Context: Consider a circuit with only two linear time invariant capacitors. If I charge one the capacitors and then throw a switch that closes the circuit, there will be some redistribution of charge. The capacitors are ideal and there is no resistance in the circuit.  Problem  I calculated the energy before the circuit was closed and after the circuit attained a steady state. There was some energy dissipation.  My question is: In what form is the dissipated energy leaving the circuit?
The energy stored in a capacitor is $$ U= \dfrac{1}{2} CV^2 $$    So when I have a 1F supercap charged to 1V the energy is 0.5 J. When I connect a second supercap, also 1F in parallel the charge will distribute and the voltage will halve. Then    $$ U = \dfrac{1}{2} 2F (0.5V)^2 = 0.25 J $$  What happened to the other 0.25 J?
Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? In Java Edition, I can name a mob by using NBT tags like this: /summon zombie ~ ~ ~ {CustomName:'{&quot;text&quot;:&quot;TheUndead&quot;}'}  But in Bedrock Edition, I've heard NBT is not accessible from commands. What can I do to summon a mob with a custom name tag using the /summon command? If there is a unique left identity, then it is also a right identity Let $(R,+,\cdot)$ be a ring, and $e \in R$ be an element such that $ea=a$ for all $a\in R$. I'm trying to prove that if $e$ is unique with this property, then $ae=a$ for all $a\in R $.  So far I have $e^2 = e$ (using uniqueness), but I am stuck. I saw a proof of this fact for groups which used the existence of inverses, which we don't have here. I wonder if the result is really true here. Can someone help? Thanks. Prove that $f$ is differentiable How to Add Background Images in 2.8 and later 2.81a here. I am trying to add a "background image" similar to how , so that I see a screen that looks something like this:    However I can't figure out how/where to access this screen in 2.81a as the UI is wildly different. Any ideas?  I am new to Blender so if you can provide a click-by-click list of instructions it would be enormously appreciated! How can I make a .jar file executable? I'm trying to run a jar application under Ubuntu, so I installed OpenJDK Java 7 Runtime, but when I open this application I got this message :     The file '/home/aimad/Programms/jMerise/JMerise.jar' is not marked as   executable.  If this was downloaded or copied from an untrusted   source, it may be dangerous to run.  For more details, read about the   executable bit. OAuth 2.0 access token request failed with error "must use HTTP POST" OAuth 2.0 Auth token request failed with below error   { "error": "invalid_request", "error_description": "must use HTTP POST" }   What does this error mean?  I am using Postman. Have a connected app. I have used Post method, Url has https. Same request works for other Orgs. Did I missed any configuration/Permission check?  https://testOrg.lightning.force.com/services/oauth2/token?grant_type=password&amp;client_id={{CLIENT_ID}}&amp;client_secret={{CLIENT_SECRET}}&amp;username={{USER_ID}}&amp;password={{PASSWORD}} What defines a AAA game? I tried to find a precise definition. I found clues on  and , but I cannot find more than an approximation like:     Equivalent of blockbuster movie in cinema, an AAA game is a game with highest development budgets and levels of promotion.   The definition seems imprecise. How can I be sure a game is AAA?   Let's imagine a small indie studio making games and growing up. They hire more and more people through the years and invest more and more money in their game. At which milestone would their game be considered as AAA? There should be infinitely many primes of the form $5+6n$. How do you prove it? The same should be true for $7+6n$. In the 1997 film "", the antagonist is attempting to elude some assassins who are after him. When they are pursuing his van, he quickly      pulls the van into a parking garage and washes off the color-changing paint he had earlier painted the van with, thus changing the color of the van.    He then takes a small can and sprays it onto the door handle of the van before taking off. A few minutes later, the assassins      enter the parking garage and notice the dyed water running away from the van. When one of the men goes to open the van using the tainted door handle, he pulls his hand away like it hurt, then starts foaming at the mouth. He immediately has a seizure of some kind and falls down dead.   What was the substance sprayed on the handle, and how could it do this so quickly? How can I make Firefox download different file types to different locations? 98% of what I download is music, so I set the download location to my music folder. However, the other 2% has no place there, so every time I download .doc files or PDF files I have to remove them. Is there a way to make Firefox change the download folder based on file extension? I'll settle for all non-MP3 files getting saved to the desktop.  