But judging from this interview, I think we have already learned a lot of useful things thanks to our tracking. And I'm wondering for professionals, for subtitles who want to keep abreast with all the new results of research, what would be a good way to follow all the new knowledge that we are gathering? Like, should they go to some conferences? Should we read like abstracts of papers? Are there any like journals that people should follow? Like what would be your advice for people who maybe don't have a lot of time but would like to keep abreast of all the most important takeaways from recent research? Yes, I think there are plenty of places where you can find information about this. For instance, when you're looking for a journal, I would recommend, for instance, the Journal of Audiovisual Translation, which is open access, openly available, that means you don't have to pay anything to be able to read the papers. It's a very good source of recent research. I would also recommend checking their websites and social media channels of different associations, for instance, ISIS or some subtitles associations, as well as getting interested in some research groups that work on audiovisual translation, which, again, share the results of research. One of such groups is obviously Audiovisual Translation Lab, AVT Lab that I'm the head of. We tend to share lots of things and we're very happy to share them. If you need anything, just reach out to us and we'll be very happy to share. And yes, going to conferences, finally, is a great idea as well. You can meet not only academics who do all the research, you can meet other professionals, as well as a company. And there are several interesting conferences, the two major ones are languages in the media, which takes place in Berlin every two years. And every alternate year it is media for all traveling across the globe next year in Antwerp 2023. I guess we can add links for you guys to all these places where you can learn more about these journals or websites or conferences. I think it's fair to say we are a bit Eurocentric when it comes to those events. So I guess for somebody who is maybe based in Latin America or Asia, you can also look for events which are available locally and there are more and more conferences now on Audiovisual Translation also in other regions. That's right. Thank you for chatting with me today, Agnieszka. It's been great to talk about high tracking research and the results of different studies including your own. I think we can certainly learn a lot about subtitling for my tracking research and we hope you and other researchers will keep bringing us answers in the future. Yes, thank you. It's been a pleasure and please bring the questions on so that we have something more to study.


A fiery horse with a speed of light, a cloud of dust, and a hearty hyosilver, the Lone Ranger. With his faithful Indian companion, Tato, the daring and resourceful mask writer of the plains led the fight for law and order in the early western United States. Nowhere in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeats of the Great Horse Silver. The Lone Ranger rides again.  Ma Hawkins ran the plains hotel in Cedar Bend, but the town itself was virtually controlled by Big Bill Carmichael, owner of the gambling palace and cafe. Carmichael was never seen without his three experienced gunmen. Lefty, here's your pay. Whitey, here's yours. And the breed. Thanks boss. Looks like you two could learn some manners from the breed. Because he thanks you for the week's pay. We earn all we get from you boss. You earned it mighty easy this week. All you three did all week was to sit around the cafe here. Yeah, be ready to gun down anyone who comes looking for you. I still say you get well paid for what you do. You haven't had to raise a hand in weeks. I've got things under my thumb now. I'm the head man in Cedar Bend, there's no one to argue the point with me. Don't forget boss, how you got to be head man. What do you mean by that Lefty? Our guns were mighty accurate, wiping out the opposition while you were climbing to the top. Boss, maybe the boss figures he can get along without us. Yeah.  Why do you, I'm not complaining. You seem to think we don't earn our pay. Maybe you'll start working for your money before midnight. How's that? I'm going across the street to make a call. There's only one place across the street. That's the hotel. That's where I'm going. If you're thinking of making a call on Molly Hawkins, I can tell you right now you're wasting your time. I am, huh? You know doggone well you are boss. I aim to marry that girl. You haven't got a chance. She's head over heels in love with young Dave Seton. Yeah, that young whipper snapper. Molly Hawkins is too fine a girl to throw herself away in a tin horn like Seton.  He'll be owner of the Plains Hotel one of these days. He marries Molly, and after, Ma Hawkins steps down. And what's more, boss, if you think Ma Hawkins would let you marry up with her daughter... She likes you the same as she likes a case of smallpox. Yes. Well, maybe I can change your ideas. I'll change your car, Michael. What's on your mind, Breed? Oh, it is not much. It is only that I wish to say left and righty there, all right? You say you want to run the town, I agree. But when you say you want to marry Senorita Hawkins, well, no, Senorita, that you cannot do. I'm not asking any of you for advice. I'm just telling you what I aim to do. If I meet any opposition, well, that's when you three start earning your money. Now follow me across the street and we'll have a talk with Ma Hawkins. The Lone Ranger and Tonto were stopping at the Plains Hotel. To avoid a lot of questioning, the Lone Ranger had removed his mask and disguised his face. He sat in the window of the front room he shared with Tonto on the second floor and looked out on the street. Tonto, I got the window. Well, what you see? The man had just left the cafe across the street. He's followed by three others. Ah, let me see him now. That's Big Bill Carmichael. He's a man we're here to investigate. Him plenty bad. The stories we've heard about him are true. He practically runs this town. If that's the case, something must be done about it. That's right. Bodyguard following him. He'll come here to hotel. I hope he doesn't do anything to interfere with Ma Hawkins' plans. Well, what plans? He has an appointment with Banker Lone Street. She's trying to get him to extend her loan. Ma Hawkins, a kindly woman of middle age, was behind the desk in the hotel lobby when Bill Carmichael came in. Oh, it's you. That's right, Ma. Were you expecting someone else? Yes, I was Carmichael. And I just assumed you called me Mrs. Hawkins. In fact, I'd rather you didn't come here. I came to talk about something important. Well, it'll have to keep until tomorrow. I'm expecting Mr. Lone Street, the banker. Well, now that's downright interesting. I reckon he'll just have to wait till I get through. Wait? Oh, indeed. If you look out front, you'll see my three pals at the door to make sure I'm not interrupted. Oh, you're pretty high-handed, Carmichael. I've got a way of getting what I want if that's what you mean. What's on your mind? Ma Hawkins, you said a lot of things about me. Some of them were downright unkind. I'd have been a darn sight more unkind if I hadn't been raised up a lady.  Now, have your say, you skunk, and then clear out. Ma Hawkins. I told you not to call me that. I'll make you just plain ma. Why, you... You see, Ma, I'm in love.  I'm in love with Molly. What's that? Your daughter. Well, of all the cussied downright nerds. I aimed to marry her. Well, I do declare. I already spoke to Molly. Well, I hope she slapped your face good and proper. She did. But I don't mind that. I aimed to ask her once again. But before I do, you'd better have a talk with her and tell her she'll prevent no end to trouble if she marries me. Why, you... If you're threatening me... A lot could happen in a place like this, Ma. A fire, for example, might bust out most any time. Or some gents might come in and start a fight that would smash things up considerably. You're telling me those things will happen if my daughter don't agree to marry you? Well, now, after all... Oh, get out of here. Get out of this place right away or I'll... I'll swear I'll take a gun to you. Go on now, get out. Ma, what's going on? We were in the other room, Mrs. Hawkins. We couldn't help hearing you.  I can handle this. Hey, Miss Molly, I'm glad to see you. I was just speaking to your mother about you. You better get out. You heard that, Carmichael. You're not wanted around here. This is no affair of your seat and you keep out of it. Oh, Miss Molly, I was just telling your mother a few things that could happen to this hotel. Mr. Carmichael, mother told you to leave. Get out, Carmichael. Get out of here. We'll thrown out. I'll be thrown out? Who's going to do the throwing? I aim to try. Or you'll show you. You missed him. Oh, Dave, let him have it. All right, just now. Who are you? And here's another. Better not to get Dave. Hit him again. I'll get you for that. Dave, Dave, look out here. Cut his brains. Hey, come on, boys. It looks like the boss is eating. Step back, boss. We'll take care of him. Oh, yeah? Take care of boys. We'll teach him a lesson. Oh, Dave, Dave, look out behind you. Look out. Be a watery poket. You, get out of here right now. Dave knew he didn't have a chance against Bill Carmichael's bodyguards, but he put up a gallant fight, dodging, ducking, weaving, side-stepping. His fists worked like pistons, but he took many blows in return. He felt himself weakening. What help came from an unexpected source as a tall man and an Indian raced down the stairs from the second floor. We come help fight. Where with you, Dave? Dave, Dave, these men are going to help. You keep out of this. We're all ready in it. Oh, Marty, did you see that? I know you take the breathe. He got him. I'll teach you to keep out of this too. You've got to let me, but you won't get me. Look out. Look out, mister. Look behind you. Well, if you want some more, I'll Carmichael. I'll accommodate you. Whew. Gosh, I guess that takes care of all four of them. How about it? Any of you want an encore?  You just wait. Come on, I'll help you up. No, no, no. Let me go. Let me go. Don't hit me again. Get out that door. That goes for you, too. I'm going. I'm going. You want help? No, no. Oh, sakes alive, mister. I'm mighty obliged to you for helping, David. We heard the commotion down here. It was four against one. Oh, David, you heard. Oh, I'm all right, Molly. Now, we're right back where we started, with Carmichael still standing there. Carmichael, I told you to clear out. Come on, Carmichael, your move. Just remember this, all of you. I'd come here peaceful. It was Dave's seat that started fighting. Whatever happens from now on, you can blame on him. This way out, Carmichael. You're going back to your own side of the street. If you know what's good for you, you'll stay there. All right, get going. Let go of me. I've got you here. I don't need no help from you. You're getting help whether you need it or not. Dave, you poor thing.  Oh, never mind me, Molly. Look at this room. Gosh, tables and chairs busted all over the place. I'm sorry, Molly. I guess I shouldn't have started any trouble. Oh, I'm glad you did, Dave. And I'm a special glad that Tom and the engine came to him. I guess I owe plenty to them. Where are they? They left with Carmichael. Molly, this is just the beginning. Before we're through, we're going to have plenty of trouble with Carmichael. Oh, my, look. The Baker. Oh, my goodness. Well, if it's not Mr. Longstreet, come in, Baker Longstreet. Yeah, I'm in. I'm sorry the place is in such a wreck. I've already heard about the fight in the air. It was Bill Carmichael and his parents. There seems to have been considerable damage. Oh, well, nothing that can be fixed up, you know. I've heard quite a bit of talk in the past few minutes. Bill Carmichael seems to have become a sworn enemy.  