Integration By Parts (Continuos maths)
Integration of $e^{ax}\cos bx$ and $e^{ax}\sin bx$
Why can't I import a file in the init.m file? What medium should be used for long term, high volume, data storage (archival)? How to use manual partitioning during installation? I'd like to see the full How-To on how to use manual partitioning during Ubuntu installation. The existing guides (at least those I found here) cover only automatic part and leave untouched the manual part (or extremely short and contain no pictures).  I'd like to cover such situations:     If your disk contains other systems: Rough Smart objects problem in Photoshop I am using Adobe CC(2015) latest version and the behaviour of the smart objects isn't normal. When I paste a vector from Illustrator to Photoshop, the vector looks low quality or rough.   ORIGINAL  IN PHOTOSHOP   However, if I click over the smart object layer(in Photoshop)and this is opened in Illustrator, the vectors looks as the original one.   VECTOR OPENED IN ILLUSTRATOR FROM PHOTOSHOP SMART OBJECT   How can I solve this? Is zero input impedance good or possible when considering impedance matching? For RF applications, we are usually considering of impedance matching to choose load impedance as the conjugate of the source input impedance for the maximum transferred power. But how about design the source having zero input impedance? Is it even possible or good? A naive thought is that all the power will be on the load if so. I might think it is true for DC case and for amplifier design to have a small output impedance and big input impedance. I lack the knowledge to find the missed chain to put all the knowledge together. How do you think? Thanks! When quoting a quotation, how do you handle the double quotes? Assume there is original source text:     This restaurant is amazing with "delicious lasagna" and great service.   Make sure you go 6-7pm for the quietest times.   I want to quote "delicious lasagna" but not sure how to handle the outer double quotes.  If I was quoting more than just that quotation (e.g. is amazing with "delicious lasagna" and great service) I'd just do:     "...is amazing with 'delicious lasagna' and great service."   However, when quoting just that quotation, it looks like:     "'delicious lasagna'"   Is this the correct way or is there something better? I have a registered StackOverflow account which I normally log into using OpenID.  Recently I logged out in order to post a question anonymously (supplying a fake name and of my secondary email addresses).  The problem now is that I'm logged in to StackOverflow as this "dummy" user, unable to see a way to log out.  The top menu normally has a "logout" link, but when you aren't fully registered this link is replaced with "register".  There is no "logout" link for me. :(  So..   When logged out there is a "login" link. When logged in there is a "logout" link. When "logged in" with an unregistered account, there is only a "register" link (no "logout"). nginx config fails with SSL key/pem (unique case) I am trying to install SSL on my nginx reverse proxy with certified ssl keys but i get this message when i try to restart server:  Restarting nginx: [emerg]: SSL_CTX_use_PrivateKey_file("/etc/nginx/conf.d/cert.key") failed (SSL: error:0906D06C:PEM routines:PEM_read_bio:no start line error:140B0009:SSL routines:SSL_CTX_use_PrivateKey_file:PEM lib) configuration file /etc/nginx/nginx.conf test failed   everyfiles are root:root with 600 permissions i've tested the certificats and they are validated with this website:   there are no trailing weird caracters in my keys, and has 64 caracter per line  here is my config file  server {     listen   443;     server_name     my.domain.com;     ssl on;     ssl_certificate      conf.d/cert.pem;     ssl_certificate_key  conf.d/cert.key;      location / {          proxy_pass         http://upstream1;          proxy_redirect     off;          proxy_buffering    off;          proxy_set_header        Host            $host;          proxy_set_header        X-Real-IP       $remote_addr;          proxy_set_header        X-Forwarded-For $proxy_add_x_forwarded_for;     }   }  Any ideas? Thank you Redirect all subsequent commands' stderr using exec Will some parents be offended when being asked, "Is it male or female?" If I ask the parent about a baby's gender, will it be impolite or not appropriate to say, "Is it male or female?"  Is there any subtle difference, in terms of politeness, among   "Is it a boy or girl?" "Is it he or she?" "is it male or female?" What is a historical lock, and what is it used for? Historical locks are sometimes applied to questions.   