \right| =     \sqrt{{- \, {e}^{-t} \left( \cos t + \sin t \right)}^{2} \, + \, {{e}^{-t} \left( \cos t + \sin t \right)}^{2} \, + \, {(- \, {e}^{-t})}^{2}} \end{equation*}
Understanding how references and labels work I'm trying to understand why I cannot effectively reference figures or equations that I have defined with labels.  For example:  \begin{figure}   \label{fig:area_Treasuries}   \caption{Treasuries as a portion of total financial flows.}   \centering   \includegraphics[width=0.75\textwidth]{graphs/Area_Treasuries.png} \end{figure}  \paragraph{} Figure~\ref{fig:area_Treasuries} presents Treasuries (both flowing into and out of the United States) as a share of total financial flows.  From 1985 to 2010, Treasuries account for, on average, 53.2\% of total financial flows.   With the above code, I get this warning:      LaTeX Warning: Reference `fig:area_Treasuries' on page 37 undefined on   input line 477.   The result is "Figure ?? presents Treasuries..."  Why is this happening?  Related, I don't understand why I can't reference, say, an equation before (I mean physically above in the text) the actual equation.  Isn't this what compiling multiple times and cross references is supposed to take care of? Heathrow change in terminal flight UK Border control check? I am traveling from NYC to Mumbai via London. Assume my connecting flight belongs to different terminal. If I have to change terminal at Heathrow, do I need to go through UK Border control ? Is it possible to install Ubuntu on my Windows 8 computer without any CD or USB drive? Please read entire post CAREFULLY before answering.  This question will make you confused if you don't.  Information (May skip :P)   OS : Windows NT 6.2 (Windows 8 K) Equipped hard disk   Total 1TB, 1 disk C: (Simple Layout, NTFS, Boot, Pagefile, Crash dump, Main): total 488,039,776,256 bytes, used 93,473,599,488 bytes D: (Simple Layout, NTFS, Main): total 486,859,075,584 bytes, used 8,426,016,768 bytes hidden: Ask if needed  Brand(manufacturer): Samsung Electronics Processor(CPU): Intel(R) Core(TM) i5-3230M CPU @ 2.60GHz RAM: 8GB , 64-bit , OS 64-bit   Question (READ THEM ALL VERY CAREFULLY)   Is there any way to install Ubuntu on this computer without any external disk (CD, USB drive, etc) Note : This computer is 64-bit, so  did not help me. WUBI does not support UEFI, and This computer uses it. No Virtual PC programs like VirtualBox or VMWare, because it takes memory.   EDIT : I already found a USB drive in my home, so now it is installed on my computer xD Let $S$  be a square of unit area. Consider any quadrilateral whose $4$ vertices lie on each side square $S$. Let the length of the sides of this quadrilateral be $a,b,c,d$. Then prove that $$2 \leq a^2+b^2+c^2+d^2 \leq 4$$     This problem appeared in IIT JEE $1997$ (re-exam).I really do not know know how to approach this problem properly.I have managed to prove $a^2 + b^2 + c^2 +d^2  \leq 4$ but not the initial inequality. sf:INVALID_OPERATION: INVALID_OPERATION: testLevel of NoTestRun cannot be used in production organizations While deploying code in vsCode from sandbox to production I get the below error      sf:INVALID_OPERATION: INVALID_OPERATION: testLevel of NoTestRun cannot   be used in production organizations   As per the error, I need to change the value of testLevel but I am not able to find where and how can I change it to RunLocalTests  Could someone please help me to change the value of testLevel in vsCode What are good reasons to prohibit inheritance in Java, for example by using final classes or classes using a single, private parameterless constructor? What are good reasons of making a method final? Ubuntu 13.10 Macbook Air Mavericks Parallels 9 Black Screen I can install Ubuntu 13.10 in parallels ok and then log in.  Problem is Ubuntu does an update and I get black screen / desktop such that I can't see any app windows that I open.  I've tried a few of the other suggestions and they don't work for me. Notation: Why write the differential first? From reading answers here, I've noticed that some people write integrals as $\int dx \; f(x)$, while other people write them as $\int f(x)\;dx$.  