My mic's a little loud. Hello, welcome everyone. My name's Sean Degg. I'm in the IBM Linux Technology Center. I'm a core contributor on Nova, the QA team, Tempest, DevStack, some of the upgrade testing and grenade. I review a lot of patches. And so, today, I figured I would give an introduction about what it really takes to get from having an idea about something that you want in OpenStack and getting it all the way through to commit. The sort of the origination of this talk was the fact that I find that I end up explaining this a lot to first time developers trying to get stuff into OpenStack.  So try to lay it out as much as possible and walk people through so that hopefully your first or some of your early development contributions can be successful. And you can understand when things are bad and when things are good as part of the process. That QR code has a link to these slides or HTML. They're up on my personal website. There's a lot of links embedded in here. I'll stick this out on Twitter afterwards so that people can catch it later and dive into the links. So I realized that we don't have just a U.S. audience. So this whole soup to nuts thing. I use a lot of American idioms. I apologize for people that aren't native English speakers. It just means all the way from the beginning to all the way to the end. So we start off with where do you start in this process? And we start with having an idea. I've got this great idea for a feature. I wanna land an open stack or behavior that I think really should change. And so that's great. So you've got this idea. And the first thing you wanna do when you have a new idea is actually go and talk to other people about it. Socialize it either on our mailing list, OpenStackdev or on the OpenStackdev IRC channel because as it turns out, OpenStack is a rapidly evolving project. A lot of people have a lot of the same great ideas all at the same time. And so it would be good to figure out if someone else is already working on what you think should go in next. And if possible, then go and work with them on it. From a review perspective, the last thing I wanna see is three completely different incompatible approaches to the same thing that we wanna add because that just makes everything terrible to figure out. When we're reviewing code, we typically don't wanna play politics in the middle of that. It's like if all you guys want this thing in, go back, work together, come up with some common thing and propose it. That's the right thing to do. And it's much better to join an existing effort than to then cut off on your own. The next thing that you really need to do, it's great to have an idea, it's great to bring it to the mailing list, it's great to talk about it. It is much, much better if there is code. English only works so well in specifications of what this feature is, what this terminology is, whatever. OpenStack has a language, it's called Python, it's really good at describing solutions to problems because you can execute them. So start with the prototype. It doesn't have to be complete, it doesn't have to be everything, but it's something where people can actually now address this as a real, as a thing they can get their hands in and see not just what you're talking about, but the approaches to it. Things are just clearer in code. It also, we get a lot of people that will show up and suggest these great grandiose ideas. If you've been to a design summit a few times, you will notice that some topic sessions have shown up at every design summit and they don't seem to actually make traction. So there's a cautiousness about people with just ideas and not willing to do work. And so you show up with some code and that is huge. That shows you're serious, you're actually gonna do some work. That's great, we love that and we want it.  We're gonna go into this in detail. This is most of what this talk is about is explaining what this diagram really means. But this is basically the contribution process to OpenStack. I'm using Nova as a specific example as just one project, but this is true for anything that's core and anything that's incubated and anything that's in Stack Forge, they all work the same way.  We have a specific extension to Git called GitReview that makes it much, much simpler to interact with these Garrett review servers which I'll show you some details of in the moment. Otherwise you get some really gnarly URLs that you have to hard code all over the place. So you need to know Git, we're not going into that. We'll assume that as an exercise for the reader. But once you get to this point, we don't use Git push, we don't use merge requests. We use this Garrett review system and you have to install this Git review thing and you run it and it submits upstream.  And in every project, we've already got config files which say when you review this project at this branch, you push to this location, so you don't have to do all that nasty stuff yourself. The first time you do this, something will probably go wrong. Many things will go wrong. But this will go wrong to a lot of people. If you just run GitReview, you've made your patch and you push it up there, you will get an error which looks very much like this, which is we can't look at your change because you have not signed the contributor license agreement. And we actually reject inbound changes for people that aren't on the CLA with a URL to go deal with this in Garret, which is a URL. So the contributors license agreement is something that OpenStack has as protection for any code that you bring to the project, you have signed an agreement legally that says you're allowed to bring this here and your employer says it's okay for you to bring this here. So we don't end up in a situation where there's code in OpenStack, which was illicitly brought from some other third party environment that is not appropriate for the project.  Now we're into actual reviews. Is that as washed out head on as it is from the side? Okay, great. Be a little harder to read some of the smaller text. Okay, what's important about these vague, unclear blocks of text here? So Garret is a code review system at review.opensack.org. When you push up a Git commit, you've got, it will demonstrate that it's got the commit message in here. You can specify things like blueprints or bugs that it implements. And then what's important that you'll see here is there's a whole voting process. And we'll start with humans and then we'll move to non-human voting. So every change that goes up has a formal review process by humans. And anyone on the internet, anyone in this room can go start reading OpenStack code and can start adding reviews to it. Just by logging in to Garret with an open ID, you can start reviewing code and helping us make things better and add your comments to it. Everyone gets a plus one or a minus one vote. These are fundamentally advisory, but they are very useful as a core contributor that has a lot of code I should be reviewing. One of the first things I go and look for is did someone else plus one or minus one this code? Because if someone else minus one did, that's at the bottom of the queue I might get to it. Someone else plus one did. Okay, somebody thinks this is good enough to at least go in and dive a little deeper. That's a huge indicator and that means that that's where I'm gonna spend my time. Core contributors within each of the projects and it's a separate sort of bit for every project gets a plus two and a minus two vote. And so the formal policy for all projects in OpenStack is two plus twos are required to make any code go further to actually approve. There's a separate actual approve bit that gets set, but usually the second person, the plus two code, does that. If a minus one vote, you can upload a new copy of your code, a new iteration and all the minus one and plus one votes and the plus two votes all reset and so it's like this is a new patch, whatever. There's also the minus two vote is really, we call it the band hammer. This is someone throws this down if the approach is fundamentally flawed or dangerous for whatever reason they feel as a core contributor and that sticks. So that will block this code from ever going in until that person goes and pulls that hold on it. It is used very rarely because minus one advisories are pretty useful. The comments can be general or line specific. Those have links showing instances of both of them where you can actually, we can annotate per line of code and typically a detailed review will actually go through and say, okay, minus one and like this, you did a wrong thing here. This thing should be better. This, like why did you add this new variable? And people will give very detailed feedback. Minus one to a patch is a normal first reaction. People often freak out. They submit their first bit of code and they get a minus one like three hours later and they're like, oh my God, what did I do wrong? What did I do wrong? Nothing, this is exactly normal. This is normal behavior. The reason we do code reviews is to make the code better on every iteration. So minus one is normal. We actually ran some statistics and like basically every commit that actually lands in Git takes on average three iterations before it lands. And that's across the entire spectrum, right? When people are first new with this is probably a couple more. I've been on the cells bare metal. I was one of the key reviewers to help the bare metal stuff into the pipeline. And I mean that was six months that they were working that patch series and like 30 iterations before we got it to where it needed to be. And that's fine, right? The point is what lands an open stack, eventually it has to be ready for the tree. It has to be code that the core contributors believe in. It doesn't go and modify things in ways that we don't feel we can support in the future. In the process of contributing, this is becoming owned by whatever the core community team is and they have to be able to feel like they can support it going forward. If you've gotten minus one, make sure to iterate on your code quickly because it will be ignored. Typically, again, like I said, I've got a limited time. I'm trying to review as much code as possible and those things fall to the bottom of my list. This is a link to a URL of the code that I'm supposed to review on a regular basis and you will understand why I look for easy things to ignore because there's a lot on it. Responsiveness is super critical. You really want to iterate quickly when someone provides you feedback, not sort of sit on it and figure out if someone else is gonna accept it later because they won't. And responsive is highly appreciated, right? As a reviewer, I comment on something and I'll probably be in the code review system for the next hour or two working on stuff. And if I see comments coming back immediately, I'm actually in a mode to handle that. That's huge, I remember that, I remember who you were. It means when I see code from you come through again, I'm going to preferentially go look at that code because I know that if I provide you feedback, you are gonna respond quickly and it's an actively really good use of my time. So responsiveness is awesome be as responsive as possible. Don't get argumentative, which is sort of the inverse of that. You, in almost all cases, cannot argue your way out of a negative review. And that's a new idea for people, some people. And realize that the feedback was there for a reason and be nice about it, we all try to be nice. And when you're updating patches, it's