So welcome and thank you for joining my talk today. I want to give you an overview on a proof of concept we have worked on. And with that, I want to underline the importance of Cloud Foundry and such future scenarios. And I have a lot of hardware here with me today. So finger crossed that everything will work out as planned. But before we get started, let me introduce myself first. So I'm Thorsten Born. I'm part of the SAP Hypress Organization, and SAP Hypress stands for Customer Engagement and Commerce. So to make it short, we are focusing on front office applications, B2C. And when looking on the product portfolio of our organization, OmniChannel is key for sure. But we also have solutions like a content and experience management solution. We have a billing solution you just saw before in the talk. There's a commerce suite where you can build up a commerce door. Big brands are counting on us with that. There's a marketing solution, so you can do marketing planning, but as well execute it. There's a service and a sales solution, and so on. But we also have a technology stack we might have thought of in one of the last Cloud Foundry summits. It's called SAP Hypress as a service. It's our microservice orchestration framework. Very important because we deeply believe in the ecosystem around us. And it's running on SAP Cloud Platform, which provides us the needed Cloud Foundry instance. And my team is responsible for research and innovation. And we have a lot of innovation teams spread around the world. So for example, there's an innovation team in Munich located. It's called SAP Hypress Labs, and they are mainly focusing on innovations around commerce. But we also have a physical lab, a physical innovation lab in China. It's called SAP Hypress, the digital innovation space. It's located in Chengdu, China. And my colleagues are over there doing a lot of research in the area of social media, machine learning. So for example, how we better can integrate and reach it, and how we can get use of AI technologies and something like that. And because Chengdu is the so-called Silicon Valley of China, we are working a lot with local startups to do co-innovation and to get new ideas. And that's the labs here on the picture. And my team is mainly focusing on the idea to combine as many SAP Hypress products as we can to build up an innovation lighthouse or showcase to tell a story. So to help customers and partners to understand how our products can help them to transform their business into the digital world. So we want to tell a story. We want to be a mind opener. We really don't want to sell our proof of concept. It's really about telling a story. And as you can see, we have showcases in all different kind of industries. So public transportation, for example, but as well as entertainment and hospitality, and as well as in the automotive industry. And we as a team, we are not an expert in all of those industries. Because remember, it's not about that we go too deep. It's really about to tell a story everyone gets. Even I can tell my family, and we can discuss about that. And then, people and companies out there can transform this idea into their own business. This is really the goal, what we are aiming with innovation lighthouses. And today, in this talk, I want to talk about one of our latest and greatest showcase. It's called Smart Driving. We trust released it in May on Suffire. It's an SAP conference, and I'm really happy to show it here on stage as well. And when talking about Smart Driving, everyone has in mind self-driving cars. State of the art technology right now. And it's not any longer science fiction. When I'm coming from Europe, I'm based in Germany, and I'm coming to the US, here to Silicon Valley. At least a few weeks back, there was all that kind of Google cars around me, the self-driving cars. So it's reality already. It's just a matter of time we can get hands on and have our own self-driving car. But what also we already have access to is, for example, Tesla. And Tesla is doing cars with a lot of software in them. And that's something we really love to see, right? As engineers, I think what they're also doing good is they're regularly doing software updates and really taking care. So that's really something we are looking forward. But what they're also doing is they are sometimes releasing new features in the car. So for example, the autopilot in a major update, so to call. And what they are doing is from a business model perspective, they are asking to charge upfront so that you want to access those kind of functionality because it's just software you need to pay money for that you can use those functions and features. And that is fine, don't get me wrong, they should earn their money because it's a lovely car and I would love to own one by myself and the software is great. But it's just, we want to think about how we can re-sync that model because, right? I mean, we are cloud natives. So we are used to cloud. We are used to transaction-based systems. We are used to pay-per-use, as you have just seen in the talk before. So we want to re-sync the business model in regards, why do I need to pay upfront for that kind of functionality? It's like on-premise, right? It's like sending out the DVD and you get me to check for it. So we want to bring pay-per-use scenario into the car. So an example could be with the, by keeping with Tesla with the autopilot, something like, tomorrow I have a business meeting, I will be a long drive on the highway. And yes, an autopilot would definitely make sense. And I only want to pay for it while I'm on the highway and while I'm driving to the business meeting. But maybe on a regular day, when I'm just going to the office and going back home and doing shopping, the autopilot is not needed. So I don't need to pay for it. Or another example could be, maybe you drive a new Porsche with a lot of horsepower. And you might know in Germany, some highways are unlimited. So you can really have some fun with it. You can impress your girlfriend and so on. And yes, I want to have full access to the full horsepower during the time. But maybe again, when I'm just on a regular day and going to the office and going back home, I don't need the full horsepower all the time. So I can just reduce it. And by doing so, immediately, my insurance rate will go down because it's not so whiskey, I'm more safe driver and something like that. So this is really new business models behind that concept when you think about pay-per-use scenarios in a car. And that is something we want to come up with in this showcase smart driving. So we want it, as explained, really re-sync the business model in this car, in this example. We want to rethink about functions and features, pay-per-use, in the car, okay? But for that, we definitely need to have a high flexible and scalable infrastructure. That's why we are going for SAP Cloud Platform with the Cloud Foundry Edition as a foundation. And yes, we want to be totally open that why we are going for a microservice architecture, an API-first pattern. And I would definitely love to show you the whole showcase in a real car here on stage, right, to have your Tesla or to have your Porsche. But as you can imagine, it's not always so easy to have access to that car here on stage. So that why we as a team decided to make it more simple, we will go for virtual reality, okay? And I'm not a lucky guy, I can have some fun here on stage driving a car, right? So now, for that, for a moment, let's go to the demo and skip PowerPoint, okay? And what we first need to do in order to start the demo, we need to create a new driver, okay? For that, we have built an, sorry, we have built a custom UI following the SAP UI pattern fury. It's built with UI5, as you can see, you can sign up a new driver and there as well as a challenge object. And let me just explain for a second what we mean with challenge. A challenge for us is bringing gamification into driving a car. Think about what Apple is doing with the Apple Watch or Nike is doing. They try to motivate you with kind of challenges or something like getting more on the street, do more running, be more healthy, something like that. And that's something we want to bring into cars as well with challenges.  Something simple, okay? And if I'm achieving that goal, I will earn some loyalty points maybe at the end of the week or when I achieve the goal, sorry, or maybe I get some discount or maybe again, my assurance rate will go down because I'm a more secure driver, okay? So it's really about motivation and that's behind the function of the challenge. I don't want to get into that too much today because we want to focus on the pay-per-use but it's still the single point of NT to create a new driver. So let us do that. So I go to sign up, let's go there. Oops, select the challenge, just take the software here for example and create a new driver. You only need now the first name so let's take my name with Cloud Foundry and I now can select the vehicle. And there are two options in there for the moment so there's game car and show car. So I will choose game car because remember I want to show the virtual reality scenario but it is completely working with real cars as well. So we have done that as long as the car is IoT enabled we have access to the data, we can do that. So but again, let's stick to game car. So now the driver is created, what I can do now I will immediately start the challenge so that we don't need to go back to that UI, okay? So that we can get rid of it. So here we are, now I can start it and what I will do now, now it's the time for some fun, now I can go into the cockpit, get into my car, okay? Let's just turn up. So now as you can see and you would expect from virtual reality I now can put the classes in my hand over here, no magic behind that. Now one more click is missing, here we are. So what you can see, you are now in a new Porsche it's SAP Hyperspranded, the way it should be, right? You can look around in the car, you can have some fun and what is very important to understand we are currently on a very famous German racing track it's called the Nürburgring. And then what's happening when you are getting into the car as you can see on the left top side there's kind of an overview on subscriptions and functions and features that are available to me, okay, a subscription based. Think about you getting your today's car, you know it's like a head up display or might be integrated in the navigation system or yes in the near future it might be argument reality where you have those informations. And because we are on a racing track it wouldn't make fun to tune down and tune up the horsepower, right? I mean we want to have the full access to the car. So it's more about in this case in this showcase about supportive functions. So if you are a good driver you don't need them but if you need some help like I will you will see in a minute, they definitely make sense. So for example you can turn on here you have the overview on ABS. You can turn on traction control or maybe yes or something like a perfect line assistant. So it helps you know to do better timing. And yes to make some fun every time you horn we will charge you as well, okay? You will see that in a second. So yeah there you can see all the subscriptions like a starting point like information. Let me put the classes just to the side for a second because otherwise it's too hard for me to drive. So what we can do now I will start driving and I will get into the road. So here I have my controller. A little bit nervous here on stage, right? So what will happens now as you can see in a left top corner again the actual driver Torsten Cloud Foundry is just selected the one we created before. All functions and supporter functions are disabled because I want to do my best. But as you can see maybe I'm not the best driver. Let us least try to get around here. And what's coming up here is kind like an recommendation. Think about and remember we are SAP Hypers customer engagement and commerce. So it's all about marketing. Oh, maybe we keep on the street. And there's a recommendation coming up there. What is happening and why is this coming up? Because based on machine learning we were watching and looking how you behave as a driver. And if you know that there is some support needed we can do kind of feature recommendation product recommendations like you can see here. And what I can do now definitely ABS seems like it makes sense to me. I can now just activate them and get use of them. So now it's turned on, turned on. Let's turn traction control on as well. And what you can see now I can try. Hopefully it will go a little bit better now. And what's happened as well as if you closely look on the bill we also charged money for as soon as you turned on those support functions, right? Here now we are $12 and so on. It's time best, right? So it's measured. And what I promised you remember every time I horn I will also try to get charged for. So let's do that. So you can see they all get now charged for as well. Okay, let's stop the car. I think you got the story, right? It's about activating deactivating functions in a car, bringing this business model and at the end you get charged for. So now let's go just back to the UI for a second and stop the challenge we created before. And what happens now is that the car we just were driving is getting to the starting point so that you can later on have some fun as well.  