I realize that there is no mathematical difference between the two notation forms, but was wondering why some people choose the first method over the second.  Is there some place in higher maths that it becomes beneficial to write the differential first?  (I, personally, have always used the second method, just because I was taught that way...) Use physical harddisk in Virtual Box Using Virtual Box, how can I install an OS to a secondary, physical disk, and boot it in both (at separate times) Virtual Box, and as a typical secondary OS install? Can I "fill" an empty object? How to distinguish Nexus 7 (2012) and Nexus 7 (2013) I am having trouble with Bluetooth Low Energy (BT 4.0) on a Nexus 7.  I think I may have a 2012 model.  How to tell if I have a 2012 or 2013 version of the Nexus 7? How to speed up 4e combat I DM a group of four PC's and even "easy" battles take at least an hour to resolve. Normal encounters take even longer! I want to speed up combat so my players can do more in a session.  I've been trying a lot to speed up combat, we are already using:   Initiative cards that the players keep up 30 second bonus rule: if someone take his turn within 30 seconds, he receives a token. This token can be used to give a +1 on attack or damage, after rolling. Completely removed healing surges Checked all character sheets, they are roughly equal Roll damage and attack at the same time   I even introduced an experienced player, which helped my party to play more strategic, but speed hasn't improved.  Also the party is Lv 8, nearing Lv 9.  This is not an issue of the DM's turn taking too long. My turns take about 60 seconds tops. The 30 second rule helps a lot, most of the the players turns are within or near 30 seconds.   The major issue appears to be the sheer number of rounds, averaging on 25-30 rounds needed to resolve even a "normal" encounter.  What can I change to resolve combat faster?  I'm looking for both 4e solutions, system agnostic and home brew solutions. Multiple Sub Query using child parent relationship Consider in my basket, I have a package (Main Product-just a holder) which will have 2 standalone products (child) and again the standalone products will have child products (Grand Parent). All these products are from same object called Product Configuration.   We have a child relationship to itself(Parent Configuration) using a custom lookup field. The problem here is, I could only fetch details only up to 1 level (i.e.,package and child details) and I was not able to drill deeper to grand child products.  Query I used to get 1 level of relation ships is below:  SELECT id, name, Access_Type__c, Circuit_Bandwidth_Value__c, QuoteType__c,     Upstream_Speed_Value__c, IP_Address_Type__c, Care_Level__c, Base_Plan_Value__c, Site_Address__c,      cscfga__Quantity__c, Quantity_of_Ip_Address__c, cscfga__Contract_Term__c, Connection_Price__c,      Monthly_Rental_Conga__c, Total_Annual_Rental__c,      (         SELECT id, name,cscfga__Product_Family__c,Upstream_Speed_Value__c, cscfga__Quantity__c, Quantity_of_Ip_Address__c,              Connection_Price__c, Monthly_Rental_Conga__c,cscfga__Parent_Configuration__r.Circuit_Bandwidth_Value__c,Circuit_Bandwidth_Value__c          FROM cscfga__Related_Configurations__r         WHERE cscfga__Parent_Configuration__c &lt;&gt; ''          ORDER BY name     )  FROM cscfga__Product_Configuration__c  WHERE cscfga__Product_Basket__r.cscfga__Opportunity__c='{pv0}'      AND cscfga__Product_Basket__r.csordtelcoa__Synchronised_with_Opportunity__c=True     AND cscfga__Parent_Configuration__c = ''  ORDER BY name   Not sure how to write another sub query to get grand child details. When I tried the below query:  SELECT id, name, Access_Type__c, Circuit_Bandwidth_Value__c, QuoteType__c, Upstream_Speed_Value__c,      IP_Address_Type__c, Care_Level__c, Base_Plan_Value__c, Site_Address__c, cscfga__Quantity__c,      Quantity_of_Ip_Address__c, cscfga__Contract_Term__c, Connection_Price__c,      Monthly_Rental_Conga__c, Total_Annual_Rental__c,     (         SELECT id, name, cscfga__Product_Family__c, Upstream_Speed_Value__c, cscfga__Quantity__c,              Quantity_of_Ip_Address__c, Connection_Price__c, Monthly_Rental_Conga__c, cscfga__Parent_Configuration__r.Circuit_Bandwidth_Value__c, Circuit_Bandwidth_Value__c,         