Begin{equation} works better with \ than $$
What are the differences between $$, \[, align, equation and displaymath?
I have always believed that it was ok to replace a capacitor with a slightly higher voltage rated one. eg 16v with 25v.Going higher than this would risk the capacitance value being out at the working voltage. However I just read the following quote from this       Electrolytic capacitors are non-ferroelectric with a very low dielectric constant. Their capacitance is derived from a very high surface area and nanometer thick dielectric layers. Their capacitance is not a function of applied voltage.‐Design Solutions For DC Bias In Multilayer Ceramic Capacitors (August 2010 Electronic Engineering Times)   So does this rule not apply to aluminum electrolytics? Eg will I have no issues replacing an electrolytic 25v 100uf with a 50v 100uf assuming both are low esr, similar footprint and good quailty? How do I wrap a macro definition in an environment? I'm creating a style file, and want to store the body text of the abstract environment so that I can put it on my custom titlepage. I could have required that my users enter the abstract as  \customabstract{Abstract text goes here}`   which I would have implemented as something like  \newcommand{\customabstract}[1]{\gdef\abstracttext{#1}}   However, I would prefer that the user is able to use environment notation,  \begin{customabstract}Abstract text goes here\end{customabstract}   To do this, I thought I could define something like  \newenvironment{customabstract}{\gdef\abstracttext\bgroup}{\egroup}   But this definition makes \abstracttext expand to \bgroup, which is not what I wanted. I tried to solve the problem by \expandafter,  \newenvironment{customabstract}{\expandafter\gdef\expandafter\abstracttext\bgroup}{\egroup}   but this results in a runaway error.  Is there any way to acheive what I want? Answers that helps me understand the inner workings of TeX (instead of just referring to a custom package) are preferred. permission denied for root@localhost for ssh connection I just installed Ubuntu 14.04 and LAMP on that. Then, I wanted to configure my server, so tried out  tutorial.  When I give the command:  ssh root@localhost   I get : Permission denied, please try again. I have logged in as root user through the command :  sudo -i   I also tried the same, by logging in through:  sudo -s   I use the same password as that I used to log in as user, but still am getting the same error message.  Could someone help me out here?  PS: I looked into  but didn't seem to work for me. What is Interface method in salesforce The roots of the equation $z^n=(1+z)^n$... The complex roots of the equation      $$z^{n}=(1+z)^{n}$$   $A.$ are vertices of a regular polygon  $B.$ lie on a circle  $C.$ are collinear  $D.$ none of these  Don't know where to start.. Please help.!  NOTE:  $z$ is a complex number. Countable union of countable sets(ZF) I wrote a simple backup script which back ups my stuff on a remote server, everything is working great but I'd like to have some sort of report like "backup successful or not".  this is my script   # backup CHECK date1=`date +"%d.%m.%y - %H.%M"` host=`hostname` twdate=`date +"%d.%m"` performtw=`ls -la|grep "tw"|grep "$twdate" &gt; tmp1.txt` echo $performtw if cat tmp1.txt|grep "tw" then echo backup successfull printf "tw backup success!" | mail -s "tw backup check $date1 repor$ rm tmp1.txt else echo backup failure printf "sitename backup failure!" | mail -s "site backup check $date1 repor$ rm tmp1.txt fi exit   But this isn't working really well and I ask you if there's some simpler and more powerful way to do it? Basically it just needs to check if file exists with the name starting xyz and was created at date xyz. How do you make corrections to a published paper? How can I solve this integral using the Residue theorem? $$ \int_{-\infty}^\infty \frac{\sin(x)}{x^2 + 4x + 5}dx$$  What I now is you can use residue theorem, and evaluate this integral  $$ \oint \frac{e^{iz}}{z^2 + 4z + 5}dz$$ and through calculating the residues and using the residue theorem I get that the answer for the above integral is $$\pi e^{-1-2i}$$  However after this I am completely lost.  Any guidance will be much appreciated. I would like to know why I can evaluate the integral as an exponential integral as well. Apex PMD: Problem: Validate CRUD permission before SOQL/DML operation Background   I am using the Apex PMD plugin for VS Code and it's giving me this problem:     Validate CRUD permission before SOQL/DML operation   For this line of code:  insert contentVersion;   Which is part of this method:  private void attachReport(Id recordId) {      ContentVersion contentVersion = new ContentVersion(         versionData = Blob.valueOf(buffer.toStr()),         title = 'Import Report',         pathOnClient =  StringUtils.format('/Import-Report-{0}.txt', DateTime.now().getTime()),         FirstPublishLocationId = recordId);      insert contentVersion; }   Questions    Why am I getting the problem? What should I do to not get the problem?     Reference D+ and D- on USB I'm making a small project which will take +5v from USB, What should I do with the D+ and D-, keep it open or short them to ground or do I have to add some components?  I want to run ATMEGA168 and 16x2 LCD with back light. Duplicate application icons in Ubuntu dock upon launch PHP variable variables I want to store courseworks marks of n courseworks into n variables, such as cw1 and cw2 etc. Using variable variables how can I come with cw1, cw2 etc.   How can I dynamically create variables? The drawer has M different colored socks. What is the least amount of socks I that I need to draw to guarntee N pairs So in my discrete math class, we all know that if the drawer has 2 different colored socks, you need to pull out 3 socks to ensure a pair.   However, I am puzzled after there are more different colored socks and more pairs of socks.  For example, if there are 3 different colored socks in the drawer and I need to draw out 50 pairs, at least how many socks do I need to draw out to ensure that I have 50 pairs of sock?  How about if there are M different colored socks in the drawer and I need to draw out N pairs, at least how many socks do I need to draw out to ensure that I have N pairs of sock?  Are there any general formulas for these types of problem? Or are there any rules for this type of question? Can't see a glass object through another glass object in Eevee Why was the MCU Super Soldier program considered a failure? In Marvel Cinematic Universe, military tried to create super soldiers like Hulk, but they failed. So, the program was shut down.  Where did they fail? Didn't Blonsky get Wolverine-type super healing capability? Why couldn't it make the military stronger? Other than this, wasn't Abomination a success (despite the fact that it wasn't an original work of the military)? He was defeated by Hulk, but enemy forces don't have a Hulk. When it comes to anger, who cares as long as you are focused on the target? Abomination was indeed in full control and he was always after Hulk. Ideals in valuation rings How do I prove the fact that for any valuation ring $V$ the ideals are totally ordered under inclusion? Reserved words as names or identifiers Is there any tricky way to use Java reserved words as variable, method, class, interface, package, or enum constant names? I am having a problem running the CDC change capture job against some of my test databases.  The error message I'm getting is the following:     Executed as user: NT AUTHORITY\NETWORK SERVICE. Cannot execute as the database principal because the principal "dbo" does not exist, this type of principal cannot be impersonated, or you do not have permission. [SQLSTATE 42000] (Error 15517).   How can I fix this? I think it would be a very useful and quality-improving feature.  As for me, when I speak on something, I often have a visual representation of how it works, or something. It's obvious there are many things (in algorithms, or, say, UI) which are much easier understood with pictures and diagrams, than from scarce text.  So I'd really like here to be a special answer form, where you can attach some visual things to better explain your ideas.  I imagine this form as just a canvas with few painting tools and some basic blocks and patterns.