Gather elements in sublist by first element for the purpose of summing
Combining values in one column (or part) when values in another column (or part) match
Is it possible to encrypt a message in such a way that multiple keys can independently decrypt it?  In other words:  Having knowledge of $key_1, key_2 ...key_N$, which are different symmetrical keys, is it possible to generate a ciphertext that can be independently decrypted using either $key_1$ or $key_2$ or $key_N$, in such a way that the length of the ciphertext is less than directly proportional to $N$? Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$ Compute   $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$ Infectious chicken pox My 21 year old son has chicken pox and has been home for a few days now. The spots are just starting to crust over.  I work with elderly people but have had chicken pox as a child - should I carry on working while he is here (hes usually away at Uni) and infectious? The usage of singular and plural has always been confusing for me.   I often see sentences like these         People are using cell phones.   People are using a cell phone.      Does the first sentence mean everyone has a phone and they are all using their own?  Does the second sentence mean they are sharing one cell phone?   If I see a group of people holding a cell phone in their hand(s), &lt;- even this is confusing for me, should I use the first sentence then?   Another example: you see two men, and both of them are carrying a bag. Which sentence should I say/use?        They are carrying backpacks          They are carrying a backpack      Could you please make it clear for me? Could not open file archive.ubuntu.com_ubuntu_dists_eoan-updates_restricted_cnf_Commands-amd64.xz Greetings from Bangladesh. I am an intermediate user of Ubuntu OS. I am facing problem with apt update. I have searched online but could not find any answer to my problem so I am posting this question please help me.  Err:20 http://archive.ubuntu.com/ubuntu eoan-updates/restricted amd64 c-n-f Metadata   Could not open file /var/lib/apt/lists/partial/archive.ubuntu.com_ubuntu_dists_eoan-updates_restricted_cnf_Commands-amd64.xz - open (13: Permission denied) [IP: 91.189.88.152 80] Ign:35 http://archive.ubuntu.com/ubuntu eoan-updates/multiverse amd64 c-n-f Metadata Err:37 http://archive.ubuntu.com/ubuntu eoan-backports/main amd64 c-n-f Metadata   Could not open file /var/lib/apt/lists/partial/archive.ubuntu.com_ubuntu_dists_eoan-backports_main_cnf_Commands-amd64.xz - open (13: Permission denied) [IP: 91.189.88.152 80]   Reading package lists... Done E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/eoan-updates/restricted/cnf/Commands-amd64  Could not open file /var/lib/apt/lists/partial/archive.ubuntu.com_ubuntu_dists_eoan-updates_restricted_cnf_Commands-amd64.xz - open (13: Permission denied) [IP: 91.189.88.152 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/eoan-backports/main/cnf/Commands-amd64  Could not open file /var/lib/apt/lists/partial/archive.ubuntu.com_ubuntu_dists_eoan-backports_main_cnf_Commands-amd64.xz - open (13: Permission denied) [IP: 91.189.88.152 80] E: Some index files failed to download. They have been ignored, or old ones used instead.   I have tried with         removing partial folder's content completely.   Cleaning apt by sudo apt clean   moving the lists to lists.old   then updating the apt      But without luck. Tax considerations for selling a property below appraised value to family? I own a property that recently appraised for $350,000 in the state of Maryland that I purchased for $300,000 7 years ago. I wish to sell this property for a value of $240,000. Here are my questions:   Is this legal? The state of Maryland has a transfer/recordation tax of 1.5% for each, the buyer and seller. Would this be computed on the appraised or sale value? Will this pose any problem if the buyer needs financing? Would I be able to deduct a capital loss on my tax return?     From comments: I should have mentioned - the buyer is a sibling. DeleteDuplicates[] does not work as expected on floating point values I understand that for resistors in series we need to add R for each resistor to get the equivalent resistance, where R is resistance. I also understand the mathematical manipulations that show that for resistors in parallel we need to add the 1/R for each resistor to get the equivalent resistance. However I have a couple of questions that have to do with the physical interpretation of the mathematical manipulations involved.   