I have two really long equations that don't fit into one line. I would like to display them as  first_eq LHS, super super super super long =                                         first_eq RHS, aligned right, also not short second_eq LHS, not as long as first eq =               second_eq RHS, aligned right, pretty loooooooooooooooooooooooooong too   Note that all lines are aligned to a side, either left or right. How can I achieve this within latex? I'm somewhat familiar with align, so if I wouldn't have to learn new packages that'd be great, but not a deal breaker.   I'm not sure whether the two equation signs should be vertically aligned, that could potentially look neat.  Neither of the solutions in the closed-as question work here. For example,   \begin{multline} (\rho + \delta  + (1-\beta)f(m(a, \bar u, l))J(a, \bar u, l) = \\ \left((1 - \beta)(p(a, \bar u, l) - b) + dJ(a, \bar u, l)\mathbf z(a, \bar u, l)\right)\\ \rho U (a, \bar u, l) = \\ b + f(m(a, \bar u, l))\frac{\beta}{1-\beta}J(m(a, \bar u, l))  + \eta \underbar U + dU(a, \bar u, l)\mathbf z(a, \bar u, l) \\  \perp \underbar U \leq U(a, \bar u, l) \leq \bar U(a, \bar u, l) \end{multline}   does not align them as I want to but equations rather hover weirdly in the center. Wrapping it around in dmath has no impact whatsoever.
I am having the following equation:  \begin{equation}   Q(\lambda,\hat{\lambda}) = -\frac{1}{2} P(O \mid \lambda ) \sum_s \sum_m \sum_t \gamma_m^{(s)} (t) \left( n \log(2 \pi ) + \log \left| C_m^{(s)} \right| + \left( \mathbf{o}_t - \hat{\mu}_m^{(s)} \right) ^T C_m^{(s)-1} \left(\mathbf{o}_t - \hat{\mu}_m^{(s)}\right) \right) \end{equation}   which does not very well fit on one line. How can I split this over two lines? What I have in mind is that I specify the splitting place, and that the first line is left aligned and the second line right aligned to make clear that it is still the same equation.  The linebreak \\ does not work.
What happens if I beat Ganon in Zelda: Breath of the Wild? I'm close to maxing out my character and I want to beat Ganon solely for the TRUE ending, but I'm too scared of losing some of my personal favorites from the Guardian Spear++ to fighting those damned Guardians (it was so fun).  So, after beating Ganon    Do monsters disappear? - Including the corrupted Guardians, but also the blood moons, I don't want to just face off against the Yiga Clan... Am I gonna run out of resources? - As a survival game Zelda BOTW has some emphasis on the survival genre but to me it is a survival-esque action-adventure game. Are special weapons still available when you max out? - Like the Savage Lynel Spears or Swords) Story about workers repeatedly doing trivial work I'm trying to remember a (short) story I read in school some time ago. I don't have much, but here it is:   Numbers of workers are assigned to trivial task, like changing broken lightbulbs (or something similar). Once they finished their daily work, another group of workers are putting the broken lightbulbs in again, allowing for an endless, trivlal working circle.   I know that isn't much, but maybe someone has an idea, thanks. If $A\subseteq\mathbb N$ and $\sum\limits_{a\in A}\frac1a$ converges then $A$ has natural density $0$ In this  to a question about a series, a theorem was stated:     If $A= \{a_i \}$ is a set such that $\sum_{i = 1}^{\infty} \frac{1}{a_i}$ converges, then $d(A) = 0$, where $d(A)$ is the  of the set.   My background in number theory is basically zero and all my attempts to prove this have been utterly unseccessful; would anyone please help me, or at least provide me with a hint to prove it? I want to find an example of a homomorphism $f:G\to H$ such that $A$ is a normal subgroup of $G,$ but $f(A)$ is not so in $H.$  I know that if $f$ was onto $f(A )$ must be normal , but otherwise i want to find an example! Should the first word after a colon be capitalized? Finding the maximum likelihood estimators for this shifted exponential PDF? Methods to work around the problem of missing data in machine learning Virtually any database we want to make predictions using machine learning algorithms will find missing values ​​for some of the characteristics.  There are several approaches to address this problem, to exclude lines that have missing values ​​until they fill with the mean values ​​of the characteristics.  I would like to use for a somewhat more robust approach, which would basically run a regression (or another method) where the dependent variable (Y) would be each of the columns that have missing values ​​but only with the rows of the table that contain all the data , and predict the missing values ​​with this method, complete the table by the table and move to the next 'column' with missing values ​​and repeat the method until everything is filled.  But that gives me some doubts.  Why any column start? I believe that the one with the smallest missing values ​​until the one with the most  Is there any threshold of missing values ​​that is not worth trying to complete it? (for example, if this characteristic only has 10% of the values ​​filled would not it be more interesting to exclude it)  Is there any kind of implementation in traditional packages or other methods that are robust to missings? I have several AppExchange apps installed that are failing tests. What is the recommended approach to resolving this? Are tests run when a new package is installed? Is there a way to determine what is actually failing besides the name of the method and something like "expected true, actually false"? The test results rarely show enough information to be useful.   