We gon' talk, we gon' have fun We be on fire, we be live lit It's a unique hustle, big, big Check it, check it, check it, it's a unique hustle It's your boy, E-C-E-O, you know what I mean? With the lovely, amazing, official, outstanding All that other stuff I be saying I'm good at this mic stuff, man Mic check, man Boss talk 101, man Mr. Mako Y'all be havin' a lot of fun Y'all be havin' a lot of fun Y'all be havin' a lot of fun Man, man 20 years, man Bless you That's a hard cork What?  That came from Floor That came from him You know, it was Ryan that day He was headed to LA He had to go pick up a bag As usual He was like, what's up What's your schedule like, man I gotta get back to the highlight Nah, nigga, I'm kidding After you for a couple days, man I gotta get back to get it Let's go get it So we just, you know what I'm saying It was Ryan real bad Just jumped on the plane He was like, hey, let's do something Let's put something together I told him to play Shit, he executed it And it is what it is, you know Man, I seen that thing, man It ain't playin' this short goin' crazy I seen it I was like, these boys goin' crazy on here So like, like How much preparation goin' to say? Is this just natural? Natural Floor, I think he a comedian, man One take, Jake That was two takes Two takes, okay That was two takes, that one But Floor, I think he a comedian So, you know He jokin' all day long Any down with He be jokin' all day long Man, that's the I think that was hard, man When you got an organic relationship With somebody, you know They just pretty much Just doin' their thing, man You know what I'm sayin'?  And get me I don't have to own the plane But I got to be able To rent it a bar at some time Well, I tell you like he tell me Anybody can get a plane But can you keep it?  We want the L.A. in bag It was 20,000 See what I'm sayin'? You want the gas?     When he found out He said, ooh 40 to what? 40 to what? 40 to what? 40 to what? That's the first thing He thought about I knew that Mama, we back No, no, no, no, no Let me tell you Let me tell you They're always back During this time of the year You know that We go hard But playoffs We go hard But playoffs is totally different This year This year So you feel like this year is the year? Them niggas are already Telegating mama We already out there Normally, nigga, Telegate gon' sag Nigga been Telegating since Monday It's only in the city, baby All these families got their jerseys on Everywhere I go There's Corona everywhere Man, they're cowboys, man I think this is the year for us Yeah, yeah Exactly He ain't looking sad I think this is the year for us I feel it though, man I ain't never felt I ain't felt anything in my own time Look, we were 140 and no And that wasn't even that good Yeah That first game You felt it the last time Before you burned the jersey That was the proof That was the proof That was the proof I'm back on the whore tab Yeah, about the end of the year We gon' show y'all And when we win the Super Bowl It's different It's different You know what it is The whole world's shittin' there You can't say that Cause when was the last time When was the last time y'all won the Super Bowl? I watched it, it was in the 90s It was in the 90s You know how long ago that is? It don't matter If we was down this They say last time we won Barry White, R.I.P. Was 170 pounds I think that was what Barry Switzer Got called with the gun At the airport Indeed, indeed Yeah, so yeah They said Michael Irvin was sweating Like Bobby Q.B. Michael Irvin is so You know, right now He caught up on the Colorado I got to ask you about priming Priming this whole lookin' good Man, the prime doin' his thing Is everybody going down there? That's who everybody watchin' right now Every game seemed like The Super Bowl with this n***a Cause he walk out He different He different, man Cause n***a feel good When he walk out there Prime different, man He get a lot of hate, though I don't care I love it, man I tell you a little My boy, they all hang out with him That's dope So I'm lovin' that You know my prediction When the Cowboys gonna win?       Everything Everything I touch I want to own At least have ownership in it Because at the end of the day Why shit They make a hundred million I make ten Why can't I make seventy And they make thirty See that's the flow of mentality That I get from him As well on shit man It's all about ownership He not doing shit Unless it's favorable That's why I like the generation That we're in because You know yes We have This generation have a lot of bad But I like the way how They're more vocal Because back in Twenty, thirty years ago People wasn't talking about On and on and on These niggas vocal But these niggas own power Shit They don't power Like my mother That too That too I want to go back to Damn a little bit man I just always admire this Like you said I'm going to be independent I'm going to own this And I'm going to help my people On some You don't see that much A lot of people talk down And say whatever But the dude to me Is just a real Entrepreneur And I always rock with him So shout out today man And I got to get him on Boss Talk 101 For show Man like So Being with Mike What do you Some things When you see his comedy And the way he carries His whole Dynamic What do you see in him For his Being Because he liked The OG in the game For you right Mike is smart And it's all about marketing With more But Mike Mike If you know It's what he did He took what he did In the movies And brought it to the stage No matter where he goes He's dang it Mm-hmm Yeah He's going to say a lot Regardless Mike's selling 10, 12,000 tickets Dang it That's all it All he got to do is Come out there and Grow out of Mike It's up It's up Like it And the reason I I just see how Man The movies I watching all about The Benjamin The other night With them That nigga can act That's how I act That nigga He got It's just certain roles Man And nobody Never looked at it Like this And me and him Had this conversation I sure would Y'all Right here on I never told this Mike Ips had to come Behind Chris Tucker For Friday We all know How great Chris Tucker was On Friday Mike Ips was so good We never complained We were all All of them We never complained Like Damn We miss Chris Tucker Man He ain't hit no more Think about how Good Mike Gives Being For that To help That's true Yeah That nigga Pulled it out That nigga Pulled it out And he told me He came to L.A.  I'm gonna be in DC. No, no, no, we're gonna rock it out. We gonna figure it out He told me I got my cameras already if I get you and him to get up in the movie Then I got some brisket Big slab of brisket for the homie Nigga on tube it blow that whole up for me.   You know I respect the phaser bro, man Don't be honest with you I went to this dude's show brother do just like you show me so much love man It's been a few people that just really rock with boss talk 101 Chico bean too, but I'm just telling you man Phase on show that's crazy man love always trying to look out for boss talk 101 Don't call and check on us too.  Yeah got to my phone where I'm gonna eat. I see you with a deal hugely. Yeah Doing talking, you know Listen that mean why anything he asked me I was like, I don't know. I'm not I haven't done it yet. Why oh He's straight. Let's get it. Like he's an example of something. I ask you He asked me about a couple comedy clubs. I haven't done yet and I couldn't explain to him I haven't done him. He got pissed off He got pissed off like he gonna ever want to talk to me again and I'll tell him He don't know why I don't show him, but let me ask you question Do a certain comedy show I mean a certain comedy club don't they have to reach out to you and say they want you at their show No, I can reach out to work two ways. Oh, okay. Well, that's what that's real But only he gave me the connection. He gave me his manager connection to and made I get this brother here That's good. And that was your first time eating first time meeting. He knew you or he didn't know me. What'd he say? When he seen you trash I'm screaming trash when I walked into the room Me love what I do.   