So remember, if you later come by and want to drive a car please bring some cash with you because I don't accept credit cards, okay? Okay, that's just about some having some fun and connecting internet of things stuff and so on. For sure, the whole invoice is available as in PDF as well. You can print it out, you can send it around. Yes, no magic behind it, right? What we have seen so far is really the consumer side. I am as a driver, in the car, I can work with the features, I can activate them and can benefit of them. What we also want to do is have a quick look on how it looks like from an OEM perspective. So if you are the car manufacturer and you are enabling those features, how it looks. And you have seen this already in the demo before and in my talk before, we are using as one of the foundations to make that happen SAP Hypers, we have a new cloud, okay? So I don't want to repeat everything you already have seen. You have already seen SAP Hypers Avenue cloud. There are experts in the room, more than I am in this functionality. What we only have used in this scenario is we have built up subscriptions. You have seen them at the beginning and the billing information. So just to have a quick look again on that, when I go into billing, there are all the bills and users and drivers we created so far. So let's just take one, it doesn't matter now. Torsten SAP, for example, there you can see again, there are the subscriptions, there are the functions I assigned to that subscription and to the driver and you can see what you've used and what we will charge them by the end of the month. So pay as a use, but that's the background of the solution and of the showcase. With that, back to the slides for a moment. So what we have seen, just to repeat, there's an overview when you get into the car, what subscriptions are available to you, what you can access and what's the price tag for it. You have seen the overview on what functions are activated and what you will be charged for and to have some fun, yes, we printed out with a thermal printer as well as we have a classical invoice as in PDF version available and you have seen from an OEM perspective how they can use SAP Hypersphere Avenue Cloud. So what we mainly talked so far is really the inner circle. What I can do as a car manufacturer by providing this data and this functions to a customer. But remember, I already told you at the beginning, we are heavily believe in a scalable environment based on Cloud Foundry as well as an open API microservice-based architecture and just think about, we cannot only do this now on an inner circle, we can also have an outer circle. We can ask our ecosystem and as I already mentioned, we heavily believe in to be part of such scenarios as well because if they have access to the data and to the interfaces based on an API first driven architecture, they can access the data. They can create additional business models and they can be another benefit for me as an end user. And so for example, the insurance case I explained before, like okay, when you have more horsepower, the insurance rate goes up and goes down and so on. A partner of us, we try to do so. What they have done is they built a proof of concept and top of our proof of concept. So it's really about getting access to the data we are providing of the car and getting use of them and bring a new business model. And let me just show it to you as well. So the partners MSG Global, they have a lot of experience in the area of insurance. And what I have done is they built that kind of dashboard on top of our proof of concept. And what you can see is you have a list of all drivers that we are driving so far. There should be somewhere here, here I am. There's the driver I created before and I was driving. And what they are just doing it because we are now in an open world and we are providing our data based on APIs, they are just connecting to our services and fetching all the car data we can provide them. So on the left-hand side, on the right-hand side, you can see all the data they have access to and we can provide them to. And what I have done is, and this is now a really simple example, but it can be very complex, they just enrich the data with third-party data. So while I was driving in virtual reality on the racing track, the Nürburgring in Germany, they looked up what is the real weather information currently in Germany to enrich the data. And yes, there could be of course a lot of more data to enrich. And what I have done is they built up a so-called driver score or an insurance score. Together with data scientists, they had kind of a concept, don't ask me how it works out, how the algorithm looks like. MSG Global are more the expert in that. So that they are bringing up this insurance scoring that based on my driver behavior, my insurance rate goes up and goes down. Okay, and there's really a market for that. So back to the slides again. What I was just explaining with the insurance example is also not any longer science fiction. This is already a reality. So for example, in Europe, and I guess in the US, it's the same, you can have everything in insurance, okay? And healthcare is a very complex part in regards to insurance. And what you can have is an insurance for your teeth. And but sometimes they are very expensive because there's a lot of risk, you know, that you might have some problems and so on. And in some countries, for example, in Switzerland, insurance, the insurance rate is very high to have kind of an insurance for your teeth. And that's something insurance companies are thinking about how they can reduce the rates to have a bigger, you know, customer base. And what's out there, there's a company, they are providing Two's Plus, which are IoT enabled.  And what they have done, remember, that's the inner circle. That is the OEM, that's the one who provides the Two's Plus with the data. And what they have done is they opened the APIs and now letting insurance participate in. And you can now have an insurance rate for your teeth with a personalized insurance rate based on your behavior, how you clean your teeth, okay? So this is really something which happening and which is a concept not only of the future is already reality. And that's why I'm talking about the inner circle, IoT as well as now the circle. But back now for a second from our product portfolio, you know that slide, I've showed that on the beginning. So what we have used in the showcase I trust presenting to you. So yes, it's mobile, it's cloud for sure. We've used IoT, so we have an IoT enabled car. Maybe it's in virtual reality or maybe it's in a real car. Or again, you can transform that to any other industry as well. And yes, we are doing notifications and recommendations or product recommendations based on your behavior. We are using SAP Hypers Revenue Cloud as the billing solution, we have seen it, we have heard about it in the talk before. And we are using SAP Hypers as a service as the orchestration framework for the microservices we've built. And again, SAP Cloud Platform provides us the needed cloud foundry as a highly scalable infrastructure. And this is now very important to understand why we couldn't do that before. And the inner circle as well as the outer circle based on the interfaces we are providing and the scalability we have the cloud foundry to be open for an ecosystem and to let them participate in such scenarios and can extend our solutions wouldn't be possible before we have access to that kind of technology. And this is very important for us and I hope you get it from all our cloud platform talks in regards to cloud foundry. It's really a very important foundation to be open and flexible, which brings me to a quick look on the architecture overview. Not too much details, but you get an understanding how it looks like. So on the left hand side, you can see there's my desktop machine with the race simulation running on with we have high-checked and added functionality like enabled the gaming car with IoT information and the thermal printer is connected to my local machine. What we have in the bottom line as a foundation are our products. So we have SAP hyperserve in your cloud, we already talked about what I haven't talked about so far as SAP vehicle insights. So all the IoT data we're getting from the car, we store in SAP vehicle insights and SAP vehicle insights is a solution based on SAP HANA running in the cloud platform, very scalable, you can put all that lot of data in what we're getting out of the car. And again, hyperservice is one foundation for us. We are using it as a persistency package where we can store additional data as well as a customer object when you are creating a new driver, for example. How looks the orchestration of this scenario? What we have done is I already explained the heart of the scenario and we call it a mashup is the challenge object, right? That's the place where the scenario comes together. We have a register client where you can set up and sign off a new driver. We have a new service and rules engine based on machine learning so that we can do different kind of recommendations. And yes, we have wrapped a few of our services and products as you can see the revenue cloud facade as well as the vehicle insight facade to enrich the data while we are accessing it. And based on the open framework and APIs, now a partner like MSG Global can easily extend the solution. And what they have done is they have built an Internet of Things analyzer. That's the engine they have built to do together with data scientists and building our model. And for a demo purpose, they also created an insurance scoring dashboard you have seen on top of it. And everything connects to our interfaces in an API-first pattern, so it's really easy. And now let's just talk from an SAP hypers perspective now. Everything which is marked orange is really following the microservice architecture and the API-first pattern. Again, we heavily believe in that. And everything also in orange is running on a cloud foundry so that we have the scalability. And even a very important strategic project for us, so for example SAP hypers revenue cloud is completely rebuilt as explained in the session before and is completely utilizing cloud foundry scalability and using microservices as a foundation. So just to wrap it up, what have you seen? So we have seen another example of a paper use scenario to get SAP hypers revenue cloud. You have seen a digital transformation of a scenario powered by a needed and scalable environment and architecture provided by cloud foundry. And you have seen, when you follow that kind of concept, how partners easily can enrich businesses and business solutions out there and you can enable with that ecosystem. Everything I told you now in 25 minutes is available in 30 seconds. I don't want to roll the video, there's something on YouTube available, I will keep it in the slides if you want to have a look at FreeFreeze to do so. It explains the scenario high level. With that, I will set up the whole showcase on our SAP cloud platform booth for today. So if you want to have some fun, want to drive our Porsche on our famous racing track, come by, but please remember, bring some cash, right, no credit card. And with that, thanks a lot for listening and if there are questions right now, you can ask them now or maybe later on the booth if you'd like to. Thank you.