Mrs. Hawkins, I think I can save a lot of time for both of us. There is no need to discuss any business. Well, what? What do you mean, Mr. Longstreet? Mrs. Hawkins, you wanted to get an extension on money. You owe my bank. Yes, I'd like to get the mortgage on this hotel extending for a spare. You have until the first of the month to pay off that mortgage. Well, I won't have the cash for the first of the month. I can tell you that. Well, I'm sorry, Mrs. Hawkins. I'm very sorry. To be perfectly frank, I was dubious about extending the loan when I came here. Now, after learning of Carmichael's ill will toward you, well, I simply cannot take the risk of extending the mortgage. Now, say here, Mr. Longstreet, what's Carmichael got to do with it? There is already considerable damage done right here in the lobby by Carmichael. He might carry the destruction farther. Now, if I extend the mortgage, he might make this hotel quite worthless just to get even with you people. I can't take that chance. You mean to say you're afraid of what Carmichael might do to this hotel? Yeah, yeah. Frankly, I am. I'm sorry, but that's the way things are. Then if it weren't for Carmichael, you'd extend the mortgage. But because of Carmichael, you've got to foreclose and take Ma's hotel away from him. That's just about it, Miss Molly. Then Bill Carmichael runs you as well as everyone else in town. I have no reply to that. Now, I'll bid you all good evening once more, let me say. I am sorry. Well, I must say Bill Carmichael sure picked a fine time to come here. Golly, Mom, it hadn't been for him. Mr. Longstreet would have extended the loan I'm sure he would have. Well, he won't extend it now. There's nothing we can do about it, Molly. Now, the thing. The curtain falls on the first act of our loan ranger story. Before the next exciting scenes, please permit us to pause for just a few moments. Now to continue our story. After the fight in Ma Hawkins' hotel, Dave Seaton helped restore order to the lobby. Then talked at length with Molly and her mother. It was after midnight when he went to his room in the rear of the first floor. What? Masked? He uttered a gasp of surprise when he saw a masked man sitting in a chair near the open window. Close for you. What is this? Don't misjudge me because of this mask.  But who are you? I'm here to help. Help who? Longstreet wouldn't extend the mortgage, would he? No. Do you think he would change his mind if he could be sure Bill Carmichael wouldn't make trouble? He probably would, but how can anyone be sure of that? Sit down, Dave. Sit down and listen to a plan. Dave listened to the plan as outlined by the masked stranger and agreed to do his part in the faint hope of saving the hotel for Ma Hawkins and her daughter, Molly. It was the following evening when Bill Carmichael and his three gunmen sat in a smoke-filled office in the rear of Carmichael's gambling hall. The boss was still complaining about the affair of the previous evening. I'll put that old woman on a business. I'll bust Dave Seton, too. Who is it? Open up. I want to talk to Carmichael. Hey, it's Dave Seton. Let him in right. Come in. Carmichael, I want to speak to you. You're on the wrong side of the street, aren't you, Seton? You've been talking to Mary and my girl. Well... Well, just this. It's you and me. I'll be at the Red Rock in just two hours. I'll wait there for you, Carmichael. I'm going alone. And you'd better come alone. If you take these three polecat pals along with you, that'll be the same as murder. And Molly'll do something about that. So will the sheriff. If you're not scared, you'll come alone. Scared? Who are you? I'll take you with guns, knives, or bare knuckles. I'll be waiting, Carmichael. Oh, and one thing more. Before you leave here, you'd better appoint one of these three to take over as the boss. In case you don't come back. In case I don't come back? Probably just one of us coming back from the Red Rock, Carmichael. And I expect to be that one. Bill Carmichael and his men watching from the cafe saw Dave Seton right out of town toward the south. A little later, Carmichael left town and headed in the same direction. He knew his strength and was confident of his ability to dispose of the smaller man with little difficulty. A mile from town, the trail led through a clump of cottonwoods. Suddenly, the road was blocked by a tall man on a white horse. In the moonlight, Carmichael saw that the other man was masked and that he held a gun in readiness. Hey, what's this mean? Hold it, Carmichael. I'll go for a gun. Who are you? What do you want here? Rope him, Tutto. You, Redskins, I saw you before. All right.  Let me go. I'll help you, Tutto.  This is a double-crossin' trick. This isn't fair. It's two to one. Dave Seton tricked me. That's what he did. Wasn't Dave's idea. I was gonna meet him fair and square. Fair and square? What are you gonna do with me? Tie you up and take you to camp. Tonneau can keep an eye on you. Word of the fight spread through the town and became the subject of everyone's conversation. Did you hear the news? Dave's got no chance.  Too bad about Dave. He's outweighed 50 pounds or so. Well, at least he's got nerve. No one thought of going to bed that night.  It was time for one or the other of the dualists to return. The biggest crowd had gathered in front of Carmichael's gambling palace and café. Finally, a horseman rode in shouting. He's coming. He's coming. I've just seen him. He's riding in the town. The fight's over. Carmichael, look. Is he not beat up, son? No. No, it's Dave Seton. Dave Seton? I can't believe it. There he comes. See him? Great day. Boys, I don't like this. Hold on. Hold on, fellas. Dave, Dave, thank goodness you're all right. Sure I am, Molly. Molly's all right. He hasn't even hurt. Great work, Dave. Great work. Let me through here. Let me through. Let me share him through. Let him get to Dave. I heard about the fight. I was waiting to put Carmichael under arrest for murder. Now it looks like it's the other way around. Oh, but Sheriff... Come along. You're under arrest. But Sheriff, you can't arrest me without finding a body. I'll find it all right. It won't be far from Red Rock.  I know your fight was a fight to the finish. Now come along. I'm holding you in jail while I go look for Carmichael. Three killers, the bodyguards of Boss Bill Carmichael, sat in the office of the café. All three were dazed, stunned by the sudden turn of events. Dave licked him. Dave got him. I don't know how he did it. Yeah, but he got him. That's what counts. And if he's hit the body, you'll maybe get away with it. Well, seniors, what's eating you, Breed? Oh, now that senior Carmichael is gone, we must have a new boss. I admit, does anyone care to argue? Yeah, I do. Go on, Lefty. What'd you hit him with? My fist. Must have busted his jaw. Now pick him up, Whitey.  Tell the bartender to come pick up the pieces of that chair. Now hold on, Lefty. Who said you was the one to give orders?  What are you talking about? I'm next in charge after Bill Carmichael. Who says so? I've been with him the longest. What's more, you've seen what I've just done to Breed. That don't make you boss. If it's fists that make the boss, well, try mine. Boy, you, I'll show you. Come on and try it. I've been wanting to pace you for a long time. While Lefty and Whitey fought with naked fists, Breed recovered consciousness, sat up, studied the situation, and got to his feet. I'll show you who's boss. The office had been made nearly soundproof. Moreover, customers in the cafe beyond the door were used to minding their own affairs, and those who heard the fight ignored it. The three-cornered battle was at its peak when there was a crash of glass. All three of the fighters turned toward the window. That man is mess. Which one of you is boss to take the place of Carmichael? Me, I am. But why you ought to know? Who are you anyway? I want to make a deal, a big deal, with a man who's going to run things in Carmichael's place. Well, you can talk to me. That's fun. I'll do the talking. Neither one of you are the boss. You keep out of this, Breed. Remember what I gave you a few minutes ago? I have not forgotten. Now I pay you back. Boy, you, take that. Now I got the same for you, Whitey. We'll find out who's boss. Oh, yes. The lone ranger moved away from the window with a smile as he saw the fight well underway. The men were like a pack of wolves fighting among themselves for the undisputed leadership. Lefty finally triumphed. Though bruised and battered, he was able to order men to carry Whitey and Breed out of the office and take them to the doctor for repairs. Then he sat beside Carmichael's big desk in the only chair that had remained unbroken. He was smoking one of Carmichael's cigars when the door opened. Dave Seaton, what are you doing here? Come along. Dave is here to speak for me as manager of my hotel. The sheriff put you in jail. I'm out. That's right, Lefty. I was mistaken about Seaton. Uh, where's the boss? You're looking at him, Seaton. I've taken things over in Carmichael's case. You've taken things over. I wonder what Bill Carmichael will say to that. What? What do you mean? Did you think Carmichael had been killed? Why, I... You're wrong, Lefty. Carmichael's coming here on foot, and he's vowing to get even with a man who captured him. He'll be looking for his guns, will he? Oh. I expect he'll be like a wounded bear when he sees you put a couple of them out of commission.  I'll be back in a minute. Show this to a few things. Well, you're pretty lucky. Where are you? Uh-oh, you just tell him that you took over, Lefty, because you thought I had licked him. You see, you and Ma, what are you doing here in my place? What's this I hear about a fight that...  I'd quit. Come back here. It looks like that busted window was real convenient for him, eh, Carmichael? What's the meaning of this? Sheriff, who smashed up this office? Well, the boys thought you were licked, Carmichael. They had little disagreement, deciding who would be the boss in your place.  And Lefty's just cleared out.  I'll see you, Sheriff Carmichael. You're going to miss those three. I'm serving you with a bill of complaint. It was the following morning when Longstreet the banker came into the lobby of the plane's hotel. He glanced at the back of a man who was repairing furniture and turned to Ma Hawkins, who sat behind the desk. Good morning, Mrs. Hawkins. Oh, bank along Street. I didn't expect to see you here. I've just been talking to the chef and learned that Lornaughty was about to prevail in our community once again in place of gun rule. I guess that's right. If that's true, Mrs. Hawkins, if it is true that the power of Boss Carmichael has been completely broken, and if I may be certain that this hotel will not be wrecked beyond repair, well, I would be willing to extend you alone. Oh, great day. That's the best news I've heard in a long time. I see you have it covered there. They can repair. Oh, we sure have. Well, if I could only be sure that Carmichael is true. Without his gunsling, he'll be easy to manage. I wonder. You wonder, eh? You look over yonder. See that critter swinging the hammer? Eh, eh, I see his back. You! When you get done putting that chair together, go out back and get the mop and swamp this floor. Oh, are you all... Yes, ma'am. Eh? Why, that's Carmichael. Oh, you're doggone right, it is. The sheriff took him before the judge last night, and the judge handed down the special ruling. Carmichael is to work for me until he's made good the damage he did. Oh, mother does it. Your loan is extended. And if you want more money, just let me know. Well, the mask man figured you'd act this way. Eh, mask man? Yep, the man who planned for Carmichael to lose his gunman, the Lone Ranger. This is a feature of the Lone Ranger Incorporated, created and produced by George W. Trendle and directed by Charles D. Livingston. Tonight's story was written by Fran Stryker. The part of the Lone Ranger is played by Brace Beamer.