important to use the get, commit, amend. We put this item potent version string and all the get commit messages. So when you upload version two or version three or whatever of your code, then it will properly be identified as Garret as the same code and list as an update. And so all the history of the past code reviews will be in there, which is really useful to understand how this thing evolved over time. Yes. It doesn't, right? But responsiveness is the important thing. If it's a day, that's good. If it's a week, that's bad, right? And the reality is the core teams are, I mean, that's something like Nova, we've got people in a lot of scattered time zones. So it may not be that I pick up something, but other people will notice that a patch went in and somebody said, no, you gotta go fix this thing. And then you did when it was sort of a natural cycle for you within 12 hours or whatever. And then it gets noticed, right? And that's the thing is that in reality, we spend a lot of time looking at these code and this code reviews and part of you as a new contributor and contributing to OpenStack, building kind of a personal reputation. Once you start a lot of code, you remember, oh, Boris always throws out some awesome stuff. He's this database guy that we've got on the project. And it's like, great. Whenever Boris throws out something, I go try to look at it immediately because he's always hyper responsive to what's going on and I wanna help him through the process. Because that's the thing, realistically as a core contributor, we are sort of shepherding things. That's part of our goal. It's keeping stuff out that really can't go in, but then stuff that people are showing up and being very willing to work on things, it's part of like, okay, so how do we make this work within OpenStack in a way that doesn't break anyone else, doesn't break any of our core tenants of scale out and share nothing. But we do want more contributors. And the growth of the contributors you've seen released to release is sort of a reflection of that general attitude. Minus twos are very much reserved for code that can't go in for various reasons. It might be, there might be horrible, like it goes in a direction, the project just doesn't wanna go in, it goes in, it does something that's just not possible, it would be really bad, it breaks backwards compatibility. It happens, it goes in at the wrong time, we have freeze areas, and once we pass freeze myself, like on Nova this past cycle, we passed freeze and people kept pushing features. And I was just like, nope, minus two, minus two, minus two, all that stuff's held will reopen in Havana, but don't show up with features after freeze, we're done. And realize what's part of the natural cycle. So if you get a minus two, make sure you figure out with the person, you get enough feedback to understand why it can't go in. Was it a timing reason? Was it a structural reason? Was it something that's just not appropriate for the project at all? Because that needs real serious reconsideration about the approach. Tips for being successful, start small. If you are a new contributor, and coming here and you have like a super important feature that your particular company or area is interested in, don't start with your first introduction in the community, 4,000 line change throwing in. It's just not a good idea. And a lot of people don't realize this, right? It's like, here we go, here's my giant new vendor driver and I've never seen anyone before and I haven't followed the style guidelines and like stop. Do some small things first. Go fix a couple of bugs first. Get familiar with the process. Get familiar with the people involved. It's just a lot easier. Smaller is always better than big. If you do changes, they should be minimum possible that they can be in size. They're just easier to review. When I start my day, I get a cup of coffee. I sit down on my laptop. I bring up the code review system and I start looking. And so the first thing I do is I go and look for 12 line changes that I can just say like yep, that was obviously a bug and that's a plus two, right? And I try to bang as many of those out as quickly as possible. I go look at stuff that other people have plus twoed because I'm on East Coast time and the entire continuous integration system is basically there's nothing in it when I wake up. So I've got the entire merge CI system more or less to myself. So I start with everything that somebody else's plus twoed on projects that I can and figure out what's mergeable because if I merge it early before the Pacific Coast guys wake up, we got all the code in and they didn't have to worry about it and we have more run time for testing later in the day. So easy things that it's super easy for someone to say put that in is great.  It seems like a minimal thing. It seems like a thing that people don't tend to want to worry about sometimes but really good commit messages are huge because people will just like read and when I look at a piece of code I need to understand why. Like what is the rationale for this changing? And if it's just a link to a bug somewhere else that I then gotta go read and then figure out like wait was this really the fix for this bug or what was the issue, whatever. All right, maybe I'll deal with that one later but if it's like in the commit is like very distinct one line here's what this is about. A paragraph or two explaining exactly what's going on and why this is the approach to fix it then I can look at that. I can look at the review, the code and I just be like oh yeah, clear, go, right. And whenever possible if there are relative bugs or blueprints reference that. We can also do patch series within Garrett if you're familiar with that and get if you have a whole bunch of changes that you need to make don't make them as one big block make them as a series, you know dependent patch series and you know basically a whole bunch of commits and a get branch and you do get review and it pushes them all up in sequence and they're all tied to each other and they'll do all the right things and again it's easier to review. So people review code, machines review code too. So when you push, we start off with immediately we run a whole bunch of tests by Jenkins, so Jenkins is very chatty on all the reviews and if you've ever wondered who this Jenkins guy is it is our continuous integration system that runs all our tests and it will, the moment there's code out there it will go and run a series of tests. When Jenkins minus ones things it will provide a report, you know it won't like go into a detailed list of what was in your code but it will provide a report of well I ran the following, you know we had test failures and here's links to all the logs of the results of these tests and these are all hot links you can go into them and you can figure out like why they failed. Make sure you do that. I have seen many times when people just you know like don't understand and we have this ability to rerun tests and they just keep running tests that are failed and it's like no, your tests failed for a reason you have to go read the logs and figure out why. The tests that we run are, we have a whole bunch of different checks so we have a style checker we enforce style in the code that's the pep8 python style we also have additional style rules that we enforce programmatically. It's easier to review for them we try to make any time we've said like this is adjusted style we enforce it in a machine so that you know people don't have to spend brainpower on that. We build docs, we run unit tests on two different versions of Python we set up a full node environment run dev stack on it and tempest and we'll dive into the detail and starting very soon we're gonna be doing upgrade testing from Grizzly to master on every commit to make sure that you didn't the proposed change didn't break an offline upgrade of all the services so that we ensure compatibility of upgrade to the next release. The style checker everything that's in the style checker is in this get repo it's based on flake eight it actually finds some interesting Python issues like reuse of variables in funny ways or code that is going to break when it runs as well as the pep8 rules style checking and we run this early before everything else so that we don't bother to run all the rest of the tests if it doesn't fail the style guidelines because it just can't go in otherwise. You know this seems like a minor thing it seems like we're nitpicking but when you have 550 active developers over a six month cycle and you know half a million lines of code consistency is the only road to sanity so we have to enforce this. We run unit tests on every project itself defines what its unit tests are in the NOVA instance there are over 5,000 unit tests in tree. They get run on Python 2.6 and 2.7 on Ubuntu we're working to get them running on 2.6 on Rails 6 and you know believe it or not there's actually enough differences between 2.6 and 2.7 that we run them both because there's a failure we'll get fails in one and not in the other. These unit tests are basically when they do database stuff it's typically an in-memory database so it's very synthetic although we do a little bit of upgrade testing on real databases within here when it comes to our migrations. We do on every commit on every proposed commit you push a piece of code you push a one line change we go and spin up three virtual machines on each of the virtual machines we spin up DevStack which is an installation tool for developers to get an easy version of OpenStack running right off the master of Git and we bring up a one node OpenStack within that guest with a specific configuration we do this sort of three different ways to do a matrix of different configurations and then we have a battery of 700 integration tests that runs that ensures that when you call through Nova to Cinder the right things all happen over the course of running Tempest which is that test suite we spin up around 75 virtual machines and do various horrible things to them we do the same with volumes and images and glance and sum to the network quantum's a little less tested in here and then we also run against the Nova and glance command lines and do some basic operations from the command line approach and pretty soon like we have this mostly working it'll be gating within two weeks probably where we're also gonna make sure that you can upgrade from Grizzly to whatever your code version was compatibly and that gets looked at every proposed code commit not on the merge it's on every proposed so the numbers sometimes get staggering about like how many OpenStack instances we create a day it's in the thousands as just part of a normal run cycle so hopefully this graph looks a little bit more clear now of what all these extra blocks were here about the review process that we've got how Jenkins automates it and once you get through all of this right, success you have successfully turned your idea into an OpenStack commit you've landed it hopefully it didn't take you in an order amount of time but it's a victory and you get to do a victory lap on it there's a couple more useful links that are in my slides which again, I'll stick this out on Twitter in about 10 minutes once all things are said and done here talking about what the Garrett workflow is what it means to be a core developer and part of the whole plus two voting model and we've got some decent how to contribute pages as well on the wiki and you can follow me on Twitter too I'm pretty