What's good job your boros back again with another video, so I did get to check out some clips from Monday night raw I wasn't able to upload the video or even record it because I've been busy these past couple days Just trying to get content out for the main channel But best believe I wanted to make this video because I thought this was important to talk about and a post on our channel so Drew comes out to Basically talk about what happened at the Royal Rumble him beating Old Berg now.  Well, guess what? I'm sorry. I'm gonna call him that because he doesn't need to be out there. Let's keep it a stat He does not need to be out there wrestling anymore. You guys saw what happened with the fiend You guys saw what happened with the Undertaker both of those matches were overseas Both of those matches probably shouldn't have taken place at the end of the day Goldberg pretty much killed the fiends momentum in my opinion His momentum was never the same. He couldn't beat somebody in their damn fifties I'm not supposed to take him as a credible threat anymore that whole situation with the Undertaker That was just a shambles of a match that sounds good on paper Maybe ten years ago, but no that that's that match shouldn't have never happened in my opinion And I'm sorry just Goldberg coming back to steal these these high profile moments from these younger talented Wrestlers is I don't like it I would say the same thing if the rock not the rock if stone cold came back if stone cold came back all The time were frequently to have these high profile matches with other younger talent Hey, don't put them over where they don't get pulled over. I put over I would call stone cold old stone cold Like is it's not to be disrespectful. It's just the facts man Goldberg shouldn't even have a man had a match at the Royal Rumble. That's just in my opinion I didn't care for the match, but either way He started talking about Oldberg and his you know him, you know earning his respect and you know how it was a grueling match it wasn't but he's just trying to sell the match for what it was for those who missed it then outcomes Edge I want to say Edge comes out there or what not actually no I take that back. I think he started talking about Edge prior to No, no, I take that back. He did edge came out there edge the music it comes out there He's the Royal Rumble winner He comes through the ropes and basically drew McIntyre is giving him all this type of praise and you know admiration and it says something pretty serious. He's like I'm glad that you know, I could have been a mentor to you But what's wrong with you man? Like when you hear my music, you know, I've won the Royal Rumble You should be in defensive mode like you should be said you should be Kicking my head through these ropes as soon as I come down here You should be ready to fight because I am a legitimate threat to your title now Then it shouldn't be buddy buddy. No And I like that he said that because it makes sense the end of the day When it comes to you being the champ and you admiring somebody It's different when you're mine somebody and they're not coming for your title But when they're starting they have an opportunity to take the title from you all that admiration that goes out the door you put that aside it's business now and It's like if Stone Cold won the Royal Rumble, but then all of a sudden he comes out there to you know, somebody Give him adulation on him winning the Royal Rumble. You know what Stone Cold would do He'd like I appreciate that son and stun him He would give him a stone cold stunner and be like I'm facing you at WrestleMania. Get prepared. I'm taking your title That's what happens.  You know saying he's he's gotten softer in the sense of his character He's not as aggressive as he should be he is with heels But this is such a situation where I feel like hey man, it's just not playing He didn't come back just to say I want to win and that's it or you know, I just want to win the Royal Rumble and you know Headline WrestleMania one more time. No, he's trying to win a championship So you got to take him as a serious threat. So I did like the fact that edge mentioned that And then it looks like they're trying to plant seeds of him potentially going against Drew McIntyre at WrestleMania at this year's WrestleMania. I'm not sure You know, there has been some rumblings on the dirt sheets that it's not even gonna potentially be Drew that he's facing it may actually be Roman Reigns So I'm gonna talk about that at the end of the video to give my real in-depth thoughts on that but after that, of course What's his name? Sheamus comes out there basically defending Drew And they they you know Drew's like, yo, I got this I can handle this edge leads the ring and then all of a sudden Sheamus hits Drew with a bro kick. So I'm guessing they're gonna start a little potential feud into the elimination chamber So I doubt that that this will be the WrestleMania match But I believe this is gonna be a few leading into the potential WrestleMania match So I thought that was a nice opening segment. I thought it was interesting WWE's not giving you a clear hint that if he's going to face Drew or not, but they're teasing it So I like that.  No, I'm not gonna let you make it to WrestleMania That's pretty much Randy Orton's thought process I love you so much not only am I going to Attack you with chairs and you know potentially put you on the shelf and try to end your career I'm gonna RKO your wife because that's how much I love you Friends how many of us have them? And then of course edge promo response into that was Passionate as always.  This is it's done after this. I'm going to take care of business I will get rid of you and move on to WrestleMania I thought that was pretty cool that little exchange I knew that we're gonna eventually have one more actual match And I think this was the perfect timing to have that match on raw This doesn't need to be a pay-per-view match. This needed to be the last time they interacted with each other on that level so Like I said, I really kind of skip through all because I didn't really care for anything else I just went to see what the edge storyline was going to be how what would they want to do and They end up having their match, you know, what you it's what you've seen before it was nothing too crazy You know edges selling the effects of lasting almost an hour in the Royal rumble. He's kind of banged up He's selling that and you know, they're having there, you know, it was a nice TV match It was enjoyable for what it was But then as edge or Randy Orton's about to go ahead and hit the infamous RKO out of nowhere Alexa Bliss is sitting on the top turnbuckle. He turns around and she's bleeding from the mouth and Looking at him and Then all of a sudden he Randy Orton obviously is distracted turns around gets hits with a spear one two three Randy Orton loses the match edge wins this feud is done and he can focus on WrestleMania That's how the feud ends. So I'm guessing they're literally going with Randy Orton in the fiend At WrestleMania, they've been building this up for since Since Since the fiend has been set on fire. They've been building this up. Obviously. He's coming back If the question is how what he's gonna look like, but they've been using Alexa Bliss as this bridge to continue that storyline I'm kind of intrigued but I'm kind of not The only reason why I'm kind of iffy about it because it's just like I Don't know if I can buy into the fiend anymore. His character has just been so depleted at this point He can barely win any matches. This is like, I don't I don't really know if I do care But it's somewhat interesting. So, you know, I'll probably try to keep some high hopes about it So one thing I want to talk about before I do in this video is I want to give my Thoughts and opinions on these rumors that Roman Reigns may be the opponent for Edge. Now on paper. It sounds great. Actually Roman Reigns is probably the biggest heel in the industry in my opinion. Not even just WWE in the industry Edge winning the Royal Rumble coming back trying to relive his dream and recapture the title He never lost even though it's not the WWE universal championship because the WWE universal championship had been created But that's not here or there. He's just trying to recapture a major championship. Fine, whatever Him living out that dream that's awesome. That's amazing.  So He'll face dynamic. You can never go wrong with that at a WrestleMania. I think the build up to this match would be Fantastic. The promos will be fantastic. Do I think this should happen? No Here's why Roman Reigns who whoever he faces Will not lose. I want him to face Daniel Bryan. But guess what? I don't even want Daniel Bryan to win because guess what? Roman should be the guy to win Anybody that faces Roman at the Royal Rumble. I mean at WrestleMania will lose It does not make sense for a Roman to win the match I mean from Roman to lose the match at any point anytime soon because he's one of the best heels in the business, bro hands down So you have Edge come back. He wins the Royal Rumble You could have gave that to a another person that you know a young and up-and-coming talent You could have gave that win to them, but you gave it to Edge I'm sorry if you're gonna give edge to Royal Rumble and he entered in that number one and he won it all the way You're gonna put the strap on him.  All right, cool. It doesn't matter. Roman is that guy I crushed her dreams. It makes him the ultimate heel, but if he beats Roman Reigns You've killed all of Roman Reigns momentum He can beat all these younger talent that his that is that is in his age group But he couldn't beat someone that is damn there. You know saying double his age Like what he couldn't beat someone that is uh, you know saying like Someone that was part of the attitude error A guy that's had I don't know how many countless surgeries, you know, I'm saying he just came back for injury Now he can't beat him and I love edge. I think it would be a fantastic match But like I said, it doesn't make sense to book that match only because edge would have to lose And I kind of think you you gave that that royal rumble win to somebody that you could have gave it to Anybody else that could potentially use that to get themselves a championship shot and win it You know, I'm saying edge could have came back lost the royal rumble and still face Roman Reigns and still put him over I don't know if they're going to put Roman over For the sake of edge, you know I'm saying so that's why it's a little bit too much uncertainty or not in Now if they go with the drew route, they can make sense You can give the strap to To edge in this situation even though they're both faces you can turn drew heel You can turn drew heel because of this whole situation because his mentor beat him took his title took his Opportunity away from him and now drew feels some type of way granted I like drew as a face But you can't turn him heel in this situation if you wanted to just keep it a stack So it's I don't know man. It's like I said, they they both could work I just would prefer him to face drew McIntyre because on the raw end of things drew really doesn't have an opponent At least on the smackdown in the things you can find an opponent for Roman Reigns to face at WrestleMania Drew needs a viable opponent. He doesn't have one at this present moment. So Comment down below. Let me know who do y'all think edge to face shitty face Roman Reigns shitty face drew McIntyre and let me know down in the comment section why I want to get y'all opinion on Why he should face one or the other I gave my opinion on it And I really want to have this discussion with you guys because this has been the topic of discussion Ever since the royal rumble ended who should edge face. So comment down below. Let me know I appreciate all the love and support road to 40k appreciate y'all kicking with me now. See y'all next one. Peace