Hello, everybody. How deep have we gone so far? Are we all very deep into javascript? i was here earlier. We were waiting above. We're all very deep. Oh, yeah, yeah, yeah. This is going to get real. Does anybody hear when i gave my talk earlier intro to angular? Okay, cool, cool. So that was very foundational, and that Was kind of we can do, we can do, that could have been Front-end stuff, that could have been back-end. I want to get a little bit deeper. There's one other thing i need to talk that's Almost as exciting as angular. It's a little bit less exciting, which is about ice cream. I've been asked to inform you that you will see people bringing up ice cream. They have asked that we wait until the end, because they're Worried that others are bringing up ice cream, and they're not ready.  Keep it right out there. Also, you should finish my talk. But for real, they want to make sure that they wait until They can control it for release, which will be roughly when this is over. There is a q and a panel coming up later with speakers to be announced as well. So those are your updates throughout the day. So here's a really long title. Does anybody use co-schedules Headline analyzer for the content? it's a good tool. If you write content, this would not have passed. But single-page web apps as wordpress admin interfaces using Angular j s and the wordpress rest api. It's a big topic. But really, what i'm talking about is my experience building the In-get admin. Sorry, my ab testing plugin. This is josh. Hello. I'm josh malik. I'm a plugin developer. I make an ab testing solution For wordpress called ingot, which we're talking about. I have to build a drag and drop form builder called caldera Forms. If you go to my twitter at Josh412, my last tweet was a link to slides, resources, Example code. Everything's going to be front. All the example code today is going to be simplified from In-get. It's on github. You guys want to really get into it. And this is actually a link that will take you to it. This is the most important meme in the entire stack of memes That are available to us as developers. Gpl has a lot of virtues. Our ability to learn from Each other and to share what we've learned with our Neighbors is most important. So that's what i spent the Last three months on. That's what i'm commercializing. But one of the things that's exciting about this and this type Of event is that what i've been able to do, which is new to me, I've played with it before, but i wanted to do this. This was a quick gain for me. I'm going to show you some Gifts as we go on of what we were able to do in the admin, Where we need to move between states very quickly and have Lots of interactions and having tons of page reloads. Right? That's all gone. That's all out of the window from the way that these Things used to be done. That's why i'm excited about it. I hope that you'll take a look at my code. I hope you'll also find Stupid things that i didn't put in full request. I hope that you'll look at it and go, this isn't so hard. We can do this. So that gets into why. I think this is the new way. This guy, anybody met this guy? This guy called matt mollowanky. He does this word press Thing. Saying that javascript and ABI-driven interfaces are the future. I agree. And i do think that a lot of word press has been around for a While. It's awesome that what we've built, we're Maintaining a lot of legacy systems and a lot of legacy Patterns that we've repeated throughout our plugins and it's Time to level up that game. People who expect these Dynamic interfaces. Don't expect page refreshes. Expect to be able to move between tabs dynamically. Oops, i'm in the wrong space and go back right away. Browsers are fast, computers are fast, the internet is still Catching up. I think this is how we catch up. This is why wordpress.com rewrote into a single page web app. They were looking to catch up. This should be a gif. Oh, no, this isn't a gif. That's bad. Okay, imagination time. Six changes. No page refresh. What we're able to do in this Imagine that you click on content tests and that changes Into a interface. Do you want to create a new one? Do you want to show one? Do you want to go into this group? Do you want to jump back out of that because you're in the Wrong place? Do you want to see stats? Do you want to move Through all these cynics? i had a gif, a three-second gif With six state changes. That were no page refreshes. This isn't like that because angular is magic. That's exciting. That's a why statement. Deep linking. This gif. It was working before. All those different state Changes kind of paste it, drop it into another page and it Glows like that. We're able to use the angular Router that was built so we could have a website that has Different states moving through it. We're able to use that in our admin. You'll notice this is wp-admin. Right here. We could do this with admin agedx. We could write this all bespoke. Many of us have done this.  Sucks for the user and all this weird magic that goes on Behind that i haven't figured out myself of what do i put in The cache, what don't i put in the cache, what partials do i Put in, this kind of stuff. Who knows how many engineers Are sitting around that google figuring out how to do all That magic for me. I like that. Because i don't have the google-sized group of engineers. Common uiux patterns. I'm using angular js and boot Strap. That's great for me as a developer. I don't do a lot of front-end stuff but i know how to do a Column small three. Bootstrap is easy and it's a Design pattern that everybody knows. Every person that's using the internet today is familiar With bootstrap. If they're not a developer But they're used to bootstrap because it's everywhere. For us, we're combining angular and bootstrap. We're sure with the wordpress rest api. We're able to build a really cool interface that's portable. I could very easily lift this out of wordpress. And it's familiar. And also because custom rest apis, Where does angular consume a rest api? Custom rest apis are so easy in wordpress now. For me to say, oh, i'm missing an end point, i can get that up With unit tests in less than 30 minutes. Because all the hard work for me is done. I've spent so much time in the past building custom apis for Plugins that were not half as good as what i'm able to build In less time because this is why we use open source People that are smarter than us, have more time than us To build this stuff for us. Why angular? I like the fact that it uses standard. It uses html5 for the system that's data binding. It's not reinventing the wheel. If i want to add a class to an Element, i type class equals, you know, double quotes, the Name of the class, end quotes. I like that. And i like the separation of concerns. I love that my views are put in an html file. If there needs to be funny logic to get them to work in That view, that's in a javascript file. I like that. It's relatively easy to learn. If today is your first javascript day, this is not for day two.  It's testable. We're going to take a look at Factories, which i didn't cover in my last talk, that allow Your html interface to be injected into it. So instead of making an html call in the middle of your Controller, you call a method that does your html request. So you can mock that. Now all of a sudden it's De-coupled from the remote api, so you can write a unit Test using fake data. Beautiful. Also, someone else pays to maintain it. Hashtag thanks, google. That's great. I don't want to do this stuff. Accessibility. One thing that really scares me About everybody, myself included, saying, hey, let's All go javascript interface. One of the great things about The php templating systems we use in the back of the wordpress Is the translation strings. The attention to detail that's Been done in wordpress core to accessibility. This has been a priority. It's awesome. And we can't go back on that. We can't say, oh, look at This. Everything's moving around. It's so usable. Who is it usable for? People who have good vision, people who are able to control Their computers with their hands, people with disabilities All of a sudden, we can't leave them out in the road, out in The dark. For us to say, oh, we can make this More usable but become less accessible is unacceptable. And one of the things that i like about angular is that It has a very good aria library built in. It's not going to do everything for you. But it does a lot of the work for you. And that stuff is built in and there are a lot of ways to Handle translation strings. Sean hoober is around. He's built out a wpml add-on for the rest api to do the Strings. He's built one that can give you Your translation strings from wpml script and i'll show You in here how we're using wpml script directly. It's very clean the way we're able to make it work. So we have an html file or i can't call php function. I can't call underscore e. We have a very good way to make it Translatable. And that's important. These two things making it translatable and making sure we Have our aria tags in the right place. These are essential. Let's talk about this for a bit. Setting it up. You're doing it at a menu page. You're doing this as a single-page web app for your Plug-in. At a menu page the same way. All back as a php function that just puts out the skeleton of Your html. That's short link. We'll get you to it. My slides are online. If you want to click it very later. It's very simple. And then we use wpml script for two things. One, the way it was originally intended to be used, which was To put translation strings into javascript. And then the other thing is one of the good gotchas that You're going to see is that lots of angular tutorials will Show you your template paths and assume that they're relative to The root of the url. But they're not, right? In a wordpress stack, they're in wp content. Except for wp content. It might not be called wp content. Slash plug-in. Slash the name of the plug-in. Which we don't actually know. So the same thing. So we need to localize admin path and our nonsense and These sorts of things. Nothing new. But slight twist on the challenge we've always had. And then obviously the directories. So what's totally out of scope for today is building your api. Unless you're using something that works with the defaults. If you're a plug-in, you're not going to be able to get away With using the post routes. So you're probably going to Need to build your own api endpoints. This isn't dphp day. So if you go on wordpress tv, You can see my extending the wordpress rest api talk. Wp engine has a free book on the rest api that i wrote. And that's chapter eight. And then i have a course at Learn.joshpress.net. In part three is all about extending The rest api building your own custom routes. So that's essential. But we're talking job script today.  