What is a historical lock? What is the purpose of a historical lock? How are questions affected by historical locking? When is it appropriate to lock a question for historical reasons?  When is it not appropriate? How do I request a historical lock for a question? What should I do if I notice a serious problem with a historically-locked question or one of its answers? Having trouble indexing and executing a query in O (log n) time.  The query includes an INNER JOIN, an ORDER BY, and an equality operation. If I understand the laws of databases correctly, a query can be indexed and executed in O (log n) time (or thereabouts) if a non-equality operator is not used on more than one column. In this case, I believe the INNER JOIN does count as an equality operator and the non-equality operator would be the ORDER BY portion of the query. This table has upwards of 10,000,000 rows and needs to handle several reads and writes per second.  Using PostgreSQL. This is what the table looks like. As you can see, the column 'Names' is a list property and it is the column that the INNER JOIN goes against:  Age Names                       Date 34  ['carla', 'john', 'sam']    3/13/2011 26  ['json', 'cindy', 'joel']   3/13/2011 72  ['beth', 'amber', 'susie']  3/13/2011 14  ['john', 'jim', 'debie']    3/13/2011   This is the query that we are trying to do:  SELECT * FROM the_table WHERE Age==26 AND Names=='john' ORDER BY Date   My background is from using App Engine's Big Table, so I've used equality operators here to indicate that 'john' should be one of the names in the Names column. This would be an acceptable query in GAE's big table, it would execute in O (log N) time as all Big Table queries are reqyured to do. I am assuming there is a way to do this in PostgreSQL as well since PostgreSQL accepts list data types as columns.  Is this possible to do in PostgreSQL?  If so, how should the index be set up (we can't figure out how to set up an index that takes into account the three properties)? The new top bar is out on meta. Consider it a beta EDIT Dec 4 -  We're doing it live! Please post bugs or concerns as questions tagged [top-bar]  We have rolled out our 95% completed top bar for feedback.  Note:   We are still adding a few final features, so if you have a request for a feature that is not there you might hold off on that for a day or two Yes, the bar is black1. Also give that a day or two to sink in.   I also want to specifically address the meta/main/chat links.  I'm very aware that many of you like having the links at the top of the page and that this new version is different.  The thought process behind moving these links is that the "site switcher" should be an automatic place to go when you are on a site and want to go to another one. If you haven't already developed the muscle memory for these links, getting between them required a bit of a cognitive load: You must first decide that you want to switch sites and then you have to decide which area to go to to switch.  Also, we find that less familiar users aren't entirely clear what a standalone link that says "main" or "meta" actually does... Not to mention that it hurts my UX sensibilities that we are dynamically changing links in an element that should be fixed.  It is true that we have added a click in the process, but we have also removed a lot of clicks for other common actions that are much more frequent than switching between main and meta.  All I ask is that you give it a few days and see if the new "switch sites at the top left" paradigm grows on you.  What do you think?  1.  points out that technically it's not quite black. Like many others, I commonly find myself ending a sentence with a preposition.  Yes, it makes me cringe.  I usually rewrite the sentence, but sometimes (in emails) I just live with it.  To, with... you know who you are.  Should I keep fighting myself on this one, or is it okay in some circumstances? Redshifting of Light and the expansion of the universe So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to lowering its energy.  My question is, where does the energy of the light go? Energy must go somewhere!   Does the energy the light had before go into the mechanism that's expanding the space? I'm imagining that light is being stretched out when its being red-shifted. So would this mean that the energy is still there and that it is just spread out over more space? How to interpret the output of XGBoost importance? I ran a xgboost model. I don't exactly know how to interpret the output of xgb.importance.  