Alright cyber traders welcome on back here this Wednesday afternoon March 23rd shortly after 2.30 p.m. Eastern time and this ALLG is ready to blow the roof off the freaking place great to see Brian and Bruce rejoining us live right now including Pedro and Patrick we have Marie joining us Bill as always as well as Chuck great to see all of our students members alike inside cyber group including Deb and Norman rejoining us too loud and clear from all and hey if you're rejoining us as well in social media Facebook live or YouTube welcome on welcome on back as well so you know of course right now we'll start off by talking about the ALLG trade give me a quick second here I'll flip this back to a daily chart so you could see that ALLG is a relatively new ticker joining the New York Stock Exchange really over the last week and it's just exploded so you know this was really our first look at it today this morning and you know since it's just obviously been just taking off going completely parabolic right now but this is not an easy trade you know as a stock that had a 15 20 cent spread in the morning we actually saw this stock get halted on the way down in class I was doing our phase one stock course this morning which is continuing later on this afternoon but you know simply as a newly enrolled student it's not to say you know hey don't trade this stock and miss out on a giant opportunity no it's to say don't trade this stock if you don't know how to trade this stock because if you don't know how to trade this stock like this getting in there at the right place just at the wrong time that could be dangerous and we ended up seeing this stock like spike up here at this time smack in the middle of class and then I turned away from it funny thing is I turned away from it so I take a screenshot and we were talking about that picture screenshot and then I didn't know where I saw on my other computer that ALG just completely dropped off and got halted down so that couldn't have proved my point any better live in the phase one stock course but man this thing ended up making a hell of a bounce didn't it ended up basically bottoming out roughly off 16 moved up just about five and a half points higher so far so it's right back to all-time highs you know hey I'll put this easily on our watch list here for the close it's not an easy trade though that's for damn sure so you know let's see if maybe even 20 or 20 50 could hold as a big support level for it to generate a higher high later on off of so yeah ALG will put on our list here to begin before I go further across the gainers or losers lists here and perhaps you would have found this on the gainer side but I got to give the answer now so for all this live inside cybergroup I played a quick game here with you folks I said I'm currently in one trade I sent this right at 229 Eastern time I said I'm currently in one trade not ALG so that eliminated ALG any guesses well longtime members here like Brian you know me too well I mean I was actually in two trades and one of them I got out on early and it was the Neo I went break even it actually squeezed back up a tiny amount while I was in the other trade that being AMC so AMC is up over 18% right now it's been making a really good move from the morning of course I ended up catching this really nicely off the opening print off of 1875 ran it up towards just about two bucks higher and still left the fortune on the table so from there I've been waiting for my next opportunity I took a couple of ins and outs here a break even and then I ended up taking a 12 cent loss so I ended up getting chopped up by tiny amount right here heading into the early afternoon no I was trying to get the slingshot right off of not just 21 bucks but 20 94 $20 94 cents really briefly for this one because I gotta go through this meeting I also got to manage this trade if it ends up pulling back but we talked about this just over 24 hours ago not on AMC as much as on Neo during traders talk workshop that was from yesterday morning but we ended up seeing in relation at least to a big print not the opening bell print this was but at 20 94 there was a 500,000 share print filled at the ask is that someone you know looking to load up and buy is that someone looking to just get out and just you know sell and that's it we don't know that answer and for anyone that says that they know they don't know they're blowing smoke so it's to say we need to read the reaction after and reading the reaction after will give us a better idea than not if the stock is going to make the move so even over here this led actually to a nice little slingshot prior to 1 o'clock that I had missed I didn't take this trade here at the time but I started to get chopped up heading into the you know 130 time frame here looking for that squeeze right here I thought I had it up and down right here I got chopped around and then recently right before we started the meeting when it broke back over 21 right away I ended up taking the entry anticipating the slingshot that we have here so for right now AMC we're definitely going to just put it on our watch list alongside the ALLG my opinion you know it's each thrown here but I think that a stock like AMC even though it's still pretty damn volatile I just think that at least having the penny spread the easier to read order book it will make it easier for you to anticipate taking a trade or anticipate to get out of a trade so for right now there's actually about an 82,000 share iceberg on the ask I'll show that once more right up top at 22 so we'll definitely put the AMC trade on our list let me just jump back because you know AMC is moving if AMC is moving as well as it was yesterday then I'm assuming that GameStop is going to make a similar move albeit GameStop is not nearly as close to its high so far roughly over 150 whereas AMC is holding a lot stronger so you know I was hoping actually see GameStop closer to the highs because on these like meme stock days you know when like you know you get all the people on Reddit you know trying to squeeze these stocks up historically over the last year year and a quarter we've seen that GameStop and AMC have really good correlation in that sense so hey you know keep GameStop on the side keep it as a potential guide for you to try and follow some of the other meme stocks like AMC or I haven't even checked in on Bed Bath Beyond yet today that was one of the ones back a year ago back in the beginning of last year this thing's doing trash right now Express was another one same thing this one's looking really bad all right might just be a GameStop AMC day Norman says AMC is not that easy to read depends on what you're following do you have book map because with book map it makes it pretty easy to identify the 22 level and the 2094 print doesn't mean that on every second of the trade it's easy so you know if you got chopped up a couple of times like I did at least heading into the early afternoon you know we're not perfect right but it's a matter of knowing when it's best to get into a trade or really you know hey I took the same set up a couple of times if I got chopped up a third time perhaps I'd lack the confidence to take it that next time so you know that's where I'll say at least on this instance thankfully it paid off nicely and hey I'm still not fully out of the doghouse yet this still may come back down so I'm gonna manage this trade as we continue to go through this meeting but let's see what else is across the gainers and losers lists here otherwise we have the C ELZ and really quick folks I'll just tell you right out the gate so hopefully the stream doesn't get messed up in between but oh man my computer has been like lagging today I don't know if it's computer issue browser issue and it just I've been private chatting some students and the messages have been like really delayed so kind of odd so let's see if we can go through this meeting as best as possible but C ELZ right now so that not really too interested in this I had a really good entry on this trade off of 272 that was a pretty strong chart level that we had from the daily chart I'm more so referring to what we had back here right back like you know late January 274 272 270 right there I was anticipating for a former resistance to act as a new support level and that's what happens here at least a little break under and over and then ran pretty nicely you know I know one of us was watching this trade hoping for a squeeze back up earlier in the afternoon but doesn't look like it honestly so I'll pass on it right now if it ends up popping during this meeting I would definitely give it a second look alright XRTX not looking great either and we'll kind of pass over alright we keep it going LBPS this one's trying to eat back up you got a keyword trying I mean from a zoomed out look still looks really flat but you know over the last 30 45 minutes it's been moving up just about 50 cents or almost 50 cents so you know it doesn't look bad recently here just still has this patchy and you know thin order book so you need to be careful for a false break here and also it is to say the stock made such a big move in the pre-market and dumped off so it made such a big move after the market opened up and dumped off so I feel like this type of stock is just going to be more exhausted than anything so we'll see but I'm gonna pass on this right now NEO is running back up pretty nicely I shouldn't have gotten out of that trade at first there I took a break even right from 2160 level that I called out inside the trading room all right CISO will definitely put this on our watch list not just because I know the Fausta is listening in he typed that in you know inside the trading room just about 30 or so minutes ago the CISO trade so of course I have to put it on the list if he's watching it right well you know he's watching with great reason it's up over 26% he had called it out prior to 2 o'clock so when it first made this breakout here which is a great call at the time but now even more so you know I pulled back but now it's trying to move back up again so it's more of the recent sling here that I'm a fan of hopefully this continues it is a bit of a gap fill isn't it it's like a funky gap to fill here as well I don't know what the heck happened to your back in mid-January stock at one point was like a $48 stock then next thing you know the next morning it was set $723 where it had opened up so I don't know about that folks it's above those prices here so we'll call it a gap fill I'll call it one but for right now it just needs to break higher and show more signs of life around that 1050 area AMC is starting to cruise back up anybody in on the AMC trade by the way right now on AMC or even Neo I'd call that out at least before the meeting started let me know if you're in either or even a LLG let me know as well how about that all right let's keep it going across the gainer side here for right now DRTS trading about just over 10,000 shares a minute you could say it's trying to make a move up but the order book is like paper thin really really thin so that I'm not a fan of more than anything and Charles be in on a LLG while James be James is in on the AMC trade with me nice catch James let's get the test of 22 on AMC all right getting through this gainer side here first though folks the IQ trade great stock to keep on your side list pretty much on a day by day basis now that doesn't mean it will be a great trade every day but I personally think every day you should at least you know check this out in pre-market see if there is some sort of trend or you know levels to work off of because just over the last week and a half this thing's been on a huge tear you know I made reference to this just a month ago and I told you at the time you know transparently so you know listen I don't know when it's gonna happen might be next week next month next year but for this stock IQ that got clobbered crushed from 45 all the way down you know that type of stock is gonna make some sort of short squeeze just look what happened on AMC and GameStop right so you know the same as to be said on this stock IQ and plenty others perhaps but you know great run from earlier this