easy to find so with that we got about 10 minutes left in the session and I want to end a little early for questions and because it's the end of the day and people are probably as fried as I am right now but so we'll throw it out there if anyone wants to ask a question about things yes, yeah so in Garrett itself there's actually a way to add reviewers you can add them by name or email address so if there are specific reviewers that you think should be checking out your code and put it in there the reality is it works in some people's cases it doesn't in others because just in my case my review queue is so long and I get so much email from the system I'm just mostly going through a normal filter mechanism the other thing that can happen is that most most teams have like a weekly meeting an IRC and so if you've got some change that you really want to get some eyes on and it's not people aren't looking at it it's usually a pretty good time to raise that there's usually a section at the end that's sort of left for like what are reviews that people are looking for that people like haven't seen attention on so far I know we do that some in the NOVA and the QA meetings I assume some of the other projects do the same thing but again getting active on IRC just in general on the dev channel and kind of asking questions there and asking if someone would take a look at this is probably a good thing to do don't be hyper insistent about it I'll pick on some of my friends on the Red Dwarf project they were trying to get some stuff in the dev stack and like literally every six hours they're like look at this review, look at this review, look stop I'm going to eventually get to it but you're not making your case right now it'll take a little time one of the key bout trade-offs that we try to manage within the core projects is making sure that we have a core review team that's big enough that the review backlog is not getting too crazy right that we have enough people so we keep moving the review backlog and honestly one of my strategies again for processing the queue you know not the like let me move as much code through as possible but my other strategy that I go and do is I actually for exactly the folks that like no one's looked at their stuff yet I go visually scan my review for anything at Jenkins is plus one that's like a day old that no one else has seen a review on because like that's not cool right we need to be more responsive than that and try to provide feedback and I know a lot of other reviewers try to do the same sort of tactics but like stuff gets missed right like you know my I can probably actually show you what my well maybe I can it'll actually come through my review queue is kind of stupid big and I can find out where my cursor is there it is yeah non mirrored screens what oh it only took the really that's can't be right there's no way that fits on one screen it is pay yes there's a next button nevermind yeah yeah no actually on the other oh because I'm not signed in that's why my preference on my user account I have like a hundred items per page and like typically it's a couple of pages of that so it's just like you know okay I'm gonna go after what I can go after and you know and the rest of it like if anyone's here trying to push a review this week you won't get reviewed we're all here and we're all a little too fried to look at code right now other yes sure yep yep that's a good piece of feedback there's a question over here okay is there something you're looking for not really the only thing is so we have a if you write in your commit message like bug and then a number the the system automatically turns that into a hyperlink that goes back to launchpad for that bug ID so like and if you do that there is there's actually another interface into all of this called review day which hangs off of the main open stack project which actually does another thing where it it's sort of priority weights the reviews based on the severity of the bugs that they are fixing so like fixing important bugs your stuff goes all the way to the top um so like linking to if you're actually fixing a bug linking the bug is it'll actually generate a lot more visibility for it other than that the process is all just the same right um and if you're working on a blueprint right you know we use this process by which new features any substantial new feature really needs to have a blueprint in launchpad so that we kind of track it towards release and we use it as the release notes and features and everything um in the same thing you like there's a put blueprint and then the name of the blueprint um it will automatically link it and it will actually bump your stuff up on the review cycle as well yes there's a yep so yeah yeah no absolutely so um so we recommend to everyone that when you're working on a feature or bug you create a dedicated branch for that specific thing um so you'll make your commit so your your branch will be one commit off of master right and then you you push it and um this get review script that we do uh what it one of the things that it does is it it generates and declares another id field and it injects it into the commit message and so that goes out to Garrett and Garrett will track based on that id in the future so when someone says like no no no you know like you know gives you a minus one and says go fix this and this and that the other then you just all you have to do is go into that branch fix whatever it was and do a get commit amend and that will instead of generating another commit on top of that it'll actually modify the previous one and then you just run get review again and it will then update and that will show up as patch two on that same thing and you can do this as many times as you want um if you're doing patch series you can um they'll all end up with ids and dependent on each other and and all the like fun rebase-i stuff like it does everything you expected to do you just got to make sure you keep that that id that got injected the same um and people get really mad if you submit like duplicate stuff for the same thing and you didn't keep that id because they see it over here and then you lose the the history of review and that's actually kind of important because people have left a lot of comments about like no do this no do that and also you know realize that like the core teams on these projects are we are not always of one mind so sometimes it's real useful when someone like no no minus one I don't like that and you're like but but but but Russell said to do exactly that in this previous part of the review and they're like um uh okay right yeah that's fine that's fine right um and so it's helpful for us too to realize like when we're being inconsistent and to try to like you know be nicer to people about that or I mean honestly the right thing to do you know if you know we're doing it right is like oh you push review three there were three other core reviewers that have reviewed this in the past go look at what it was before how they commented on it and ensure that that you're following what they asked of it right and because we do try to work collaboratively like that where it's like well this was the recommendation and like okay did they follow the recommendation if they did I'm cool with it I don't see any new issues and like you know the person that originally starts reviewing the patch may not be the person that eventually gets it all the way to the end we we definitely hand off work like that just you know it's part of the nature there was a question here that's true the yeah yeah so the the docs have a couple of checks that are specific to them they're kind of unit tests per se right it's got to build because all the docs are based like you know xml or sgml stuff and so it's got to actually compile out and be able to be published to the site and so the checks are just a little different it's conceptually the same model and so if you're working in the open sec manuals tree or like the api site tree or any of those other documentation projects conceptually the same approach like obviously we don't run the code tests right but you know otherwise it's it's the same any other questions one in the back um so right now all of the core projects are python um all of them um I don't know that it's if you were to create a new core project um well it's in and I'll put an exception there are some of the tools which also have shellcode in them that aren't core projects but they're part of our testing infrastructure um it if you were to start a new core project that you would want to incubate through open stack I don't know that's a hard and fast rule that it's python but but this this is where the community has has emerged on so it might be a hard sell um try to if you're committed if you're adding features to existing stuff use whatever they're doing right um otherwise it's just it's just not going to fly so there's another question here yep yeah so um uh I think official policy is two past stables yeah um so we have stable branches if you check out the stable like stable grizzly branch of nova um that's there's actually a separate stable maintenance team that has plus two on that that's that's handling the stable on that um and if I think official policy is two back so so stable grizzly and stable fulsome are currently being maintained stable sx is sort of not you know it means that if people really want to still do some stuff there they might but like but but typically after three like the stable maintenance team that's on that just doesn't care anyway no no so yeah um there is yeah so this right here this is a stable grizzly change um that's you know that's in my review tool as well the reality is the volume in stable is much less by nature like it should be right stable stable we only bring back critical bug fixes security issues and whatnot anything else there was one there and we'll take one here and then we'll call it beer time yeah so all the unit tests um there is typically either literally a run test.sh or like a in the readme like how to run the unit tests directly locally um on so that will give you all the unit tests run so in nova right you'd run 5000 tests they take you know six minutes on a laptop um the tempest dev stack what we do in the gate um you can do locally as well um if you check out dev stack you can you can bring it up dev stack actually lets you specify the get URLs that you want to pull each of the projects from so instead of pulling from the default upstream master you could actually point it at your own get repo wherever it is on the network on local or make changes directly in the dev stack tree um and then run the tempest tests those will take you about um we automatically configure at the end of a dev stack pull we automatically configure tempest for you to work on your machine um and it's in it's in a tree just an op stack tank pissed um that you can run the tempest tests they'll take about 45 minutes yeah and when you run the unit tests it'll run the style checker up front or maybe it's at the end it runs a style checker them but yeah yeah so the style checker is baked into the unit tests and then um and then run tempest and that that should basically give you what happens in the gate there's a couple edge conditions around the way the docs get generated everything else that you might hit once you get upstream but in reality if you run all the rest of that stuff everyone will love you because honestly half the half the changes that get pushed the first time they clearly didn't run the unit tests right and it's like there we are we're cut off it's beer time if you want to talk to me I'm hanging out up here um for a little bit after this