I know I can right click, choose Save Link As and pick the download location myself, but it seems like there should be a better way. How do I install iTunes on Ubuntu? I've tried different ways to install iTunes, but to no avail. I tried with Wine, but it didn't work. Is it possible to have iTunes on Ubuntu? TikZ is undergoing lots of development with new features being added, but the versions distributed with standard TeX releases are often a little old. How do I get the latest version? If I want to be sure that I get the latest stable version, how do I do that?    Note: I'm not asking this question for myself, but because a question like this seems to be useful for pointing to it when a new feature of TikZ is mentioned in an answer to some other question. Feel free to post answers for any operating system/TeX distribution combination. Equation mode, labelling equations I have the following   \[K^{-1}\left\|\sum\limits_{n=1}^N a_ny_n\right\|    \leq \left\|\sum\limits_{n=1}^N a_nx_n\right\|    \leq K\left\|\sum\limits_{n=1}^N a_ny_n\right\| (\dagger)\]   But the dagger doesn't appear at the right hand end of the page. How can I Get it so that it does appear on the end of the page? the \hfill command doesn't seem to work. Thank you. Algorithm to find Largest prime factor of a number What is the best approach to calculating the largest prime factor of a number?  I'm thinking the most efficient would be the following:   Find lowest prime number that divides cleanly Check if result of division is prime If not, find next lowest Go to 2.   I'm basing this assumption on it being easier to calculate the small prime factors. Is this about right? What other approaches should I look into?  Edit: I've now realised that my approach is futile if there are more than 2 prime factors in play, since step 2 fails when the result is a product of two other primes, therefore a recursive algorithm is needed.  Edit again: And now I've realised that this does still work, because the last found prime number has to be the highest one, therefore any further testing of the non-prime result from step 2 would result in a smaller prime. Understanding the length extension attack I have been trying to understand exactly how a length extension attack works on SHA-1. I'll detail below what I've understood so far, so that I can convey my understanding of the same and hopefully get advice on where I'm going wrong.  Lets assume that for a message $m$, a secret $s$ is appended to it and the SHA-1 hash is calculated. If $\textrm{len}(m) + \textrm{len}(s)$ is not a multiple of the block size, a certain amount of padding is added to it to make it a multiple, and the hash is generated using what is essentially $s || m || \textrm{padding}$.  Now SHA-1 internally uses 5 registers — it takes in an block, generates new register values, turns the crank, takes in another block, generates new register values, turns the crank ... and so on till the end. When all blocks are exhausted, the register values are concatenated and spit out.  Assume that an attacker knows a certain value of $m$, for which he also knows the hashed key. In such a case, he knows the state of the 5 registers when $(s || m || \textrm{padding}$ was processed. Lets also assume that the attacker knows the length of $s$, so that he can predict how much padding was added.  Here is where I get confused. From what I've read so far, the attack involves taking the known hash, adding a certain amount of padding and then the value that we want. However, isn't the padding already used up in creating the hash? Why are we using padding in our attack? 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? File list command line (hidden and subfolders) I need to get a text list of all the files (hidden and visible) off a hard drive, subfolders included. Ideally the list would have the filename, path, size, and creation (or last modified) date if possible. Can someone please tell me what command I need? Also, is it possible to have this created as a .csv file or something similar for use in Excel?  I am not super proficient with Ubuntu so an explanation of each command item would also be greatly appreciated. How do I change Wi-Fi Hotspot settings in Ubuntu with GNOME 3? How do I manage my hotspot connected devices or change the hotspot password? I can only see the Network Name, Security type and the Password but I can't seem to manage users or the network properties. Is there a published way to take text that may have accent marks and remove the accent marks?  For example:  System.assertEquals('Hello', transform('Ḧéļḻṏ'));   I believe there is an equivalent method in Java, C# and JavaScript. I can't seem to find the Apex equivalent and I'm disturbed that I might have to do it on my own.