morning and still trading a lot of volume per minute but little flat here for right now so for this afternoon not as keen to it but you know tomorrow morning right away check back in with it right away tomorrow morning blue apron trying to eat back up a little short squeeze stock as well but I don't know not really trading a lot of volume per minute right now that one isn't alright here's GameStop I'm just gonna skip over that for right now we already talked about that one at least alongside IQ how about this CENN keep this on your side list as well at a minimum just you know it's trading a lot of volume day by day has really a liquid order book consistently tight spread obviously really cheap to like the IQ trade so you know I like this on it on it like a side list you know type basis here the CENN all right to round out the gainer side here a couple other familiar names we'll check in on Kodak KODK former runner I know Fausta was calling that out shortly after the market had opened here but and I guess you could say it's trying to eat up a little bit but not really trading a lot of volume right now BTU is pretty close to the highs HOD here close to it on BTU it's also close to the highs that we had back from like early March right wow really that's like 52 week highs as well I knew that this was on a huge tear back from 2021 but it's my first look in a little while in the daily here so not only is it continuing to push up here today but it's approaching the monthly highs here for right now that's roughly off of 27 28 I don't know if this is all-time highs though oh you might want to be a little careful on this BTU trade huh getting pretty damn close to historical resistance that we had back from like you know late 18 early 19 27 81 27 23 27 36 27 10 right around that 27 area 27 and change that is definitely a pretty strong historical support and you could even see back in early March it came right up to that area and bounced right off it so you know what BTU I'll put on our list I mean as a day trade more than anything it's pretty close still to the highs just be wary of that historical resistance here all right let's see anything else here on the gainers side we got to jump on over to the losers list you got to finish this meeting up rather quickly I want to make sure our students have enough time to get into the classroom make sure that they're squared away with the tech and audio stuff themselves can think this was a Bitcoin mining affiliated stock little egg in my face sometime like over the last six months I remember this I was like oh Canon the film company right photography company Canon right nope I mean I don't check the news so it's to say I know that Canon this stock CNN is a Bitcoin miner ended up making the huge run with all the others back you know in the early parts of last year with that in mind it could be a good use a short squeeze type of play given the right circumstances but right now you know I can kind of say the same with this as I said on the others you know good sideless stock for right now I already made such a big move from the morning so I'm not expecting a bigger move for this afternoon all right there we go we got a couple profits coming in on AMC Donald and don ended up getting about 20 cents on his trade he was in from 2150 so he got out under that 22 level I think that was a good idea and then Jean picking up some good dinner money on the ALLG trade he got about 44 cents on it all right so vain I will jump back to AMC I already talked about AMC in full to start off the meeting I will jump back to that though at the end and especially for anyone else that's joining us here a bit late let's move on over to the losers list here I'll just jump back to Deb's comment in just a moment let's see what else we have on the loser side here at first bunch of crap that is hard to borrow I mean that's easy for me to say for doing this meeting as long as I've been doing it but you know normally if there's a stock on the top of the losers list I would only focus on it if it's down enough which these nest aren't really or otherwise if they're easy to borrow which at least I know number 11 is GIN but this is flat not doing a whole lot here skin the beauty health company this actually looks like a nice downtrend as of late kind of bounced off the lows there there at the time 1626 good order book you know I wish it was actually closer to the lows here let's see what else we got here you know in the meantime and RSN familiar name at least I just want to check in with it I know it's not shortable but you know hey for as much as this stock ran the last two days back on Monday broke all-time highs keep it on your side list right you know I knew I was not as likely to follow this one for this morning but it did make a good run at first but completely died off in that point just in relation to the range it made back from Monday's trading it's going to make you know a decent little move for us across this week and that's what happened this morning I mean hey hopefully it makes a bigger run over the next two days here all right let's see what else we got here otherwise we got a couple of familiar names at least at least I see PRPL you have Adobe pretty damn expensive got crushed here in the after hours last night all right I'll tell you what folks let me just do this here first but I think that just about does it at least on the loser's side hey there could be something moving with the market perhaps heading into the afternoon but even the market right now is making a tiny bounce nothing to big for us and then otherwise it's not really dropping back down I don't know if there's any stocks that are near the lows heading into the close Bobby calls out the IMPP trade making a pop oh yeah that's starting to make a little bit of a move I like that it's up over 7% for as much as the stock drop back from Monday morning we saw the direct offering news that came out you know it's possible to see this begin to fill a bit of a gap so for right now especially given the afternoon spike that we have I love this good call IMPP grants his IQ looking good yeah it's inching up a little bit here it wouldn't hurt us to put this one in particular on our watch list but then I open it up to like the 15 to 20 other stocks that look like this if I put this one on our list and I got to put the others on you know what I mean so you know that's where I'll say if you've done really well on this IQ trade over the last few days you know who you are already that's a great stock to at least keep on the side the CRK trade how about that Norman picking up 12 cents on it he was in from like 11 or so yeah nice little move here just broke a new high a moment ago and up over 12% comma stock resources interesting looks like it's testing the highs back from October of last year roughly around that 11 area 1134 is the high back then let's just take a look on the monthly chart oh no this is nowhere near all-time highs that's what I was checking but you know what hey it is that a pretty significant resistance not only from the peak that we had back you know earlier last year but just looking at the monthly chart it's like kind of itching for a breakout right now so you know what even if it doesn't do it today this is definitely one to keep on our watch list here for this afternoon the CRK the AMC trade just blasted 22 just melted through that all right folks on YouTube or Facebook live let me know if there's any other stocks that you would want me to look at or check out here before we wrap up Patrick on the AGRI trade which I'm also catching right now from the cybergroup room AGRI it's at the highs it's up over 15% so all of that I do like a bit of a spread liquid order book though which is kind of interesting like you know the orders here on the bid and the ask aren't necessarily too thin but it's got a bit of a spread there so you know I'm sure it will tighten up in a moment but it's gonna jump around afterwards too so gotta be mindful of that for right now it's like kind of a spotty chart so I'm gonna keep this on the side list for right now Patrick but you know if it ends up showing more signs of life later on for those that aren't going to be in class with myself you know I know that Rich will be on the mic coming up in just about seven or eight minutes so you know he'll talk about this if it ends up making the pop at that time all right folks we're gonna call it oh actually really quickly before we wrap up let me just make sure I show the AMC trade AMC is coming back down quite a bit after it broke out from that 22 clearly a false breakout at that time so right now we got to see AMC build up new support again I do see an order on the bid at 2160 I actually just see that on the matrix there on the far right side of my platform for about 45 46,000 shares currently on the bid you know listen when AMC is trading nearly 400,000 shares a minute I'm not gonna put all of my faith into a 46,000 share order that is definitely the biggest order out there on the bid at this time so you know I certainly hope to see that area hold this support over time here in the next coming moments I'll tell you what I also have class to teach here and in about 13 minutes exactly right at 305 to be exact we'll start but I'm not gonna hold this trade going into class so I'm gonna get out at some point in the next eight or 12 minutes from right now folks all right for all of a sudden YouTube and Facebook live I appreciate you sticking with me each and every day each and every afternoon and we got to make sure we have enough time to get ready for class so if you have any other questions you would like to send on over my way feel more than free to do so send it right on over to Josh at C2 trading calm it was like to post my email here at the stream at the end and then otherwise if you're joining us on YouTube or Facebook live if you're interested in joining our live trading room of ours feel more than free to do so all you got to do is go right down to the link on the banner below the yellow banner below the stream right there to get yourself started so it's a week long trial for nine bucks so you know it's more or less just to see if this is something that you could personally do going forward or not you know listen not everyone is meant for trading and you know that's certainly to be said here right you know we have a couple of us that have found a really good groove early on but at the same time as that though this moves relatively quick right so you know day trading isn't for everyone the trial membership to our live trading room is just for that test to see if this is for you or not so for all of a sudden social media if you wanted to join us continue our audio commentary for this afternoon one more time just go right down to the link on the banner below to sign up from Robert he says I'm ready to join can somebody call me absolutely I'll make sure that one of our education advisors reaches out to Robert inside our chat board here in just a moment let me just post and tweet the picks first we'll post the link for class coming up in a moment from that point and then Robert will give someone will make sure your education advisor gives you a call alright for all this otherwise I look forward to speaking to you in the phase one stock course coming up take care come a cyber group member today just click the link below and receive all these amazing products and a world of knowledge for just nine dollars


Here we see a pair of barred spiral galaxies that have just begun a merge. Though their nuclei are still separated by a large distance, the shapes of the galaxies are significantly distorted. For example, the galaxy on the left contains very pronounced tidal tails, long extended ribbons of gas, dust, and stars. The bright blue areas are stellar nurseries. These vigorous bursts are triggered by the massive gravitational interactions which stir up interstellar gas and dust out of which new stars are created. The galaxies in this system will continue their merger for millions of years before finally becoming a single galaxy.