Let's see it Again blue shimmer parallel to five and a blue shimmer auto not numbered Is what we're looking for as well as case hits obviously manga national landmarks and national pride and then the very rare color we all get awesome hits is USA with a tough draw today not not the not not the best result, but You know looked good at times, which was nice starting off with a true blue rookie for brasil bruno guimaris guimaris 231 of 299 with a nice color match mosaic joys bays. Well, that'll be fun man. That'll be fun. All right silver ultimendi England will put up on iran today netherlands Pretty close game. They want to know about us really close the entire time. They pulled They put two goals in at the end blue shimmer. Here it is blue shimmer And it is casper dolberg pretty solid one there numbered five of five Dean casper dolberg Five of five again solid card there. Denmark should uh do pretty well at the tournament blue mojo uh, tanjuma netherlands 12 of 75 A silver scores club do son blavich All right, let's see another nice color in the box here Make up for just an okay blue shimmer hyper rubin deus Oh, I thought usa should have won They're they're more talented than wales at one point. It felt like they were silver rookie steven estakio card show, uh I don't think anyone at this table went I didn't go Got cracked ice jackson ervine When I hear it man, it was packed It was a bigger venue and it was packed It sounds really good Yeah, I said they sold a lot of stuff So the blue shimmer auto is going to be a redemption. There's a nice red leon gretzka 358 of 399 a silver united states team badge is rookie albert sambi lakunga the belgian rookie international ink prisms blue shimmer Here we go solid auto there saw blue shimmer solid auto Not the best blue shimmers. Let's see a big parallel in the last few packs here for shawen Let's go shawen silver rookie deus and benet Pretty good coaster reek and rookie cody gock post for today The big netherlands rookie Blue shared on chiciri They all done playing for the day 81 to 299. Yep. Yeah Halfway through the us match. It was like 10 p.m. Katari time. Oh really? Matches start at 5 a.m. Eastern for like today. Really? Yep Which is like Like in the early afternoon there Got a hyper dominic levaka beach They the only start so late. So they get let's go dolphins So they get more european the usa watching Europe in the america as I should say. Yeah, what's happening cop? Silver granted shaka And a pink downy ulmo Not the best box shawen unfortunately We appreciate it man. There were some decent stuff in there And we'll get right out to you


What's up everybody once again it's Brand Man Sean and this video right here is brought to you by brandmannetwork.com because I signed myself and I'm excited to talk to you guys about this snippet right here from my interview with Wa'Soo and Ghost because man they went a completely different route than so many people get told from a popular standpoint and it's really because they have this strategy, this strong philosophy against paying for things but not from a standpoint of being cheapskates. I want you guys to hear this conversation. Can you post it and they will post it? Hey so what it all comes down to because if you're not going to it's the basic three currencies right is relationship, money and then the other one's really just your own hustle and time and actually have that content but really is relationship and money as far as the things that matter most in music when it comes to getting your stuff seen and when you said I'm not spending money you just double down on all these relationships that we even talked about earlier in the conversation that you- Yeah bro because like look man let's give an example of like ten racks right put ten racks into music it's going to be a slow return I can put ten racks into something else to make like in a week I can put ten racks into 15 you know what I'm saying?  We just don't want to because like I said when we started this it was really just yo me and ghost a couple of other friends like yo let's try to put some money in this to see where it is but we really came approached it like blindly we didn't know where to put the money or what to do with it and you know we have to go through trial and error but now it's like yo we're not gonna use we're trying not to use our own bread at all to do any of this it's like yo we can make the relationships if we can build the relationships and in those relationships get us like people who are willing to put money into it then that's good too.   Now I want to make clear that this situation isn't something that everybody can make happen for themselves you have to have the right people on play while Sue and Ghost have a great duo relationship while the artist is focusing heavily on the music and the managers out there hustling hustling hustling making connections and you know being very entrepreneurial and how to flip stuff and there's still heavy exchanges of value at the same time it's not like the original people that they have no real relationships with them trying to actually get them to do something for them without giving them value in exchange. Now if you watch that full interview back when I drop that you'll see a little bit more and get an understanding from that backstory but even more importantly than that Ghost expressed this hunger for understanding how to spend certain money because money does get spent at the end of the day. Yes they got to a certain level and while Sue has actually he has a real legitimate level of success music is dope by the way but when you start having to push and blow up to a certain level of money needs to get spent you need to know how to do that what to do with it so he's still getting all this knowledge on Facebook ads and things like that so don't get it twisted and be like I have to never spend any money ever even if it's getting investment because he talked about getting investment from other folks where he can push that money you still got to know how to utilize whatever investment you get or you're not gonna get any more money from anybody. So I just want to make sure that I was understood that there's a lot more that you probably can do or get done if you're in the right situation without spending money but at the end of the day you really need to know how to spend money and market. You will hit some sort of ceiling. I didn't make an extremely in-depth Facebook marketing specifically for artists course just for my health. I know that at the end of the day it's a need I wouldn't make it if it wasn't a need. If you guys want to check that out I got a link in the description below I'm making a super cheap for artists because these things are extremely expensive. I saw a lot of courses out there that was just you know a thousand plus dollars and of course this video is brought to you by brandmannetwork.com. If you like this video go ahead and like button if you like it you might as well share it and if you're not subscribed you know what to do. Hit that subscribe.


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Alright so what we are discussing is the Schwartz lemma okay which where we are looking at a function f which is defined on the unit disc and it is taking values in the closure of the unit disc okay and we assume that it maps 0 to 0 okay then the Schwartz lemma says that if you take any complex number z in the unit disc then the modulus of its image cannot exceed the modulus of the the modulus of the image of that complex number under f cannot exceed the modulus of the complex number okay so and the fact is that you get equality even at one value if and only if its rotation okay and in which case you get equality everywhere okay and of course you know rotation is a bilinear transformation. And it will map the unit disc isomorphically on to the unit disc and it fixes the origin and a corollary to Schwartz lemma is that every automorphism of the unit disc every holomorphic self map of the unit disc onto itself which is an isomorphism namely which has an inverse which is also holomorphic and which fixes the origin has to be a rotation okay. So now so let us try to prove these things so the first thing is so let me prove Schwartz lemma so the idea of the proof is very easy actually you are just going to apply the maximum principle and nothing else okay so what you do is put g of z is equal to fz by z okay put g of z is equal to fz by z for z not equal to 0 okay because I am dividing by z I should put z not equal to 0 then but the beautiful thing is that of course g is analytic on the punctured unit disc namely if z is not 0 then fz by z is also analytic because numerator is fz which is analytic denominator is z which is analytic and you know the quotient of analytic functions is analytic wherever the denominator does not vanish okay therefore this g as I have defined is it as I have defined it is analytic on the punctured unit disc but the fact is it is even analytic at the origin the reason is because f of 0 equal to 0 okay so you see f of z if you write the power series if you write the power series of f of z centered at 0 namely the Taylor expansion of f of z okay so what you will get the Taylor expansion of f of z at z equal to 0 which is you know classically called the Maclaurin expansion x the Taylor expansion at 0 is called the Maclaurin expansion so the Maclaurin expansion is what it is just f of z is equal to you know f of 0 plus z f dash of 0 plus z squared by factorial 2 f double dash of 0 and so on this is what it is this is the Taylor expansion but what is f of 0 f of 0 is 0 because f is supposed to fix the origin it maps 0 to 0 so what I will get is I will get z f dash of 0 plus z squared by factorial 2 f double dash of 0 where h z is analytic on delta on the unit disc why is h z analytic because you know h z will have h z will have this power series expansion that is gotten by taking this power series expansion and you divide it by z okay namely h of z will be f dash of 0 plus z by factorial 2 f double dash of 0 and so on and that will be a convergent power series okay. So h z is given by convergent power series at the origin so it is analytic at the origin alright but on the other hand outside the origin h of z is actually f of z by z okay so what you are saying is this function g of z extends to an analytic function h z at the origin in other words g of z itself is an analytic function at the origin okay. So as h of z is equal to g of z for z not equal to 0 this shows that actually 0 is a removable singularity for g of z okay see g of z is like sin z by z g of z is like sin by z by z which a priori cannot be defined at z equal to 0 because it is a z in the denominator but actually if you write as a power series sin z by z is also defined at z equal to 0 because at 0 it has a limit okay it has a finite limit. So h removal singularity theorem says that if you have h if a function at a point where it is not defined h but h suppose there is a function which is analytic in a deleted neighbourhood of a point okay then it can be extended to analytic function at that point if one of the following three conditions satisfied or satisfied is satisfied namely the first condition is that if it tends to limit as h as you tend to that point the second condition is that if the function is bounded in a deleted neighbourhood of that