What is the meaning of Gain, Cover, and Frequency and how do we interpret them?  Also, what does Split, RealCover, and RealCover% mean? I have some extra parameters   Are there any other parameters that can tell me more about feature importances?  From the R documentation, I have some understanding that Gain is something similar to Information gain and Frequency is number of times a feature is used across all the trees. I have no idea what Cover is.  I ran the example code given in the link (and also tried doing the same on the problem that I am working on), but the split definition given there did not match with the numbers that I calculated.  importance_matrix   Output:             Feature         Gain        Cover    Frequence   1:            xxx 2.276101e-01 0.0618490331 1.913283e-02   2:           xxxx 2.047495e-01 0.1337406946 1.373710e-01   3:           xxxx 1.239551e-01 0.1032614896 1.319798e-01   4:           xxxx 6.269780e-02 0.0431682707 1.098646e-01   5:          xxxxx 6.004842e-02 0.0305611830 1.709108e-02  214:     xxxxxxxxxx 4.599139e-06 0.0001551098 1.147052e-05 215:     xxxxxxxxxx 4.500927e-06 0.0001665320 1.147052e-05 216:   xxxxxxxxxxxx 3.899363e-06 0.0001536857 1.147052e-05 217: xxxxxxxxxxxxxx 3.619348e-06 0.0001808504 1.147052e-05 218:  xxxxxxxxxxxxx 3.429679e-06 0.0001792233 1.147052e-05 I am trying to find a story where a children's nursery turns into a jungle I read this short story(I believe it was under novella length, but I could be mistaken) a while back, and I am trying to identify the title for a friend.   Plot:      Parents(male and female) get a computer aided/holographic nursery for their children. The mother becomes increasingly agitated as the children withdraw more. The children are barely even featured in the story, and the ending concludes with lions possibly eating the parents.   Publishing date: Years ago.   Tech level: Seemingly functional AI, not much more. So Black Holes Actually Merge! In 1/5th of a Second - How? I've read a lot of conflicting answers in these forums. However, today saw the awesome announcement of gravitational waves. Two black holes merged:   Not only that, they merged FAST. In 1/5th of a second revolving around each other 250 times a second. The entire event was quicker than a heartbeat. Moreover, we observed this happening as distant outsiders. So now we can say for sure:   Objects approaching the event horizon DO NOT appear to slow down Black holes CAN merge in a finite (and quick) amount of time And all this is wrt a frame of reference far, far away   To quote the NYTimes article:  One of them was 36 times as massive as the sun, the other 29. As they approached the end, at half the speed of light, they were circling each other 250 times a second.  And then the ringing stopped as the two holes coalesced into a single black hole, a trapdoor in space with the equivalent mass of 62 suns. All in a fifth of a second, Earth time.  However, everything I've read so far has let me to believe that an outside observer should never be able to measure the collision happening in a finite time. So what exactly is happening here? I must have read at lest 5 different versions of this so far everywhere in these forums over the past several years. Permission for snap applications I have some trouble with the Ubuntu notepadqq package. After opening a file from my apache webroot I cannot see any content. Saving the file is also not possible. I thougt this would be a classic permission issue. Therefore, I changed the group of the webroot from root to www-data and added my user to this group. Permissions are 775, so in theory it should now be possible for me to edit files in my webroot. But nevertheless, when I open a file of this directory with notepadqq, it still only shows an empty file.  When using gksudo notepadqq I get the following error message:  No protocol specified QXcbConnection: Could not connect to display :0   I figured out that notepadqq is a so called snap application and I wonder if this is the reason for my problems.  Can someone give me a hint how I could fix this issue (without using 777 permissions)? For example: $$7x \equiv 1 \pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a general modulo equation: $$5x + 1 \equiv 2 \pmod{6}$$ What is the fastest way to solve it? My initial thought was: $$5x + 1 \equiv 2 \pmod{6}$$ $$\Leftrightarrow 5x + 1 - 1\equiv 2 - 1 \pmod{6}$$ $$\Leftrightarrow 5x \equiv 1 \pmod{6}$$ Then solve for the inverse of $5$ modulo 6. Is it a right approach? Thanks.