Zdaj mi se odličiti, da smo prišli, da je omega in u, c2, omega in u je harmonijna v omega. the we have shown that for any x0 in omega for any rho positive so that the bowl of radius rho centret at x0 is contained in omega then you satisfies the mean value property, u of x not, u歪-de-歪. So this condition can be also written as follows, the distance of x not from the boundary of omega is larger than rho. V što je vsega površenja, vzivaj smo inočnje vsega. Zdaj je x0, zdaj je izgleda vzivaj vzivaj x0 in vzivaj vzivaj vzivaj omega. Zdaj, na toj površenji razkaj je, da je to. In na zelo, z vzivaj vzivaj x0, to je rho. Kaj sem komputenja, da je to zelo, Tukaj je to zelo, da je 1 divided omega n rho to n integral. To je vzela, da je vzela. Tukaj je to zelo. Tukaj je, da je vzela, da je integral vzela, da je vzela, da je vzela. In nekaj notčenje, da je poslut, da vsezajte, da je taj, taj je u, taj je vsezaj, taj, taj je zelo, zelo vizajte, taj volum vsezaj, rečenje radii, zelo vsezajte, taj je vsezajte, OK? Tako za vsezajte, da u in za zelo zelo vsezajte, to je bilo, da smo, da smo, je bi izvrs àn za solid-buljeinnji. Mi重ini že vsi squadu občinujeva, su da su tamšelji nad bin, in da je volaitiasne odlič knowle do Lake. Nič je goto flashing. Ja bi mo chính malo ... ali če da se zelo prišli na zelo. Tako, če to je začelovano do zelo. Zato vse malo otvrili, da srečno so nalib smo drugi povod, ne? Moj bo se na taj subarmonijkičnjih vse. To nekaj, da se nekaj dobrote, čekaj na pravdje, ali, da je to vzeločno, da je svojo neč del, neč nekaj dve, da je inakvalitet, kar je. Tako, na pravdje tudi je teorema. Čekaj, da se prišli, da je to način, da je tudi konditon equivalent na odlično. Mene se počučili, da je harmonija, če je tudi to vzela. Tukaj smo imeli zvom, da je to tudi vzela, da počutek je, kako jim dobro tega je, da je in vzela, če je to kaj je vzela, kako je tudi vzela, zelo se vzela, da je to na njim rešenem, na njim fisku, na njim x0. Če je to tudi harmonija? Ne zelo. Ne zelo. Poznačaj. Daj sem zelo poznačil na taj dobroz. Srečno, da bo pomečila nešto boljške vseh. Nezelo. Poznačila, da jasne? Uvaj, da je vseh vseh lepšča. in pričelega, da je... naredajša je za nedaj, da je... zame, da ja izpravim, nekaj. Tih, tih, tih tih tizi. Zame, da... zame izpravim, nekaj s tem보je. Vse vične teže, da taj vsi izpravim, je to različno najgratne glasice. Zato bomo našlično vsečenje, ki se nalidem. Zelo je, da je to, da bomo vsečenje. Zelo je, da bomo vsečenje.  Zelo taj gradječ je vse, kaj je vse zelo zelo zelo zelo zelo, In tudi, nekaj bilo problemi v zelo, kaj je zelo. Kaj je taj teorem? Zelo, da sem izgleda taj teorem. Zelo, da sem izgleda taj teorem 1 in taj teorem 2. Zelo, da sem izgleda teorem 1 in teorem 2. Zelo, da sem izgleda taj teorem 1, zelo jaكرere, da charge n gu Messiah, neko, da, ceh čutih čutih čustih, neko zelo tanem, da taj teorem test početsub glueva, da парim na začinку koptype. Zelo, da je stvarte angole parom do temnev vek pač preko ne rangedivn Clinic, bojo tudi in zelo makir. In ne da se naredite, nekaj je do svoj naša好好ja otoga? Ovo, tako, tko se bo v štom, in vs. c2 je, ki jih septimo, tako tudi je harnessa v klas, Čekaj, kaj je tudi tudi početil, da je tudi početil, in kaj je tudi početil, da je tudi početil, In ki pa vse blinki nekaj, bral sem, ok .. bral sem na vse druh sekolov, na vse druh sekolov, 3, 5, 4. Druga je, da sem na vse priredena bez zrbunje njal poest, da sem na vse priredena bez zrbunje njal poest, ok. to je, da, if this assumption holds, then this assumption holds. Therefore, it is clear that theorem 2, if I prove theorem 2, I prove sort of stronger version than theorem 1. Simply because the assumption of theorem 1 implies the assumption of theorem 2. It is stronger. So, actually, therefore, theorem 2 is stronger than theorem 1. Let us try to prove it. Remembering that, we can never write explicitly Laplacian of U, because this is not possible. OK, so, let us take, so, these are called test function. You see, this assumption is an infinite number of hypothesis, because for any test, this must be true. And, of course, the test has an infinite number. So, this assumption actually is an infinite number of assumptions. Now, we have to produce, we want to show this assertion, that we have to produce a clever choice of test phi. So, fix, so, proof of theorem 2, fix x naught omega, rho positive, rho less than the distance, rho less the distance from the boundary. And now, choose, define phi of x 1 half rho square minus x minus n naught square. This is the definition, OK? And then, actually, sorry, this is not enough, maximum with zero. So, it is, this means, what does it mean, this symbol? It is the max between this number and zero. Simply a symbol. What is this function here? OK, this is a sort of object. So, if I have x naught here, then this is positive till the distance. So, then I take the bowl of radius rho centered at x naught. This is rho, sorry, this is rho. When this is less than rho, then this is positive, and then it becomes negative. But then I take the maximum with zero, sort of function like this, OK? So, this function phi is concentrated on the bowl, and then in zero else. In particular, it has compact support in omega, because the bowl is strictly inside omega, and therefore the test function has compact support in omega by this assumption here. Is this clear or not? So, phi has compact support, and it is also lip sheets. It is not C1, of course, but it is lip sheets. Namely, what it is true is that the slope here of phi is finite. See? It is sort of object like this, and here the slope is finite. It does not happen in a situation like this, where the slope is infinite. This is not lip sheets. The slope of the gradient is infinite, but here the gradient, this is a sort of object like this, and then tronkated. So, where I tronkate, I am arriving like this, and not like this. It is clear by the definition of... Therefore, this function phi is admissible. I can put phi here. So, phi is a test, so-called test function admissible test function. Namely, phi is in the class. So, why I am taking this phi? Well, first of all, I want to have something concentrated on the bowl. Therefore, it is natural to take something which is zero out of the bowl. Next, essentially, this is a radial test function. In some sense, it depends. It is sort of radial symmetry. So, maybe it is the most natural choice of phi that one can do. So, now we can... So, remember, we are proving theorem 2. Therefore, this is our hypothesis. Phi, we have chosen one possible phi. Now, see what happens when I put phi here. That's special phi. So, let me raise... So, inserting this phi in this equality, we have... Now, phi... Another property of this leap sheets function is that grad phi. Since phi is leap sheets, it is almost everywhere. Moreover, it is zero out of the bowl. Simply because phi is constant. So, actually, this integral here concentrate on the bowl. So, this is equal to this and this is zero. Therefore, we have this. Now, let us see... So, let us compute the gradient of phi separately. So, the gradient of phi at x is equal to is the identity, essentially, x minus x naught. And therefore, we have the following grad u at x, x minus x naught. And I claim that from this equality and I claim that from this equality I should be able to deduce the assertion. So, let us see what can I do here. Remember, my u is only leap sheets. So, I cannot differentiate it twice. But this is a gradient. So, I can integrate by parts, putting the gradient on this side. Okay? Integrating by parts. What's happening? First of all, I have a minus u of x. And then I have the divergence of this vector field. Which is the divergence of this vector field plus the integral. Then I have... Sorry, let me rewrite for you the divergence formula. So, u eta on, say, an open set is minus divergence of u eta on an open set is the integral over a of grad u scalar product eta plus u divergence of eta. But this is also equal to u eta So, I am using the standard version of the... So, now, I have this. So, now, a is the ball, eta is x minus x naught. Therefore, this is equal to minus u divergence of minus this, which is written here, plus u and then I have the scalar product between x minus x naught and normal to the ball. Outward normal to the ball. Okay? Now, let me compute... So, now let me compute the divergence of that vector field. Do you know what is the divergence of this vector field here? It is equal to... So, it is equal to minus... The divergence of the vector field x minus x naught, the identity. Remember, the divergence of any vector field is the sum of the... of this. And constant... Is a constant divergence vector field and this is equal exactly to the dimension. Okay? Minus n integral over b rho of x naught, u of x dx. And then I have also that quantity there. Now, the... The outward unit normal to the ball. Do you know? What is this? Divided by... Okay? This is x minus x naught divided by rho. Okay? So, this is the unit normal and therefore this becomes... I have the scalar product so this actually becomes... So, the scalar product between this and this. It is just rho. U of y. Is it okay? Here, let us compute now d over d rho separately. Let us compute this. So, what happens here?  So, now, if I compute this I have minus n omega n rho to the n plus 1 v rho over x naught u of y dx plus rho to the n and you already know that... So, sometimes I write the variable integration x or y is of course the same. Sorry, I can write it x if you want. It is of course the same. Okay? Therefore, this is zero and so minus n now if I divide it by rho to the n plus 1 1 over omega n I find so that this equal to zero implies that this is equal to zero. Do you see it? So, from this equality equal to zero it follows that this derivative is equal to zero. Hence, this means that this quantity is constant is independent of rho. Okay? Since u is lep, she said that therefore is continuous I can let rho go to zero and therefore u at the center is... So, this constant... So, let me write it, maybe it is better. So, one... So, this is constant independent of rho. Now u is continuous therefore the value at the center is equal to the limit of this. Okay, so we have proven a slightly stronger version theorem 2 you see is slightly stronger than theorem 1. Now, assume that you want to... So, I leave you this as an exercise now. Assume that you want to simulate a similar statement, but for sub-solutions. Okay, so for sub-harmonic functions. So, assume that you want to modify this statement for sub-solution. You would like to have as assumption this but you don't have it. You don't have it because u is just lep, she said not c2. So, you want to write this in a weak form like this. How can you write this in a weak form? So, we have already observed that this is a weak way to write minus laplace of u equal to 0. So, it is a natural way without writing to derivatives of u. Do you agree? Now, the point is which is the weak way to write this condition. Say, u lep, she is now in this condition. Okay. How can I write this in a weak form? Exercise. So, you see, what happens? Let us try to reason as before. Let us multiply by a test function and then integrate by parts. So, now, is this true? No, when it is true? Fine. Therefore, we have already the answer to our... because if phi is positive, this is still true. Then, when I integrate by parts, I have to put the minus in front of this minus, which becomes a plus. And therefore, grad u grad phi less than or equal to 0 for any non-negative phi. This is a weak... So, this less than or equal to 0 for any non-negative phi in this class is the weak form, the weak formulation of this condition. Do you agree? Or not? So, this... Okay. No. Do you agree? That's okay. Therefore, this is the weak natural form of writing this inequality without never writing two derivatives of u. And so, the exercise homework is... This