point and of course the third thing is if the function has h the function can be extended h it has a power series expansion at that point okay and in fact all the three are happening here okay. So g of z is analytic on the whole unit disc so you know I will keep writing f z by h z I mean I will simply write g of z is equal to f z by z and just remember that this is the expression for g when z is not equal to 0 when z is equal to 0 it is actually h okay and h is actually the power series expansion of g at the origin at and the origin is a removable singularity so it is a it is a point to which g can be extended analytically okay. So well fine so after that remark what we do next is now we are in a position to apply maximum principle okay so what you will do what we will do is the following thing so what you are going to do is you are going to take this disc is the unit disc and so I have this function g which is going from the unit disc what I am going to do is I am going to take a circle centre at the origin radius r small r okay so and I am going to look at the function g of z which is f z by z alright and I am going to look at what its modulus is on the circle okay so on mod z is equal to r which is less than 1 okay so I am looking at all the points on a circle centre at the origin radius 1 radius r small r where r is a fraction okay what is mod g z mod g z is mod f z by z because mod z is equal to r and r is positive okay so certainly z is not 0 and g has a expression f of z by z when z is not 0 and if I calculate mod g I am going to get mod f z by mod z and that is well that is less than or equal to 1 by r because mod f z is always less than or equal to 1 is something that is given to me that is just analytic expression for the geometric fact that f takes values in the closed unit okay and mod z is equal to r is already assumed because I am estimating the mod g z on the circle where mod z is equal to r so I get this if you take mod z less than or equal to r mod z less than or equal to r if you take this closed disc centre at 0 radius r including the boundary okay and if you look at the function g z it is analytic there okay the maximum principle will tell you that it is modulus will be maximum on the boundary so here is where I am applying the maximum principle so on mod z less than or equal to r mod g z has maximum on mod z is equal to r okay but on mod z is equal to r mod g z is less than or equal to 1 by r and therefore maximum principle will tell you that on this whole disc mod g z is less than or equal to 1 by r so the upshot is on this whole closed disc on here what you are getting is mod g z is equal to 1 by r I mean see the point is you make an estimate of mod g z on the boundary of that closed disc which is mod z equal to r and that will also be an upper bound for the values inside because this is the maximum principle the maximum principle tells you that the mod will attain its maximum only on the boundary so if you know a bound for the function on the boundary that bound will also be a bound for the function values on the interior and of course the function in this case is the modulus of the analytic function okay so by the maximum principle okay so you know when in applying maximum the maximum principle I am using the fact that you see g is analytic and therefore harmonic because g is analytic means that both its real and imaginary parts are harmonic and therefore g is also harmonic and I am using the maximum principle for harmonic functions okay so it applies to g so mod g has a maximum on mod z equal to r but on mod z is equal to r it is bounded by 1 by r therefore 1 by r is a bound for g on the whole closed disc okay so for mod z less than or equal to r mod g z is less than or equal to 1 by r this is what you get now what you do is that you take the limit as r tends to 1 minus okay if you take the limit as r tends to 1 minus we get mod g z is strictly less than is less than or equal to 1 for mod z less than so and mod g z less than or equal to 1 will tell you that mod fz by z is less than or equal to 1 and that translates to mod fz less than or equal to z for mod z less than 1 which is the first assertion in the shorts lemma okay so this implies so you get this of course you know there is a little bit of trouble at z equal to 0 but at z equal to 0 this holds because mod f mod f0 is 0 and of course here I have to put mod mod f0 is 0 which is equal to mod 0 further let z0 be such that mod z0 is less than 1 I will of course need z0 not equal to 0 and mod of f of z0 is equal to mod z0 okay so in this statement I should correct myself so z0 should be non-zero because if I do not put that condition then this is always true for z0 equal to 0 okay so z0 should be non-zero so suppose there is an z0 which is not 0 where mod fz0 is equal to mod z0 okay so then what you are going to get is that you are going to get then mod gz0 is going to become equal to 1 okay because after all z0 is not 0 so mod g I mean gz0 is just fz0 by z0 and mod gz0 will be mod fz0 by mod z0 and that will be 1 okay but then again you apply the maximum principle to mod g okay that will tell you that mod g will always be equal it will tell you that g has to be constant okay so because mod g can attain its maximum only on the boundary of the unit disc it can provided extends to the boundary of the unit disc if it does not extend to the boundary of the unit disc it can never attain the maximum so whereas mod g is bounded by 1 mod g is bounded by 1 maximum value 1 cannot be attained in the interior if it is attained in the interior then g has to be a constant this is the maximum principle okay so by the maximum principle g is a constant so and with g is a constant and mod gz0 constant with modulus 1 so I will get g of z is equal to e power i alpha because a constant a complex number with constant with modulus 1 has to be a form e to the i alpha and that means that because g is f of z by z it will tell you that f of z is just e to the i alpha z so it is a rotation okay so that finishes the proof of the Schwarz lemma okay that finishes the proof of the Schwarz lemma and I must again point out that I had made earlier the mistake of not saying that z0 is non-zero okay that is important because if I did not say that then I already have mod f0 equal to 0 equal to mod 0 right so this is the proof of the Schwarz lemma I mean what you must understand is that the moment f is a rotation then f becomes a bilinear transformation therefore it is 1 to 1 also it becomes a conformal isomorphism okay so what your Schwarz lemma actually says is that if you take a analytic function from the unit disk into the unit disk the closure of the unit disk which takes the origin to the origin then either it is strict contraction in terms of length okay that is mod fz is strictly less than mod z for all z with mod z less than 1 or it is a rotation okay so let us look at this corollary let us try to prove this corollary proof of corollary so what I have to do is I will have to take a holomorphic automorphism of this which fixes the origin and I have to say that it is a rotation so let f from delta to delta be a holomorphic that is analytic isomorphism such with f of 0 equal to 0 okay so you take a holomorphic isomorphism self isomorphism of the unit disk right now of course to f I can apply Schwarz lemma because condition of conditions for Schwarz lemma is that f should be analytic on the unit disk it should take values inside the closed unit disk in this case it is taking values in the unit disk itself and it is defined on the unit disk and it takes 0 to 0 so all the conditions Schwarz lemma are satisfied so I can apply Schwarz lemma and I will get by Schwarz lemma f of z mod fz is less than or equal to mod z for all z with mod z strictly less than 1 I will get this by applying Schwarz lemma to f but mind you what is given is that f is a holomorphic isomorphism which means f inverse is also like f f inverse is also a holomorphic map from delta to delta and f inverse will also take 0 to 0 because f of 0 is 0 f inverse 0 will also be 0 so I can also apply Schwarz lemma to f inverse ok since Schwarz lemma also applies to f inverse f inverse mod f inverse of w is less than or equal to mod w for all w with mod w less than 1 I can apply Schwarz lemma to f inverse which is the inverse of f which is given to me to exist because f is given to be a holomorphic isomorphism which means f has an inverse and that inverse is also holomorphic ok but then you put w equal to fz in this put w equal to fz in this will give you that mod z is less than or equal to mod fz ok and then you compare these two opposite inequalities mod fz less than or equal to mod z mod z less than or equal to mod fz and you will get mod fz is equal to mod z ok and that is it that should tell you that f is a rotation. So mod fz is equal to mod z for all z with mod z less than 1 but we already seen the proof of the Schwarz lemma that whenever mod fz is equal to mod z holds for a single z not different from the origin then f has to be a rotation. So here it is what you are getting is that it holds for all the points of the unit disk ok you have more than what you need ok. So this will imply again by Schwarz lemma that f is a rotation. So that proves the fact that proves the corollary it says that the only holomorphic automorphisms of unit disk that fix the origin they are all rotations ok fine. So having done this what I am going to embark upon is to go into discussion of the Rayman mapping theorem which is something that I want to whose proof which is what I would like to discuss in the coming lectures. It is a very deep theorem and the proof is not easy it involves several facts and so but to make a preliminary discussion about it I wanted this fact about automorphisms of the unit disk. So let me start with the Rayman mapping theorem which is what our long term goal in the next few lectures is proof of the Rayman mapping theorem ok. So Rayman mapping theorem so this is a theorem which says that you take any domain in the complex plane which is simply connected and assume that it is not the whole complex plane then that domain can be mapped by a holomorphic isomorphism or to the unit disk. So in other words if you take simply connected domains in the complex plane and you go modulo holomorphic isomorphism you will get only a set containing two elements one will be the isomorphism class of the whole complex plane and the other will be the isomorphism class of the unit disk and mind you the unit disk is isomorphic to the upper half plane in fact it is any disk is any disk is any open disk is holomorphically isomorphic into any open half plane because you can always find a mobius transformation that will map the interior of a disk to any half plane ok. So geometrically up to holomorphic isomorphism unit disk is the same as a half plane any disk is like the unit disk alright any finite disk it looks like a half plane that is one holomorphic isomorphism class the other holomorphic isomorphism class is a isomorphism class of the whole complex plane and these are the only two holomorphic isomorphism classes of simply connected domains in the complex on the complex plane ok and that is the statement of the Rayman mapping thing. So let me state that any simply connected domain not equal to C I am writing it also in words I also put it in symbols D is simply connected the proper domain in the complex plane is holomorphically isomorphic isomorphic to the unit disk ok so this is the Rayman this is the celebrated famous Rayman