Why wont this equation split using \begin{align} and \end{align} I have this equation here and I am trying to split it up.  I use the \begin{align} and \end{align} commands and I use \\ where I want the equation to split onto the next line.   Here is the code  \begin{align}         \mathcal{H}_{q1} \mathcal{H}_{q2} \mathcal{H}_{q3}...\mathcal{H}_{qn}0 \\         =\frac{1}{2}H_{q1}\{\mathcal{H}_{q2}\mathcal{H}_{q3}...\mathcal{H}_{qn}0\} \\         +\frac{1}{2} h_{q1}\} \\          =\frac{1}{2}H_{q1}\{\frac{1}{2} H_{q2}[\mathcal{H}_{q3}...\mathcal{H}_{qn} 0]+\frac{1}{2}h_{q2}\} +\frac{1}{2}h_{q1} \\          =  \frac{1}{2}H_{q1} \frac{1}{2} H_{q2} \\ [\frac{1}{2}H_{q3}(\mathcal{H}_{q4}..\mathcal{H}_{qn}0)+\frac{1}{2}h_{q3}]+          \frac{1}{2}h_{q2}+\frac{1}{2}h_{q1}.. \\          =(\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn}0+   \\ (\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn-1}h_{q1}+(\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn-2}h_{qn-1}+.. +          (\frac{1}{2})h_{q1}=\sum^n_{j=1} (\frac{1}{2^j}) H_{qo}H_{q1} H_{q2}H_{q3}..H_{qj-1} h_{qj}         \end{align}   I try and compile this but nothing is outputted in place of this equation, just a blank space.      What can I do?
Aligning equations within multline I have this really long equation and I have used multline to break it up. I also want to align the broken bits of the equation to the left. When I use  align, for some reasons it aligns to the right when I want it to be on the left. How can I align to the left?  \begin{multline} \begin{align} \mathcal{H}_{q1} \mathcal{H}_{q2} \mathcal{H}_{q3}...\mathcal{H}_{qn}0=\frac{1}{2}H_{q1}\{\mathcal{H}_{q2}\mathcal{H}_{q3}...\mathcal{H}_{qn}0\}+\frac{1}{2} h_{q1} \\ =\frac{1}{2}H_{q1}\{\frac{1}{2} H_{q2}[\mathcal{H}_{q3}...\mathcal{H}_{qn} 0]+\frac{1}{2}h_{q2}\} +\frac{1}{2}h_{q1}=\\ \frac{1}{2}H_{q1} \frac{1}{2} H_{q2} [\frac{1}{2}H_{q3}(\mathcal{H}_{q4}..\mathcal{H}_{qn}0)+\frac{1}{2}h_{q3}]+ \frac{1}{2}h_{q2}+\frac{1}{2}h_{q1}=...\\          =(\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn}0+ (\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn-1}h_{q1}\\+(\frac{1}{2^n})H_{q1}H_{q2}H_{q3}..H_{qn-2}h_{qn-1}+.. \\+ (\frac{1}{2})h_{q1}=\sum^n_{j=1} (\frac{1}{2^j}) H_{qo}H_{q1} H_{q2}H_{q3}..H_{qj-1} h_{qj} \end{align} \end{multline}
The blackboard bold font in the AMSFonts package only has capital letters.  I sometimes wish to use a blackboard bold "1", for which I can use \usepackage{bbold}. But this changes the entire blackboard bold font, and I like the original AMSFonts versions of the capital letters better.  Is there a simple way for me to get \mathbb{1} from one package and the blackboard bold capitals from another? Why does demand for stock rise when a company appears to have high future value? So a company decides to raise money by selling shares of its stock. The stock is offered at an initial price of their determination. The stock is then traded in a market where forces of supply and demand, as well as speculation, affect its price.  When a company performs well (or makes decisions that will likely increase the company's earnings in the future), more people want to buy that stock than do people wanting to sell it. This creates demand for that stock which causes its sell/bid prices rise. When a company performs poorly, the opposite occurs; more people want to sell the stock than want to buy. This creates a surplus that causes sell/bid prices to fall.  Understanding this, people speculate over company performance to determine the future behavior of a stock, and attempt to "buy low, sell high" or "borrow high, return low" in order to make a profit.  But my question is regarding the first part of that process. What is it about company performance that causes the perceived value of its stock to rise? This is especially perplexing since I would guess that most people don't exercise their voting rights, and many stocks don't pay dividends.  It's not like a shareholder has any direct financial gains from increased company earnings (speculative stock pricing notwithstanding).  What is the intrinsic value of the stock?  It seems to me that all participants in a stock market tacitly agree that stock price will have a direct correlation with company performance. So another way of asking the question is, would an opposite agreement hold? What financially (this isn't a question about logistics, communication, or feasibility) stops all participants in a market from agreeing to value a particular company's stock inversely with respect to the company's performance?  Since I feel like I can't quite nail down my question, another form of it would be, why is stock market behavior driven by company performance? Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer. How do you define an arbitrary sort sequence for views? Maximize the product of the partitions of an integer I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference? wrappers and JavaScript pop-up? Use Case:  What i want is a list of records, and allow this user to choose 2 of those records, then click a button to go to a new VF page, if the user selects more than 2, i want him to get a notification of some kind saying you need to select 2 records, I do not want the page refeshed though.  