I can hear you. I'm alive. I'm living That's really I'm never too old and I never get too big where I can't Take criticism or learn from somebody because he been in the game 25 30 years and regardless what the people say Oh, he ain't that funny. He doing something, right? Motherfucker doing something right regardless of what people say they say Kevin Hart ain't that funny, but he doing something, right? Man, I can watch Kevin Hart movies all day Kayla that nigga be have me laugh And I don't know what it's just the movies like you said movies Just like they said that the cowboys in that good I'm with you mom. I'm a cowboy right now, right?   You got wings on the way That's not the only way man. So Texas man, you know, what when you look at Texas and the Comedians that comes the internet got it where it don't matter where you from everybody see you everywhere Correct, but they do they even label you as a heat from Texas. Well, people don't know where you from now They don't know where you from. I just didn't look at my this nigga is from Alabama Man from Texas I'm from East Texas. I had to correct Alto, Texas born and raised Alto, Texas born and raised Slash Lufkin Texas if you want to say yeah quite a few years in Lufkin, Texas as well But yeah, a lot of people don't think don't know where I'm from and I have to continue to remind them You just say Google me. Yeah, that's just if you're gonna use shows up. Yeah Yeah, but this nigga right here. He ain't got time to wait on Google. He's moving fast Say so when you when you think about the the 40 years the trash what's next is there anything else here that you Yeah, I got some I got someone coming over. I got some But no, you understand this 40 years thing that trash thing they different Yeah, he said a lot of stuff and he do a lot of stuff in this stand up But those two things right there are signature moves. It's like chess just single playing chess So yeah, but when it when it come to get you got to come hard because you already done set up a level that he Can't go backwards. Mm-hmm.  That's gonna reach Joe Biden. Mm-hmm. Joe Biden. Is he still a president?  Joe by 96 I'm gonna say it's on boss talk. He gonna say I won't trump back What let me out? And I know my black people Let me tell y'all something when Trump was in office It was so many black people had so many I had so much money man.  I'm by Reggie here never up on somebody Time's all my mom. I'm not gonna see you not playing because I'm serious, bro in LA. They just running in stores Trump was off that one going on niggas with a Gucci buying Louis all Frenchies. I Just bought a fridge. He died big.  Yeah stage eight No way a puppy supposed to be stage a diabetic No 96 man Nigga look at Dom on that little a kid. Mm-hmm niggas are veterinarians now nigga giving a dog shots worm medicine Nigga nigga burp for them and burp for them back to life the game change on the bottom with Trump You have money to pay people Joe buying getting the people 300 out he was having a bread had money on the trunk Yeah, and I get it. He might be a racist.  I ain't going to room I ain't going that room. I'm a nigga.   That's what I'm saying now until I'm in that room and put that money in my hand and I count and I look at What you do a residency in Vegas? Could you could you handle it?   I'm gonna look at found thought that I'm gonna go to him early cuz I got that privilege I'm gonna go look at we're gonna come holler tonight.  She knows she's in a guy. We got egos.   How you I'm good. I do interview Bob. Good. Don't just happen a good time But Kiki man wasn't there that night with her soul man. He was in his feelings like It's crazy. So what what do you think? Oh, okay Superbowl predicts outside of Dallas who gonna shoot Why outside of that I got to say I know we won't See she's I can't know about this my home Yeah, man right down the road. That's why you said that I say the chiefs That's the AFC You don't see either. It's not the cowboys. It's gonna be the 49ers on egos again Nobody else beat number. Oh, I come skip keep sliding you man. Cuz you got the knowledge skip know what it is You won't be on you and he'll just be on that show together either. He's nervous. He almost said besides you Maybe scale what I'm gonna say. I'm gonna build my best behavior skip skip Off and he pissed him off Do you think okay podcasting is cold right now it's going good, right? What's next? I always be like what's next? What's next because podcasting is cool. Don't get me wrong But and it's sexy right now everybody doing it anybody got one. I see I don't know. I don't know the good ones. It'll be good in the bad ones gonna be bad average ones gonna be average Do we see something at the end of the tunnel is or what cuz whatever next we need to be on it, huh? streaming streaming how You'll be streaming in Africa. Oh Yeah, that's money wherever you stream, right? Cuz it's always on everywhere where it's streaming right now.  You gotta go to a Mexican meat market. They got the bed meat They damn show got it. I go there too. I go there too real talk But yeah, people say you need to go to farmers market. That's really the best one. They say that's it that food better for you Yeah, they said that's better. You don't have to worry about that. You see him He'll gain no way to somebody can be skinny and still be on the healthy. I got a stomach man I'm going away. No, you be old man. Listen, I see you walk out when you fit do your ski I know it for to be a good one the way you walk How long do I take you to come over this material man split second Seconds split second.  He had a skit. I said, man Why ain't no we got no skit with Baba dole, man. He calling all the day Y'all kid that I was a long time ago. He holding in the vault.  I see them with zero this nigga went down through there. Hmm the nigga rapping They did millions of views rap. I said this nigga been rapping since Phil is my father. He can rap You do you think that did he move to Texas or he ain't got a house? I heard he got houses everywhere. Yeah, he live out here though Oh, yeah, yeah living those This nigga need to bring man. He need to come on boss talk. Look Shaq I mean, I know you in Dallas now. It's already out.  Cause I'm I definitely got to get that part out for show Take this out with the Anderson improv First show 730. Don't worry about it. So that second show already sold out Second show 945 get them tickets right now. It's going down man. Texas this Sunday night If that gets sold out, you're gonna think about adding 1145 show. It's up to the club. It won't be up to me Bro, I had to get it cleared to get the second show Because you know because they just gave me the show two weeks ago and I just started promoting it two weeks ago And you know guys good. I got got great fans Who want to come out and see me and support me? So I really do appreciate all the love everybody's showing me Even the haters. I appreciate it Selling our shows, you know at one point in time they say I wasn't selling our show And then it's funny how time changed Want to change up? Want me to do it? Sometimes they want you to speak on things sometimes you're gonna have to say nothing You can sit back and just keep working and grinding and grinding and grinding and all of a sudden There you go. Won't he do it? Won't he do it? How often do you come out with new content? I definitely got new content. I'm gonna stand up or I'll stand up Alison new new new new new content You won't you won't see it. It's a new year. It's a new year Okay If I already done been there now come out next year in new material.  