Three talks in a day. So let's talk about this. Making it work. Angular ui router. The older router is the ng router. The newer one is ui router. ng router is still there. ui router is superior for lots of reasons. It's based on states, which is very cool. And you can have multiple nested states and multiple nested views. So imagine that you have an interface, let's call this Main content area and sidebar. You can have three controllers, Three states that all have the same sidebar, but have a Different main view. So as you switch, this stays the Same, this changes over here. Right? That's pretty cool. Also, the parameters of the current state of this are Available to you throughout your application. So if you want to know, like, if you have a url that's, you Know, post slash nine, you can grab, you have an object Available where you can grab that nine off there and use it, Or the slug of it. So that's available. I love this a lot. And it's not that hard to use. This is slightly simplified from ours to fit it on the Screen. This isn't too complicated. This is a function. You know, our variable config. And then we say, at the top, that's my default state, slash. Nothing else matches, otherwise, we're just at slash. But when we're at, when we can call our state clicks Test, when we're at url slash click test, right? You see, i've used wp localize script to get this Variable and get admin. Partials, right? That's the directory and then pull in that html file. What controller? we don't even have one for that. But the next one has a controller. Clickers. Call that controller. It's pretty easy. It's just saying, when the url is this, we go there. And you'll see that that can have dynamic sections. This one here at the bottom. This is like my single group, Right? We have groups of tests. This is a state for editing an individual one. And the last url segment is dynamic, right? Group test slash edit slash seven. We'll get there. We'll be able to load up seven. We'll go a little bit deeper to get to that. We have a new state, these sorts of things. So that's not too complicated, but it's really powerful, Because it can change your application on the fly. And all these things are still sitting there once they've been loaded. Sending it all up. Right? We're making a variable that has the application. Calling angular.module and naming it. Right? Because you have multiple angular apps running at the same time. And then we're listing out all of my dependencies. These also have to be included in the page as javascript files, right? But i'm going to trust we're all wp and qscript savvy, right? But look, this is all the things that we use. We use ui bootstrap, ui router, ng aria, ng resource.  These sorts of things. And then we just run it. We go into it. This is very important. Right here. Root scope.Translate equals Inga translations. That's my localize variable for All my translation strings. When we're inside of a Template, when we're inside of review, we have scope, which Is unique to the current model available to us. We have root scope, which is essentially like a global Variable in angular. Root scope is sort of everywhere. So i put translations into root scope. And as a result, anywhere in my templates, i can say Translations dot whatever in i have a string that is Translated using word presses native translations functions. Which is, for me, beautiful, right? I can use exactly the same thing. Double underscore. Well, escape it properly. The http interface. This is my delete state. Where i need to make a Delete request back to delete something. You see state grams dot group id. What group am i going to do? Whatever state we're in. It knows the group id. That's how i define what Idea i'm working on. This interface here is very Similar to j query ajax. So i'm able to say, you know, Method delete headers this, that url. And then i have a call back. They've got a very deep system. It starts with just success but then goes to then and then They have the whole deferred library built in. But i'm saying function success call back. Use sweet alert to message this. And then you see state dot go. That's a state switch. Right? Because i was in a state for a group. But i just deleted the group. Why would i want to still be in That state? So state dot go takes me back to the list. It switches the state like that in that one line.  In your client we'll see it as A simple error. I don't know what this back is, But they figured it out. And so i just check to see if, Because it also could just be like a server side error that's Totally malformed. So i just checked that's a Low dash that is object. This is avoiding some things. To see if data dot message is set. Because if the rest api Returns an error, i can get the wp error message. And then i can display that. And then i use state dot go. Pretty neat. Factories. This is where it gets real cool. Who here has been down that Rabbit hole of, okay, i've got some jQuery ajax over here. That's almost identical to this jQuery ajax over here. That's bad software design. I should make a function to do That abstract way. Who's been down that rabbit Hole, anybody? Doesn't end well, does it? Factories are your way of having an abstract way of putting data. This is my group's factory. This is where i get groups. Imagine it could be a post factory. Where this is a simple, I've cut it off because we only have this much. But this shows you how to do a query. So i can say page equals three, limit equals two. Get the third page to two or i can do id equals seven. But i also have all my methods. So i have update. When i want to do an update, i do put. And i make sure that these headers are sent there, right? Standard word press authentication to xwp nonce. Pass that nonce that i localized in. But if you go and you look, there's a short link here. By the way, they'll jump you right into the code where we Have that. I've got delete. I've got get. I've got post. The whole thing is there. It's one place where i wrote It out. This might get a little bit more Complicated later on if we need to do more manipulation That always happens in the same place every time. Just to get it ready to be put into the view.  Right? I can build a mock version of this. Theoretically jQuery is unit testable. I never figured out how. This is great because i just mocked this. I just built a new version of this with fake data. To see if it works. And this handles every use Case. And it's really neat. This is the example of it. See here? I'm injecting groups factory into this controller. Over here on the right. And instead of making an http Request, i say groupsfactory.query. Page equals one. Limit equals set up there A little bit at ten. Context equals admin. These are just url parameters to put into my get request. This gets translated into a query variable. I could type this out. Add equals. And sign equals. And then break it. Forget that. I just do this. And then when it's done, run that function. If you go into the actual source code, you'll see there's An error and all that stuff. But when it's done, i can Say, well, i could get back no matching and then we don't Have any data. That's my pagination. But what we normally do is say, and then we make scope. Groups empty. But what we hope for is we do Scopes.Group, the data, total groups. We get our header. We sort of modify, following Core's pattern. When you do a core endpoint, it'll give You like x total pages, x total posts, these sorts of Things. So we have x and get total. They'll give us our total. And then we're able to do A little bit of math to put it in there so that way we Can have pagination in our interface. Other benefits. api-driven plugins. When you're able to build a plugin from scratch. This is something i started in november. When you're building a plugin from scratch now, your Rest api isn't a bolt-on. It's not a thing that came Along later because you thought it would be a feature. It's essential in its necessary to the functionality Of your plugin, which means that when somebody says, hey, I'm using rest api to build this third-party integration, They're not second-class citizens of your code. They're doing it the same way you do. That does require some Discipline. That means that the code that is Used, the php side, to get read and write data from the Database needs to be totally decoupled. It can't be mixed in at all with your rest api endpoints. It needs to be called by your rest api endpoints. Your code that creates your front end needs to be totally Decorated out from reading and writing from the database. You need an abstract crud system to make this work. I think that's good coding. That's good software design. That's testable software design. Writing php code to serve this system? We do writing better, testable, decoupled code. That's important. Obviously, that means that it's Easier for third-party add-ons. If somebody comes along and says, i've inherited this Site and it's wordpress, but i don't really know that. Do you know jQuery? awesome. You can work with us. There's a lot more people out there that know javascript than There are professional wordpress developers who know what a hook is. That's awesome. That means that you can make the Jump to sass as a business person, but also that your Users can make the jump to being a sass. That your users can write their own integrations. With your hooks. Wordpress hooks aren't going anywhere. They can do that. They can do php, but they have a whole new Way in which they can do their integrations. Empowering other people to be performers. This guy again. He says that an api is the key to the open web. That is pretty good. Yes, sass is good for me as a Business person. What's awesome about wordpress, and the reason why we can have a conference of 600 People is it's empowered all of us to take control of our Data. When we empower other people to Be service providers of their data, we empower them. We empower them to create their own unique businesses that Maybe don't scale up for one central location, but we give Them the tools. This is why people are going out There and grabbing a bunch of e-commerce stuff and building Something unique with it on top of wordpress every day. As we've empowered them to do so. When we start making our Plug-ins available so our users can be service providers, we Open up a whole new range of possibilities for them to help Build the open web with us. And that, to me, is super Important in the time and place that we are right now Where the open web is threatened, but there's lots of Exciting work being done, let's encrypt apple taking the Stand that they're doing. Our ability to empower other People to control their own data is essential. That is why wordpress is a great cause. And that is where it gets to you. Does this make sense for you? Is that important to you? Is that fundamental to your Business? Is user interface design doing better with that Essential to your business? We can go high minded, but At the end of the day, the point of business is getting People that they want to use your product enough that They'll pay you for it and continue to. I think you can make a better product this way, which is Essential. So go do it. Angular docs are awesome. I love the Angular documentation and It's interactive. You can fork all the code examples and Play with them live on plucker. I have more links and Slides at joshpress.net, such word camp, miamiangular, Including my talk earlier today, all these slides. I know there's been a lot of links and i've moved through. I don't think anybody became an expert on this in the last 20-30 minutes, but i hope that i've helped you feel like, hey, This is something i can do. And hopefully you've been going to Other people's talks and hearing why they did it in Backboner. They did it in react. I did this because it's a very thin layer on top of a php Application, which is what ai happened to be better at. Different use cases. I hope that everyone is going to go Home and take all this to use and do really cool things. My name is josh pollock. It is so awesome that there's a roomful Of people here that want to learn this stuff and they want to Learn it from me. That means a ton for me. I don't know where on time if i'm going to be able to do Questions or we're just going to bleed into the qa panel. If you guys have questions on this or the intro to angular Stuff, i know my last talk butted up against lunch so i ran On out because that's what y'all wanted. But i'm at josh 412. What's the ice cream state? Okay, so if y'all want to find me, i'm going to be hanging out Getting some ice cream or at josh 412. Y'all are awesome. Thank you so much.