now is the assumption, which is the thesis. Can we deduce that u of x naught say is less than or equal than the mean value? Can we deduce something like this? Try to do by yourself a similar proof and see what happens. Okay. Now, another exercise maybe that we do together. So, assume that u now is just only continuous than u. Satisfaj the mean value property in the volume sense. So, for any x naught, for any rho, et cetera, et cetera. The previous exercise is take an open set omega over m. Take a Lipschitz function u and assume that this is true. So, for any Lipschitz test function non-negative, this is less than or equal than zero. Then, of course, you cannot deduce that this is equal to this. But maybe you can deduce that this is less than or equal than this, or larger than or equal. So, try to find the right inequality. Try to prove, for instance, this. What you have to do is exactly the same proof as before. Notice that the previous proof, our test was this, which is non-negative. Therefore, you can make exactly the same proof, because this test is allowed. So, you have exactly to follow the previous reasoning. And you can use the same test function, because this is outside this. So, sorry, here it is for any x0 in omega, for any rho with the distance less than etc. So, write correctly. This is equivalent for any boon. It is equivalent to say that u of x0 is equal for any. So, the mean value property on solid bowls is equivalent for a continuous function. Is equivalent to the mean value property on the hypersurface, on the boundary of the bowls. So, this means, I recall, that this means 1 over omega n rho to dn by definition. This means 1 over I think this the boundary integral and this is a surface integral. So, instead that integrating here and divided by the volume you integrate just only here and divide by the area. So, actually if this exercise is true then we have two possible ways of writing the mean value formula. Depending on what you prefer. There is just one point here that you see, for writing this kind of mean value formula in principle you just need that u is l1 log, because you integrate if your function is locally integrable then you can integrate locally around the bowl. But if your function is a in l1 log this is not defined. Because an l1 log function is defined almost everywhere and therefore there is no sense of the trace of u on an hypersurface. A zero labor measure. The hypersurface is zero labor measure. Therefore there is no way to give a meaning of an l1 log function on an hypersurface. What it is not defined is the trace of u on this hypersurface. Because this hypersurface has zero labor measure and you can assign whatever value you want remaining inside the l1 log plus. So this is not well defined. This integral is not well defined. I mean if you have an l1 log function in the plane say or if you have an l1 log function on the line you cannot say and then you have a ball so this is a ball on the line. Of course you can integrate u here but you cannot say which is the value of u here on the boundary or the value of u here on the boundary. This is not defined. You cannot define the values of u on the boundary. You can always change whatever value you want remaining inside the back class. This is essentially the difference and so in order to not to have problems with this definition we assume at least continuity. Of course a continuous function leaves a trace on an hypersurface. So let us see the proof of this exercise. Assume for instance that your function satisfies the mean value property in the sense of surfaces and consider and so this is our assumption and I want to prove this. So now I start from this integral and therefore I write it so this is equal to this now it is clear I make the integral in polar coordinates. So this is equal to now I write this in polar coordinates so this is equal to the integral from zero to rho and then I have what do I have? I have the integral on the ball of radius r say x0 u of y dr this is double integral so this is dr also dr Now our assumption is this so this actually is a mean value on a surface of radius r therefore our assumption says that omega n-1 r to the n-1 u of x0 is equal to u of y d h-1 y so u of x0 is the mean value on this ball, on the surface of this ball by assumption so now I can substitute inside this integral this so this is actually equal to 1 over omega n rho to the n then I substitute inside the integral and this is a constant and this is also another constant so omega n-1 u of x0 and then the integral from 0 to rho to r n-1 dr hoping that I am doing the correct computation so what I find so this I can compute so this is equal to omega n-1 divided by omega n then I have u of x0 and then this integral is what is 1 over n rho to the n rho to the n so this seems to be a constant u of x0 but this is equal to 1 I was starting from the volume so I have shown that this is equal to this from this therefore we have shown that if u satisfies the mean value formula on surfaces of the balls then it satisfies the mean value formula inside the balls because at the end we have shown that this is equal to this so we have proven such implication now let us see the other implication so assume that for any x0 for any balls strictly contained in omega this is true and then I want to show that then this is true do you have suggestions for doing this so my starting point is this red box is equal to this so I know that this is true and I want to find something on the surface which could be the idea remember that we want to pass from a volume integral to a surface integral and there is a way to do this and the way is to differentiate so actually the left hand side is independent of rho therefore if I differentiate this with respect to rho must be 0 we have already done this computation so we have 1 omega n minus n sorry rho to the n plus 1 the integral over b rho u of y dy plus 1 over omega n rho to the n the integral over boundary of b rho u of y so 0 is equal to this now what do I do well therefore this is equal to this so let me write it as follows so minus so sorry I find that the integral over b rho u of y is equal to n over rho times this integral times this integral ok and this should be all because now I divided by omega n minus 1 rho to the n minus 1 rho to the n and then I have omega n minus 1 and again omega n 1 over omega n is n over so this is equal is it ok? so it is interesting to have at our disposal therefore 2 possible mean value properties for continuous function this is equivalent to this ok now let us do this let us do this following this theorem another interesting theorem here in the direction of the question so theorem 3 let you see omega satisfy the mean value property mean value property mvp now by mean value property is one of the two because for continuous functions they are equivalent so this is mvp then u is so what is the situation for the moment so uc2 minus laplace of u equal to 0 u and lip minus laplace of u equal to 0 in the weak form implies mean value property now we are showing that u continuous mean value property implies uc infinity in particular c2 and then we will prove this will imply that actually u is harmonic in the classical sense ok so let us see the proof of this theorem so let us choose let me denote it by eta epsion standard standard mollifiers what does it mean standard it means that they are radially symmetric radially symmetric it means that they are non negative it means that they are c infinity c infinity it means that they are the support of eta epsilon is contained in b epsilon 0 for instance the usual way is maybe eta of x equal e minus x2 if less than equal to 1 in 0 else maybe let me call this eta tilde and then eta of x 1 over the integral of eta tilde ok so it is simply a smooth infinity function and then there is eta epsilon of x epsilon to d minus x over epsilon ok so that we always have that we always have this normalization ok so standard sequence of mollifiers ok let us consider the function u epsilon for any x in omega such that the distance of x from the boundary of omega is larger than epsilon so I have omega here then I have all points so epsilon is very small actually so this is so say this is epsilon so I take a point here the distance of which from the boundary is larger than epsilon so let me call this maybe this set omega epsilon minus a little bit smaller than omega of the factor epsilon ok so for any namely for any x in omega minus epsilon I can consider the following the convolution of u with eta epsilon u convol ok so this is the integral over let me use the same symbols u of y eta epsilon x minus y by y y so this is the definition of convolution why I am taking x in this set well because it is obvious that if I take x here for instance then I am involving values of so I am actually integrating so the convolution is like integrating in a small ball centered x of radius epsilon so I go outside omega and u is not defined anymore ok therefore in order to have a meaning of this quantity I need to take x a little bit inside otherwise this integral is actually inside the ball of radius x ball centered x of radius epsilon and therefore I have problems for u so this is why but on the other hand for any x here this is well defined so u of x is equal to the integral over omega of u of y eta epsilon x minus y dy so now this is equal to what now let me recall who is eta epsilon so eta epsilon so at the end I want to show that this is equal to u so if I am able to show that u of epsilon is equal to u for any x in this smaller set then what I have proven is that u is infinity inside this smaller set because it is well known that u of epsilon because it is well known that this is infinity this is known ok so if I prove of course that u of epsilon is equal to u then I have that u is infinity in this set but then I can always take epsilon smaller and smaller so at the end at any interior point if I take epsilon small enough u would be equal to u epsilon in neighborhood of that point and u is infinity inside in the interior and therefore it is enough to show that this equality holds ok so let me compute this so this is equal to this is concentrated the support of this is just inside the bowl of radius epsilon centered at x therefore this is equal to u of y at epsilon of x minus y now it is radial ok so this is just an integral concentrated here at epsilon is radial ok now what is at epsilon remember that at epsilon of z is epsilon to the minus n eta of z over epsilon this is definition so we can construct just by commodity starting from just only one and we have this ok now what do I do so here now now I integrate in polar coordinates so that is equal to epsilon to the minus n integral from 0 to epsilon ok then integral over the boundary let me call this r maybe we call this r yes and then what do I have I have u of y dy and then I have eta of x minus y actually now x minus y is equal to r therefore I just have eta of r divided by epsilon and then I have u of y dh in minus y so I simply write this integral as the integral of 0 epsilon same quantity dh in minus y now I observe that when y is on the boundary of this ball this difference is actually r so since it is r is independent of y and therefore I can put it outside the inner integral ok now for the moment I have just used the definition of convolution I have used that the kernel is radially symmetric and supported in the ball that's what I have used now I use the mean value property because now my assumption is that u is continuous that is by the mean value property now I use it in the surface form I know that it is equivalent the volume and the surface form now I use it I see it from the proof it is for me convenient to use it in the surface form therefore I know what is this ok so this is equal 2 r to the n minus 1 omega n minus 1 u of x ok so I can substitute ah sorry thank you thanks so this is equal to this