Oh my god.    I don't want that energy transferred to my crowd I'm gonna spend the order and money to come see me.   Yeah, that's just me Got it. I'm feeling good. I want y'all you gonna feel it. So I'm I'm a vibe. I go out vibes I can't fake it. I'm going through some storm. I'm going through a storm. I guess it just what it is I'm human, you know, like everybody else, but I try not to put that off on to my My fan base. Definitely.   Who would happen bg or bird man bg and bird man Bird man, she's a million To a man, I'm ready for it. I'm right man.   What music who who who you think you you know what I said? He ain't made no So let's be real. Y'all really thank bg for coming home and be jamming Yeah Hey bg out here, man, you know, they got a meme of him too Why he got there? Who let them take pictures of my boy bg and I'm gonna tell you something Much time is that nigga done. They should show him a homage, but the nigga just they they called him slipping He don't know about the Me and him took that picture look right there.  He's gonna be jammed. It's gonna be terrible But that's But I'm telling you look I want that man to get all the money in the world, but I don't want to hear no motherfucking bg You want to hear it? I want to hear these young niggas coming up They need the spotlight. No, they need the spotlight. They really tell my son What what bg for to tell us how many niggas he was whooping ain't with nobody in them Ain't nobody for the fight bg in the pen He status too. I don't want to hear no more lies running the pen. I don't want to hear no more lies How many niggas you think wrapped? I'm gonna bg. Come on. Get your money. Take care of his family and live life I don't want to hear that nigga. Nigga ain't getting up playing my motherfucking car I'd rather listen to king g I was not listening to old bg. No motherfucking. I ain't listening to any of you Who is your favorite? Who are you listening? Who bubble dove listen to right now right now? That nigga that's a bow bow bow All right, man twisted black I'm listening to that old twist black and the new one.   That's all he's saying he got to come win Give him time to go right now. Hey wait what we're in a different area man.  They been hearing free bg for the longest man. They ain't saying free free my uncle They don't know y'all Man, look what my word They gonna go on tour They're not dropping no album.  They're not gonna.  They hold up and really that's what they're gonna do a reunion tour. I don't have to Oh The people gonna come out for Lil Wayne never to hit this thing Lil Wayne They could bring Drake out. They're gonna have to they're gonna have to bring Drake. Lil Wayne Otherwise juvie Nigga juvie would jam it.  It ain't deep. No he nigga girl. Because he was gone My point exactly he can bring ti. You know him and ti did a whole that that uh, uh, uh that uh stand up You don't like what i'm saying to him bro. That wasn't juvie doing cumming I can't break man juvie now juvie ain't hitting like that no more like that You would just win ti too. Yeah ti good nigga if i ain't cumming here But that's juvie It's a shiv right now That nigga just did a song with djk Nah that's on jamming We who? Not solo It's a shiv. It's gonna come back See people look at ti like he already done made it. They don't really want to hit no more, but the nigga jamming So it's a shiv right now. He's in this comedy zone doing his thing another year or two They're gonna be right back on tip again like they used to be Tip on stage tip tip go hard man. How is it? I want to see this see it. He's supposed to be When he get when he get on there i'm i'm going to see ti not too funny when he come to the d I'm going to see it. He's supposed to be coming out.   I don't know how about that's for sure uh I got hit Bubba love man, I love you bruh I want y'all to cry playing now tip go hard No, i'm gonna be honest with you. He didn't go hard. People have been done told him.   He's pulling it off. He's pulling it off And he got good help too try to k-dub them and other people now green them. They be pulling it off man I can't knock them. That's hard. Now. Now he could pull this off now be she No, no hear me out because the dude can rise different if he couldn't rap it's gonna be hard in this generation He young nigga. It's gonna be hard. He ain't gonna let him make it. He gonna have to get NBA young boy on the song the really Bruh, I talked to some young niggas and they told me Scarface with trash, man. Who? Scarface. Who say face to trash? Some young niggas. These young niggas don't care, bruh They say we don't know who that nigga is. Because Scarface is old So why are you laughing at that? These young niggas crazy, man They is hard on the niggas. Because it's hard on the niggas. They ain't letting niggas lay down If they say face trash, then you know I ain't got a chance. They're gonna come with it. They ain't face trash enough for You saying if I'm to the young niggas at the barbershop, you're older right now. You're not even young no more I know. I think they booed him one time in Dallas No, they didn't You think they're the young niggas. P.C. Roll Nugs and Gray The young niggas don't care. I love facing I tell you he the best ever to do it, but these young niggas crazy The young niggas crazy Man, I'm a Scarface fan, but P.M.C. I'm P.M.C. all day. I ain't even playing with Tupac I'm P.M.C. then Tupac I only reason because I've been studying the game lately with P.M. And P.M. just he from Texas first of all, but the niggas just The niggas got good jam, bro And he musical he could do things that other people couldn't he produced and and he make them songs, man Man shout out to all the rappers man. You knocking nobody man.  You better not slip one time. These rappers coming for you nigga. I can't I can't slip, baby. Has there been any rappers that mentioned you and any of their songs yet?  Yeah. Yeah sitting there playing niggas I'm big or not.  Send that plaque nigga Man, not for real though. Real talk. Send that plaque. You got to have it man. Thank you for coming on the show, bud Bubba dub, how can they get over you? You go? Yeah, I can get a host of these man on I.G. Bubba dub 94 TikTok the real Bubba dub Was a YouTube Jerry Bubba dub morning. I guess Google me. I'm gonna pop up. Just Google me. I'm on tour right now I'm in Agasson, Texas This sunday night two shows first show sold out 945 is available. There's brand hollywood, baby Tony dorsi janova ching steven jones.  We'll be in the building mama in the building building with the cameras It's gonna hurt. We bring the camera this time. You didn't know he was gonna be in the building. I'm bringing the camera this time It's going down boss talk 101 Bubba dub Amen, it's been another great segment of boss talk.


Hi, my name is Shawna McGraw and I'm Jackson Henry. We're interns with Migrant Justice. We're excited to be here at Pomeroy Park spreading the news. Migrant Justice is a farm worker-led organization, mostly dairy farmers around Vermont, and we are assembly-based. There's different assemblies in different counties in the state that come together and organize to have their rights represented and have fair treatment and basic human rights through their careers. Yeah, we're always looking for new volunteers to check out MigrantJustice.net online. Yeah, at MigrantJustice.net online and we're going to this campaign to get Hannaford to sign on to help these migrant farm workers get basic rights, so spread the word. Let's convince Hannaford to do some some good and help us out. Yeah, always looking for volunteers and we're happy to be here at Pomeroy. Thank you.