mapping theorem right and so in other words what you are saying is that if you give me a simply connected domain which is different from the complex numbers then there is a holomorphic isomorphism from D to delta which is unit disk ok and that holomorphic isomorphism can be made in fact unique uhhh in the following way. So let me explain that in fact given z0 point of D a real number lambda greater than 0 there exists a unique holomorphic holomorphic is the same as analytic or conformal isomorphism f from D to delta with f of z0 is equal to 0 f dash of z0 is equal to lambda. So uhhh so the Rayman mapping theorem says that uhhh any simply connected domain uhhh which is not the whole complex plane can be holomorphically mapped on to the unit disk and you can make that mapping unique if you fix a point if you if you require that a point of D a fixed point of D goes to the origin under this map and also that at that point the derivative of the map at that point is a fixed real number ok. So these conditions uhhh make the map f uhhh unique ok and it is uhhh uhhh so so you know there are two parts to this one part is to find a map f ok then which is uhhh which is rather the hard part the easier part is to say that once you have a map f like this it is it is unique and it is the uniqueness part that will use Schwarz's lemma ok or the corollary of Schwarz's lemma. So what I will do is uhhh uhhh I will I will first try to uhhh apply Schwarz's lemma which we have just seen to show that you know if a map like that exists it is unique such a map uhhh a map like that is called uhhh uhhh is given a special name it is called the Riemann map it is called the Riemann map of the domain D ok and the Riemann map is unique if you fix the value of a point on the domain and the derivative at that of the map at that point ok uhhh I of course you I have fixed the value of the point z0 to be 0 for convenience and most people uhhh are in several textbooks you would you will see that lambda is taken to be equal to 1 ok. But in principle you could take lambda to be any positive uhhh real value ok. Now uhhh so let us let us first prove uniqueness ok. Suppose f1 and f2 f1, f2 for R uhhh from D to delta are holomorphic isomorphisms with these conditions f1 of z0 is 0 is also equal to f2 of z0 and derivative of f1 at z0 is the given lambda which is equal to the derivative of f2 at z1. I just want to show that f1 and f2 are one and the same map right. So what I do is that I compose f1 with uhhh one of the f i's with the inverse of the other and realize that I get a conformal automorphism of the unit disc which by Schwarz lemma is a rotation because it will fix the origin ok. So you see so the situation is like this. So I have I have D I have delta I have f1 then I have f2 then I have delta here ok. So if I if I go like this I get the map which is f2 inverse followed by f1 ok. And this f2 inverse followed by f1 uhhh what is the property of this map this is holomorphic it is a holomorphic uhhh map.  The inverse of a holomorphic I the inverse of an isomorphism is always an isomorphism ok. So this is a composition of isomorphism therefore this is also an isomorphism and uhhh so this is uhhh this is an isomorphism is a holomorphic isomorphism and uhhh where does 0 go to 0 goes to 0. Because you see z0 under this map goes to 0 and under this map also goes to 0. So if I compose it I will get 0 goes to 0 alright. So it is a holomorphic isomorphism from delta to delta which fixes the origin and as we have seen just now seen as a corollary of Schwarz's lemma uhhh this has to be a rotation ok. So by uhhh corollary to Schwarz's lemma f1 circle f2 inverse of w is equal to uhhh e power i alpha w it has to be a rotation of course whenever I write e power i alpha of course I am assuming alpha is real ok. Because if I write e power i alpha with alpha complex then it is uhhh no longer uhhh your rotation ok whenever I write e to the i alpha I am always assuming alpha is real. So uhhh so this is because of the corollary to Schwarz's lemma ok. And uhhh you see you know if I calculate f1 circle f2 inverse uhhh uhhh uhhh so if I if I take the derivative of this ok if I take the derivative of this what I will get is that I will get f1 circle f2 inverse derivative at w is equal to derivative of e power i alpha at w which is e power i alpha ok. The derivative with respect to w of e to the i alpha w is just e to the i alpha ok. And on this side I will get derivative of this expression but then for this you apply the chain rule ok. So what you will get is you will get f1 dash of f2 inverse of w into f2 inverse f2 inverse dash of w is equal to e to the i alpha ok. This is just uhhh applying the chain rule of differentiation alright. And uhhh and mind you uhhh in particular you know I I can put I can put any value for w here. So uhhh because it is an identity for all w. So I can put w equal to 0 ok. Put w equal to 0 and what I will get I will get f1 dash of f2 inverse of 0 times f2 inverse dash of 0 is e to the i alpha this is what I will get ok. But then uhhh you have to uhhh remember that f2 inverse of 0 is actually uhhh z0 because f2 of z0 is 0 ok. And therefore uhhh the uhhh so what you will get is you will get f1 dash of z0 f1 dash of z0 right into f2 inverse derivative at 0 is e to the i alpha ok. Now you see f1 dash z0 is given to be lambda. So I will get lambda and the fact is uhhh so let me write that separately ok. Now I claim that f2 inverse derivative at 0 is also uhhh is is equal to 1 by lambda ok. That is just because uhhh again uhhh chain rule applied to f2 and f2 inverse ok. So f2 uhhh circle f2 inverse of uhhh uhhh w is w ok. And if you apply the chain rule you will get f2 dash of f2 inverse of w times f2 inverse dash w is equal to 1 ok. You put w equal to 0 and you will get f2 dash of z0 into f2 inverse dash fdup of 0 is equal to 1. And this will tell you that f2 inverse dash of 0 is 1 by lambda ok. Mind you lambda is a lambda is a non is a it is nonzero it is positive. And therefore you know well uhhh if you if you look at both uhhh what you will get is that you will get e to the i alpha is equal to 1 ok. And once e to the i alpha is 1 uhhh you will get f2 f1 circle f2 inverse w is equal to w. And this will actually tell you that f1 equal to f2 ok. So uhhh uhhh so that so by using the uhhh shots is lemma or rather the color of the shots lemma namely that every automorphism of the unit disc that fixes the origin is a rotation. You are able to show that a Rayman map uhhh if it exists which is specified at a point of the domain at the simply connected domain which is not equal to the complex plane. And it is uhhh uhhh if if it is if it is image is specified at one point and it is derivative at that point is specified then the map is unique. The uniqueness comes from shots lemma actually ok. Now uhhh so this is the easier part this is the uniqueness of uhhh this Rayman map. But now we have to prove the existence of the Rayman map ok. You have to show that there is a map from the uhhh from the given simply connected domain which is not the whole complex plane to the unit disc ok. So, let me let me recall the the the the fact that the domain is simply connected is uhhh by definition it means that the any two uhhh any any curve uhhh any path in the domain starting at any point can be continuously shrunk to a point to that point. That means that there are no holes in that domain ok. If you think of it uhhh as uhhh in terms of the region that in that is enclosed by any closed curve in the domain then you do not want any holes there. The domain should not contain any holes ok. Because if there is a hole then you cannot continuously shrink a closed curve to a point ok fine. So, uhhh it is very very important that you have the simple connectedness. So, the question is how do I produce uhhh how do I produce a uhhh holomorphic map from this domain to the unit disc ok which is an isomorphism. So, the first step is you try to get hold of some holomorphic map which maps the domain into a sub domain of the unit disc ok. So, let me explain to you the the first step towards the proof of the Riemann mapping theorem namely the first step towards the proof of the existence of the Riemann map. The first step what you do is you show that the domain D can be conformally that is isomorphically it can be mapped in onto a sub domain of the unit disc. First of all you do that then you modify that map so that it can fill out the whole unit disc ok. And I am I am saying it loosely modify means it is not just modify you will have to do a lot of things ok. But first of all given any simply connected domain how do I land at least into the unit disc. So, uhhh the the beautiful point here is uhhh uhhh existence of uhhh a logarithm for a non vanishing holomorphic function on uhhh on a simply connected domain that is uhhh essentially used. So, so let me explain that. So, what I am going to do is uhhh step 1 so this is existence of the Riemann map. So, I am going on with step 1 uhhh find holomorphic isomorphism h from D to h of D which is a subset of uhhh the unit disc ok. So, the first step is to map first of all D into holomorphically isomorphically into a sub domain of the unit disc. So, what you do what we do is a following thing. So, so here we exploit all the uhhh we exploit the fact that the domain is not the whole complex plane and the fact that the domain is simply connected ok. So, what we do is since uhhh the domain is not the whole complex plane there exist need or not complex number which is in uhhh which is outside the domain I can find such a complex number because uhhh it is not uhhh the domain is not the whole complex plane. So, there is something outside the domain which is in the complex plane ok. You take this we have uhhh now now the next thing I am going to use is the fact that this domain is simply connected ok. The function z- uhhh uhhh g of z is equal to z-neta not is non vanishing on uhhh on D that is obvious because that because the point neta not is not in D. So, z-neta not with z varying in D can never be 0 ok. And since it is a non vanishing uhhh function and it is of course analytic ok it is it is an analytic function after all it is a translation. It is translation by minus neta not ok it is an analytic function. This analytic function uhhh is non vanishing on this domain D which is simply connected therefore it has a logarithm ok. Since D is simply connected we have an analytic branch of log z-neta not on D ok and therefore the moment I have log z-neta not I will have analytic branch of the square root of z-neta not on D and my claim is that function will do the job of mapping D uhhh I can use that function carefully to map D onto a sub domain of the unit disc ok. So, let me write that and stop thus we have an analytic branch of root of z-neta not as exponential of half log z-neta not on D. We can use this branch branch of root of z-neta not to get the holomorphic isomorphism. So, I will stop here we will continue in the next lecture. So, I am just trying to say that you are using a square root of z-neta not to get to map cleverly to map D first into a sub domain of the unit disc ok. And the fact is that you are able to write this z-neta not because there is a netonaut which is outside your simply connected domain your simply that uses the fact the simply connected domain is not the whole complex domain. And the and the fact that you have a analytic branch of the square root is because uses it uses the fact that the domain D is simply connected ok. So, I will stop here.