FROM cscfga__Related_Configurations__r         WHERE cscfga__Parent_Configuration__c &lt;&gt; ''          ORDER BY name     ),     (         SELECT id, name, cscfga__Product_Family__c          FROM cscfga__Related_Configurations__r         WHERE cscfga__Parent_Configuration__c &lt;&gt; ''          ORDER BY name     ) FROM cscfga__Product_Configuration__c  WHERE cscfga__Product_Basket__r.cscfga__Opportunity__c='0066E000002Xrr0'      AND cscfga__Product_Basket__r.csordtelcoa__Synchronised_with_Opportunity__c=True      AND cscfga__Parent_Configuration__c = ''  ORDER BY name   I got below error:     MALFORMED_QUERY:  from cscfga__Related_Configurations__r ^ ERROR at   Row:6:Column:6 Cannot follow the same aggregate relationship twice:   cscfga__Related_Configurations__r   Can someone please help here. Note: I am executing these queries in Workbench. Remove empty elements from an array in Javascript How do I remove empty elements from an array in JavaScript?   Is there a straightforward way, or do I need to loop through it and remove them manually? Can I replace a 15 ampere circuit breaker with a 20 ampere breaker? When I plug-in a conventional heating pad or a hair dryer into any bedroom duplex, the lights dim; and/or trips the circuit breaker. The home is of new construction-- placed in service 31 Dec 2013. My question is: Can I safely replace the existing 15 AMP Breaker with that of a 20 AMP? . . . the service cable is of 14 Gauge Copper Conductor. Concatenate several columns into one in Google Sheets I am in the process of updating my CV. Since I often get labeled as "the bioinformatician" I get to play with many different languages and technologies, and similarly what people expect from a bioinformatician varies from person to person. So I figured it would be a good idea to indicate how much I feel I know in respective fields/languages.  Inspired by , I came to wonder whether or not its acceptable to have self-assessed ratings of your technical skills, such as: proficiency programming languages, familiarity with relevant software etc.   My own feeling is that such ratings are useful to indicate what you feel most confident or comfortable with. It would also be useful to show any potential future employer the level of competence you have in different fields. If you think about it a bit, it is common to have some type of rating for the languages one speaks, so I think an analogue to programming language proficiency should not be that alienating.  On the other hand there is the risk of rendering your CV like, as a friend of mine put it, a role-playing game character sheet.   Is it common to have such ratings on skills? Are there any potential problems with it?   Edit: What I was thinking is a small listing something like: What are the survival limitations of alcohol? This question was inspired by watching one of the Pirates of the Caribbean movies; particularly where Jack Sparrow allegedly survives on a desert island by finding an unlimited supply of rum. I've heard alcoholic drinks dehydrate you more than hydrate you, so this seems like an unsustainable strategy.  My question is threefold.    How long can a human survive by drinking hard liquor (40% alcohol by volume) for their sole water intake (ignoring food)? If it's unsustainable, what will finally take you down? If the hard-liquor approach isn't viable, what % alcohol can keep you hydrated (beer, wine, etc.)?   Related: 1.  2. Usage of “when” or “while” in this context He left the house _ I was still sleeping   Would this sentence be better completed with when or with while? Can I color text by using an image, so that the color isn't flat? I'm using tikz to attempt to make a book cover, and I have a "wallpaper" image that looks like leather (not that I've handled that many leather-bound books). I'm using the node command to place text over the top of it, but none of the colors I've experimented with look decent.  Can I use an image of gold-leaf as the fill/stroke for the text? Or for that matter, for the path lines as well?  I've tried googling for this, but I can't figure out a set of keywords non-generic enough to pull back useful results.