Hi, we are discussing iterative methods for capturing isolated routes for a given non-linear equations. In this today, we will discuss fixed point iteration methods. Fixed point iteration methods is a class of iterative methods and it can be seen as a generalization of the certain iterative methods. In fact, you can see that Newton-Raphson method that we have discussed in the last class can be obtained as a particular case of the fixed point iteration method, but second method does not come under fixed point iteration methods. However, Jacobi and Gauss-Seidel methods can be viewed as fixed point iteration methods. In this lecture, let us try to understand the fixed point iteration methods. Mostly fixed point iteration methods are used as a good tool for theoretical studies, but not much used in the computations. However, some of the particular cases like Newton-Raphson method or Gauss-Seidel method and Jacobi method for linear systems, they are used in the practical situation. Let us try to first get the idea behind the fixed point iteration methods. The idea of fixed point iteration method is to first rewrite the given non-linear equation f of x equal to 0 in the form x equal to g of x. That is we have to find a suitable function g such that f of x equal to 0 is equal into x equal to g of x. That is a root of the non-linear equation f of x equal to 0 should be a fixed point of the function g. Now, the question is what is mean by a fixed point? Let us first see that suppose the graph of the function g is given like this. This is y equal to g of x in the x y coordinate. Now, what you do is you draw the straight line y is equal to x. The point of intersection of this line with the graph of the function g is what is called as a fixed point of the function g. Now, you have to find a function g such that the root of the equation f of x equal to 0. What is that? That is nothing but the point of intersection of the graph of the function y equal to f of x with the x axis. This is r. Now, you have to find a suitable g such that the root of the equation f of x equal to 0 is same as the fixed point of the function g. That is the first step of a fixed point iteration method. Well, how will you find such a g? That is not very difficult. In fact, you can find many such g for a given equation f of x equal to 0. Let us see an example. Let us take the equation x square minus x minus 2 equal to 0. Here, f of x is x square minus x minus 2. Now, this equation can be written as x is equal to x square minus 2. That is one way of rewriting this equation. In this case, our g is nothing but x square minus 2. You can see that a root of this equation is the fixed point of the function g. This is not the only way that you can get g. You can also get g by keeping x square on the left hand side and push the other terms on the right hand side and then take the square root. Well, you can take the plus or even you can take the minus also. In this case, g is given like this and you can in fact do it in many other ways. For instance, you can also write the given equation in this way where g is given like this and so on. Once you have chosen your g suitably, then you have to define your iterative sequence as x n plus 1 equal to g of x n. In this case, the function g is called the iterative function. If you recall, we have written the Jacobi method as x is equal to b x plus c. So, this is also coming in this form where the solution of this system is equivalent to the solution of this system also. That is solution x of the system A x equal to b is also the solution of the system x is equal to b x plus c. The same thing here. As we have seen in the last example, the iterative function for a given equation f of x equal to 0 is not unique. You can find many iterative functions. Let us give the algorithm now. As I input, we have to also give the iterative function g. Well, we need not give the function f.  Once you give, you will generate the iterative sequence using this formula. So, this is a very simple algorithm for setting up fixed point iteration method. Well, in the practical situations, we have certain iterative functions which are commonly used. One is that g of x is equal to x minus f of x divided by f dash of x. You should recall what is the method that you will get if you take your iterative function like this. Well, that is nothing but the Newton-Raphson method. Similarly, you can take the iterative function as I have shown here that is g of x is equal to b x plus c. In the case of linear system, we have studied this as the Jacobi method. Similarly, we also have Gauss-Seidel method which comes under this fixed point iteration method. Now, you can see that fixed point iteration method is a framework. It is not one single method like Jacobi method or Gauss-Seidel method or Newton-Raphson method for non-linear equations. It is not like that. It is a framework where you choose your own iterative function. That is how the fixed point iteration method is more like a general framework. There are certain particular choice of iteration function that leads to very efficient and fast methods. But in general, you can show that the fixed point iteration method will converge with at least order 1. That is, it has at least a linear order of convergence. But that does not mean it will only converge with order 1. It will converge with order at least 1. In particular, we have a method which is Newton-Raphson method that we have shown that it converges with order 2. But it still sits in fixed point iteration method. That is because we will show that fixed point iteration method is of order 1. That means at least 1. That is very important. I am just emphasizing again and again. You should not get confused. Why Newton-Raphson method which is a fixed point iteration method is order 2? That is the common question that people ask. That is why I am emphasizing again and again. Now, you can understand that in the fixed point iteration method, the crucial step is to choose the iteration function. Will we have freedom to choose our own way of defining the iteration? That gives us also the responsibility of choosing a right iterative function that is a good iterative function. But now, what is mean by a good iterative function? So, that is the question. Let us try to understand it. A good iterative function should have certain properties. What are they? The first one is that for a given x naught, the approximations x 1, x 2 and so on all should exist. That is the first thing. If they do not exist, then there is no meaning for saying that it is a method to calculate the root. Therefore, the sequence should exist. That is the first property that we will look for from our iterative function. The next one is the convergence. Once the sequence is obtained, then the next worry for us is whether that sequence is going to converge or not. So, we should choose our iterative function in such a way that the sequence should exist and then it should also converge. Now, once it converges, the next question is, is the limit of the sequence a fixed point of the iterative function g? That is our next question. Well, we should choose our iterative function in such a way that the sequence should exist and the sequence should converge and the limit should be a fixed point of the function g. Because remember, we have constructed g in such a way that the fixed point of g is precisely the root of our equation f of x equal to 0. Therefore, the limit of the sequence should be a fixed point of the function g. So, these are the three properties that we wish to have from our iterative function. Now, the next question is, how to choose such a iterative function for a given non-linear equation f of x equal to 0? Let us see one by one. Let us take the first property that is, we want our g in such a way that the sequence x n generated by that fixed point iteration method should be well defined. Let us illustrate this situation with a bad example. Let us take the equation x square minus x equal to 0. We can take our iterative function in many ways. One bad choice is to take our iterative function as g of x is equal to minus root x. Why? Because this equation can be written as x square equal to x. From there, you can get x equal to plus or minus root x. If I take g of x equal to minus root x, that will be obviously a bad choice. Because if you choose x naught as any positive number say 1, then g of x naught is equal to minus 1 and that is your x 1. And now, x 2 is g of x 1 and that is root minus root minus 1 which is not a real number. So, that is the problem. Therefore, even if you choose your initial guess x naught as positive, we will get into the trouble of generating a real sequence. Therefore, this choice is obviously a bad choice. Now, how to obtain such a iterative function? Well, what you have to do is that our iterative function g should be in such a way that g of x should also be in the domain in which g is defined. That is, you take g in such a way that it is defined say on an interval a, b. Then what happens? You take any x in a, b and find g of x. Then g of x should also be defined. Because for the next iteration, you are going to apply g on this one line. That is how the sequence goes. Therefore, x belongs to g of x should imply that g of x also belongs to a, b. Then only when you go to apply one more time g on this, that will be well defined. It means g should be a map from an interval a, b to itself a, b. Such a map is called the self map. We make our first assumption on the iterative function as g is a self map. That is the first assumption we have to make. That is, g is defined from some interval a, b to itself. That is the first assumption on our good iterative function. That precisely means this.  