Hi, I'm Zor. Welcome to Unisor Education. I would like to continue talking about general aspects of functions, what function actually is, what kind of functions you can deal with, and specifically, today's topic is monotonic functions. So very, very briefly, monotonic means it's basically either increasing or decreasing. It's kind of natural understanding of what this function is about. But let's talk about what it means, increasing or decreasing. First of all, if this is a function, it means there is a domain for this function, where the function is defined, and there is a range, there is a co-domain. Now, let's ask a question. If I have a function which for each flower puts into the correspondence the color, can we talk about increasing or decreasing of this particular function? Obviously not. So what does it mean? The function is increasing or decreasing. Well, first of all, it means that in the domain, there must be something which we can talk about as a relationship less than or greater than or equal, etc. Now, the most typical example of this domain is real numbers. So basically, in the mathematics we will be dealing with, mostly we will deal with the functions which are defined on the domain of the real numbers. Among real numbers, we do have this relationship. We can say that one particular real number is less than another. Okay. Now, since we are talking about increasing or decreasing, the same kind of relationship must exist among the various of the function. Now, the various belong to the co-domain. They are in the range of the function. So wherever the function takes the values from, also should be the same kind of relationship. So we can always talk about two particular values of the function. Function of one should be less than or greater or equal, whatever, than the value of the function at another point, at another value of the argument. So to define increasing or decreasing functions, we have to have a relationship like this one. Less than or greater than or whatever, among the arguments and among the values of the function. And again, the most typical example of such a set which has this type of relationship is real numbers. We can always talk about two real numbers as one being less than another. So to make the long story short, we are considering right now when we are talking about monotonic functions. We are talking only about the functions which are defined on the domain of the real numbers and take the values real numbers. Okay, that's done. No flowers, no colors. We are talking about numbers, real numbers, two real numbers. Now, let's just put together definition of the monotonic function. So the monotonic function is the following. If you have two different arguments, u and v, both belong to the real numbers, both are real numbers, then the value of the function in these two arguments has exactly the same relationship. So if the function is defined at two different points, real numbers, u and v, and u is less than v, monotonic function has this property. The value of the function in the lower, in the smaller number is less than the value of the function in the bigger number. Now, does it mean that the function is supposed to be defined for all real numbers? Not at all. There are some monotonic functions which are defined only on the very narrow interval or something like this. Not necessarily entire set of real numbers. Same as values. Not necessarily the function values are covering all the real numbers, it can be a subset. But in any case, wherever it's defined, if we pick two different points from the domain, then the values of the function must comply with this particular inequality. Now, let me ask you this question. Does it mean that this results in this? So if the function is monotonic, so for any two numbers, one is less than another, the values of the function are in exactly the same relationship, does it mean that if the value of one is greater than another, then the value of the function would be greater in this point than in this point? Absolutely yes, because u greater than v means v, this is exactly the same, it's equivalent to v less than u, right? Now from this, using the property of monotonic function, we can say that f would be less than f of u. And this is exactly the same as this. So if one value is less than another, then the other is greater than this one. So basically, if function is monotonic, then not only less than is preserved, but also greater than is preserved. Finally, how about this? What if we will take values which are exactly the same? Well, then obviously we will have to have the same value of the function just because the function always have one and only one value for some concrete value of argument. So these relationships are preserved always. This is just because it's a function, and these two just because it's a monotonic function. Now, what does it actually mean as far as relationship between domain and the range? Well, the very basic and very fundamental and extremely important property is that monotonic function establishes something which we call one-to-one correspondence. So domain and the range are in one-to-one correspondence relationship. What does it mean? It means for any one value of the argument, we can find the value among the range, and for any value in the range, we can find one and only one. That's very important, value of the argument. So the first one that for any point in the domain exists something in the range, that's obvious, because this is exactly the function of a relationship. That's the definition of the function for every element from the domain. From every element from the domain, there is some kind of element in the range. But now we're talking about the inverse relationship. If it's a range, it means it's value of something. So my most important question is, is it the value of some one particular argument or two arguments actually match the same value among the range? Now, that is impossible. For a monotonic function, we cannot have two different arguments which are pointing to the same value of the function. Why? Because of this. If these two arguments are different, then one is less than another, which means that the corresponding value of the function should be less, not equal, less than another. So if we will take any element from the range, which means it's the result of the function applied to something. So that something should be unique. It cannot be the same value. This is impossible for a monotonic function just because the monotonicity of the function itself. If arguments are different, then because of this, function values must be different, which means for every single point, every single element in the range, there is one and only one element in the domain function of which is equal to that element in the range. And that's what it actually means one-to-one correspondence. For every element in the domain, X, we can find the corresponding value of the function just applying the function itself. But then that particular element from the range can correspond to only this particular value of the function it came from. There is no other because other would be less or greater and the function value will not be the same. So one-to-one correspondence, that's extremely important for monotonic functions. And one of the consequences of this one-to-one correspondence is existence of the inverse function. So if you have the main to range with a function F, so X goes to F of X. Now, there is an inverse function which always finds what exactly was the element in the domain, the result of which is a particular element in the range. So we have the function which goes this direction, which we will call G. And this function puts into the correspondence for every element in the range, some element in the domain, which actually a prototype from which this particular element was obtained using the function F. So we were talking about the inverse function before, but this is a perfect example of the case when the inverse function definitely exists. So for any monotonic monolithic, for every monotonic function, there is always inverse function. And since we are talking about real values for the main and the range, we are talking about only the function which is defined on the domain of real numbers and take values, the range is also among the real numbers. So both functions F and G are both real values to real values functions. Okay, now, well, probably would be nice to have some kind of example. Well, let's have a very simple example. Let's put the function, something like this. So for every element X, real value, we take one-third of it and that's the value of the function. Now, what is the reverse function? Let's just think about it. If we take, for instance, one, this is X, this is Y, we will have one-third. We have three, we will have one. We have 27, we have nine. So this is the function which is our original monotonic function. It's obvious to monotonic when X is increasing, Y is increasing as well. Now, what is an inverse function? Well, the inverse function would put into correspondence to one-third, one. To one, it would put into correspondence three, to nine, 27. So obviously the inverse function would be this. And it's also monotonic. It's also increasing, because obviously this is true. And this, from this being true, we basically follow that this is true since it's one-to-one correspondence. It means that the reverse function is also monotonic. So, but now these two functions are inverse to each other. Both establish one-to-one correspondence between all the real numbers, in this case, the main is all the real numbers, and the range is also all the real numbers. And this is just one of the examples. Another example would be, for instance, just give you another example. One function would be Y is equal to a cube root of X, and inverse function would be X cubed. Now, let's just think about it. If we will start with some domain element, for instance, 27. Now, if we will apply this function, we will get three, right? The cube root of 27 is three. Now, if we will apply this function now, three to the power of three would be, again, 27. So, direct function maps number to another number, and inverse function maps this function back to the original. And that's the purpose, basically, of having inverse function. So, these two functions are inverse to each other as well. So, we're talking about one-to-one correspondence. We were talking about inverse function. Here's an interesting comment, which I actually planned, this is my plan, by the way, I planned to mention. So, we know that every monotonic function establishes a one-to-one correspondence between domain and a range, and there is an inverse function. Now, here's my question. Is opposite true? So, if, for instance, we have a function which has inverse function, a function which establishes one-to-one correspondence, between domain and a range, does it mean it's monotonic? The answer is no. And to prove it, let me just make the following example. I will use the graph, although we didn't really talk about graphs much, but probably you understand what graph actually means. And here is the graph of the function. I will start with the graph and then we'll derive the formula. So, let's say I'm defining the function only on this particular interval from minus one-to-one. And the way how I define it is the following. Here, I will define it this way, but here I define it this way. I'll put a little arrow here, which means that a point zero function is equal to zero according to this graph. So, this is x, this is