no with the dr with the dr sorry without the dr thank you now I can substitute and therefore what do I have so let me go maybe here so I use now the mean value property in the surface version u is continuous by assumption so I can do so I find epsilon to the minus n omega n minus 1 epsilon to the minus n u of x the integral from 0 to epsilon r to the n minus 1 eta over epsilon dr ok now homework by the property normalization property of eta we know that what do we know we know that the integral omega n on the ball of radius epsilon centered at 0 say of eta z dz eta epsilon z dz we know that this is equal to 1 remember we always have this eta equal to 1 and also this so I claim that this actually is equal to 1 check this at home if this is true then this is equal to u of x and this is true by our properties of normalization ok now I have erased my small scheme unfortunately so let us now show that the answer to our initial question so theorem let me call this theorem 3 maybe theorem 3 ok assume that u is c2 assume that u is continuous and u satisfies mean value property then u is harmonic and this statement is correct in the sense that in principle u is only continuous and therefore we cannot write Laplacian but we know that if u is continuous and satisfies the mean value property it is infinity so let me just add here actually there is also a remark that we made let me write it here that it is interesting remark we have already proven this remark actually if u is c2 and u is harmonic then u is infinity this is actually very interesting so this is a regularity first example of regularity theorem so regularity theory is maybe the most difficult part of partial differential equations it asserts that like this I mean you have functions satisfying a PD involving only two derivatives so it is rather surprising that if you look at this statement then actually u is infinity this is really surprising and this is I mean the point of regularity theory in PD is the most difficult part in theory is exactly this and why is this true because we know that in the proof we know how to do this u satisfies we know that if it is harmonic it satisfies the mean value property and if it satisfies the mean value property it is infinity so at the end it is interesting maybe theorem more than remark theorem it is a theorem first surprise so now so this says if we prove this this says that actually being harmonic or satisfying the mean value property is equivalent for continuous functions for proving this result let me introduce the function phi of r that is the mean value over the solid no maybe this again u of y dy let me compute this now let me define this for any r for any x for a point x in omega and r sufficiently small and therefore now we want to compute phi prime of r now to compute phi prime of r maybe it is better there is a difficulty here in computing phi prime of r because the dependence on r is on the surface so the idea is in order to overcome this problem here we are calculating on this make a change of variable and integrate it on the ball of radius 1 so that r goes inside here yeah but still let me let me compute this ok so I rewrite this as follows so I rewrite this as follows v prime do this u of x plus r z dhn minus 1 z so we know that this derivative has b0 ok but let me write it as follows so let me see if I am correct so if z is in the boundary of the ball then rz is in the boundary of the ball of radius r it is ok and then I am also translating the center now let me compute phi prime of r which is 0 at the end so this is equal now there is no r anymore neither here nor dividing by the unit volume unit surface area scalar product of grad u I already know that u is infinity so I can differentiate I am differentiating with respect to r therefore this is scalar product with z dhn minus 1 z ok and now I come back to the previous integral in the variable r so I come back to the boundary of br x grad u y and now z is z is this and therefore it is x minus y x minus y dhn minus 1 mistake y minus x integral of the ball of radius r centered x on the translated ball centered the origin of radius 1 so I do this first computation because for me it is easier to compute the derivative with respect to r now I come back to this and now what do I do this is you see what is this it is the scalar product of the gradient of u with the unit normal outward unit normal on the ball which we know to be equal now we have integration by parts ok so this is equal so let me divide it by the correct quantity r to dhn minus 1 and then I have now solid ball ok so this is equal to 0 because phi we know is dependent of r so phi prime is 0 ok ok so this is equal to 0 and therefore now I think that the proof should be almost concluded because since assumed by contradiction now so assume now that by contradiction that u is not harmonic so therefore there is a point where this Laplacian is non-zero therefore u is continuous actually it is c2 so assume for instance that this is positive at the point therefore by continuity there is a small ball where the Laplacian is positive which contradicts this therefore we have this interesting result that actually it is difficult you see but we have a sort of characterization of harmonicity even for continuous function if you have a continuous function which satisfies a mean value property then it is harmonic in the classical sense maybe I can leave you another homework very not so difficult perhaps consider the ball of radius rho center at the origin r2 so let call this omega ok take a function phi of theta equal cosine of n theta 0 to pi say and then find an harmonic extension so phi of theta is essentially defined on the boundary of the ball unit ball find an harmonic extension of phi in omega what does it mean that is equivalent to find anomorfic function function in the ball such that the restriction of its real part on the boundary so take for the ball of radius 1 for simplicity ok, such that find anomorfic function in the ball such that the restriction anomorfic function f such that the restriction of the real part of f on the boundary of omega is equal to phi this means that you are solving in the ball you equal phi and the same can be done sin and theta one of the two so it is not difficult not so difficult to find anomorfic function having this having this is not difficult can you imagine what it is theta is in no, actually yeah theta yes, theta is complex number of modulus one ok ok, theta is a complex number of modulus one but it is, I mean I mean, if you take f of z z to the n this is anomorfic and let us write it so if I write rho with now theta the argument so this is equal to theta now if I take the real part and I restrict it on the boundary of the sphere of the circle on the disk of radius one this is equal exactly to the cosine of n theta so in this sense theta is just the argument of the complex number so it is in between zero and two pi just the so maybe you can keep it like this so this is the answer to well, once you have this do this also for sinus then for the sum of two you can do because this is a linear function it gives you some example of harmonic function on the ball


Good morning and welcome to the chart of the week video with me David Madden Today's date is Thursday the 15th of August 2019 and the time has just gone 909 British summertime and this week's chart of the week is copper We can see here at the metal has been in a fairly clear downward trend the last number of months since April We've we've been pushing lower on the on the metal and in fact the level it fell to at the beginning of the month Was a level last seen in January of this year So we're talking eight months lows for hate on the metal not too long ago And copper basically ties in with the with the with the kind of overall Perception that the global economy is slowing down. China is a major importer of metal Its manufacturing sector is in contraction during the week We saw industrial industrial production numbers and also a fixed asset investment number that china which were also disappointing Only yesterday. We saw contraction in a german economy a big manufacturing big manufacturing a country this talk of a recession of a recession in germany These are all feeding into the view that the global economy is slowing down And if if that is the case It's likely that we could see a fall in in demand for copper That's what we're seeing, you know, that's what we saw copper at eight months lows only a few days ago Now there is a small bit of good news in the past 12 hours We heard from president trump who tweeted out to china's premier Xi Jinping talking about the Expressing concern for what's going on in hong kong and essentially Sated that if the US and china want to strike a trade deal there must be a humane handling of the situation in hong kong and even called for a private meeting between the two leaders and that's That's just seen as at least as a step in the right direction. So the overall mood For financial markets is a bit more positive on the back of that But who knows whether something will come of it or not is a different story For the time being it seems to be it seems to have Lifted spirits a little because they were quite negative and down a bit yesterday Take a look at the price action. So it's in the clear. It's a fairly clear downward trend The market in the last few after hitting it in eight months. Love managed to kind of bounce higher but you know markets not moving straight line, so credit tracking and fasting themselves Is this push higher? just a temporary Rebound before the market turns over itself yet again looks to retest the recent lows in around the 254 area And if it does manage to break below that it could take its back down towards the 250 region 250 cents per pound that is and if you go below 250 cents per pound We could be looking heading back down towards this area this area here at 243 cents per pound Now this area at 250 54 cents per pound has acted as support on a number of occasions Essentially over the last couple of years. We've seen this region act as support So a break below 254 cents per pound on copper on copper is likely to be likely to be very significant That being said if the market has managed to hold above it on a few occasions We could see the metal we could see the metal maintain above these levels So if we do manage to actually press on higher from here Resistance could could could be found in around this blue line here the 50 moving average Which comes into play at 266 cents per pound We can see that this blue line here the 50 moving average act as both support and resistance Not too long ago and if a metric is acted as support and or resistance Not in the in the recent past it makes it more likely that it will do so in the near future But there are obviously no guarantees If you go below above 266 cents per pound the 270 region You saw a lot of consolidation in around that area in the last few months that area Might act also might act as resistance But in order for us to to kind of shake off or start to believe that the wider negative trend here Has come to an end We really need to see the metal get above and close above on a daily basis above the 200 moving average Which was this red line here and that comes into play at 274 cents per pound We can see here there's a spike in in mid july with metal trader above the 200 moving average But it had failed to actually close above it So we really need to see a close above that metric before we could think you know what the wider downward trend has come to an end And we and we look at we kind of pressing higher So the downward trend is still very much in play and keep an eye out for the 254 cents per pound area Just one thing before I go if you have any cobbles to make on this video or any of the other videos We've made here at CMC markets. Please feel free to leave a review on your views. Thank you very much