to you. We are so glad that no matter if you have a significant other you're spending time with or you're just spending a little time with us on Valentine's Day we are so happy to be with you today. I'm here with Pastor Jay and Angela Madden and I know Pastor Jay is so excited because it's Love Day and he's like all geared up and Angela we have something that's so apropos for Valentine's Day today. Tell us about our guests that are coming up. Yes we do. Are you familiar with a little website called YouTube? Most of us are quite familiar with the video streaming site but our guests today know their way around it better than most. With 1.5 million subscribers watching their content aimed at young married living, Nick and Chelsea Hurst join us today to offer some valuable insight into dating, marriage and how to know if the one you are with is the one. Jay and Sydney I'm so excited to dive into this especially given the struggles we see in our culture today. Yeah there's a lot going on out there and I'm so excited I can't lie it is Love Day. I feel the Holy Ghost already.  I mean y'all know how it is I mean it's a lot and if you aren't full as a person you will bring a deficit into a marriage and when you become complete as an individual you have the ability to invest without any expectation of return because you've already become whole as an individual so I'm loving that we're gonna be able to get into this on a little bit deeper. You know I'm just like grateful we're talking about this conversation because it like we have to keep it real like love it takes work and it's hard and I just always think of you know Jesus is love the agape love that sacrificial love and that's what's called to be modeled in marriage and just how we do life in every day but also we just want to take for a moment and pause and talk for a moment about the tragic news that came out of Michigan State University you probably all have heard or gotten alert on your apps and on the news about the shooting that took place and so we just want to just pray for the universities I mean the shooting that it's really it's out of control in our country and it just seems like you know Angela day after day we hear something else happening and we just want to lift up that community and this conscience could you just pray for a second for absolutely father we just come to you lord and we ask that your tender mercies and your love that is unconditional that is unending and is full of peace would cover every single person impacted by this recent shooting we ask lord that you would spread your arms wide embrace your people and allow them to know that there is hope on the other side of this god we pray that you would guide lead and direct those who are in leadership as they come up with preventative measures for this in the future be with all involved in Jesus name we pray amen amen you know as you're praying you know I think there's so many things that are under attack you know whether it's the lives of people we have to understand that Jesus Christ is coming back soon but you know marriages are under attack as well you know and there's never been a time for us to be aware and understand what it takes to have a happy healthy holy marriage this is the time that we have to do it it's the truth like marriage singles couples there is just an onslaught of attacks left and right and being able to properly navigate that with Jesus is critical so i'm excited that we're going to get to dive into the today's conversation with nick and chelsea and excited to just hear more because it is so important that we have a proper viewpoint of what life and what love is supposed to look like and be and we always just want to offer our prayer line because we understand that today can be hard for a lot of people you know maybe you've been waiting on god for a really long time for a spouse maybe you're walking through a separation or a divorce or maybe you're just going through and sometimes i think these holidays they can be a little triggering so we just want to let you know that we are here for you no matter what state you are in and so give us a call at our prayer line at<PHONE_NUMBER> angela so today we are joined by youtube sensations and authors chelsea and nick hurst in their new book marriage minded 10 ways to know if you've found the one chelsea and nick share guidance they received lessons they've learned and deeper questions to ask while navigating one of the biggest decisions in life nick and chelsea we are so glad to have you with us today welcome to hope today thank you we're so excited to be here and it's so cool like technology is amazing we're literally sitting in our living room having a conversation with you guys in your studio that's so cool it is it's wonderful joining from south carolina here with us in pittsburgh and going out all over the globe we are excited to dive into this so i wanted to just start off first and just say listen throughout your book you say oh countless times weren't we don't have 30 years of marriage behind us or under our belt to give advice but i want to truly thank you for the fresh perspective that you offer and truly it is that perspective that we need in this hour and in this culture so thank you for taking the time thank you for being obedient to the voice of the lord and passing along these much needed lessons to a generation of young people when we go here today in your book marriage minded you talk a whole lot about being singled and about being married but let's just hop from the gate what do you think is the biggest issue that is facing our singles today oh man the biggest issue i know that nick and i probably have two different answers but i would say one thing that i see pretty consistency is lack of clarity for our generation and intention i think there's a lot of confusion around even how to pursue another person and how to exactly communicate those expectations up front about what you desire in a relationship and what you've maybe seen that has hurt you in the past whether it's your parents marriage not being so great in an example or um maybe marriages that you saw growing up that were just kind of damaging it could be a whole array of things but i would say just the the phones that we have all of the distractions that can really take hold of our attention they rob us of really sitting across from one another and getting to know truly who that person is and being intentional with one another so i would say that's what i would say but nick probably has a different answer yeah i think i would i i think personally the biggest thing that i've just noticed is a struggle for our generation and for the best time in history is really just the idea that having a spouse or having a great dating relationship or anything like that is going to be what completes us that's going to be the final it's you know there's this really common saying that goes around and you know i think we all have made a joke about it one time or another but you know this is my better half or you know this is the other half and you know while a marriage does take two people i think that when we walk into a marriage when we walk into a relationship thinking that someone else is going to complete us or someone else is liable for fixing us or for for fulfilling all of our deficits and needs then i think that that's a really poor starting point if i'm just being a hundred percent honest i think that when we both walk into a relationship filled up by the love of jesus for us and walk in knowing who we are in him then i think that we're on a much firmer foundation and a much better footing as we start off into a relationship or into a marriage so that would be pertaining to believers and probably you know even unbelievers alike i just think that that would be one of the biggest points of contention that i've seen in this generation i think it's one of the biggest needs right now transparently i agree with both of you i think distractions and not coming into a relationship hoping that somebody else is going to fulfill you and satisfy you what beautiful insight do you feel like when the two of you met that you both felt very much like you were your own person yeah i would say we both come from very different backgrounds we joke about it all the time i come from a really really small town in southern illinois kind of close to st louis missouri and just grew up with the same people seeing the same you know truck stop town just not much to do and then make can kind of share where he comes i come from a farming background in north florida so a very very different culture to how chelsea grew up i think we both grew up in really pretty small towns pretty small places but as far as the culture and the people and just our upbringing they were absolutely very different but i think the benefit is that it afforded us to walk into marriage and really and even into our dating relationship feeling like two very different individuals we felt like two individuals who god had his calling on and his hand on um you know by his grace and so that really afforded us the ability to have some individuality as we walked into our relationship and learn how we work together and uh how our strengths may be complemented one another's weaknesses to you uh nick chelsea i see chelsea you looking at nick i can see you got that glow in your eye how long y'all been married for that's my first question i got a follow-up but what how long you have been married for we've been married for four years next month yeah which is why i think you are a great couple you're young you both are attractive you all got a lot going on you got a year and a half old baby everything's looking good with you guys you're in ministry i think it's outstanding four years into it what is the biggest thing that you would tell single people while they're dating you need to make sure you don't leave this stone unturned oh man yeah i got one ready to go hot off the burner i would say do the hard work and i don't mean just like sit around and read some great books hey i wrote the book like i wrote a book on this and i hope that people will read it but i'm not talking about just sitting down reading a book going through it and making some notes in a journal i mean like really sitting with god and also sitting with leaders in your life who trust you and you trust them and really asking the very difficult questions what are my intentions why am i doing this what do i hope that a relationship will serve and i think really getting down in those deep deep deep um valleys of our hearts and understanding why we're doing certain things not just the what but the why and doing the hard work and allowing god to work in that and to maybe change some things change some opinions change some intentions as time goes on and lead us to being a more holy individual for his namesake then i think that that's probably you know that's that's how i would answer that question transparently i think that that's um i think that that's really needed and i think that that's what i would say to someone who's in a state of singleness right now but knows that they want to date or knows that they want to be married but is just kind of wondering what the first step is yeah and alongside of that just quickly like i think to take it a step deeper a lot of us come from different backgrounds but also we may have different trauma that we've been raised up with and uh naturally psychologically our brains try to forget about that um just to protect ourselves it's just what you know is wired in us but being able to sit down maybe with a counselor or somebody who just really understands that world and helps you unpack and even bring up the memories that you've tried to forget and heal from them and allow God to actually walk you through forgiveness for people and all of those things if i knew to do that before i got married i feel like i would have started so much more healed and whole um rather than you know discovering that i had all this work to do later on into marriage now there is grace in the midst of that if you're already married and you're walking through that great you have another person to do that with too but i will say there's so much uh just wisdom and knowing that that is something that you could potentially do before you even step into a relationship and you'll be better off for it so i would say those probably go hand in hand you know chelsea i just love what you brought about the whole trauma because i think not alone i think a lot of us it's like you get into a marriage and these things just start coming out and you're like oh my gosh because our spouse is like helps to be a mirror where we just see things within ourselves that we never thought would come out and i just curious from you know four years in so i'm like five years in so it's just like in that i guess we're not we're not newlyweds but we are so you know the old people that are older couples would be like you're y'all still newlyweds but just want to ask like what has god done in your life that you've seen a change and a transformation because i feel like that's a huge thing that takes place so what would you say for each of you the biggest thing that you've seen christ do within you in your marriage that's great i love that question i would say lately uh because i've been going through some pretty intensive what i call discipleship counseling i've been walking through a lot of healing and forgiveness for different people i didn't even know i had unforgiveness for and as a result of that my marriage has seen positive benefits from that um and so really just me even working on the things that were unhealed in my heart has helped our marriage and i would say our intimacy and just growing closer to one another um and just even being able to see you in a way where i'm not trying to nitpick every little thing that he's doing i would say that was probably my biggest struggle in the first couple years was why do you the things that i even enjoyed in dating with you bug me now you know like these little things that you're like oh i i enjoy that about you but then as you're doing life together more and more um like we just start to get on each other's nerves in some ways and i'm just being honest you know i think some of us really we walk through that but