y. So, for every x to find the value of the function, I have to draw a perpendicular and this is the corresponding y. Now, this is from minus one-to-one domain of the function. Now, this is, let me just make it a little better here. Don't need this anymore. Okay, this is the range of the function from zero to two. So, the function is defined from minus one-to-one and for each value of x to find the value of the function, we will draw a perpendicular to the x-axis, to the intersection with my graph and then to the right or to the left to get the value of the y. Now, is it the function which defines one-to-one correspondence? Oh yes, absolutely. Pick any point here, you will get the point on the y. Pick any point on the y, y-axis, let's say this point and then draw the horizontal line until it intersects the graph, in this case, at this point and draw down the perpendicular to x. Now, if it's something else, let's say this is y, then you draw the line parallel to x until it intersects the graph and go down. It's always one particular point, wherever we pick the y, we will always, drawing a horizontal line, we will always intersect our graph in one and only one point, either on this piece or on that piece. So, one-to-one correspondence is established. Now, how about the formula? The formula is y is equal to, on this particular, it's equal to x, this is x, this is y, and they have the same value, if x greater or equal than zero. And this is minus x plus one, minus x plus one for all x less than zero. So, this is the formula which represents our function. It's a formula, it's two different formulas, but it doesn't really matter because these intervals are different. So, the whole interval will be covered by these two inequalities. So, the function is defined. For any x, I can find the value of the function. Okay, if x is greater or equal to zero, I use this function, this formula and for negative x, I will use this formula. So, I will always find the value of the y. Now, can I find the value of the y? Well, obviously yes, because if my value of the y is below one, I will use this formula and if it's above one, I will use this formula. So, basically the inverse function would be y is equal to x again if x is greater or equal to zero. And this function, how can I resolve that would be one minus x, right? One minus y, one minus x. If x is less than zero. Now, in both cases, x belongs to minus one, one interval. So, the function is defined only within this domain. Or I can put this restriction here, greater than zero or and less than one and here less than zero but greater than minus one. That's the same thing. All right, so these two formulas are basically describing my inverse function. So, inverse function exists in many cases, not necessarily in the case of monotonic function because this function is obviously not monotonic. It's decreasing here and increasing there, right? So, this is the relationship. Any monotonic function is inversible. Not every inversible function is monotonic. There are inversible functions which are not monotonic. Okay, that's fine. And now there is an interesting aspect of inverse function which is more about inverse than monotonic but obviously since every monotonic is inversible so it's true for monotonic function as well. Let's talk again about the graph of the function. Let's talk about monotonic function and their graph. So, again, let's draw our system of coordinates and let's think about some monotonic function. Just as an example, this function. Doesn't matter what's the formula behind it. What is important is that this function as we see is monotonic, right? Question is, how will the graph of inverse function look like? That's very interesting. Now, let's think about it this way. Let's say this is the graph of the function y is equal to f of x. Now, if there is one particular point on that graph which has coordinates a, b. Now, what does it mean? It means that if I will draw down, I will get to the a and if I will draw across, I will get to the point b. That's what it means. Now, again, it's a little bit ahead of all my discussions about graph, but if you want, you can go there and then return back to this because it's important property of the inverse, inversible and therefore monotonic functions as well. So, if the function belongs to a graph, it means that projections on both co-ordinate axes are correspondingly a and b. Now, from another standpoint, since this point belongs to the function y is equal to f of x, what does it mean? It means that b is equal to f of a, right? So, if I will use the a as an argument, I will get the b. That's what actually means that this particular point belongs to the graph of this function, right? Now, what is inverse function? Inverse function is the function which, if you take b as an argument, you will get a as the value, right? So, direct function takes a as argument and gets b as an argument. Inverse function takes b as an argument, it gets a. So, if my function is called g inverse function, if I will take b as an argument, I will get a. Now, from the graphical perspective, it means that if I would like to draw graph of the g function, it means that function with, the function g being applied to the point b as an argument, b as an argument, will get a as a value. This is point a b, sorry, b a, right? So, if point a b belongs to this graph, point b a belongs to this graph. So, always, if there is a one point which has coordinates a and b on the graph of the function y is equal to f of x, and there is an inverse function which can be designated as y is equal to g of x, if we will put b as an argument, we will get s a as a value and the point b comma a. So, x coordinate will be b and y coordinate will be a. This function belongs to the inverse function, this point. But now, let's talk about these two points. Points a b and b a, how do they position one relative to another? Well, it's actually very easy. Let's draw a bisector of this angle. So, this is 90 degree, this is 45 degrees. Now, where is point a b? Now, very easy statement in this case is that these two points are symmetrical relative to the bisector. Now, it's very easy to prove genetically, but since this is not a geometry lesson, I will probably refer you to the whole chapter called geometry in this course. You can try to basically prove it yourself, but believe me, it's very easy to prove that these two points are symmetrical relative to the main angle bisector, which means basically that the whole graph of inverse function would be symmetrical relative to the bisector. So, let me again draw, let me try maybe a different color, draw the original graph, which looks like this approximately. And it goes through, okay, something like this, right? This is original. Now, let me draw a graph which is symmetrical to this one. Relative to this bisector. Well, it probably looks like this. So, these two graphs are symmetrical relative to the angle bisector. This is the original monotonic function, and this is an inverse function. So, inverse function always symmetrical with the original function relative to the angle bisector. Well, that's actually all the general properties of the monotonic functions, which I wanted to talk about today. As usually, I do encourage you to register as a student, have somebody, or maybe yourself, if you want and register as your supervisor or parent, maybe, go to Unisor.com and try to take the complete course with all the lectures, exercises, and exams, which is very, very, very important. Good luck, thank you very much.


Suspense and it's 96,000 dealers present. Mr. Joseph cotton in blood sacrifice a suspense play produced and edited by William Spear Happened me boy. Here's one that'll rattle the ivory between your ears What is it that carries water has plates gives continuous service and is associated with a good tip a waiter Oh, how dumb can you be listen? I'll make it easy it needs water only three times a year in normal car use and it's a tough little bundle of potent energy Now what is it? Camel I'll give me strength look slap happy It's the famous auto light stay full battery the battery that needs water only three times a year in normal car use Why the stay full has over three times more liquid reserve above the plates than batteries without stay full features You caught me with my brains down well cocks glad to hear you admit it because the auto light stay full battery is known from coast to Coast as the battery that gives 70% longer average life as compared to batteries without stay full features And this is proven by tests conducted according to SAE life cycle standards. You're absolutely right Harlow Of course, you're always right with auto light And now with blood sacrifice and the performance of Joseph cotton auto light hopes once again to keep you in Suspense His dressing room Gary his arm through mine his great beautiful voice purring assuring Lee in my ears is wonderful Johnny wonderful 200,000 why they didn't pay that for gone with the wind. You're a success boy a success a success Well on the way towards being rich on the marquee above the theory in lights Garryk Drury and bitter Laurel and then in slightly smaller lights By John scales new clothes best food a fashionable hotel new and fashionable queen And I owed it every bit of it Everyone said that everyone except Gary We're just finished seeing the men from the motion picture company Gary had been charming courteous thoughtful protecting my royalties Protecting his rights and finally they were gone Walters Gary's valid came into the room Not tonight I'll pick you up in the car at the stage door at five minutes. Yes, I'm going to see mr. Scale Taxi sure I can't drop you anywhere John. No, no quite sure. Thanks glad who you know. Oh, well Walters Oh, yes, bring along that play of young. What's his name? Ruggles bugles? You know who I mean I promise Fanny Taylor. I'd read it. But well, it's perfectly useless, of course We'll be playing bitter Laurel for another two or three years. Yeah, they were John. Well, come on five minutes water Now look here don't you worry about his movie deal. I've handled these characters before Before before Listen to that John wonderful sound the empty theater the empty echoing endless theater John you know what sure There's a play in in the last scene the actor dies in the empty endless theater Pouring out his death on eight pages to the ghosts of all the audience who didn't realize how great he was alone His wife scorned to her Hollywood perfect. Well, what are we waiting for Johnny? I'll put you in your taxi you go home and write it Bring it to me tomorrow night. We'll fix it and there we are. I can read the notices now Sensational aren't there Gary Grury does it again actors death scene draws Bravo sir. Gary Grury may be Well, come on. We'll get you on your way I thought your performance was exceedingly fine tonight. Thank you. Good night, Scotty Waters will be right out. You've been locked up. Good night. Mr. Drury. Nice guy Well, this is his reigning. There's a cab stand right at the corner. We make a run for it. John John are you all right? Oh No, no, Dr. Lee dr. Brett on him. Yeah, my side How about you? You all right? Yeah, let me help here. Bye. You are hurt.  