Let us see what is the point number 3. We have achieved this by putting g is a self map. Next, we have to worry about the convergence. But I will just go to point 3 where I will assume that the sequence is converging. Then I will see what is the condition that I have to impose on the iterative function g. So, that the limit of the converging sequence is a fixed point of g. Why I am jumping to the third point? Because that is more easy for me to address. I will address this easy point and then I will come to the second point. So, let us first take the third point. What is the third point? The third point is that the sequence is converging. Then the limit is a fixed point. To have this, what is the assumption that I have to give on g? That is the question. Let us see. It is not very difficult to see that we have to impose that the function g is a continuous function. Why it is so? Well, suppose the sequence x n is converging say to x star. Then what you know is x star is equal to limit n tends to infinity x n. Therefore, you can write x n as g of x n minus 1. Remember that is how you are defining your sequence. x n is equal to g of x n minus 1. That is what I am writing here. Now, if g is a continuous function, then you can push this limit inside g. That is what is a intuitive definition of continuity. With that, we can see that limit n tends to infinity g of x n minus 1 is equal to g of limit n tends to infinity x n minus 1. Now, that is precisely g of x star. So, what you have seen is x star is equal to g of x star. That is precisely the definition of x star being a fixed point of the function g. Therefore, if you choose your g such that it is a continuous function defined on a interval a b to itself, then we have achieved two properties. That is your fixed point iteration sequence exists and if the sequence converges, then the limit will be a fixed point of your function g. With this, let us now move on to the next property that when will the sequence x n converge. This is little involved. We have to get a good picture about how this fixed point iteration works. Geometrically, let us see that in this I will give you two examples. Geometrically, where in one example the fixed point iteration converges and in another example the fixed point iteration diverges. Then you try to see what is the condition that we have to impose on g in order to get a convergent sequence. Let us take our first geometrical example where my function g is such that its graph is shown in this blue solid line. Now, what we are interested in? We are interested in capturing the fixed point of the function g. Let us denote the fixed point by xi and what is that? That is nothing but the point of intersection of the line y is equal to x with the graph of the function g. That is the fixed point of the function g. Now, let us see if we take this g and form our sequence x n using the fixed point iteration approach. Then how this sequence goes? Let us start with an x naught. Say, let me start the x naught at this point. From here, you can see that you have to first take the value of g at x naught and then how will you define x 1? If you recall x 1 is equal to x 2. 1 is equal to g of x naught. So, it means what? I am taking this point and seeing where this point intersects this line. This is nothing but x equal to y. So, this is y is equal to g of x naught. That is this point and this point is nothing but y is equal to x. That is what is this point. Therefore, this point is nothing but y is equal to g of x naught. That is what precisely I want to call as x 1. So, therefore, this is my x 1. If I start my x naught and define my x 1 as g of x naught, then my x 1 is precisely this point. I hope you understood what this iterative definition geometrically means. Once you get x 1, now you have to go to find x 2. How will you find x 2? Well, for that you have to take this point. You have to take this point which is the value of g at the point x 1 and that is given like this. Now, x 2 is defined as g of x 1. So, x 2 is now obtained by going and catching this point. So, from here I went up to here and from here I went up to here. Now, together I get x 2. What I have to do? I have to go from here to here and capture this point and that is my x 2. So, you see how our path is going. So, this is what is called the fixed point iteration path. It started from here, it went here and then it from here it went to this point and from there it went to this point. This is a geometrical interpretation. Whereas, analytically how you obtain this values x 1 is equal to g of x naught and once you get x 1, x 2 is obtained as g of x 1 and so on. So, once you get this, this is your x 2. Now, how will you get x 3? Well, you will come across this, catch this point catch this point and you should find corresponding x 3 for it. So, you just see where it intersects and that point is your x 3 here. Now, once you have x 3, now you have to go to find x 4. For that you will go like this and find this point that is your g x 3. So, that is how you get x 3 and from there you will go and trace where this line intersects x axis and you will see the corresponding x coordinate that is your x 4. Once you get this, similarly you will go here and then go here to get x 5. Once you get x 5, you will go here and here and then you will get x 6. You will see observe how the convergence is happening in this geometrical. So, it goes like this, like this, like this and how it is getting attracted towards the fixed point. See, there is a nice geometrical interpretation for this. You can see that it goes like this and it converges nicely to the fixed point xi. So, the fixed point xi is attracting this sequence towards it, that is what we are seeing. So, from here we go here and then here and then it goes on like this. So, this is one example where the sequence is getting attracted towards the fixed point. In other words, the fixed point iteration sequences converging to the fixed point. Now, let us take another example which is a bad example. Here I am taking the graph of the function g like this, which is shown in the blue solid line and what is the fixed point of this function? Well, that is the point of intersection of the graph of the function g with the line y equal to x and that is given like this. Let us denote it by xi as we did in this example. Now, let us see how the iterative sequence goes. If we take this g as the iteration function, I hope you understood the geometrical idea behind this sequence. Analytical is very simple, but geometry is something which you have to once think and see how I have constructed this fixed point path. This is called the path and you just have to put the arrows here. So, the arrows indicates how this fixed point iteration moves and goes towards the fixed point. So, it goes like this. Now, let us start with some x naught. Now, purposely I have taken it very close to the fixed point. Unlike in the previous example where I took the x naught pretty far from the fixed point, but then it was the nice story that it was getting attracted. But now I am purposely taking x naught close to xi. Now, it will go away from the fixed point. Let us see how the sequence goes. To build the sequence, we need to find x 1 and x 1 is given by g of x naught. g of x naught is this point and you have to see the point of intersection of this line with the, that is this horizontal line with the line y equal to x and that is taken as x 1. Once you have this, then you compute g of x 1 and that is given like this. From there, you approach to this point and then once you get this point, you know what is x 2 and that is given like this. Now, you see unlike in the previous case where we were going towards the fixed point, you can now see that our path is set in such a way that we are going away from the fixed point. So, we have just traced this path outside the inner box. That is what I meant by saying we are going away. Now, you see you get x 2. Once you get x 2, you can find g of x 2 and from g of x 2, you can get x 3 defined as precisely the value of g at x 2, that is precisely this point. x 3 is precisely g of x 2. This is how we define the fixed point iteration. Therefore, it comes to be this point. Once you get x 3, again you will go to find the value of g at the point x 3 and that is given by this and once you have this, you will trace back x 4. For that, you will first see where this horizontal line hits the line y equal to x and from there, you will get this point as x 4 and your path goes similarly. You can see that g of x 2 is equal to x that you went like this and then like this and then you are going away. As you go on computing the iteration, you are going away from the fixed point in this case. You see it goes like this. Like that it will keep on going away from the fixed point. Now, just observe what is the difference between this function and this function? What is the condition that you have to impose in order to get your fixed point iteration sequence as a convergent sequence? Well, it is all depends on what is the slope of the function g when you are very near to the fixed point. That is in this small neighborhood of the fixed point, you want your g to have smaller slope. Here, you see the slope here is little smaller when compared to here. g is growing more rapidly here when compared to how g grows in this example. Now, what is the precise condition that we have to put? Well, we understood that we have to put a condition on g dash, but what is that condition? You see this function that is this line has slope 1. Now, if the slope of the function g dash is something less than 1 that is what is happening in this case, then the sequence will converge. Otherwise, you have no guarantee, you may face a situation like this. So, that is the condition that you have to impose on g in order to get a convergent sequence out of your fixed point iteration method. So, let us finally, put our assumption 3 on the iterative function that the iterative function g should be differentiable on the interval where you have chosen g as a self map. Remember that is the first assumption. And now, the g should also be such that there exists a constant k which is strictly less than 1 this is very important such that mod g dash of x is less than or equal to k and that is less than 1. It means the slope of g should be less than 1, it means g should not grow more than 1. So, that is the idea because the other line that is this line is growing with slope 1 and therefore, this should not grow with slope more than 1 that is the idea and that is what is imposed here. And such a map is called contraction map. If a function g satisfies this condition with k less than 1 it means g is a contraction map. So, to summarize in order to get a good iterative function we need to choose the g. Remember you are given a equation f of x equal to 0. Now our job is to choose a suitable g such that root of this equation is equivalent to the fixed point of the function g that is the basic idea of the fixed point iteration method. Now there are many ways that we can choose such a g. We have seen what all the assumptions that we have to impose in order to get a good g. What is mean by good g? Good g should have that those three properties for that we need the following assumptions. One is g should be a self map, second is g should be a continuous function and finally, more important and more involved assumption is that g should be a contraction map. It means that g dash should exist and it should be a continuous function and that more g dash of x should be less than or equal to some constant and that constant should be less than 1. It means g dash should be bounded away from 1 that is more important. It should not grow either equal to 1 or more than 1 it should be something less than 1 it is growth that is what is called the contraction map. So, with all these assumptions we can show that the corresponding iterative sequence is a convergent sequence and it will converge with linear order of convergent. It means it will converge at least linearly that is what we can show which we will show in the next lecture. Thank you for your attention.