What I'm doing atm, is checking for updates for the packages, and then writing the company with the failing test results.   Any feedback would be appreciated. How do I install Ubuntu from an USB drive / create a live USB-stick in Windows? I tried to use the usb-creator.exe from Ubuntu 10.10 desktop i386 ISO image and it does create an USB stick that doesn't boot. When I try to boot from it I get:     Operating System not found.   I try to do this from Windows 7 x64. I'm not looking to create a live Ubuntu media, only an installation USB disk.  I repeated the process several times and I even tried to reformat the USB drive (FAT32), no success yet.  The USB stick is a 8GB one. Making data points different sizes based on data using QGIS? I am trying to plot sales data on a map using QGIS. I will add the disclaimer that I am a rookie at using the program. I added the different sales types by adding delimited text layers (utf16). The data included Longitude, Latitude, and Amount. I want to make the dots on the map scale with the value of the sale. Ive had no luck with trying to use Simple Marker->Data defined properties-> size and writing case functions. Some data points show up at different sizes while others show up at all data points. Here are my functions under different simple markers:   CASE WHEN Amount &lt;= 10000 THEN '.2' END CASE WHEN 10000 &lt; Amount &lt; 75000 THEN '.4' END CASE WHEN 75000 &lt; Amount &lt;= 250000 THEN '.6' END CASE WHEN Amount &gt;= 250000 THEN '1' END   The majority of my data set falls into the 10-75k range. However the .4 and .6 size circles show up at every data point on the map, while the .2 and 1 sizes only show up where the data specifies (along with the .4 and .6 sizes). At this point I am trying to figure out what is wrong with the equations, however I am stuck.   Is there a better way to go about this or am I just simply messing up the equations?   I wish I could share my whole map with you but it is looking great. I went with U/Joseph 's solution and here is an excerpt of the results for those interested. I would like to ask a question about Java that doesn't have a specific answer. It's a question to see what people think and to share their opinion.    Will Stack Overflow tolerate this, or is there another Stack Exchange resource where I may ask a question like this? Is a memory leak created if a MemoryStream in .NET is not closed? I have the following code:  MemoryStream foo(){     MemoryStream ms = new MemoryStream();     // write stuff to ms     return ms; }  void bar(){     MemoryStream ms2 = foo();     // do stuff with ms2     return; }   Is there any chance that the MemoryStream that I've allocated will somehow fail to be disposed of later?    I've got a peer review insisting that I manually close this, and I can't find the information to tell if he has a valid point or not. How can I trigger a command when a player is hit by a Snowball? I am trying to make a snowball that triggers a command when it hits a player in 1.15, but I don't know how to do that. When I do execute at @e[type=snowball] run gamemode spectator @a[distance=..2] it only runs the command if it goes right next to them. I'm looking for all the ways to increase Friendship in Pokemon X and Y.  Note that Friendship is different from Pokemon Amie Affection; they both do different things. How do I beat the Reaper on Rannoch? I'm having trouble with the last of the Rannoch missions, where Shep wakes up and takes on a Reaper.   Shepard has a targeting laser which will call in an orbital strike with the combined might of the Quarian Migrant Fleet, but there's two major problems standing between the commander and victory.   The Targeting Laser takes a while to power up. The Reaper is trying to kill you.   I can consistently avoid the Reaper's attacks for the first volley, but each time you hit it, the Reaper moves forwards, giving you less time to dodge future assaults. Is there some key to avoiding the Reaper's attacks? Strafing doesn't seem to be enough. Specifying geography with cardinal directions So here in America we are in "the West".  Would this become "the Western world" or "the western world? "  I'll assume the same applies to "the East" (Asia). Initializing a member array in constructor initializer Margin of caption different than text body in 2-column table (cas-dc) I'd like to play Dragon Age Inquision in english instead of the language of my operating system, but it seems to default to that and I can't find a way to change it. I already tried setting the Origin client language to english, but that didn't change anything.  Where can I change the language for Dragon Age: Inquisition? Why Does Harry Have a Scar When Avada Kedavra Leaves No Trace? Why does Harry have a scar when Avada Kedavra leaves no trace?     ‘The Muggle authorities were perplexed. As far as I am aware, they do not know to this day how the Riddles died, for the Avada Kedavra Curse does not usually leave any sign of damage ... the exception sits before me,’ Dumbledore added, with a nod to Harry’s scar.   Half-Blood Prince - page 343 - Bloomsbury - chapter 17, A Sluggish Memory   What caused Harry to retain a scar from Avada Kedavra, when no one else in know history showed any signs of cause of death when Avada Kedavra was used?  What caused Harry's scar?  I'd love an answer based in canon, such as the books, interviews with J.K. Rowling, or Pottermore.