I Picked myself up from the curb with a card thrown me when it hit us my side hurt in my head real but Gary So I'm staggered out from the other side of the car saw the jagged pain of broken glass and the store window Saw the bright spurts dying the pavement crimson where Gary's right hand clutched his left arm The policeman came running for it. Yeah. Yeah, what happened? It's Mr. Drury officer. They've been cast skidded over the curb and knocked it through the window. Yeah, let's have a look You know catch him catch him. It's your fate. They've got him there. Oh, no wonder. He's got an artery Hey, you call an ambulance get a doctor. This little bleep today. We're not quick. Are you all right, sir? I hurt the side a little all I feel that faint. I'll be all right. Good. Good We've got to stop this bleeding here now help me. You put your hand right here. That's right Squeeze odd yes, and keep on squeezing you. You come on. Give us a hand. I'll take you said you take his feet now What happened in an accident what if here give me a hand hang on to the artery now trying to know The jury cut an artery Mr. Drury is dressing them off. They're right around this way What end of the light and up the light painted guy All right. All right here.  Scales at me over and now you were helped we'll rig up a tourniquet Well, Walt is whatever your name is there was someone tried to get a doctor Just call for the doctor. There's no one on emergency everyone's out and so are the ambulances and call a private hospital This man is bleeding to death Bleeding to death This was the end with it. No doctrine duty and Garrick Drury bleeding to death and then I came to I'll find a doctor But it was 40 minutes before the doctor finally came 40 minutes while Garrick Drury's life Seeped out from the improvised tourniquet. The doctor sat down his bag and took one look We're still trying to get hold of an ambulance doctor. Don't ever mind. We couldn't move him now Anyway, there's only one thing to do give him a transfusion right here. Yes First we'll make a decent tourniquet now. This is blood for type. Oh, by the by wait around all of you I have to find someone among you with type of blood that matches his Gary lay on a couch behind a screen in the dressing room There was a plate on the table one with a border of pink roses which during rehearsals We'd often eat in hasty sandwiches Now there were four round blobs of red on it blood Two blobs of mine and two of Gary's valid waltters behind the screen waltters was blubbering with grief while an intern arrived At last for the ambulance was murmuring fearfully my doctor. I can't find his But wait a minute. Yeah, let me see We must hurry you will be gone Steady now Walter steady. We know you love him. We're doing all we can now Go look at those tests Important thing is to give transfusion as soon as possible. Let me give it. I'll give my life for mr. Drury Let me give the child now. We'll see I've already told you Drury's blood is type 3 very difficult I can only give him a transfusion from someone of his own type or a type 4 universal donor Anything else would be like giving him prusik acid. I only hope that you are mr. Scales will do We'll have to make sure All right. Let me see The doctor bent over the plate pouring liquid out of vials onto the red drops I stood where I'd been standing when he put the blood onto the plate before the intern's voice had cried out Oh, that's right. I can't find his pulse Walters and the doctor had plunged around the screen to where Gary lay unconscious I watched while the doctor finished with a vial And he picked up a grease pencil from the dressing table and drew a line across the plate cutting it in half Then with a pencil he marked the side on which I stood with an S and the side on which Walters it stood with a W Now I will be sure of which is which We'll take a few minutes to see if there's any agglutination Let's hope that's all we can do is hope He disappeared once again behind the screen It was then that I noticed the one rose on the border of the plate which had been blurred in the firing I noticed it before many times. I've noticed it today in the last few minutes looking Stupidly at it as you do it such things but before Before the doctor had marked it before he and walters had gone running behind the screen Then hadn't the blood rose been on the left my left But now it was on the right Might Walters in passing have brushed it and turned it around I stood and stared at the tiny pool on the side marked W Little hard purple crystals were beginning to form around the edges I looked at the side of the plate marked S my side supposedly The blood was clear and bright But what if the plate had been turned around and the blood on the other side was mine? It was mine that was forming little purple crystals. I Stood staring at the plate as the doctor came around from behind the screen. Oh, let's have a look at this Hmm. Yeah Looks as though we're in luck. Is it mine me arguing the transfusion. Sorry old man Not unless you want to murder. Oh, no, no, but mr. Scales here it looks as if he were that useful animal or universal donor Alright, mr. Scales. Let's make ready. What you're it mr. Scales. Oh, there's something guy. Oh Well, I ought to mention that you're not frightened are you not that I danger from giving a transfusion No, no, no, no, no, I'm not right. Come around here. Let's get busy.  I long shot.  He's mr.  Yes to be sure. I'll sit down here. Oh, still you will hardly notice this make a fist like this That's it. Maybe feel a little dizzy for a minute afterward, but in an hour. You'll be right away. No, not still Not bad was it my back. That's right. Good old John Lord what a publicity story this will make Playwright had actors bedside gives blood to save famous stars life It kept quiet if he'd only It might not have been too late then But then I knew I I knew that I would never tell the doctor. I would never tell anyone But only wait and see The revulsion that contempt the hatred that had been caged up in me for that smiling post ring ape on the couch Sleep now clawing at the bars howling for revenge Going all right scale. Yes Yes, perfect me. Thank you, doctor Auto light is bringing you Joseph cotton in blood sacrifice tonight's production in radio's outstanding theater of thrills Suspends now. It's my turn Wilcox riddle me this What is it that lives a long time has great power and endurance and can store water? Well, that's easy happen auto light stay full battery. Oh, no Yes, yes that auto light stay full battery needs no more water than a cactus because it has more than three times The liquid reserve above the plates is compared to batteries without stay full features stop that Wilcox and answer my riddle Now, let's see now. You mentioned long life.  Wilcox. Why man this auto light stay full batteries tops in batteries talk about power It's phenomenal endurance Sensational and remember it's the battery that needs water only three times a year in normal car use Elephant is what I had in mind hollow, but I'm right to have because you're always right with auto light And now auto light brings back to our Hollywood soundstage our star Joseph cotton in blood sacrifice A tale well calculated to keep you in suspense I lay back there on the chair in the dressing room The doctor had been right to the snow pain about it I could feel little tingling as the blood said goodbye to my body on the way to inhabiting the much bluer veins of a distinguished actor No, no, I felt nothing only a gentle warmth doctor of wild and I love this And with it Came little visual effects inside my closed eyelids at kaleidoscope like they use in films to dissolve into flashbacks That that was it. Yes. I was having a flashback. I Haven't wanted to send the play to Gary in the first place But I was new in London and good old George so parts with handling me said he had a hunch about everything to gain my boy Nothing to lose may as well try you know can't get her trying Lord George. Gary. Drury. It's just just not his kind of play It's a tragedy of bitter cynical disillusioned tragedy. He may he just may like it You know, I'll sit it along over to his hotel. We'll see I've never met Gary Of course this tremendous charm of his this flashing winning infectious and comparable style of the man when When you talk to him you were lost He did like the play at least he said he liked. Oh, yes, wonderful idea very strong Perhaps a little grim, but then these are grim time Of course, there are one or two things that lead touching up and we may have to make a change here and there There's never been a play produced. It didn't have to have a certain amount of rewriting during rehearsal. You understand But I didn't understand I was still too bewildered to understand man had this Fantastic charm and it used it before I was out of his office I'd signed a contract giving me a very pretty share of the royalties and Gary the right to make any Reasonable changes he might be necessary to the script reasonable changes During rehearsals. We said halfway back in the theater Cocktail scene in the first time It seems out of character Keep wouldn't have acted that way He's been shocked and angry at the change Nonstra and left the body And then at the very end Keith rolls up his uniform to put all the decorations on it Lays it under his head for a pillow and lies down in the vision Wonderful curtain line. He said I'll rest upon my laurel Wonderful, can you write it boy? You're not serious. I'm serious. I look here Johnny. This is your play. I'm only good But that's not the play Gary It's all out of key with the rest of it. Oh, you said remind me I've been a little bothered about the ending too Was very dramatic of course, but just at this time it seems a little bad taste, don't you think? Play all too butchered finally open We sat up waiting for the morning papers and then they came I read them and I wanted to run away Couldn't the voices of the critics saying to the public This broken back play is only held together by the magnificent acting of mr. Gadot Grury Sacran as it is bitter Laurel provides a personal triumph to get it through it Nothing in the place consistent except the assured acting get it through it Mr. John's scales has constructed his situations with great skill to display mr. Drury in all his attitudes And that is a sure recipe for success. We prophesy a long run for bitter Laurel And run it dead. There was no stopping it I caught myself wishing Garrick Drury would die or lose his looks or his voice or his popularity so that the Old thing could be buried and forgotten well now Perhaps he was going to die I watched the blood from my veins fill up the container Thought of the blurred rose on the plate that might have got turned around I heard walters still complaining about something. I listened to the doctor Lucky for mr. Drury that mr. Scales was around good man ever on universal donor blood mixes with all types But was it my blood or walters that mixed with all types I didn't know I couldn't be sure Yet somehow I was sure that the plate had been turned around and That would mean that if the doctor used my blood for a transfusion it What was it he said Would be like giving Gary prusik acid Would be murder No one would ever know the doctor might guess but he would never dare speak it would be put down to his own negligence Came over to me and looked at the level in the container Not at its head approvingly and then turned to gary again I felt myself Pulsing and drifting like a man dosing in a snow drift Good evening, buddy. Oh good evening, mr. Drury looks like Ryan down. He does indeed, but then we can't complain Well, john, you must let me run. Yes, sir Take a flower. Thank you. Laurie. The show must go on, you know Oh We have a connation. Yes, sir You shilling sir. Mm-hmm. Hey, well, send it on for you. Oh, thank you It's wonderful about your plane. Mr. Scales has been a wonderful runner But then mr. Drury does know how to pick them. Yes. Yes, it does Looks as if it might run forever, doesn't it no matter what he's in they all come to see him Not that yours isn't a wonderful play. Mr. Drury gave me a ticket for the second night. Oh, it is always so thoughtful What'd you think of it? I thought it was lovely. I cried ever so When mr. Drury came back with only one arm and found his fiancé with that other fellow at the cocktail party exactly I will rest on my lord With a beautiful curtain line you gave him there mr. Scales and the way you put it over Yes, there's no one like Drury to put over that kind of line Leaving flurry Better love Oh, good lord. Molly Sheridan. Hello. It's good to see you've been months. Look who's here New york's rising drama. Oh, no, don't don't have you seen it. I I sent you tickets. Yes Kind of you think of us in your busy life? Yes, we saw the show.  