Hello people of the internet, my name is Johnny and welcome back to another FNAF news video. This one should be quick, I don't think I'll need to stretch it out to 8 minutes because frankly there's just not enough news to do that so let's just hop into it. So recently we've been talking quite a lot about the FNAF physical copies and it seems like we are finally getting some information on the core collection. I will say there are bits of information for the core collection that I'm very excited about and some that I'm a little disappointed about, you're going to see what I mean when we get to it. So previously we looked at the help wanted physical copies, if you missed that it's linked down below and so now in today's video again we're going to be looking at the core collection. So again, let's not waste any more time, I've said that already, PS4 we'll start off with that. So this is the hopefully work in progress cover for the FNAF core collection and it seems like it is confirmed that the core collection is going to be one game with all of the FNAF games on it. I say all again we're going to get to that later, but looking at the screenshots you got FNAF 1, you got FNAF 4, you got FNAF 4, you got FNAF 3, you got FNAF 3 and you have FNAF 2. And sister location, I'm recording this while editing because I totally forgot to mention this one. So the reason why I say the cover is most likely just a work in progress is because I mean just look at it, does that look like something you want to buy if you see it at let's say GameStop? No, of course not. I will say I actually really do like the core collection banner up at the top, but the logo obviously that's going to get smaller, they're going to have some of the animatronics on the cover, at least I hope. And then also Steer Wall Studios is down in the bottom right for some reason even though they are not working on the core collection that is Clickteam. I do think the team rating is going to stay and of course the PS4 logo is also going to stay. As for the price it's going to be $40 which again may seem odd but once we get into what games are actually in this collection you'll understand why it's just $40. Surprisingly the core collection is going to be released on January 12th of 2021. That is so much more sooner than I thought it was going to be released. I think I said like quarter one or quarter two at the latest and while January is quarter one I definitely did not think it was going to be a mid-January release. That is so exciting honestly. But now we have to get into some disappointing news for the core collection. Two years of Freddy right off the bat we are not off to a good start when it says two years and so far we've had over six. The core collection includes the first five titles that started it all. FNAF, FNAF 2, FNAF 3, FNAF 4 and FNAF Sister Location. So that is something that I'm not too happy about if I'm being honest. The fact that it includes just FNAF 1 through SL that genuinely makes me very upset. I realize they probably did it this way because Pizza Sim and UCN just are not ready to be released just yet. They're still working on them but to be honest I'd much rather have this collection come out later where it can include all the games including Pizza Sim and UCN then have it come out now and not include those titles like that. That's so unfortunate. Yeah that's why it only costs 40 bucks because it's just the first five and yeah, I mean, god dang. Moving on we got Celebrate with New Friends. Meet a colorful cast of robotic companions that are ready to welcome you to the FNAF family including Bonnie, Chica, Foxy and Freddy FNAF himself. Hide and Seek. Survive the night by monitoring the suspicious activity of the haunted animatronics that come alive at night. They can run, but you can hide. Also exclusive features, a new achievement and trophy system as well as optional cheats that give new reasons to revisit Fazbear Entertainment. So yeah that's been part of the console ports for quite a while now, having cheats and having trophies. Something I wish the Steam version had, you know Steam in-game achievements, but whatever. Maybe Scout will update them sometime in the future, I doubt it. And then the Xbox One is the same thing it just, you know, is for the Xbox One. Surprisingly no Switch covered just yet, there's not even an Amazon page as far as I'm aware. But yeah, the main, like I'm so hyped about this, don't get me wrong, I'm so hyped about physical copies for FNAF and Help Wanted. It's just I'm so genuinely upset that it doesn't include Pizza Sim and Usain. Because what do you do then? Do you release them separately? Like you can't, if you're not going to release them in the core collection, how are you going to release them physically? Are you going to have core collection two with just Pizza Sim and Usain? I honestly don't know why they're releasing it, I say right now, but you know, in a couple months. But like just wait until the last two are done. Or maybe it is going to include Pizza Sim and Usain. It's just, since they are not ready, they're not announcing them just yet. Because they do still have until mid-January. And Pizza Sim is right around the corner coming out later this month. And having two, almost three more months to work on Usain after over a year of making it, then again I know they haven't been working on all of the games at once, they were working on them. I believe they worked on one and then the next one. I don't know. But they've been working on Usain for quite a while now. So hopefully by January 12th they're going to have all of them done and they can include them in the core collection because again, I don't see how else they would do it. Yes, that's really it. Either today or tomorrow, I don't honestly know which one it is. It might be tonight, but at the same time last week it was, tomorrow, on Friday, we're getting a new FNAF A.R. skin. Obviously it's going to be Jack O'Bonnie if it is someone else I'm going to sue, a little mix that is a joke. Yesterday I also recorded my review for the Security Breach Plushies, so that should be coming out hopefully in the next couple of days. And then, honestly, I'm just waiting until the 31st so then we can get Pizza Sim on consoles because I'm so hyped to play that. Because after that, it's Usain time. So that's it. Thanks for watching. See you all on the flip side. Maybe tonight, maybe tomorrow. I don't know. Goodbye. Gregory. Be still. I think she's found us.


Dierre de Montréal, you are the president and the founder of the World Policy Conference. Congratulations on what I think has been a very successful conference. Now, what are your conclusions from the conference? Well, I think we all agree that we are going through an extremely critical period. Trump or Brexit are symbols of these difficulties, these difficult hard times, but the world is clearly threatened from fragmentation, nationalism, populism, et cetera, et cetera. And the WPC Forum is a place where people from the five continents try to fight hard against this risk. And I think we have covered almost all the difficult subjects in a very positive and friendly atmosphere. Yes, you've spanned the whole world, in fact. I think so, in the Middle East, the U.S., et cetera. And also, I must say, I'm proud that we have succeeded to engage the catarrhid themselves, you know, in terms of speakers or interventions from the floor, which is very unusual. And that's part, I think, of the mission and, I should say, the success of this WPC. A final question. What do you hope will be the consequence, or consequence, says the plural, if you like, of this conference? You know, it's always extremely difficult to assess influence. Influence is a very loosey, ill-defined concept, but I hope that even if it's only one drop of water in the ocean, I hope that this drop might be significant and might even change the world. Well, it's important to irrigate the world. Absolutely. Thank you so much. Thank you. And congratulations again. Thank you very much. I think it's been a very good conference. Thank you very much.