Strategy:  I'm creating a wrapper class for the records like this:  and i have that part going by creating a custonm controller... I need the notification part working.   Problem:  I don't know how to call methods from the customController in javascript Also, i do not want to refresh the entire page. I just want them to go back to where they were. I was thinking a pop-up notification but I'm flexible.. How do I diff two text files in Windows Powershell? I have two text files and want to find the differences between them using Windows Powershell. Is there something similar to the Unix diff tool available? Or is there another other way I haven't considered?  I've tried compare-object, but get this cryptic output:  PS C:\&gt; compare-object one.txt two.txt  InputObject                                                 SideIndicator -----------                                                 ------------- two.txt                                                     =&gt; one.txt                                                     &lt;= Give moderators the option to select a deletion reason when removing posts I have a raster image (Sentinel-2 band 4) and a shapefile covering the same area than the image (same projection and extension). The shapefile has different polygons which are agricultural fields.   I want to create a new file where, for each polygon, the mean value of the pixels that are inside it is calculated.  Could you please help me to find an appropriate R code for that? Can we have the table name as "option" in MySQL? I am very, very new to MYSQL.I tried to create a table named "option". My SQL Query is :  create table option(   id int not null primary key auto_increment,  choice varchar(30)  )  While executing this query it shows the following error  Error Code : 1064 You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'option( id int not null primary key auto_increment, choice varchar(30) )' at line 1 (0 ms taken)  If I try with the table name as "choice" it is working.  can we have the table name as "option" in mysql?   thanks I want to talk to someone about the house that my wife and I own.  Saying, for example, "My wife's and my house is awesome," sounds a bit funny to me.  What's the best way to express this?  Clarification  I'm asking specifically about the grammar of multiple nouns in possessive form.  I'm particularly curious if it's possible to do this with a first-person pronoun (me).  I am capable of rephrasing this in other ways - my question is not how to express the idea, but about this particular grammatical construction, if it is even legal. Why are swap partitions discouraged on SSD drives, are they harmful? I often read that one should not place swap partitions on a SSD drive, as this may harm the device. Is this true? Can you please explain the reason to me?  Because I otherwise would have thought that placing swap on an SSD is the best choice, as it's much faster than HDDs and therefore swapping RAM contents to the SSD is not as slow as it would be with the HDD... How do ideal quotients behave with respect to localization? Suppose $R$ is commutative ring with unity. For ideals $I$, $J \subseteq R$, the ideal quotient $(J:I)$ is $$(J:I) := \{x\in R \, : \, xI \subseteq J\}$$ Let $S\subset R$ be a multiplicative set. When does localization at $S$ commute with taking quotients, i.e. when does the equality $$(S^{-1} J : S^{-1} I) = S^{-1} (J:I)$$ hold? More generally, when is it true that $$S^{-1} \text{Ann}_{R} (M) = \text{Ann}_{S^{-1} R} (S^{-1} M)$$ for an $R$-module $M$? Install 0bda:f179 Realtek Semiconductor Corp. (rtl8188fu), or Netgear rtl8812au USB WiFi adapters Is the total variation function uniform continuous or continuous? What's a word for lack of confidence? The maximum energy stored by a capacitor is when it’s (theoretically) fully charged, or just before it reaches dielectric breakdown, if you will. It seems, then, that the maximum energy ($E$) $=QV$, where $Q$ is the maximum charge attained and $V$ is the maximum ‘voltage’. However, the correct equation for the maximum energy is $E=\frac{1}{2}QV$. Why? I’m looking for a simple, intuitive explanation because my reasoning that $E=QV$ seems sound to me. I know about , but I’m looking for a reason to disprove my specific argument that $E=QV$ and not the “Oh, it comes from integration.” response. Quick question about ideals of field $F$ in $F[x]$ are principal. Just got a question about ideals of $F[x]$ being principal with $F$ being a field.  The proof basically starts assuming $g(x) \in N \subset F[x]$ where $N$ is an ideal and $g(x)$ is a minimal degree element. The rest is just deducing the what the division algorithm says.  But my question is that shouldn't we let $g(x)$ be arbitrary? Why are we choosing the minimal element? When using complete sentences in parenthetical e.g. or i.e. situations, should the first word be capitalized? In a bulleted list of very technical sentences, where each bulleted item has one or two parenthetical examples or restatements which are complete sentences, should the first letter of each e.g. or i.e. sentence be capitalized or not?  Example:   Here is my technical sentence. (e.g., Should the first word of this e.g. be capitalized like this?) Here is another technical sentence.  (i.e., this really isn't a i.e. different example to highlight whether the first word should or should not be capitalized after a parenthetical i.e.)