now i'm like wow i'm seeing you in a totally different light now i feel like i'm being able to see him and even myself in a way where like i actually see how jesus sees him and like myself and so i think that would be probably transparently honestly one of the biggest things that um i've been growing in yeah that's man that's good and i've seen that in you too so i would affirm that i you know i think for me one of the biggest things that i've just been noticing and growing in is really kind of trifold i think one is communication i think two is expectation and uh and then i think honestly the um the third one is really just having a deeper understanding of like where all this stuff is coming from as far as maybe frustrations or things that happen or come up that i just didn't really expect and having patience through that that was really the the third one is the patience factor and so those are really the big ones that i've just seen god work in and like understanding how to communicate with more grace understanding how to be more patient in the midst of maybe things that just didn't go my way or didn't go how i thought that they were going to go and then expectations on my wife i think a lot of times we walk into marriage or into a relationship with different expectations of what they'll do or how they will serve us or how they can maybe meet a need that we have and sometimes those needs are deeper than something that our spouse can provide and we really need to go and seek the lord about that and maybe work through what is causing that and so those are just three really quick things that i've just seen and noticed in myself that i would say that i've grown in as a result of being married and especially being married to chelsea um i just think that yeah you've grown so much and we've grown so much together and i think a lot of people will disparage young marriage in the sense that you're not ready and you can't do it and there's so much that life is going to throw at you and part of that i understand but part of that's also the point is that you get to do this with another person and you get to learn and grow and experience the lord in a whole new way along the way and so i think that's a really beautiful thing i love that advice and those three things are critical i don't care where you are in your marriage if it's one week or you're 50 years into this thing so i am so thankful for you too i love how you are together even if pastor jay said just the way you look at each other and how you giggle never lose that and we are so thankful for your example on youtube and across every ministry place that you go into the beauty in your heart and the example that you set through your christian perspective and your values is phenomenal we need and want more of it so we hope that if you are watching today that you find nick and chelsea hearse on their youtube you get their bug and look more into them because they have plenty to give to all of us thank you nick and chelsea for being here with us and we look forward to seeing you in the future on your youtube channel stay with us as we take a break and we'll be back for some ministry hey tom what you doing oh i can't find anything good on youtube to watch the commentaries the blogs the tier videos the gaming videos it's all boring oh have you thought about subscribing to cornerstone's youtube channel cornerstone has a youtube channel of course it does hold on taking a pause to remind you to subscribe to our channel hit that like button and ring that bell for notifications now back to the video i'll show you how to subscribe just search for cornerstone television network and hit the subscribe button so you can stay up to date getting filled with the holy spirit with consistent uploads every day keep up with your favorite moments and never miss a beat will you help us as we race to 100 000 subscribers we can't do it without your health the content is never ending with countless hours of entertainment so subscribe to the cornerstone youtube channel today hope happens here well i tell you what if there's ever been a time that we need the word of god in marriages it's right now in matthew 19 we want to give you a scripture verses four through six says haven't you read the scriptures jesus replied they record that from the beginning god made them male and female and he said this explains why a man leaves his father and mother and is joined to his wife and the two are united into one since they are no longer two but one let no one split apart what god has joined together you know as we're looking at that scripture you know i was thinking about nick and chelsea and all that they were discussing and what they were going through you know i think every one of us i always say it like this before you get married this is the analogy i like to give when you go to an airport before you go 40 000 feet in the air there's two places you have to visit one is the security place we got to go through and check to make sure you're not carrying anything that can bring the plane down the second thing we have to do we have to go through baggage check you know ladies we get the louis baton bag you're looking all cute but we don't know what's in the trunk everybody needs to know what's the junk in your trunk and if you think about it too what do they always do they weigh your baggage because it might look all cute and nice and you all in love and this that and the other but everybody needs to go through baggage check they send that thing through the conveyor belt they take your shoes off take your belt off why because once we're 40 000 feet in the air we can't afford to crash and i love what chelsea was talking about and i don't know how few guys have noticed this god did not create marriage to make you happy he created marriage to make us holy and we all have to look at the junk in our trunk because if we don't we will blame our spouse we'll look at our spouse and blame them for stuff that's really in our own world and i think the first thing we have to do we have to have self realization and understanding what's really in me that's why we have to become complete as single people this book that they just put out is so outstanding because it's really helping us to prepare for marriage you know i was thinking ladies what are some of the things that you saw in yourself after you got married because i'll be honest with you let me just let me put myself on blast i would i thought i was like Jesus i thought i had it all together y'all i mean i was grinning i had all the i had it all i i mean i thought i was perfectly and then i got married and i turned in the gallery in demoniac i had legions of devils all sorts of stuff was coming out of me i didn't realize the frustrations i had my wife brought it all out of me and it wasn't her fault but god really used it to show me what was in my heart and i think having an understanding of who we are if we realize that god is working in us and the junk in our trunk and we can get rid of some of that stuff before we get 40 000 feet near our marriage would be so much more better who you just dropped like a whole word and plus like a comedy skid in between because you said you're like Jesus and you became like the demoniac but i feel like we all can relate to that and when you talked about the plane like having explosives i was the explosive i feel like i was like oh my goodness like you checked me it was like explosive city because it's like just trauma just things i had to like process and work through but one thing i just i can't remember i think it was our dear friend pastor keenan bridges there was like two things i remember uh like he shared we were like in the green room was talking to him and he said you know a lot of times when it comes to marriage i think or excuse me the wedding day there's so much like happenstance around it we're so excited he's like it's a funeral service everybody's watching around you to die and i even i was like thinking i heard recently you think about like oh let's come to the altar you're walking down the altar in the bible what happened on the altars there were sacrifices you had to die and i think nobody talks about that we're sort of like oh it's all pretty and you have your party and then it's like week one you're like oh my gosh and you might be crying like what did i get myself into jesus can you help me like i mean this is some real stuff that no one wants to talk about so if you're like a newlywed and you're going through things and you're like this is really tough and hard no it's like welcome to the party welcome to the club it's part of marriage but also it's like the years going like god really does do angela like it is some deep work you're like man i didn't know i was a sinner until i got married i was the same way i thought i was good no it really does make you hold me like you said pastor j like it purifies you it causes you to stretch your patience and to grow deeper and to use that one three-letter word which is why why did i respond like that why did i just lash out i love that nick hit on that because that has been i tell everyone that is the most powerful word and it's only three letters that we can ask ourselves why why did my husband aggravate me when he came in like that why am i already on the defense as soon as he brings up a certain topic like these things are in us and when we're in close proximity to someone honey they come all the way out they do well you know i had so many things when i first started marriage i had a rough time letting my wife finish i would always want to cut her off you know i mean i was always trying to get my point across you know something that they mentioned let me ask you guys this question how is communication in your marriage how did i mean how does that work for y'all because i mean i know with me i had a rough time letting her finish because you know i just i don't need the whole bible i just need a few verses and my wife she wanted to preach to me for like seven hours every time that we got into a discriminatory she ain't here right now but baby i love you uh but you know i mean i don't know how communication was for you guys but i know we really struggle that she communicates more from an emotional place i communicate more from an analytical place she was always looking for me to understand and i'm looking to try to fix it and try to make it better give the people some pointers at least give me some pointers i need some help still because i think like one thing i definitely think is women we're very emotional we talk a lot and i remember there'd be times he's like where are you going because i'm over here and then i'm talking about the world and all this and he's like i'm lost i don't get what's going on so we just really i think it's just having understanding i think it's just coming from that place and i remember watching i actually on youtube i remember this woman i don't even know who she is i can't quote you but thank you for your advice but she said you have to be understanding but or do you want to be right or do you want to be in a relationship because sometimes you just can't be right because i'd be fighting i feel like i was a lawyer i was like let me prove my point here's a b c and z why this is supposed to be the way that it is but god really had to be like no it's like you're you're tearing stuff down it was hard communication is always difficult you know i think that the biggest thing with um as a married couple is that you see the world so differently and your worlds are colliding your world views are colliding how you process is colliding so the communication piece is critical in their book nick and chelsea actually talk about how communication um conflict when you enter into conflict it's actually a gateway into intimacy and i love that they said that because a lot of us are truly um avoiders we try to keep it on the backburner oh i'm not going to bring that up because i know what reaction i'm going to get from her but really engaging those spaces in a healthy way can lead to great intimacy and really build you up to know yourself more like you said sydney that it's a mirror when we look at our partner or you know helps them to grow as well well intimacy is into me see yeah if you ever see that and you know a lot of times we can hear each other's words but still miss their heart and maybe somebody out there listening right now you know you're in the middle and you see all sorts of communication conflicts that you have i have learned i have to understand my wife ladies is it true for us men most time you said you hit a word that my wife always says to me she goes i just want you to understand me the you were jaw understand and i can't begin to tell you guys so many times that i had to learn how to understand and get her heart not just hear her words it's really important i think it's just like communication a lot of it's non-verbal as well because you can be you know you can talk a lot with your eyes and the way you're sitting like looking at us cross-eyed like what you're saying right now but it's so important that i think it's just understanding like that's that you word of understand me listen to me take the time to just hear what i have to say and i think don't get on the defense and i think we have to know that we are a team that we are in partnership that we are fighting together because the enemy would love to just throw bows and he loves to tear apart marriage he loves to separate that's why you see so much chaos and division because marriage angela is the greatest visibility of what christ does for the church it represents it yes perfect love beautiful companionship where we are together as one literally two flesh becoming one and we only do that effectively and perfectly through the one who is love today if you find yourself whether you're single or you're you're dating someone or you've been married for quite some time christ at the center makes everything better in fact i would venture to say you can't know or experience true love without knowing him we are honored we are blessed that you joined us today we pray that as you go forward in this beautiful holiday of love that you are centered on the god who is love and his love never fails it never gives up and it continues to trust hope is yours today