Let me introduce Mr. Steadman. He's been very, very significant to the restoration of the bridge and to the history of the bridge. He is a de facto dean and senior statesman of the San Antonio and South Texas Society of Professional Engineers. He retired as president of the W.E. Simpson Company of Professional Engineers. He worked as a founding member of the restoration group and was the person responsible for listing the bridge as a Texas civil engineering landmark.  He worked on that centrally. He also got it listed on the National Register of Historic Places. So he's going to talk about kind of the engineering history of the bridge based on his long history of working in that capacity. Mr. Steadman? Good morning. Good morning. Glad to be here and at my age I'm glad to be anywhere. If you talk about age, historic, the Hay Street Bridge was built originally in 1881. It's 132 years old. The trusses themselves. It served as a railroad bridge across the Nueces River west of Uvalde. When the railroad wanted to cross all the east side streets, the city demanded a viaduct for traffic to get over the main line of the railroad. So the bridge then was moved and it could be moved because the members were all pin connected. Large metal pins connected each joint. At that time it was new enough that the pins could be removed and it could be brought over here in pieces and re-erected. It was re-erected, brought over here in 1910 and re-erected where it is now and has been since 1910. So again, something that's older than I am. As you mentioned, it was designated as a historic structure by the Texas Society of the American Society, the Texas Section of the American Society of Civil Engineers, as a Texas Historic Civil Engineering Landmark. It's also listed as a historic bridge by the city, by the historic foundation, by the Texas Historic Commission, and as she mentioned, it is now listed on the National Register of Historic Places. In 2000 really the effort began to restore the bridge and it was about that time that the restoration group was formed. The street bridge restoration group was composed of east side citizens, the city planning commission, conservation society, and my interest, the engineering groups. I might mention that the conservation society was the first big contributor, something like 53,000 from the conservation society. Our engineering firms and individuals contributed something like 50,000. We were able, the restoration group was able to donate to the city, $189,000 toward the cities required 20% to restore the bridge. We were fortunate in getting federal funds to restore the bridge. We went to Austin before the Texas Highway Commission, went there, there were 100 projects looking for funding, only five could be funded, and we had only five minutes to make our presentation. So we made the presentation and just at the right minute Senator Wentworth came in and addressed the commissioners and answered questions that they might have. We then were one of the five projects that were granted the federal funds. The 80% amounted to $202,089,000, $2.89 million. The city was required to raise the other 20%. In order to do so, the city thought, when we first approached them, that the city thought that they owned the bridge, but it turned out that the railroad owned the bridge and the property that it was owned. And that cost us about five years while the city and the railroad were using legal means to make an agreement to transfer the property from the railroad to the city of San Antonio. The restoration took place after a five-year delay and another delay. Finally, about 2007, the restoration really began with the Patrick Sparks company who had restored the New Braunville South Street Bridge during the engineering for its restoration. It was all handled very well and since the trusses themselves were out of raw iron, they didn't rust, they were very durable. All we had to do in restoring the trusses was to clean them and paint them with linseed oil. Now, it was different because when we brought the cross members supporting the deck, when it was brought here, it was widened from 16 feet to 25 feet. So the 25-foot members both on the deck and on the overhead were regular steel and they had to be brushed, sanded and repainted. But the trusses themselves, raw iron, were very durable and you can see as you cross the bridge that in fact we did have to replace the rivets. And in order to do that, there was no one in this area that knew how to do riveting. So a man was brought in from Michigan, sort of a donated service to show our contractor how to do the riveting. That was part of the restoration the rivets replaced and then the restoration was complete. And the main cost of the restoration I might add was the replacement of the two long concrete approaches that had deteriorated. That was the main cost of the restoration. Let me add that as part of the restoration, those approaches became historic in themselves because they replaced the historic portion of the bridge. The brewery was making a comment that he was going to attach to the non-historic part of the bridge. You can't do that, it's all historic. And in 2005 some members of the restoration group, three of us, Nettie and I and the president of the Conservation Society at that time, across Budco who was selling their property along Cherry Street, we approached them to see if they would donate the land north of the bridge for parking or regular parking and tour bus parking and for a small park for the neighborhood and for this whole city to use. Budco quite easily donated that property to the restoration group. The restoration group of course was not incorporated so we couldn't give them the tax deduction that they needed. So we approached the city and the city said, well we can't do anything with it now but we will take it and hold it until you can develop it. In the city council, in October 4, 2007, the city council accepted that property for public use and it is a great link to the historic Hay Street Bridge. That was the council's decision in 2007. The bridge with restoration was completed and reopened for bicycle and foot traffic in July of 1910 with a great big ceremony at all. Did I go back to 1910? I was born in 1926 so I spent most of my life in the 1900s. My wife catches me saying that also. Thank you for correction. Most recently, of course, is the question of the brewery and someone else probably will tell you more about that. But the new city council in a sense gave that property that they said they would hold for us. They gave it to the brewery in a sense. They were going to sell it to him and then give him $800,000 in free money. So the Esperanza group have been very helpful in putting our case before the city, before the community and the city and where now, as someone else would tell you, involved in the lawsuit to see that that property returns to its rightful owners. There are two spans on the bridge, one about 140 feet, the other about 240 feet. The longer span is a Whipple Phoenix span. Squire Whipple, Squire was his given name. Squire Whipple wrote the first textbook on the design of bridges. And Phoenix was the ironwork out of Pennsylvania that fabricated the Whipple Phoenix bridge structure. So it is very rare and in addition to being historic. Mr. Steadman, didn't the two spans, were they not at separate locations before they were combined here? I've heard that. I know for a fact that the longer span came from the crossing of the new valley. When we're seeing the two stretches, what are we seeing from an engineering perspective? In other words, is it the way the weight is distributed or could you tell us a little bit about what we see when we see those two different kinds? I know it's hard. Structural members spanning a distance defend a whole lot on depth. There's that post tensioning has cured some of that. But the longer span of course is a deeper trust. And that's the reason because it's spanning much farther. And what's the trust? You said it's a deeper trust. What's a trust? The trusts are all the members and you'll find that they're mostly triangles. A triangle is the only stable geometric figure. So you'll see a lot of triangles in a trust. So all the members making up those triangles, both the top part and the bottom part, top part takes compression. The bottom part takes tension. And then they're connected with the diagonals and verticals to form the trust. It seems to me there's two different kinds of supporting members. The one is round and it's in four parts and it's riveted together. The other one looks kind of like an IV to me on the other span. Can you talk to the different construction techniques? No, they're both in length. He's talking about the actual makeup of the members. One of the members are round and the other is more like IV. Oh, you're talking about the members that are made up of sections of a circle and riveted together. That's the designation of the Phoenix part. That was a particular design of the Phoenix Bridge Company out of Pennsylvania to make those members out of sections riveted together. That's beautiful.