First, I am trying to understand why in the case of parallel resistors we have to add 1/R's instead of adding R's as in the case of resistors in series i.e. could it be thought that the current in the wire is like a sort of water flow in the pipe that has two horizontal parallel pipes positioned one on top of the other and in between connected by a number of vertical pipes that have a tap each that could be adjusted to represent different resistances. Then at the top of each vertical pipe the water pressure P exists and at the bottom the pressure will be reduced by P*R.   For example, suppose we have three vertical pipes, so then the pressure at the bottom of each (after the tap) is P*R for the total of 3*P*R so why is the equivalent resistance not 3*R*P but 1/R = (1/R1 + 1/R2 + 1/R3) and how can I be able to visualize this relation? Is there a word for happiness made possible by a tragic situation? I frequently find myself needing a word to express happiness that acknowledges a tragic or unfortunate circumstance underpinning that happiness. Preferably the word could have both adjective and verb forms. For example, "Gregory [verb-ed | felt adjective about] the balmy February day, suspecting it was yet another consequence of catastrophic and irreversible climate change."  "Bittersweet" is close, but not precisely right. It implies ambivalence rather than genuine gladness. "Schadenfreude" is also in the neighborhood, but I don't want to imply that the tragic part of the situation is what causes the pleasure. (Also, I recognize that the word may not quite exist in English, and I don't know if this is forbidden for this forum, but I'd welcome a loan word or phrase if there's a better one.) Finding the limit of $\left(\frac{n}{n+1}\right)^n$ What developer text editors are available for Ubuntu? The X button stopped working on one of my PS3 controllers. It's hardly through abuse, the controller isn't a year old and I don't play a lot.  The button doesn't stick, it presses like the others, only the system isn't aware that I'm using it. I tried resetting it with the tiny reset button in the back, to no avail.  What can I do? the structure "like for somebody to do something" What is the sum of $$\sum_{n=0}^{\infty}\frac{1}{2^n(n+1)}$$    I've spent an insane amount of time on this problem. I checked on Wolfram and it gives $ln(4)$, which I assume you get from $2\ln(2)$.   I know that the integral of $\frac{1}{n+1}$ is $\ln(n+1)$. What am I missing?  Thank you! Difficulty in finding a counterexample My understanding is that GPUs are more efficient for running neural nets, but someone recently suggested to me that GPUs are only needed for the training phase. Once trained, it's actually more efficient to run them on CPUs.  Is this true? 19MB/s Net Speed but Only 2MB/s Usable Hi so i just got internet a about a month ago and my net speed is 19MB/s, I have tested it on loads of sites they all say the same thing(19MB/s), but it wont use more than around 2MB/s i have tried downloading different ways, and with more than 1 download at a time and I still get capped at about 2MB/s. It affects everything like loading websites and playing games as well. So if I'm downloading (max 2MB/s) and I load up a web page, every thing slows down, the download speed slows and web sites take for ever to load up, what can it be that makes it thus, and speed test say's 19MB/s Can't quantum teleportation be superluminal some percentage of times? I apologize if this is a really silly question.   In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical information to Bob, she is about to send one of the following values: 00,01,10,11.   What if Bob doesn't want to wait and simply takes a guess? Wouldn't there then be superluminal communication 25% of the time? Is it safe to change the lens on my new DSLR? I recently bought myself a shiny new DSLR camera. Before I can use it, I had to do something kind of terrifying: mount the lens.  Now of course, half the advantage of SLR cameras is that the lenses are interchangeable. But sitting there holding an extremely expensive brand new camera and staring into its bare innards, I'm just terrified that if I make one wrong move, a hair or a piece of dust could fall in there, and then the camera will be irreparably damaged and I'll never be able to use it again.  This might sound like a stupid question, but&hellip; is it actually &ldquo;safe&rdquo; to change the lens on the camera? Is this likely to destroy it?  (Obviously it goes without saying that you should limit the time spent with no lens attached to the minimum number of seconds possible. But even if you have lightning fingers, the camera will still be lenseless for some number of seconds. And it's not like I'm standing in a class 100 cleanroom here! Besides, you don't want to be too rough with the delicate lens mounting either&hellip;) UV mapping not filling faces