Now. Look, let's forget the play and go have a drink together. Shall we? Sorry. Oh, but we have to think of our reputation, you know Good night, John. Come along, Sherry John John it was a good play How under any circumstances could you have let them do this to it? Come along, Sherry. Good night, John. Yes Good night Almost full court. That ought to do it. You're all right, Mr. Scales. Yes Good. Now we'll fool you out of here and go to work The doctor should be out of the room onto the stage I saw him disappearing around the screen with a flag in his hands as I closed the door Just as I thought There were the reporters waiting. I sat down. I I felt weak not not right Hey, Mr. Scales, how is he? Where he lives do they think? Well, they think he may they're giving him a transfusion with your blood. Oh, what a story Please don't use that.  He was my friend.  You don't know how people feel about get it to worry. Don't I? Incidentally, Mr. Scales, we hear you sold these screenwriters. Oh, no. No, not yet. It was well We've been talking it over tonight But if anything happens to mr. Drury, I mean you we won't sell Anything happens to Gary bitter Laurel will never be performed again My hands were wet and cold I could feel the perspiration running down my back My head was light and I seemed to be walking on air The voices of the reporters were distant and indistinct. I felt a sudden need to lie down to rest The door to Gary's dressing room opened and I saw the doctor standing there his face and his voice was blurred Will you come please what is it? Complaining of a pain in his back. He did almost immediately. We started the transfusion. He's he's asking for you. Of course Don't understand it. I don't understand We all did our best so much hemorrhage shock cardiac strain It's always a gamble to see when the operation is left so late Sometimes there is a particular idiosyncrasy. I should have preferred a direct test No good of the patient dies while you wait to make sure Mr. Drury First brand He'll be here in a minute mr. Drury waiting brand That's brand The cutting Must go up. Yes. Yes. He's dead.  But I don't understand it This is the scale of the type 4 universal donor Still there are sometimes personal idiosyncrasies I caught Walter's gaze and followed it. He was staring fascinated at the plate which still stood on the table The rose that one there they smart from the firing I remember noticing it was originally on my right now.  Why should I want him dead? You hated him I've known I've seen it all the time because of the plate You killed it.  Too fantastic. What current or coroner's funeral? What current? The roaring in my ears is the spastic constriction of my stomach The room began to deteriorate. Well, let's stagger to a chair Now I can hear the dr. Veatley's Go from a long, long way on He's in shock. No, no, no here here my My style where where the car hit me. Well, show me just Dear good lord, man. Why didn't you tell us you're hurt? Walter just tell them to bring in the stretcher from the ambulance quickly, man Yes It's ironic when the car hit me it was an injury to the spleen The spleen think of it So you see all the time I was giving gary blood for a transfusion. I was Leading to death inside myself Ironic isn't it death from shock and loss of blood Hey, they gave me a transfusion too Too late But I wouldn't have to die. They said I would have lived If I hadn't given my blood To kill gary curry Spends presented by auto light night star joseph cotton Simmer down harlow no more of those explosive riddles I'm exploding with good news hap the news that auto light makes more than 400 products for cars trucks planes and boats in 28 plans coast to coast These include complete electrical systems used as original equipment on many makes of america's finest cars Batteries spark plugs generators coils distributors electric windshield wipers starting motors bullseye sealed beam headlights All engineered to fit together perfectly work together perfectly because they're a perfect team So folks don't accept electrical parts supposed to be as good Ask for and insist on auto light original factory parts at your neighborhood service station car dealer garage or repair shop Remember you're always right with auto light Next Thursday for suspense our star will be carry grant the play is called salvage and it is as we say a tale well calculated to keep you in a spin Tonight suspense play was produced and edited by william spear and directed by norman mcdonnell music for suspense is composed by lucian morroweck and Conducted by lud bluskin blood sacrifice was adapted for radio by malcolm meacham from the short story by dorothy sears Joseph cotton may currently be seen in the carol reed production the third man a david o-cells nick release You can buy auto light staple batteries auto light resistor or regular spark plugs Auto light electrical parts at your neighborhood auto light dealers switch to auto light. Good night. This is cbs the columbia broadcasting system


The body of a 60-year-old swimmer who went missing after failing to resurface on Sunday was found Monday afternoon according to the Crowland County Sheriff's Office. The victim, William James Murray of St. Paul, was recovered in nine feet of water in Adney Lake, southeast of Crosslake. The body was found in the vicinity of where he had jumped off a pontoon and went underwater. The incident was reported around three Sunday afternoon. Recovery efforts were made difficult by an incoming storm, forcing the search to be called off on Sunday, but it resumed on Monday.


What's up everybody jc over jazby's case breaks calm 2020 pinini absolute baseball just sold out This is a five box half case break random teams number 10 all-card ship all teams in here We go guys second half of the case Dice really here is the cousin ranes from Jeremy down to Don and we got ourselves D-backs down to the Washington Nationals So let's roll the dice and we got ourselves a six and a three eight. Sorry six and three nine times one two three four five six seven eight nine Don down to Don nine times one two three four five six seven eight Marlins down to the mats I If anybody wants to trade guys, oh actually sorry, I didn't go through the teams with you one second Don with the Marlins Jeremy with the Cubs Jeremy as well the Dodgers Jeremy with the Mariners Don with the Royals Jeff with the Rays Danny with the Padres Jeremy with the Cardinals Indians Jeffrey with the Twins down with the Astros Jeremy with the Brace as well as the Nationals Jeremy with the Tigers as well as the Phillies down with the Rockies Reds Red Sox Jeremy with the Brewers down with the A's as well as the Angels Ben with the Blue Jays Jeremy with the D-backs Don with the White Sox Barry with the Pirates down with the Orioles Yankees Giants Jeremy with the Texas Rangers and Don with the Mets Sorry about that. I almost blanked it for a second. So now Alphabetize it and if you guys want to trade give you guys a quick minute Chairman the clothes guys All right guys, this is the last five boxes of the case. We had one ten box case Tomorrow is Monday. So we might get some new shipment of stuff. So stay tuned. But this is what we got for tonight You have Shane Bieber to one 89 Jose Verrios to one 99. I go guys. Let's go to hits first one is Nolan or not a Trevor story both for the Colorado Rockies Which would be dawn Debbie grew long to 99 That is for Philadelphia. Philly is going to Jeremy and Quang Yung Kim to one 99 or 149 I should say Rico Garcia to 99 Paul Molliver out of 15 From Milwaukee Brewer. That's going to Jeremy Jeremy with the Milwaukee Brewers and Will Castro to 50 Detroit That is going to Jeremy We have a Jonathan Villar from Miami number 299 Preston 299 and We got Jorge Soler Good luck. Let's go with the hits. We got Jordan Yamamoto Miami is going to dawn Cavendizio six-way relic and autograph tools of the trade to 99 for Toronto and Matt Dias to one 49 Frank Thomas the Big Hurt to 99 Jalen Davis out of 50 That is for San Francisco Don Las Palmo Joe and we got a redemption It's gonna turn it faster guys. Bam Louise Roberts Rookie baseball material signature blue. I don't know if this is blue. It looks like baby blue, but blue Anybody wants to look that up actually, you know what I have the checklist out. See ya so let's see rookie baseball signatures and Blue is out of 50. There you go. No, actually, that's light blue blue is out of 99 So there you go for the Chicago White Sox dawn sweet. Hey, man. I knew there was kind of a little Robert Harding in here So they go blue is out of 99 Next box. All right, we got Raphael Deverson 25 Raphael Deverson 99 We got Jack Flattery Chipper out of 15 He's the bat and through color at the bottom Jalen Davis out of 75 another one for the Giants When a dong and very nice for the Dodgers Gavin Lux Dodgers it's going to Jeremy Jordan Yamamoto to 99 Miami when a dong Chris Paddock to 99 absolute heroes and Jake Fraley to 175 All righty two more boxes guys Yogi Vera to one 99 Chris and Yellich Sean Yamaguchi Jordan Yamamoto Quad relic tool to the trade to one 99 and that is Dylan Carlson to 99 for St. Louis St. Louis going to Jeremy you have Gavin Lux rookie materials All right Adrienne Morjean to 49 That is numbered to 49 that is 38 It's like a little chipping around the top corner and Logan Allen to one 49 All right guys last box I Got last box of the break Oh, we got Evan White to 99 and other Yogi Bear to one 99 We have a Joe DiMaggio for the Yankees to 25 and Johann Moncada You're done Alvarez for the Houston Astros You're done that's going to dawn Donnie Walton Quad relic and Otto to 75 and Sean Murphy nice autograph Sean Murphy to one 49 It is for Oakland and Don our last three hits guys Jake Fraley triple relic To 49 Wow This is the next hit. It's really nice guys Tommy La Sorda 7 out of 10 for the Dodgers iconic ink RIP Tommy that is pretty sweet Dodgers Jeremy there you go man. That is pretty awesome Tommy the Sorda And Last hit is Willie Castro to 50 All right, sweet guys. There you go. That was the break. So that was a nice way to end it off right there with little Tommy La Sorda We did get some really nice hits over here on this side including a Luis Robert out of 99 redemption. It's gonna look like one of these bad a 99 little Gavin Luxe as well Chipper Jones patch. There's a Luis Robert redemption So again, absolutely always has some nice stuff guys for an affordable price All right, there's two pretty nice palm all of her So appreciate everybody that was absolute five bucks half case rate random teams number 10 on Jasper's key our number two Sorry, you know number 10 actually on Jasper's case breaks calm