Personal Finance PowerPoint Presentation. Zero coupon bond versus regular bond. Prepare to get financially fit by practicing personal finance. Most of this information can be found at Investopedia. What is the difference between a zero coupon bond and a regular bond, which you can find online. Take a look at the references, resources, continue your research from there. This by Chad Landgager updated August 31, 2020 in prior presentations. We've been taking a look at investment goals, investment strategies, investment tools, keeping them in mind. We're now asking, what is the difference between a zero coupon bond and a regular bond? The difference between a regular bond and a zero coupon bond is the payment of interest, otherwise known as a coupon as coupons. So if we just think about bonds in general, note that if we are the investor, we're thinking from the perspective of the investor. Then we typically want the balance portfolio. So we might be investing some into equities into stocks, some into the fixed income into the bonds on the bond side of things. We could think of it in essence as a kind of loan, us loaning the money to the issuer of the bond. That being typically either the government or the a corporation. And usually then if you think about this and compare it to say when you take out a loan, say like a mortgage. Usually then you are if you're the one borrowing in the mortgage, you're paying back both interest and principal. Each time you make the payment, they try to even it out over the payments as you pay them back. And the case of a bond that's structured a little bit differently normally, right? Say we're going to give the money to the corporation or the issuer of the bond. The could be the government. And then we're going to be receiving in return instead of regular payments that include the principal, just the interest portion, just the rent portion. Often that normally would happen like in a semi annual or twice a year instead of monthly type of basis. And then at the termination of the bond, we would in essence receive the principal back. We can also buy the bond at a discount or a premium, for example. If you're talking about zero coupon bonds, then you have a situation where you're not getting the payments on a periodic basis, interest or principal. And instead, you're going to get the payment at the end, which will in essence account for the basically interest that has been accrued during that period. Because you will typically buy the bond basically at a premium. In other words, you're going to buy the bond for an amount less than the face amount or the amount that you're going to receive at maturity. In other words, the difference then is in essence interest when you receive at maturity. So a regular bond pays interest to bondholders while zero coupon bonds does not issue such interest payments. So you're not going to get those regular interest payments. Instead, zero coupon bondholders merely receive the face value of the bond when it reaches maturity. So again, you might say, well, why would I do that? Why would I loan money in essence, pay for something where I'm not going to get the regular interest payments? Because you're buying the bond at a premium and when you get the face amount, it'll typically be more than you paid for it. Therefore, you are in essence getting the interest, but you're getting it at the point in time when the maturity happens rather than getting the interest portion of it as regular payments over the term of the bond. So regular bonds, which are also called coupon bonds, pay interest over the life of the bond and also repay the principal at maturity. The difference for investors, long term zero coupon bond investors gain the difference between the price they pay for the bond and the amount they receive at the bond's maturity. So this amount can be substantial because zero coupon bonds are typically purchased at deep discounts to the bond's face value. And you can kind of compare this like if you were to take out a loan, for example, instead of the normal structure of the loan where you basically pay back the same amount each month, which includes an interest and principal component. You can imagine one where you just pay back the interest and then you give back the loan at the end or you can imagine a situation where you're going to say, I'm going to pay you the lump sum at the end, which includes the interest and basically the principal. That's kind of what's happening here on the bond side. We on the investing side of things, in essence, loaning money and we're promised to pay back the face amount. They're going to give back the face amount, but we're going to purchase it at something below the face amount. And the difference between the two, you know, is in essence interest that has accumulated over the time. So this discount frequently leads to higher returns in the long run. A zero coupon bond was usually have higher returns than a regular bond with the same maturity because of the shape of the yield curve. So obviously you're kind of taking on more risk and that you're not getting payments. You're not getting the income throughout the timeframe. You're getting paid all at one lump sum at the end. So you would expect that you would want a bigger return in order to buy those bonds as compared to bonds that were paying you periodically. So with a normal yield curve, long term bonds have higher yields than shorter term bonds. The interest payment made by regular coupon bonds are due before the date of maturity. So those payments are like small zero coupon bonds that mature earlier. Interest payments cut down the wait time and the risk. So they also reduce expected returns. The difference for speculators, zero coupon bonds are more volatile than coupon bonds. So speculators can use them to profit more from anticipated short term price movements. So again, if you're looking at it in terms of a long term investor, then again you're probably trying to get exposure to kind of bonds in general to balance out your portfolio. When we're talking about speculators, then we're talking more about people that are on possibly on the short term trading type of thing, trying to make money predicting the market, beating the market in essence basically on the short term looking for the short term kind of activity. So remember that you want to know where you stand in terms of what kind of investor you're aiming to be here. So all other things being equal, the price of a zero coupon bond will increase more than the price of a regular coupon bond when interest rates fall. Because US Treasury bond prices respond strongly to interest rate changes, zero coupon treasuries are preferred for speculating on interest rates. Zero coupon corporate bond prices are also volatile so they can be used for speculating on the health of the issuing company. Suppose that a company facing bankruptcy previously issued zero coupon bond and coupon bonds that both mature in five years. The market price of both bonds would have plummeted with the result that the coupon bonds now pay very high interest related to their purchase price. That creates a cushion if the company should go bankrupt before maturity. The zero coupon bond has no such cushion, faces higher risk and makes more money if the issuer survives. So zero coupon bonds and taxes, zero coupon bonds may also appeal to investors looking to pass on wealth to their heirs. If a bond selling for $2,000 is received as a gift, it only uses $2,000 of the yearly gift to exclude for gift tax exclusion. So note when you get into like estate planning and gift kind of planning, those things are kind of tied together. You're looking at the estate taxes which typically will be applicable to people that have larger income. So when someone, a wealthy person dies, we all know that the government rejoices, comes in and rolls the corpse over and starts going through the pockets and seeing if there's any diamonds that have been established in any cavities or anything like that. So that's what, so obviously then and then you know that the person that was doing estate planning might say, well, I'm just going to gift everything to my inheritance to my children or something like that before I die. So they don't take my money after I'm dead, but then the government didn't like that. So of course now you've got the gift, the gift tax, it's tied into the exclusion for the estate tax or the death tax. So now there's all this estate, you know, this tax planning for estate planning can get quite complex and using ways to maximize the amount of gifts that you can get to lower the level of the estate. So there's less taxation upon death of a wealthy individual. So that gets into a whole nother kind of topic. However, the recipient ultimately receives substantially more than $2,000 after the bond reaches maturity. Unfortunately, the zero coupon bond holder, some taxes can reduce the effectiveness of this strategy. So in the U.S., zero coupon bonds create a tax liability for interest payments even though they don't actually pay periodic interest. That creates a phantom income problem for the bondholders. So it can be challenging to come up with the money to pay taxes on income that was not received. So notice that if you were to look at the interest, like the income, you have kind of an accrual basis kind of concept and a cash basis type of concept. And if you have an income tax and you're saying, well, you earned the income, the income has accrued on it. If the tax code is saying, I want you to pay the tax on income when it is accrued, not necessarily when it's paid because you have earned it. And normally when we think about a loan, for example, the income is accruing interest accrues because there wouldn't be a loan if there wasn't income related to it on a market transaction, arms length transaction. But the problem with taxes and income tax is that if you charge income on income that has accrued, but you haven't received the cash, then if it's a substantial tax, you might not have the cash to actually pay the income tax because you haven't got the cash even though you recognize the income. So consequently, it is often a good idea to hold zero coupon bonds in a tax deferred retirement account to avoid paying taxes on future income. So that would be under like an IRA or 401K, possibly the most common kind of deferred tax accounts. A zero coupon bond issued by US local or state government entity is another alternative. The municipal interest on these municipal bonds, including input interest for zero coupon bonds, is free from US federal taxes. Municipal bonds are often free from state and local taxes as well.


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